Inverse Problems of Magnetometry

Inverse Problems of Magnetometry
CZECH TECHNICAL UNIVERSITY IN PRAGUE
Faculty of Electrical Engineering
Department of Measurement
Inverse Problems of
Magnetometry
–
Theory and Applications
DOCTORAL THESIS
2009
Jiří Tomek
Czech Technical University in Prague
Faculty of Electrical Engineering
Department of Measurement
Inverse Problems of Magnetometry
–
Theory and Applications
DOCTORAL THESIS
Ph.D. Program: Electrical Engineering and Information
Technology
Branch of study: Measurement and Instrumentation
Supervisor:
Supervisor-Specialist:
2009
Prof. Ing. Pavel Ripka, CSc.
Ing. Antonín Platil, Ph.D.
Jiří Tomek
PODĚKOVÁNÍ
Mé velké díky patří všem, kteří mě podporovali ve všech směrech a to
zejména psychicky, byť pochopitelně bez finančního zázemí by také nic být
nemohlo. Nástrah, překážek a problémů se vždy najde nesčetně a na mnohé je
člověk sám příliš slabý, tím se i tato práce stává týmovým dílem a to ne exkluzivně
jen co se týče přímých spolupracovníků na jejích jednotlivých částech. Těm
samozřejmě vděčím za mnohé.
Při dokončování práce nastaly navíc komplikace nepředpokládané, spojené
s koncem studia, přinášející značné množství stresu. Zde zaúřadovali rodiče, má
úžasná přítelkyně a jistě i přes dva roky praktikovaná jóga, zřízená bývalou
spolužačkou a kamarádkou. Role kamarádů a kolegů na pracovišti, ale i milých
známých, je rovněž nezastupitelná.
Není možné zde zmínit všechna jména, vděk patří všem kolem mě ☺ I těm,
co si myslí, že ani nějak významněji pomoci nemohli.
Za nedocenitelnou pomoc při opravách faktických, formálních a jazykových
velice děkuji Pavlu Ripkovi - svému školiteli, Antonínu Platilovi a Harveymu
Cookovi.
ACKNOWLEDGEMENT
My great thanks belong to everyone, who supported me in any way but
primarily psychologically, though without the financial backing there would also be
nothing. Innumerous constrictions, obstructions and problems always turn-up and
one is too weak to cope with them alone, thus they made this work a team product
and not just in means of taking into account the direct co-workers dealing with
particular tasks, to whom I am bound for much.
During the completion of this work some unexpected complications arose
with the end of my studies, bringing a dose of stress. Here, my thanks go mainly to
my parents, to my wonderful girl-friend and certainly also to yoga, which I have
practised for more than two years and which was established by my friend and
former classmate. A great part was also played by my friends and my helpful
colleagues at school.
It is impossible to name all the people here. My thanks go to everybody
around me ☺ even to the ones who think that they could not help significantly.
Many thanks for invaluable help with corrections of the thesis - issue-of-fact
ones, formal ones and in language go to my supervisor Pavel Ripka, Antonín Platil
and Harvey Cook.
Doktorská práce vznikla ve spolupráci s těmito institucemi:
The research was performed in collaboration with the following institutions:
Veterans Research Foundation in Oklahoma City, USA
JanasCard – Ing. Vojtěch Janásek, CSc
Výzkum (a)nebo autor disertace byli finančně podpořeni následujícími granty:
The research and/or the author of the thesis were funded by:
Kontakt Me756 (2005-2007)
CTU 06 10-86216 (2006)
Fond ČVUT, CTU foundation (2006 a 2007)
Výzkumný záměr MSM6840770012 "Transdisciplinary Research in the Area of
Biomedical Engineering II"
Introduction
Jiří Tomek
Contents
1.
INTRODUCTION...........................................................................................1
1.1
2
ORGANISATION OF THE THESIS ......................................................................1
STATE OF THE ART ....................................................................................3
2.1 CONTACTLESS MEASUREMENT OF DISTANCE .................................................5
2.1.1
Electronic devices in medicine.............................................................6
2.2 MEASUREMENT OF MAGNETIC MOMENT ........................................................7
2.2.1
Measurements of the magnetic moment of solid samples containing
magnetic materials ...............................................................................7
2.2.2
Magnetic field of the lungs...................................................................8
3
OBJECTIVES .................................................................................................9
3.1 RESEARCH TASK I..........................................................................................9
3.1.1
Magnetopneumography......................................................................10
3.2 RESEARCH TASK II.......................................................................................10
3.2.1
On-demand gastric pacer – basic analysis ........................................11
3.2.2
Volume measurements for AGES (Active Gastric Electrical
Stimulation)........................................................................................12
4
MAGNETOPNEUMOGRAPHY (MPG)....................................................13
4.1 MAGNETIZATION PROBLEM - AN ELECTROMAGNET .....................................13
4.2 SCANNING DEVICE .......................................................................................15
4.2.1
Probe setups & noise .........................................................................20
4.2.1.1
4.2.1.2
4.2.1.3
4.2.1.4
Separate (reference) gradiometer sensing the outer fields ......................... 21
Probe array ................................................................................................ 23
More coaxial first order gradients ............................................................. 24
Higher order gradients, averaging, statistical analysis of the field in the
measurement region and compensation..................................................... 34
4.2.2
Video controlled positioning ..............................................................34
4.3 FORWARD MODELLING ................................................................................35
4.4 INVERSE PROBLEM .......................................................................................36
4.4.1
Basic overview of some techniques ....................................................37
4.4.1.1
4.4.1.2
4.4.1.3
4.4.2
4.4.3
4.4.3.1
4.4.3.2
4.4.3.3
4.4.3.4
Neural networks ........................................................................................ 39
Automatic differentiation of the forward model for optimization ............. 40
Newest optimization methods ................................................................... 40
Estimation of total dust load ..............................................................41
Neural network inversion in MPG .....................................................47
Restraints & limitations............................................................................. 47
Localized sources ...................................................................................... 48
General problem........................................................................................ 54
General problem with more scanning planes............................................. 59
4.4.4
More probes & fitting to model function............................................68
4.5 DISCUSSION .................................................................................................68
5
MEASUREMENT OF THE STOMACH VOLUME.................................71
5.1
THE TASKS ...................................................................................................71
Introduction
Jiří Tomek
5.2 METHOD...................................................................................................... 71
5.3 OVERVIEW OF SOME APPLICABLE METHODS ................................................ 72
5.4 IN-VIVO APPLICABLE SYSTEMS .................................................................... 78
5.4.1
First version....................................................................................... 78
5.4.1.1
5.4.1.2
5.4.1.3
5.4.1.4
5.4.1.5
5.4.1.6
5.4.2
5.4.2.1
5.4.2.2
5.5
6
Summary ................................................................................................... 78
The principle of the sensors and the system .............................................. 79
How it is designed and made..................................................................... 83
Final measurements ................................................................................... 88
Practical application on laboratory animals............................................... 90
Possibility of a three-axial probe introduction........................................... 98
Second version – tri-axial system .................................................... 105
Practical application on laboratory animals............................................. 106
Examples of the in-vivo measurements ................................................... 107
DISCUSSION............................................................................................... 109
CONCLUSIONS ......................................................................................... 111
6.1
6.2
ACHIEVED OBJECTIVES.............................................................................. 112
OUTLOOK .................................................................................................. 113
7
REFERENCES ........................................................................................... 115
8
APPENDIX.................................................................................................. 122
8.1 PUBLICATIONS .......................................................................................... 122
8.1.1
Articles in SCI journals ................................................................... 122
8.1.2
Papers in other journals .................................................................. 122
8.1.3
Papers in international conference proceedings ............................. 122
8.1.4
Papers in other conference proceedings.......................................... 122
8.2 ABBREVIATIONS ........................................................................................ 122
Introduction
Jiří Tomek
1. Introduction
In general, an inverse problem can be considered as an interpretation of
measured data (e.g. magnetic field values) for the purpose of finding sources (or
information about them) creating, for example, a tested field. The determination of
sources plays crucial role in all branches of science. Everyone wants to interpret
measured data sets and wants to know their sources, no matter if some background
or “a priori” knowledge is available or not, we have or do not have the domain of
the possible solutions or whatever solution-specifying information. What is more,
the inverse problems are usually ill-posed (under-determined), which means that
more variables should be assessed out of a small collection of measurements. Thus,
any realistic solution has to first match various constraints and empirical knowledge
of the specific problem. Solutions are usually obtained iteratively, not in one step by
mathematical calculations. In case of an electromagnetic field, which we are going
to deal with, there is inherent non-uniqueness arising from the basic definition given
by Maxwell’s Equations (partial derivatives, thus the constants of integration).
Definitely, the subject of this thesis is not the argumentation about the fundamentals
of physics and proven theories, the aim is to try to show, on two different cases,
how I, together with my colleagues (and others), coped with the inverse problem of
magnetometry. The primary target will be thus forward modelling necessary for the
simulation of the problem, the methodology and the software for the realization of
the inversion, in which a number of estimated parameters depends strongly on the
amount of acquired independent data. This thesis is not focused too much on the
sensors and their principles. However, to a certain depth it is necessary to reveal
even this aspect as the methods depend partially on the means of data acquisition.
Therefore, processing electronics and software are to be discussed too.
One relatively small problem is going to be solved. It is severely limited by
the feasible set of hardware that could be utilized, as it is intended as an implantable
device in human medicine; therefore, the dependability and the ease of surgery are
the main goals. Another problem, on the contrary, is a bulky one, comparable in
size with the problems solved in geoscience and also in the disciplines of medical
imaging, within which in fact it falls. It utilizes a DC field, though in the established
applications, alternating fields are mostly employed. Measurement techniques and
sometimes even inverse strategies, which are the main target, are thus different than
those we can utilize in this static problem.
1.1 Organisation of the thesis
The work is written as an accompanying text to scientific publications that
were issued in reputable journals or submissions to journals that came from papers
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Introduction
Jiří Tomek
in international conference proceedings. I have rewritten and included a report to
our US partner - demanded for the purpose of a new US grant application - and also
included the scientific parts of the final report of an international grant from which
comes the second presented application described in this thesis. The scientific
papers and respective documentation pieces are inserted into the corresponding
chapters.
The thesis consists of four main chapters besides this one and the concluding
section. The following Chapter 2 is devoted to the magnetic measurements with
respect to the inversion aspect. It also mentions several branches of science using
the respective state-of-the-art inversion methodologies and tries to provide
background information for the applications described later. Chapter 3 reveals the
motivation and objectives of the thesis. And then, in Chapter 4, comes a complex
problem of magnetopneumography with the description of our experiments (probes,
their configurations, positioning device, magnetometers and processing software)
and the development in the inversion strategy, while dealing with the project. The
next Chapter 5 is devoted to a relatively easier grant task being concurrently solved.
It deals with an implantable device enabling the measurement of the distension of a
stomach wall. The main challenge was, naturally, the practical application and the
selection of the most effective solution to track the wall relaxation and motility.
Besides the chosen method and the in-vitro experiments, the sensors and processing
electronic units as well as several in-vivo testing results will be described there also.
Finally, the conclusion is provided in the last chapter, which summarises the
whole work and proposes the tasks to be dealt with next.
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2 State of the Art
Inverse problems, i.e. the determination of certain parameters of sources out
of the measured data, are one of the basic tasks of measuring processes. In
magnetometry, the interpretation of the data is usually not trivial. Usually, we have
the problem posed badly and there is an inherent non-uniqueness of D and H
coming directly from Maxwell’s Equations that describe electromagnetism. In case
of magnetostatic measurements, further problems turn-up, especially in the case of a
general problem, where we do not know the direction of magnetization of the
sources, etc. [Shearer 2004, Lelièvre 2006, He 1998, Forsman 1998]. We are
speaking about the non-uniqueness of the inversion as there can be a number of
solutions for the acquired data. [Shearer 2005] speaks about the concept of nonuniqueness such that a particular set of the observed data could be reproduced by an
infinite number of models. Such a complication arises because there is a finite
amount of inaccurate data describing the subsurface. To support the idea, she cites
[Menke 1989; Parker 1994 and Scales 1997]. This non-uniqueness may be
overcome to a certain extent by simplifications and empirical knowledge
incorporated into the models.
The scanning of the magnetic field or its point measurement is used in many
branches for the purpose of determining some information. There are several
applications in geosciences, such as metal ore location. Additionally, many
applications are in industry, including flux leakage inspections or eddy current
testing of imperfections or cracks in metals. Others still are plenty of applications in
medicine. Many methods are still in the stage of research like MEG
(Magnetoencephalography), MCG (Magnetocardiography) as well as MPG
(Magnetopneumography) which we are also going to deal with. A method that is
widely used in non destructive testing of metals and experimentally in medicine is
MIT (Magnetic Induction Tomography), which is an imaging technique used to
show electromagnetic properties of an object by using the eddy current effect. It is
also called electromagnetic tomography (EMT), eddy current tomography or eddy
current testing [Griffiths 2001, Telford 1976, Korjenevsky 2000]. Another one still
more or less an experimental medical application, is the measurement of
susceptibility for the determination of iron retention in the liver. Though the
detected fields are also low, as in the case of MPG, it can even be realized by a
room temperature device [Avrin 2007], however cryogenic superconducting
quantum interference devices (SQUIDs) are more established, e.g. [Carneiro 2002].
On the contrary, one very effective application has been commonly used for more
than a decade, NMR (Nuclear magnetic resonance) or more often called MRI
(Magnetic Resonance Imaging), which belongs to the best imaging methods in
medicine.
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The fields used by the above mentioned methods vary a great deal, anywhere
from fT of the fields created by the human body sensed by SQUIDs to the present
7T steady field electromagnets of the NMRs with extremely good resolution.
The measurement of magnetic fields is excellent for the possibility of noninvasive contactless examination of sources; moreover, there is no clinically
detectable adverse effect on human health. There are even appliances for
magnetotherapy based mainly on an AC magnetic field. This work also
concentrates on applications of contactless magnetic methods in biomedicine and
deals with the inverse problem
Inversion in magnetometry depends on the known parameters of the sources,
which are usually reduced to discrete magnetic moments representing a certain
volume of the examined object. Measurements of magnetic moments (either DC or
AC) can be then divided into the following basic cases, according to the parameters
of the moments - magnitude (strength), position and orientation. At first, let us
concentrate on the case that we have a single magnetic source:
•
The magnetic moment of the source is known (both size and its orientation)
– we can measure the distance by a single coil.
•
Just the magnitude of the moment is known, but not the orientation – the
distance cannot be measured precisely without an array of detectors, but
e.g. when sensing the vector of its field, the distance can be determined
with maximum error less than 26% (the base is the smallest distance from a
dipole with given field intensity), as the difference between the intensities
of signals that can be measured in the 1st and 2nd Gaussian position is one
half, thus the proportionality constant is 3 2 , thanks to the cube inverse
proportionality between the measured field and the distance from a
magnetic dipole.
applied in the measurement of the distension of the stomach wall
for determination of the volume changes for the purpose of active gastric
electrical stimulation (AGES) – obesity treatment method – see Chapter 5.
•
The position of the moment is known as well as its orientation – the size is
measured precisely
used e.g. in perhaps one of the most interesting medical
applications: MRI (Magnetic Resonance Imaging) where the position is
given by different Larmor frequencies in voxels given by gradients of the
strong DC field and by phase coding.
