Oberlaender PhD Thesis

Oberlaender PhD Thesis
Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
Put forward by
Diplom-Physicist: Marcel Oberländer
Born in: Blankenburg (Harz), Germany
Oral examination: December the 16th, 2009
Three-dimensional reengineering of neuronal
microcircuits
The cortical column in silico
Referees:
Prof. Dr. Bert Sakmann
Prof. Dr. Karlheinz Meier
iii
Abstract German
Die hier präsentierte Dissertation beschreibt eine Pipeline zum Nachbau drei-dimensionaler,
anatomisch realistischer, funktioneller neuronaler Netzwerke mit subzellulärer Auflösung. Die
Pipeline besteht aus fünf Methoden:
1. ”NeuroCount” ergibt die Anzahl und drei-dimensionale Verteilung aller neuronalen Zellkörper
in großen Hirnregionen.
2. ”NeuroMorph” ergibt verlässliche neuronale Rekonstruktionen, inklusive dendritischer and
axonaler Morphologien.
3. ”daVinci” registriert neuronale Morphologien in ein standartisiertes Bezugssystem.
4. ”NeuroCluster” gruppiert die standartisierten Rekonstruktionen objektiv in anatomische
Neurontypen.
5. ”NeuroNet” kombiniert die Anzahl und Verteilung der Neuronen mit den standartisierten
Rekonstruktionen und bestimmt die Anzahl synaptischer Kontakte, in Abhängigkeit von
Neurontyp und Neuronposition, für jedwede zwei Neurontypen.
Die entwickelten Methoden werden anhand des Nachbaus eines Netzwerkes im somatosensorischen
System der Ratte demonstriert. Dort existiert eine eins-zu-eins Repräsentation zwischen der
sensorischen Information, aufgenommen durch ein einzelnes Barthaar, und abgetrennten Bereichen im Thalamus und Kortex.
Der Nachbau dieses Kreislaufes resultiert in einem zylin-
derförmigen Netzwerk Modell bestehend aus ≈15200 anregenden kortikalen, durch Kompartemente repräsentierten, Neuronen. Dieses Netzwerk ist mit ≈285 präsynaptischen thalamischen
Neuronen verbunden. Anregung dieser ”kortikalen Kolumne in silico” mit gemessenen physiologischen Signalen, wird einen Beitrag zum Verständniß neuronalen Informationsverarbeitung in
Säugetiergehirnen leisten.
iv
Abstract English
The presented thesis will describe a pipeline to reengineer three-dimensional, anatomically realistic, functional neuronal networks with subcellular resolution. The pipeline consists of five
methods:
1. ”NeuroCount” provides the number and three-dimensional distribution of all neuron somata
in large brain regions.
2. ”NeuroMorph” provides authentic neuron tracings, comprising dendrite and axon morphology.
3. ”daVinci” registers the neuron morphologies to a standardized reference framework.
4. ”NeuroCluster” objectively groups the standardized tracings into anatomical neuron types.
5. ”NeuroNet” combines the number and distribution of neurons and neuron-types with the
standardized tracings and determines the neuron-type- and position-specific number of
synaptic connections for any two types of neuron.
The developed methods are demonstrated by reengineering the thalamocortical lemniscal microcircuit in the somatosensory system of rats. There exists an one-to-one correspondence between
the sensory information obtained by a single facial whisker and segregated areas in the thalamus and cortex. The reengineering of this pathway results in a column-shaped network model of
≈15200 excitatory full-compartmental cortical neurons. This network is synaptically connected to
≈285 pre-synaptic thalamic neurons. Animation of this ”cortical column in silico” with measured
physiological input will help to gain a mechanistic understanding of neuronal sensory information
processing in the mammalian brain.
v
Acknowledgements
A very special Thanks to:
• my supervisor Prof. Dr. Bert Sakmann for his unlimited support, trustfulness and
encouragement during the past years and the opportunity to continue the presented
work at the Max Planck Florida Institute.
• my family and friends, especially to my parents, who supported me during my entire
life and the past years of study.
• my girlfriend Aline, who supported me during the past five years and took care that
I also spent some time outside the institute.
A special Thanks to:
• my collaborators: Albert Berman, Dr. Philip J. Broser, Dr. Randy M. Bruno, Dr.
Christiaan P. J. de Kock, Vincent J. Dercksen, Dr. Moritz Helmstädter, Dr. Stefan
Hippler, Dr. Stefan Lang and Hanno-Sebastian Meyer. Without teamwork and your
help, none of the presented results would have been possible.
• the undergraduate students under my supervision: Caroline, Firas, Jasmin, Kristina,
Melanie, Rita, Robert, Stefan, Stefanie and Tatjana. Without you doing all the tedious, time-consuming tracings, counts, programming and sample preparation, none
of the presented results would have been possible within three years.
• my thesis committee, Prof. Dr. Bert Sakmann, Prof. Dr. Alexander Borst and Prof.
Dr. Tobias Bonhöffer, for fruitful discussions and continuous encouragement.
• Chris Roome, Wulf Kaiser, Klaus Bauer and Marlies Kaiser, who helped me with
every technical problem, even after I moved to Munich.
vi
Contents
1 Introduction
2
1.1
Neuronal circuits: from in vitro/in vivo towards in silico . . . . . . . . . .
2
1.2
The ”whisker-barrel-system” in rats . . . . . . . . . . . . . . . . . . . . . .
10
1.2.1
Anatomy of the whisker system . . . . . . . . . . . . . . . . . . . .
11
1.2.2
Functional organization of the barrel cortex . . . . . . . . . . . . .
15
1.2.3
Whisker-related behavior and plasticity . . . . . . . . . . . . . . . .
20
2 Methods
2.1
2.2
23
3D counting of neuron somata . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.1.1
Sample preparation and imaging . . . . . . . . . . . . . . . . . . . .
28
2.1.2
Manual detection of soma positions . . . . . . . . . . . . . . . . . .
29
2.1.3
Computing hard- and software . . . . . . . . . . . . . . . . . . . . .
29
2.1.4
Threshold-based filtering (pre-processing) . . . . . . . . . . . . . . .
31
2.1.5
Morphological filtering . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.1.6
Model-based cluster splitting . . . . . . . . . . . . . . . . . . . . . .
40
2.1.7
Colocalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3D reconstruction of neuron morphologies . . . . . . . . . . . . . . . . . .
48
2.2.1
52
Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
2.3
2.4
2.5
2.2.2
Image acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
2.2.3
Shack-Hartmann-analysis-based deconvolution . . . . . . . . . . . .
55
2.2.4
Computing hard- and software . . . . . . . . . . . . . . . . . . . . .
68
2.2.5
Automated image processing . . . . . . . . . . . . . . . . . . . . . .
69
2.2.6
Semi-automated post-processing . . . . . . . . . . . . . . . . . . . .
79
3D registration of neuron morphologies . . . . . . . . . . . . . . . . . . . .
83
2.3.1
3D reconstruction of reference contours . . . . . . . . . . . . . . . .
84
2.3.2
Calculation of most likely vertical column axis . . . . . . . . . . . .
86
2.3.3
Translation and rotation to standard barrel system . . . . . . . . .
86
2.3.4
Inhomogeneous z-scaling to standard barrel system . . . . . . . . .
88
3D classification of neuronal cell-types . . . . . . . . . . . . . . . . . . . .
88
2.4.1
Cluster algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
2.4.2
Cluster features . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
3D reengineering of average neuronal networks . . . . . . . . . . . . . . . .
97
2.5.1
99
NeuroNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Methodical results
3.1
NeuroCount: 3D counting of neuron somata . . . . . . . . . . . . . . . . . 106
3.1.1
3.2
106
Automated vs manual counting . . . . . . . . . . . . . . . . . . . . 107
NeuroMorph: 3D reconstruction of single neuron morphologies . . . . . . . 111
3.2.1
Optical aberrations of cortical tissue . . . . . . . . . . . . . . . . . 111
3.2.2
Automated vs manual reconstruction . . . . . . . . . . . . . . . . . 118
4 Anatomical results
4.1
122
Quantitative 3D structure of S1 . . . . . . . . . . . . . . . . . . . . . . . . 124
4.1.1
3D distribution of neuron somata in S1 . . . . . . . . . . . . . . . . 125
viii
4.2
4.3
4.1.2
3D average cortical column of neuron somata
4.1.3
Dendritic excitatory neuronal cell types in S1 . . . . . . . . . . . . 134
4.1.4
Axonal projections of L5A neurons within S1
. . . . . . . . . . . . 131
. . . . . . . . . . . . 141
Quantitative 3D structure of VPM . . . . . . . . . . . . . . . . . . . . . . 145
4.2.1
3D distribution of neuron somata in VPM . . . . . . . . . . . . . . 146
4.2.2
Axonal excitatory neuronal cell types in VPM . . . . . . . . . . . . 150
3D reconstruction of lemniscal thalamocortical pathway . . . . . . . . . . . 154
4.3.1
The standardized 3D cortical column in silico . . . . . . . . . . . . 155
4.3.2
Number and 3D distribution of VPM synapses in S1 . . . . . . . . 160
5 Discussion
170
ix
List of Tables
3.1
Manual vs automated neuron counting . . . . . . . . . . . . . . . . . . . . 108
3.2
False positive/negative analysis of neuron counting . . . . . . . . . . . . . 110
4.1
Comparison of NeuroCount and sparse sampling results . . . . . . . . . . . 130
4.2
Dendritic and axonal length of L5A pyramidal neurons . . . . . . . . . . . 144
4.3
Number of neurons per VPM barreloid . . . . . . . . . . . . . . . . . . . . 149
4.4
VPM axon length with and without whisker trimming . . . . . . . . . . . . 153
4.5
Neuron-type-specific average recording and registered soma depth . . . . . 155
4.6
Layer- and type-specific boundaries . . . . . . . . . . . . . . . . . . . . . . 156
4.7
Type-specific depth overlap ratios . . . . . . . . . . . . . . . . . . . . . . . 159
4.8
Thalamocortical lemniscal pathway in numbers . . . . . . . . . . . . . . . 164
x
List of Figures
1.1
In silico single neuron model . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
Elementary building blocks for neuronal microcircuits in silico . . . . . . .
7
1.3
One whisker one barrel hypothesis. . . . . . . . . . . . . . . . . . . . . . .
10
1.4
Anatomy of the whisker system. . . . . . . . . . . . . . . . . . . . . . . . .
11
1.5
Scheme of lemniscal and paralemniscal pathways . . . . . . . . . . . . . . .
14
1.6
Layer- and cell-type-specific suprathreshold activity in a barrel column . .
16
1.7
Spreading of subthreshold activity in barrel cortex . . . . . . . . . . . . . .
18
1.8
Learned whisker-related behavior . . . . . . . . . . . . . . . . . . . . . . .
21
2.1
NeuroCount Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.2
Local intensity mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.3
Watershed filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.4
Model-based splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.5
Large neuron correction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.6
Colocalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
2.7
Mosaic microscopy for neuron tracing . . . . . . . . . . . . . . . . . . . . .
51
2.8
Shack-Hartmann wavefront measurement . . . . . . . . . . . . . . . . . . .
60
2.9
Degree of coherence in TLB images . . . . . . . . . . . . . . . . . . . . . .
63
2.10 Simple imaging model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
xi
2.11 Simple aberration model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
2.12 NeuroMorph illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
2.13 Voxel neighborhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
2.14 Splicing of tracings from individual sections . . . . . . . . . . . . . . . . .
81
2.15 3D reference contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
2.16 3D registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
2.17 OPTICS clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
2.18 Anatomical neuron features . . . . . . . . . . . . . . . . . . . . . . . . . .
94
2.19 Illustration of NeuroNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.1
SH measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.2
Isotropy of cone of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.3
Deconvolution of axons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1
3D neuron soma distribution in L1-L4 of S1 . . . . . . . . . . . . . . . . . 126
4.2
3D neuron soma distribution in L5-L6 of S1 . . . . . . . . . . . . . . . . . 127
4.3
3D neuron soma distribution in S1 . . . . . . . . . . . . . . . . . . . . . . 132
4.4
Neuron soma distribution of average cortical column . . . . . . . . . . . . . 133
4.5
OPTICS cluster results in S1
4.6
Anatomical and physiological neuron types . . . . . . . . . . . . . . . . . . 139
4.7
Axonal projections of slender tufted L5A pyramidal neurons in S1 . . . . . 141
4.8
GABAergic innervation of VPM . . . . . . . . . . . . . . . . . . . . . . . . 146
4.9
3D neuron soma distribution in VPM . . . . . . . . . . . . . . . . . . . . . 148
. . . . . . . . . . . . . . . . . . . . . . . . . 135
4.10 Classification and deprivation of VPM axons . . . . . . . . . . . . . . . . . 151
4.11 Layer- and neuron-type-specific boundaries in S1 . . . . . . . . . . . . . . . 158
4.12 3D neuron-type-specific spine and VPM synapse distributions . . . . . . . 161
xii
4.13 Neuron-type-specific position dependence of synapse numbers
. . . . . . . 162
4.14 Subcellular distribution of VPM synapses in L4SS neurons . . . . . . . . . 165
4.15 Subcellular distribution of VPM synapses in L5B neurons . . . . . . . . . . 166
4.16 Subcellular distribution of VPM synapses in L3 neurons . . . . . . . . . . . 168
5.1
3D neuron-type-specific VPM innervation volumes . . . . . . . . . . . . . . 173
xiii
Chapter 1
Introduction
• Definition 1: In vivo refers to studies conducted in the living organism.
• Definition 2: In vitro refers to studies performed (literally in glass) in the laboratory.
• Definition 3: In silico refers to studies of mechanistic numerical computer based
models to complement experiments done in vitro or in vivo.
1.1
Neuronal circuits: from in vitro/in vivo towards
in silico
One fundamental challenge in neuroscience is to understand how brains process sensory
information about the environment and how this can be related to the animal’s behavior.
The here presented work will focus on this question at the level of anatomically realistic
functional neuronal networks with subcellular resolution. In general, neuronal networks
are composed of chemically or electrically coupled local and long-range microcircuits of
anatomically and physiologically classified cell types. Specifically, each neuron is composed
2
1.1 Neuronal circuits: from in vitro/in vivo towards in silico
a
3
c
b
Figure 1.1: In silico single neuron model. (a) Figure adopted from [1]. Left: the 30-50 Å
thin bilayer of lipids isolates the extracellular side from the intracellular one. From an electrical
point of view, the resultant separation of charge across the membrane acts like a capacitance. Ion
channels (here voltage-independent) provide a conductance through the membrane. Right: Associated passive electrical (RC-)circuit, consisting of a capacitance and a resistance in series with
a battery, which accounts for the neuron’s resting potential Vrest . (b) Figure adopted from [2].
Multi-compartment neuron model. Spatial discretization of the cable equation results in multiple
coupled compartments, where each one is locally equivalent to a uniform cable and may contain
nonlinear (e.g.voltage-dependent) ionic currents. (c) Figure adopted from [3]. Realistic fullcompartmental model of a cerebral Purkinje neuron. Reconstructed bifurcations and variations
in diameter and electronic properties are incorporated into the model. Such models are capable to reproduce measured sub- and suprathreshold physiological responses and complex dendritic
computations.
4
Introduction
of a cell body (soma), multiple dendrites and one axonal tree, which receive electrical input
from and transfer output towards other neurons, respectively. Hence, pioneered by Ramón
y Cajal about a century ago, neurons are usually grouped anatomically with respect to
their soma shape, dendrite morphology and/or axonal branching pattern.
Functionally, their (electro)physiological membrane properties can be described by electrical circuits containing a capacitance and resistance (RC-circuit) (Fig.1.1a). During
equilibrium states, a voltage difference arises from deviating ion concentrations between
the inside and outside of the cell’s membrane. This resultant resting potential (Vrest ) is
cell-type specific, but typically around -70mV. The membrane itself functions as a capacitance (C), which contains small pores (ion channels) with channel-type specific resistances
(Ri ). These pores mediate ionic currents across the membrane. Some channels are continuously open (passive or leaky) and others open and close actively with respect to voltage
or chemical ligand concentration. Such active (e.g. voltage-dependent) conductances were
first described in a neuron model by Hodgkin and Huxley (HH) in 1952:
C
X
dV
= −(
Ii + Ileak ),
dt
i
(1.1)
where
Ii =
V − Ei
,
Ri(V,t)
(1.2)
represents voltage-dependent channel kinetics and Ei the reversal potential of each ion
channel type. Positive signs of Ei (e.g. EN a = 54mV ) reflect lower ion concentrations
inside the neuron, resulting in inward currents upon depolarization of the membrane. In
contrast, negative signs (e.g. EK = −77mV ) represent outward currents upon depolarization. This model, successfully explains a fast membrane depolarization, called action
potential (AP) or spike, which is believed to be the fundamental electrophysiological unit
in information processing. Simplified, fast channels permeable for inwardly streaming pos-
1.1 Neuronal circuits: from in vitro/in vivo towards in silico
5
itively charged ions (e.g. N a+ ) open once a channel-specific voltage threshold is reached.
The resultant depolarization opens more and more channels and hence an AP is elicited.
By immediate inactivation of the depolarizing channels (in case of N a+ by reaching an
inactivation threshold) and simultaneous slow opening of channels permeable for outward
streaming positively charged ions (e.g. K + ), the membrane potential is reset to rest. This
process is called suprathreshold activity, in contrast to subthreshold activity, which describes changes of the membrane potential mediated largely by ligand-gated rather than
voltage-gated ion channels.
Further development of electrical neuron models by Wilfred Rall, who believed that the
complexity of the dendrites and axonal arborization would affect the neuronal processing,
resulted in a cable theory for neurons. Numerous bifurcations as well as variations in diameter and electrical properties along the neuronal branches, however diminish the possibility
to find analytical solutions for the resultant cable equations [4]. This lead to numerical
solutions of spatially discrete, anatomy based neuron models composed of multiple HHtyped compartments (Fig.1.1c), each locally resembling a uniform cable (Fig.1.1b).
Initiated by Roger Traub and colleagues, many of these full-compartmental neuron models with active HH-type properties were synaptically interconnected, resembling realistic
microcircuits and carrying out realistic neuronal operations. Following this tradition, attempts to reengineer the three-dimensional anatomy and connectivity of functional networks of many thousand full-compartmental neurons, were started [5], [6]. Such goals
would be unfeasible without continuously increasing computing power and recently available large scale imaging techniques.
Initiated by Bert Sakmann, my colleges and I aim to reconstruct a functionally well defined
network in the primary somatosensory cortex (S1) of four week old rats (i.e. post-natal
day 28, p28). The so called ”cortical (barrel) column” is related in a one-to-one fashion
6
Introduction
to information acquired by a single facial whisker hair on the animal’s snout. It has a
diameter of ≈400µm, a height of 2mm and contains about ≈18000 neurons. Functional
output from this network, based on single whisker information, is sufficient to trigger simple behaviors, such as decision making. Hence, animation of a realistically reengineered
cortical column with single whisker input, measured in vivo, will potentially yield new
insights and understanding of principle mechanisms that explain how the brain translates
environmental input into behavioral responses.
The mammalian cortex is organized into six layers (L1-L6) and receives input from, or
transfers output towards other brain areas, such as the thalamus. Hence, many anatomical
and functional studies of cortical columns in S1 revealed neuronal microcircuits between
(interlaminar) and within (intralaminar) layers, from the thalamus to the cortex (thalamocortical) and vice versa (corticothalamic). However, due to its complexity, a quantitative three-dimensional anatomical description of these circuits, their constituents and
connections is still missing. Figure 1.2 summarizes the general elementary building blocks
necessary to quantitatively describe and reengineer in silico neuronal microcircuits, such
as an average cortical column [5]:
1. To model full-compartmental neurons with active HH properties, three-dimensional
axonal and dendritic morphology, ion channel composition, and distributions and
electrical properties of the different types of neuron are required, as well as the total
numbers of neurons in the microcircuit and the relative proportions of the different
types of neuron.
2. To model synaptic connections, the physiological and pharmacological properties of
the different types of synapses that connect any two types of neurons are required. In
addition, statistics on which part of the axonal arborization (presynaptic innervation
pattern) connects to which regions of the target neuron (postsynaptic innervation
1.1 Neuronal circuits: from in vitro/in vivo towards in silico
7
Neurons
Gene expression profiles
Electrophysiological profiles
Morphological profiles
Morpho-electrophysiological types
Ion channel compositions
Ion channel distributions
Total number of neurons
Frequency of occurence
Locations
Pre-synaptic neurons
Structural connectivity
Post-synaptic neurons
Total number of
synapses
Synapses per
connection
Total number of
boutons
Total number of
targets
Post-synaptic
innervation pattern
Transmission
statistics
Terminals per
connection
Pre-synaptic
innervation pattern
Synaptic biophysics
Synaptic
dynamics
Functional connectivity
Functional connectivity
Post-synaptic neurons
Pre-synaptic neurons
Figure 1.2: Elementary building blocks of neuronal circuits. Microcircuits are composed
of neurons and synaptic connections between them. To model neurons, three-dimensional morphology, ion channel composition, distributions and electrical properties of the different types of
neurons are required. Further the total number of neurons in the microcircuit and the relative
proportions of the different types of neurons are needed. To model synaptic connections, the physiological and pharmacological properties of the different types of synapses that connect any two
types of neurons are required. In addition the pre- and postsynaptic innervation statistics are
necessary. The red items will be addressed in the presented thesis. Figure adopted from [5].
8
Introduction
pattern) needs to be known. Further, the number of synapses involved in forming
connections, and the connectivity statistics between two types of neuron need to be
determined.
The here presented work will focus on the anatomical prerequisites of in silico microcircuits
(red in Fig.1.2), which will be obtained by five custom designed new methods:
NeuroCount, NeuroMorph, daVinci, NeuroCluster and NeuroNet.
NeuroCount automatically extracts the number and three-dimensional distribution of neuron somata in some cubic millimeter large volumes. NeuroMorph is a semi-automated tool
to reconstruct the full three dimensional branching pattern of dendrites and axonal arbor of
single neurons. Both methods are less time-consuming and more objective than previously
used manual approaches. In consequence, statistically significant samples of anatomical
data are generated, which yield a quantitative determination of:
1. average absolute numbers and three-dimensional distributions of excitatory (glutamatergic) and inhibitory (GABAergic) neuron somata,
2. average three-dimensional dendritic and axonal features of individual morphological
neuron-types.
daVinci registers the neuron tracings into a standardized reference frame of a cortical barrel
column. NeuroCluster then enables to objectively group the neurons into morphological
classes. Finally, NeuroNet combines the three-dimensional neuron soma distributions, the
determined neuron-types and reconstructions, with the standardized reference system of a
cortical column and finally yields:
1. the three-dimensional presynaptic innervation of local and long-range microcircuits,
1.1 Neuronal circuits: from in vitro/in vivo towards in silico
9
2. the three-dimensional postsynaptic innervation for individual neuronal cell-types,
3. the average number and subcellular three-dimensional organization of synapses between any two types of neurons.
Ultimately, the presented methods and results lead to an in silico network model of a cortical column, which contains ≈15200 excitatory full-compartmental neurons within a volume
of 0.24 cubic millimeters in S1. The neurons are divided into eight classified cell types and
synaptically connected to ≈285 thalamocortical axonal trees. The anatomical, functional
and behavioral relevance for this network will be introduced within the subsequent section.
10
Introduction
1.2
The ”whisker-barrel-system” in rats
a
From Whisker to Cortex
b
Whiskers and Barrels
Figure 1.3: One whisker one barrel hypothesis. (a) Information about deflection of a
single whisker is transmitted to the brain stem (1), to the thalamus (2) and finally to S1 (3). (b)
The layout of whisker follicles on the snout of rodents is identical between rats and mice (left,
C-row whiskers shown). Anatomical structures in L4 of S1 are termed ”barrels”. The spatial
organization of these barrels resembles the one of the whiskers, giving rise to the hypothesis that
each barrel processes the information from its corresponding whisker. The nomenclator for both
whiskers and barrels consists of rows (A-E) and arcs (1, 2, 3, etc.). Figure adopted from [7].
About forty years ago, Thomas Woolsey and Hendrik Van der Loos first described a
remarkable correspondence between the pattern of the whiskers on the face of a mouse and
the spatial organization of neuron clusters (barrels) in its primary somatosensory cortex
[8]. They hence suggested the ”one-barrel-one-whisker” hypothesis, which proposed that
each cortical barrel is activated by an individual whisker. Shortly after, anatomical as well
as functional evidence for this hypothesis was observed (Figure 1.3).
1.2 The ”whisker-barrel-system” in rats
1.2.1
11
Anatomy of the whisker system
Face
Trigeminal
nerve
Brainstem
Thalamus
Cortex
Figure 1.4: Anatomy of the whisker system. Each peripheral axon in the trigeminal nerve
innervates one whisker follicle. Centrally the whiskers are aggregated in whisker related bundles
that terminate in several nuclei in the brainstem. From top to bottom: principal sensory nucleus
and spinal trigeminal complex subnuclei: oralis, interpolaris and caudalis. ”Barrelettes” are
present in all but the subnuclei oralis. Whisker-related aggregations of afferent fibres and somata
are also observed in the thalamus and S1. Figure adopted from [9].
The subsequent anatomical description of the whisker system is in parts adopted from
Daniel Simons and Peter Land [9] and illustrated by Figure 1.4.
Rats, like most nocturnal rodents, use their whiskers as complex tactile sensory organs
to explore their environment. Muscle slings around the whisker follicle move the whisker
hairs back and fourth in a rhythmic 10-Hz pattern, called ”whisking”. A whisker follicle
12
Introduction
is innervated by 100 to 150 large myelinated axons of primary afferent neurons located in
the trigeminal ganglion. Each fibre innervates only a single follicle and their functional
response differs in three features:
1. their preferred direction of whisker movement,
2. their AP firing patterns caused by whisker movement versus steady state displacement,
3. and their relative sensitivities to deflection amplitude and velocity.
Further, each primary afferent neuron responds to stimulation of only a single whisker.
The peripheral pattern of innervation is thus as discrete and punctuate as the whiskers
themselves. In consequence, these discrete peripheral nerve fibres transmit information
that can be used by the brain to determine the location, size and texture of touched objects.
In the central nervous system (CNS), whisker nerves terminate in several nuclear groups
in the brainstem: the principle sensory nucleus and three divisions of the spinal trigeminal
complex: oralis, interpolaris and caudalis. Small, whisker-related cell groups, called ”barrelettes”, are clearly visible in the principle sensory nucleus, somewhat less discernable in
spinal trigeminal complex: interpolaris and caudalis, and absent altogether in oralis. The
clearly visible barrelettes in nucleus pricipalis reflect a functional correspondence between
the barrelet neurons and a single whisker, whereas the other nuclei are responsive to multiple whiskers.
The brainstem neurons transmit whisker-related information to somatosensory regions of
the contralateral thalamus. The major recipient of input from the principal sensory nucleus is the medial division of the ventral posterior nucleus (VPM), which like the principle
sensory nucleus and S1, contains groups of neurons, that are related to the information
1.2 The ”whisker-barrel-system” in rats
13
from a single whisker. In VPM these groups are in the form of elongated ovoids, called
barreloids. The response properties of barreloid neurons is actively regulated by inhibitory
circuits involving feedback connections from thalamic reticular nucleus (RT). Moreover,
both VPM and RT receive feedback from corticothalamic neurons in the barrel cortex,
influencing how whisker information is pre-processed in the thalamus, before it arrives in
the cortex itself.
Barreloid neurons are the major source of afferent input to the barrel cortex, and neurons
in a barrel receive thalamic inputs largely, although not exclusively, from their corresponding barreloid. Thalamocortical VPM axons arborize selectively throughout the centers of
individual barrels and mainly innervate dendrites in L4, the lower part of L5 (L5B) and
the upper part of L6.
The barrels are separated from one another by cell-sparse zones, called septa. Unlike
their barrel counterparts, septal neurons often extend their dendrites into neighboring barrels, where they are likely to be contacted to barreloid (VPM) axons. Septal and barrel
neurons, mainly in L1 and the upper part of L5 (L5A), receive additional afferent thalamocortical input from the medial division of the posterior nucleus (POm), the major thalamic
relay for interpolaris and caudalis processing streams. Hence, related target neurons typically receive information involving many neighboring whiskers. In summary, information of
whisker deflection is processed along two independent pathways (Figure 1.5). One, refereed
to as the ”lemniscal” pathway, comprises clear anatomical maps segregating neighboring
whisker representations from the periphery, via barrelettes in the principal sensory nucleus
of the brainstem, barreloids in the VPM of the thalamus, up to barrel regions in S1. There,
the primary input is within L4, L5B and L6. This pathway is regarded as a labeled-line
single-whisker signaling pathway.
In contrary, the second pathway, referred to as ”paralemniscal”, represents multi-whisker
14
Introduction
barrel column 2
barrel column 1
barrel column n
L1
L1
L1
L2/3
L2/3
L2/3
L4
L4
L4
L5A
L5A
L5A
L5B
L5B
L5B
L6
L6
L6
primary
somatosensory
cortex
VPM barreloids
thalamus
1
2
n
primary sensory nucleus
barrelettes
RT
POM
oralis
caudalis
interpolaris
brainstem
1
2
n
spinal trigeminal complex
trigeminal ganglion
peripheral
nervous
system
discrete punctuate input from afferent nerve fibers innervating whsiker follicles
Figure 1.5: Scheme of lemniscal and paralemniscal pathways. The lemniscal pathway
(red) transmits sensory input from a single whisker via clear anatomical maps: from barrelettes
in the primary sensory nucleus of the brainstem, to corresponding barreloids in the VPM, up
to corresponding barrel columns in S1. The main thalamocortical input via this pathway arises
in L4 barrel and L5B neurons. L4 conveys this input to L2/3 neurons, which in turn spread
the excitation to the entire barrel cortex and to the main cortical output layer L5B. L5B and
L6 are further involved in a corticothalamic feedback loop giving input to the VPM/POm and
nucleus reticularis (RT). The related inhibitory feedback loop between RT and VPM regulates the
strength and precise timing of the thalamocortical VPM input. The paralemniscal pathway (green)
processes multiple-whisker information. Clear anatomical maps are lacking for this pathway: from
the spinal trigeminal complex interpolaris and caudalis in the brainstem, to the POm, up the L1
and L5A in S1. L5A in turn conveys this input to L2/3 of the surrounding barrel columns. This
pathway is suppressed under anesthetized conditions.
1.2 The ”whisker-barrel-system” in rats
15
signaling from the periphery, via the nucleus interpolaris and caudalis of the brainstem,
POm in the thalamus, up to barrel and septal regions in S1. There, the major input addresses L1 and L5A.
However, the above presented anatomical description of the whisker information pathways
is so far rather qualitative and any quantitative description, especially in three dimensions, is lacking and will therefore be subject of this work. Here, I will mainly focus on
the lemniscal pathway from one barreloid in the VPM to its corresponding barrel column
in S1. By quantitatively determining the number and 3D distribution of neuron somata
in VPM and S1, classifying postsynaptic excitatory cell types in S1 and reconstructing
the presynaptic innervation of VPM axons, the number and subcellular distribution of
thalamocortical VPM synapses for every postsynaptic neuron will be estimated.
1.2.2
Functional organization of the barrel cortex
During in vivo experiments, sensory input into the barrel cortex arises from different kinds
of stimuli. First, controlled deflection of a single whisker under anesthesia (a passive
touch for the animal) results in strong cortical sensory responses. Extracellular recordings, by introducing an electrode into S1, allows for direct measurement of stimuli evoked
suprathreshold activity (APs) of individual neurons [10]. This data suggests that the AP
activity, evoked by passive touch, is well aligned with the anatomical barrel map, but differs significantly between different cortical layers (Fig.1.4).
