Active Bidirectional Coupling in a Cochlear Chip Abstract

Active Bidirectional Coupling in a Cochlear Chip Abstract
Active Bidirectional Coupling in a Cochlear Chip
Bo Wen and Kwabena Boahen
Department of Bioengineering
University of Pennsylvania
Philadelphia, PA 19104
We present a novel cochlear model implemented in analog very large
scale integration (VLSI) technology that emulates nonlinear active
cochlear behavior. This silicon cochlea includes outer hair cell (OHC)
electromotility through active bidirectional coupling (ABC), a mechanism we proposed in which OHC motile forces, through the microanatomical organization of the organ of Corti, realize the cochlear
amplifier. Our chip measurements demonstrate that frequency responses
become larger and more sharply tuned when ABC is turned on; the degree of the enhancement decreases with input intensity as ABC includes
saturation of OHC forces.
Silicon Cochleae
Cochlear models, mathematical and physical, with the shared goal of emulating nonlinear
active cochlear behavior, shed light on how the cochlea works if based on cochlear micromechanics. Among the modeling efforts, silicon cochleae have promise in meeting the
need for real-time performance and low power consumption. Lyon and Mead developed
the first analog electronic cochlea [1], which employed a cascade of second-order filters
with exponentially decreasing resonant frequencies. However, the cascade structure suffers from delay and noise accumulation and lacks fault-tolerance. Modeling the cochlea
more faithfully, Watts built a two-dimensional (2D) passive cochlea that addressed these
shortcomings by incorporating the cochlear fluid using a resistive network [2]. This parallel structure, however, has its own problem: response gain is diminished by interference
among the second-order sections’ outputs due to the large phase change at resonance [3].
Listening more to biology, our silicon cochlea aims to overcome the shortcomings of existing architectures by mimicking the cochlear micromechanics while including outer hair cell
(OHC) electromotility. Although how exactly OHC motile forces boost the basilar membrane’s (BM) vibration remains a mystery, cochlear microanatomy provides clues. Based
on these clues, we previously proposed a novel mechanism, active bidirectional coupling
(ABC), for the cochlear amplifier [4]. Here, we report an analog VLSI chip that implements
this mechanism. In essence, our implementation is the first silicon cochlea that employs
stimulus enhancement (i.e., active behavior) instead of undamping (i.e., high filter Q [5]).
The paper is organized as follows. In Section 2, we present the hypothesized mechanism
(ABC), first described in [4]. In Section 3, we provide a mathematical formulation of the
of Corti
i -1
Figure 1: The inner ear. A Cutaway showing cochlear ducts (adapted from [6]). B Longitudinal view of cochlear partition (CP) (modified from [7]-[8]). Each outer hair cell (OHC)
tilts toward the base while the Deiter’s cell (DC) on which it sits extends a phalangeal process (PhP) toward the apex. The OHCs’ stereocilia and the PhPs’ apical ends form the
reticular lamina (RL). d is the tilt distance, and the segment size. IHC: inner hair cell.
model as the basis of cochlear circuit design. Then we proceed in Section 4 to synthesize
the circuit for the cochlear chip. Last, we present chip measurements in Section 5 that
demonstrate nonlinear active cochlear behavior.
Active Bidirectional Coupling
The cochlea actively amplifies acoustic signals as it performs spectral analysis. The movement of the stapes sets the cochlear fluid into motion, which passes the stimulus energy
onto a certain region of the BM, the main vibrating organ in the cochlea (Figure 1A). From
the base to the apex, BM fibers increase in width and decrease in thickness, resulting in an
exponential decrease in stiffness which, in turn, gives rise to the passive frequency tuning
of the cochlea. The OHCs’ electromotility is widely thought to account for the cochlea’s
exquisite sensitivity and discriminability. The exact way that OHC motile forces enhance
the BM’s motion, however, remains unresolved.