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Inverse Problems of Magnetometry
•
Jiří Tomek
Position of the moment is not known, but we know its orientation – the
estimation of the size and position of the measured moment is possible
depending on the measured field maps of the moment
applied in Magnetopneumography (MPG), but there is usually a
need to determine more than one moment. However, even determination of
the total moment of the ferromagnetic particles in the lungs may be useful.
This was my first goal in the task concerning the MPG (Chapter 4).
More moments have to be determined by some optimization
procedure, which is dealt with in the latter parts of Chapter 4.
•
Nothing is known about the moment, altogether there are all six degrees of
freedom (3 for position in space, 2 spatial angles for orientation and 1 for
size). For the detection arrays of sensors are needed.
This is the most general case applied e.g. in tracking of magnetic
markers in space or the centre of the electrical activity responsible for some
simple action in the MEG. Such general problems are solved for multiple
moments e.g. in geoscience.
2.1 Contactless measurement of distance
As the above states, the examination of the magnetic field is usually
performed in order to determine the distance of a source or distribution of sources
from a measurement probe or from their array. Such contactless distance
measurement is important in analysing the vibration, alignment, position or
bending. It is practical in applications, where the motion of an object would be
damped or otherwise affected by a coupled mass or force exerted by a measurement
device; when sensitive surfaces must not be damaged; or when rapid motion must
be tracked or simply when tested objects cannot be removed and measured another
way like it is with magnetic particles deposited in the lungs. Such testing and
measurement tasks are commonplace in research and development, automation,
quality control, machine control applications and naturally in various biomedical
applications.
Besides the magnetic field, other phenomena are often utilized for contactless
testing including: ultrasound, capacitive principle, optical triangulation or
interferometric principle, etc. Magnetic phenomena are based on the inductive
principle (induction of the voltage in a sensing coil), the induction principle (change
of induction of the magnetic circuit e.g. eddy current principle, etc.)
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2.1.1 Electronic devices in medicine
As I am going to deal with applications for medical purposes I would like to
add more details about this branch. There is a relatively long history of biomedical
applications of electronic devices from simple ones like digital thermometers to
high resolution functional MRI (Magnetic Resonance Imaging) devices. Now we
cannot even imagine specialized medical investigation without the use of
sophisticated imaging instruments like an ultrasound, a CT (Computed
Tomography), an MRI, a SPECT (Single Photon Emission Computed Tomography)
and many others. Between these diagnostic imaging methods we could classify
even an MPG which we are going to deal with in Section 3.1. MPG is in the stage
of experiments, on the one hand with extremely sensitive but expensive SQUID
technology, on the other with not such sensitive types of sensors like fluxgates. It
has just been used for several studies of workers e.g. [Zheng 2004] and mostly for
estimation of the total amount of dust in lungs e.g. [Huvinen 1997] so it is not as a
pure imaging technique. But there is still continuous progress. The development in
the sphere of implantable devices is more rapid. They sometimes incorporate quite
complicated electronics and firmware. When just counting the commonly used
ones, not various intensively developing artificial organs, there are pacemakers
[Mediline Plus] and cochlear implants (a detailed description of the development at
[Tomek 2004a]). Nevertheless, just the devices in development or research employ
sensors for distance measurement, usually as a control or for feedback of their
function or as a kind of switching mechanism or measurement of deformation, etc.,
e.g. in measurement of the deformation using laser triangulation in dentistry [Lukas
2001].
Use of implants naturally struggles with the biocompatibility of used
materials and their mechanical and chemical durability. No one is surprised when
the implants use noble metals and materials that arise from space exploration, thus
manufacturing them is expensive not just because of the sophisticated electronics
and firmware inside and long development and testing time.
New methods of treatment of obesity [Chen 2004] and of gut motility
disorders [McCallum 1998, Ouyang 2003, Zhang 2006, Familoni 2006] plan to use
implants similar to cardiac pacemakers. For treatment of gastroparesis [Xing 2004],
a stimulating device and method of its use was already approved by the FDA (Food
& Drug Administration - USA) for ordinary treatment. A series of experiments have
been performed by several research groups with the stimulation of the stomach or
intestine [Zhang 2006]. Currently, there is also the task of controlling the
stimulation according to the food intake instead of the continuous operation of the
device, not only in order to save power of the implant but also to make its function
more effective and efficacious. Measurement of the distance in the abdominal
cavity is quite a challenging task, but it can be used not only in future obesity
treatment but can also help a great deal in gastric studies.
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2.2 Measurement of magnetic moment
The magnetic moment or magnetic dipole moment is a measure of the
strength of a magnetic source. In the simplest case of a current loop, the magnetic
dipole moment is defined as:
m = I ∫ da
(1.1)
where a is the area of the current loop. This is the definition for Ampere’s
magnetic moment. The direction of the vector of the magnetic moment is given by
the right-hand rule according to the direction of current (I) flowing through the
loop.
In the more complicated case of a spinning, charged solid, the magnetic
dipole moment can be found by the following equation:
m=
1
r × JdV
∫
2
(1.2)
Where dV = r2sinθ·dr·dθ·dφ (r, θ, φ are coordinates in spherical coordinate
system) is a volume element, r is the position vector pointing from the origin to the
volume element and J is the current density at the location of the element.
In case of a static magnetization M of a volume element we can integrate the
overall moment of such magnetized body using the expression (1.3).
m = ∫ MdV
(1.3)
2.2.1 Measurements of the magnetic moment of solid
samples containing magnetic materials
Among various applications, there are some used, e.g. in occupational
medicine to examine aerosols in the working environment – i.e. testing the
magnetic moment of ferromagnetic dust or fumes. An interesting biomedical
application connected to this task is the measurement of deposited dusts in human
lungs that have suitable magnetic properties. It is an examination method mentioned
several times before: Magnetopneumography [e.g.: Cohen 1975, Ripka 1997,
Forsman 1998, Tipek 2002, Tomek 2005a, Tomek 2006a], which was being
developed as a possible substitution of a less sensitive X-ray; moreover, it does not
load the patients with radiation.
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There are several possibilities how to measure the magnetic moment of the
solid samples containing magnetic materials (which we consider ferromagnetic
except for the last point) after their magnetization in a strong DC field:
•
Measurement (AC) in a rotating sample magnetometer in the case of small
samples usually up to 1cm3
•
Integration of induced voltage (semi-DC) in Helmholtz coils when rotating
the measured sample by 180°, according to Equation (1.4) [Trout 1988,
Stupak 1995, Tomek 2006]
mA =
u dt
Φ
= ∫
k H ⋅ µ0 k H ⋅ µ 0
(1.4)
•
Computation of the moment from the measurements of the magnetic field
(magnetic induction (B) or gradient of B) created by the magnetized
material. This method is, naturally, well applicable even on subjects in
medicine.
•
Measurement of the susceptibility of ferrimagnetic materials stored in
tissues by SQUID magnetometers [Brittenham 2003] or by utilization of
AC fields by a room temperature susceptometer of special design [Avrin
2007]. These methods are used, e.g. for the detection of an iron overload in
the liver.
It is possible not only to compute the total magnetic moment of the measured
sample but also using some inverse methods, to estimate the distribution of the
detected content in it [Tomek 2005a, Tomek 2007a]. This is the primary aim in
geological prospecting [Li 1996, Lelièvre 2003], MEG and of course in the already
mentioned Magnetopneumography.
2.2.2 Magnetic field of the lungs
Magnetopneumography as a non-invasive technique to measure the amount
of magnetisable dust deposited in the lung tissue has been or is still being dealt with
by the research groups of Högstedt [e.g. Högstedt 1995, Forsman 1998] Freedman
[e.g. Freedman 1982] Kalliomäki [e.g. Kalliomäki 1983], Bohákova [e.g. Boháková
2003 and 2006], Ripka [e.g. Ripka 1997 and 2000] and others. Their works have
proven its high sensitivity in assessing the amount of retained magnetisable dust
and in [Ripka 1997] even the applicability of fluxgate probes has been
demonstrated. In this thesis, we continue with the utilization of these sensors and
prepare new configurations. MPG could be used in examinations of welders, metal
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grinders or even miners. In most of the works mentioned, just the estimation of the
total dust amount based on various methods had been performed, e.g. mean value
and multipolar expansion methods [Forsman 1998]. Attempts were by Kotani and
Chiyotani and others with the multi-dipole model, however not providing stable
solutions [Kotani 1985]. Important to note are the works using SQUID
magnetometers, which provide a much higher sensitivity, thus do not need such
high magnetising fields [e.g. Boháková 2003 and 2006], however, not too much
accent is put on the estimates of dust distribution.
The problem of the non-uniqueness of the analytical solution to such
complex static magnetic problems [He 1998, Lelièvre 2003, De Lange 2003 and
Shearer 2005] leads to discretization of the space and utilization of multiple-dipole
models for inversion.
3 Objectives
The objective of this thesis is first to develop new methods of solving the
inverse problem of magnetometry and second to test them in two different
applications:
I. magnetopneumography, where the location and magnitude of the source
is not known, while its orientation is given by the static magnetization in
strong magnetic field.
II. distance measurement, where in general case only the magnitude of the
source is known.
The following text gives a more detailed description of the objectives together with
the motivation.
3.1 Research task I
During my study at CTU FEE I have dealt with the long term project of
Magnetopneumography (MPG). Our approach to the measurements is based on
fluxgate gradiometers used for mapping of weak remanent field of ferromagnetic
dust deposited in lungs. Nowadays, the project continues under the research project
Transdisciplinary Research in the Area of Biomedical Engineering II No.
MSM6840770012. The development of the methodology is mostly carried out on
verified models or in-vitro scans. We will describe primarily the progress in
scanning of potential patients and in suppression of noise from distant sources. A
lot of space is to be dedicated to the forward modelling and particularly to my main
task - inversion of the MPG data.
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3.1.1 Magnetopneumography
For the inversion in this task, we have adopted the idea of a multiple-dipole
model. We are going to describe successes using artificial neural network (NN)
models, including a novel approach of their application in a direct one step
inversion, not an iterative one mostly presented in literature. Promising results on
phantoms and computer models are to be shown. All this, except the last step
revealed, is in a relatively rough resolution and in small tested volumes. The most
recent work increases the examined volumes and shows the applicability of the
approach to a whole volume of lungs, though further steps are to be made to reduce
inversion artefacts, etc. The limits are to be revealed and the magnetic fields that we
can measure are to be described in details.
For the inverse task we need a perfectly working forward model as well as a
system for the real measurements to support and verify our results. During the
work, a special positioning bed has been built for subjects enabling the scanning of
field maps. Several setups of gradiometers for the bed have been proposed and are
to be dealt with here. Naturally, the computer forward models had to be improved
according to these configurations.
The main objective is definitely a complete experimental
magnetopneumographic system, which also includes an air-gap electromagnet for
magnetization of subjects. It is to be briefly described, including the models
intended for improvements of its construction to obtain a better homogeneity of the
magnetizing field.
For future automatic reading, or better determination of the scanning
position, we are going to mention first steps dealing with video tracking using a
camera and an appropriate system of control points in the view, as well as a small
array of six-probe gradiometers for the next generation of the scanning system that
should integrate our experience and enable in-vivo data inversion relevant even for
practise.
3.2 Research task II
As has been outlined the second focus of my Ph.D. study concerns
measurement of distance by means of a magnetic field. Particularly, it is a special
medical application of stomach volume/distension and motility measurement for the
purpose of active gastric electrical stimulation (AGES). This is proposed for obesity
treatment. This project was part of international grant of cooperation with a team of
Professor Chen from the Department of Gastroenterology at the University of Texas
Medical Branch who leads the research group of the Veterans Research Foundation
at the Veterans Affairs Medical Centre, Oklahoma City, dealing with various
studies of the gastrointestinal tract.
The targets are: working on the development of a gastric pacer that is
controlled by means of measurement of the elongation of the gastric wall
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proportional to the volume of the stomach and also to analyse the gastric motility
according to chymus (food content) composition - this especially for research
purposes. Unfortunately, the mechanisms of gastric wall function and also the
effects of various kinds of stimuli to different regions on its activity, are still not
well known [Zhang 2006].
The tasks in this part are to:
•
suggest a proper method of measurement of the stomach size and motility
using magnetic moment
•
design applicable implantable sensors that can be used during in-vivo
testing
•
test electronics that drives the sensors and process the measured data
•
develop software for data recording and further processing
3.2.1 On-demand gastric pacer – basic analysis
Continuous electrical stimulation still used in the research of our US partner
and other groups unfortunately results in the adaptation and resistance to stimuli
and so its efficiency gradually decreases. The proposed on-demand stimulation
should be more effective and less energy consuming. The final system should help
in the treatment of obesity and gastro-intestinal malfunctions. This idea is supported
by several previous studies of the American partner showing the positive effects of
chronic gastric electrical stimulation on weight reduction and on the gastric motility
disorders [Zhang 2006]. Chronic electrical stimulation led, in the case of healthy
animals, to the reduction of the daily food intake and therefore, may lead, especially
in obese subjects, to a significant weight reduction, without adverse yo-yo effects of
fasting or the not always long lasting effects of the gastric bandage [Chen 2004].
The problem is of course more complex, the diet has to be well-balanced in order to
provide all the essential nutrients. Obesity is unfortunately not just a matter of high
consumption but also of bad food composition and this device may only provide
help in the reduction of the food intake.
Similar to heart pacemakers, the surgery concerning implantation is miniinvasive and it does not intervene any organ except for small sutures on the outer
layer of the stomach wall; moreover, stimulation of the stomach wall by different
frequencies and voltages has been approved by the FDA for treatment of one of
gastric diseases - gastroparesis [Tomek 2009b].
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3.2.2 Volume measurements for AGES (Active Gastric
Electrical Stimulation)
Our US colleagues suggested, at first, ultrasound for the measurement of
the distension of the stomach; however they did not succeed because of the varying
speed of sound in different media, which was varying too much during operation to
get some relevant data for volume estimates. Another reason for the failure was the
large power consumption. We are going to reveal a method that uses magnetic field
sensors. Again it is based on the measurement of the distension of the stomach wall,
which provides information about the volume of the consumed food; furthermore,
the setup should give good enough signal for analysis of an action of the stomach
wall corresponding to different stages during the food intake. Electrical activity
beyond this movement can also be measured by EGG (Electrogastrogram), which
was analysed by our colleagues in parallel during our lab experiments in November
2007. The motility of the stomach is, however, quite complex and needs further
analysis. There is also some action without the food and before the meal, etc. For
more information, the reader should see some publications about Gastroenterology
[Friedman 2002, Butcher 2003] as this exceeds the range of this thesis
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4 Magnetopneumography (MPG)
Many publications are dedicated to Magnetopneumography, an experimental
diagnostic method for determination of ferromagnetic dust load in lungs. Some of
the papers of mine are included in this thesis, see Sections 4.2.1.3, 4.4.2, 4.4.3.2,
4.4.3.3 and 4.4.3.4. Others are just in the references [Tomek 2003, Tomek 2005a,
Tomek 2005b and Tomek 2007c]. Many others have been written by my former
colleagues e.g. [Navrátil 1999, Tipek 2002] and other teams as have already been
mentioned in Chapter 3. MPG deals with very weak steady magnetic fields, usually
detected by SQUID magnetometers however, it has been proven that fluxgate
probes can be utilized too, as the amounts of ferromagnetic particles in the lungs,
especially of certain heavy industry workers can reach several grams [Tipek 2002].