Sensory information related to passive deflection of a single whisker arrives in the S1
barrel column foremost via the lemniscal pathway, namely by the dense excitatory thalamocortical innervation of neurons located in the corresponding VPM barreloid. Strong
inhibitory feedback from the RT to the VPM sharpens the timing of the sensory input to
the cortex [11], [12]. As first-order approximation, a single deflection therefore evokes a
16
Introduction
Figure 1.6: Layer- and cell-type-specific suprathreshold activity in a barrel column.
The number of APs per layer of a cortical column was derived by extracellular recordings in
anesthetized rats, before (spontaneous activity) and after (evoked activity) passive deflection of a
single whisker. The average number of APs per cell was multiplied with estimates for the total
number of cells per layer. The barrel column is activated by approximately 60 thalamic APs fired
within 20ms after deflection. The strongest response to passive deflection arises in L5B and L4.
Figure adopted from [10].
1.2 The ”whisker-barrel-system” in rats
17
nearly synchronous volley of 50-70 APs in one barreloid, which is mainly conveyed to L4,
L5B and L6 of the corresponding barrel column. The fast 10 fold increase in suprathreshold
activity in these layers (Fig.1.6) is hence primarily and directly caused by synchronously
active thalamocortical synapses [12].
L4 barrel neurons have dendritic and axonal arbors laterally confined to a single L4 barrel
[13], [14], [15], and the thalamic input arriving in L4 will therefore largely remain confined
to the barrel for the initial step of cortical processing [7]. The excitatory L4 axons prominently innervate L2/3 in the immediately overlying area. In contrast, axonal arbors of such
L2/3 pyramidal neurons extend well beyond the boundaries of a single barrel column [16].
Being activated upon whisker deflection, either directly by VPM innervation or indirectly
by L4 neurons, these excitatory neurons hence depolarize cells widely distributed across the
barrel cortex. In addition, L2/3 cells form a prominent input to L5. L5 hence integrates
excitatory synaptic input from VPM, L5, L4 and L2/3, and is thought to be the main
cortical output layer, projecting into subcortical regions like the PONS and the striatum.
Using voltage-sensitive dye imaging (VSDI) [18] the described spread of activity can be
directly monitored at millisecond temporal and subcolumnar spatial resolution. By rapidly
changing its fluorescence linearly with respect to the membrane potential, VSDI is further
very sensitive to subthreshold changes. The earliest response evoked by brief passive deflection of a single whisker occurs after ∼10ms and is highly localized within its corresponding
barrel column (Fig.1.7)[17]. This is in very good agreement with the suprathreshold measurements (Fig.1.6).
However, during the following milliseconds the response increases in amplitude and propagates horizontally to cover a larger fraction of the barrel cortex. This suggest that the more
localized suprathreshold activity reflects the ”tip of the iceberg” of a large and distributed
subthreshold activity [19], involving many cortical neurons and multiple local microcir-
18
Introduction
Figure 1.7: Spreading of subthreshold activity in barrel cortex. By injecting a voltagesensitive-dye (VSD) the spread of activity after passive deflection of a single whisker can be
monitored with ms time resolution and subcolumnar spatial resolution. The first activity arises
∼10ms after the stimulus and is laterally confined to the anatomical barrel boundaries. During
the following milliseconds the activity spreads to the surrounding columns, but the peak amplitude
remains in the barrel column. Figure to some extend adopted from [17].
1.2 The ”whisker-barrel-system” in rats
19
cuits.
In summary, passive deflection of a single whisker in the anesthetized animal results primarily, although not exclusively, in sensory processing within a functionally well-defined
cortical barrel column and can be described (in a simplified way) by an excitatory synaptic
circuit from VPM to L4 barrel to L2/3 to L5 [20]. This pathway will subsequently be
referred to as the cortical lemniscal processing pathway.
A second kind of stimulus arises when the whisker touches an object during active whisking
in the awake animal (an active deflection for the animal). In addition to the canonical cortical lemniscal pathway, there are numerous other important synaptic connections that are
likely to be involved in information processing during active touch. In contrast to passive
touch, where L4, L5B and L6 neurons are dominantly activated, L4 and L5A cells show
the strongest response to active touch [21].
Since the paralemniscal thalamocortical pathway from the POm mainly innervates L1 and
L5A, L5A seems to be the starting point of a paralemniscal cortical pathway [7] that is
coactive to the lemniscal cortical pathway when the animal is awake. It is currently of great
interest to determine the functional interactions between these different synaptic networks
and how they contribute to different aspects of whisker-related sensory perception [7].
To address this question a description of the paralemniscal cortical pathway, similar to the
one of the lemniscal cortical pathway (VPM → L4 → L2/3 → L5) needs to be done. In
cooperation with Dr. Christiaan P.J. de Kock (VU Amsterdam) and Dr. Alexander Groh
(TU Munich) I started this by reconstructing both POm and L5A axons. As previously
shown, POm axons innervate L1 and L5A, whereas L5A axons innervate L2/3 [22], [23].
However, reconstructing the full three-dimensional extend of L5A axons, it will become obvious that these cells project specifically into L2/3 of multiple surrounding barrel columns.
L2/3 is hence subjected to lemniscal and paralemniscal processing streams, which indicates
20
Introduction
that lemniscal and paralemniscal pathways converge within S1 and are not as separate as
in subcortical areas [24], [25].
Summarizing the anatomical and functional organization of the whisker system, the separation into single-whisker (lemniscal) and multi-whisker (paralemniscal) pathways is reflected in every brain region, including the barrel cortex, that is involved in processing
whisker-related sensory perception. Apart from being constituted of anatomically distinct excitatory circuits (Fig.1.5), these pathways reflect functionally different contexts.
Whereas the paralemniscal pathway seems to be inactive in the anesthetized animal, the
lemniscal pathway is active during active touch in the awake and during passive touch in
the anesthetized animal.
In the here presented work I will mainly focus on the anatomy and connectivity of the
thalamocortical lemniscal circuit (VPM → S1) and briefly on the starting point of the
cortical paralemniscal pathway (L5A → L2/3). The three-dimensional reengineering of
these functionally important microcircuits will potentially allow for in silico experiments,
that will shed light on the mechanisms of activation of a cortical column by passive touch
or spreading of activity during active touch.
1.2.3
Whisker-related behavior and plasticity
Apart from its clear anatomical and functional correlation with a single whisker, another
important reason to investigate whisker-related sensory processing in rodents, is to gain
insight into the basis of decision making in mammalian brains. Sensory information serves
to guide behavior and sensory processing can therefore be viewed as the starting point for
motor control and the planning of future actions [7].
In the laboratory, rodents can learn to use their whiskers to perform various behavioral
tasks. One example is the detection of edge locations. Shown by [26], [27], [28] rodents
1.2 The ”whisker-barrel-system” in rats
21
can use their whiskers to reach across a gap between two platforms (Fig.1.8). If reaching the other side, the animal reliably jumps over the gap and receives some reward (e.g.
sweet milk). If the two platforms are too far apart, the animal will refuse to cross this
gap. Moreover, this gap-crossing behavior can be performed with a single intact whisker.
Object detection and location
Figure 1.8: Learned whisker-related behavior. Edge detection and location forms the basis
of the gap-crossing task. A rodent must reach across a gap with its whiskers to locate a target
platform where a reward is placed. The decision to cross the gap or to remain in the home
platform depends on the gap size. If the animal cannot touch the other side, it will never jump.
The decision is reliably made even upon a single touch by a single whisker. Figure adopted from
[7].
This situation is achieved by acute whisker removal (trimming), which means clipping off
the whisker hairs near the skin surface, without damaging the follicle. Whereas whisker
trimming within the first five days after birth results in an abnormal organization of the
barrel field, trimming in adult animals does not alter the barrel pattern [7]. Nevertheless, compared to untrimmed animals, VSDI and extracellular recordings reveal decreased
activity in barrels corresponding to removed whiskers and increased activity in barrels corresponding to remaining intact whiskers. The mechanisms underlying these functional or
22
Introduction
anatomical changes, in general termed plasticity, are yet unknown.
However, notably no trimming effects are observed in thalamic neurons. This is strong
indication that plastic changes occur at the level of thalamocortical synapses and/or in
the local cortical circuitry [7]. By reconstructing thalamocortical axons from barreloids
corresponding to either trimmed or intact whiskers, in cooperation with Dr. Randy M.
Bruno (Columbia University, NY), I will show that whisker removal in adult rats results
in a significant pruning of VPM axons.
In consequence, the tools designed to reengineer a three-dimensional average cortical barrel
column will not only yield possibilities to study synaptic mechanisms underlying simple
whisker-evoked behaviors, such as decision-making, but will further help to understand
plasticity effects on neuronal networks after deprivation or injury of sensory organs.
Chapter 2
Methods
A cortical barrel column contains many thousand neurons of various types and thalamocortical, as well as intracortical axons can spread over some cubic millimeter volumes, reaching
a total length of several centimeters. Hence, a quantitative three dimensional reengineering
of such large functional neuronal networks and circuits will hardly be achieved by manually
counting, reconstructing, classifying and interconnecting neurons.
Using newly available mosaic/optical-sectioning confocal and widefield microscopy, in combination with powerful computing hardware and custom designed software, I developed
methods to quantitatively derive all anatomical data necessary to reengineere average in
silico networks.
The first tool, NeuroCount, automatically extracts the midpoint positions (landmarks)
of histochemically labeled fluorescent neuron somata from large three dimensional confocal image stacks. Further, in combination with cell-type-specific markers, the fraction
of individual neuronal types among all neurons can be obtained. Here, the number and
three-dimensional distribution of excitatory and inhibitory neurons in all six cortical layers
of S1 and the single layered thalamic VPM will be presented. As stated above, this data
23
24
Methods
is an ultimate prerequisite for reconstructing the lemniscal thalamocortical pathway of the
rat whisker system.
The second tool, NeuroMorph, allows for a semi-automated tracing of both dendrites and
axons, from in vivo labeled single neurons, using transmitted light brightfield microscopy
(TLB). By measuring the properties of the TLB imaging system and of the cortical tissue,
a compensation of optical aberrations by deconvolution becomes possible and guarantees
an authentic and reliable detection of usually too faint axons next to intensely stained
dendrites.
Here, I will present representative samples of excitatory dendrite morphologies from all
cortical layers as well as thalamocortical VPM and intracortical L5A axon morphologies.
Registering these tracings to standardized column dimensions will then allow for statistical
analysis and classification of neuron anatomy.
Finally, the third tool, NeuroNet, combines results from the two previously introduced
methods and yields realistic anatomy and connectivity of neuronal microcircuits. Here,
starting with the average three dimensional soma distribution of each cortical layer in S1,
an average standard barrel column is built up with reconstructed and classified excitatory
dendrite morphologies. By superimposing thalamocortical VPM axon tracings, the three
dimensional axo-dendritic overlap with each neuron population is calculated. By estimating the number of synapses per axonal length, NeuroNet will finally yield an estimate of the
absolute number and three dimensional distribution of VPM synapses for each excitatory
neuron.
In summary, the subsequently presented tools result in an in silico network model of approximately 15200 realistically distributed full compartmental excitatory cortical neurons,
which are synaptically connected to about 285 thalamic neurons in the corresponding VPM
barreloid. This model network anatomically resembles the thalamocortical lemniscal path-
2.1 3D counting of neuron somata
25
way, which is involved in processing of sensory information from a single whisker, both in
the anaesthetized and awake rat. Animating this cortical column in silico with thalamocortical input, measured in vivo, will potentially allow to gain understanding of cortical
information processing and ultimately show how cortical output can trigger simple whisker
related behaviors, such as the decision to cross a gap.
2.1
3D counting of neuron somata
As previously described in [29], the estimation of absolute numbers of neurons, densities
or rates of density change in neuron populations is usually based on random, sparse sampling methods [30], [31] such as stereology [32]. These methods determine cell densities
by inspecting a representative sub-volume of tissue and extrapolating the obtained density
values to a reference volume. Usually these density values are given with an accuracy of
about 10% [33] for large anatomical units, such as primary visual (V1), somatosensory
(S1) or motor cortex (M1). However, deviation between densities in previous studies is
much larger. For instance in V1 a variety of densities values is reported (40000 [30], [34],
[35], 52000 [33], 75000-80000 [36], [37] neurons per cubic millimeter). It is hence difficult
to determine density changes within or between neuron populations, or across functional
sub-units, such as the cortical column. In consequence, it would be favorable to count
the absolute number of neurons in large volumes and hence derive the detailed three dimensional neuron distribution of the brain area of interest. In case of the cortical barrel
column such a volume should be around 0,5mm x 0,5mm x 2mm (0.5 cubic millimeter [38])
in order to avoid edge artifacts.
Recently available three-dimensional imaging techniques (mosaic/optical-sectioning confocal laser scanning microscopy) and suitable neuronal stains opened new possibilities for
26
Methods
the determination of neuronal densities within entire volumes. Neuronal stains, like NeuN
[39], [40], [41], [42] labeling all neuron somata, or GAD67 [43], [38], [44], [45] labeling
GABAergic interneuron somata, as well as genetically encoded labels of specific neuron
populations in transgenic mice [46], allow in principle the quantitative determination of
density differences between neuron populations at high level of detail (e.g. between or
within cortical layers).
Several neuron counting and detection methods have been reported, both manual and automated ones. The obvious disadvantage of manual neuron detection, apart from possible
subjectivity, is the amount of time needed for neuron counting. In consequence, automated accurate detection and segmentation of neurons from microscopic images has been
extensively studied [47]. In general, these algorithms can be divided into three categories:
threshold-based [48], [49], watershed-based [50], [51], [52], [53], [54] and model-based approaches [55], [56], [57], [58].
None of the three automated algorithm categories yield satisfying results for the here presented sample data. This is due to the fact that model-based methods have comparatively
better specificity in detecting the targets, i.e. such methods find all objects satisfying the
model-shape but only those. In contrast, threshold- or watershed-based approaches display relatively better detection sensitivity, i.e. they find all objects, but usually result in
incorrect numbers [47], e.g. for our sample data, touching, densely clustered neurons are
counted as one, resulting in about 20% less neurons.
Here, I present an automated 3D neuron counting approach, developed in cooperation with
Vincent J. Dercksen (Zuse Institute Berlin (ZIB)), that combines all three approaches to a
novel high-throughput system for detection of neuron somata [29]. The system is described
on the example of confocal image stacks of NeuN-labeled neurons from S1. The slightly
adapted method for co-localization in multi-channel images is described on the example
2.1 3D counting of neuron somata
27
of NeuN neurons counterstained with GAD67. This allows to measure the fraction of
GABAergic interneurons among all neurons [38].
The presented processing pipeline consists of three steps: pre-processing, morphological
and model-based filtering. The goal of the first threshold-based step is to create a binary image, separating foreground (i.e. stained neurons) from background. It consists of a
number of image processing steps, including compensation for imaging or staining artifacts
such as bleaching, shading or uneven uptake of the stain. This threshold-based approach
is usually not sufficient to detect the true number and position of neurons. High neuron
densities and limited microscope resolution result in clusters of neurons that cannot be
separated by the local threshold step. The first processing step is therefore regarded as a
pre-processing step that guarantees a similar input to the second (watershed-based) and
third (model-based) processing steps. The implementation of the latter two steps is independent of the data type.
In the second watershed-based step, clusters of neurons which are connected by narrow
links are separated by a morphological filtering process, resulting in an image of distinct
watershed regions (3D objects of connected foreground voxels, identified by a label number), and ideally representing individual neurons. Some clustered neurons appear however
like a single, large and uniformly stained neuron. The morphological filters are not capable
of splitting such clusters into distinct watershed objects.
The third, model-based processing step addresses this problem. It assumes a single dominant neuron population within the image stacks with a Gaussian-distributed neuron (i.e.
soma) volume. The mean neuron volume and its variance are calculated from a volume
histogram of the watershed regions. Undivided clusters are then split according to their
volume, assuming that it has to be an integer multiple of the mean soma volume. An
additional advantage of this constraint is that its parameters are not specified by the user
28
Methods
but automatically calculated during the image processing. In a correction step, eventually
present spatially separated neuron sub-populations with larger mean volumes are investigated and remain unsplit.
I also present an extension of the method to multi-channel image stacks for co-localization
of counterstained neurons. Here, NeuN-labeled neurons were counterstained with GAD67
in order to measure the fraction of GABAergic interneurons among all neurons [38].
2.1.1
Sample preparation and imaging
All presented image data was acquired by methods described in detail before [59], [60], [61].
Development and validation of the automated counting pipeline was performed on confocal image stacks of NeuN/GAD67-stained neurons [43], [38] provided by Hanno-Sebastian
Meyer (MPI for Medical Research, Heidelberg). These stacks were acquired from 50µm
thick physical vibratome sections from brain tissue of adult wistar rats, cut either along the
thalamocortical, coronal or a specified tangential axis. Large three-dimensional confocal
image stacks were generated by mosaic/optical-sectioning using confocal laser scanning microscopes (SP2 or SP5, Leica Microsystems GmbH, Wetzlar, Germany; Flowview FV1000,
Olympus, Japan). SP2 or SP5 images were acquired by 40x (HCX PL APO CS; N.A.: 1.250.75; oil-immersion) or 63x (HCX PL APO CS; N.A.: 1.3; glycerol-immersion) magnification objectives, yielding a pixel size of 0.366µm x 0.366µm or 0.232µm x 0.232µm, respectively. FV1000 images were acquired by a 60x (PLAN APO N, N.A.:1.42; oil-immersion)
magnification objective, yielding a pixel size of 0.331µm x 0.331µm. Mosaic refers to multiple overlapping 2D images (e.g. 5x5), each representing one microscopic field of view.
Sampling along the z-direction during optical-sectioning was 0.6µm.
2.1 3D counting of neuron somata
2.1.2
29
Manual detection of soma positions
Image stacks containing single mosaic tiles were loaded into Amira 4.0 or 4.1 [62], [63].
Landmarks (3D voxel coordinates) were assigned manually to the center of all stained
neuron somata (soma landmarks) during a careful examination of the image planes (optical
sections).
Objects at the stack border in the x- or y-direction were always counted. The x/y overlap
was set to approximately 5 microns. In consequence neurons at the x/y border (overlap
area) of mosaic tiles were detected twice. By aligning the mosaic images, twice detected
neuron somata coincide and can be erased. If the mosaic area is chosen larger than the
area of interest, x/y border effects can hence be completely neglected.
The x/y border rule is not applied at the z-borders of the image stacks. Here neurons are
regarded to be within the image stack if their diameter increases to a maximum value and
decreased again or was constant for three more optical sections before reaching the stack
border. A detailed description of the manual counting, the validation of the border criteria
and the approximate inter-user-variability of 2.1% can be found in [38].
2.1.3
Computing hard- and software
The software and algorithms are custom written in C++ [64]. The raster image file I/O,
iteration through a raster image, as well as multiple of the subsequent image filters use the
ITK Image Processing Library [65]. The software is executed on AMD dual-core 64-bit
Opteron computers, equipped with either 1 CPU and 2 Gigabytes of memory, 4 CPUs and
32 Gigabytes of memory (DELTA Computer Products GmbH, Reinbek, Germany) or 8
CPUs and 64 Gigabytes of memory (fms-computer.com, Netphen, Germany).
30
Methods
a
e
i
b
f
j
c
g
k
d
h
l
20 µm
Figure 2.1: NeuroCount Illustration. X/y-, x/z- and y/z-projections of a representative
small volume of NeuN-stained somata. (a) original image stack, (b)-(g) pre-processing: (b) local intensity mapping → amplification of weak somata., (c) local lower threshold → reduction of
background, (d) hit-or-miss transform → reduction of small isolated noise artifacts, (e) median
filter → reduction of noise and smoothing of structures, (f ) closing filter → filling of small holes
within the structure, (g) cropping filter → structures are cropped from their artificial halos, (h)-(k)
watershed-based processing: (h) Euclidean distance transform, (i) regional maxima = markers, (j)
grayscale reconstruction → starting basins for watershed segmentation, (k) marker-driven watershed segmentation → individual foreground regions representing individual or clustered somata,
(l) model-based processing, splitting of remaining clustered watershed objects according to object
volume → set of position landmarks (orange); for illustration: landmark projections (red circles).
Figure adopted from [29].
2.1 3D counting of neuron somata
2.1.4
31
Threshold-based filtering (pre-processing)
Fluorescent images can suffer from two kinds of artifacts. First, shading or bleaching of the
stain, as well as deviating neuron densities, lead to an uneven illumination across mosaic
images and usually affect the image acquisition itself. It results in different signal-to-noise
ratios (SNRs) across and between individual image planes. The second artifact is caused
by uneven uptake of the fluorescent dye, resulting in varying intensity values across individual neurons. The first issue is addressed by subdividing the large mosaic stack into
approximately 400µm x 400µm large sub-stacks, overlapping by 5%. The entire processing
pipeline is then successively applied to these individual smaller stacks. Each image plane
of such a sub-stack is further split into rectangular bricks and processed individually, in
order to compensate for local SNR variations within and between the sub-stack planes
(see next subsection). The second issue is addressed by processing each three-dimensional
object (e.g. neuron soma) individually (see subsection: Removal of artificial halos).
It should be emphasized that the mentioned artifacts are strongly dependent on the imaging instrumentation and the used staining method. If the imaging system incorporates
automatic shading correction that reduces deviations in SNR already during the image
acquisition, the subsequent filters will not affect the image quality negatively. However,
the here presented imaging systems yield no sufficient intrinsic correction and hence the
pre-processing is essential for an authentic neuron counting.
Bricking
Uneven illumination across individual image planes prohibits the application of global
image operators. Further, illumination deviations between individual image planes limit a
general application of 3D image operators. Each image plane (i.e. one sub-stack, ≈400µm
x 400µm) is hence subdivided into 2D bricks. In the case of the SP2 confocal microscope at
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Methods
40x magnification, the optimal bricks size was determined to be 256x256 pixels for a substack that resembles exactly one field of view (375µm x 375µm; 1024 x 1024 pixel). This size
was determined by systematic testing and is linearly adjusted for different magnifications,
pixel resolutions or sub-stack sizes, in order to guarantee a similar brick area for all kinds
of images. Hence, the number of bricks decreases with decreasing magnification (or pixel
resolution) and fixed image size.
Intensity mapping
Direct application of a lower threshold operator on each 2D brick, which sets all pixels
having a value smaller than the threshold value to zero, proved to be problematic. The
SNR is usually too low to set an adequate threshold value that separates somata from
background. Hence the intensities for each brick are mapped by a non-linear sigmoidshaped filter 2.1 [65] onto a new range:
I0 =
255
,
1 + exp(−(I − αβ ))
(2.1)
where I 0 and I denote the new and old intensity (gray) values, respectively. β ideally represents the center and α the width of the neuron’s intensity range. This filter progressively
attenuates intensity values outside this range and produces a very smooth and continuous
transition to the specific intensity range of interest (Figure 2.1b). It results in a per-brick
amplification of the neurons with respect to their surroundings (Figure 2.2a/b). Systematic testing yielded an intensity range of neurons that is best described by the following
values for α and β:
β = µoriginal + 0.75σoriginal ; α = σoriginal ,
(2.2)
where µoriginal and σoriginal refer to the mean gray value and standard deviation of each 2D
image brick, respectively.
2.1 3D counting of neuron somata
33
a
b
100 µm
c
6000
original 2D image brick
after intensity mapping
4000
3000
original 2D image brick
after intensity mapping
8000
frequency
frequency
5000
100 µm
d
6000
4000
2000
2000
1000
0
0
0
20
40
60
8-bit8-bit
gray
greyvalue
value
80
100
0
20
40
60
80
100
greyvalue
value
8-bit8-bit
gray
Figure 2.2: Local intensity mapping. (a) Single thalamocortical x/y image plane affected by
uneven illumination. The high-contrast in the upper brick results in a broad gray value histogram
(panel c; width of black histogram=6.22), whereas the low-contrast bottom brick has a more narrow
histogram (panel d; width of black histogram=3.58). (b) Image plane after local intensity mapping.
The neurons across the entire plane are of similar intensities. The noise in the prior low-contrast
brick is high, resulting in a much broader histogram (panel d; width of red histogram=56.52),
whereas the width of the histogram of the high-contrast brick remains more or less unchanged
(panel c; width of red histogram=4.36). (c) In high-contrast bricks the intensity mapping leads to
amplification of the somata and attenuation of the background. Hence, the lower threshold should
be approximately the mean value of the mapped image. (d) In low-contrast bricks the structures
and a significant part of the background are amplified, resulting in a broad histogram. Hence, the
lower threshold needs to be higher than the mean value after mapping. This is realized by the
threshold t1 in equation 2.3. For high-contrast images t1 is essentially µnew (here: µnew + 1),
whereas in the low-contrast case t1 is significantly increased (here: µnew + 17). Figure adopted
from [29].
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Methods
Lower threshold
Once the neurons are amplified with respect to their surrounding, a lower threshold t1 is
applied in order to separate the neuron somata from background:
t1 = µnew +
1.1
σoriginal
· σnew ,
(2.3)
where µnew and σnew refer to the mean gray value and standard deviation of each 2D
image brick after intensity mapping. This thresholding step sets all voxels below t1 to
background, i.e. to value zero. The local threshold function comprises a term inversely
proportional to the standard deviation of the image brick prior the intensity mapping.
This accounts for possible uneven illumination within each image plane. The width of the
intensity distribution (σoriginal ) can vary significantly from one brick to the next. Two extreme situations occur when neurons are surrounded by low background, resulting in broad
intensity distributions (Figure 2.2a, top brick/2.2c), and when neurons are surrounded by
background values similar to the neurons’ intensities, resulting in a narrow distribution
(Figure 2.2a, bottom brick/2.2d). In the latter case, the width of the intensity distribution
after mapping will be much larger than the original one (σnew À σoriginal ), resulting in
an approximate threshold of t1 = µnew + σnew (Figure 2.2d). In the other case, the two
widths will be of similar order of magnitude, resulting in a threshold of t1 = µnew (Figure
2.2c). Thus, this filter is capable of discriminating neurons surrounded by high and low
background values (Figure 2.1c and 2.2b).
Hit-or-miss transform
The two previous filtering steps result in image stacks of significantly reduced background.
However, small ”speckle” artifacts are usually still present. The image planes are therefore
subjected to a hit-or-miss transformation with rectangular frame masks of increasing size
2.1 3D counting of neuron somata
35
as structuring elements [66], [61]. The transformation is applied to every image plane.
Isolated foreground objects that are completely surrounded by a frame are converted to
background (Figure 2.1d). Beginning with a radius of one pixel and increasing the frame
size subsequently to three pixels, small and isolated artifacts are removed.
Median filtering
In order to smooth the intensity distribution within neurons, a median filter is applied as
implemented by the ITK [65]. Each voxel is assigned a new intensity value, which is the
median value of its surrounding voxels within a 5x5x5 voxel large neighborhood (Figure
2.1e). The neighborhood size was obtained by systematic testing. This filter is computed
in three dimensions because neurons are 3D objects, which consist of 2D planes that may
vary systematically in gray values. 2D median filters would not decrease these inter-plane
deviations.
Closing transform
Next, a grayscale closing filter [66] is applied as implemented by the ITK [65]. Its geometrical interpretation is that a ”sphere” rolls along the outside boundary of a foreground
object (i.e. neuron soma). It tends to smooth contours, fuses narrow breaks, eliminates
small holes, and fills small gaps in the neurons (Figure 2.1f). The 3D structuring element
(sphere) has a radius of five voxels (approximately 2/3 of a soma radius) and was derived
after systematic testing.
Removal of artificial halos
The uneven uptake of stain results in neurons of weak intensities in intermediate neighborhood to neurons with high intensity values. The intensity mapping described above causes
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Methods
amplification of the surrounding of such weakly pronounced neurons and sometimes fuses
them with other neurons (”halos” (Figure 2.1g, green)). By removing halos that were
introduced by the intensity mapping, the neurons are cropped to their original volume
(Figure 2.1g, yellow/orange). This is realized by processing each 3D object of connected
foreground pixels individually. For each 2D plane of each object, a lower threshold value
t2 is calculated, defining the foreground for this object plane:
t2 = µf ilter − 1.2σf ilter +
40
σoriginal
,
(2.4)
where µf ilter and σf ilter refer to the mean gray value and standard deviation of each 2D
object plane after the closing filter. The local threshold function comprises a term inversely
proportional to the intensity deviation of the 2D object plane σoriginal in the unprocessed
image, again compensating for uneven illumination between the bricks as described in
subsection ”Lower threshold”. The parameters for the threshold function are obtained by
systematic testing. This is the final result of the first (pre-processing) step.
2.1.5
Morphological filtering
The filtering described in the previous section results in a stack of 2D gray value images,
which is then transformed into a binary stack by setting all pixels with a gray value
different from zero to 255. In the following such stacks will be considered as single 3D
binary images. In order to find the total number of neurons in the image, one could simply
count the total number of 3D connected foreground objects (groups of connected voxels) in
the image. However, the limited resolution of light microscopy imaging systems in addition
to high neuron densities results in clusters of neurons that cannot be separated by the preprocessing pipeline. In consequence, direct counting produces total neuron numbers which
are generally too low, because a single foreground object may consist of multiple connected
2.1 3D counting of neuron somata
37
a
b
c
Figure 2.3: Watershed filtering. One-dimensional illustration of the separation of touching
somata by marker-based watershed segmentation. Objects containing two (or more) maxima in
the distance field separated by a minimum are assumed to consist of two (or more) clustered
neurons and need to be separated. (a) Regional maxima of the distance field D. Due to contour
irregularities multiple maxima per object may appear (left object), which is undesired. (b) By
subtracting 1 from the distance field at the position of regional maxima, and computing the regional
maxima of this modified distance field, better markers are obtained. (c) The adopted distance
field is ”flooded” using the marker positions as initial basins. Positions where the levels from
the different watersheds meet, are marked as crest regions. After the flooding is completed, crest
regions are turned into background. (D has been inverted to better illustrate the basin flooding
metaphor.) As a result, clustered neurons are split at the minima of the distance field, i.e. where
the connection between two neurons is thinnest. Figure adopted from [29].
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Methods
neurons. Therefore such clusters are divided into their constituent neurons, using a method
described by [67]. This method consists of three steps:
• Computation of a distance transform for each 3D foreground object of the binary
image.
• Finding exactly one marker for each neuron (i.e. multiple markers for neuron clusters), where marker refers to a single voxel or a group of connected voxels.
• Computation of a watershed transformation, using the markers as initial basins.
Geodesic distance transform
First, a distance transform [66] is computed for each 3D foreground object in the binary
image. This results in intensity values for each voxel that resemble the physical Euclidean
distance to the closest background voxel. Thus, voxels in the interior of objects have high
values, object voxels close to the boundary have low values and background voxels have
zero value (Figure 2.1h). These values are computed by repeatedly (binary) eroding [66],
[65] the objects in the pre-processed image, successively peeling their outer boundaries.
During each erosion step and for each foreground object, the physical Euclidean distance
to the prior erosion level is assigned to voxels of the current most outer layer. A 3x3x3
voxel binary cross is used as structuring element for erosion.