We propose that the triangular mechanical unit formed by an OHC, a phalangeal process
(PhP) extended from the Deiter’s cell (DC) on which the OHC sits, and a portion of the
reticular lamina (RL), between the OHC’s stereocilia end and the PhP’s apical tip, plays
an active role in enhancing the BM’s responses (Figure 1B). The cochlear partition (CP)
is divided into a number of segments longitudinally. Each segment includes one DC, one
PhP’s apical tip and one OHC’s stereocilia end, both attached to the RL. Approximating
the anatomy, we assume that when an OHC’s stereocilia end lies in segment i − 1, its
basolateral end lies in the immediately apical segment i. Furthermore, the DC in segment
i extends a PhP that angles toward the apex of the cochlea, with its apical end inserted just
behind the stereocilia end of the OHC in segment i + 1.
Our hypothesis (ABC) includes both feedforward and feedbackward interactions. On one
hand, the feedforward mechanism, proposed in [9], hypothesized that the force resulting
from OHC contraction or elongation is exerted onto an adjacent downstream BM segment
due to the OHC’s basal tilt. On the other hand, the novel insight of the feedbackward
mechanism is that the OHC force is delivered onto an adjacent upstream BM segment due
to the apical tilt of the PhP extending from the DC’s main trunk.
In a nutshell, the OHC motile forces, through the microanatomy of the CP, feed forward
and backward, in harmony with each other, resulting in bidirectional coupling between
BM segments in the longitudinal direction. Specifically, due to the opposite action of OHC
Distance from stapes HmmL
Figure 2: Wave propagation (WP) and basilar membrane (BM) impedance in the active
cochlear model with a 2kHz pure tone (α = 0.15, γ = 0.3). A WPp
in fluid and BM. B BM
impedance Zm (i.e., pressure divided by velocity), normalized by S(x)M (x). Only the
resistive component is shown; dot marks peak location.
forces on the BM and the RL, the motion of BM segment i − 1 reinforces that of segment i
while the motion of segment i + 1 opposes that of segment i, as described in detail in [4].
The 2D Nonlinear Active Model
To provide a blueprint for the cochlear circuit design, we formulate a 2D model of the
cochlea that includes ABC. Both the cochlea’s length (BM) and height (cochlear ducts)
are discretized into a number of segments, with the original aspect ratio of the cochlea
maintained. In the following expressions, x represents the distance from the stapes along
the CP, with x = 0 at the base (or the stapes) and x = L (uncoiled cochlear duct length) at
the apex; y represents the vertical distance from the BM, with y = 0 at the BM and y = ±h
(cochlear duct radius) at the bottom/top wall.
Providing that the assumption of fluid incompressibility holds, the velocity potential φ
of the fluids is required to satisfy 52 φ(x, y, t) = 0, where 52 denotes the Laplacian
operator. By definition, this potential is related to fluid velocities in the x and y directions:
Vx = −∂φ/∂x and Vy = −∂φ/∂y.
The BM is driven by the fluid pressure difference across it. Hence, the BM’s vertical motion
(with downward displacement being positive) can be described as follows.
Pd (x) + FOHC (x) = S(x)δ(x) + β(x)δ̇(x) + M (x)δ̈(x),
where S(x) is the stiffness, β(x) is the damping, and M (x) is the mass, per unit area, of
the BM; δ is the BM’s downward displacement. Pd = ρ ∂(φSV (x, y, t) − φST (x, y, t))/∂t
is the pressure difference between the two fluid ducts (the scala vestibuli (SV) and the scala
tympani (ST)), evaluated at the BM (y = 0); ρ is the fluid density.