Much about this task is also written in the introduction of the paper in Section
4.2.1.3.
During the project several improvements have been made even with the
measuring system, which is going to be described in Section 4.2 and in the papers in
the further chapters. The set-ups exhibited many changes as well as the forward and
inverse models that were developed according to them or several times it was also
vice versa. The last and most progressive modification described in Sections 4.2.1.3
was inspired by a lack of data for the purpose of determining the problem and also
to study the fields of the measured sources more. Unlike the state-of-the-art in
geosciences, we do not have so much a priori information about the task which
could reduce the non-uniqueness of the badly posed inversion task.
In order to be able to measure content of the ferromagnetic dust in the lungs,
these dust particles have to be primarily magnetized in a strong DC field. This may
be performed in an electromagnet which was modified for this purpose already
during [Navrátil 1995]. Some modelling of the field of the magnet is to be revealed
in Section 4.1. When the subject or a phantom is magnetized we can perform
scanning on a special bed with a separate portal for fixing the probes arranged in
gradiometric configurations. These are described in Section 4.2. The crucial task is
modelling. Forward modelling is foreshadowed in Section 4.3. Inverse tasks in
general and our several approaches are the most extensive in Section 4.4., where my
most important published papers describing the work over MPG are also included.
4.1 Magnetization problem - an electromagnet
For several experiments with human subjects, we have utilized an
electromagnet for magnetization of the volume of their lungs. It is a big
electromagnet between whose pole pieces the subject can stand. The device is not
perfect for this purpose, because the created field is not very homogenous and even
not as strong as we would need. The picture of the electromagnet without insulation
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that was used during the magnetization of the subjects is shown in Figure 4.1 and in
Figures 4.2 and 4.3 the drawings of the device are shown. A photo during
magnetization of one volunteer is visible in the paper in Section 4.4.3.2.
Fig. 4.1. The electromagnet without insulation
Fig. 4.2. Top view cross-section of the
electromagnet [Hlaváček 2007]
Fig. 4.3. Side view of the
electromagnet [Hlaváček 2007]
During my doctoral studies two BSc. students dealt with the modelling of the
field of the electromagnet. The first one measured the field between the yoke ends
and tried a simple 2D extended model in Gemini [Hlaváček 2007] and the second
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one under my supervision has completed more valuable work in the 3D software
ANSYS and has also proposed one relevant modification of the yoke to obtain a
bigger volume of more homogenous and stronger field [Janský 2008]. Both these
works are included in an attached DVD (/Works).
4.2 Scanning device
In previous works [Navrátil 1999, Tipek 2002, Tomek 2003] a measuring
table was used, which was just suitable for measurements on models. I have
proposed and partially designed a glass fibre reinforced composite positioning bed
[Tomek 2005a]. It has been built and a great deal of testing and improvements have
been made during the four years of my cooperation on the research program No.
MSM6840770012 of the Ministry of Education of the Czech Republic - branch
concerning Magnetopneumography. This device is suitable for general use,
especially for measurements in vivo. It is modular, having several separable parts: a
table, a base module, a support frame, a bed, a portal in which tubes with probes are
fixed and a box for added weight screwed to the bottom of the portal. This weight is
there together with some rubber at the bottom to damp vibrations and to give
stability to the portal. The bed enables, without any problem, the scanning of
people, which has also been performed with several metal workers during practical
exercises with students at the faculty (Figure 4.4). Unfortunately, when considering
the application of our methodology on real data we have to say that we are still in
the phase of modelling and preparing of the methodology, so there is no
sophisticated interpretation of the data that were measured in-vivo.
Fig. 4.4: A scanned volunteer – a metal worker
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The bed is composed entirely of non-magnetic materials. In fact no metals
were used. The complete documentation that describes the construction, materials
and our testing of its magnetic cleanliness is in [Tomek 2005a], which is included
on the DVD (/Works). Utilization of glass fibre reinforced composites in
electromagnetic applications is quite common: the cases of the transmitting
antennas of broadcasters for cellular and wireless networks use these materials, etc.
One very famous application in the Czech Republic is also the housing of the
broadcasting tower on Ještěd. The material can have interesting properties
depending on its composition. Its matrix can be various fibres of glasses, carbon,
basalt, etc. and different resins are used as fillers: polyester, epoxy, vinylester, etc.
It can be light but extremely tough.
The original design had been substantially changed during the development
and construction, not everything was economically feasible or mechanically
optimal. The final concept is rational and meets the desired properties. During my
Ph.D. study there have only been changes made on the portal and naturally several
innovations of the gradiometers have been implemented. Schematic pictures
showing the main dimensions of the system are shown in Figures 4.5 - 4.7.
Photographs of some of the important parts are given in Figures 4.8 – 4.10 and on
the DVD appendix (/Photos). Detailed documentation is not part of this thesis and
can be found in [Tomek 2005a].
Fig. 4.5: The positioning bed – scheme[Tomek 2005a]
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Fig. 4.6: The portal [Tomek 2005a]
Fig. 4.7: Tubes for fixing the
sensors [Tomek 2005a]
The bed moves on rails in two axes using special, double helix, trapezoid
screws with a rise of 12 millimetres. The range of movement is 445 millimetres in
length (y-axis) and 460 millimetres in width (x-axis), which is enough for testing of
human lungs. The bed is laid on two rails placed on a frame that runs in four rails
embodied to the base, respectively to the square pultruded profiles. This layout
provides enough space for putting additional weight onto the base in order to
preclude movement during scanning.
The current portal can bear two tubes holding sensors or other equipment.
The sensors can be adjusted to the proper positions on glass fibre tubes elsewhere in
a calibrating field and then fixed to the portal without any disassembling of their
set-up. One of the tubes was intended originally for two probes that were measuring
the first order gradient [Tomek 2006, Tomek 2007a], but later we have introduced
four more sensors forming a coaxial multi probe gradiometer to pick-up more
information at once. This set-up can still use the same holder. Some gradiometer
can also be placed under the bed [Tomek 2009a] as it is magnetically “transparent”.
An array of the first order gradiometers based on the PCB fluxgate sensors [Kubík
2006, Janošek 2008] is planned as an option for the second generation of the
positioning device that has been recently built for a project in 2008 [Pribula 2008].
This needed a new stronger holder. The tube in it can be tilted by screws, into an
ideal perpendicular position independently from the base. All the sensors – an array
of them – may be fastened to the holding tube together with a camera on a new
boom enabling simultaneous adjustment of their height above the bed. The camera
is intended for tracking the position of the object on the bed, which was pioneered
even during [Nováček 2006]. Also some reference sensors can be fastened to the
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second tube. The system is quite versatile and enables various experiments and the
proper settings to the right distance from the measured object and a good
adjustment of the probes. In the case when we need more space above the bed, the
portal can be supported to a higher position as it is completely independent from the
positioning table. Separation was necessary to ensure the least amount of
transmission of vibrations caused by the moving bed, see Figures 4.8, 4.10. with the
old design of the portal. The damping of vibrations is solved by 4 centimetres of
rubber and the weight of 18 – 26 bricks that can be placed into the box base. This
also disables any unwanted movement of the configuration during the
measurements.
The bed is heavily ribbed and U-shaped to minimise deflections while the
test object or person is laid on. It moves on 6 wheels in two rows in rails on a strong
frame made from square profiles that has 8 wheels in 4 rows on the bottom side
moving in rails on supports on the base of the bed. The base is freely placed over a
sandwich table and secured by long margins of the base that overreach the table.
Manual scanning is very time consuming as in 1 centimetre resolution
there are 2025 positions so we use usually 4 centimetre resolution with just
144 positions. Actuators for automation could be added thanks to the design which
counts with that, but it is a rather complicated and expensive task. The number of
scanning positions can be sufficiently reduced using the intended probes’ array for
the mentioned project [Pribula 2008] together with the sophisticated video control
of the object’s position.
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Figure 4.8: Completed positioning bed, bricks just at the base of the portal, two
probes fixed to the holders and then to the tube
Fig. 4.9: Probe and parts of the holder used for the two-probe gradiometer
[Tomek 2005a]
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Fig. 4.10: Portal with the tubes, two sensors and boom [Tomek 2005a]
The product does not have many accessories for precise adjustment of
position of the portal, gradiometers or the bed, but it is a robust, rigid device that
can be easily set once and work without constant interventions, until a different setup is to be assembled.
4.2.1 Probe setups & noise
The most obvious problem of the performed weak magnetic fields’
scanning is the magnetic disturbances during the measurements for which the
utilized first-order gradiometric measurement is not usually sufficient (more on this
problem is also written in the paper [Tomek 2009a] in Section 4.2.1.3). This can be
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solved by the location of the lab faraway from the sources of disturbance, i.e. not in
the city but in the country side.
Better background noise suppression is possible with shorter gradiometric
bases (or baselines, i.e. the distances between the probes); however it is always a
question of optimization of the noise suppression and intensity of the wanted signal
from the considered source types [Braginski 2004a]. SQUID magnetometry (MEG,
MCG, etc.) can be a good source of inspiration how to deal with noise in such
medical applications thanks to extensive practical and experimental knowledge. The
principles are similar, but our sources are stronger and moreover, we do not have
shielding that is common to SQUID applications. The noise of the probes and
electronics itself is also higher. One of the main limits, why we cannot fully
automatically adopt the established MEG techniques is the fact that our sensors
contain high permeability materials and have compensating feedback. Thus, not
such short baselines and the presence of the sensors extremely close to each other as
in the case of SQUIDs are possible.
Higher order gradients realized by more coaxial probes can partially help
as well as having the same gradiometer placed as close to the measuring one but
also far enough away not to be affected much by the scanned object. Magnetic
shielding of the necessary size is very costly, so we have not even tried it.
Moreover, our aim is in fact a system that can be used elsewhere and will be more
or less movable.
4.2.1.1 Separate (reference) gradiometer sensing the outer fields
This is the method of using a reference gradiometer to suppress variations
of the background field. Together with the other methods it is extensively
described, mainly in the works devoted to SQUID magnetometry, e.g.
Magnetoencephalography [Vrba 2002, Vrba 2004 and Braginski 2004]. Some more
references are revealed in the paper [Tomek 2009a] in Section 4.2.1.3.
We have tried that with another first-order gradiometer placed about 1.5
meters (at the same height above the ground) sideways from the measuring
gradiometer in order to have a reference almost not influenced by the measured
object. Considering the distance, we cannot suppose that even with the same
gradiometer the detected gradients should be the same because of the nonhomogeneity of the field in the measurement region. This gradiometer was
supposed to track the background during the period of the measurement. By this
means, we could keep information about the level of the background gradient in
time and subtract it from the gradients taken over the objects.
It would also be necessary to optimize the distance and relative position to
the measuring gradiometer and to find the appropriate constants for the chosen sites
in the room as the fields are supposed to have different intensities due to the
different distances from the sources and different angles to them. This is a problem
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independent of the facts that the gradiometers are identical, properly aligned and
calibrated. The measured signals should be well correlated if we want to use such a
method. One overnight measurement presented at the conference OIPE 2006 is
presented. It shows a calm period between 1 and 4 o’clock in the morning, see
Figures 4.11 and 4.12. “Grad 1” is the signal from gradiometer over the
measurement node and “Grad 2” is the reference signal coming from the same
gradiometer 1.5 meters sideways. The distance between the probes of these two first
order gradiometers was 40 cm. One can observe an excellent correlation between
the signals, however the amplitudes are not the same and due to the different closer
sources of disturbances, there are significant differences in amplitude variations.
The situation would be far better in a place where the field is nearly homogenous,
like in the countryside away from ferromagnetic rocks or inside some shielding
system. We could consider a similar shielding as is used for SQUID MEG
(Magnetoencephalography), however it is costly. There is a question of
optimization of the distance between the two gradiometers and the distance of the
reference from the object. It is similar to the task of finding the best gradiometric
base between the probes of the individual gradiometers. Again, one can find much
about it in [Braginski 2004a], which is focussed on SQUID magnetometry.
This method has not been closely examined further until now, because we
have focused more to other perspective solutions.
-8
x 10
Gradient [T/m]
4
2
0
Grad 1
Grad 2
-2
19:00
0:00
5:00
Time [hr:min]
10:00
15:00
Fig. 4.11: Overnight measurement that maps the background field during the day in our lab.
The noisier the signal is from the measuring gradiometer Grad 1,the less noise comes from
the reference gradiometer Grad 2. In both tracks there is the calm period approximately
from 1 to 4 o’clock AM also reported in [Tipek 2002]. The differences are mainly due to the
different positions of the gradiometers in the room and slightly different alignment of the
sensors. Both gradients are filtered by a 0.67 mHz high-pass filter and a 30nT/m gradient
field has been added to Grad 2 in order to visually separate the two traces.
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-8
x 10
Gradient [T/m]
4
Grad 1
Grad 2
2
0
-2
4:50
4:55
5:00
Time [hr:min]
5:05
Fig. 4.12: Detail of the measurement, showing a perfect correlation of the signals
4.2.1.2 Probe array
An array of probes, respectively of the first order gradiometers, is one of
the key parts of the already mentioned ‘FRVŠ’ project for the year 2008. By
scanning of the interesting region in one moment with a well calibrated assembly of
sensors connected to separate channels of a new magnetometer based on
[Janošek 2007], we can get rid of the problem of magnetic disturbances in time,
however others arise. The sensors inevitably influence each other so we cannot have
the array too dense. Also, these probes contain ferromagnetic cores and work in a
compensating feedback loop cancelling the field in the core region as is discussed in
the paper in Section 4.2.1.3. The minimal cross-axial spacing of the sensors is
planned to be 2 cm and the standard one 4 cm, which still suggests several
successive readings in order to obtain a higher resolution. The optimum axial
distance, i.e. the gradiometric base, is to be determined experimentally while getting
the best ratio between the useful signal from the object and the background field
suppression [Braginski 2004a]. The details of the realization are subject to the
project itself and are available in the final report [Pribula 2008].
The main problem that remains is the non-homogeneity of the background
gradient field in the scanning region. Definitely, the map of the non-homogeneity
can be obtained by a number of measurements without the tested object and by
averaging. Averaging of the data obtained in a certain period of sampling during
examination is supposed to suppress the stochastic field variations satisfactorily,
however extending scanning time, which is problematic. We even plan to test an
array of gradiometers having more probes in one axis to measure in several heights
simultaneously and to test one method, revealed later on. It applies a mathematical
calculation of a magnetic field function for the tested object eliminating some noise
sources and to a certain extent also the imperfections of the probes alignment. The
suggested approach unfortunately needs, e.g. 6 or even more, sensors coaxially
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aligned over one scanning node (see next chapter). This alignment also enables the
further investigation of efficiency of a reference gradiometer technique discussed in
the previous Section 4.2.1.1.
4.2.1.3 More coaxial first order gradients
During experiments with a mathematical description of the fields above
the sources, we have come to an interesting idea having several benefits. If the
noise levels are not too high and affect the measured gradients almost equally, it
may help to separate the background fields from the desired close ones. The fitting
method revealed below provides a relatively simple description of the measured
functions (the decay of the field of the source with distance) and for smaller
compact homogenous sources, it directly calculates the position of such a source
even out of the measurements over a single node. Naturally, the bad homogeneity of
the background has the biggest effect on the performance.
We have built a coaxial six-probe gradiometer providing 5 successive first
order gradients. These gradients, above a magnetic dipole, should be described at a
given scanning node by a relatively simple equation based on the Biot-Savart law
[Fitzpatrick 2006] applied on Ampere’s magnetic moment of an ideal point source.