Grayscale reconstruction
This second step should ideally generate a single marker for each neuron within a foreground
object (Figure 2.1i). One approach to realize this would be to compute the regional maxima
of the distance image (Figure 2.3a). A regional maximum M of a grayscale image I is
defined as a connected region of voxels with a given value h (plateau at altitude h), such that
2.1 3D counting of neuron somata
39
every voxel in the neighborhood of M has a value strictly lower than h. An efficient method
to compute regional maxima uses a morphological operation called grayscale reconstruction
[68] as implemented by the ITK [65]. Computing all regional maxima results however in
too many markers: some objects have multiple very close regional maxima, due to contour
irregularities and discretization artifacts. Usually these markers differ by only one level in
the distance function. Therefore such regional maxima are reconnected by subtracting 1
from the values in the distance image at all marker positions and computing the regional
maxima (Figure 2.1i) of this modified distance function (Figure 2.3b).
Watershed segmentation
The final step uses the set of markers M to assign the set of foreground voxels belonging to
each neuron. These neuron regions are found using a procedure called marker-driven watershed segmentation. The general watershed algorithm uses intensity information to divide a
gray value image into foreground regions (catchment basins), separated by watershed lines
(background). This algorithm can be illustrated by a landscape flooding metaphor. The
inverted distance image D0 = −D can be regarded as a landscape where the minima of D0
correspond to valleys (Fig 2.3c). When this landscape is flooded, the water level starts to
rise from the valleys (or catchment basins) until the different basins meet at the watershed
lines (or crests). Afterwards, each basin corresponds to one of the desired neuron regions
and is bounded by the watershed lines and/or the image background. The marker-driven
watershed segmentation ensures that one obtains exactly one region for each marker, by
creating an input image D∗ adapted from D0 such that
1. its only regional minima are located at the marker positions and
2. its only crest-lines are the highest crest-lines of D0 that are located between the
minima (marker positions)
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Methods
The image D∗ is then flooded as in the general watershed case. For details I refer to [67].
Further, the flooding algorithm described in [69] was chosen to efficiently find the neurons
that correspond to the markers (Figure 2.1k).
2.1.6
Model-based cluster splitting
The preceding processing steps result in individual 3D objects (neuron regions) that represent the neuronal somata within the image stack. However, some clusters of neurons are
still not separated because they have similar intensities and are so close to each other in
the original image that they appear like a single, almost spherical neuron. To separate such
clusters I chose a model-based filter. It is based on the assumption that within each substack there is a single dominant neuron population of neurons with Gaussian distributed
volumes and that most clusters could be split by the filters of the first two pipeline steps.
Volume histogram and mean neuron size calculation
Regarding the assumption above, the voxel volume of each watershed region is calculated
and results in a histogram of these volumes. The first histogram bin always comprises
many small artificial objects. Hence, taking the second peak of the histogram as the
mean volume of the dominant neuron population, a Gaussian distribution is fitted to the
histogram at this value (Figure 2.4a). The distribution for individual neurons (i.e. not
part of a neuron cluster) is parameterized by three values, the mean value, the standard
deviation and the peak amplitude (µ1 , σ1 , A1 ). Clusters of n = 2,3,..N connected neurons
will also be parameterized by Gaussian distributions. Their according mean value µn is
simply given by:
µn = 1.1 · n · µ1 .
(2.5)
2.1 3D counting of neuron somata
a
50
41
1.
frequency
40
30
20
2.
10
3.
4.
0
0
10
20
30
voxel volume
b
3
50x10
40
normalized cluster probabilities
1.0
0.8
1.
4.
2.
0.6
3.
0.4
0.2
0.0
10
20
30
40
3
50x10
voxel volume
Figure 2.4: Model-based splitting. Volume histogram of watershed objects. The first mode
is assumed to reflect the dominating neuron population and is fitted by a Gaussian (red 1). The
higher modes are assumed to be integer multiples of the first mode (→ here: 3 more Gaussians
representing clusters of 2, 3 and 4 neurons, respectively). The pink plot represents the sum of
the four distributions. (b) Normalized probability values for each object volume. According to the
above distributions four probability values are calculated for each object volume and normalized to
1. The resulting four plots are shown. The intersections (vertical dashed lines) represent volumes
the separate the clusters. Figure adopted from [29].
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Methods
The additional multiplication with 1.1 is due to the assumption that the unresolved gaps
between the neurons add a small amount to the cluster volume and is derived by systematic
testing. The standard deviation for each cluster type σn is calculated by standard error
propagation:
n
1 X
σi ,
σn = √
n i=1
(2.6)
and the according amplitude An is calculated by averaging the height of the five bins
around µn . This is done until the largest 3D region (object) in the watershed image is
covered by a distribution (Figure 2.4a).
Evaluation of cluster type
Each watershed object can only belong to a single distribution. Therefore the probability
pmn for each object and for each distribution is calculated, where m refers to the object
number and n to the nth cluster distribution (number of connected neurons). Each pmn
value is normalized to one (Figure 2.4b), resulting in N normalized cluster probabilities
for each watershed object.
pmn
.
p̄mn = PN
p
mn
n=1
(2.7)
Each object is regarded to consist of as many neurons as is its highest normalized probability value. However, objects that are smaller than the mean neuron volume minus twice the
standard deviation are considered to be artifacts and are ignored during further processing.
Splitting of clusters by k-means cluster analysis
Once each watershed object is assigned a most likely cluster type (i.e. n = k = 1, 2, , N
neurons), the according k reference voxels (landmarks) are calculated, by using a k-means
clustering algorithm as implemented by the ITK [65]. The k-means algorithm works as
2.1 3D counting of neuron somata
43
follows:
1. The input for each watershed object are k (= n; i.e. most likely number of neurons
in a cluster) initial mean values (default landmarks) specified as k random voxels
within the object.
2. Each voxel of a watershed object is assigned to its closest landmark among the k
mean values.
3. Calculation of each k-means cluster’s mean from the newly assigned landmark voxels
within the objects and hence updating the k mean values of a neuron cluster.
4. Repetition of step 2 and step 3 until the termination criteria is met, here if no voxel
changes its cluster membership from the previous iteration.
This results in k landmark voxels for an object (consisting of k = n neurons). Each
landmark is used as position reference of an individual neuron and a list of these landmark
voxels is visualized in Amira [62], [63] (Figure 2.1l).
Correction for 2nd population of larger neurons
The assumption of a single Gaussian distributed neuron volume across the entire image
stack can cause miss-counting if two neuron populations of significantly different volumes
are present. I therefore assume that there is only a small spatial overlap between these
populations and that one of them is dominant. This is a reasonable assumption for the
presented sub-image sizes of ≈400µm x 400µm x 50µm. If the minor population is smaller
in volume than the majorities’ mean volume (i.e. GABAergic interneurons), these neurons
will still be counted as one. However, if the minority population consists of large neurons
(Figure 2.5) the prior described splitting will result in an overestimation of the neuron
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Methods
100 µm
Figure 2.5: Large neuron correction. Maximum z-projection of NeuN-stained confocal image
stack. The yellow box represents the volume shown in Figure 2.1. This stack is from an area
of S1 where L4 neurons (upper part) overlap with larger L5 neurons (lower part). Even though
two neuron populations with significantly different volumes are present, the correction algorithm
avoids miscounting (e.g. neurons indicated by arrows). Figure adopted from [29].
2.1 3D counting of neuron somata
45
density.
This issue is addressed by evaluating the local surrounding of each watershed object before
model-based splitting. If more than 10% of the watershed objects in a surrounding box of
300 x 300 x 100 voxels have the same cluster probability (larger than 1), the object will not
be split (Figure 2.5). This filter also corrects for systematic errors of the pre-processing
step. In bricks with low SNR the neurons are slightly enlarged compared to bricks of
high SNR. If significant SNR gradients are present within the image stack, the systematic
increase in volume in low SNR bricks can lead to an artificial second neuron-type. This
means that the neuron volume in some regions of the image can be systematically larger
compared to the original image stacks. This effect is also compensated by the described
correction filter.
2.1.7
Colocalisation
NeuN reliably labels all neuron somata within an image [39]. It is hence possible to counterstain specific neuron-types and to image them simultaneously at a different fluorescent
wavelength, acquiring so called multi-channel image stacks. Since all neurons within the
NeuN channel are detected by the prior described pipeline, the local surrounding of each
landmark voxel is inspected in the other channels. If a neuron is also detected in one of
the other channels, not only the position and density of all neurons within the stack can
be evaluated, but also the neuron-type can be obtained.
Figure 2.6 shows an example for this procedure. GAD67 positive interneurons were colocalized in a second fluorescent channel (Figure 2.6a/b). The pre-processing of the second
channel is again dependent on the staining and imaging techniques. In the case of GAD67,
imaged by a confocal laser scanning microscope, immunoreactive GABAergic interneurons
show a strong somatic GAD67-signal [43], [38]. However, GAD67 positive synapses will
46
Methods
e
b
f
1.0
normalized frequency
a
0.8
0.6
0.4
0.2
0.0
100
120
140
160
180
200
220
240
8-bit grey values
g
normalized frequency
c
1.0
0.8
0.6
0.4
0.2
0.0
100
120
140
160
180
200
220
240
100
120
8-bit grey values
d
h
140
160
180
200
220
240
8-bit grey values
1.0
normalized frequency
0.8
0.6
0.4
0.2
0.0
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120
140
160
180
200
220
8-bit grey values
240
100
120
140
160
180
200
220
240
8-bit grey values
50 µm
Figure 2.6: Colocalisation. (a) Max x/z-projection of NeuN-stained confocal image stack.
(b) Max x/z-projection of GAD67 counterstained image stack. (c) Automatically detected NeuN
landmarks. (d) GAD67 positive landmarks generated by evaluating the surrounding of each NeuN
landmark in the pre-processed version of b, (e) overlay of a and b with automatically detected
GAD67 landmarks (green = counterstained somata). (f ) normalized gray value histogram of
GAD67 image (g) left: normalized gray value histogram in GAD67 stack around a NeuN landmark
position, right: left histogram divided by ”background” histogram from f; due to the presence of
a GAD67-positive neuron, high gray values are dominant (h) due to the absence of a GAD67positive neuron, low gray values are dominant → if the divided histogram is dominated by gray
values below 150, no GAD67 landmark is assigned; if it is dominated by gray values higher than
150, a co-localized GAD67 landmark is set. Figure adopted from [29].
2.1 3D counting of neuron somata
47
also be stained, resulting in small (<10 voxel) bright spots (Figure 2.6b). Hence, the major
step of the pre-processing of the GAD67 channel is to get rid of these synapses.
Here, the pre-processing is based upon a gradient magnitude filter [66] as implemented by
the ITK [65]. The resultant gradient image is further subjected to an exponential intensity
mapping using the following equation:
I 0 = exp(
log(256)
· I) − 1,
255
(2.8)
where I 0 and I refer to the intensity (gray) values after and before the mapping, respectively. This mapping effectively attenuates low background values and enhances the synaptic signals. The result is then subtracted from the original image. After these additional
GAD67 specific filters, the brick-wise intensity mapping as described before is applied. A
final median filter with a structuring element of 1 pixel radius reduces any remaining small
artifacts, leaving only GAD67 positive neuron somata (Figure 2.6d).
Figure 2.6f shows a histogram of such a pre-processed stack. Since the fraction of GAD67positive neurons among all neurons is low (≈15%) [33], the stack histogram is dominated
by the background. Figure 2.6g/h show intensity histograms around landmark positions
that were generated for the NeuN channel images. Figure 2.6g (left) shows the landmark
histogram of the k-mean cluster around the corresponding NeuN landmark in the presence
of a GAD67-positive neuron, whereas the k-means cluster of the landmark used for the
landmark histogram in figure 2.6h (left) does not contain such a neuron. All histograms
are normalized to one and landmark histograms are shifted so that the bin with the maximum number of gray values coincides with the maximal bin of the stack histogram. These
matched histograms are bin-wise divided and the resultant ratio histogram is again normalized to one (Figure 2.6g/h, right).
If no GAD67 positive neuron is present at the landmark position, the landmark histogram
resembles the shape of the stack histogram, since this is dominated by background. There-
48
Methods
fore the divided histogram shows no contribution at high gray values that correspond to
foreground (Figure 2.6h, right). In contrast, if a GAD67 positive neuron is present, the
amount of foreground pixels is overrepresented in the landmark histogram with respect to
the stack histogram. Hence, the ratio histogram shows a significant distribution at high
gray values (Figure 2.6g, right). The criterion for co-localization can therefore be defined
as a threshold function. If 20% of the object’s pixels fall into bins from 150-255 of the ratio
histogram the neuron is considered to be present in both channels.
2.2
3D reconstruction of neuron morphologies
As derived above and described in detail before [61], the accurate tracing of single neurons is
one prerequisite for the determination of anatomical features of different neuron cell-types
required for biophysical modeling of single cells and signal processing in neuronal circuits.
Several automated reconstruction approaches have been reported previously. These reconstructions, made with two-photon [70], confocal [71], [72], [73], [74], [75], [76], [77],
[78] or brightfield images [79], focus mainly on the dendritic tree and the extraction of
geometrical features such as volumes or surface areas of dendrites or spines. Hence, these
approaches completely lack a reconstruction of the axonal arbor. The reason is that the axonal branching pattern is more complex and that axons spread over a much larger volume
(cubic millimeters) compared to dendrites (a few hundred cubic micrometers). Furthermore, axonal staining is fainter than that of dendrites because of their smaller diameters
and greater distance from the soma where a tracer is loaded into the cell. Thus, no successful automated tracing of these widely spreading neuronal projections has yet been reported.
The method presented here, was developed in cooperation with Dr. Philip J. Broser (Royal
Queen Mother Hospital, White Chapel, London) and focuses on the accurate tracing of all
2.2 3D reconstruction of neuron morphologies
49
neuronal projections. The dendritic tree and the extensively spreading axonal arbor are
traced and reconstructed simultaneously.
Typically the cells are filled in vivo with a tracer like biocytin [80]. The brain is then
perfused with fixative and cut in sections of about 50-100µm thickness. The current approach for tracing these neurons and their axons in 3D is a manual one, based on the
Camera Lucida technique (e.g. The Neurolucida System (MicroBrightField), FilamentTracer (BITPLANE)). Here, neuronal structures in each section are traced manually. A
human user interacts with a microscope that is enhanced with computer imaging hardware
and software [79], [81]. The user recognizes patterns and marks neuronal structures on
a live camera image displayed on a computer screen. By moving the stage horizontally
in x and y and focusing through the brain slice in the z-direction, a progressively larger
volume is inspected. The 3D-tracings of neuronal branches from this volume are collected
by the computer system interfaced to the camera and result in a 3D-graph representation
of neurons.
Manual tracings of dendritic trees are very reliable. The reliability is due to the localized
branching pattern and the relatively large diameters (≈2µm-5µm) of dendrites. However,
the axonal arbor frequently extends further away from the soma. The average volume that
has to be inspected by the user is for most cell-types around 1.5mm x 1.5mm x 100µm
per brain section. For accurate tracing, this volume should be inspected in a raster scan
order, moving from one field of view to the next and progressively focusing through the
specimen.
Using a 40x objective and a standard CCD-camera (e.g. Q-icam (Q-imaging, Canada)),
the number of fields of view is around 12000, with an average sampling along the optical
axis of 1µm. Since axons can have diameters less than one micron, a 100x objective is usually used for manual tracing. In this case around 77000 fields of view have to be inspected.
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Taking a typical cell (e.g. L2/3 pyramidal neuron of rat cortex), which spreads over 10 to
20 brain sections, the number of fields of view that have to be inspected is of the order of
105 − 106 . Manual reconstruction of axonal branching patterns is hence tedious and time
consuming. Therefore, correct manual tracing of axons requires experienced users to reach
a reliable level of reconstruction quality.
I present a semi-automatic reconstruction pipeline that traces reliably both dendrites and
axonal arbors by extracting their skeleton (approximate midline). In addition the method
presented here needs significantly less time compared to manual tracing. The automated
tracing is carried out on large image stacks acquired by mosaic scanning [82] and optical
sectioning [60] using a TLB microscope. The manual inspection of thousands of fields of
view is replaced by the acquisition of a stack of mosaic images. A rectangular pattern of
overlapping mosaic tiles (adjacent fields of view) is scanned, covering an area of a brain
slice sufficient for the tracing of axonal arbors usually 1.5mm x 1.5mm (Figure 2.7a). The
3D information is obtained via optical sectioning, meaning the recording of such mosaic
planes at multiple focal positions that are separated by 0.5µm.
This large 3D image is then deconvolved (see sec. 2.2.3), based on measured optical properties of the microscope, as derived in cooperation with Dr. Stefan Hippler (MPI for
Astronomy, Heidelberg) [83]. This guarantees an improvement of SNR and resolution, in
particular along the z-direction. A local threshold function that checks for connectivity
extracts neuronal structures from the background. The extracted foreground objects are
transformed into thinned approximate midlines (the skeleton) and yield a graph representation of dendrites and the widely spreading axonal arbor. The automatically reconstructed
branches from serially sectioned brain slices are than manually edited and automatically
spliced using custom made software in Amira [62], [63].
2.2 3D reconstruction of neuron morphologies
a
51
b
1 mm
c
10 µm
500 µm
d
500 µm
Figure 2.7: Mosaic microscopy for neuron tracing. (a) Overview of a biocytin-filled neuron
(L2/3 pyramid) from a brain slice taken with a 100x objective. The black mosaic indicates the
scanning area (1,5mm x 1,5mm). A 3D image stack is acquired by mosaic/optical-sectioning.
(b) The pattern of overlapping tiles (adjacent fields of view) is stitched to a large 2D mosaic
image. Mosaics are recorded for all focal planes separated by 0,5µm, resulting in a 3D stack.
(c) Enlargement of the box shown in b showing a faint axonal branch about 1mm away from the
soma. This illustrates the requirement to scan large volumes at high resolution. (d) Result of
semi-automated reconstruction pipeline. Figure adopted from [61].
52
2.2.1
Methods
Sample preparation
All cells were filled in Wistar rats (P28 - 31; Charles River Laboratory). Experiments were
carried out by Dr. Randy M. Bruno (Columbia University, NY) and Dr. Christiaan P.J.
de Kock (VU Amsterdam) in accordance with the animal welfare guidelines of the Max
Planck Society.
Cells were filled with biocytin either extracellularly using juxtasomal recording and electroporation [84] or via whole-cell recording [85]. In both cases patch pipettes, pulled from
unfilamented borosilicate glass on a Sutter P-97 puller (Sutter Instruments) were used.
The outside diameter of the shank entering the brain varied from 25 to 75µm, and the tip
opening had an inside diameter less than 1µm.
At least 1h was allowed to pass after cell filling and prior to tissue fixation to insure sufficient
diffusion of the biocytin throughout the axonal arbor. The animal was deeply anesthetized
and perfused transcardially with phosphate buffer followed by 4% paraformaldehyde. Cortex and thalamus were cut tangentially and coronally, respectively, in 50-100µm thick
vibratome sections. Biocytin in these sections was stained with the chromogen 3.30 - diaminobenzidine tetrahydrochloride (DAB) using the avidin-biotin-peroxidase method [80].
Sections were sometimes counterstained for cytochrome oxidase [86]. Processed sections
were then mounted on slides and coverslipped with Mowiol (Hoechst, Austria).
2.2.2
Image acquisition
A standard TLB microscope (Olympus BX-51, Olympus, Japan) equipped with a motorized x-y-z stage (Maerzhaeuser Wetzlar, Germany) was used for image acquisition. It can
be used for TLB and fluorescent microscopy. In order to obtain monochromatic illumination, if used in TLB mode, a 546nm ± 5nm band pass illumination filter (CHROMA
2.2 3D reconstruction of neuron morphologies
53
AF-analysentechnik, Germany) was attached to the diaphragm of the lighthouse. This
band pass filter minimizes the chromatic aberrations of the imaging system and simplifies
the theoretical description of the optical pathway from a polychromatic to a monochromatic one. The light is transmitted by a high numerical aperture (1.4NA) oil immersion condenser (Olympus, Japan), assuring parallel illumination of the specimen under
”Koehler”-conditions [87].
In fluorescent mode, a 100W xenon arc lamp is used with a 470nm ± 10nm band pass
filter and a 485nm dichroic mirror (Olympus, U-MGFPHQ) to excite the samples. Fluorescent emission is controlled by the dichroic mirror and a 520nm ± 20nm band pass
filter. The specimen is imaged by a 100x high numerical aperture oil immersion objective
(Olympus 100x U PLAN S APO; 1.4NA) in combination with a 0.5x TV-mount (Olympus
U-TV0.5XC-3) or a 40x objective (Olympus 40x U PLAN FL N; 1.3NA) in combination
with a non-magnifying TV-mount. The immersion oil has a refractive index of noil = 1.516
similar to glass. In addition the aberrations for a 40x dry objective (Olympus 40x U PLAN
FL; 0.75NA) are measured to illustrate the advantages of immersion objectives.
The stage is navigated in three spatial directions by an OASIS-4i-controller hardware and
software (Objective Imaging Ltd, Cambridge, UK). It allows the acquisition of large mosaic
images [82] at different focal planes. Mosaic in this context refers to a two-dimensional
image of overlapping tiles (i.e. adjacent fields of view) that are aligned automatically and
then stitched during the image acquisition, resulting in a large composite image (Figure
2.7a/b). The user defined scan area is automatically divided into a series of overlapping
fields of view which are called tiles. For each tile location a stack of images is acquired
using optical sectioning [60] with a typical separation of 0.5µm between the focal planes.
For each focal plane the corresponding tiles are then stitched together, resulting in a threedimensional stack of two-dimensional mosaic images for each focal position (Figure 2.7b).
54
Methods
This process is executed by the Surveyor Software (Objective Imaging Ltd, Cambridge,
UK).
The images are recorded by a ”Q-icam Fast” 1394 camera (Q-imaging, Canada), equipped
with a CCD chip, which in combination with the 100x objective and the 0.5 TV-mount
yields an x/y sampling of 92nm per pixel (116nm per pixel if the 40x objective and a
non-magnifying TV-mount are used). Since the illumination is limited to one wavelength,
8-bit gray value images, rather than RGB color images are acquired.
In order to guarantee a similar dynamic range of the gray values for mosaic image stacks
from different brain slices and animals, the exposure time of the CCD camera is set semiautomatically by the Surveyor Software. Therefore the mean gray value in a typical field
of view within the scan area is calculated and is set to be 210. ”Typical” here refers to a
field of view without any stained neuron somata or blood vessels. This highly important
feature of the image acquisition is the basis for an optimal deconvolution and therefore a
robust neuron tracing. However, significant exposure gradients within the scan area are
a considerable constraint to this method. Its consequences and the limitations for neuron
tracing will be discussed later.
In summary, image acquisition results in a high-resolution 3D mosaic image. The typical
image stack size used for neuron tracing is 1.5mm x 1.5mm x 100µm. However, the mosaic
pattern can be adjusted to smaller or larger areas. Using the 100x objective in combination with the 0.5 TV-mount or the 40x objective with a non-magnifying TV-mount the
sampling is 92nm x 92nm x 500nm or 116nm x 116nm x 500nm per voxel. Hence, the data
volume for such a stack is approximately 15-30 Gigabyte.
Despite the fact that the TLB microscope is probably the most widely used instrument in
a lifescience laboratory [88] it has one significant disadvantage in comparison to the above
mentioned high-resolution fluorescent techniques. Out-of-focus light caused by diffraction
2.2 3D reconstruction of neuron morphologies
55
effects due to the finite aperture of the objective and aberrations induced by the optical
components or the specimen result in a blurred contribution to each 2D image plane. As a
consequence the resolution, especially along the optical (z-)axis, is not sufficient to obtain
a high-resolution visualization and quantification (e.g. of neuronal morphology) from raw
TLB data [88].
The optical limits of the imaging system can be described in terms of its 3D point-spread
function (PSF) or its Fourier Transform the optical transfer function (OTF) [87]. The PSF
specifies the appearance of an idealized point (delta function) after being imaged by the
microscope system. Neglecting coherency effects and noise caused by the CCD camera,
the imaging of an object is then given in terms of a convolution of the PSF s(x, y, z) with
the object’s intensity distribution o(x, y, z) [89], [60]:
i(x, y, z) = o(x, y, z) ⊗ s(x, y, z),
(2.9)
where i(x, y, z) refers to the stack of recorded 2D images and the symbol ⊗ denotes the
convolution operation described in standard textbooks.
2.2.3
Shack-Hartmann-analysis-based deconvolution
According to equation (2.9) image formation could be reverted if the PSF is known. This
procedure is called deconvolution or image restoration. The intensity distribution of the
object could then be obtained, apart from spatial frequency domains of the OTF that are
dominated by noise or at the zero crossing [90]. For any further considerations the noise
caused by the CCD camera, which becomes more dominate with low light intensities [91],
will be neglected. The camera’s exposure time is automatically adjusted to guarantee that
stained neuronal processes cover a maximum gray value range and to ensure none-zero
background of unstained tissue [61]. Therefore, throughout this section, noise refers to un-
56
Methods
stained light-absorbing cortical tissue that surrounds stained neurons and does not include
the CCD noise which can be problematic in fluorescence microscopy.
It is obvious that the deconvolution result approaches its optimal performance if the applied PSF resembles the properties of the imaging system. Hence, a correct PSF will
reduce artifacts from unstained background that are interpreted as noise and consequently
improve the quality of an incoherently illuminated wide-field TLB image stack in terms of
SNR, where SNR here refers to the ratio between stained neuronal processes and the unstained tissue background. In addition, the resolution will improve significantly, making a
high-resolution visualization and quantification of wide-field data possible. In consequence,
the correct determination of the microscope’s PSF is essential.
Several theoretical [92], [93], [94] and experimental [95], [96] methods have been described
to obtain the 3D PSF of a microscope. A common approach is to measure the PSF by
recording a series of 2D images of a sub-resolution object with different amounts of defocus,
where sub-resolution refers to an object whose dimensions are smaller than the diffraction
limit [87] of the microscope’s objective. Fluorescent objects (beads) of this size yield a
weak signal that requires an extremely sensitive detector and limits the axial range over
which the PSF can be measured [97], [98], [96]. When the optical influences of the tissue
need to be investigated, this method is exceedingly difficult [88] for two reasons. First, the
fluorescent bead needs to be inserted into the tissue making its signal even fainter, and
second it is laborious to measure the PSF for every single preparation.
The alternative, application of a theoretically modeled PSF for deconvolution, is also delicate. Significant discrepancy has been noted between theoretical and experimental 3D
PSFs. The difference results in part from inaccurate choice of parameter values (e.g.
unknown refractive index of tissue), or the theoretical model assumes ideal imaging conditions, e.g. the absence of any aberration [89].
2.2 3D reconstruction of neuron morphologies
57
Since a correct description of the imaging system in terms of its PSF is not trivial and both,
theoretical and experimental approaches seem to be not satisfying, alternative solutions
have been suggested. The ”blind deconvolution” approach [88] uses a nonlinear, iterative
and constrained maximum likelihood estimation (MLE) algorithm that requires the PSF
not as an input parameter, but reconstructs the PSF concurrently with the image data.
However, it is arguable that this approach is only applicable for rather small image stacks
(one or a few fields of view), because application of this filter on large image stacks with
high resolution has severe limitations.
First, iterative algorithms are strongly influenced by the estimation of the background
intensity [99]. An underestimation of background intensities will make the constraint ineffective. This results in a performance similar to that obtained by linear restoration
algorithms. An overestimation of the background is problematic, since it results in clipping of the object intensities. Usually, TLB image stacks of the above described dimensions
yield neither a uniform background nor can it be assumed that structures dwell in similar
intensity ranges throughout such volumes. These inhomogeneous conditions influence the
background estimation negatively and result possibly in a loss of performance. Examples
for this phenomenon will be illustrated in the result section.
The second limitation is a rather practical one. An 8-bit image stack of the size of 1.5mm
x 1.5mm x 100µm with a sampling rate of 0.116µm x 0.116µm x 0.5µm comprises a data
volume of approximately 20 Gigabyte. Even on a multi-core server computer a MLE
deconvolution carried out by Huygens Professional 2.9 deconvolution software (ScientificVolume-Imaging, 1995-2007) takes around 24 hours, whereas a linear, non-iterative filter
needs only around 45 minutes.
In the work presented a method for fast deconvolution of large mosaic image stacks is
described. It combines the experimental determination of aberrations caused by optical
58
Methods
components and specimen with a modeled PSF that assumes ideal imaging conditions.
The optical system was sought to be optimized by minimizing the aberrations induced by
its optical components and the cortical tissue, here 100µm thick cortical slices from rat
brains. Further, it was experimentally verified that it is possible to obtain nearly ideal
imaging conditions. Once these imaging conditions are achieved, the complex process of
image formation is simplified by reducing the optical pathway to a single refraction and
a single diffraction event. Refraction occurs at the interface between the specimen and
the immersion medium, which fills the space between the tissue and the objective lens.
Diffraction arises at the finite entrance pupil of this objective lens. Further it is shown
that the modeled PSF describes sufficiently accurate the image formation for this combination of specimen and microscope. Therefore a linear, non-iterative deconvolution algorithm
already yields significantly improved image quality and resolution.
To verify that the degree of aberrations is indeed negligible and constant for similar specimens (e.g. brain slices from different animals and different cortical depths), aberrations
are measured by analyzing the deformation of a plane wave front behind the optical system
using a Shack-Hartmann (SH) wave front sensor [89]. The samples were either fluorescent
beads in Mowiol or beads between two slices of tissue, also embedded in Mowiol. The
resultant measured wave front function is essentially the OTF [89]. It yields the amount
of aberrations induced by the optical components or the tissue for the two sample types,
respectively. This measurement allows then the determination of the average refractive
index of the specimen.
The major advantage for using a SH sensor for PSF measurement is that the bead size is
not limited by the diffraction limit of the objective [89]. Therefore a larger (e.g., 10µm
diameter) and hence brighter bead can be used which allows the measurement of the PSF
over a larger axial range (10µm) even when the bead is embedded within cortical tissue.
2.2 3D reconstruction of neuron morphologies
59
Finally it is shown that the modeled PSF, which is based on measured aberrations that
are of a negligible amount, describes the optimized (TLB) imaging system quite well.
A high resolution visualization and quantification of neuronal morphology from linearly
deconvolved mosaic data is hence possible.
Shack-Hartmann wave front measurement
The aberration function W , which represents the deviation of the measured wave front
from a plane wave, can be expanded as a power series in exit pupil polar coordinates [87],
[89]):
W (ρ, θ) = Alnm ρn cosm θ,
(2.10)
where ρ represents the normalized pupil coordinate, θ is the angle between the pupil and
the field vectors and l, m, n are integers [87]. Due to rational symmetry conditions and
neglecting of off-axis aberrations, the expansion is limited to l + n = 0, 2, 4... and m = 0,
respectively. Therefore the aberration function reduces to two terms when expanded to
the 4th order and when the 0th order term is ignored, assuming incoherent illumination:
W (ρ, θ) = A020 ρ2 + A040 ρ4
(2.11)
The coefficients A020 and A040 are expressed in micrometers and represent the wave front
deformation caused by defocus and spherical aberration, respectively. These coefficients
are measured during the SH wave front analysis. For a detailed derivation of how the SH
analysis is related to the wave front coefficients see [89].