The FOHC(x) term combines feedforward and feedbackward OHC forces, described by
FOHC (x) = s0 tanh(αγS(x)δ(x − d)/s0 ) − tanh(αS(x)δ(x + d)/s0 ) ,
where α denotes the OHC motility, expressed as a fraction of the BM stiffness, and γ is
the ratio of feedforward to feedbackward coupling, representing relative strengths of the
OHC forces exerted on the BM segment through the DC, directly and via the tilted PhP. d
denotes the tilt distance, which is the horizontal displacement between the source and the
recipient of the OHC force, assumed to be equal for the forward and backward cases. We
use the hyperbolic tangent function to model saturation of the OHC forces, the nonlinearity
that is evident in physiological measurements [8]; s0 determines the saturation level.
We observed wave propagation in the model and computed the BM’s impedance (i.e., the
ratio of driving pressure to velocity). Following the semi-analytical approach in [2], we
simulated a linear version of the model (without saturation). The traveling wave transitions
from long-wave to short-wave before the BM vibration peaks; the wavelength around the
characteristic place is comparable to the tilt distance (Figure 2A). The BM impedance’s
real part (i.e., the resistive component) becomes negative before the peak (Figure 2B). On
the whole, inclusion of OHC motility through ABC boosts the traveling wave by pumping
energy onto the BM when the wavelength matches the tilt of the OHC and PhP.
Analog VLSI Design and Implementation
Based on our mathematical model, which produces realistic responses, we implemented a
2D nonlinear active cochlear circuit in analog VLSI, taking advantage of the 2D nature of
silicon chips. We first synthesize a circuit analog of the mathematical model, and then we
implement the circuit in the log-domain. We start by synthesizing a passive model, and
then extend it to a nonlinear active one by including ABC with saturation.
4.1 Synthesizing the BM Circuit
The model consists of two fundamental parts: the cochlear fluid and the BM. First, we
design the fluid element and thus the fluid network. In discrete form, the fluids can be
viewed as a grid of elements with a specific resistance that corresponds to the fluid density
or mass. Since charge is conserved for a small sheet of resistance and so are particles for
a small volume of fluid, we use current to simulate fluid velocity. At the transistor level,
the current flowing through the channel of a MOS transistor, operating subthreshold as a
diffusive element, can be used for this purpose. Therefore, following the approach in [10],
we implement the cochlear fluid network using a diffusor network formed by a 2D grid of
nMOS transistors.
Second, we design the BM element and thus the BM. As current represents velocity, we
rewrite the BM boundary condition (Equation 1, without the FOHC term):
I˙in = S(x) Imem dt + β(x)Imem + M (x)I˙mem ,
where Iin , obtained by applying the voltage from the diffusor network to the gate of a
pMOS transistor, represents the velocity potential scaled by the fluid density. In turn, Imem
drives the diffusor network to match the fluid velocity with the BM velocity, δ̇. The FOHC
term is dealt with in Section 4.2.
Implementing this second-order system requires two state-space variables, which we name
Is and Io . And with s = jω, our synthesized BM design (passive) is
τ1 Is s + Is
τ2 Io s + Io
= −Iin + Io ,
= Iin − bIs ,
= Iin + Is − Io ,
where the two first-order systems are both low-pass filters (LPFs), with time constants τ1
and τ2 , respectively; b is a gain factor. Thus, Iin can be expressed in terms of Imem as:
Iin s2 = (b + 1)/τ1 τ2 + ((τ1 + τ2 )/τ1 τ2)s + s2 Imem .
Comparing this expression with the design target (Equation 3) yields the circuit analogs:
S(x) = (b + 1)/τ1τ2 ,
β(x) = (τ1 + τ2 )/τ1 τ2 ,
and M (x) = 1.