By means of fitting of the data acquired at a moment above one of the nodes, we
can mathematically derive what is the value of gradient due to the distant sources
that appear between the probes at that moment. This background gradient changes
in time as much as is reported in the Figures 4.11, 4.12. So when we are scanning
the map in successive steps, we need to keep the information about the background
or have to be able to derive it.
The presented configuration is quite effective. It preserves data from five
scanning heights above the measured object so there is much more data for
inversion with an acceptable resolution and we can still separate the level of the
additive field from background in scanning moments, thus the data may be less
biased. The truth is that in an ordinary environment, this component of the
background field is not the only one that disturbs the measurement. The fitting may
also suppress, to a certain extent, noise and differences from the ideal measurement
caused by the non-homogeneities of the field from the distant sources and
differences caused by the non-perfect mutual alignment of individual probes.
Something should also be written about the algorithm itself. In order to
obtain a good fit of the measured data by our function, appropriate initial conditions
have to be used. Otherwise the algorithm stops at the local minimum and the fitting
is bad. This is one of the features of the chosen Nelder-Mead procedure
[Rowan 1990, Bogacz 2003]. Some more sophisticated minimization method can
definitely be utilized, however, that would be a task for another work. With the five
gradients, a good fit is possible with just the parameters that are close to the ideal
solution. In the case of the total outliers (data too biased), the fitting performs badly.
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The most important thing is that such a gradient function can be found even for
sources that cannot be interpreted as dipoles because of the very short distances of
the closest probe from the phantom. The function is then the same for a fictive
dipole that would act as if the source fields were summed and located at an
appropriate distance.
The idea, configuration of the gradiometer and some supporting
experiments were published at IEEE Sensors 2007 Conference, Atlanta, Georgia,
USA and are dealt with more in the extended paper published in IEEE Sensors
Journal [Tomek 2009a] which can be seen on the following pages.
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IEEE Sensors Journal – accepted paper, 2009
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IEEE Sensors Journal – accepted paper, 2009
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IEEE Sensors Journal – accepted paper, 2009
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IEEE Sensors Journal – accepted paper, 2009
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IEEE Sensors Journal – accepted paper, 2009
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IEEE Sensors Journal – accepted paper, 2009
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4.2.1.4 Higher order gradients, averaging, statistical analysis of the
field in the measurement region and compensation
During the “Project in team” [Křížová-Huňka 2008, included on the
DVD/Works] we have been analysing the suppression of a strong disturbing
artificial field created by small Helmholtz coils, which were formerly intended to
create a field over distances where they could have been interpreted as a dipole.
However, the students have also experimented themselves with very short
distances, where the coils produced strong non-homogeneities of the disturbing
field. The six probe gradiometer has been used in the way reported in the paper in
Section 4.2.1.3, but with the averaging of several subsequent measurements of the
same phantom at the same node above it. They tried two approaches: Subtraction of
an averaged measurement without the tested phantom (i.e. just the background)
from the phantom measurement and calculating of the second order gradients using
the last gradient as the reference. The experiments would require more study, but
show that averaging and especially subtraction of the averaged gradient levels
without the presence of the phantom seem to be more helpful than we have
assumed. Unfortunately, some compromise between scanning time and acceptable
noise would be necessary. The length of scanning has to be cut down for real
applications at least because of various artefacts and gradual decrease in the
remanet field after magnetization of the subject. An array of gradiometers should be
introduced if we wanted to adopt longer term averaging to suppress the background
variances. It should be clearly stated that all the presented testing utilizes averaging,
but only by means of the integration times of the ADC that were 0.2 s or 2 s, not by
averaging of a defined number of readings.
4.2.2 Video controlled positioning
For better repeatability of the measurements and especially for optimal
placement of the subjects and tracking of their movement on the bed in the
examination area, we have proposed to use a camera and image processing tools to
determine the relative position of the object to the probes.
The first step has been completed during the thesis [Nováček 2006]. Further
work with a higher resolution CMOS chip and software including calibration based
on the fixed points (spot lights or reflex reflectors) in the scene was made during
[Pribula 2008]. Utilization of the camera is going to eliminate the positioning errors
caused by the subjective reading of the meters and errors caused by accidental
displacement of the bed or the portal. Three non-colinear spots on the moving bed
would be sufficient for calibration as well as to reveal any displacement. This is
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possible only if the camera is fastened to a tube on the portal, i.e. having rigid
connection with probes. If it is independent, also the portal position has to be
tracked. In order to keep the distance of the camera the same from the measured
object, the construction plan is to have the camera and the probes on a single tube
that can be moved in the portal vertically in the necessary range, i.e. a subject with a
bigger chest will need the probes higher above the bed and the focus of the camera
has to also be higher by that distance, because we are tracking the subject not the
bed below him.
4.3 Forward modelling
The most crucial part of most inversion techniques besides obtaining proper
sets of data, is to develop a good forward model of the examined problem. Usually
we need to make a computer model that replaces our physical measurements for the
purpose of generation of representative sets of measurements that could be
processed to obtain the inverse model or very often to use it to determine the error
for the calculated measurement of the certain estimate of the sources while using
iterative approaches. The model quality has to be proven by several sets of physical
measurements. The forward model is an excellent tool for analysis of the
possibilities of various inverse processes or for modelling of the efficiency of the
different measurement setups, i.e. whether more information from scanning (data in
better resolution or from different sensors layout) would be more effective, etc. It
enables one to first simulate various experimental configurations before choosing
improvements of the older setup that should be realized physically.
The model we use utilizes an ordinary summation of fields of point dipoles
representing the total magnetic moment of the lungs in discretized voxels each
having a volume of 8 cm3. We apply the Biot-Savart Law to calculate the fields.
The software has formerly been programmed in Matlab even during [Tomek 2003]
but many significant improvements have been made during my Ph.D. studies. For
details, see [Tomek 2006a, Tomek 2007a] or an older version in [Tomek 2005a])
and the code on DVD appendix (/Software/Matlab/ForwardMPGsolver) The
described approach was mainly chosen for better versatility of the model and better
applicability in the inversion which is not the primary purpose of the specialized
software for FEM (finite element modelling) like ANSYS and COMSOL or others.
The problem itself is not very complicated thanks to the measurements in air and of
non-magnetic tissues, which have susceptibilities almost zero. The created PC
solver is in perfect accord with the physical measurements, as is confirmed by the
included papers in Sections 4.4.3.2 and 4.4.3.3 and also in [Tomek 2005b]. The
forward problem is unique thus, it is possible to create a weight matrix using the
solver for a defined distance or distances of the probes from the phantom and make
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the field calculation without program cycles, thus, the quickest possible. We can
also use tools like artificial neural networks [Tomek 2005a], etc. However, in our
case multiplication of a proper weight matrix by a vector describing the source
seems to be the ideal method. Such a matrix can be can be implemented as a fast
solver for the purpose of an iterative optimization, e.g. using genetic algorithms
(GAs) see the paper in Section 4.4.3.4 [Platil 2008]. The program for GAs has been
created by the co-author.
The described matrix can be obtained using the phantom model. Imagine that
we put a single magnetic cube having a magnetic moment of one unit to the first
phantom position. This creates the respective unit field matrix that we scan. This
matrix is then reshaped to the first row of the weight matrix. This is done for all
possible cube positions, so we obtain unit constants of the scanned magnetic field in
all scanning positions we need, meaning the complete weight matrix. When such
constants are multiplied by the respective moments of the cubes of the phantom and
summed up at the respective scanning nodes we get the right simulated field data.
For a mathematic explanation of the process, again see the paper [Platil 2008] in
Section 4.4.3.4.
4.4 Inverse problem
The inverse problem, as we have it defined here, i.e. the determination of the
sources of the measured signal no matter if on a DC or AC base, is usually solved
as an optimization task, if there is no direct mathematical solution. Inversion of
such complex magnetic data that we have in this case, is unfortunately non-unique
and not only because of the fact that we have a smaller set of measurements than is
the number of sources to be determined. This comes from the inherent nonuniqueness of D (electric flux density) and H (magnetic field intensity) in
Maxwell’s Equations [De Lange 2003, Li 1996] thus, the range of the possible
solutions has to be limited by the constraints of the model and a priori knowledge,
like the positivity of susceptibilities, no thin layers of high susceptibility, etc.
Experience with the characteristics of the given problem is thus crucial. An
overview of various techniques applied mostly in geophysics can be found, e.g. in
[Oldenburg 1990, Lelièvre 2003]. The more data and conditions of the problem we
have and incorporate into our models, the more it reduces the available degrees of
freedom. This is, e.g. the reason for utilization of measurements in several layers
above the tested object revealed in Section 4.2.1.3. Most of the other theoretical
aspects of our DC MPG inverse problem has also been revealed in [Tomek 2005a at
DVD/Works] to which I would like to refer the reader for more details.
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Our problem even when discretized in relatively rough resolution is not well
conditioned; furthermore, there is the mentioned non-uniqueness of the magnetic
inverse problems generally. We have added more scanning heights reducing the
number of degrees of freedom or we even have reduced the region where the
possible source unit could be calculated in case of the general solution (3D
inversion of a model containing multiple sources, which are randomly distributed).
In the task of the general problem, we have performed experiments that imply the
possibility to obtain a good solution by means of direct inversion utilizing
multiplication of the measured values in each scanning node in each layer (height)
by their respective weights. The basic idea is to calculate an inverse matrix and use
it for the inverse calculations. The computation then enables one to compose the
right value of the respective magnetic moments in the voxels of the lung phantom.
These weights can be found by the Least Square Method utilizing the Singular
Value Decomposition (SVD), such a technique is common for linear neural
networks, which we have tested several times on smaller problems. The idea has
unfortunately serious mathematical and computational limitations as the data is
bulky. Little bit better results are supposed after forcing the positivity of the
magnetic moments. However, this needs non-trivial modification of the process.
One idea is to also experiment with this tool iteratively. The method is further
described including several experiments in Section 4.4.3.4.
Some problems, not having much clear interpretation or being as bulky as
ours, are solved by artificial neural networks (NNs) very often or other evolution
algorithms or iteratively by various techniques. Neural networks have been thus
extensively examined, partially also genetic algorithms, again see paper [Platil
2008] in Section 4.4.3.4.
4.4.1 Basic overview of some techniques
In practice the inversion of magnetostatic data is widely used in geology [Li
1996, Lelièvre 2003, Shearer 2005], in some non-destructive testing [Chelouah
2000, Pechenkov 2001, Ramuhalli 2002], in detection of metal objects either in
industry or e.g. in some landmine locators and several other applications. An
alternating field is utilized much more often. Many such applications are again, in
non-destructive testing, based either on eddy-currents or flux leakage, but great
research in this field is taking place in medicine: in Magnetoencephalography
(MUSIC algorithm [Mosher 1999, Juany 2007], an explicit identification method
for electric dipoles in a conducor [Popov 2002]), examination of iron in the liver
(biomagnetic susceptometry based on SQUIDs) [Carneiro 2002, Brittenham 2003],
a technique called magnetic induction tomography (MIT) [Korjenevsky 2000,
Merwa 2005 is also being developed].
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We can think about three concepts of solving inverse problems:
o Direct mathematical solution if we can derive the proper formulas
o Iterative optimization procedure
o Evolution algorithms (NNs, Genetic algorithms…)
The iterative optimization procedures utilize many specialized techniques to
search for the optimal solution. Some are gradient based, where it is usually
necessary to know the first and also mostly the second derivative of an error
function, others do not need such information. Some guarantee finding of the global
extreme of such a function, thus the best possible solution, others unfortunately not.
Examples of the optimization techniques are e.g. Nelder-Mead technique (one of
the simplex methods) [Lagarias 1995, Chelouah 2000] which does not need the
derivatives or BFGS (Broyden-Fletcher-Goldfarb-Shannon) method, belonging to
Gauss-Newton gradient methods [Avriel 2003, netlib 2008]. Gauss-Newton global
optimization methods are used in tasks in geology that are generally similar to our
MPG problem, though stronger fields are detected and the resolution is in several
units of meters [Li 1996, Oldenburg 1999, Shearer 2004, Lelièvre 2006]. They
utilize problem specific simplifications and incorporate geo-specific constraints and
experience (depth weighting, etc.). But also relatively simple problems like the
detection of a magnetic marker in space can be realized by such a technique
[Hashi 2005 and 2008].
The evolution or genetic algorithms (GAs) are in fact also iterative, but use
specific methods originating from their inspiration in natural processes and the
evolution theory of the survival of the fittest. They are general-purpose global
optimization techniques based on randomized search and incorporating some
aspects of iterative algorithms [Caponetto 1997]. GAs can tolerate noisy and
discontinuous function evaluations [Chipperfield 1997], which would be excellent
for us as our data is always pretty noisy. I am mentioning this technique, because its
utilization is subject of our further research whose first part has already been
published in [Platil 2008]. The paper is also in Section 4.4.3.4. After mastering the
fast forward solver, we have also tried this approach. For some more descriptive
information about the GA, the reader can see [Tomek 2005a at DVD/Works] and
the references mentioned there.
For all types of iterative methods, the fast forward solver is essential to cut
down the iteration periods. In cases where the model cannot be realized so
effectively by direct mathematic computation, models are estimated commonly by
trained neural networks. I have also worked on it earlier [Tomek 2005a]. NN
derives solutions very quickly in comparison to the more complex e.g. iterative
forward solvers and is thus used to determine the fields corresponding to the
estimate of the sources during the iterative optimizations to achieve better
computational efficiency even though a certain error is present in the neural
network estimates [Ramuhalli 2002].
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4.4.1.1 Neural networks
As has been partially revealed, I have used this “evolution” technique for the
inversion of our MPG data. There has been continuous progress from the inversion
of the simple compact sources [Tomek 2005a, Tomek 2006a and Tomek 2007a] to
the more complex multi-source phantoms to the latest adoption of the simplest NN
algorithm to calculate an inverse matrix for processing of appropriately formatted
data by a direct one step mathematical calculation [Platil 2008 (Section 4.4.3.4)].
Thus, artificial neural networks are in this thesis the most important tool in the
means of the inversion of the magnetic field data.
Neural networks (NNs) have been quite a popular tool for several decades,
various types and techniques have been developed and are used as a powerful tool
to find relations in complex data, where we do not see a clear interpretation and
moreover, they are able to generalize, meaning their ability to find the correct result
even for unknown (i.e. not trained for) inputs. NNs are practically used in medicine
for diagnostics, control of devices; in banking for investment risk estimation, in
weather forecasting and several other areas. Their ability to successfully solve
strongly non-linear problems belongs to the advantages of NNs, moreover in
multidimensional space [Jiřina 2004]. They can be used for classification problems
or for, in our case, the needed, regression ones. They can solve both discrete and
continuous problems. The biggest deal, except for obtaining representative set of
data for learning process, is to choose the right type of network. Only the suitable
type will enable one to reach the best possible results. Usually, one has to do it by
trial and error though there are nowadays software tools (MATLAB’s Neural
Network Toolbox by Mathworks, STATISTICA by StatSoft, Inc., etc.) that enable
one to test the datasets at least with the most typical configurations. Usually, one
finds that the simplest solution is the most effective one and probably even the best
one. Which is coincidentally an idea formulated long ago by William Ockham
living in 1285–1349.