An illustration of the wave front measurement experiment is shown in Figure 2.8. The
SH sensor and the aberration measurement unit are implemented within a ”Wavescope”
(Wavescope Model WFS-01, Adaptive Optics Association, Inc.; USA). It comprises a 32x32
array of square micro-lenses (focal length: f=3.5mm, micro-lens spacing: d=300µm) to
60
Methods
a
P1
P2
P3
MIP
L1
b
WaveScope
b
Distorted wavefront
P2
P3
∆x,∆y
Figure 2.8: Shack-Hartmann wavefront measurement. (a) The wavefront in the microscope’s image plane (MIP) is created by fluorescent beads that are embedded in Mowiol and is
relayed by a plano-convex singlet (L1) onto the array of micro-lenses (P2) of the SH sensor. The
spot displacements within the according spot image are compared with the spot image of a plane
wave created by a laser. The ”Wavescope” measures these spot deviations and relates them to
the coefficients of a power series that expresses the aberration function. (b) Principle of the SH
wavefront sensor as shown in [89]. Each lenslet forms an image that is displaced from the local
optical axis by an amount (∆x, ∆y). The displacement from the local optical axis is determined
by the average slope of the wavefront over the lenslet area and the focal length of the lenslet array.
Figure adopted from [83].
2.2 3D reconstruction of neuron morphologies
61
sample the wave front in the exit pupil of the microscope as piece-wise planar wavelets
and an optical relay system that guarantees correct illumination of the implemented CCD
camera. The ”Wavescope” measures the displacement of spots created by each micro-lens
with respect to a prior calibrated reference spot-image of a plane wave. It further calculates
the coefficients of the aberration function. Coefficients are manually scaled to match the
normalization, as presented above.
To relay the sample image distribution from the microscope’s image plane (MIP) on to the
micro-lens array of the SH sensor (P2), a plano-convex singlet (L1) with a focal length of
fL1 =40mm was used and located 40mm behind the MIP. Hence, this lens provides the SH
sensor with a collimated and de-magnified sample distribution of the exit pupil. A grid of
7x7 micro-lenses was always illuminated, independent whether the light was supplied by a
bead or a laser. This 7x7 grid (Figure 2.8) was used for the wave front measurements.
Before recording through-focus SH-images of a bead, the SH sensor was calibrated with
a monochromatic plane wave. A single mode glass fiber that was connected to a laser
(emission wavelength 632.8nm) was therefore located at the MIP, 40mm in front of the
plano-convex collimator lens (L1). By temporarily placing a shear plate within the light
beam between the collimator lens and the lens array, collimated illumination of the SH sensor could be monitored. The resulting SH reference image defines the imaging properties of
the SH sensor, if the exit pupil wave front is described by a plane wave. It accounts for any
on-axis aberrations introduced by the sensor optics. Off-axis aberrations can reasonably
be neglected due to the size of the micro-lenses [89].
To measure the aberrations caused by the microscope’s optical components, a sample with
a fluorescent bead embedded in Mowiol was centered in the field of view of the microscope. Through-focus SH images were then recorded at 0.5µm axial intervals over a range
of 10µm, between the in-focus position of the bead and the coverslip. To improve the SNR,
62
Methods
100 frames were recorded and averaged at each focal position, using an integration time of
60ms per frame. For measuring additional optical influences on the light beam caused by
the tissue, the same measurement was repeated for a bead sample that was placed between
two layers of tissue. These measurements were repeated for eight beads respectively.
Simplification and modeling of image formation
As indicated above, the modeling of the image formation within a TLB microscopy is not
trivial due to the partially coherent illumination [87] of the specimen. However, considerations about propagation of mutual coherence within a TLB microscope [100], [101], [102]
showed that the OTF can be characterized by the ratio of the effective NAs of the condenser and the objective (i.e. ratio between the radii of the entrance pupil of the objective
and the illuminating source (microscope field stop)). It is hence possible to model the OTF
for the coherent limit (ratio = 0.1), the incoherent limit (ratio ≈ 1) or any intermediate
partially coherent case (e.g. ratio = 0.5) [102]. These three settings are illustrated by
Figure 2.9a-c on the example of one x/y-plane of a stained neuron. The arrows in Figure
2.9a and b indicate coherency artifacts from out of focus planes. The presented imaging
system is always adjusted to meet ”Koehler conditions” [87], resulting in an effective NA
ratio of 1.0 (Figure 2.9c). The microscope then approximately satisfies the theoretical
incoherence criterion [102]. In consequence, the high contrast images generated by our
imaging system are assumed not to suffer from coherency effects. Hence, the TLB imaging
system is treated as if incoherent light originates at the specimen, i.e. the image formation
is modeled as in the case of a fluorescent microscope.
However, inverting the gray values and hence treating the TLB like a wide-field fluorescent
microscope, the question remains of how to determine the optical properties of the imaging
components or the tissue, in order to derive the correct PSF of this system. The simplest
2.2 3D reconstruction of neuron morphologies
63
a
b
c
10µm
Figure 2.9: Degree of coherence in TLB images. The degree of coherence depends on the
ratio of the effective NAs of the imaging system. For illustration an x/y-plane of a neuron imaged
by a TLB microscope is shown for three different ratio configurations (0→0.5→1), showing the
coherent (a) and incoherent (c) limit, as well as an intermediate case (b). The degree of coherence
increases with decreasing NA ratio. Coherency effects result in out-of-focus artifacts as indicated
by the arrows in a nd b, which are absent in the incoherent limit (c). It is therefore justified to
treat incoherent TLB images like a fluorescent one by inverting the gray values. Figure adopted
from [83].
64
Methods
solution is to assume ideal imaging condition. This means, assuming that neither the optics nor the specimen introduce any aberrations to the path of light. Image formation can
then be reduced to a 3D diffraction at the finite entrance pupil of the objective [87], [92].
However, because of the refractive index mismatch between the embedding (nmowiol = 1.49)
and the immersion medium (noil = 1.516), this simple model is not sufficient. Figure 2.10
Θ1
interface
n1
n2
∆s
∆f
Θ2
Figure 2.10: Simple imaging model. Simple geometrical model of the refraction at the interface between a homogeneous specimen (n2 ) and an immersion medium (n1 ) which fills the space
between the specimen and the objective’s entrance pupil. It relates optical (∆f ) and mechanical
(∆s) defocus and hence allows the derivation of the specimen’s refractive index. The angles are
slightly exaggerated for illustration. Figure adopted from [83].
shows a geometrical model for this configuration [103]. Since the coverslip and the objective lens have the same refractive index as the immersion oil, these components can be
optically neglected. Image formation can hence be reduced to the refraction at the interface between the embedding and the immersion medium and to the diffraction at the finite
entrance pupil of the objective lens. This model is implemented in the Huygens software.
The parameters are the two refractive indices, the emission wavelength and the effective
2.2 3D reconstruction of neuron morphologies
65
NA of the objective.
All of these are known for beads embedded in pure Mowiol. However, the cortical tissue
could influence the image formation by causing aberrations due to inhomogeneity of the
refractive index. To estimate the possible influences of the tissue the following model is
used. It assumes that neurons keep their original refractive index, which is approximately
nplasma = 1.35, and that they can be simplified to spherical somata. The remaining tissue
(e.g. extra-cellular space) is assumed to adopt the refractive index of Mowiol. Therefore
neurons are treated like convex lenses with an average radius of 10µm in a homogeneous
environment of Mowiol. The focal length of these neuronal lenses is then given by:
fcellbody =
1
r
·
.
2 nmowiol − nplasma
(2.12)
Therefore, according to Figure 2.11 the length difference between a diffracted and a nondiffracted light beam (∆l) would be approximately:
q
l = l02 + r2 and∆l = l − l0 .
(2.13)
This simple model yields that the wave front deformation ∆l is about 1.37µm and therefore
already about 2.5 times the wavelength, assuming the light penetrates only one soma within
the image stack. It is therefore required to show that neuron somata do not function as
spherical lenses and to prove that the influence of the tissue is negligible, in contrast to
the above estimation. Otherwise the simple ”refraction plus diffraction” model could not
be applied. In the result section this will be described. Further, the average refractive
index for the cortical tissue from rat brains is determined. For the subsequent sections on
deconvolution this ”refraction plus diffraction” model will always be applied.
66
Methods
∆l
l
Plasma
r
l0
Mowiol
incoherent monochromatic plane wavefront
Figure 2.11: Simple aberration model. Simple model illustrating effects of neuron somata on
deformation of a plane wave. If neurons keep their original refractive index, they would function as
convex lenses within an environment of Mowiol. This would cause deformations of the wavefront
and would hence lead ta a significant amount of position dependent spherical aberrations. Figure
adopted from [83].
2.2 3D reconstruction of neuron morphologies
67
Deconvolution algorithms
Treating the TLB microscope like a fluorescent one and reducing the complex process of
image formation to refraction at the interface between embedding and immersion medium
and to diffraction at the finite aperture of the objective’s entrance pupil, the Huygens
software is able to model a PSF. This PSF can then be applied by various algorithms
to the inverted mosaic image stacks. Here, a linear Tikhonov/Miller (TM) filter and a
non-linear, iterative MLE filter are used. Both of them are already implemented in the
Huygens software. However, since Huygens cannot process a 25 Gigabyte image stack in
one run and estimation of a single background value for such a large volume is rather
impracticable, the mosaic image stacks are split up into by 100 pixels overlapping ”bricks”
with a lateral size of 3100 x 3100 pixels. Thus a background value is estimated for each
brick.
In contrast to the MLE filter, the image restoration filter of Tikhonov and Miller has
no constraints and yields a result after a single deconvolution step. The MLE algorithm
ensures non-negative solutions and needs various iterations before it converges or meets a
user defined stop criterion. It is further strongly influenced by the background estimation,
making the algorithm ineffective when the background is underestimated or causes a severe
performance loss if the background is overestimated. More details about these algorithms
and their properties can be found in [104], [99], [105].
Deconvolution samples and resolution measurements
In order to verify that the assumptions about ideal imaging conditions, incoherent illumination and a homogeneous refractive index of the tissue are correct, biocytin labeled
neuronal processes (dendrites and axons) within mosaic TLB stacks from the cortex of six
different rats and at different cortical depths are investigated.
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Methods
First it was checked whether the results from the SH analysis about an homogeneous refractive index of the tissue are confirmed by an alternative approach. This is done by
comparing the theoretically determined angle of the light cone of the modeled PSF with
light cones from 15 dendrites and 15 axons, arbitrarily chosen from various locations and
depths within the raw image stacks. These cones were further checked for z-dependence
and symmetry with respect to the optical axis and the focal plane.
Second, the SNR and the lateral (x/y) as well as the longitudinal (x/z) half-widths are
measured from 22 dendrites and 36 axons. This measurement is performed for the raw images and their deconvolved counterparts. These measurements were performed on stacks
either containing only dendrites, only axons or both types of structures in intermediate
neighborhood. Since axons are usually fainter and thinner than dendrites, the influence of
the background estimation for such ”mixed” stacks will become important.
2.2.4
Computing hard- and software
Here, the data size is in general between 15 and 30 Gigabyte per section. Therefore, as in the
case of NeuroCount, a fast image processing pipeline based on multi-processor-computing
that can handle such large data sets was developed. Again, the algorithms are written
in C++ [64] and the raster image file I/O, iteration through a raster image and several
filters use the ITK [65]. The algorithms were parallelized by applying the OpenMP standard [106]. They are executed on AMD dual-core 64-bit Opteron servers, equipped with
either 4 CPUs and 32 Gigabytes memory (DELTA Computer Products GmbH, Reinbek,
Germany) or 8 CPUs and 64 Gigabytes memory (fms-computer.com, Netphen, Germany).
Once the mosaic image stack has been saved to disk, a software-demon (a custom written
”Perl” script) detects new data on the hard drive and starts the processing pipeline. Additional image stacks are added to a queue and processed sequentially. The script initiates
2.2 3D reconstruction of neuron morphologies
69
the subsequent image processing steps, inversion of the gray values, subdivision into bricks,
deconvolution, down sampling and finally the 3D neuron tracing (Figure 2.12). Therefore
the automatic tracing routine can run 24 hours a day, since the queue of scanned image
stacks is sequentially processed. The next step needing user interaction is the manual
post-processing of the final 3D reconstructions.
2.2.5
Automated image processing
A major feature of image acquisition is the semi-automated setting of the exposure time
of the CCD camera to control the image histogram as described previously. This feature
is critical to the downstream neuron tracing algorithms. Their parameters were adjusted
and systematically tested to derive the best possible tracings from such images.
Maximum down-sampling
After deconvolution, the data size is reduced to facilitate further computationally intensive
steps. Maximum down-sampling is applied for each deconvolved image brick in the x and
y plane. Two neighboring voxels are merged to one voxel, computing their maximum gray
value. Since this procedure is done in both lateral directions (x and y), the data set is
reduced in size by a factor of four. Since neuronal structures are local intensity maxima,
all branches will be conserved.
As a consequence the new lateral sampling is 184nm x 184nm per voxel if the 100x objective in combination with the 0.5 TV-mount is used or 216nm x 216nmn per voxel if
the 40x objective in combination with a non-magnifying TV-mount is used. Therefore the
sampling in both cases is still below the physical resolution limit (approximately half the
wavelength; ≈232nm) according to the Rayleigh criterion [87].
The down-sampled 3D image bricks are now subjected individually to segmentation algo-
70
Methods
Vector Image Based
Midline Extraction
Image Restoration /
Deconvolution
a
g
b
h
i
Neuron Tracing
Raster Image Based
Segmentation
c
j
d
k
e
l
f
m
10 µm
Figure 2.12: NeuroMorph illustration. (a) Max z-projection of inverted image stack cropped
from the mosaic image shown in Figure 2.7b (box), showing a weakly stained, fragmented axon. (b)
Max z-projection after TM deconvolution. (c) Local threshold function 1: intermediate voxels are
shown in gray. (d) Local threshold function 2: intermediate voxels are assigned to fore- or background. (e) Hit-or-miss transform: removes small and isolated artifacts. (f ) Dilation/Closing:
smooths foreground objects and fuses narrow gaps. (g) Setting of end-line locations: local maxima
after distance transformation. (h) Iterative layer-by-layer thinning. (i) Determination of loops
in the thinned graph. (j) Removal of loops. (k) Pruning of short branches. (l) Final result of the
automated pipeline. (m) Final result of NeuroMorph by manually editing and splicing. Figure
adopted from [61].
2.2 3D reconstruction of neuron morphologies
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rithms (Figure 2.12). The purpose is to separate voxels that represent neuronal structures
from voxels that are part of the background.
Local threshold filtering
A target image with the dimensions of a deconvolved image brick is created and initialized
with gray value zero. The voxels of the deconvolved bricks are then separated into three
groups.
One group, below a lower threshold is set to background (gray value zero in the deconvolved
brick). A second group of voxels belonging to potential neuronal structures, with values
above an upper threshold, is assigned as foreground (gray value 255 in the target image).
The foreground consists of disjoint voxel regions which will be referred to as foreground
objects. Voxels with values between the two thresholds form the third group of intermediate value voxels. The intermediate voxels are tested for local features defined by a local
property function, to decide whether they belong to foreground objects or to background.
The lower threshold is determined by calculating the intensity distribution of the deconvolved image brick. The deconvolution produces a thin unimodal histogram with the
background clustered near zero, structures in the high range, and some remaining intermediate gray values. The lower threshold is taken as the histogram’s mean value plus 1.5
standard deviations (STDs). This gray value is usually between 1 and 15. It was derived
after systematic testing and essentially deletes the background noise from unstained tissue.
The upper threshold assigns the prominent and most intense structures to foreground. The
value of the upper threshold is determined by calculating the histogram of the maximum
z-projection of the deconvolved image brick. The upper threshold is then taken as the
mean value plus 3.0 STDs. Systematic testing yielded that this is the best value to detect dendrites, well-filled axons and the prominent parts of fragmented filled axons (Figure
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2.12c). This upper threshold usually has a gray value between 30 and 60. The remaining
voxels between the background (1-15) and the foreground (30-60) margin are referred to
as the intermediate voxels.
The local property function comprises two steps. First each intermediate voxel is set as the
center of an 11x11 voxel mask in the x/y-plane and the mean intensity of the voxels, regardless of group (background voxels were already set to zero), within this 2D neighborhood is
calculated. If the centered intermediate voxel has a gray value that is larger than this mean
intensity plus an epsilon value of 5 gray values, it is set to an intermediate gray level of
125 (Figure 2.12c) in the target image. Otherwise it is set to background (gray value zero
in the target image). The optimal value of epsilon was derived by systematic testing. The
group of intermediate voxels consists usually of isolated artifacts or dim bridges between
bright structures. These dim bridges are often found between axonal boutons (swellings
of the axon that are likely sites of synaptic contact) and should therefore be part of the
foreground. The resultant target image comprises three gray values: 0, 125 and 255 for
background, intermediate and foreground voxels respectively.
The second part of the local property function inspects the intermediate voxels of the
target image for connectivity to a foreground object. Systematic testing suggested that
an intermediate voxel is set to foreground if 10% of the voxels from a 17x17 mask in the
x/y-plane centered on this intermediate voxel are part of a foreground object, otherwise it
is set to background (Figure 2.12d).
Hit-or-miss transformation
The application of the above local threshold filter results in a binary image. This is then
subjected to a hit or miss transformation [66] with rectangular frame-masks of increasing
size as structuring elements. The transformation is applied to every image plane. Isolated
2.2 3D reconstruction of neuron morphologies
73
foreground objects that are completely surrounded by a frame are eliminated to background. Beginning with a radius of 1 voxel and increasing the frame size subsequently to
three voxels, small, isolated artifacts that were introduced by the linear deconvolution are
removed (Figure 2.12e).
Dilation and closing
Next dilation and closing filters [66] are applied. The dilation filter bridges gaps between
the axonal boutons that have not been closed by the local threshold filter. Finally a closing
filter as described before is applied (Figure 2.12f). It tends to smooth sections of contours
and fuses narrow breaks as well as long thin gulfs, eliminates small holes, and fills small
gaps in the contour [66]. The 3D structuring element (sphere) for the closing and dilation
has a radius of three voxels. Larger radii could result in a fusion of objects that should not
be connected, and smaller radii would have no significant effect on the foreground objects.
The radius of three therefore proved to be the best compromise after systematic testing.
Object labeling
The brick-wise segmentation yields binary image stacks. Regrouping of these segmented
bricks leads to a binary 3D image stack with the dimensions of a down-sampled mosaic
image stack. This large 3D binary stack is subjected to an object labeling algorithm.
Once a foreground voxel is detected, a region growing algorithm [66] fuses all connected
foreground voxels to a sub-region and assigns a unique integer label. The binary image
is thus transformed to an image of N individually labeled sub-regions, each representing
a foreground object. Labeled objects are sorted according to their number of voxels. The
largest foreground object is labeled as number one, and the smallest object is assigned
number N. The background voxels are labeled as zero.
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Raster to vector image conversion
Since the neuron occupies only a small fraction of the scanned image volume, the 3D raster
image representation requires inappropriately large data storage. A more sophisticated vector data folder is created that stores only foreground objects but keeps the 3D information
of the image. The voxels of each foreground object are replaced by vectors, hereafter called
compartments. Each compartment stores the three-dimensional coordinates of the prior
voxel and can store additional morphological information, such as local properties (e.g.
radii, surface distance).
Furthermore, each compartment is linked to its neighboring compartments by inter - compartmental smart-pointers, which allow access of neighboring compartments (e.g. top-left,
bottom, left, etc.). Therefore the implicit neighborhood representation by voxel coordinates
of the 3D raster image is mapped to an explicit neighborhood construct in the compartment representation. The neighborhood pointers between the compartments preserve the
3D topology of any object. Fast navigation through the object is possible using these intercompartmental smart-pointers. The compartments representing one object are grouped in
a ”double linked” list, which guarantees fast access to each compartment. Therefore the
3D raster image of N labeled foreground objects is converted to N compartment lists. This
transformation replaces the 3D raster image of labeled foreground objects by a ”double
linked” list, where each list item represents one of these disjoint foreground objects by a
list of topology preserving compartments (vector image representation).
Vector image based midline extraction
Representing objects by their main structure or skeleton (approximate midline) is a commonly used technique in image processing. A fast and reliable way to calculate the skeleton
of an object is thinning. Generally, thinning is a layer-by-layer (boundary compartment)
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Figure 2.13: Voxel neighborhoods. Panels a-s show different neighborhood topologies in 3D
images. Compartments (voxel representatives) are visualized as boxes with edge length 1, centered
on their position in image space. The central compartment is shown in red, neighboring compartments in cyan. (a) The six-adjacent neighborhood (N6). Compartments are N6 if they share a
face with the central compartment. (b) The 18-adjacent neighborhood (N18). Compartments are
N18 if they share at least one edge with the central compartment. (c) The 26-adjacent neighborhood (N26). Compartments are N26 if they share at least one point with the central compartment.
(d)-(f ) Examples of neighborhood templates for thinning. Removal of the center compartment in
f preserves the connectivity (→ simple compartment), which is not the case for d and e. Figure
adopted from [61].
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erosion until only a unit-width skeleton is left [107], [108], [109]. Therefore three different
classes of compartment topologies are defined: 6-adjacent (N6), 18-adjacent (N18) and 26adjacent (N26) [108]. Two neighboring compartments are N6 if their Euclidean Distance
is equal to one, N18 if their Euclidean Distance is between (or equal to) one and square
root of two and N26 if their Euclidean Distance is between (or equal to) one and square
root of three [109] (Figure 2.13).
A thinning algorithm has to obey the following demands that are derived from a 2D definition by [110]:
1. Connected objects must thin to connected line structures.
2. The thinned lines should be minimally 26-connected. Two compartments are 26connected if they are connected by a chain of N26 adjacent compartments.
3. Approximate end-line locations should be maintained.
4. The result of thinning should approximate the midlines of the structures.
5. Extraneous short branches introduced by thinning should be minimized.
To address these demands a template matching algorithm described by [111] is used. It
is one of the most efficient thinning algorithms and can be briefly summarized as follows.
First a set of end-line locations is determined, necessary to represent the topology of the
object. The end-line locations will not be removed. All other compartments, starting
from the object boundary, are tested to check whether or not their removal affects the
26-connectivity of the object (Figure 2.13). If compartment removal has no affect on the
connectivity, this compartment is termed simple.
In order to determine whether a compartment is simple or not, its N26 neighborhood is
compared with all possible N26 neighborhood templates that preserve local connectivity
2.2 3D reconstruction of neuron morphologies
77
(Figure 2.13). If the compartment neighborhood matches one of these templates, the removal of this compartment will not affect the local connectivity and the global connectivity
will be preserved as well [111]. Hence, this compartment is assigned to be simple and is
removed. Whether or not a compartment is simple or not may change after deleting compartments. Therefore the algorithm is iterative and finishes when no more compartments
are removed. The implementation of this thinning approach is described in detail below.
Detection of end-line locations
The end-line locations are determined by calculating the compartment, which is most distant to the object boundary (compartments with less than 26 neighbors). This is done by
calculating the Euclidean distance map [112] of the object. The compartment with the
highest distance number is selected and called the seed point. In case of several compartments sharing the highest distance value, one of them is selected randomly. Now the Euclidean graph distance [109] from each compartment in the object to the seed compartment
is computed. This is the shortest connection along the graph between two compartments.
Compartments with a local maximal graph distance are assigned as line endings (Figure
2.12g).
Thinning
One disadvantage of thinning is the possibility of inward erosion, which could potentially
create wholes in the object. To prevent these artifacts, an iterative approach is used [108].
Using the N6 and N18 topologies defined above, boundary layers are assigned that are
peeled by an iterative algorithm (Figure 2.12h):
1. collect the set of N6 boundary compartments (compartments where at least one of
the N6 neighbors is missing)
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2. delete all simple compartments (according to the N26 topology) in this set, starting with those who have the lowest number of neighbors (i.e. inter-compartmental
pointers)
3. collect the set of N18 boundary compartments (compartments where at least one of
the N18 neighbors is missing)
4. delete all simple compartments (according to the N26 topology) in this set, starting
with those who have the lowest number of neighbors
5. continue with 1) until no more simple compartments are found.
A detailed description of such an algorithm can be found in [108], [111].
Graph validation and pruning
Imaging and segmentation can lead to artifacts like loops and clusters in the thinned
midline representation of the objects, which have to be removed by post processing. Loops
are removed by selecting one end-line location and calculating the shortest path from this
end-line location to all other end-line locations in the object. Compartments or intercompartmental pointers that are not used by any path within this validation step (Figure
2.12i/j) are removed from the object.
Since the approximate end-line locations were local distance maxima from an inner seed
point, swellings within the neuronal branches will result in short sub-branches that are
regarded artificial (Figure 2.12k). Therefore these short branches are removed within this
pruning step from the object if the distance from the according end-line location to the
first intersection compartment is shorter than 3µm (derived by systematic testing). Non
artificial axonal sub-branches below this length threshold will hence be pruned as well.
However, for most scientific problems this error is negligible.
2.2 3D reconstruction of neuron morphologies
2.2.6
79
Semi-automated post-processing
The image processing, so far, transformed the deconvolved raster image into a vector image
representation of thinned foreground objects. Each object is therefore represented as a 3D
graph with end-line locations (endings). Furthermore, compartments that are connected
to more than two neighbors will set to be an intersection. This set of endings, intersections
and normal compartments is converted to an ASCII file that can be either visualized in
Amira or Neurolucida. Up to this point, all processing steps are automated. Final editing
and splicing of the reconstructions is done manually.
Editing
The automatically traced graph is converted into a custom designed ”SpatialGraph” format, representing points, nodes (intersections, endings) and edges (lines between nodes,
connecting points). Each of the three structures can store multiple data, such as radii,
structure type or even membrane potential. This data format, established in cooperation
with Vincent J. Dercksen (ZIB) is the basis for any visualization of and interaction with
traced neuron morphologies. Using the Amira-based ”SpatialGraphEditor” it is possible
to select any structure in the tracings, to delete, connect are labeled them individually.
Artifacts that were similar in shape or gray value to neuronal structure have to be erased.
In most cases these artifacts are astrocytes (star shaped glial cells). This dirt-removal is
done by superimposing the SpatialGraph with the maximum z-projection of the original
image stack in the SpatialGraphEditor in Amira. Within the projection image neuronal
structures can be easily distinguished from artifacts. Neuronal branches appear as elongated structures within the projection image, whereas falsely traced artifacts are either
small spots (most intense parts of unstained neurons) or star shaped if they are the remains of glial cells. These artifacts are then selected and erased.
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Further, axonal branches that were not well filled and therefore traced as fragmented structure can be restored by selecting the fragmented edges and splicing them by automatically
connecting their closest ending nodes, resulting in a single continuous axon arbor.
Within this interactive step, additional anatomical landmarks, such as section outlines, can
be integrated. Superimposing the edited neuron reconstruction with a low magnification
image, any visible anatomical structure (e.g. pia or barrel outlines) can be manually added
to the automatic reconstruction of the neuron.
Splicing
The results of this automated reconstruction pipeline are 3D tracings of neuronal branches
from adjacent, 50-100µm-thick sections. To obtain a complete reconstruction of a cell, the
reconstructions from different sections (i.e. brain slices) have to be aligned and spliced
(Figure 2.14). Fortunately, large radial blood vessels are running perpendicular to the pial
surface and retain their positions within each tangentially cut brain slice, rendering them
ideal as position reference points. The blood vessel pattern is therefore extracted during
the automatic tracing procedure. Blood vessels are detected via a region-growing algorithm
in a maximum intensity z-projection of the original image stack, prior to the deconvolution.
Voxels with values close to zero (maximum transparent regions) are used as seed points for
a region-growing algorithm.Region-growing seeks dark and almost circular shapes (shape
number algorithm [66]) and labels these structures as blood vessels.
Using the ”SpatialGraphEditor” introduced above, multiple adjacent sections can be
placed on top of each other, by manually entering their section thickness (e.g. 50µm).
According to the vessel pattern, the individual reconstructions are aligned coarsely, either manually or automatically, using a transform interface or a point-matching algorithm,
respectively. More accurate alignment is then achieved by matching the upper branch
2.2 3D reconstruction of neuron morphologies
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Figure 2.14: Splicing of tracings from individual sections. Automatically aligned stack
containing VPM axon fragments from 30 tangential cortical sections (segments colored by section).
Figure adopted from [113].
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endings from a lower slice with the lower branch endings from an upper slice, again manually or automatically. Once all branches from individual sections are aligned with their
counterparts from the adjacent section, the nearest nodes are spliced as described before.
If splicing is performed manually, it proved to be convenient to start at the slice including
the soma and to progressively connect the adjacent sections until a complete 3D neuron is
reconstructed. If no soma is present (e.g. cortical part of the thalamocortical VPM axon
arbor) the splicing starts at the deepest (most distant from the pia surface) section.
Even though the manual 3D alignment proved to be reliable, the automated alternative,
especially for axonal reconstructions, can save a lot of time (from 1hour to 20 seconds)
(Figure 2.14). The automated algorithm was tested and is described in detail in [113].
Briefly, based upon the point matching approach first described by [114], the correspondence between two 3D point sets and the rigid transform that optimally maps one point
set to the other (in a least square sense) are calculated. Given two sections containing
multiple polylines (i.e. SpatialGraphs representing traced neuronal branches), an optimal
transform is computed, i.e. a rotation angle around the z-axis (perpendicular to the cutting
plane) and a 2D (x/y) translation parallel to the cutting plane, using the following steps:
1. Find the set of points P = {pi } from the first slice S0 and Q = {qi } from the other
slice S1 , to be matched. Using the edge ending nodes only in the boundary regions
r0 and r1 respectively, 2D point sets are obtained by orthogonal projection onto the
x/y plane. The region size is chosen as a fraction of the total section thickness.
2. Find the set of candidate matchings and compute a starting transform for each matching.
3. For each starting transform, optimize the matching and transform with respect to a
scoring function. The result is the transform corresponding to the optimal score.
2.3 3D registration of neuron morphologies
2.3
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3D registration of neuron morphologies
The aim of the presented work is to realistically reengineere the three-dimensional anatomy
and synaptic connectivity of neuronal circuits. This requires the placement of any reconstructed neuron in a reference frame that is sufficiently precise and can correct for variability
between experiments.
Several quantitative two-dimensional registration methods have been reported for neurons
traced from in vitro preparations [115], [116], [117]. Here, I present a three-dimensional
registration method (daVinci), established in cooperation with Dr. Moritz Helmstädter
(MPI for Medical Research, Heidelberg) and Dr. Christiaan P.J. de Kock (VU Amsterdam) [118], that allows to combine neuron tracings from many in vivo experiments and
hence to build up a standardized model of a cortical barrel column. The method compensates for differences in cortical thickness between animals, shrinkage of physical brain
sections and deviations in cutting angle, which is usually not perfectly perpendicular to
the vertical column axis. The registration can be summarized by the following five steps:
1. reconstruction of neuron (soma, dendrites, axon) from 20-40 adjacent tangential (with
respect to S1) 50-100µm thick brain sections,
2. reconstruction of reference contours (pia, barrel, white matter (WM)) for each brain
section,
3. calculation of the most likely vertical column (z-)axis using the pial surface above
the neuron and the center of the barrel closest (lateral) to the soma (”home barrel”),
4. rotation of the neuron with respect to the calculated most likely vertical column axis,
5. application of inhomogeneous scaling along the most likely vertical column axis in
order to register the pia, barrel and WM to fixed standardized distances.
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Methods
3D reconstruction of reference contours
All presented morphologies are obtained from in vivo stained neurons, traced from tangential (i.e. perpendicular to the vertical column axis) brain slices. For each of these
reconstructions, the outlines of the pia, barrels and WM are traced manually by superimposing a low magnification (2x) image of each brain slice with the neuron tracing in
Neurolucida or in the ”SpatialGraphEditor” in Amira (Fig. 2.15a). The pia outlines are
drawn for the top ten brain slices, whereas the barrel and WM contours are usually only
visible in L4 or some bottom slices, respectively (Fig. 2.15b).