Note that the mass M (x) is a constant (i.e., 1), which was also the case in our mathematical model simulation. These analogies require that τ1 and τ2 increase exponentially to
( )
Iout+I out
B Iin-
To neighbors
From neighbors
- - +
Figure 3: Low-pass filter (LPF) and second-order section circuit design. A Half-LPF circuit. B Complete LPF circuit formed by two half-LPF circuits. C Basilar membrane (BM)
circuit. It consists of two LPFs and connects to its neighbors through Is and IT .
simulate the exponentially decreasing BM stiffness (and damping); b allows us to achieve
a reasonable stiffness for a practical choice of τ1 and τ2 (capacitor size is limited by silicon
4.2 Adding Active Bidirectional Coupling
To include ABC in the BM boundary condition, we replace δ in Equation 2 with Imem dt
to obtain
FOHC = rff S(x)T Imem (x − d)dt − rfb S(x)T Imem (x + d)dt ,
where rff = αγ and rfb = α denote the feedforward and feedbackward OHC motility
factors, and T denotes saturation. The saturation is applied to the displacement, instead
of the force, as this simplifies the implementation. We obtain the integrals
by observing
that, in the passive
(x − d)dt =
−τ1f Isf and Imem (x + d)dt = −τ1b Isb . Here, Isf and Isb represent the outputs of the first
LPF in the upstream and downstream BM segments, respectively; τ1f and τ1b represent
their respective time constants. To reduce complexity in implementation, we use τ1 to
approximate both τ1f and τ1b as the longitudinal span is small.
We obtain the active BM design by replacing Equation 5 with the synthesis result:
τ2 Ios + Io = Iin − bIs + rfb (b + 1)T (−Isb ) − rff (b + 1)T (−Isf ).
Note that, to implement ABC, we only need to add two currents to the second LPF in
the passive system. These currents, Isf and Isb , come from the upstream and downstream
neighbors of each segment.
IT +
IT Is+
Vsat Imem
Is+ Is+
Is- IsBM
IT + IT +
IT +
IT Is+
Figure 4: Cochlear chip. A Architecture: Two diffusive grids with embedded BM circuits
model the cochlea. B Detail. BM circuits exchange currents with their neighbors.
4.3 Class AB Log-domain Implementation
We employ the log-domain filtering technique [11] to realize current-mode operation. In
addition, following the approach proposed in [12], we implement the circuit in Class AB to
increase dynamic range, reduce the effect of mismatch and lower power consumption. This
differential signaling is inspired by the way the biological cochlea works—the vibration of
BM is driven by the pressure difference across it.
Taking a bottom-up strategy, we start by designing a Class AB LPF, a building block for
the BM circuit. It is described by
+ −
τ (Iout
− Iout
)s + (Iout
− Iout
) = Iin
− Iin
and τ Iout
Iout s + Iout
= Iq2 ,
where Iq sets the geometric mean of the positive and negative components of the output
current, and τ sets the time constant.
Combining the common-mode constraint with the differential design equation yields the
nodal equation for the positive path (the negative path has superscripts + and − swapped):
C V̇out
= Iτ (Iin
− Iin
) + (Iq2 /Iout
− Iout
) /(Iout
+ Iout
This nodal equation suggests the half-LPF circuit shown in Figure 3A. Vout
, the voltage on
the positive capacitor (C ), gates a pMOS transistor to produce the corresponding current
signal, Iout
and Iout
are similarly related). The bias Vq sets the quiescent current Iq
while Vτ determines the current Iτ , which is related to the time constant by τ = CuT/κIτ
(κ is the subthreshold slope coefficient and uT is the thermal voltage). Two of these subcircuits, connected in push–pull, form a complete LPF (Figure 3B).
The BM circuit is implemented using two LPFs interacting in accordance with the synthesized design equations (Figure 3C). Imem is the combination of three currents, Iin , Is , and
Io . Each BM sends out Is and receives IT , a saturated version of its neighbor’s Is . The
saturation is accomplished by a current-limiting transistor (see Figure 4B), which yields
IT = T (Is ) = Is Isat /(Is + Isat ), where Isat is set by a bias voltage Vsat.