NNs are also usually utilized to realize the forward problem as has been
already mentioned above and then the inversion is performed in an iterative loop
utilizing some of the optimization methods. This is possible, because the trained
network performs the calculations quickly. However, the possibility to apply the
tool directly on the inverse problem if enough data is provided exists as the inverse
problems are usually undetermined, so we cannot want a better resolution than
enables the provided data. If so, iterative procedures are the only choice.
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4.4.1.2 Automatic differentiation of the forward model for
optimization
We should mention here a method that would enable one to apply gradient
optimization methods to our problem, which we unfortunately have not examined
much even after creating a far more efficient forward model, that is discussed more
in Section 4.4.3.4 and [Platil 2008] for which the discrete differences would be
easier to calculate than it was with the old model based on the program cycles
[Tomek 2005a]. Automatic differentiation provides an excellent possibility to
calculate the gradients or better differences of the error functions with multiple
unknowns in a reasonable time, which is crucial during iterative inversion tasks.
Analytical calculation of the gradients of such problems is very elaborate,
sometimes even impossible. The basic function describing the relation between the
single magnetic dipole moment and the magnitude of the gradient of the magnetic
induction, which is derived form the Maxwell’s Equations is not so complicated,
but in general we need derivatives at each measuring point by the position and
magnetic moment of every single cube of the source. There exists software in
Fortran, C and also in Matlab for this purpose. The Matlab package ADiMat
(developed by Andre Vehreschild - Institute for Scientific Computing Aachen
University, Germany) redesigns the prepared Matlab function to provide differences
with respect to the input parameters.
The old model from [Tomek 2005a] has been realized, where the reader
can find more details and the derived software is available on [DVD appendix at
DVD/Software/AdiMat].
4.4.1.3 Newest optimization methods
Faster and better optimisation methods are constantly being developed. I
had the possibility to get acquainted with research in this branch at the Czech
Academy of Sciences. As we now have a very precise mathematical description of
the problem, finally formulated into a relatively simple equation, we can on one
hand realize the differences and on the other hand apply some new efficient
gradient based optimisation method. There was also suggestion to apply a
SUBPLEX technique, for which we have found a basic code that could be applied
after several modifications to our task [netlib 2008 (http://www.netlib.org/opt/)]
New sophisticated methods are also used for alternating signals; however
these are usually not adaptable to our task.
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4.4.2 Estimation of total dust load
The most common task in magnetopneumography is the estimation of the
total amount of deposited dust. There have been several approaches in the past,
which are briefly mentioned later on in an application oriented paper
[Tomek 2006a]. I have come up with an idea to use the integral (summation) of the
individual gradients measured in multiple nodes of a single plane lattice over the
subject or phantom. The best solution would be to sum the total gradients over the
biggest plane possible, ideally by the definition over the area all-around the
measured object, which is suggested for good determination of EEG source
proposed by [Popov 2002].
We have mathematically modelled our ordinary set-up with the basic first
order gradiometer and tried to model the situation. We have generated random
distributions of the magnetite contaminated model cubes in the phantom volume
and summed the calculated gradients. This has been done for several cases where
the magnetite amount in each of the distributed cubes was always the same and just
the number of them varied. As is shown in the graphs in the paper below (page 3 figure 2) the estimate error is about ±10 cubes mainly depending on the distance of
the measuring plane from the phantom.
The necessary prerequisite for the estimate of the dust load is the knowledge
of the magnetic properties of the expected dust in the locations where work and live
the examined subjects. This is a major subject of the following paper. The paper
also deals with related topic concerning the dynamic characterization of
ferromagnetic nanoparticles intended for hyperthermia cancer therapy, when heat is
induced in the region of the concentrated particles by a high frequency magnetic
field.
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Sensor Letters 2007 – extended paper
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Sensor Letters 2007 – extended paper
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4.4.3 Neural network inversion in MPG
As has already been mentioned above, the idea of utilization of the artificial
neural networks for our problem comes even from [Ripka 2004] (then [Tomek
2004b]). It has been more deeply examined in [Tomek 2005a] and continuous
progress has been recorded in three SCI journal papers [Tomek 2006a, Tomek
2007c (from a conference in 2005) and Tomek 2007a]. The two more important
works are included later in respective chapters.
4.4.3.1 Restraints & limitations
We have already said that just the discrete model of the problem is
feasible. The primary question is thus the resolution we would like to achieve. Then
we need to prepare a measurement set-up that can feed the inversion with enough
data to reduce the non-uniqueness of such complex magnetic inversion problems,
together with the fact that the individual measured gradients themselves are nonunique. Furthermore, we just use a component of the total vector of magnetic field
that is in the sensitive axis of the gradiometric probes, thus again there is less
information from the testing. Just one first order gradient in a rational resolution of
2 cm provides 552 scan locations (44x46 cm surface) however, we would need to
determine up to 574 magnetized sources distributed in the space of the lung
phantom. Introduction of five coaxial 1st order gradients in the new set-up improves
the situation, but the data cannot be independent when obtained in such a
configuration.
The phantom of the lungs is simplified for the modelling purposes not
only in the resolution to the cubes of 8cm3 but also in the direction and size of their
magnetic moments. The direction of magnetization is known – in the sensitive axis
of the gradiometer – and the moment can be either zero or a given value, so we just
deal with a binary problem, however the moments of the cubes are calculated in a
continuous range. Another reduction of the degrees of freedom is the known
position of the phantom in relation to the probes.
To sum it up, in the most general problem, we deal with the need to
determine the positions of randomly distributed magnetized cubes in the phantom.
Their number may vary from 0 to 574. It may even happen that there is a nonmagnetic cube surrounded by magnetic ones. Mathematically, the position of each
cube is defined by three unknowns, its moment is another unknown though in the
simplified phantom it is zero or one. This implies that the inverse problem is in a
mathematical and physical point of view badly determined, thus non-unique.
Moreover, in real data some noise is present which disturbs the inversion
techniques.
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The above briefly listed limitations of the inversion are also valid for
neural networks and others are added with the fact that required number of the
representative sets of the training data is high. The problem can therefore, be hardly
handled using standard desktop computers and software, see the problems reported
in the papers [Tomek 2006a and 2007a and 2007c]. Either the software cannot deal
with so much data or so many variables or there is not a long enough nonfragmented memory space for processing memory-intensive problems like singular
value decomposition (SVD) [Platil 2008].
The first experiments just used the single scanning plane and were aimed
to determine the dimensions of a single homogenous compact source in the
phantom’s volume, see Section 4.4.3.2. To further simplify the neural network
applied on the inverse problem, we have chosen an approximate function to fit the
measured gradient. That reduced the number of inputs, however, it was also causing
a bad estimate of the source when having noisy data.
From the beginning, the mentioned general distribution has been
examined. We have found out to what number of phantom cubes the inversion
works in the case of single 1st order gradient, see Section 4.4.3.3. As the number
(just 64 cubes) was totally unsatisfactory, more measurements in more planes were
introduced and a relatively successful inversion for 100 cubes was presented [Platil
2008], see Section 4.4.3.4.
Noise, set-up inaccuracies, background noise and the noise of the
electronics itself are the most important limitations for the real application. We have
experienced serious noise sensitivity with all of the already tested neural network
models, the last one is no exception. Nevertheless, this is common for almost any
inversion technique, so we need to cope with that and reduce the noise levels in real
data. A lot about this has been already discussed in Section 4.2.1.
4.4.3.2 Localized sources
The basic simplification of the problem was to recognize the single
localized compact source in the lung phantom. Certain diseases (e.g. lung
emphysema) may result in a higher concentration of the deposited particles in the
place where the lung tissue is damaged, where the air with diffused particles is
cumulating and it cannot easily pass away. However, our experiment is totally
artificial. The presented method could also be applied well for the total dust amount
estimate, but this aspect was not examined as the primary reason was to test the
neural network inversion process with all the possible dimensions and positions of
one source in a clear phantom.
The forward model was programmed to generate the training data in a cube
scribed over the phantom’s volume. The maximum dimension of a source was
10x10x10 cm, the minimum was a single cube. The placement was random in all
three dimensions. A trained network (e.g. MLP – multiple layer perceptron one)
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was supposed to realize our goal, which was an estimate of an unknown source (its
size and position) from any measurement, even the one which was not in the
training set. The chosen fitting that compresses numerous data from a measured
map into several parameters that become inputs of the neural network was
surprisingly quite sensitive to noise. More on this is presented in the included
papers [Tomek 2006a, Tomek 2007a].
The first inverse model has been developed for the old system with
phantom between two fluxgates [Tomek 2005a, Tomek 2005b]. A Gaussian-like
function has been used for the approximation of the measured fields to compress the
measurements in order to have less inputs of the neural network and thus simplify
the training process. It was a generalized 2D Gaussian. Generalized, because of the
fact that the exponents were also between the fitted unknowns together with the
amplitude, mean values (location of the peak) and generalized dispersion (defining
the “width” of the lobe) see Chapter 4 in the next paper [Tomek 2006a]. The same
approach remained even with the new measurement setup, where the gradient
matrix is being measured in two or more levels just above the phantom, which is
placed horizontally. The reason for utilizing this function comes from the fact that
we fit the data that is a difference of two planar cross-section measurements of a
source that acts almost like a dipole. This gradient distribution is a certain
combination of goniometric functions, thus it has this exponential character. The
chosen function provides a very effective fit for the wanted simplified purpose.
For the fitting, we have chosen the Nelder-Mead Simplex method
embedded in Matlab to find the optimum coefficients of the Gaussian. This
software (Matlab script) is included on the DVD – see folder
[/Software/Matlab/Fitting_Gaussian].
The following paper published in Sensors & Actuators – Physical
[Tomek 2006a] describes most of the work done with the MPG until experiments
with multiple sources, including the improvements of our forward model, which is
compared with real phantom data there. In the paper, a method of measurement of
magnetic moment of a magnetized sample using Helmholtz coils and fluxmeter is
also revealed. This measurement had to be performed to determine the moment of
phantom cubes, which could not be measured more precisely by our other
laboratory equipment because of too strong fields. The source was too strong for a
geological rock-sample generator, i.e. rotating sample magnetometer.
Some further experiments with these localized sources, but in this case
without fitting the Gaussian like function are in the paper [Tomek 2007a] in Section
4.4.3.3. We have utilized a far bigger network there, a four layer perceptron one,
and have achieved very encouraging results even with a smaller training data set
(10 000). The number of examples was limited by the software utilized for the
inverse model experiments (StatSoft’s Statistica 6). The results of the same sources,
as were presented with the fitting, are closer to the ideal values, especially thanks to
the elimination of the inaccurate fitting.
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4.4.3.3 General problem
Though the problem is not well conditioned we have tried to estimate the
smaller subsets of the lung phantom composed from 574 cubes of a volume of
8cm3. As was already mentioned, we have reduced the problem to a binary one so
that there could be either magnetic or non-magnetic cubes, however randomly
distributed. Such a resolution may seem realizable, however the problem is still
quite bulky and we may reach the limits of the used hardware or software in means
of computational demands. Our software had problems even with 552 (24x23) input
parameters for the neural network, when we wanted to use single scanning height in
resolution of 2 cm. [Tomek 2007a]. We needed to make several improvements and
especially prepare some custom software, which would only have the limit in size
of the non-fragmented memory for the necessary mathematical operations.
The first attempts are described already in [Tomek 2005a]. Further
experiments are then in the paper below where we reveal that in a relatively small
volume of the phantom – 64 model cubes, we can distinguish the magnetic and nonmagnetic cubes/voxels quite well and what is more, even in several layers. Again
one-step inversion based on neural networks was used. The best performance
provided a simple linear NN [Jirina 2004]. Other NNs were considerably worse.
The presented results give us the suggestion that with even more examples for
teaching or for the inversion done on the mathematical basis of SVD (which is the
algorithm used for calculation of weights of the linear network, explained more in
Section 4.4.3.4) and incorporating some more a priori knowledge we could achieve
even better results. How much added data would be optimal, has not been fully
tested yet. But in the next chapter, we are going to describe results while adding
more heights in which the gradients are measured.
The paper below [Tomek 2007a] describes the lung phantom and the models
and gives another example of a single planar measurement of the magnetic field that
is processed by the NN inverse model.
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IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290
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IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290
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IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290
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IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290
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4.4.3.4 General problem with more scanning planes
With the availability of better PC configurations and while having more data
from the measurements due to the innovation with 5 coaxial 1st order gradients
[Tomek 2009a] we have decided to make further steps in the work concerning the
inverse problem applied to the multiple source general problem. The main progress
was the realization of a custom software based on the simplified experiments as the
commercially available programs can readily process only much smaller problems.
The paper [Tomek 2009a] in Section 4.2.1.3 deals with, for the first time, the
new setup with six coaxial fluxgates. Thus five synchronous first order gradient
scans above the object are available, which provides a bigger quantity of data for
experimenting with gradiometric setups and mathematical processing and of course
reducing the degrees of freedom with the inverse problem. The paper again
mentions the approaches in geology where scientists can utilize a lot of empirical
knowledge to obtain good estimates also in badly posed tasks. I deal there however,
mainly with the analysis of the fields and some practical proofs of my hypothesis
about noise suppression and utilization of the fitting for processing of the rough
data for inversion. However, in the next paper [Platil 2008] we again deal with the
inversion of the general problem and compare 2 approaches. We utilize not only the
algorithm adopted from a linear neural network but also try a simple genetic
algorithm. The extension of the work concerning the general problem was a logical
move after the previous unsatisfactory results on larger volumes of the lung
phantom. We have stayed with the already well described phantom model with
cubes of 8 cm3 volumes and synthetic, usually random, configurations of the
sources in the non-magnetic environment, so there are still reserves in the feasible
source arrangements and their real properties. The aspects of the real cases could
not be studied on the subjects, nor is such knowledge included into the models. The
primary task was again to recognize the magnetic and nonmagnetic cubes. We have
started with just a single layer of the phantom, respectively 50 cubes in both lung
lobes. So we had 100 cubes altogether. The development of the method for
complete lungs should be the subject of further work.
We have made several experiments with different spatial resolutions of the
scanned data. At first, the resolution in the horizontal plane was 4 cm, thus we had
144 nodes, each with five 1st order gradients and we have generated 60 000 training
cases. Then we came with an idea that the smallest effective training set would be
represented by an identity matrix of possible sources and the respective fields
computed in the nodes of the measured planes. So we have generated data for a
resolution of 2cm, which means 5x529 (23x23) nodes and finally also in a
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resolution of 1 cm which means 5x2025 nodes. Then there was the question how to
process the SVD by the available PC and software.
In Statistica, we had a problem with processing of just 276 nodes (Section
4.4.3.2) so a custom software was the only solution. It was realized as a script in
Matlab according to the definition of the analytical solution of the least square
problem which is described in the next paper [Platil 2008]. By this means, we
obtained the weights of each measuring node mapping its value to the cubes in the
phantom. The performance can be shown e.g. on the inversion of the identity matrix
sources. Ideally, we should obtain a diagonal matrix with ones on the main diagonal
and zeros elsewhere. However, because of not utilizing enough independent data,
we obtained the results that are full of artefacts (see Figure 1 in the next paper and
Figures 4.13-4.15). There are false images like when the sampling theorem is not
fulfilled or like when we reconstruct the images with an incomplete set of Fourier
series coefficients. Figures comparing the values over the diagonal for the three
mentioned cases are presented in Figures 4.13 - 4.15.