Using the ten pia contours, a two-dimensional distance transform [66] is calculated for each
slice. These distance transforms are then interpolated and smoothed in three dimensions.
Finally the isosurface at value zero of the distance transform is calculated.
The same algorithm is used to interpolate the barrel and WM surfaces. The barrels are visible as slightly darker stained regions in brain slices of L4 (Fig. 2.15a). Depending on the
slice thickness and cutting angle, the number of contours for individual barrels can differ
from two to eight. In any case the barrel that contains (or is laterally closest to) the neuron’s soma is traced and assigned to be the ”home barrel”. Further, the first neighboring
barrel in the rostral direction is traced (e.g. home barrel D2, first rostral neighbor barrel
D3). In addition, as many WM contours as visible are traced in the bottom-end sections
of the cortex. Their number usually differs from four to eight, depending on how many
brain slices were cut in total. Figure 2.15b/c shows an example of the ten pia, ”home” and
rostral barrel and WM contours and their corresponding surfaces for a thick tufted L5B
pyramidal neuron.
2.3 3D registration of neuron morphologies
85
a
b
c
Figure 2.15: 3D reference contours. (a) Traced 3D L5B neuron morphology superimposed with
a low-magnification (2x) image of a tangential (with respect to D2 barrel) brain slice. The outline
of the brain slice (green) and the ”home barrel” and its first rostral neighbor (red) are manually
traced. ”Home barrel” refers to the darker area in slices in L4 that contain the soma, when
extrapolated to all sections. (b) Manually traced contours for the ten top pia sections (green), the
”home” and first neighboring rostral barrel and the white matter (WM) (orange). (c) Smoothed
and interpolated isosurfaces created from the contours in b. The intersection points of the vertical
column axis with the pia, ”home barrel” top, bottom and WM surface are scaled to fixed measured
values, resulting in a standardized cortical column of 2000µm height.
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2.3.2
Calculation of most likely vertical column axis
The prior described contour surfaces are used to compute an approximation of the vertical
column (z-)axis. This calculation is based on two assumptions:
1. the vertical column axis is approximately perpendicular to the pial surface above the
column,
2. the distance between the home barrel center and the pial surface is minimal along
the vertical column axis.
Therefore, the approximate home barrel center is calculated as the midpoint of all its barrel
contours. Next, lines between this barrel center and all patches (surface triangles) of the
pial surface within a given distance are determined. Then, connection lines to patches
that are most parallel to the patch normal are determined. This results in a set of ”bestmatching” vertical column axes from which a user can interactively select (in MATLAB)
the most likely vertical column axis (Fig. 2.16a).
2.3.3
Translation and rotation to standard barrel system
After the vertical column axis is set, the coordinate system can now be transformed such
that the origin is aligned with the home barrel center (translation) and that the z-axis is
aligned to the most likely vertical axis (z-axis rotation). Figure 2.16b shows an example of
this rotation for a thick tufted L5B neuron. Further, this transformation is applied to the
interpolated home barrel surface. This transformed home barrel is then used to calculate
the vertical position of the barrel bottom and barrel top, which will be of importance in
the next section.
2.3 3D registration of neuron morphologies
a
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b
Figure 2.16: 3D registration. (a) Illustration of setting the ”best” vertical z-axis of the cortical
column. Minimal connecting lines from the ”home barrel” center to the pial surface are calculated.
A set of lines perpendicular to a pial surface patch (triangle) is displayed and can be interactively
chosen be the user. Here, line 5, most parallel to the neurons apical dendrite, is set to be the
optimal vertical column axis. (b) Rotated neuron. The prior tilted neuron and barrel contours
(light red) are rotated to the optimal vertical axis (red).
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2.3.4
Inhomogeneous z-scaling to standard barrel system
In a final step the translated and rotated neuron reconstruction is inhomogeneously scaled
along the newly assigned z-axis. Therefore the intersection points of the z-axis with the
pia, the upper barrel border, the lower barrel border and the WM surface are calculated.
Mean standard distances for these values were obtained by measuring them in fifteen
experiments, comprising forty 50µm thick brain slices, respectively. This measurement
yielded the following standard distances:
• pia-to-upper barrel border: 575µm,
• upper-to-lower barrel border: 360µm,
• lower barrel border-to-WM: 1065µm,
which in consequence result in a standard column height of 2000µm. These standard
measures are compared with the calculated vertical intersection points and hence result
in three z-scaling factors. Simple non-continuous transition between these factors finally
results in a depth-dependent z-scaling profile. The final, translated, rotated and scaled
neuron reconstructions are regarded as registered into the geometrical reference frame of a
cortical column with a precision of approximately 50µm [118]. This value is therefore the
ultimate resolution limit for any further consideration of the average standard column.
2.4
3D classification of neuronal cell-types
The previous sections described methods to reconstruct and standardize neuron morphologies in three dimensions. However, in order to realistically interconnect these neurons
within microcircuits in a cell-type-specific manner, one needs to objectively classify and
2.4 3D classification of neuronal cell-types
89
group the tracings into meaningful subclasses. This is usually achieved by cluster analysis
of multidimensional parameters, in the following called neuron features.
As explained in the introduction chapter, neurons can either be classified by their physiological properties in response to a stimulus, their post-synaptic (i.e. dendritic) and/or
their pre-synaptic (axonal) innervation pattern. Here, I will present a clustering method,
NeuroCluster, that reliably groups traced excitatory neurons of a cortical barrel column in
S1. The grouping is based upon thirteen anatomical dendritic features, which are determined for each object (i.e. neuron tracing). Further, their presynaptic counterparts (i.e.
thalamocortical VPM axons) are classified by anatomical axonal features. In addition it is
possible to analyze the physiological properties of these anatomical neuron classes.
2.4.1
Cluster algorithm
The effectivity, i.e. the quality or usefulness of most standard cluster algorithms (e.g.
k-means [65]) is affected by three interconnected issues [119]:
1. most algorithms require input parameters (e.g. anatomical features) that are hard
to determine for real-world data sets,
2. the algorithms are very sensible to these parameter values, often producing very different partitionings of the data set even for only slightly different parameter settings,
3. high-dimensional real-data sets often have a skewed distribution, that cannot be
revealed by a clustering algorithm using only one global parameter setting.
For these reasons, I present an alternative algorithm, called OPTICS (Ordering Points
To Identify the Clustering Structure) [119], which is not limited to one global parameter
setting. It has been adopted for neuronal data sets by my collaborators Dr. Stefan Lang
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a
p
p
o
q
p is density-reachable from q
q is not density-reachable from p
q
p and q are density-connected
to each other by o
b
ε
p1
r(p
1)
core(o)
r(p2
)
o
p2
c
reachabilty-distance
ε
cluster-order o of the objects
Figure 2.17: OPTICS clustering. (a) 2D illustration of density-reachability and connectivity.
The circles have radius ε and M inP ts = 3. Point q is core object, p not. Therefore, point p is
density-reachable from q, but not vice versa. (b) 2D illustration of core- and reachability distances.
The number of M inP ts = 3 defines the core-distance core(o). If more than (or equal to) M inP ts
points are within a radius ε around o, then o is core-object and all density-reachable points are
assigned with a reachability-distance (e.g. r(p1),r(p2)). (c) Illustration of the cluster-ordering
and OPTICS results. The reachability-distance for each object is plotted in an augmented order.
”Valleys” in this plot indicate clusters. Figure adopted from [119].
2.4 3D classification of neuronal cell-types
91
and Albert Berman (Institute for Scientific Computing (IWR), Heidelberg). This algorithm
does not produce a clustering explicitly, but instead creates an augmented ordering of
the data set, representing its density-based clustering structure. For the here presented
medium-sized data sets (78 S1 dendrite and 14 VPM axon reconstructions) the clusterordering can be represented graphically, making it easy to extract not only the ”traditional”
cluster information, but also the intrinsic cluster structure.
The basic concepts of OPTICS are subsequently introduced in order to understand how
the resultant neuronal cell-types, presented in the result section, are obtained. The key
idea of density-based clustering is that for each object (i.e. a neuron, represented by a
feature vector) of a cluster the neighborhood of a given radius (ε) has to contain at least
a minimum number of objects (M inP ts), i.e. the cardinality of the neighborhood has to
exceed a threshold. The formal definitions for this notation of a clustering, adopted from
[119], are given below and are illustrated by Figure 2.17:
• Definition 4: directly density-reachable:
Object p is directly density-reachable from object q with respect to ε and M inP ts in
a set of objects D if:
1. p ∈ Nε (q), where Nε (q) is the subset of D contained in the ε-neighborhood of q.
2. Card(Nε (q)) ≥ M inP ts, where Card(N ) denotes the cardinality of the set N
If the latter condition holds for an object p, then p is called a ”core object”. Objects
can only be directly density-reachable from core objects.
• Definition 5: density-reachable:
Object p is density-reachable from object q with respect to ε and M inP ts in a set
of objects D if there is a chain of objects p1 , ..., pn , p1 = q, pn = p such that pi ∈ D
and pi+1 is directly density-reachable from pi with respect to ε and M inP ts.
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• Definition 6: density-connected:
Object p is density-connected to object q with respect to ε and M inP ts in a set of
objects D if there is an object o ∈ D such that both p and q are density reachable
from o with respect to ε and M inP ts.
• Definition 7: cluster and noise:
A cluster C with respect to ε and M inP ts in D is a non-empty subset of D satisfying
the following conditions:
1. Maximality: ∀p, q ∈ D: if p ∈ C and q is density-reachable from p with respect
to ε and M inP ts, then also q ∈ C.
2. Connectivity: ∀p, q ∈ D: p is density-connected to q with respect to ε and
M inP ts in D.
Every object not contained in any cluster is noise.
• Definition 8: core-distance of p:
If (M inP ts − distance(p)) is the distance from p to its M inP ts’ neighbor, then the
core-distance of p is defined as:
core − distanceε,M inP ts (p) =
– U N DEF IN ED, if Card(Nε (p) < M inP ts),
– M inP ts − distance(p), otherwise.
• Definition 9: reachability-distance of p with respect to o:
The reachability-distance of p with respect to o is defined as:
reachabilty − distanceε,M inP ts (p, o) =
– U N DEF IN ED, if |Nε (o)| < M inP ts,
2.4 3D classification of neuronal cell-types
93
– max(core − distance(o), distance(o, p)), otherwise.
Intuitively, the reachability-distance of an object p with respect to another object o is the
smallest distance such that p is directly density-reachable from o and o is a core object
(Fig.2.17).
Based upon the above definitions, the OPTICS algorithm creates an augmented ordering of
the data set and additionally stores the core-distance and a suitable reachability-distance
for each object.
• Definition 10: results of the OPTICS algorithm:
If data set D contains n points, then the OPTICS algorithm generates an ordering
of the points o : 1...n → D and corresponding reachability-values r : 1...n → R≥0 .
Finally, plotting the n reachability values in the order o for medium sized data sets, allows
to identify clusters simply as ”valleys” (Fig.2.17c). In consequence, once a reasonable set
of features (i.e. parameters) is extracted for each neuron, the resultant reachability plot
will immediately and objectively yield anatomical neuron-types.
2.4.2
Cluster features
Given a reliable cluster algorithm, as introduced above, one still needs to define anatomical
features that capture the essential information of individual neuron morphologies. Such
features can either be related to the neuron’s shape, its geometry or some additional information, such as brain region or genotype. Albert Berman and I tried a large variety of
parameters (up to 70) until a specific stable cluster structure emerged for different feature
combinations.
It should be emphasized that the prior described three-dimensional registration and therefore standardization is essential for the goodness of classification. Hence, only registered
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Methods
x
1
2
3
z
Figure 2.18: Anatomical neuron features. Illustration of anatomical feature extraction. The
longest dendrite (here: apical dendrite of L5B pyramidal neuron) is subdivided into three bricks
(dashed lines) along the vertical axis (here: representing apical ”root”, trunk and tuft). Shapeand geometry-related features are extracted for each brick and the entire neuron. Red and yellow
dots mark ending and branch points respectively.
2.4 3D classification of neuronal cell-types
95
morphologies are used for the subsequently presented methods and results.
Another essential step is to split up the neuron into three bricks along the vertical column
axis. Anatomical features are then extracted for the entire morphology and these three
dendrite regions (Fig.2.18). The splitting reflects the general grouping of neurons into
pyramidal and non-pyramidal cells. Only pyramidal neurons contain a so called apical
dendrite, which is also their longest dendrite. In contrast, the longest dendrite in nonpyramidal neurons, like L4 spiny stellates, is arbitrary.
Apart from reliably separating pyramidal from non-pyramidal neurons, the brick-wise feature extraction along the longest dendrite can further discriminate between different types
of pyramidal neurons. In general the apical dendrite emerges at the soma, branches (apical
”root”) and then reduces to a single branch (apical trunk) that might branch again at the
region most distant from the soma (apical tuft). The shape and the extend of branching
of the apical tuft is cell-type-specific. Therefore the bricking of the longest dendrite also
reflects the division into apical ”root”, trunk and tuft and allows therefore to distinguish
between different types of pyramidal and non-pyramidal neurons.
After a stable classification result was achieved, the number of features (i.e. dimension of
parameter space) was reduced to a minimum using a genetic search approach [120]. The
remaining thirteen anatomical features (Fig. 2.18) are grouped into shape- and geometryrelated parameters and are listed below.
Neuron-shape-related:
• M axDendZrange: Maximal extend along the z-axis (vertical column axis) of the
longest dendrite (i.e. for pyramidal neurons this reflects the vertical extend of the
apical dendrite).
• M axDendT h3XY diagonal: Maximal extend in the horizontal x/y-plane of the upper
brick of the longest dendrite (i.e. for pyramidal neurons this reflects the horizontal
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Methods
extend of the apical tuft).
• N euronXY diagonal: Maximal extend in the horizontal x/y-plane of the entire dendrite pattern.
• N euronXY ZBox: Volume of the bounding box around the entire dendrite pattern.
• N euronESumP olarR: Sum of direct distances from the the soma to all ending
points.
• N euronEAvgP olarR: Average value of direct distances from the soma to all ending
points.
• N euronEM axP olarR: Maximal direct distance from the soma to an ending point.
Neuron-geometry-related:
• M axDendCentroidDistSXY Z: Center of Mass of the longest dendrite, assuming a
uniform dendrite thickness.
• N euronCentroidDistSXY Z: Center of Mass of the entire dendrite arbor, assuming
a uniform dendrite thickness.
• N euronBpN umber: Number of branch points in the entire dendrite arbor.
• N euronLocalAvgBranchOrder: Average branch order (i.e. max tree depth) of every
individual dendrite.
• N euronSumLength: Total trace length of all dendrites.
Additional user information:
2.5 3D reengineering of average neuronal networks
97
• P iaDistanceRegistered: Distance from the soma to the interpolated pial surface
along the vertical column axis after 3D registration with daVinci.
By extracting the same features for axons, the cortical part of the thalamocortical VPM
axon reconstructions could be clustered. Two features are absent for these morphologies. First, the PiaDistanceRegistered cannot be calculated, because the soma of these
cells is in the thalamus, and only the cortical part was reconstructed. Second, the axon
is a single structure, meaning the longest axon is identical to the entire axon. Therefore the feature vector for VPM axons has only eleven entries: NeuronZrange, NeuronTh3XYdiagonal, NeuronXYdiagonal, NeuronXYZBox, NeuronESumPolarR, NeuronEMaxPolarR, NeuronEAvgPolarR, NeuronCentroidDistSXYZ, NeuronBpNumber, NeuronLocalAvgBranchOrder, NeuronSumLength.
2.5
3D reengineering of average neuronal networks
Recently reported methods aim to reengineere morphologically realistic large neuronal
networks, like a cortical barrel column [121] or the cerebellar granule layer [122]. These
approaches distribute synaptic connections either randomly on user-defined parts of the
dendrites [122] or use geometrical constraints, like proximity of a pre-synaptic axon to a
post-synaptic dendrite [121]. Both methods have in common that the user needs to specify the potential number of synapses, and its variability, for each pre- and post-synaptic
connection-type. The reason is that a quantitative three-dimensional description of the presynaptic axonal arborization is difficult to obtain. Therefore, the axon is either completely
ignored and the number of synapses, as well as the most likely volume of axon innervation is estimated [122] or the axonal arbor is extrapolated from in vitro reconstructions.
The latter, called ”neuronal healing” [121], compensates for missing parts of the axonal
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Methods
arborization in in vitro reconstructions. These extrapolated axons are superimposed with
the post-synaptic neuronal network. Synapses are then set at touching points between the
dendrites and the extrapolated axons.
Here, a different approach will be presented. Neither the number of synaptic contacts, nor
the axonal innervation need to be estimated or extrapolated. The subsequently presented
method is regarded as a statistical approach, to contrast the geometrical method by [121].
The above presented methods (NeuroCount, NeuroMorph, daVinci, NeuroCluster) determine three-dimensional neuron distributions, reconstruct neuron dendrites and axons, standardize the tracings and objectively classify them. They supply sufficient quantitative
anatomical data to reengineere average neuronal networks, like a cortical barrel column,
in three dimensions and to synaptically interconnect different neuron populations. In consequence, the cell-type-specific number and three-dimensional distribution of synapses are
no input parameters, but results of the here presented network building tool, called ”NeuroNet”.
NeuroNet is again based upon custom written software for Amira [62]. This editor has been
established in cooperation with Vincent J. Dercksen (ZIB, Berlin) and allows to interactively reengineere and visualize neuronal networks in three dimensions, using measured and
reconstructed anatomical data. The interactive approach proved to be essential in order
to control the complex process of building up high-resolution full-compartmental network
models. In addition, NeuroNet yields cell-type- and position-specific three-dimensional innervation statics for each neuron in the network.
The number and three-dimensional synapse distribution for individual connection types
will be a major result of the here presented thesis. In particular, the cell-type-specific
number and distribution of thalamocortical VPM synapses within an excitatory cortical
barrel column in S1 will be presented in the result section. Comparing these statistical,
2.5 3D reengineering of average neuronal networks
99
purely anatomical results, with previous connectivity estimates from electrophysiological
paired recordings performed in vivo [12], will prove that the reengineered average cortical
barrel column realistically reproduces the cortical morphology and connectivity.
2.5.1
NeuroNet
Figure 2.19 illustrates the subsequently described general concept of NeuroNet:
Standardized reference frame The first step to reengineere an average neuronal network in three dimensions is to establish a standardized coordinate system for the
brain region of interest. This guarantees that the anatomical data, obtained from
many different experiments, fits together and results in a reasonably accurate average
network. In case of the cortical barrel column the pia, WM and barrel contours functioned as such standardized position landmarks along a 2mm long vertical column
axis. This coordinate system has its origin at the barrel center and will hence be
referred to as the ”barrel-centered” column. The approximate accuracy of the above
described registration method (daVinci) was about 50µm.
3D total neuron soma distribution Once a reference system is established, the average number and three-dimensional distribution of all neuron somata in this brain
area needs to be determined by NeuroCount. The resultant soma distribution is
transformed into the standardized reference system (e.g. ”barrel-centered” column)
and then converted into a neuron density distribution, by superimposing a threedimensional grid. In case of the ”barrel-centered” column, a grid resolution (voxel)
of 50µm x 50µm x 50µm is chosen, in order to match the registration accuracy. Here,
the average distribution of excitatory somata in S1 is determined for a cuboid with
dimensions of 550µm x 550µm x 2000µm, resulting in a grid of 11 x 11 x 40 (i.e. 4840)
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Methods
a
registration/standartization
cell- and connection-type definition
mapping of somta, dendites and axon
neuron distribution
somata
1
1
A
A
1
2
B
A&B
neuron reconstructions
connection
classification
4
2x type A
2x type B
(with axon)
axons
dendrites
b
bouton distribution of type B
1
1.5
1
3
spine distribution of single
type A cell
0.25 0.25
0.25
0.25 2.5
spine distribution of type A
1.5
0.25
0.25 0.25
0.25
0.25
2
1.5
synapse distribution of single
type A with pre-synaptic type B
0.75
1.5
0.5
0.25
0.25
2.5
0.75
0.5 0.75
Figure 2.19: Illustration of NeuroNet. (a) Soma distribution grid and neuron tracings are
registered to standardized anatomical landmarks (e.g. pia, WM, barrel). The numbers refer to
cells per grid voxel and number of tracings, respectively. After classification of the dendritic
and axonal cell-types (2 cells of type A and 2 of type B), the soma distribution is subdivided
into overlapping cell-type-specific soma distributions (the overlap ratio in the lower/right voxel is
1:1). Type B contains axon (blue) and a connection from B to A is defined. Cell-type-specific
somata are mapped into the grid and replaced with neuronal tracings of the corresponding type
(A: red; B: green). (b) Extension of the grid to a maximal bounding box (dashed lines) covering
all tracings. From left to right: total bouton density for type B axons; total spine density for
all post-synaptic cell-types connected by type B (here: only type A); spine density for individual
target cell (here: upper/right); voxel-wise relative proportion of each cell’s spine distribution to
the total spine distribution is calculated and then multiplied with the bouton density; this results
in synapse density distribution of each cell, for each connection type. For illustration spine and
bouton density, as well as voxel size are set to 1. Summing of voxel values result in cell- or
cell-type-specific total spine, bouton or synapse numbers. Here, total number of boutons for type
B: 11; total number of spines for type A: 6.5; total number of spines for upper/left cell: 2.25;
total number of synapses for upper/left cell: 4.25.
2.5 3D reengineering of average neuronal networks
101
voxels. For each voxel the density value is given in neurons per cubic millimeter.
Specification of neuron-types The three-dimensional neuron density distribution usually contains various cell-types. Therefore a representative number of neurons from
every part of the total distribution needs to be reconstructed manually or with NeuroMorph. The here presented dendrite tracings in S1 were mainly done manually,
whereas all axon reconstruction were obtained by NeuroMorph. By first clustering
the reconstructed cells by dendritic features with NeuroCluster, as presented above
(see sec. 2.4), the number of neuron-types within the area of interest is determined.
If, in addition, the axons for all neurons of a cell-type are reconstructed, a secondary
clustering might reveal axonal subclasses. The total number of neuron classes (i.e.
including subtypes) will be referred to as N .
Spatial extend of neuron-types Each reconstructed neuron is not only represented by
its dendrites and/or axon, but also by the position of its soma with respect to the
standardized reference frame. Calculating the mean and standard deviation of all
somata positions yields the spatial extend of a neuron-type as a three-dimensional
interval:
[pi − 1.5 · ST Di , pi + 1.5 · ST Di ];
(2.14)
where pi is the mean, ST Di the standard deviation of soma positions for a cell-type
and i = x, y, z. Hence, the total neuron density distribution is subdivided into N
mutually overlapping cell-type-specific soma distributions. The ratio in the overlap
zones is specified by the user (e.g. in the overlap zone between L5A and L5B in S1
the ratio is estimated as 1:1).
Mapping of cell-type-specific somata For each voxel of the soma distribution grid the
number of neurons is calculated. If more than one cell-type constitute to one voxel,
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Methods
the relative numbers per cell-type are assigned according to the estimated overlap
ratio. Within each voxel the assigned number of neurons is distributed, guaranteeing
identical distances between the somata and to the voxel boundaries. It is further
assured that the soma position is never outside the spatial extend of its corresponding
cell-type. This step results in N cell-type-specific neuron soma distributions.
Mapping of neuron morphologies Each of the N three-dimensional neuron distributions comprises nj (j = 1, ..., N ) neuron soma positions. A neuron tracing of the
PN
corresponding cell-type is mapped onto each soma position. Hence, n =
j=1 nj
neuron somata are replaced by n neuron tracings, represented as SpatialGraphs (see
sec. 2.2.6). Further, it is assured that the new soma position of each tracing does
not differ by more than 50µm in each direction from its standardized previous soma
position. It is optional to compensate for the change in soma position by scaling the
tracing in one or more dimension:
scalei =
somaP osold,i
,
somaP osnew,i
(2.15)
where i = x, y, z. In case of the cortical barrel column the scaling is applied along
the vertical (z-)axis. This guarantees that the transformed reconstructions still fit
into the standardized column of 2mm height (e.g. the apical tuft of a L5B pyramidal
neuron always ends in L1 and never sticks out of the pial surface or ends in L2).
However, in general the mapped dendrites and axons extend further than the original
grid, specified by the three-dimensional soma distribution (i.e. 11 x 11 x 40 for a
cortical barrel column). Hence, the grid is extended to the maximum bounding box,
covering each dendritic and axonal branch of the network.
Cell-specific spine and bouton distribution The previous steps resulted in n neuron
tracings, grouped into N types and distributed according to corresponding three-
2.5 3D reengineering of average neuronal networks
103
dimensional neuron distributions. For each neuron, its dendritic trace length per
voxel of the extended grid is calculated. The resultant dendrite density (in
µm
)
µm3
for
each cell is scaled with a cell-type-specific spine density (in spines per µm). Spines
are potential sites for synapses on dendrites of excitatory neurons. Therefore the sum
of all voxels result in the total number of spines for each post-synaptic neuron.
If the axon is reconstructed for m ≤ n tracings, in addition, the axon density is
determined. It is scaled with the cell-type-specific bouton density. Boutons are
potential pre-synaptic connection sites. Hence, the sum of all voxels results in the
maximum number of connections a pre-synaptic cell can make.
Cell-type-specific spine and bouton distribution The previous step resulted in n
SpatialGraphs, n spine distributions and m bouton distributions. By summing up
the distributions in a cell-type-specific manner, the total number and distribution of
spines and boutons for each of the N cell-types is obtained.
Specification of connection-types Each of the N cell-types can be in principle connected to any other one. Hence, the maximal number of connections is N 2 . However,
usually the axon is only reconstructed for some cell-types and some connections are
functionally not obtained in vitro or in vivo. The number of connections K is therefore usually smaller than N 2 . Nevertheless, each pre-synaptic cell-type can connect
multiple post-synaptic types. Here, I present connections from one pre-synaptic celltype (VPM) to eight excitatory post-synaptic types in S1.
Connection-, cell- and cell-type-specific synapse distribution Once all cell- and connection types are set, total post-synaptic spine distributions are calculated as the sum
of all distributions for cell-types innervated by the same pre-synaptic type (e.g. VPM
is pre-synaptic ⇒ sum of eight post-synaptic spine distributions). Again, the total
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Methods
pre-synaptic bouton density defines the number of synapses that can be distributed.
Then, for each post-synaptic neuron, its proportion to a total spine distribution (i.e.
identical pre-synaptic connection type) is calculated voxel-wise. This ratio value is
multiplied with the number of boutons in each corresponding voxel. This process
results in a three-dimensional synapse distribution for each post-synaptic neuron:
synapseDistrj,(x,y,z) =
individualSpineDistrj,(x,y,z)
· boutonsk,(x,y,z) ,
totalSpineDistrk,(x,y,z)
(2.16)
where j = 1, ..., n and k specifies the pre-synaptic cell-type. A maximum of M
connection-type-specific synapse distributions is possible for an individual cell. Summing up all synapse voxels, hence results in the absolute number of synapses per cell.
Cell- and connection-type specific summing of all synapse distributions results in total numbers and three-dimensional distributions for a specific pre- and post-synaptic
connection type.
Resultant three-dimensional anatomical network model In summary, NeuroNet receives a three-dimensional neuron distribution, N cell-types with classified dendrite
and axon reconstruction and M connection types. Specifying the spatial extend, as
well as spine and bouton density for each cell-type finalize the input. As output,
NeuroNet then calculates:
1. the number and distribution of neurons for each cell-type,
2. a post-synaptic dendritic and a pre-synaptic axonal network, by mapping classified neuron tracings at each cell position,
3. the number and distribution of spines and boutons for each neuron,
4. the number and distribution of spines and boutons for each neuron-type,
5. the number and distribution of synapses for each neuron and connection-type,
2.5 3D reengineering of average neuronal networks
105
6. the number and distribution of synapses for each neuron-type and connectiontype.
In consequence, NeuroNet yields an anatomically realistic network model of n fullcompartmental neurons (i.e. SpatialGraphs). Each neuron in addition has maximally
M synapse distributions that specify the total number and position of connections.
The network can then be transferred to a simulation environment, called ”NeuroDune”, established by Dr. Stefan Lang (IWR, Heidelberg). There, HH-typed neuron
models can be mapped onto each neuron. Further, synapses are mapped according
to corresponding synapse distributions. NeuroDune allows to simulate these large,
full-compartmental and realistically interconnected networks with input measured in
vivo (e.g. volley of synchronous thalamocortical APs from VPM into S1 after passive
whisker deflection [10], [12]).
Connection and cell-type-specific sub-cellular synapse distribution In addition to
the above results, NeuroNet also yields the possibility to investigate the sub-cellular
synapse distribution for each cell- and connection-type. This is achieved by transforming each distribution in a way that voxels, which contain the soma, are superimposed. The resultant ”soma-centered” distribution is a standard way to illustrate
sub-cellular connections, which can hence be compared with results from other methods, such as the channelrhodopsin-2 (ChR2)-assisted functional mapping of synapses
[123].
Chapter 3
Methodical results
So far, five custom designed methods for reengineering of three-dimensional neuronal microcircuits were presented. NeuroCount and NeuroMorph are designed to obtain indispensable anatomical data in a quantitative and objective manner. Further, they yield results
within much less time than alternative manual standard methods. However, before this
anatomical data can be standardized, classified and placed within a network by daVinci,
NeuroCluster and NeuroNet respectively, the performance and accuracy of NeuroCount
and NeuroMorph need to be validated. Therefore, automated results are compared to
manually derived counterparts [61], [83], [29].
3.1
NeuroCount: 3D counting of neuron somata
The evaluation of the automated counting pipeline is done for eleven confocal image stacks
of NeuN/GAD67-stained neuron somata. In general, the scientific interest focuses on neuron densities. Hence, the absolute number of neurons within the stack volume and the
deviation of the neurons’ position from manual counts need to be investigated. For this
106
3.1 NeuroCount: 3D counting of neuron somata
107
error analysis it is necessary to determine the corresponding landmarks from the manually
and automatically processed sets. If the deviation in position between the automated and
manually detected landmarks is of negligible amount, the absolute difference in landmark
numbers can be regarded as a meaningful error value. In addition, the numbers of false
positive (FP) and false negative (FN) landmarks are checked. Manually determined landmarks are used as the ”gold standard” and compared with the automated counting results.
It should however be emphasized that the results of the manual counting are only accurate
within 2.1% precision [38].
The eleven image stacks were randomly chosen from a large data pool that was used for
evaluation of neuron densities within a cortical column of S1 in rats [38]. The stacks
were taken at various magnifications (40x, 63x) resulting in different resolutions and stack
volumes, at various cortical depths (300-1800µm from the pia surface) yielding different
dominant neuron populations in each sample (e.g. L4 spiny stellates or L5 pyramidal
neurons) [124] and at various slice orientations (i.e. thalamocortical, coronal, tangential).
Further, comparison was performed ”double blind”, meaning stacks were first evaluated
manually by different individuals and afterwards processed by the automated pipeline described above, without prior inspection of the manual counts.
3.1.1
Automated vs manual counting
Table 3.1 shows the results for the comparison of automatically and manually detected
landmarks. No systematic miscounting is performed by the automated pipeline. The
number of detected neurons differs similarly in both directions resulting in an average
counting difference that is less than 1% (0.92% averaged over the number of data sets).