4.4 Chip Architecture
We fabricated a version of our cochlear chip architecture (Figure 4) with 360 BM circuits
and two 4680-element fluid grids (360 ×13). This chip occupies 10.9mm2 of silicon area in
0.25µm CMOS technology. Differential input signals are applied at the base while the two
fluid grids are connected at the apex through a fluid element that represents the helicotrema.
Chip Measurements
We carried out two measurements that demonstrate the desired amplification by ABC, and
the compressive growth of BM responses due to saturation. To obtain sinusoidal current as
the input to the BM subcircuits, we set the voltages applied at the base to be the logarithm
of a half-wave rectified sinusoid.
We first investigated BM-velocity frequency responses at six linearly spaced cochlear positions (Figure 5). The frequency that maximally excites the first position (Stage 30), defined
as its characteristic frequency (CF), is 12.1kHz. The remaining five CFs, from early to later
stages, are 8.2k, 1.7k, 905, 366, and 218Hz, respectively. Phase accumulation at the CFs
ranges from 0.56 to 2.67π radians, comparable to 1.67π radians in the mammalian cochlea
[13]. Q10 factor (the ratio of the CF to the bandwidth 10dB below the peak) ranges from
1.25 to 2.73, comparable to 2.55 at mid-sound intensity in biology (computed from [13]).
The cutoff slope ranges from -20 to -54dB/octave, as compared to -85dB/octave in biology
(computed from [13]).
230 190
BM Velocity
Phase HΠ radiansL
BM Velocity
Amplitude HdBL
0.1 0.2
0.5 1 2
Frequency HkHzL
10 20
0.1 0.2
0.5 1 2
5 10 20
Frequency HkHzL
Figure 5: Measured BM-velocity frequency responses at six locations. A Amplitude.
B Phase. Dashed lines: Biological data (adapted from [13]). Dots mark peaks.
We then explored the longitudinal pattern of BM-velocity responses and the effect of ABC.
Stimulating the chip using four different pure tones, we obtained responses in which a
4kHz input elicits a peak around Stage 85 while 500Hz sound travels all the way to Stage
178 and peaks there (Figure 6A). We varied the input voltage level and obtained frequency
responses at Stage 100 (Figure 6B). Input voltage level increases linearly such that the
current increases exponentially; the input current level (in dB) was estimated based on
the measured κ for this chip. As expected, we observed linearly increasing responses at
low frequencies in the logarithmic plot. In contrast, the responses around the CF increase
less and become broader with increasing input level as saturation takes effect in that region
(resembling a passive cochlea). We observed 24dB compression as compared to 27 to 47dB
in biology [13]. At the highest intensities, compression also occurs at low frequencies.
These chip measurements demonstrate that inclusion of ABC, simply through coupling
neighboring BM elements, transforms a passive cochlea into an active one. This active
cochlear model’s nonlinear responses are qualitatively comparable to physiological data.
We presented an analog VLSI implementation of a 2D nonlinear cochlear model that utilizes a novel active mechanism, ABC, which we proposed to account for the cochlear amplifier. ABC was shown to pump energy into the traveling wave. Rather than detecting
the wave’s amplitude and implementing an automatic-gain-control loop, our biomorphic
model accomplishes this simply by nonlinear interactions between adjacent neighbors. Im-
500 Hz
BM Velocity
Amplitude HdBL
BM Velocity
Amplitude HdBL
Input Level
48 dB
32 dB
Stage 100
16 dB
0 dB
Stage Number
0.5 1 2
5 10 20
Frequency HkHzL
Figure 6: Measured BM-velocity responses (cont’d). A Longitudinal responses (20-stage
moving average). Peak shifts to earlier (basal) stages as input frequency increases from
500 to 4kHz. B Effects of increasing input intensity. Responses become broader and show
compressive growth.
plemented in the log-domain, with Class AB operation, our silicon cochlea shows enhanced
frequency responses, with compressive behavior around the CF, when ABC is turned on.
These features are desirable in prosthetic applications and automatic speech recognition
systems as they capture the properties of the biological cochlea.
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