X-Z projections of the result of the inversions of the unit sources composing an identity
matrix – ideally, there should be a straight plane without any waves.
Fig. 4.13: Weight matrix was derived from 60000
Fig. 4.14: Weight matrix was derived from 100
randomly generated cases. Scanning resolution
unit cases. Scanning resolution 4 cm.
4 cm.
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Fig. 4.15: Weight matrix derived from 100 unit cases. Scanning resolution 2 cm.
The last case was in a resolution of 1 cm, but could not be processed as we
could not reserve enough defragmented space of the memory, including the virtual
memory on the disk. The process is unfortunately very memory demanding, so we
should deal with the representation of the data in more memory saving formats, if it
does not have a bad effect on the precision. We could work only with 2 layers out
of 5 which means 4050 nodes, and the result was identical to Figure 4.15 where the
resolution is 2cm with 2645 nodes, which means that not much more linearly
independent data was added.
The utilization of the identity matrix set of sources is definitely effective;
however it is still like calculating the weight matrix for any set of 100 cases, so the
inversion works best on these cases and should have worse performance on other
more complex examples. The inclusion of several more representative cases should
help the quality of the inversion matrix without any effect on the needed memory
for the computation, as the dimension of the matrix undergoing SVD is always
limited just by the number of scanning nodes and not by the number of cases.
The early results were published at the EMSA 2008 conference [Platil 2008]
and we have prepared an extended paper for Sensor Letters journal. It comes next.
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EMSA 2008 - paper for Sensor Letters, accepted
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EMSA 2008 - paper for Sensor Letters, accepted
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EMSA 2008 - paper for Sensor Letters, accepted
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EMSA 2008 - paper for Sensor Letters, accepted
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EMSA 2008 - paper for Sensor Letters, accepted
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EMSA 2008 - paper for Sensor Letters, accepted
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4.4.4 More probes & fitting to model function
As it has already been shown in the paper [Tomek 2009a] in Section 4.2.1.3
with several coaxial gradients, we can perform the task of determining some
compact source quite well with data coming just from a single scanning node. The
difference from the task discussed in Chapter 4 is that we just obtain its overall
magnetic moment (amplitude) and relative position in the cylindrical coordinate
system, which means the distance of the source from the closest probe and the
radius from the scanning node. From the single scan, the dimensions of the source
cannot be determined well. The absolute coordinates of a source centre can be
derived by eliminating the degrees of freedom by using the data obtained in two
nodes. What can be actually calculated is a centre of the magnetic moment
corresponding to the measured signals not the centre of the source in the case that
the source cannot be interpreted as a dipole from the scanning distance. The data
obtained in these multiple scanning heights can also be used in a neural network
inversion similar to the one described in Section 4.4.3.2, ideally without any fitting
or using a lower compression of the input data than is described in Section 4.4.3.1.
The mathematical optimization used for determining the best analytical
gradient function describing the measurement partially suppresses certain sources of
errors in the data. Between them are: imperfect probe alignment and also outliers,
which is excellent for in-vivo experiments. Time variations in the field coming from
the background, that result in the same 1st order gradient changes in all the
measured heights can be also subtracted from the scanned matrices; however the
differences that appear between the coaxial gradiometers cannot be suppressed. The
configuration and its properties have not been fully studied yet. A more detailed
investigation over the performance of the algorithm and effectiveness of again
applied Nelder-Mead optimization technique is to be made.
4.5 Discussion
In this task we have made many successive steps in the development of all
parts of the magnetopneumographic system. Except for the magnetizing device,
whose modelling I was just supervising, the other parts are mostly my work.
Demands for better inversion results lead to changes in the scanning device, mainly
of the gradiometers. That lead to the need of modifying the forward models and the
inverse processing was then developed by means of trial and error to achieve the
optimum. The experiments with the localized sources proved applicability of neural
networks to the inverse processing and lead us to their further application.
The most important experiments were done with general distribution of
magnetized and non-magnetized phantom cubes in one layer. We have obtained
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very satisfactory results using tailor-made software utilizing the SVD algorithm,
applied in one type of artificial neural networks. Utilization of this type of
“evolution algorithm” may be arguable, but iterative mathematical gradient based
optimization or other iterative procedures were not seen as applicable in the
beginning. Now, as we have a relatively simple description of the forward problem,
which enables fast single step calculations, the door is opening.
There has been made also a first trial by my colleague with the genetic
algorithms, which showed their applicability, though the results were not precise.
Some experiments should be made even with the gradient based methods, which
were just briefly touched. We now have an ideal linear equation describing the
problem, though the number of variables may easily exceed 1000, but such
mathematical description is one of the conditions for the sophisticated gradient
methods.
I have mentioned complications with high numbers of variables that bring
problems with processing, especially in the means of the operational memory of the
computers as the datasets and matrices are large.
In such big problems, a successful inversion, as has been discussed, needs the
maximum possible reduction of the degrees of freedom. We have made much
progress in the acquisition of more data describing the sources but could not analyse
enough real cases, where the distributions are different Definitely, if we had
sufficient data available from real measurements of subjects’ lungs, we may have
found similarities and could define what constraints the inversion results have to
respect (a priori information), etc. In this respect, improvements of the
measurement method according to practical needs - including e.g. video control of
body position during scanning – should be made also, which would help improving
the reproducibility of the measurements. This naturally needs a representative set of
volunteers and are costly and extremely time consuming.
The scanning method utilizing fluxgates and up to now, just step by step
measurement of the field maps over magnetized phantoms, especially in the
presented DC mode, may be disputed because of the relaxation (the effect of the
rotation of the formerly aligned particles to random low-energy directions) and long
scanning periods during which the subject may move and the background disturbing
field may change a great deal. The system may be relatively easily adapted to AC
enabling the measurement of even ferrimagnetic oxides, which do not preserve
remanent field after magnetization. This change should help with the problematic
suppression of low-frequency disturbing fields, moreover, the measurement in the
AC mode may be more attractive for practical applications. The adaptation would
require just slight changes in the signal filtration and synchronous detection of the
signal from magnetometers. The mentioned probe arrays should reduce the time
necessary for scanning. The proposed inverse processing is quite universal as well
as the principle of the forward model, thus in this theoretical point of view the
system, may be applied to various tasks.
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An altogether different situation is with the magnetization device, which
would have to be built as a part of the scanning bed. It should be made from
Helmholtz coils of proper size enabling the creation of strong enough fields.
Work on the inversion, utilizing the least squares has not stopped with 100
volume elements of the lungs but continues with 600 to which both lung lobes are
inscribed, though it again requires a higher computing power because of the
increasing size of the matrices to be inverted. We are also considering methods of
compensation for the errors arising from discretization and pseudo-inversion of the
almost singular matrices. The question arises whether we should not introduce some
iterative processing to this method. The one step inversion provides a very good
estimate (model) of the distribution of the ferromagnetic cubes and the errors could
be decreased by several successive improvements to this model.
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5 Measurement of the stomach volume
The inverse problem solved in this medical application is in its theory a
relatively simple task, however as common during work on the instruments for
practical use, many problems rolled out. We had to especially cope with several
contradictory requirements and needed to reach an optimal solution in the
contemporary conditions and budget. Nevertheless, the work has been welcomed at
three prestigious international conferences (including two oral presentations) and
two smaller conferences and there are even now two publications in excerpted
journals plus one minor journal and we have material for at least one further
medical paper.
I am going to reveal the important steps of the development, the technical
details including even the manufacture and naturally to provide the data measured
in-vivo and try to show some interpretation of them and outline targets of future
research.
5.1 The tasks
This task was part of the Project of International Cooperation (1P05ME756)
with a team falling within the University of Texas Medical Branch. Here are the
main points concerning the system intended for treatment of obesity or various
gastric dysfunctions:
•
•
•
•
Development of a new generation of experimental implant enabling “ondemand” stimulation. Thus, the device giving impulses to the stomach wall
just at the specifically detected moments, i.e. after detection of food
consumption (gastric pacing).
o Implantable system for stomach volume (or distention)
measurement – minimal number of sensors
o Potentiality of estimation of stomach chymus composition – mostly
liquid vs solid food
o Selection of the most suitable sensors
Design of the system utilizable for in-vitro experiments and verification of
its function
Appliance for measurements in-vivo (dogs)
Testing in the USA, Veterans Administration Hospital in Oklahoma City
5.2 Method
There were many suggestions how to solve the measurement task, however
we have chosen the measurement of the voltage induced to (a) solenoid pickup
coil(s) from an AC magnetic source – another solenoid. This basic system has many
imperfections and may fail to detect reasonable signals because of misalignments.
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Thus eventually we came up with a compromise between the system complexity
and reliable function. It is also relatively little dependent on the alignment of the
transmitter and receiver. The following chapters and papers thoroughly describe the
reasons for selecting the magnetic induction method as well as the considered
configurations of coils, see Section 5.3 and Section 5.4.1.6.
5.3 Overview of some applicable methods
In one less important Czech journal (Acta Polytechnica) arising from an
international student conference Poster 2007, I have published an overview of the
possibilities how to measure the distance of two points in space by means of the
magnetic induction principle from the simplest one to those enabling higher
precision [Tomek 2007b]. Considered, are mainly such alternatives that could be or
are well applicable in our task. Two of them were employed in our successive
experiments.
In the submission included below, those methods are highlighted that are not
only independent from the environmental properties a great deal, but they can also
be made for relatively low power and the data processing from those systems would
not be too complicated.
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5.4 In-vivo applicable systems
Except for the relatively short work with the laboratory instruments and the
first home-made sensors, there were directly two generations of in-vivo applicable
systems. The task needed to be solved quickly, as the first in-vivo experiments were
planned in a short time. The first system is well described in the report for our
partner, which is reedited and follows in the next section and in two papers included
in Sections 5.4.1.5 and 5.4.1.6.
Our partners were quite satisfied with the first tested module and the sensors
and even applied for a grant on the further development, which made us continue
our work on a more reliable device. The gained experience has opened several tasks
which we have tried to fulfil in the next generation utilizing more channels and a
three-axial sensor. The description of it is in the paper in Section 5.4.1.6 and in the
whole Section 5.4.2 and also back in the overview in Section 5.3.
5.4.1 First version
The first applicable system was the simplest one possible, utilizing a single
transmitting and a single receiving coil. This system is described in detail in the
following chapters up to Section 5.4.1.5. We have described the materials used, the
way the coils were manufactured, electronics built and also the firmware and
software for data acquisition and processing. The appropriate parts of the report are
revealed below, including references to the electronic appendices.
Fig. 5.1 Single axial distance measurement module with probes
5.4.1.1 Summary
•
The developed system measures distance by using induction method.
Distance range: 2 to 10 cm
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•
Accuracy: 5% below 7 cm, 10% from 7 to 10 cm
One transmitting and one sensing coil can be attached to the surface of the
stomach. The external electronic box powers the transmitting coil by peak to peak
3 mA/3.025kHz sine-wave and the signal induced in the sensing coil is amplified
and converted to distance. The electronic module is powered by a USB from the
attached PC. It requires individual calibration of each coil pair plugged in.
5.4.1.2 The principle of the sensors and the system
2a) The coils (solenoids)
-
one driving coil (air core)
o excited by 3025Hz, 3 mA p-p sine-wave
o serial inductance at driving frequency approx. 1 mH*
o serial resistance approx. 205 Ohm*
-
one sensing coil (ferrite core, material H11)
o serial inductance approx. 13 mH*
o serial resistance approx. 215 Ohm*
* measured by an RLC meter HP 4284 A, see file:
/Measurements/Coil_measurements.xls – set of measurements including the first
final coils’ experiments in a saline solution.
The magnetic field created is decreasing by the third power of the distance
(Fig. 5.4); therefore, the dynamic range of the device has to be wide. Furthermore,
from the character of the magnetic field, if the coils are not aligned in one axis,
angular mismatch and displacement (perpendicular shift between coils) cause
significant errors, see Fig. 5.5 and 5.6, though ± 10° distortion and ±10mm do not
cause big deviations in the distance determination as the third power reduces the
error.
pick-up coil
driving coil
distance
Fig. 5.2. Schematic picture of the sensors
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Fig. 5.3. Photo of the first sensors in comparison to a 3.5mm jack connector
Distance - Induced Voltage
160
140
Uind [microV]
120
100
80
60
40
20
0
0
2
4
6
8
10
12
Distance [cm]
Fig. 5.4. Measurements using laboratory equipment, axially aligned coils
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Effect of lateral displacement
3
Uind [mV]
2,5
2
1,5
1
0,5
0
-80
-60
-40
-20
0
20
40
60
80
Position [mm]
30mm
40mm
50mm
Fig. 5.5. Effect of the lateral displacement
(Illustrative measurements with an older experimental system)
Angular mismatch - induced voltage
5
Uind [mV]
4
3
2
1
0
-100
-50
0
50
Angle [°]
25mm
30mm
40mm
50mm
Fig. 5.6. Effect of the angular misalignment
(Illustrative measurements with an older experimental system)
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2b) The system
-
Consists of analogue and digital boards
Distance evaluation made in the PC software, with graphical user interface
o USB interface
o EXEcutable file
Programmed micro-processor of the device
o Data acquisition
o Averaging
o Communication with PC
Basic description:
A sine-wave generator excites the driving coil. The magnetic field produced
is picked-up by the sensing coil (with a ferrite core). The induced voltage is shifted
in phase by approximately 90° in comparison to the exciting signal. Therefore, the
generator also provides a correspondingly shifted reference signal for the
synchronous detector. The signal from the sensing coil is AC-amplified by 2000x,
processed by synchronous detector and DC-amplified by 7x. The higher harmonic
frequencies from the detector are suppressed by the low pass filter. The amplified
voltage is sampled by a 24-bit ADC. Samples are picked by the micro-processor
and averaged. The number of the averages is user selectable from 1 to 128 samples
in powers of two. The data is then sent using a FIFO/USB converter to the PC to be
processed further, see Figure 5.7.
Fig. 5.7. Block scheme of the system
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5.4.1.3 How it is designed and made
3a) Sensors
Coils (solenoids):
- 2000 turns (bigger experimental coils have 2500 turns)
- about 2 mm in diameter without leads and coating
- 8.5 mm in length
- core diameter 1 mm
- wound by company TRONIC s.r.o., Prague, CZ
Materials:
•
Paint used for reinforcement and fixing of coils:
o Dispersed acrylic varnish lacquer or similar - dull (e.g.
SPORTAKRYL-mat by TEBAS, CZ) - several extra thin layers
(cca 60% of water added) and high temperature drying, several
layers also after a coat of plastic spray
o plastic spray, rapidly drying protective varnish (PRF 202 by
Taerosol Oy/Ltd. - GES electronics, CZ) - 1 or 2 layers after
soldering the leads to the cables and one after attaching them to the
coil
•
Cores:
o Ferrite cores Fonox, material H11 – company DOE s.r.o., CZ
o Diameter 1 mm, length 8 mm
•
Winding:
o Enamelled Copper wires - ERMEG s.r.o., CZ – (Electrisola http://www.elektrisola.com/, Germany)
o Product name: Butybond alcohol 155
o Product code: Ba155
o Base coat: mod. Polyurethane
o Bond coat: Polyvinylbutyral
o Standards: IEC 60317-35, IEC 60317-2
o Wire used: Cu 0.034 mm in diameter
•
Coating:
o ChronoFlex AR solution - medical grade polyurethane (PUR) by
Cardiotech International Inc., USA http://cardiotech-inc.com/
o A minimum of 3 thin layers of cca 70°C solution
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Cable:
o
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2 conductor shielded cable STC-32T-2 by BLH, Germany, silvered
copper wires, PTFE (Teflon) insulation, www.blh.de, VISHAY
The biocompatible polyurethane (ChronoFlex AR) layer gives a very high
insulation resistance even after being in a saline solution for more than 1 month.