However, the average absolute counting difference in landmark numbers is around 4%.
This value is regarded as the absolute error of the automated counting.
108
Methodical results
manual automatic
relative ]
absolute ]
position
]
]s
]s
difference [%]
difference [%]
deviation [µm]
1
430
425
1.16
1.16
4.54
2
846
896
-5.91
5.91
3.93
3
570
594
-4.21
4.21
4.23
4
871
915
-5.05
5.05
4.74
5
1219
1237
-1.48
1.48
4.75
6
809
776
4.08
4.08
1.92
7
719
670
6.82
6.82
2.05
8
739
680
7.98
7.98
2.07
9
1035
983
5.02
5.02
2.70
10
862
846
1.86
1.86
2.96
11
975
976
-0.10
0.10
3.16
mean:
0.93
3.97
3.37
STD:
4.77
2.53
1.11
Table 3.1:
The number and position of automatically detected NeuN landmarks is compared to manually
generated counterparts for eleven image stacks. Each image stack comprises a single field of
view acquired either with a 63x or a 40x objective, using a Leica SP2 confocal microscope. Table
adopted from [29].
3.1 NeuroCount: 3D counting of neuron somata
109
Deviation in landmark position
The average radius of neurons in S1 is between 5 and 15µm. If the deviation between
a manually placed landmark and its automated counterpart is sufficiently lower than the
smallest radius value of 5µm, the error in position can be neglected and the absolute
difference in landmark numbers is regarded as a meaningful error value. For evaluation of
position deviation the following algorithm was used:
1. Calculation of distances from each automated landmark to each manual landmark.
2. Sorting of distances, starting with the shortest one and assignment of this manual
landmark as the nearest neighbor (NN) of the automated one.
3. Checking for multiple times assigned NN. If more than one automated landmark has
the same NN, the closest automated one will keep this NN, the other automated
landmarks are assigned to have their second closest manual landmark as their NN.
4. Step 3 is repeated until no manual landmark is assigned to more than one automated
landmark.
5. The distance of all automated landmarks to their assigned manual NN is then averaged (see Table 3.1).
The average deviation in position of 3.37±1.11µm is sufficiently less than 5µm. It is further
important to notice that the position deviation for each data set is smaller than 5µm. Hence
the error in position can be neglected, because each automated landmark has a manual
counterpart within reasonable distance. It is therefore justified to state that the absolute
difference between manually and automatically detected neuron somata is 4%.
110
Methodical results
False positive/negative landmarks
In addition to the above considerations about average differences between manual and
automated counts, a false positive/negative analysis for five randomly chosen stacks is
performed. Two corresponding landmark sets are visualized in Amira and coinciding landmarks are manually deleted. The remaining automated landmarks are regarded as FP and
the remaining manual landmarks are regarded as FN. These FP/FN objects are usually
ambiguous cases of touching neurons that could for instance either be counted as one or
two neuron somata. Table 3.2 shows the results for this analysis. Both, the average FP and
FN values are around 5%. This compensatory effect explains the average relative counting
difference of less than 1%.
FN [%]
FP [%]
9.30
2.78
7.23
6.31
4.71
7.58
4.65
5.35
3.19
3.01
mean:
5.82
5.01
STD:
2.43
2.08
Table 3.2:
Five corresponding landmark sets were visualized in Amira and coinciding landmarks were manually deleted. The remaining automated landmarks are regarded as false positive (FP) and the
remaining manual landmarks are regarded as false negative (FN). Table adopted from [29].
3.2 NeuroMorph: 3D reconstruction of single neuron morphologies
111
Detection of GAD67 neurons from 2-channel images
The detection of neurons in the second channel is strongly dependent on the performance
of the detection in the first channel. If the neuron is identified correctly in the first (e.g.
NeuN) channel, the detection in the second (e.g. GAD67) channel was 100% correct.
Hence, the absolute error value of 4% is also regarded as the error for the detection of
GAD67 positive interneurons.
3.2
NeuroMorph: 3D reconstruction of single neuron
morphologies
The reconstruction of neuron morphology, especially of thin axonal arbors, is impossible
from raw TLB image stacks [88]. Hence, special focus on the optimization of the imaging
system and the resultant deconvolution proved to be essential for a reliable tracing of both,
dendrites and axons. Therefore, before comparing the semi-automated tracing results
with manual counterparts, the influence of the optical components, the tissue and the
deconvolution algorithm on the SNR of faint axons will be investigated.
3.2.1
Optical aberrations of cortical tissue
In Figure 3.1 the measured optical defocus coefficients (A020 ) of the aberration function
are plotted for a mechanical defocus from 0 to 10µm in 0.5µm steps. Each plot shows
measured values averaged from eight samples. Figure 3.1a (plot C) illustrates the 40x dry
objective in combination with fluorescent beads embedded in Mowiol. The optical defocus
of almost 15µm for a mechanical defocus of 10µm is caused by the inhomogeneous refractive index within the optical pathway. The refractive index of the air between the specimen
112
Methodical results
and the objective is approximately 1 (nair = 1.003) and therefore refraction effects cause
the apparent difference in optical and mechanical defocus. Consequently the use of dry
objectives results in a much thinner appearance of the tissue.
The situation is different when oil-immersions objective are used (Figure 3.1a; Plot A/B).
Figure 3.1a (plot B) illustrates bead samples embedded in Mowiol. Here the optical defocus is nearly identical to the mechanical one, because the refractive index between the
objective and the specimen is homogeneous.
Using the marginal ray model described by [103] and introduced in the method section, the
refractive index for bead samples embedded in tissue (Fig.3.1a; Plot A) can be calculated
from the measured optical and the known mechanical defocus. At 10µm mechanical defocus the average resulting optical defocus from eight bead samples surrounded by tissue is
7.84±0.55µm. Using this value, the approximate refractive index for slices from cortical rat
tissue embedded in Mowiol is ntissue = 1.44 ± 0.02. Since the deviation in optical defocus
and hence in refractive index is small (±0.02) for bead samples embedded in tissue from
different rats and slices, at random positions between these slices, the refractive index is
regarded as homogenous for such specimen.
Regarding the tissue as an homogeneous medium, the deviations for spherical aberration
measured for bead samples between slices of tissue should also be small. This prediction is
verified by the results shown in the graphs in Figure 3.1b. Here the average measured coefficient for spherical aberration A040 is normalized to the wavelength λ of the illuminating
light. Both plots for the oil-immersion objective (Figure 3.1b; plot A/B) show a constant
coefficient for spherical aberration, independent of the mechanical defocus. However, the
absolute coefficient value for bead samples between sections of tissue is slightly higher
compared to the one for bead samples without tissue. This is reasonable since the major
source for this type of aberration is the refractive index mismatch between the embedding
3.2 NeuroMorph: 3D reconstruction of single neuron morphologies
a
113
16
C
14.83
optical defocus
14
12
B
10
9.34
7.84
8
A
6
4
2
0
0
2
4
6
mechanical defocus
8
10
1.0
spherical aberrations
b
D
0.8
C
0.6
A
0.4
B
0.2
0.0
0
2
4
6
mechanical defocus
8
10
Figure 3.1: SH measurements. a) Measured optical defocus (A020 ) averaged for eight samples each. Whereas beads embedded in Mowiol (B) yield almost identical optical and mechanical
defocus, beads between two layers of tissue (A) appear thicker. This suggests a slightly lowered
refractive index. b) Measured spherical aberrations (A040 ) averaged for eight samples each and
normalized to the wavelength. As suggested by a, the spherical aberrations are slightly increased
if the beads are embedded in tissue. However, the total amount of aberrations is independent
of mechanical defocus for the oil-immersion objective (A/B) and well below one wavelength. In
contrast, the spherical aberrations increase rapidly with defocus for the dry objective, reaching
one wavelength at about 10µm mechanical defocus. Figure adopted from[83].
114
Methodical results
and the immersion medium, which is slightly higher for tissue, as shown above.
For completeness, the spherical aberration coefficient for the dry objective is also measured.
Figure 3.1b (plot C) shows that the coefficient for spherical aberration increases strongly
with increasing defocus reaching the order of the wavelength at 10µm mechanical defocus.
These measurements suggest that the used oil-immersion objective can be regarded as well
corrected with respect to spherical aberration, since the normalized aberration coefficient
meets Maréchal’s tolerance condition [87]. It is therefore justified to assume ideal imaging
condition and to reduce the image formation to the ”refraction plus diffraction” model.
Model point spread function and cone of light
According to the above results of the SH wave front measurements, the tissue is regarded
as homogeneous in refractive index. Therefore the light sources, here the neuronal processes from inverted TLB stacks, should have light cones which resemble the theoretically
modeled cone. Figure 3.2a/b shows an x/z-plane from an inverted TLB stack with various
light cones from neuronal projections and the modeled PSF, respectively. It can be clearly
seen that the light cones qualitatively resemble each other. Quantitatively this was shown
by measuring four angles, as specified by Figure 3.2c. The mean value for the four angles
was between 42.42 and 45.9 degrees (α1 = 44.6 ± 1.8; α2 = 42.4 ± 2.0; α3 = 43.6 ± 1.8;
α4 = 45.9 ± 1.8). Hence, the four angles are approximately similar. This is consistent with
the assumption of refractive index isotropy. Further, the average angle of a light cone from
neuronal projections in cortical tissue embedded in Mowiol, imaged by an oil-immersion
objective is θ2 = 44.1 ± 2.3 degrees. This value is in good agreement with the theoretical
one of θ2 = 44.0 ± 1.54 degrees (see method section) derived from the simple geometrical
model, if a NA of 1.0 is assumed for TLB image stacks.
I further checked whether the angles are z-dependent. Therefore I subdivided the image
3.2 NeuroMorph: 3D reconstruction of single neuron morphologies
115
a
b
c
10 µm
α1 α2
α3 α4
5 µm
Figure 3.2: Isotropy of cone of light. a) x/z plane from an inverted mosaic TLB image
stack. The bright structures are characteristic light cones from neuronal projections. Quantitative
analysis of these cones from various preparations proved that the cones resemble each other and
the cone of the modeled PSF. b) Central x/z plane of the modeled PSF cone of light. The imaging
system is reduced to a simple ”refraction plus diffraction” model and based on the assumptions
of ideal imaging conditions and a homogeneous refractive index of 1.44 of the tissue from rat
cortex embedded in Mowiol. These assumptions are verified by the SH wave front analysis. c)
Enlargement of two typical light cones from a. All for angles were measured for 15 dendrites and
15 axons from 6 different rats. The measured average angle is in very good agreement with the
theoretically modeled one. Figure adopted from [83].
116
Methodical results
stacks into four bins with 20µm thickness along the optical axis and calculated the corresponding average angles. Neuronal processes close to the interface between the tissue and
the immersion medium (0-20µm) have an average angle of 43.8 ± 2.1. The angles for the
subsequent bins of 20-40µm and 40-60µm are identical at 44.1 ± 2.3. The angles in the
most distant region from the cover slip (60-80µm) are 44.9 ± 2.4. This implicates a slight
depth dependence of the refractive index from 1.45 at the top to 1.42 at the bottom of the
specimen. However, this deviation is still within the error margin of 1.44 ± 0.02 that was
measured with the SH sensor.
Hence, this angle measurement confirms the SH analysis by an alternative approach and
illustrates the limits of the described PSF simplification. The refractive index of the tissue
is not perfectly homogeneous. Both, the SH analysis, as well as the angle measurement
showed small deviations and slight depth dependence of the refractive index. However,
for the investigated 100µm thick slices from cortical tissue and for quantitative tracing of
neuronal morphology, these deviations are of a negligible amount.
Influence of background estimation
Since the modeled PSF resembles that of the measured one of the imaging system as shown
above, a deconvolution should significantly improve the image quality in terms of SNR and
resolution. However, the estimation of the background value can have a significant influence
on the performance of a MLE filter [99]. I therefore checked the loss in signal and background for three groups of structures. First, dendrites in the absence of the much fainter
axons were investigated and second, axons in the absence of dendrites. The third group
contained both, dendrites and axons. Figure 3.3 (bold markers refer to mean values) shows
the relative signal and background loss for the three groups and for two algorithms (TM
and MLE). Whereas the background reduction is essentially independent of the structure
3.2 NeuroMorph: 3D reconstruction of single neuron morphologies
117
dendrites/
axons
axons
dendrites
20
40
60
80
100
(average) signal/background amplitude loss [%]
Figure 3.3: Deconvolution of axons. Illustration of performance of two different deconvolution filters for three distinct groups of structure. Whereas the TM (signal/background reduction
= red/orange) filter treats stacks containing only dendrites, axons or axons in the presence of
dendrites in a similar way, the MLE (blue/green) algorithm tends to fade away the fainter axonal
structures in the presence of more intense dendrites. Figure adopted from [83].
118
Methodical results
type and deconvolution algorithm, the loss in signal amplitude differs significantly. The
tendency that the MLE algorithm decreases the signal amplitude more than the TM filter
holds for all three groups. However, whereas the average decrease in signal amplitude is
usually much less than the reduction in background, this is not the case for axons surrounded by dendrites. These axons lose around 85% of their signal amplitude, on average.
This means that faint structures, in the presence of much more intense structures, tend to
fade after application of a MLE deconvolution filter. In consequence, an authentic tracing
of axonal arbors from TLB mosaic image stacks is impossible without the application of a
linear TM filter.
3.2.2
Automated vs manual reconstruction
State of the art technique for the 3D reconstruction of neuron morphology especially of the
largely extending axonal arbors is the computer-aided interactive Camera Lucida technique
(e.g. Neurolucida, [81]). Therefore the performance of the semi-automated reconstruction
method is compared to such a manual reconstruction approach, as implemented with the
Neurolucida system.
First it is checked whether manually traced branches are detected by the automated system
and vice versa. I quantified whether branches are missed by either of the reconstruction
approaches. In a second comparison step the relative deviation in shape between manually and automatically traced neuronal structures is determined. Finally the time frame
for reconstructing complete cells with their entire axonal arbor was compared with the
conventional method systems. The comparison is done for 54 slices containing 4 different
filled cells (from 4 different rats). They were randomly chosen from a pool of already
manually reconstructed cells. Each manual reconstruction was done by a different individual. Users manually traced a L2/3 pyramidal neuron, two star pyramids from L4 and one
3.2 NeuroMorph: 3D reconstruction of single neuron morphologies
119
thalamocortical VPM axon.
Number of identical branches
Each automatically reconstructed cell was inspected for missing branches that have been
traced by the manual system and vice versa. The amount of manually reconstructed
branches that were missed by the automatic system was similar for all four traced neurons.
5.4% were missing for the thalamocortical VPM axon, 3.5% and 3.4% for the L4 neurons
and no manually reconstructed branch was missing for the L2/3 neuron.
In the case of branches that were missing in the manual tracing but found by the automated
system, the result was less homogeneous. Approximately 4% of automatically reconstructed
branches were missing in the manual version of the thalamocortical VPM axon, 29% and
47% were missed for the L4 neuron and almost 70% of the automatically traced branches
were not found manually for the L2/3 neuron.
For the 4 cells, the automated method missed 29 of 682 manually reconstructed branches
in 54 sections from 4 different rats. In other words the new reconstruction technique found
96% of the manually reconstructed branches. The manual tracings were missing 268 of
923 automatically reconstructed branches from the same 54 slices. This means only 71%
of the neuronal structures traced by the automated method could be found in the manual
reconstructions. All of the missing branches, independent of whether they were missed by
the manual or automatic system, were part of the axonal arbor. The dendritic branches
were traced equally reliable by the two methods.
The amount of missing structures varied widely between 4% and almost 70%. The missed
branches can be grouped into two cases:
• The first group consists of branches that were filled and stained but do not belong to
the cell of interest. In some cases surrounding neurons take up the tracer molecule,
120
Methodical results
and some of their dendrites or their main axon will be traced.
• The second group comprises neuronal structure that was missed by the human tracer.
The user usually starts tracing at the soma. If an axonal branch ending is missed in
that section, the human tracer tends to ignore these areas in the subsequent sections
and therefore sometimes misses large parts of the axonal branching patterns. In some
cases this error becomes obvious during splicing. Then the human tracer has to go
back to the tissue and needs to identify the connections missed previously.
The size of the group of missing branches is closely correlated to the experience of the
user. Only training, double checking and anatomical knowledge will minimize the loss of
branches and improve the manual tracing quality. On the contrary, the automated system
fails if the staining of the axon is insufficient, if the background is too high or in the presence of a strong gradient in thickness or contrast within the tissue. The latter will result
in different optimal camera exposure times depending on the location of the field of view
within the scanning pattern. Since the exposure is set to one value for the entire pattern
this may result in a failure of the subsequent deconvolution and neuron tracing.
Another limitation is that, due to the small diameters and tortuous paths of axons combined with physical resolution limits of the system, two close lying axons may occasionally
be mistakenly connected by the automatic tracing algorithm. However, resultant loops in
the axon arbor are automatically detected by the SpatialGraphEditor and can be manually
dissolved by the user.
Shape deviations of identical branches
A fractal box counting method described in detail by [61] was applied to 167 randomly
picked branches from the 54 slices that were reconstructed by both methods. It yields that
3.2 NeuroMorph: 3D reconstruction of single neuron morphologies
121
the relative deviation in shape is almost 0% at the lowest fractal resolution, meaning a box
size of 5µm. With increasing resolution (decreasing box size), the deviation increases to
a value of around 2% at a box size of 1µm and further to more than 3% at a resolution
of 500nm. At the highest measured resolution of 300nm the relative shape difference was
around 5%. This difference mainly arises from the larger number of points used by the
automatic system to represent the graph and will hence be neglected.
Reconstruction time
The average amount of time for a manual tracing of one cell (10 to 30 sections), including
its axonal arbor, is approximately 60-90 working hours. This means the reconstruction of a
single brain slice takes between 4 and 6 hours. Using the automatic system, an image size
of 1.5mm x 1.5mm x 100µm proved to be sufficient for most slices. The computing time for
an image stack of this size varies from 3 to 6 hours, depending on the amount of structure
within the volume. The human interaction time with the system is on average 30 minutes
per slice. This comprises the setting up of the scanning pattern (5 minutes), as well as
the manual editing and splicing of the automatically reconstructed slices (5-60 minutes).
Therefore the average amount of time for reconstructing one cell with the semi-automatic
system is between 30 to 90 hours of computing and 10 to 20 hours of human interaction.
Given a working day of eight hours the reconstruction using the manual system takes
around two weeks, whereas the automatic system can yield a comparable reconstruction
within 2-4 days.
Chapter 4
Anatomical results
NeuroCount and NeuroMorph proved to be reliable methods. They are hence used to
reengineer the excitatory part of the thalamocortical lemniscal pathway in the whisker
system of rats. Therefore, as derived in the introduction chapter, the number and distribution of neurons and neuron-types in the VPM and S1 needs to be known. Further,
a representative samples of dendrite morphologies for every excitatory neuron-type in S1
and of thalamocortical axon morphologies from the VPM towards S1 needs to be traced.
Only if the deviation in neuron numbers, distributions and average neuron-type anatomy
are small, this pathway can be regarded as an anatomical and functional subunit. If this
prerequisite is fulfilled, the animation of an average cortical column in silico with average
measured activity will potentially yield new insights into the mechanisms of neuronal information processing.
So far, this essential anatomical issue could not clearly be answered in a quantitative way.
This is mainly due to two problems:
• First, manual sparse sampling methods resulted in total neuron numbers deviating
by up to 50% (i.e. 200-300 neurons per barreloid [125], 10000-20000 neurons per
122
Anatomical results
123
barrel column (unpublished data by Verena Wimmer, Hanno-Sebastian Meyer and
Bert Sakmann)). Such margins would make any simulation upon an average network
unfeasible.
• Second, whereas manual tracing of the rather localized dendrite morphologies proved
to be reliable (see chapter: Methodical results), it is problematic for axonal arbors
(e.g. thalamocortical VPM neurons). The manual tracing of a single VPM axon takes
about 90 hours and can only be performed by an expert user (personal communication
with Thorben Kurz, MPIN).
NeuroCount and NeuroMorph solve these problems by yielding accurate three-dimensional
neuron distributions and reliable axon tracings.
• First, NeuroCount determines the absolute number of neurons in some cubic millimeter large volumes of S1 and VPM with high precision.
• Second, NeuroMorph allowed for the tracing of fourteen thalamocortical VPM axons
within one year. In addition 5 intracortical axons from slender tufted pyramidal
neurons in L5A could be reconstructed.
Hence, all presented axons are reconstructed by the NeuroMorph system, whereas most of
the subsequently presented 78 dendrite tracings are manually done, using Neurolucida.
Evaluation of the resultant anatomical data revealed the following results:
1. Previously obtained large deviations in absolute neuron numbers in S1 are due to
inhomogeneous distributions across and within cortical layers.
2. The deviation in total neuron numbers for an average cortical barrel column and a
single VPM barreloid is less than 3% and 5%, respectively.
124
Anatomical results
3. The 78 dendrite tracings from S1 group into 8 anatomical excitatory neuron-types.
4. The 5 axon tracings from slender tufted pyramidal neurons in S1 display characteristic
innervation of L2/3 of multiple surrounding columns.
5. The 14 VPM axons group into two anatomical types, innervating a single or two
columns respectively. In addition, 8 of these 14 tracings innervate columns of which
the respective whisker has been continuously trimmed for two weeks. These tracings
display a significant reduction in axonal length and density.
6. The number and subcellular distribution of VPM synapses is highly position- and
neuron-type-dependent.
7. Spiny stellate neurons in L4 and thick tufted pyramidal neurons in L5 display on
average the highest number of potential thalamocortical VPM synapses.
8. The functional unit called cortical barrel column can also be regarded as
an anatomical one, who’s dimensions are defined by the VPM innervation
volume and neuron-dense regions in S1.
4.1
Quantitative 3D structure of S1
All available data in the literature about neuron densities and distributions in the cortex
is based on sparse sampling [34], [35], [33], [36], [37]. This method resulted in rather contradicting density values (e.g. ranging from 40000-80000 neurons per cubic millimeter in
V1).
The commonly referenced quantitative study about neuron densities and numbers in S1
4.1 Quantitative 3D structure of S1
125
was done by Clermont Beaulieu in 1993, using sparse sampling by the so called dissector method [32]. There, a 137µm wide strip of tissue ranging from the pia to the WM
was manually investigated in 100µm thick thalamocortical sections. Such a small volume
(≈10% of the column volume) will only yield reliable density values for entire S1, if this
region of the cortex is more or less homogeneous in every lateral direction.
In order to ultimately reveal the three-dimensional neuron organization of S1 and to quantitatively determine the number of neurons per barrel column, a 1,875mm x 1,875mm x
2mm large volume of S1 has been subjected to NeuroCount. This volume, being about
250 times larger than the one used by Beaulieu, contains at least nine complete cortical
columns. It will be shown that the resultant neuron density values per layer, for entire S1
and hence for cortical columns, significantly differ from the previous estimates by Beaulieu.
This can be explained by strong density variations within and across all cortical layers in
S1, as displayed in Figures 4.1, 4.2, 4.3, Table 4.1 and described below.
4.1.1
3D distribution of neuron somata in S1
The investigated ≈8 cubic millimeter large volume of S1 contains nine complete cortical
barrel columns (here: C2-4, D2-4 and E1-3 (Fig.4.1)). The column outlines are easily
visible in low magnification images of the GAD channel in sections from L4 (Fig.4.1).
These GAD outlines are identical to the barrels first observed by Woolsey and van der
Loos [38]. Figure 4.1 and 4.2 show the distribution of all neuron somata in each of the
40 consecutive tangential brain slices (50µm thick), starting at the pia and ending at the
white matter. It should be emphasized the the colormap is adjusted for each panel to
display the respective density maximum and minimum of each slice in red and blue and
hence to visualize the neuron organization within each section.
Subsequently the organization of each layer will be briefly summarized. It should be
126
Anatomical results
L2/3
L4
500µm
Figure 4.1: 3D neuron soma distribution in L1-L4 of S1. Top/left panel: low magnification
image of GAD channel in a section from L4. Clearly visible are the barrel outlines, identical to
the ones first observed by Woolsey and van der Loos. These contours determine the x/y-center
of each column. Remaining panels: starting at the pia, the distribution of all neuron somata in
a 1875µm x 1875µm x 50µm volume as derived by NeuroCount is displayed. The colormap is
adjusted for each slide (i.e. the respective maximum density is red, minimum blue). The GAD
barrel pattern is preserved in the neuron soma distribution of L2/3 and L4.
4.1 Quantitative 3D structure of S1
127
L5
L6
500µm
Figure 4.2: 3D neuron soma distribution in L5-L6 of S1. Remaining 20 sections from
Fig.4.1. Clearly visible are small clusters of neurons in L5, which could resemble so called minicolumns as described by [126]. The last section is not show, because it is completely within the
WM and hence no neurons are present.
128
Anatomical results
mentioned that the cortex is a curved structure. Looking at the first panels of Figure 4.1,
it is obvious that the c-row is about 75µm (1.5 sections) higher than the d-row, which in
turn is 75µm higher than the e-row. Consequently some panels cannot clearly be assigned
to one or the other layer.
Organization of L2/3 Panel 4-8 of Figure 4.1 approximately comprise L2/3. This layer
displays strong density variations, ranging from ≈50000-110000 neurons per cubic millimeter. Further, the organization which is determined by the GAD image
(panel1) is preserved in L2/3. Cortical columns appear there as neuron-dense circles, having approximately the same diameter as the respective GAD contours. The
columns in L2/3 are surrounded by neuron-sparse zones, called septa. The average
difference between columnar and septal zones is about 15%. The average density
value for entire layer 2/3 is ≈74600 neurons/mm3 .
Organization of L4 Panel 9-16 of Figure 4.1 approximately comprise L4. As L2/3, L4
displays strong density variations ranging from ≈80000-170000 neurons per cubic
millimeter. In contrast to L2/3, septa between individual columns of the same row are
almost absent. However, septal regions between the rows are even more pronounced
than in L2/3, especially between the d- and e-row. The average difference between
columnar and septal zones is again around 15%. The average density value for entire
layer 4 is ≈104600 neurons/mm3 .
Organization of L5 Panel 1-8 of Figure 4.2 approximately comprise L5. The clear organization in rows or columns is absent and replaced by strong density variations
on smaller scales. Small dense zone of density values up to ≈90000 neurons per cubic millimeter are intersected by small neuron-sparse zone with densities of ≈40000
neurons per cubic millimeter. No clear pattern can be seen. Hence, the average differ-
4.1 Quantitative 3D structure of S1
129
ence between columnar and septal regions is around zero. Neuron-dense zones could
possibly reflect so called minicolumns, defined by bundles of apical dendrites and described by [126]. The average density value for entire layer 5 is ≈67900 neurons/mm3 ,
making L5 the neuron-sparsest layer in S1.
Organization of L6 Panel 8-16 of Figure 4.2 approximately comprise L6. As in L5, L6
displays no clear neuron organization. A more or less homogeneous distribution is
intersected by randomly arranged neuron-sparse zones. These deviations range from
≈40000-110000 neurons per cubic millimeter. Even though the sparse zone seem to
be organized randomly, the difference between columnar and septal regions is about
8%. The average density for entire layer 6 is ≈73200 neurons/mm3 .
Summarizing these layer-specific descriptions, the somatosensory sensory cortex is organized into neuron-dense columns and neuron-sparse septa throughout all layers, except
for L5. The average density values peak in L4 and have their minimum in L5 (L1 is neglected, because it is not innervated by the VPM). The average density value of entire S1 is
≈71000 neurons/mm3 , comprising columnar (≈73800 neurons/mm3 ) and septal (≈69000
neurons/mm3 ) regions. The total difference between these two zones is hence about 7%.
These findings are summarized in Table 4.1 and illustrated by Figure 4.3. There, average
intensity projections along all three spatial directions of the investigated volume in S1 are
shown. The x/y-projection (bottom plane), resembling a top view from the pial surface,
clearly depicts the organization of S1 into rows that are divided by prominent septa. Regarding the x/z- and y/z-plane it becomes further obvious that cortical barrel columns are
not only functional units, but can be regarded is neuron-dense columns that are separated
by septa throughout entire S1. The septa are very prominent in L2/3 and L4 (≈ −15%),
almost absent in L5 and somewhat less discernable in L6 (≈ −8%).
The density value for S1 in the commonly referenced study by Beaulieu [33] (Table 4.1) is
130
Anatomical results
Beaulieu 1993
Oberländer 2009
Layer
total
GABA
total
GABA
column
septum ≈min
≈max
1
5.3
81
7.1
80
5.3
8.8
4
80
2/3
52.6
15
74.6
14
80.4
68.8
50
110
4
85.7
11
104.6
14
111.6
97.6
80
170
5
36.1
17
67.9
18
69.0
66.9
40
90
6
48.3
16
73.2
9
72.6
73.8
40
110
S1
47.5
15
71.0
17
73.8
69.2
42.8
92.2
Table 4.1:
Comparison of average neuron densities and fraction of GABAergic interneurons per cortical
layer in S1 between results from sparse sampling (i.e. dissector) [33] and NeuroCount. Neuron
densities are given in 103 /mm3 , whereas the fraction of GABAergic interneurons is given in
%. The layer boundaries differ from the estimates done by Beaulieu and are derived in section
4.3.1. Each layer is very heterogeneous in density. Hence, sparse sampling methods can yield
average densities ranging from ≈40000-90000. The true average density is 71000 neurons per
cubic millimeter. The fraction of GABAergic interneurons is similar between the two studies.
4.1 Quantitative 3D structure of S1
131
≈ 35% less than the here presented one. This underestimation is systematically found for
all layers. Most likely this can be explained by strong density variations within each layer.
Previously published density values for rat cortex obtained by sparse sampling methods
range from 40000 − 80000 neurons/mm3 . This is approximately the range if the here determined minimal and maximal values per layer are averaged (Table 4.1). In the case of
Beaulieu, the density values are close to the minimal average density of S1 as determined
here.
Further quantification of these findings is done by counting the number of neurons in
the nine standardized column regions and a surrounding box shown in Figure 4.4a. The
midpoint of each of the nine barrel regions is determined as the center of mass of the respective GAD-contours. Circles with radius 195.44µm are centered on each of these midpoints.
This radius is adopted from [6] and has been established by measurements of the extend of
VPM synapse distributions in L4 (personal communication with Verena Wimmer and Bert
Sakmann). The resultant columnar cross-section of 120000µm2 yields a column volume
of 0.24mm3 . Compensating for curvature artifacts the number of neurons in each of the
nine columns and in the remaining box area yield three-dimensional neuron distributions
and depth-profiles (Fig.4.4c) for the average column and the septum, respectively. The
resultant numbers are subsequently presented.
4.1.2
3D average cortical column of neuron somata
As stated above, the number of neurons per standard column (i.e. cylinder with 120000 µm2
cross-sectional area and 0.24mm3 volume) is calculated for nine columns within the large
volume of S1. The resultant distributions and numbers are given in Figure 4.4b and 4.4c,
respectively. The curvature of the cortex is compensated by shifting the distributions of
the c-row by 75µm and the ones of the e-row by 150µm. Two observations are remarkable:
132
Anatomical results
C row
D row
E row
500µm
Figure 4.3: 3D neuron soma distribution in S1. Average x/z-, y/z- and x/y-projection of
neuron densities in S1. Clearly visible is the organization of the barrel cortex in neuron-dense
column, separated by neuron-sparse septa. The septa between rows are much more prominent
than between columns of the same row. Hence, the cortical barrel column is not only a functional
but also an anatomical subunit in terms of three-dimensional soma distribution.