3b) The system
•
Analogue part of the electronics
The analogue part of the electronics in blocks is shown in Figure 5.7 up to
the LP (low pass filter) block. As it has been finally designed and built by an
external company JanasCard, Prague, CZ, I am including it rather for the purpose of
completing the description of the system. It consists of the oscillator with a
frequency of 3.025 kHz which drives the transmission coil. The signal from the
input (pick-up) coil comes to the low-noise amplifier with a gain of 20x and the
second-order band-pass active filter with gain of 100x. The output from the filter is
fed into the synchronous detector and the signal then comes to the low-pass active
filter with a corner frequency of 1 Hz and gain of 7x.
A detailed scheme which follows the block diagram above, together with a
PCB layout is in the file on the DVD Appendix (/Schemes/syncdet.pdf and
../pcbsyncdet.pdf). In Figure 5.8 just the part of the scheme without the oscillator is
presented, which provides a clear sine-wave powering a driving coil by a signal
which has its amplitude set to 600 mVp-p and it also provides a square signal
produced by a comparator for a synchronous detector. The input amplifier consists
of U14 and has a gain of 20x, the second order band-pass consists of U1 and U2A
and has a total gain of 200x, U2B and U4 forms the synchronous detector, U3 with
R1, C2, R3, R4, C3 forms an output low pass filter with a corner frequency of 1 Hz
and gain of 7x. The total gain of the whole input part is approximately 14000x.
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Fig. 5.8. A detailed scheme of the analogue circuitry based on the JanasCard company documentation
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Digital part of the electronics
The block scheme starts from the ADC (analogue to digital converter) in
Figure 5.7. This was designed, built and programmed by Ing. Pavel Mlejnek, my
colleague from the department. The full scheme of the circuitry is included on the
DVD Appendix (/Schemes/Schema_dig.pdf).
The digital board consists of three main parts. The first part is the 24 bit
analogue-digital converter ADS1210, which samples the input voltage with a rate of
300 Sa/s. The sampled data is processed in the microcontroller ATMEL AT89S51. .
Next, the data is sent to the PC via a USB. The integrated circuit FTDI FT245BM is
used for the communication between the microcontroller and the USB. Finally the
digital value of the voltage is converted to the value of distance in the PC. The
source code files are stored at /Files/uController and /Files/PD_V_1_0.zip. An
update of the firmware and software that is in /Files/DMM_20_install has been
made, which includes a necessary installation guide.
Fig. 5.9. The electronics with connected probes, without the case.
•
Software
The software is developed in National Instruments’ LabWindows/CVI. It
can be compiled to an EXE file that works on any USB equipped PC with the OS
MS Windows XP. No additional libraries or programs are needed.
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Fig. 5.10. User interface of the program
Features:
•
•
•
•
•
•
automatically establishing a connection with the device after plug-in.
setting the calibration information for a given pair of coils
setting the identification of the connected pair of coils
conversion of the data (voltage levels) to the distances
distance in centimetres and inches
range of measurement approx. 2-10 cm
Data processing in the PC consists of several steps:
1. Sampled 24bit data is converted to voltage value
2. Voltages are converted to distance values
o 1/d3 characteristic is not satisfactory due to the non-negligible size
of the coils and imperfect alignment
o Calibration over several distances necessary
o Fitting to power function by Levenberg-Marquardt method
(implemented in LabWindows) – still not sufficient
o Deviations fitted by polynomial of 3rd order good linearity
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Measured distance (mm)
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110
100
90
80
70
60
50
40
30
20
10
Real distance (mm)
0
0
10
20
30
40
50
60
70
80
90
100
110
120
Fig. 5.11. Mutual characteristics and data dispersion
Fig. 5.12. Linearity deviation
5.4.1.4 Final measurements
We have manufactured several pairs of sensors. All were in saline solution
for at least for 14 days and the insulation resistance of the PUR coating did not
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show big changes. The expected minimal acceptable 1MΩ value was highly
exceeded.
For testing and calibration measurements, we use a plastic positioning
device that can be easily used even in the saline solution. The sensors and their
leads are coated by biocompatible materials.
The system is designed to measure distances from 2 to 10 cm. Lower
distances than 1 cm overload the electronics, for higher ones the signal to noise
ratio is low. This is due to relatively low inductances of the coils and the necessity
of using relatively low frequency 3025 Hz because of the presence in a conductive
environment, where the signals would be too sensitive to the parasitic capacitances
and eddy currents if the frequencies were higher.
Noise measurements
-
several measurements of the complete circuitry made (one pair of coils)
Table 5.1. showing noise dependency on averaging
o Noise of the digital part and ADC (input of the ADC in short)
o Noise of the electronics, equivalent resistor connected instead of a
pick-up coil
o Noise of the whole electronics with pick-up coil perpendicular to
the driving one at a distance of 12 centimetres
Tab. 5.1. Noise values measured at the ADC output. The sampling frequency was
300 Sa/s. Values “Max – Min” record the maximum deviations of the measured
dataset. “RMS” value was calculated after removal of the DC offset
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Fig. 5.13. Measurement device with probes on a calibration device
5.4.1.5 Practical application on laboratory animals
We had an opportunity to test the performance on living animals. For this
purpose we have made tests and calibrations in a warm saline solution and also
tested the probes in it for a certain period. Several sets of probes and two electronic
boxes were used for in vivo experiments on laboratory dogs by the US partner.
Experiments were conducted at the Veterans’ Administration Hospital in Oklahoma
City, where there are some research labs of the University of Texas – Medical
Branch. During the first phase just one dog was implanted with two pairs of probes
and a relatively little set of experiments was conducted. Some of the data was
officially authorised for publication at the submission to a World Congress on
Biomedical Engineering 2006 [Tomek 2006b] from which a later paper results. It
was revised several times as there was not enough statistically relevant supporting
data for proper publication. Finally, it was submitted to a specialised journal about
Gastroenterology [Tomek 2009b].
I describe, in the paper, the motivation for this new method, include many
references to similar experiments, to statistical data about obesity and, of course, the
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applied system is again briefly described. The crucial part is the description of the
in-vivo experiments and an example of the measurements with a statistical graph.
The simple system showed to be very dependent on the quality of the surgery
as the coils need to be oriented as co-axially as possible and not changing their
angular tilt much on the stomach wall. This cannot be assured however. It even
happened that the mutual position of one pair after surgery was totally skew and the
signals were not reliable. Thus, we have started to develop a more complicated
system later on.
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5.4.1.6 Possibility of a three-axial probe introduction
Further experiments and analysis of the data appeared in the paper finally
published in Sensors & Actuators A - Physical 2008 [Tomek 2008]. This paper
resulted from a Eurosensors 2006 conference submission. There is also a frequency
analysis of the measured signal and longer experimental curve for liquid intake.
After the first in-vivo tests there was a strong demand for smaller probes utilizable
even on rats, thus less noisy and far more sensitive electronics. The new version of
analogue part has been thus developed and tested. Then it was decided to use this
more sensitive variant to build a three-channel version of the analogue part that
could work with smaller coils composing a three-axial receiver. We demonstrate
here the benefits of the later completed three-channel system. The pick-up probe
scheme with three smaller orthogonal solenoids is revealed and the in-vitro
experimental data is depicted.
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5.4.2 Second version – tri-axial system
Fig. 5.14. Three-channel electronic box
with accumulators
Fig. 5.15. Electronics connected to a NI
A/D converter
As has been written above in Section 5.4.1.6, this is the more sensitive and
less noisy version of the electronics. But here, we use three totally separate
analogue channels with similar parameters. Amplification of the channels is
42 000x and the noise at output is 25µV with 200Ω resistor at input. Table 5.1.
compares the parameters of the tri-axial and the single-axial system.
version
single axial system
tri-axial system
turns of (ø 34µm Cu
wire)
2000
1000
coil length
8.5 mm
5 mm
coil diameter
2 mm
2 mm
inductance
with H11/without
13mH/1mH
3mH/0,6mH
core diameter
1 mm
1 mm
14 000
42 000
250 µV
25 µV
amplification of the
electronics
Output noise rms
value (0.1Hz-1kHz)
Table 5.1. Parameters of the two versions of the electronics and of the utilized
sensors. The driving coil for the in-vivo testing even in the second version had 2000
turns.
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Jiří Tomek
For the experiments, we have introduced a four channel high speed USB A/D
converter by National Instruments (Hi-Speed USB Carrier “NI USB-9162” with
module “NI 9215 with BNC”) enabling simultaneous sampling, which is a feature
absolutely necessary for our purpose. Data from the tri-axial sensors digitalized by
the converter was processed by the newly developed software in LabView
environment (Fig. 5.16, see DVD appendix /Software/LabView {the ADC
converter has to be installed first}). Recalculation of the acquired voltages to the
distance has been realized by an expression whose constants have been derived
from the calibration data. This optimization has been performed by a Matlab script
based on the Nelder-Mead simplex algorithm (see DVD appendix
/Software/Matlab/3axialExample). The module enabled direct on-line monitoring of
the last 10 minutes of the measurement of the distance as well as of the voltages and
calculated magnitude corresponding to the size of the total vector of the measured
field. The program, naturally, also saves the data into a default or selected file for
the purpose of offline processing.
Fig. 5.16. Window of the data acquisition and display software. Analysis of the
induced signals, recalculation to the distance and storage of the data. Redesigned
during the in-vivo tests in the USA
5.4.2.1 Practical application on laboratory animals
Just at the end of the project we were able to arrange a second session in the
USA with another set of experiments. We have applied the new device and probes
presented in the above Section from 5.4.1.6. After onsite testing I assisted during
the surgery of the same race of dog as two years ago. Two pairs of sensors were
sewed on its stomach wall. One was fixed to the bottom part “antrum” where quite
regular contractions originate after a meal and second to “fundus” where the wall
relaxes a lot with food ingestion, see the Figure 5.17.
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Inverse Problems of Magnetometry
Jiří Tomek
Fig. 5.17 Scheme of the regions to which the coils were sewed
As has been mentioned, the two regions differ in their relaxation and
muscular action before and during food digestion. In the antrum, the coils were
sewed in parallel, the pickup coils were in the 2nd Gaussian position in respect to the
transmitter and in the fundus, the alignment was with probe in the 1st Gaussian
position. The reason for this was the size of the stomach in the respective areas and
the possibility to attach the cables in the proper way. The contractions that can be
observed better in the antrum can be even studied in the means of the food
composition – percentage of fats, sugars and proteins or just liquid e.g. water, that is
not processed by the stomach. Such studies have not been started yet. Big sets of
repeated measurements are necessary and for this there is still little finance and
support.
5.4.2.2 Examples of the in-vivo measurements
The data presented below was recorded on November 8th 2007 in the USA on
the stomach of the laboratory dog. As we did not have two devices to record both
stomach parts simultaneously we had to do it in succession which does not give
complete information. However, the doctors have chosen this procedure, though we
could also use the one channel older type of module to record at least one channel
of the second system. At first we started in the fundus, where we were tracking the
baseline for 20 minutes, i.e. signal without any food. However, the dog definitely,
by Pavlov’s reflex, knew that some feeding experiment was coming so there was
some action seen by the team. Then the dog drank in one minute cca 270 ml of the
condensed sweet milk and we could observe how much the wall relaxed. The
complete measurement is in the graph in Figure 5.18.
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Inverse Problems of Magnetometry
Jiří Tomek
26
Distance [mm]
24
22
20
LP filtered
Raw data
18
16
0
5
10
15
20
25
30
35
40
45
50
Time [minutes]
Fig. 5.18. Stomach distension after drinking 273 ml of the condensed milk
55
Afterwards the fundus sensors were disconnected and a new experiment with
the antrum probes was conducted. We waited for 35 minutes and the dog was fed
with solid food. At the antrum, the elongation of the wall is not so obvious,
however, after the meal there appear distinct relatively regular contractions of the
stomach wall which result in the mixing of the chyme inside. The whole low-pass
digitally filtered measurement is drawn in the Graph 5.19. The eating lasted
approximately 4 minutes. A detail of the record just after eating the 375g of canned
meat, when the regular contractions start, is in the next Figure 5.20.
21.5
Distance [mm]
21
20.5
20
19.5
19
18.5
0
10
20
30
40
Time [minutes]
50
60
70
Fig. 5.19. Baseline in the antrum and eating 375 grams of the dog food
- 108 -
Inverse Problems of Magnetometry
Jiří Tomek
23
Distance [mm]
22
21
20
19
BP filtered
Raw data
18
17
37.5
38
38.5
39
39.5
40
40.5
Time [minutes]
Fig. 5.20. A detail of the signal just after eating the meat – the relatively regular
contractions start. Without the meal the stomach activity is irregular in short periods
with occasional strong contraction and not food-induced volume changes e.g. like in
Figure 5.18.
This detail is joined because of the planned counting of the contractions in
certain period. This is supposed to provide information about chyme composition –
mostly fat, sugars or proteins and especially to decide if it is water or some non
energetic liquid or ordinary mainly solid food, for which the simulation is
specifically designed and should be switched on. The response of the planned
gastric pacemaker implant to the detected status would differ accordingly.
Naturally, this is just the subject of further experiments.
We have repeated this experiment also the next day and the results were very
similar. The measured data and timing is in files on the DVD
(/Measurements/3axial)
5.5 Discussion
The tests on the lab animals are unfortunately very expensive and for even
some preliminary but relevant study we would need a series of repeatable tests on a
group of animals, which is nowadays impossible. The presented work however,
showed suitability of the chosen method for detection of food ingestion by means of
measuring the distension of a gastric wall. The tri-axial system especially deserves
confidence for its simplicity and relatively low errors in calculation of the distance
between the probes caused by rotations of the transmitter - Section 5.3 (Figure 8 in
the inserted paper). More complicated systems are questionable, though they would
enable higher precision, while further reducing the degrees of freedom in this
inverse task. Section 5.3 had already outlined some interesting options.
We have not discussed various wireless systems, e.g. with resonant markers
and transmitter(s) working on several frequencies in the case of the implant, where
the implantation would be easier and no additional cables would be necessary. Such
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Inverse Problems of Magnetometry
Jiří Tomek
an idea would require processing using the correlation analysis and either more
separate channels than in the three-axial version or quite a sophisticated processing
of the signals from the multi-axial markers.
Utilization of a permanent magnet and detection of just the static magnetic
field that is modulated by the wall contractions would possibly not be so reliable
because similar signals may appear in the surroundings. And again the processing
seems to be too difficult.
One may argue even about implantability of the presented design, however
the technologies of the production of the cables and connectors for pacemakers
could be applied and the circuitry could be made at least partially on a custom
designed chip with low power consumption and minimizing the size. The distension
measurement part even does not need to work continuously and may remain
switched off totally in certain periods. Experiments with pulse driving of the
transmitters have also been made, which may substantially reduce the consumption
as well [Humr 2008, Ripka 2008] (for this testing, even samples of factory-made
small tri-axial probes were used). The cables would possibly need to use different
materials than is usual for pacemakers. The reason could be the permeability of
nickel-cobalt alloy utilized in cables of electrodes. We were thinking about silverplatinum wires of similar composition to leads of cochlear implants (Cochlear Ltd.,
Australia). Silver would be also good material for winding of the coils.