4.1 Quantitative 3D structure of S1
b
E1
C2
D2
C3
C4
E2
D3
cortical depth in microns
a
133
E3
-500
-1000
-1500
D4
C2
C3
C4
20
3
160x10
3
20
140x10
3
-1000
-1500
C
D
E
3
-2000
--> 17707 ± 462
20
-500
cortical depth in microns
E1 --> 16974
E2 --> 17733
E3 --> 18343
140x10
-100
C2 --> 17264
C3 --> 17489
C4 --> 17773
D2 --> 17476
D3 --> 17978
D4 --> 18329
E1
E2
E3
D2
D3
D4
-2000
500µm
c
-100
20
140x10
3
column
septum
3
20
140x10
neuron density per cubic mm
e
0
tot column
exc column
inh column
1
Figure 4.4: Neuron soma distribution of average cortical column. (a) A circle with
195.44µm radius is centered on each column midpoint as determined by the GAD contour. (b)
The number of neurons is calculated for each circle in each slice. The resultant depth profiles are
shown for each row (three top panels). Compensating for curvature artifacts the average depth
profile is determined (bottom left panel). Calculating the number neurons within the remaining
box shown in a, additionally yields a depth profile of the septum (bottom middle panel). By
subtracting the depth profile of GABAergic interneurons, the distribution of excitatory neurons
can be calculated (bottom right panel). (c) The average number of neurons per cortical barrel
column is 17707±462. The low deviation in numbers and the identical profiles allow the creation
of an average 3D neuron distribution, centered on a cortical column (right panel). The resultant
distribution will be the starting point for reengineering the excitatory thalamocortical lemniscal
pathway.
134
Anatomical results
• First, the circle with 195.44µm radius resembles almost exactly the maximal dimensions of the neuron-dense area in L4 (Fig.4.4a C2 and C3 are already in L4).
• Second, the deviation between individual columns is considerably small. Here, the
average number of neurons per column is 17707 ± 462 (i.e. the standard deviation
between columns is less than 3%).
The small deviation in absolute numbers and almost identical distributions and profiles for
the nine columns, allows to calculate the average three-dimensional neuron distribution of
a cortical barrel column. Therefore a cuboid with 550µm x 550µm x 2000µm edge length
is centered around each column midpoint and cropped from the large distribution. The
resultant nine cuboid distributions are averaged and the result is shown in Figure 4.4b.
Subtracting the fraction of GABAergic interneurons, as determined in cooperation with
Hanno-Sebastian Meyer (MPImF, Heidelberg) [38] and shown in Figure 4.4c (bottom/right
panel), the three-dimensional distribution of all excitatory neurons in this standard cuboid
volume (0, 605mm3 ) is derived. The total fraction of interneurons is about 15%, resulting
in a number of excitatory neurons of ≈15200 per standardized column.
The cuboid distribution will in the following be the starting point for the reengineering
of the excitatory thalamocortical lemniscal pathway in S1. Subsequently the number of
neuron-types that constitute to this distribution as well as their spatial extend will be
determined.
4.1.3
Dendritic excitatory neuronal cell types in S1
In total a number of 78 dendrite tracings of excitatory neurons from S1 are evaluated. The
78 reconstructions are registered to the standardized column using daVinci, as described
in the method section. In vivo physiological data of spontaneous suprathreshold activity
4.1 Quantitative 3D structure of S1
135
a
cortical depth in 10^3 microns
0
1
1.8
b
0.8
radial cluster distance
L5A
L6CT
L6CC L4SS L4SP
L2
L3
L5B
0.5
0
Figure 4.5: OPTICS cluster results in S1. ( a) A representative dendrite tracing for each of
the determined eight neuron-types is shown at its standardized, registered soma depth. (b) The
OPTICS algorithm used by NeuroCluster produces an augmented reachability plot, where valleys
indicated individual clusters. Six neuron-types are clearly found, L5A, L6CT, L6CC, L4, L2/3,
and L5B. Further, L4 and L2/3 can be separated into two subtypes respectively, L4SS,L4SP, L2
and L3.
136
Anatomical results
and in response to passive whisker deflection (i.e evoked activity) under anesthesia is also
available for 60 of these tracings. This gives the unique opportunity to classify excitatory
neuron-types based upon anatomical features and cortical depth and to correlate these
anatomical classes with physiological properties.
NeuroCluster, as described in the method section, is used to group the tracings upon
geometry- and shape-related dendritic features, as well as by cortical depth. Figure 4.5b
shows the resultant reachability plot. Six individual neuron-types could be clearly determined as ”valleys” in this plot. In addition two layer-specific subtypes (i.e. less prominent
”sub-valleys”) could be assigned in L2/3 and L4, respectively. A representative neuron
tracing is shown for each of the eight types (Fig.4.5a) at its standardized registered soma
depth. The features of each class can be described as follows:
Layer 2 pyramid (L2) These neurons form a subclass within L2/3. Characteristic for
these neurons is a very short and usually oblique (with respect to the column axis)
apical dendrite with a widely spreading apical tuft. The obliqueness is mainly due
to their position within the top 100-400 microns of the column. There the curvature
of the pial surface constrains the apical innervation.
Layer 3 pyramid (L3) These neurons form the second subclass within L2/3. The transition from L2 neurons to L3 is rather gradual, which is also indicated in the reachability plot. Therefore, L2/3 is often regarded as a single layer of more or less one
excitatory neuron-type [16]. However, characteristically, L3 neurons are found deeper
within L2/3, resulting in a still short but straight (with respect to the column axis)
apical dendrite. Moreover their apical tuft is less prominent and spreads not as wide
as the one of L2 neurons.
Layer 4 star pyramid (L4SP) These neurons form a subclass within L4. As previously
4.1 Quantitative 3D structure of S1
137
described by [127], these neurons display a short apical dendrite with a sparsely, if
at all, branching apical tuft. As presented below (see sec.4.3.1), there is a significant
overlap between L2/3 and L4. Within this overlap zone the transition from L3 to
L4SP neurons is again somewhat gradual, making manual classification difficult.
Layer 4 spiny stellate (L4SS) These non-pyramidal neurons form the second subclass
within L4. As L4SP neurons, L4SS neurons were previously investigated by [127].
They are completely lacking an apical dendrite and display a characteristic asymmetric shape, caused by dendrites that usually point towards the column center. Their
name is also due to high spine densities, which in the following is estimated as twice
as high as for any of the other eight types.
Layer 5 slender tufted pyramid (L5A) These neurons form an unambiguous class in
L5 and were first described in rat visual cortex by [128] and have since then been
investigated in various cortical areas [129]. Characteristically. L5A neurons have a
long, unbranched apical dendrite and a moderately spreading apical tuft. The latter
feature gave this type its name.
Layer 5 thick tufted pyramid (L5B) These neurons form the second unambiguous class
in L5 [128], [129]. In contrast to L5A neurons, L5B neurons display heavy branching
at the apical ”root”, called oblique apical dendrites and a widely spreading apical
tuft. Again the latter feature resulted in the name of this class.
Layer 6 corticocortical pyramid (L6CC) These neurons form an unambiguous class
in L6. They display a wide basal tree, sparsely branching apical oblique dendrites
and a sparsely spreading, if at all, apical tuft. They were first described by their
axon morphology from in vitro tracings [130], [131]. Projecting mainly within the
cortex resulted in the classification as corticocortical.
138
Anatomical results
Layer 6 corticothalamic pyramid (L6CT) These neurons form a second unambiguous class in L6. They display a narrow basal tree, oblique apical dendrites, a long
apical trunk and a sparsely branching apical tuft. They were also first described by
their axon morphology from in vitro tracings [131]. In contrast to L6CC neurons, this
type projects from S1 towards the thalamus, resulting in the name corticothalamic
L6 neuron.
The here objectively determined neuron types have all been described before. Nevertheless, the grouping is usually done subjectively and is mainly based upon soma depth. It
will be shown in section 4.3.1 that this ”recording” depth can sometimes be misleading
because these neuron-types mutually overlap in the z-direction. In contrast, the reliable
classification by NeuroCluster is based upon dendritic, anatomical features and the standardized pia-soma distance of each reconstruction. The unambiguity of the presented eight
neuron-types is demonstrated on the example of three of the eleven features (see method
section) and is shown in Figure 4.6a/b.
Figure 4.6a displays the neuron-type-specific distribution of apical tuft length compared
with standardized pia-soma distance. The ellipses are centered around the respective mean
values and the length of the half axes is set to 1,5 times the standard deviations. Figure
4.6b is created in a similar way by replacing the length of the apical dendrite with the
maximal horizontal spread of the apical tuft. The ellipses hardly overlap. This indicates
that each neuron-type has unique anatomical features, which distinguish them from each
other. Since L4SS has no apical dendrite, L4SS and L4SP cannot be distinguished by these
parameters and are hence grouped as one type in the illustration.
4.1 Quantitative 3D structure of S1
a
139
b
0
L2
cortical depth [µm]
L2
-500
L3
L3
L4SS/SP
L4
-1000
L5A
L5A
L5B
L5B
L6CC
L6CT
L6CC
-1500
L6CT
-2000
100
500
MaxDend_ZRange [µm]
c
1000
d
100
500
MaxDendTH3_XYdiagonal [µm]
spontaneous activity [APs per sec]
6.0
4.0
L5B
2.0
L6CC
L5A
L6CT
0.0
-12
0
12
24
36
48
evoked activity within 20ms after passive whisker deflection [APs per sec]
-12
0
12
24
36
48
evoked activity within 20ms after passive whisker deflection [APs per sec]
Figure 4.6: Anatomical and physiological neuron types. (a/b) Scatter-plots showing the
neuron-type-specific relationship of registered soma depth and length of the apical dendrite (a)
and spread of the apical tuft (b). L4SS neurons have no apical dendrite and can therefore not
be distinguished from L4SP neurons upon these features. The ellipses are centered around the
type-specific mean values and the length of the half axes is set to 1,5 times the standard deviation.
Small, if any, overlap zones between the ellipses indicate anatomically well separated clusters.
(b/c) Spontaneous and whisker-evoked activity are plotted as in a/b for L5 (c) and L6 (d) neurons.
Small, if any, overlap zones between the ellipses indicate that the anatomical types also reflect
type-specific functional properties. The results for L5 were previously shown in vivo [10]. For L6
these findings were predicted from in vitro studies [131] and can now be confirmed in vivo.
140
Anatomical results
Correlation of anatomical and functional type-specific neuron properties
Apart from anatomical features, neuron-types are often grouped by their physiological
response properties. This will be illustrated on two examples:
• A significant difference between L5A and L5B neurons is their response to passive
whisker deflection. Whereas L5A neurons remain more or less silent, L5B neurons respond the most among all neuron-types [10]. If the grouping of L5 pyramidal neurons
by NeuroCluster is correct, this physiological feature should be present if the mean
whisker-evoked and spontaneous activities are compared. This is done in Figure 4.6c.
The ellipses are again centered on the respective mean values and their sizes reflect
1,5 times the standard deviation. Clearly separated ellipses demonstrate that L5A
and L5B are not only anatomical but also physiological classes. The evoked activity
within the first 20ms after whisker deflection mainly represents direct activation by
thalamocortical VPM input. The difference in response could hence reflect different
dendritic properties (e.g. ion channel distributions) or different synaptic input. The
latter will be addressed in section 4.3.2.
• Predicted by [131], L6CC should have higher firing rates in vivo when compared
with L6CT neurons. There, in vitro current injections revealed that the intensity
need to elicit APs in L6CT is significantly higher than in L6CC neurons. Both, the
spontaneous and whisker-evoked activity are shown for L6CT and L6CC neurons in
Figure 4.6d. The activity rates of L6CT neurons are significantly lower than the ones
for L6CC. Further, the two ellipses do not overlap, indicating that the anatomically
classified two neuron types in L6 are also physiological types.
The process of tracing, standardizing and clustering dendrite morphologies reproduced
anatomical and physiological findings. Hence, the above presented eight neuron types
4.1 Quantitative 3D structure of S1
141
will be subsequently investigated further. First the corticocortical axon innervation is
studied on the example of L5A neurons. Ultimately, these neuron types function as target
populations for thalamocortical VPM projections, yielding a neuron-type-specific number
of potential VPM-S1 synaptic contacts.
4.1.4
Axonal projections of L5A neurons within S1
a
b
c
0
-100
-200
-300
L2/3
-400
h
cortical dept
[µm]
-500
-600
-700
-800
-900
-1000
-1100
-1200
-1300
-1400
-1500
-1600
-1700
-1800
-1900
-2000
0
500µm
2500
5000
7500
axon density [µm per z-bin]
Figure 4.7: Axonal projections of slender tufted L5A pyramidal neurons in S1. (a/b)
Three-dimensional tracing of full axon (blue) and dendrite (red) morphologies from in vivo labeled
L5A neurons. Despite large variability in axon morphology, all traced neurons display characteristic projections into L2/3 of the surrounding columns and to L5 of its own column. The
wide-spreading axon morphology prohibits the quantitative tracing from in vitro preparations. (c)
Average axon density profile for L5A neurons. 9cm average total axon length innervate S1 most
densely in L2/3 (reaching a peak at 300µm depth) and in L5A (reaching a peak at approximately
1000µm depth).
So far, the tracing and classification revealed eight excitatory dendritic neuron types
in S1. Subsequently these neurons will be investigated as targets for thalamocortical input
from the VPM. However, this VPM-S1 circuit is only the starting step for cortical process-
142
Anatomical results
ing of whisker-evoked sensory information. Any of the determined neuron-types processes
and then transfers information towards other neuron-types, before it is ultimately relayed
to subcortical areas.
The only possibility to quantify these neuron-type-specific intracortical circuits, is to trace
the complete axonal arbor of classified cortical neurons. Here, this procedure is demonstrated for L5A neurons reconstructed by NeuroMorph.
A few in vitro studies [24], [132], [25] showed that L5A neurons project into supragranular
layers L2/3 and L1. Unfortunately, in vitro reconstructions suffer from significant slicing
artifacts. An in vitro slice thickness of usually 300µm will prove to be insufficient to study
the full extend of the axonal arbor in a quantitative manner. Figure 4.7a/b show two
of five reconstructed L5A neurons including their full dendritic (red) and axonal (blue)
morphology. Regarding the scalebar it becomes obvious that a slice thickness of 300µm
will always result in significant cropping of these axonal arbors.
Table 4.2 summarizes the length of axon and dendrites for the five traced L5A neurons.
These numbers illustrate the different efforts needed for tracing axons or dendrites. L5A
neurons comprise on average about 9cm of axon, compared to approximately 6mm of dendrite. This amount of axon per cell has significant implications. As will be derived below
(Table 4.8) L5 contains approximately 1700 L5A neurons per barrel column. Assuming a
bouton density that is similar to the one of VPM axons (1 bouton per 3µm), the number
of potential corticocortical L5A synapses on axons projecting out of a single column would
be more than 50 × 106 . For comparison, this is about 20 times more than the total number
of thalamocortical VPM synapses per barrel column (sec.4.2.2 and Table 4.8).
In addition to the potential number of L5A synapses, Figure 4.7c shows that their main innervation domains are located within L2/3 (peak at 300µm depth) and L5A itself. Further,
despite relatively large morphological deviations between individual cells, all L5A axons
4.1 Quantitative 3D structure of S1
143
share characteristic innervation patterns. Unbranched projections cross L4 and target L2/3
of the same and multiple surrounding columns. There, the axon branches frequently again.
Whereas L5A projections in L2/3 span across large areas of S1, in some cases even beyond
S1 into the ”agranular cortex” (i.e. lacking a high cell density layer), the axon stays essentially local within its home column in L5.
The tracing of the full three-dimensional axonal arborization of L5A neurons in S1 hence
suggests the presence of at least three corticocortical circuits:
L5A-to-L5A projection The first circuit suggested by the axon tracing is a local (intracolumnar) circuit within L5A. Such monosynaptic connections between pairs of L5A
neurons were recently described in in vitro studies [133].
L5A-to-L2/3 projection The second circuit suggested by the tracing of L5A axons is a
long range circuit within S1. The morphology suggests that information of whisker
movement, which is processed within the paralemniscal pathway, is conveyed from
L5A to L2/3 of the same and multiple surrounding columns. In addition to the recent
finding that L2/3 neurons are sensitive to whisker movement [134], the here presented
tracings support the hypothesis of monosynaptic connections between L5A and L2/3
neurons [22]. Since L2/3 neurons are also part of the lemniscal pathway, which
processes information about whisker touch, the presence of L5A-L2/3 connections
would indicate convergence of the lemniscal and paralemniscal pathways in L2/3
[22].
L5A-to-AGr projection The third circuit suggested by the tracing of L5A axons is a
long range circuit with L2/3 neurons of the agranular cortex (AGr). This cortex is
involved in sensorimotor processing [135], [136], [137]. A monosynaptic connection
between these populations has to my knowledge not yet been demonstrated. Direct
144
Anatomical results
transfer of information about whisker movement from L5A in S1 to L2/3 in AGr,
without further processing in S1, is suggested by these projections.
length [mm]
]
axon
basal dendrites
apical dendrite
1
87,31
4,09
2,85
2
83,50
4,64
1,66
3
77,82
6,03
1,14
4
95,01
5,23
n.t.
5
119,16
4,02
n.t.
AVG
92,56
4,80
1,14
STD
16,13
0,84
1,20
Table 4.2:
Dendritic and axonal length of L5A pyramidal neurons (n.t. means ”not traced”, i.e. the apical
dendrite was partly destroyed during filling).
The tracing of intracortical axonal arbors, demonstrated on the example of slender tufted
pyramidal neurons in L5 of S1 illustrated two important issues.
• First, the reconstruction of such axon morphologies is almost unfeasible by manual
tracing. A total axon length of up to 12cm and unpredictable innervation domains
will make a Neurolucida-based tracing tedious, time consuming and experience dependent.
• The second issue is related to the fact that the innervation domains are rather unpredictable. Like ”bulk-labeling” studies of entire neuron populations [138], tracing
4.2 Quantitative 3D structure of VPM
145
of individual axons potentially yields new information about network circuity (e.g.
an estimate of the number of synaptic contacts). However, ”bulk-labeling” studies are rather descriptive, whereas single neuron tracing yields quantitative threedimensional information about innervation density.
4.2
Quantitative 3D structure of VPM
The aim of the presented work is to reengineer the excitatory part of the thalamocortical
pathway in the whisker system of rats. So far the focus was on the target populations
of VPM axons in S1. There, eight individual neuron-types could be classified by their
dendrite morphology and position within a standardized cortical barrel column. There, a
total number of ≈15200 excitatory neurons are potentially targeted by the VPM.
In order to derive neuron-type-specific data of how many thalamocortical synapses are
potentially formed with any of these 15200 neurons, and to estimate how the synapses are
distributed throughout the column, the following anatomical information about VPM is
necessary:
1. the number of neurons that project from the VPM into a single column (i.e. the
number of neurons per barreloid),
2. the three-dimensional distribution of VPM axons in S1 (i.e. a representative sample
of single VPM axon tracings),
3. the number of boutons (potential sites for synapses) per axonal length,
4. overlap of VPM axons and cortical dendrites.
Using NeuroCount and NeuroMorph this information will subsequently be presented in a
quantitative way.
146
Anatomical results
4.2.1
3D distribution of neuron somata in VPM
b
a
RT
β
γ
C1
δ
B1
RT
A1
γ
α
D1
β
C1
δ
B1
A1
α
D1
E1
E1
VB
VB
POM
POM
500µm
Figure 4.8: GABAergic innervation of VPM. (a) Inverted maximum intensity projection of
GAD-channel from a central slice through VPM. No interneurons are present except in RT. The
VPM and each individual barreloid is clearly visible indicating that GABAergic neurons from the
RT innervate mainly the VPM in a barreloid- and/or row-specific way. (b) The GAD-contours
are transferred to the neuron (NeuN-stained) density map obtained by NeuroCount. The VPM
boundaries based upon the GABAergic innervation from the RT are reflected in the neuron density.
The VPM is hence regarded as a neuron-dense thalamic nucleus surrounded by less dense VB and
POm.
In previous studies of the VPM a number of approximately 200-300 neurons per barreloid [125] has been estimated. Even though this estimate seems to be rather precise,
the uncertainty of about 20% (250 ± 50) will be reflected in the range of VPM synapse
per barrel column. Arguably, 20% uncertainty in synapse numbers would make simulation
of neuronal activity upon an average cortical column unfeasible. Therefore, as presented
for S1 previously, NeuroCount is used to determined the number and three-dimensional
distribution of neurons from a large thalamic sample. Here, nine 50µm thick sections, cut
4.2 Quantitative 3D structure of VPM
147
at an oblique angle as described by [139] are stained with NeuN and GAD67. Large image
stacks (≈ 1, 7mm x 1, 7mm), acquired by confocal mosaic/optical-sectioning and centered
around the VPM are obtained for each of the nine sections.
Figure 4.8 summarizes the two main findings:
1. The VPM does not contain GABAergic interneurons, but still displays characteristic
structural organization in the GAD-channel, caused by GABAergic synaptic terminals. Figure 4.8a shows an inverted maximum intensity projection from a central
section through VPM. Clearly visible are individual barreloids, rows of barreloids,
septa between the rows and a significant intensity drop outside the VPM (i.e. in
VB and POm). Further, GABAergic interneurons are only found in the RT. This
indicates, as described by [140], [141], inhibitory connections between the RT and the
VPM. This innervation seems to be restricted to the VPM, defining its boundaries
with respect to surrounding thalamic nuclei. More importantly, the RT innervation
seems to be barreloid-, or at least row-specific, defining the boundaries of individual
barreloids and rows, similar to the findings in S1 (Fig.4.1). The barreloid boundaries,
visible in the GAD-channel, are traced as contours within each of the nine sections.
Alignment of these contours results in a three-dimensional reconstruction of individual barreloids. In consequence the volume of each barreloid can be calculated.
2. Superimposing the GAD-contours of the VPM and its barreloids with the respective neuron density distribution yields another important finding. The VPM differs
not only in GABAergic innervation from its surrounding thalamic nuclei, but also in
neuron density. Almost identical VPM boundaries are obtained in the GAD projection image and the NeuN density distribution (Fig.4.8). However, unlike the barrel
contours in S1, the barreloid contours do not reflect neuron-denser areas within the
VPM. There, septa seem to be purely defined by the GABAergic innervation from
148
Anatomical results
the RT.
500µm
Figure 4.9: 3D neuron soma distribution in VPM. NeuN-density distribution for nine
consecutive oblique brain slices. The VPM is clearly separated from its surrounding nuclei. The
bottom/right panel displays an overlay of the nine sections.
Figure 4.9 shows that the described confinement of the VPM from its surrounding nuclei
is true for every section. The red and yellow parts in each section correlate with the
respective GAD-pattern. Superimposing all NeuN-density maps (last panel in Fig.4.9)
again illustrates that the VPM can be regarded as a neuron-dense nucleus surrounded by
the neuron-sparse VB and POm.
Quantitatively, the number of neurons is determined for 4 barreloids (C1,C2,D1,D2). For
each section the respective barreloid contours are superimposed with the NeuN landmark
distribution (each landmark represents the 3D position of a soma) in Amira. All landmarks
found within the GAD-boundaries of a barreloid are detected. Table 4.3 shows the counts
for each of the four barreloids in each section. No significant structure within one barreloid
is present. As stated above, the VPM is rather homogeneous in neuron density.
The investigated four barreloids have almost identical volumes (4, 69 ± 0, 14 × 106 µm3 ),
which approximately resemble ovoids with 50µm x 100µm x 200µm long half axes. The
4.2 Quantitative 3D structure of VPM
149
number of neurons
slide
C1
C2
D1
D2
AVG
STD
1
28
39
17
28
2
49
42
21
19
3
40
39
21
30
4
31
32
19
31
5
33
43
54
41
6
26
31
24
37
7
39
40
46
31
8
41
19
43
33
9
10
9
26
26
SUM
297
294
271
276
285
13
volume [×106 µm3 ]
4,80
4,72
4,73
4,49
4,69
0,14
density per [×103 mm3 ]
61,81
62,25 57,22
61,49
60,69
2,34
Table 4.3:Number of neurons per VPM barreloid.
150
Anatomical results
resulting number of neurons per barreloid is 285 ± 13. This number is well within the
margin of 200-300, but deviates by less than 5% in comparison to the previous uncertainty
of 20%. It should be emphasized that even though the VPM seems to be the most neurondense thalamic nucleus, its average density of 60, 69 ± 2, 34 × 103 mm−3 is 15% less than
the average density of S1 and even 40% less if compared with L4 (in S1).
4.2.2
Axonal excitatory neuronal cell types in VPM
In addition to the number of neurons that project from one barreloid into one cortical
barrel column, the three-dimensional axon distribution of VPM axons within S1 needs to
be quantified. Therefore fourteen thalamocortical axons, filled in vivo, have been traced
with the NeuroMorph system, standardized by daVinci and grouped by NeuroCluster.
Eight of these axons projected into columns where the corresponding whisker has been
continuously trimmed for two weeks. The two main results can be summarized as follows:
1. VPM neurons are grouped by NeuroCluster into two types upon their axon morphology. Figure 4.10a/b and Figure 4.10d/e show examples for these two types,
respectively. As described before [142], these types differ in the number of innervated columns. Four of fourteen axons display a bifurcation in L6 and innervate two
columns. However, one column still contains the major part or the axon.
The remaining ten axons innervate only a single column. As shown in Figure 4.10c/f,
both types innervate S1 most densely in L4 and have a second, significantly smaller
peak in L5B. The innervation abruptly stops within L2/3 around 300µm below the
pial surface. Further, the depth profiles display a significant minimum in L5A, around
1000µm below the pial surface. It should be emphasized that the lateral extend, especially in L4, matches the estimated column diameter of 390,88µm (cross-sectional
area 120000µm2 , see sec.4.1.1).
4.2 Quantitative 3D structure of VPM
a
b
151
c
0
-100
-200
-300
-400
-500
cortical depth [µm]
-600
-700
-800
-900
-1000
-1100
-1200
-1300
-1400
-1500
-1600
-1700
VPM type 1:
control
deprived
-1800
-1900
-2000
0
1000
2000
3000
4000
5000
axon density [µm per z-bin]
d
e
f
0
-100
-200
-300
-400
-500
cortical depth [µm]
-600
-700
-800
-900
-1000
-1100
-1200
-1300
-1400
-1500
-1600
-1700
VPM type 2:
control
deprived
-1800
-1900
-2000
0
1000
2000
3000
4000
5000
6000
axon density [µm per z-bin]
Figure 4.10: Classification and deprivation of VPM axons. (a/b) Two example tracings
of the cortical part of thalamocortical VPM axons projecting into a single cortical barrel column.
The tracing in b projects into a column where the corresponding whisker has been continuously
trimmed for two weeks (deprived). (d/e) Two example tracings of VPM axons that bifurcate in L6
and project into two adjacent barrel columns. The tracing in e corresponds to a deprived whisker.
(c) Average deprived and control axon density profiles for tracings projecting into a single column.
(d) Same profile as in c for tracings projecting into two columns.
152
Anatomical results
2. Table 4.4 shows the axon length for deprived (whisker trimmed) and control tracings, respectively. In the control case, VPM axon have an average length of 56, 95 ±
13, 08mm. In the deprived case of 42, 31 ± 15, 03mm. Hence, the VPM axon length
in control animal is 34% larger when compared to the deprived animals. The absence
of functional input hence results in a diminishment of axon branches and therefore
thalamocortical connectivity within a cortical barrel column. Specifically, the axon
decrease is more pronounced in L4 and L6. In contrast, the average axon density
remains almost unchanged in L5A and decreases less in L5B.
The determined deprivation-depended decrease in thalamocortical VPM axon is supported by a recent bulk-labeling study [143]. There, VPM axons were labeled with a
virus expressing a fluorescent protein. The VPM innervation density was estimated
by measuring the fluorescent intensity in S1. Between control and deprivation a difference in fluorescence of ≈34% was also observed. However, it remained unclear if
the decrease in fluorescence reflected a decrease in bouton numbers, axonal length
or both. Further, the possibility that the fluorescent marker depends on neuronal
activity could not finally be excluded. The single axon tracings support strongly
the hypothesis in [143] that continuous deprivation of whiskers results in significant
functional long-term changes, which is based on anatomical plasticity of VPM-S1
projections.
The control group of VPM tracings will be subsequently used to reengineer the thalamocortical pathway and to interconnect the VPM with any of the previously presented excitatory
neuron-types in S1. Therefore it is essential to know the number of boutons per axonal
length, since boutons are potential sites for synaptic contacts. I therefore measured the
distance between pairs of boutons manually, using Neurolucida software in combination
with a 100x magnification oil-immersion objective. Since boutons are small swellings along
4.2 Quantitative 3D structure of VPM
153
control
deprived
type
length [mm]
type
length [mm]
single column
68,15
single column
32,20
single column
59,27
single column
17,52
single column
68,78
single column
48,67
single column
51,87
single column
55,83
single column
33,52
single column
58,36
double column
60,09
double column
56,29
double column
28,65
double column
40,89
AVG
56,95
AVG
42,31
STD
13,08
STD
15,03
Table 4.4:VPM axon length with and without whisker trimming.
154
Anatomical results
the axon arbor (≈1µm), they are hardly visible for axons projecting along the optical axis.
Hence, only axons projecting more or less perpendicular to the optical axis are investigated. The distance for 300 pairs of boutons at random cortical depth and for different
axons and animals has been measured. The resulting bouton density of 2, 94 ± 1, 15 will
therefore subsequently be regarded as constant (i.e. 3 boutons per µm axon) throughout
the entire VPM axon.
4.3
3D reconstruction of lemniscal thalamocortical pathway
The above obtained results are sufficient to reengineer the thalamocortical lemniscal pathway in NeuroNet. As described in the method section NeuroNet needs the following input
information:
3D target neuron distribution As derived in section 4.1.2, this distribution is a standardized cuboid centered around a cortical barrel column with dimensions of 550µm
x 550µm x 2mm. The distribution is chosen sufficiently larger than the estimated
column diameter of 390,88µm to avoid edge artifacts (i.e. neurons at the column
border would otherwise receive too many synapses because of absent dendrites from
septal neurons).
Number of target neuron-types As derived in section 4.1.3, eight excitatory neurontypes are classified in S1. For every of these types a representative sample of dendrite
morphologies is available (i.e. 78 tracings in total). Further, any of these types will
be connected to the VPM.
Number of input neurons As derived in section 4.2.1, 285 neurons are found in one
4.3 3D reconstruction of lemniscal thalamocortical pathway
155
barreloid. Further, the 6 VPM tracings of the control group, as described in section
4.2.2, function as a representative input sample.
Spatial extend of target neuron-types This issue has not been addressed so far and
will hence be subject of the subsequent section.
4.3.1
The standardized 3D cortical column in silico
type
AVG recording
STD
AVG registered
STD
depth [µm]
[µm]
depth [µm]
[µm]
L2
346,5
93,7
299,6
130,0
L3
475,0
189,1
392,5
103,2
L4SP
781,8
116,8
670,8
176,0
L4SS
802,2
144,5
724,3
151,1
L5A
1131,7
124,2
1133,7
106,4
L5B
1220,4
76,2
1286,6
98,3
L6CC
1477,0
65,0
1502,2
86,2
L6CT
1577,5
111,3
1587,9
172,9
Table 4.5:Neuron-type-specific average recording and registered soma depth.
The standard cortical barrel column has been described as a cylinder with a radius of
195,44µm and 2mm height. However, the spatial extend of each neuron-type within this
column remains undetermined. Since the cortex is a laminar structure, it is reasonable to
assume that each neuron-type has only boundaries along the vertical column axis (z-axis).
These are determined by calculating the average registered neuron depth (pia-soma distance) and its standard deviation of the standardized tracings of each neuron-type.
156
Anatomical results
Table 4.5 shows these values for each neuron-type in comparison to the so called recording
depth, which reflects penetration depth of the pipette during in vivo filling experiments.
As stated in the method section, this is only valid if the penetration axis is parallel to the
vertical column axis.
However, for infragranular neuron-types in L5 and L6, on average the recording and registration depth are similar. This is not the case for supragranular and granular neuron-types
(i.e. L2, L3, L4SP, L4SS). The average recording depth is systematically deeper than the
registered one. Table 4.6 shows the average ± 1,5× its standard deviation, minimal and
type/
AV G − 1.5ST D
AV G + 1.5ST D
min
max
bounds
layer
[µm]
[µm]
[µm]
[µm]
[µm]
L2
104,7
299,6
87,5
481,6
100-500
L3
237,8
547,3
182,9
531,6
250-550
L2/3
151,1
527,8
87,5
531,6
100-550
L4SP
406,8
934,8
523,6
1000,1
400-950
L4SS
497,7
950,9
460,2
1020,8
500-950
L4
452,1
940,5
460,2
1020,8
400-950
L5A
974,2
1293,3
948,5
1350,4
950-1300
L5B
1139,3
1434,25
1130,0
1381,2
1150-1450
L5
1007,0
1388,0
948,5
1381,2
950-1450
L6CC
1373,0
1631,4
1409,4
1657,2
1350-1650
L6CT
1328,5
1847,4
1286,0
1725,1
1300-1850
L6
1343,0
1732,8
1286,0
1725,1
1300-185
Table 4.6:Layer- and type-specific boundaries.
4.3 3D reconstruction of lemniscal thalamocortical pathway
157
maximal registered depth for each neuron-type and their respective layers. The minimal
and maximal type-specific depths match the values of AVG±1,5×STD depths. Since the
three-dimensional neuron distribution is given with 50µm precision, the boundaries for
each neuron-type are rounded to the next z-bin. The resultant type- and layer-specific
boundaries are given in Table 4.6 and are illustrated in Figure 4.11.
There, layer and type boundaries are compared with normalized depth profiles of excitatory and inhibitory somata and VPM axon density. Usually minima and maxima in one
of these plots are used to determine type-specific neuron boundaries [144]. Specifically,
• L4 is centered around the maximum of the VPM or the excitatory soma distribution,
• L5A is centered around the infragranular minimum of the VPM distribution,
• L5B is centered around the infragranular maximum of the VPM distribution,
• L6 is centered around the infragranular peak of the excitatory soma distribution,
• and the border between L2 and L3 is determined at the end of the supragranular
plateau of the excitatory soma distribution or at the supragranular end of the VPM
distribution.
Even though the neuron-type-specific center depths, determined by the ”profile-based”
approach, are similar to the ones determined as the average registered depth, I prefer the
latter method for two reasons:
• First, the relative central depth values for L4SS and L4SP, L6CC and L6CT cannot
be set by the profile-based methods and would hence be assumed identical as L4 and
L6.
• Second, the z-range cannot clearly be determined by the profile-based approach.
158
Anatomical results
a
mean
registered
depth
mean
registered
depth
0
0
0
-100
-100
-100
-200
-200
cortical depth
-300
-200
-300
L2/3
-300
L2/3
-400
-400
-400
-500
-500
-500
-600
-600
-700
-700
L4
-800
-800
-900
-900
-900
-1000
-1000
-1100
-1200
-1100
-1200
L5
-1200
L5
-1300
-1300
-1300
-1400
-1400
-1400
-1500
-1500
L6
-1600
-1700
-1700
-1800
-1800
-1800
-1900
-1900
b
0.25
0.50
0.75
-1900
inh. soma
-2000
0.00
1.00
0.25
0.50
0.75
0.00
0
0
-100
-100
-100
-200
-200
-400
L2
-400
L3
-500
-500
L4
SP
-700
-800
-800
-900
-900
-1000
-1000
-1100
L5A
-1100
L5A
-1200
L5B
-1300
L6
CC
-1400
L6
CC
-1500
L6
CT
-1600
-1700
-1700
-1800
-1800
-1800
-1900
-1900
0.00
0.25
0.50
0.75
1.00
L6
CT
-1600
-1700
exc. soma
L6
CC
-1500
L6
CT
-1600
-2000
L5B
-1300
-1400
-1500
L5A
-1200
L5B
-1300
-1400
L4
SS
-800
-900
-1200
L4
SP
-700
L4
SS
-1000
-1100
1.00
L3
-600
L4
SP
-700
L4
SS
0.75
-500
-600
-600
0.50
L2
-300
-400
L3
0.25
-200
-300
L2
VPM axon
-2000
1.00
0
-300
L6
-1600
-1700
0.00
L5
-1500
L6
-1600
exc. soma
L4
-800
-1000
-1100
L2/3
-600
-700
L4
-2000
cortical depth
mean
registered
depth
-1900
inh. soma
-2000
0.00
0.25
0.50
0.75
1.00
VPM axon
-2000
0.00
0.25
0.50
0.75
1.00
normalized density
Figure 4.11: Layer- and neuron-type-specific boundaries in S1. Layer- (top) and neurontype- (bottom) specific boundaries along the vertical column axis are determined as the average
registered depth of all tracings from a type ± 1,5× its standard deviation. These boundaries are
shown with respect to the depth profile of excitatory and inhibitory somata and VPM axon density
(from left to right), which are often used to determine type boundaries.
4.3 3D reconstruction of lemniscal thalamocortical pathway
depth [µm]
L2
100-250
1
250-400
1
3
400-500
1
3
1
1
1
3
1
3
500-550
550-950
L3 L4SP
L4SS
L5A
950-1150
1
1150-1300
1
159
L5B
L6CC
L6CT
1
1300-1350
2
1
1350-1450
2
1
1
1
1
1450-1650
1650-1850
1
Table 4.7:Type-specific overlap ratios.
160
Anatomical results
Therefore, subsequently the registered depth-based boundaries in Table 4.6 will be used.
The resultant overlap between neuron-types is indicated in Figure 4.11 as hashed zones
and quantified in Table 4.7. There, the overlap ratios reflect approximately the relative
frequency of occurrence of a neuron-type at a certain depth. For example, L2, L3 and L4SP
neurons are found between 400µm and 500µm below the pial surface. The ratio of 1:3:1 is
derived as the ratio of neurons from each type among the 78 tracings that can be found at
this depth. In this case, the area between 400µm and 500µm is essentially occupied by L3
neurons (3 out of 5), but L2 or L4SP neurons can also be found at this depth (1 out of 5,
respectively).
Once the neuron-type-specific boundaries and overlap ratios are set, NeuroNet determines
the type, number and position of neurons for each 50µm voxel of the standard cuboid and
replaces it by an appropriate dendrite tracing. Superimposing 285 VPM axon tracings (i.e.
each of the 6 tracings is pasted about 45 times), the number and subcellular distribution
of VPM synapses of any postsynaptic neuron is calculated by NeuroNet, as described in
the method section, and presented below.
4.3.2
Number and 3D distribution of VPM synapses in S1
The standardized cuboid distribution of excitatory neuron somata in S1 results in approximately 40000 neurons. Each of these neurons is replaced by a dendrite tracing of its
respective type. This results in a three-dimensional spine density, which is identical to the
dendrite density but multiplied with constant neuron-type specific spine densities. For all
types this density is assumed as 1 spine per 2µm of dendrite, except for L4SS, where a
density of 1 spine per 1µm of dendrite is assumed. I am currently working on methods
to determine more reliable spine density values, using serial block-face-scanning electron
microscopy (SBFSEM) [145]. However, the absolute spine densities will not influence the
4.3 3D reconstruction of lemniscal thalamocortical pathway
500µm
L2
L3
L4SP
L4SS
L5A
161
L5B
L6CC
L6CT
Figure 4.12: 3D neuron-type-specific spine and VPM synapse distributions. X/zprojections of neuron-type-specific spine (yellow) and VPM synapse distributions as derived by
NeuroNet.
calculation in NeuroNet. The relative densities between the types are decisive and it is
reasonable to assume that L4SS neurons have a spine density twice as high as the other
types.
The created spine density is superimposed with the bouton density, which reflects the
axon density of 285 thalamocortical VPM axons, multiplied with a constant bouton density. As presented above, this density value is 1 bouton per 3µm of axon. Upon the eight
neuron-type specific three-dimensional spine distributions (Fig.4.12 yellow), eight neurontype-specific synapses distributions are calculated (Fig.4.12 blue). Therefore NeuroNet
determines the contribution of every of the ≈40000 dendrite tracings to the total spine
and bouton distributions, as described in the method section. Subsequently, only neurons
with a soma position that is within the standardized column radius of 195,44µm will be
evaluated. The remaining ”septal” neurons will be neglected, since they might be effected
by edge artifacts. The results of the three-dimensionally reengineered thalamocortical
pathway can be summarized as follows (Table 4.8):
1. The here presented average cortical column contains 15289 excitatory neurons. The
largest population is formed by L4SS, followed by L6CT neurons. The L4SS popu-
162
Anatomical results
average number of VPM synapses
a
400
300
200
L2
L3
L4SP
L4SS
L5A
L5B
L6CC
L6CT
100
100
200
radial distance to column center [µm]
soma deptn [µm]
b
-1000
average
minimal
maximal
-2000
100
200 300
80
160
average number of VPM synapses
VPM synapses
per neuron
VPM axon
density
0.4
0.8
normalized values
Figure 4.13: Neuron-type-specific position dependence of synapse numbers. Depending
on the neuron-type and its three-dimensional soma position within the column, the number of
VPM synapses per neuron differ significantly. The upper panel shows the decay of the average
number of synapses per neuron with respect to the distance of the soma from the column center.
The lower panels show the average number of synapses per neuron with respect to the pia-soma
distance (cortical depth).
4.3 3D reconstruction of lemniscal thalamocortical pathway
163
lation also comprises the largest number of spines (≈16×106 ), but most spines per
neuron are found in L5B (6644). In total, the here generated average postsynaptic
network contains about 55×106 spines.
2. Most VPM synapses are formed with the L4SS population (≈1,2×106 ). This is one
order of magnitude more than for any other neuron-type. The total number of VPM
synapses that are formed with the 15289 excitatory neurons of the average cortical
barrel column is ≈2,8×106 . As derived previously (sec.4.1.4) this is about 50 times
less than the number of synapses L5A neurons from a single column form within S1.
3. On average, L4SS and L5B neurons have most synapses per neuron (283 and 262).
Neurons of these two types have on average approximately twice as many VPM
synapses than neurons of the remaining types. Specifically, if the average synapse
numbers are divided by the number of VPM neurons (285), L4SS and L5B neurons are
the only populations where on average, each postsynaptic neuron forms one synapse
with each presynaptic VPM neuron.
Further, the neuron receiving most VPM input in this network is a L4SS cell, making
948 synapses. Hence, given a convergence ratio of 0.43 [12], on average this neurons
forms about eight synapses with every connected VPM neuron.
4. The number of synapses among neurons of the same type is strongly position dependent. Distance of the soma from the pial surface and/or the vertical column axis
(i.e. column center) influence the number of synapses this neuron will form. Figure
4.13 illustrates this in a neuron-type-specific way. The upper plot shows that independent of the neuron-type, the number of VPM synapses decreases with increasing
distance from the column center. However, the slope of this decay is type-specific.
Whereas the lateral position of L2 neurons within the column has hardly any effect
164
Anatomical results
on the number of synapses, L5B neurons at the column border form about 30% less
synapses than neurons of this type at the column center.
Further, the three bottom plots in Figure 4.13 illustrate that neuron-type-specific
VPM synapse numbers depending on the z-position of the soma. Specifically, the
summed synapse profile is similar to the VPM axon profile, with one significant difference. The relative difference between the minimum in L5A and the maximum in
L5B is significantly increased in the synapse profile. This means that L5A neurons
between 950 and 1150µm below the cortical surface receive significantly less VPM
input than L5A cells between 1150-1300µm.
type
neurons
spines
VPM synapses
total
total
AVG
total
max
AVG
max per
AVG per
radial
]
] × 106
]
] × 105
]
]
VPM cell
VPM cell
decay
L2
718
2,87
3994
0,92
596
127,3
2,1
0,5
-0,10
L3
1682
6,05
3595
2,69
798
159,7
2,8
0,6
-0,20
L4SP
1524
3,52
2310
2,60
509
170,3
1,8
0,6
-0,30
L4SS
4128
15,98
3872
11,68
948
283,0
3,3
1,0
-0,53
L5A
1752
7,30
4168
2,92
392
166,5
1,4
0,6
-0,52
L5B
1135
7,54
6644
2,97
540
261,9
1,9
0,9
-0,62
L6CC
1373
4,10
2989
1,83
357
133,3
1,3
0,5
-0,50
L6CT
2977
7,97
2677
2,39
273
80,3
1,0
0,3
-0,29
SUM/AVG
15289
55,34
3781
27,99
552
172,8
1,9
0,6
-0,38
Table 4.8:Thalamocortical lemniscal pathway in numbers.
4.3 3D reconstruction of lemniscal thalamocortical pathway
165
0
300
600
L4
900
100µm
0
33
0
20
Figure 4.14: Subcellular distribution of VPM synapses in L4SS neurons. Different
dendritic length, as well as position within the column, cause significant differences in total VPM
synapse numbers on L4SS neurons; 406 synapses (left) vs. 105 synapses (right).
166
Anatomical results
0
300
600
L4
900
1200
100µm
0
21
0
10
Figure 4.15: Subcellular distribution of VPM synapses in L5B neurons. Two example
L5B tracings from the average ”cortical column in silico” are superimposed with an x/z-projection
of their respective VPM synapse distribution. This distribution is radially symmetric in the basal
tree, having its peak usually around the soma. In most cases a second innervation peak is found
along the apical trunk within L4. Almost no VPM synapses are present in the apical tuft. The
same kind of innervation has been described previously [123].
4.3 3D reconstruction of lemniscal thalamocortical pathway
167
Very little is known about numbers and distributions of thalamocortical VPM synapses
in S1. To my knowledge only three recent studies yield information that can be used to
validate the presented results by NeuroNet.
1. In vivo recordings from all excitatory neuron-types in S1 demonstrated, that L4SS
and L5B neurons respond the most to passive whisker deflection, within 20ms after
the stimulus [10]. This fast increase in AP-rates is regarded as directly caused by
thalamocortical VPM synapses.
The above presented results, based on innervation statistics of an average cortical
column, yield that exactly these two neuron-types receive most VPM input. The in
vivo results hence support these findings.
2. Based on in vivo paired recordings of VPM and L4SS neurons, the number of synapses
for this connection-type is estimated as 600, but maximally slightly less than 1000
[12]. As derived above, L4SS receive on average 283 synapses, which is only half as
much as predicted. However, the number of synapses, especially for L4SS neurons is
strongly position dependent (Figure 4.14). The average number of VPM synapses in
the upper part of L4 is about 400 (Fig.4.13 bottom/left panel). Further, the number
of synapses differs by more than 20% between the column center and its border
areas (Fig.4.13 top panel), reaching even maximal values of 948 VPM synapses per
neuron. In consequence the estimated limit of slightly less than 1000 synapses per
L4SS neuron is never crossed by any of the L4SS neurons in the presented average
network.
In conclusion, the gross estimate of 600 synapses per L4SS neuron is certainly met by
a large fraction of the here presented L4SS population. Further, it can be assumed
that during paired recordings, synapse estimates are biased by the fact that only
functionally connected neurons are investigated, resulting in slight overestimation of
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Anatomical results
synapses numbers.
0
300
L3
100µm
600
0
8
0
13
0
8
Figure 4.16: Subcellular distribution of VPM synapses in L3 neurons. The average,
soma-centered synapse distribution of L3 neurons displays a characteristic shift towards the lower
parts of the basal dendrites [123]. This effect is not present for individual synapse densities.
Asymmetric innervation of VPM axons in L3 (i.e. innervation stops at 300µm) leads to depthdependent synapse distributions.
3. Channelrhodopsin-based (ChR2) functional mapping of VPM synapses in S1, qualitatively revealed two-dimensional (x/z) synapse distributions for L3 and L5B neurons
[123]. The average distribution of L5B synapses on basal dendrites is more or less
4.3 3D reconstruction of lemniscal thalamocortical pathway
169
radially symmetric. A second connectivity peak is detected on the trunk of the apical
dendrite in L4 and almost no connections are observed for the apical tuft. Qualitatively, exactly this behavior is found for L5B neurons in the average cortical column
as illustrated by two examples in Figure 4.15.
More importantly the ChR2-based mapping yield that on average L3 neurons receive thalamocortical input mainly in the lower parts of their basal dendrites. Figure
4.16 illustrates that the same finding is obtained by the here presented statistical,
anatomy-based study. Averaging the presented three density maps and centering
them on the soma position results in a distribution, where the peak innervation is
shifted towards the lower parts of the basal tree.
However, I would argue that this finding is only true for average, soma-centered distributions. It does not reflect innervation of individual L3 neurons. Depending on
their soma depth within L3, ranging from 250-550µm below the pial surface, the innervation of VPM axon will be more or less symmetric. The VPM axon innervation
displays a significant decrease in density throughout L3, reaching zero around 250µm
below the pial surface (Fig.4.13). Hence, than deeper a neuron is located within L3
than more symmetric the innervation will be. As shown in the right panel of Figure
4.16, neurons located around the top border of L3 are constraint by the VPM axon
distribution and can therefore only make synaptic connections with the lower parts
of their basal dendrites.
In consequence, I argue that both methods presented here, innervation- and ChR2based, yield qualitatively the same results, but the interpretations are different. The
here presented quantitative anatomical data suggest an alternative explanation for
the asymmetric synapse distribution of L3 neurons. Specifically, the asymmetric
innervation of this layer is due to inhomogeneous branching of VPM axons.
Chapter 5
Discussion
The here presented thesis describes a custom designed toolbox for reengineering of average
functional neuronal networks with high anatomical accuracy, down to the subcellular (i.e.
synaptic) level. It comprises five tools: NeuroCount, NeuroMorph, daVinci, NeuroCluster and NeuroNet. Their function is demonstrated by reengineering the thalamocortical
part of the lemniscal pathway in the somatosensory whisker system of four week old rats.
There, information obtained by a single facial whisker is processed within a cortical barrel
column in S1. Excitation of columnar neurons, in response to passive whisker deflection
during anesthesia, arises from synchronous thalamocortical input from a single barreloid
in VPM. During active whisking, this lemniscal pathway is accompanied by additional
thalamocortical input from the POm (i.e. part of the paralemniscal pathway). Such single whisker information is sufficient to trigger a ”yes-or-no” gap-crossing behavior in rats.
Hence, mechanistic understanding of structure and function of the cortical column network
will potentially yield insights in how decision making evolves in mammalian brains.
However, reconstructing the barrel column from anatomical data that is obtained from
many different experiments and animals results in an average network. Simulation of
170
Discussion
171
whisker evoked activity on such an average network model is only reasonable, if the variability of network anatomy is small. Therefore, one aim of this work was to prove that
a functional cortical barrel column is also defined as an anatomical subunit with morphological features that are preserved from one animal to the next. This is achieved by
new high-throughput methods that allow determination of statistically valid samples of
anatomical data, such as the number and three-dimensional distribution of neurons and
neuron-types, as well as reliable tracings of dendrites and axons.
Previously used manual standard methods, like sparse-sampling or Camera Lucida-based
tracing, yielding neuron densities or morphology, respectively, proved to be time-consuming
and in some cases even misleading. For example, assumptions about homogeneity in neuron density were shown to be unjustified for S1, explaining deviating results about neuron
numbers in cortex in the past. Further, manual tracing of axons could only be performed
by expert users, making the tracing of a representative axon sample almost unfeasible.
The presented methods of NeuroCount and NeuroMorph are based on newly available
high-resolution mosaic/optical-sectioning microscopy and high-throughput automated image processing pipelines. Whereas NeuroCount is based on confocal image stacks that yield
sufficient resolution and signal-to-noise ratio (SNR) to detect neuron somata, TLB mosaic
microscopy lacks both, making automated tracing of axon arbors challenging. Therefore,
one essential part of the NeuroMorph pipeline is the improvement in resolution, especially
along the optical axis, and in SNR of weakly stained axonal structures. The characterization of the imaging system by Shack-Hartmann (SH) wavefront analysis and the resulting
optimization and deconvolution is hence regarded as the key prerequisite for the semiautomated tracing of widely spreading axonal arbors.
Yielding the same precision as their manual counterparts [61], [83], [29], NeuroCount and
NeuroMorph were used to determine the number and three-dimensional distribution of
172
Discussion
neurons in eight and five cubic millimeter large volumes in S1 and VPM, respectively.
This data resulted in an average columnar soma distribution and number of neurons per
VPM barreloid. Further, 78 dendrite reconstructions from S1, 5 axon reconstructions from
L5A pyramidal neurons and 14 VPM axons could be traced. Using standardization by
daVinci, classification by NeuroCluster and ultimately interconnection by NeuroNet, this
data is the foundation for reengineering the average thalamocortical lemniscal pathway. As
a result, ≈15200 full-compartmental excitatory cortical neurons, divided into eight types,
are interconnected with 285 thalamocortical VPM axons. The dimensions of the somatic
column are ≈390µm in diameter and 2mm in height. The total number of VPM synapses
for these 15200 neurons is approximately 2,8 million. The obtained number of synapses
per individual neuron, as well as their distributions resemble previous estimations and
measurements.
In addition, the cortical barrel column in S1 of four week old rats can be regarded as a well
defined anatomical unit. The described dimensions of the column correlate with higher
neuron densities and VPM axon innervation (i.e. synapse density). Further, the variability in neuron distribution and number is relatively small between individual columns. The
same is true for the number of neurons per barreloid. In addition, neuron tracings from
many different animals share characteristic geometry and shape and can hence be grouped
into anatomical neuron-types. The distribution of these neuron-types is preserved between
animals. In summary, the number of neurons per column, their three-dimensional distribution, their morphology and their VPM innervation are well defined and allow for the
reconstruction of an average cortical column in silico.
However, whereas the column dimensions are well defined by soma distribution and
VPM innervation, this observation is not true for the dendritic network. Figure 5.1 shows
neuron-type-specific VPM innervation volumes in comparison with their respective den-
Discussion
173
a
pia
WM
pia
WM
b
L2
L3
L4SP
L4SS
L5A
L5B
L6CT
L6CC
500µm
Figure 5.1: 3D neuron-type-specific VPM innervation volumes. (a) X/z-view of the
dendrite volume and its respective overlap volume with the VPM bouton distribution is shown
for each of the eight excitatory neuron-types in a cortical column of S1. (b) X/y-view. Whereas
the dendrite distributions laterally exceed the column dimensions (i.e. ≈ 390µm diameter), VPM
innervation volumes and hence synaptic connectivity resembles the columnar shape.
174
Discussion
drite volumes. This illustrates that VPM innervation determines the column dimensions,
but dendrites from neurons within a cortical column extend further into adjacent columns.
In consequence, I would argue that the reconstruction of an average cortical barrel column
connected to neurons from one VPM barreloid is justified. Nevertheless, it remains questionable if the ultimate goal to simulate neuronal activity within such a network model
will be feasible. I collaboration with Dr. Stefan Lang (IWR, Heidelberg) and Vincent J.
Dercksen (ZIB, Berlin) I am currently developing strategies of how such high resolution
network simulations should be approached.
Since the cortical column proved to be an anatomical unit with small variability, the
network morphology will be kept fixed for every simulation trial. Only the synapse distributions will be changed slightly from one simulation trail to the next. Injecting always the
same measured input to the network (i.e. number and timing of APs), simulation trials
will be evaluated by their network output (e.g. increase in spiking rates). Analyzing the
synapse distribution of trails that recover input/output relationships measured in vivo with
the remaining trails will potentially yield spatial and/or temporal constraints for synapse
numbers and position along dendrites. To accomplish such network simulations, four tools
need to be developed:
Synapse mapper The first tool to implemented converts neuron-specific synapse distributions into concrete realizations. First, each neuron-specific three-dimensional
synapse distribution is slightly altered for every trial. However, averaging across all
trials yields the original mean distributions. Second, each synapse is placed randomly
at a dendrite location within its respective 50µm bin.
Physiology tester The second tool needs to test each individual neuron for its electrophysiological properties. Neuron-type-specific HH-models are generated for each fullcompartmental neuron. By injecting standardized input to each single-cell model, it
Discussion
175
needs to be automatically evaluated if the response reflects input/output relationships measured in vitro or in vivo.
Synapse tester The third tool will activate every individual synapse and tune its EPSP
(i.e. excitatory postsynaptic potential) amplitude until a previously in vitro or in
vivo measured amplitude is obtained at the soma.
Simulation analyzer Once the previous steps yield individual ”functional” neurons, the
simulation of such a network will produce large amounts of four-dimensional data. A
100ms simulation of a cortical column most likely results in several hundred Gigabytes
of data per trial. Visualization and analysis of this data will prove to be great
challenge.
However, it should be mentioned that so far, three important issues for building the cortical
column network are missing:
1. At this stage the influence of interneurons is completely neglected. Even though they
just make up about 15% of the entire neuron population, their large variability in
function and anatomy [117], [146], will have a big influence on any network simulation.
However, there is no methodological reason that prevents from application of the
presented reconstruction approach in order to obtain the ”interneuron column”.
2. The here presented distributions of spines and boutons are estimated. Sparse sampling of spine numbers along dendrites and bouton numbers along axons resulted in
the here presented density values. These values are extrapolated to entire neuronal
trees. As for neuron somata, sparse sampling is only reasonable if the assumption
of homogeneous distribution is justified. In cooperation with Thorben Kurz (MPIN,
Munich), Dr. Kurt Saetzler (University of Ulster) and Dr. Stefan Lang (IWR,
176
Discussion
Heidelberg) I am currently working on methods to determine the absolute number
and distribution of spines and boutons along large portions of dendritic and axonal
branching patterns, using SBFSEM [145].
3. So far, there is no reliable data about ion-channel distributions for any neuron-type
available. Hence, full-compartmental HH-typed models for individual neuron-types
are usually developed by a reverse engineering. There, single neurons are physiologically classified in vitro or in vivo and their morphology is reconstructed. Conversion
into full-compartmental HH-typed models and fitting of channel distribution parameters can then yield neuron-specific models that reproduce the measured physiological
behavior. However, this tedious approach is just described for very few neuron-types,
one being L5B pyramidal neurons [147], [148].
Nevertheless, even though the described three issues need to be addressed before the reconstructed network can really be called a cortical column in silico, the here presented toolbox
and results mark first necessary steps for reengineering and simulation of anatomically realistic neuronal networks. Further, first interactions between individual neuron-types might
already be simulated and analyzed at this stage of reengineering. I would argue that the
fast activation of L5B neurons by VPM input could already be simulated with the here
presented network model. This argument is based on three reasons:
1. The input/output relationship due to passive whisker deflection is well described [10].
≈60 nearly synchronous APs originating in one VPM barreloid cause an increase in
supra-threshold activity in L5B neurons by ≈10 fold within the first 20ms after
stimulus.
2. The physiology of L5B neurons is well studied by a large variety of in vivo experiments
and resulted in a detailed HH-model for L5B neurons, which reproduces linear and
Discussion
177
non-linear properties of dendrite computation [149], [150].
3. The number of ≈1100 neurons, directly activated by ≈300000 VPM synapses within
20ms, reduces the complexity of simulation by one order of magnitude, respectively, when compared with the entire column (i.e. ≈15000 neurons, ≈2800000 VPM
synapses, 100ms).
However, simulation of lemniscal thalamocortical input, even for all eight neuron-types,
will certainly not be sufficient to unravel the mechanistic principles of how decision making is triggered by the cortical column network. Specifically, the here presented VPM-S1
microcircuits form just a starting point for the reengineering of the single whisker pathway.
As demonstrated for L5A neurons, intracortical wiring exceeds the complexity of these
thalamocortical microcircuits by several orders of magnitude. Therefore, in collaboration
with Dr. Christiaan P.J. de Kock (VU Amsterdam) I started to reconstruct representative
samples of axon morphology from all excitatory neuron-types in S1. Such intracortical axons spread much further than the lateral dimensions of one cortical barrel column. Hence
interconnection of multiple adjacent columns (e.g. a 3x3 grid) will be inevitable, increasing
the complexity of the network.
Further, corticothalamic and other subcortical projections from S1, as well as thalamocortical input from the POm need to be investigated and ultimately incorporated into the
network model. In cooperation with Mike Hemberger (MPIN, Munich), I already started
reengineering the VPM-RT inhibitory feedback loop, which is responsible for the exact
timing of columnar VPM input.
In general, the here presented strategy is to reengineer any observed microcircuit between
two neuron populations, verify its functionality and then add on the next circuit. Ultimately, this might produce a network model of a cortical column containing multiple
178
Discussion
intracolumnar circuits, which is embedded into intracortical microcircuits with adjacent
columns, thalamocortical circuits from VPM and POm, intrathalamic circuits between
VPM and RT, corticothalamic feedback circuits and subcortical microcircuits.
The here presented methodological pipeline describes a way of how this long time goal
might be achieved. Tracing of S1 axon morphologies, quantification of the resultant projection domains and characterization of these circuits will result in a step-by-step network
building process. However, I would argue that the here presented approach is not limited
to the somatosensory whisker system of rats. Functionally and anatomically well defined
networks are found in many brain regions across species. For example, insect brains display very stable network anatomy (e.g. visual system in flies) and similar approaches for
reengineering such networks are currently investigated [151].
Nevertheless, the barrel-whisker system in rats and mice is unique in mammalian brains.
Its segregated anatomical pathways, its relationship to single whisker input and finally its
direct link to simple whisker-evoked behaviors make it the ideal system for reengineering of
an average network. In general, neurons with similar interests tend to be vertically arrayed
in the cortex, forming cortical columns, throughout all mammalian species [152], for example in V1 of macaque monkeys [153]. Further, recent evidence points to generic circuit
motifs, present in primary somatosensory, auditory and motor cortex, secondary visual
and medial prefrontal cortex in rats [154]. Hence, the presented reengineering approach
might directly be transferred to columns in other cortical areas and species. However,
much more complex input patterns, as well as questionable stability of column anatomy
will be challenging.
In conclusion I would hence state that the here presented work opens new possibilities
to derive anatomical data from large areas of the brain with high accuracy. In case of
well-defined stimulus inputs and small variability of network architecture, this data will
Discussion
179
potentially allow the animation of electrical activity on average networks, which might
give some insight into the spatial and/or temporal constraints in synapse numbers and
distribution. These prerequisites are met for the thalamocortical part of the lemniscal
pathway in rats. Hence, as a first step in modeling anatomically realistic networks of multiple thousand full-compartmental HH-typed neurons, the simulation of direct activation
of L5B pyramidal neurons by VPM input could be approached.
However, whereas the scientific gain of such simulations remains open, the approach to
determine quantitative anatomical data, itself, produces many new insights into the organization and function of the brain. Specifically, inhomogeneity of cortical layers in S1,
deprivation-induced anatomical plasticity in thalamocortical connectivity in adult rats or
the complexity of intracortical projections from L5A pyramidal neurons would have not
been obtained, if this network reengineering approach wasn’t started.
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