Unfortunately copper, as has been mentioned in the presented papers, is toxic for
the human body and would not be accepted even when perfectly insulated.
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Conclusions
Jiří Tomek
6 Conclusions
This chapter is going to summarize the achieved goals and give an overview
of the work done as well as propose the directions of further research.
During my study, in the general point of view, I have dealt with various
inverse problems in magnetometry, particularly the estimation of size, position and
orientation of magnetic moment(s) out of the measured data sets. Based on the
known techniques I have come up with a non-traditional approach to determine the
multiple magnetic moments, which was fully applied in the first of my two main
projects – the measurement of the magnetic field of the lungs or
magnetopneumography. Basically, it is the utilization of the direct (one step)
inversion of the measured data. Quite commonly, just the iterative techniques with
the forward model in the feedback loop are used. This task naturally involved a
complete magnetopneumographic system, thus a magnetization device, scanning
bed, gradiometers, forward and inverse modelling. We have managed substantial
progress in all these tasks.
The main effort has been headed to inversion of the measured data and
improvements of the measurement setup to achieve better inversion results. For the
inversion, I have chosen an artificial neural network approach and a very unusual
direct one step estimate of the sources out of the data sets measured above the tested
object. Results of simulations and modelling have shown that the described
approach (and also the conventional ones) require an excessive amount of
experimental data to achieve good resolution in the estimation of the ferromagnetic
dust, thus several gradiometric configurations of sensors were tried and forward
modelled. I have finally achieved a quick one step calculation of the forward model,
which was validated by real measurements over phantoms. Having this final model,
a self-programmed software for calculation of an inverse model applicable to
general distributions, could be developed. Inversion of several types of simplified
model cases have been performed (i.e. localized homogenous sources or general
distribution of magnetized elementary phantom sources in a limited volume). Some
final types of trained neural networks were also successfully applied to the data
measured over the physical lung phantom.
The determination of position of magnetic moments based again on inversion
of measured data has also been applied in my second project - contactless magnetic
measurement of the gastric volume that is necessary for switching the gastric pacing
implant intended for obesity treatment. In this case, the inverse problem can be
solved quite precisely and directly by mathematical calculation as it is just a
practical application of the distension measurement, however, in a non-traditional
environment. Though the task may seem simple, with the limitation of the number
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Conclusions
Jiří Tomek
of sensors and the demand on the simplicity of electronics and surgery, specific
problems have arisen. The problem has especially been, from practical reasons,
reduced to a single AC dipole estimation. Beside the power consumption
optimization of the future implant, the project was also an optimization task of the
determination of the distance with satisfactory precision with the minimum number
of applied sensors. We have prepared and successfully tested two in-vivo applicable
systems.
6.1 Achieved objectives
•
Design
of
the
non-magnetic
positioning
bed
for
magnetopneumography – tests with volunteers, video control of
positioning tried;
•
Magnetization device – projects of two students concerning
modelling of the field and possible improvements to achieve more
homogeneous fields between the pole pieces of electromagnet;
•
Gradiometers – six probe gradiometer introduced; reduction of the
non-uniqueness thanks to adding more information to the inverse
processing;
•
Software for fitting of the measured gradients to feasible values
according to an empirical formula, helping in the reduction of the
measurement errors and decreasing impact of variations of the
gradient of background sources;
•
Direct neural network inversion of the localized homogenous
sources, showing excellent performance on the models but quite
sensitive to noise;
•
Estimate of the total dust load in the lungs by integration of the
measured data of the field maps;
•
Software for the inverse processing of the bulky data, utilizing a
pseudoinversion algorithm limited only by size of free nonfragmented memory of the computer;
•
Successful single step inversion in a volume of 1000 cm3 (100 cubes
+ 20 always clear between two model blocks) out of 2645 measured
gradients;
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Conclusions
Jiří Tomek
•
Testing of the genetic algorithm based inversion showing their
applicability with the new fast forward model;
•
We have proposed a feasible methodology of the measurement of the
stomach distension by means of the magnetic induction principle;
•
Proper implantable sensors were designed, tested and manufactured,
both single axial and tri-axial;
•
Quite a simple prototype of the second generation of the in-vivo
applicable device utilizing a three axial receiver and single coil
transmitter has been made and tested on laboratory animals. It has
shown good performance;
•
Two generations of software for recording the measured data. The
second one enabling on-line monitoring of the distension in a
graphical user interface;
•
Short-term in-vivo studies were performed.
6.2 Outlook
In both of the application tasks, there are many issues of further research
and improvements. In magnetopneumography, there we deal with development of
the system for video control of the position of the subject on the bed. This required
several changes to the portal, thus holders for the arrays of sensors were
simultaneously incorporated. This all is to be tested and evaluated. Arrays of
sensors will help to reduce the time necessary for scanning and reduce the observed
variations in the measured gradients due to the distant sources. Further expansion of
the sensory part could be in the placement of the probe, also below the tested
subject.
Concerning the inverse problem, other inversion possibilities could be
examined especially when we finally have a differentiable continuous forward
model. It could act as an excellent basis for gradient based optimization techniques,
suggested several times in the thesis. Utilization of genetic algorithms could be
examined more, too. There is also a question whether the estimate provided by the
single step inversion could not be improved by further application of some of the
iterative methods. As there is the quick forward model, their utilization is feasible.
The incorporation of more background knowledge based on examination of real
data is also very important. Further research should also be directed to more
attractive applications nowadays, this means particularly AC measurements able to
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Conclusions
Jiří Tomek
detect ferrimagnetic oxides also. Except for the magnetization device, this would
not require drastic changes of the presented methodology for low frequencies.
With gastric distension and motility sensing implantable device there would
be a lot of work with long term studies on animals and then with the development
of proper algorithms for switching the electrical stimulation. Interestingly, from the
research point of view, this would be a correlation of volume and motility with
electrogastrogram (EGG). However, what concerns the measuring part, there would
be the necessity to decrease the power consumption of the electronics (it could use
square wave excitation at the proper frequency, etc.) and decrease its size, so that it
could be eventually placed into an implant housing. It would be necessary to change
the materials of the coils and cables to biocompatible ones. For example we could
use silver and/or platinum as even the silvered copper is considered toxic,
regardless of the insulation, and the traditionally used nickel-cobalt wires are not
acceptable for magnetic measurements because of their permeability. A Teflon
(PTFE) coating is also not acceptable for long term use inside the body so that
appropriate silicon insulation of the standard leads of the pacemakers should be
introduced. Higher precision setups of sensors could also be examined as well as
the practical limits of the driving frequency. The experiments suggest that we were
relatively sceptic concerning the AC-excitation of the implant surrounded by a
current conducting media on almost the same potential. There the frequency could
probably be increased, which would further reduce the power consumption.
- 114 -
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Jiří Tomek
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Appendix
8 Appendix
8.1 Publications
8.1.1 Articles in SCI journals
2009
Tomek J., Platil A., Ripka., Multiple Layer Scanning in Magnetopneumography, In IEEE
Sensors Journal Vol. 9, Issue 4, 383-389, ISSN 1530-437X (2009)
Tomek J. - Platil A., Magnetic Field Inversion for Magnetopneumography, In Sensor Letters
7 (3) - Special issue on EMSA 2008 - 8th European Magnetic Sensors & Actuators
Conference. Caen: Université de Caen 2008, ISSN: 1546-187X (2009)
Tomek J., Mlejnek P., Janásek V., Ripka P., Kašpar P., Zhu H, Chen J.D.Z., Gastric
Distention Sensing for Implantable Gastric Pacemaker, Journal of Gastroenterology (2009) submitted
2008
Tomek J., Mlejnek P., Janásek V, Ripka P., Kašpar P. and Chen, J., The precision of gastric
motility and volume sensing by implanted magnetic sensors, Sensors and Actuators A 142
(2008) 34-39
Platil A. - Tomek J., Magnetic Field Inversion for Magnetopneumography. In EMSA'08 8th European Magnetic Sensors & Actuators Conference. Caen: Université de Caen (2008)
108
2007
Tomek J, Mlejnek P, Janasek V, et al.: Gastric motility and volume sensing by implanted
magnetic sensors Sensor Letters 5 (1): 276-278, Special issue on EMSA 2006, ISSN 1546198X, 2007,
Platil, A. - Tomek, J. - Kašpar, P.: Characterization of Ferromagnetic Powders for
Magnetopneumography and Other Applications. In Sensor Letters Vol. 5, No. 1, p. 311-314
- Special issue on EMSA 2006, ISSN 1546-198X, 2007
Platil, A. - Tomek, J.: Simple Digitalization of Fluxgate Sensor. In Sensor Letters Vol. 5,
No. 1, p. 200-203 - Special issue on EMSA 2006, ISSN 1546-198X, 2007
- 122 -
Appendix
Tomek J, Platil A, Ripka P: Magnetopneumography - Advances in measurement procedure,
modelling and inversion using artificial neural networks IJAEM Special volume on ISEM
2005, Numbers 1-4 / 2007, pp. 401 – 406, ISSN 1383-5416, ISBN 978-1-58603-746-8 25
Tomek J., Platil A., Ripka P.: Application of Neural Networks Inversion in
Magnetopneumography, IJAEM Volume 26, Number 3-4/2007 pp. 285-290, ISSN 13835416
2006
Tomek J., Platil A., Ripka P., Kašpar P., Application of Fluxgate Gradiometer in
Magnetopneumography, Sensors and Actuators, vol. 132, no. 1, (2006a) 214-217. ISSN
0924-4247
8.1.2 Papers in other journals
Tomek J., Inductive contactless distance measurement intended for a gastric electrical
implant, Acta Polytecnica Vol.47, No. 4-5(2007) ISSN 1210-2709
8.1.3 Papers in international conference proceedings
2008
Platil, A. - Tomek, J.: Magnetic Field Inversion for Magnetopneumography. In EMSA'08 8th European Magnetic Sensors & Actuators Conference. Caen: Université de Caen, 2008,
p. 108.
2007
Tomek, J. – Platil, A. Magnetopneumography – Suppression of Background Field
Variations in Scanned Data for Inversion Using Multiple Fluxgates. In The Sixth IEEE
Conference on Sensors IEEE SENSORS 2007Final Program &Book of Abstracts, Atlanta,
Georgia, USA, 2007, pp. 523-524
& extended:
In The Sixth IEEE Conference on Sensors, IEEE SENSORS 2007, October 28-31, 2007,
Atlanta, Georgia, USA, pp.1020-1023, ISBN: 1-4244-1262-5, ISSN: 1930-0395
2006
Tomek, J. - Mlejnek, P. - Janásek, V. - Ripka, P. - Kašpar, P. – Chen, J.: Gastric Motility
and Volume Sensing by Implanted Magnetic Sensors. In EMSA '06 - 6th European
Magnetic Sensors and Actuators Conference. Bilbao (Spain): University of the Basque
Country, 2006, p. 35.
- 123 -
Appendix
Platil, A. - Tomek, J.: Simple Digitalization of Fluxgate Sensor. In EMSA '06 - 6th
European Magnetic Sensors and Actuators Conference. Bilbao (Spain): University of the
Basque Country, 2006, p. 146.
Platil, A. - Tomek, J. - Kašpar, P.: Characterization of Ferromagnetic Powders for
Magnetopneumography and Other Applications. In EMSA '06 - 6th European Magnetic
Sensors and Actuators Conference. Bilbao (Spain): University of the Basque Country, 2006,
p. 45.
Tomek J., Mlejnek P., Janásek V., Ripka P., Kašpar P. and Chen J.,: Volume and Motility
Sensing for Implantable Gastric Pacemaker. In IFMBE Proceedings World Congress on
Medical Physics and Biomedical Engineering 2006, Aug. 27.-Sept. 1., COEX Seoul, Korea
[CD-ROM]. Berlin: Springer-Verlag, Vol. 14 (2006) 4943, ISBN 3-540-36839-6
Tomek, J. - Platil, A. - Ripka, P.: Application of Neural Networks Inversion in
Magnetopneumography. In OIPE 2006 - the 9th Workshop on Optimization and Inverse
Problems in Electromagnetism. Sorrento (Italy): Seconda Universita degli Studi di Napoli,
2006, p. 243-244. ISBN 88-7146-733-7
Tomek, J. - Mlejnek, P. - Janásek, V. - Kašpar, P. - Ripka, P. - et al. The Precision of Gastric
Motility and Volume Sensing by Implanted Magnetic Sensors In: XX Eurosensors, 20th
Anniversary. Göteborg: Eurosensors, 2006, p. 254-255. ISBN 91-631-9280-2
Tomek, J. - Platil, A. - Ripka, P.: Optimization of Magnetopneumographic System for
Successful Inversion. In Magnetic Measurements '06 - The Book of Abstracts (Závažná
Poruba 2006). Bratislava: Slovak University of Technology, 2006, p. 65-66. ISBN 80-2272452-1.
2005
Tomek, J. - Platil, A. - Ripka, P. Advances in Measurement, Modelling and Inversion for
Magnetopneumography, In ISEM 2005 Short Paper Proc. Bad Gastein 09/2005 pp.218-219,
ISBN:3-902105-00-1
Tomek, J. - Platil, A. - Ripka, P. - Kašpar, P. Fluxgate Gradiometer in
Magnetopneumography In Eurosensors XIX Proc. Vol II, WPb49, Barcelona 09/2005
Tomek, J. - Platil, A. - Ripka, P. Magnetic Field of the Lungs – Neural Network Inverse
models In IFMBE Proc. (EMBEC´05), Volume 11, 2005, Prague 11/2005, ISSN: 1727 –
1983
2004
Tomek, J. - Ripka, P. - Tipek, A.: Magnetic Field of Human Lungs: Models and Inversion.
In Magnetic Measurements 2004. Praha: Czech Technical University in Prague, 2004, s. 7172. ISBN 80-01-02994-8
P. Ripka, J. Tomek, A. Tipek: Magnetic field of Human lungs: Models and measurement, In
Proc. JEMS 2004, Abstracts p. 163
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Appendix
8.1.4 Papers in other conference proceedings
Tomek J., Options for inductive contactless distance measurement intended for gastric
implant In Poster 2007 Proc. [CD-ROM] Prague: CTU 2007
Tomek J., Mlejnek P. Volume Sensing for On-demand Gastric Electrical Stimulation In
Poster 2006 Proc. [CD-ROM] Prague: CTU 2006
Tomek, J. Neural Networks Application in Modelling of Magnetic Field of the Lungs In
Poster 2005 Proc. [CD-ROM] Prague: CTU 2005
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Appendix B
Abbreviations
8.2 Abbreviations
AC
BFGS
CT
CTU
DC
EGG
EMT
GA
LVDT
MCG
MEG
MIT
MPG
MRI
NMR
MUSIC
PLCD
SPECT
SQUID
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
alternating current
Broyden-Fletcher-Goldfarb-Shanno (optimization method)
computed tomography
Czech Technical University
direct current
electrogastrography
electromagnetic tomography
genetic algorithm
linear variable differential transformer
magnetocardiography
magnetoencephalography
magnetic induction tomography
magnetopneumography
magnetic resonance imaging
nuclear magnetic resonance
multiple signal classification
permanent magnetic linear contactless displacement
single photon emission computed tomography
superconducting quantum interference device
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