{"title": "Active Bidirectional Coupling in a Cochlear Chip", "book": "Advances in Neural Information Processing Systems", "page_first": 1497, "page_last": 1504, "abstract": null, "full_text": "Active Bidirectional Coupling in a Cochlear Chip\n\nBo Wen and Kwabena Boahen\nDepartment of Bioengineering\n\nUniversity of Pennsylvania\n\nPhiladelphia, PA 19104\n\n{wenbo,boahen}@seas.upenn.edu\n\nAbstract\n\nWe present a novel cochlear model implemented in analog very large\nscale integration (VLSI) technology that emulates nonlinear active\ncochlear behavior. This silicon cochlea includes outer hair cell (OHC)\nelectromotility through active bidirectional coupling (ABC), a mech-\nanism we proposed in which OHC motile forces,\nthrough the mi-\ncroanatomical organization of the organ of Corti, realize the cochlear\nampli\ufb01er. Our chip measurements demonstrate that frequency responses\nbecome larger and more sharply tuned when ABC is turned on; the de-\ngree of the enhancement decreases with input intensity as ABC includes\nsaturation of OHC forces.\n\n1 Silicon Cochleae\n\nCochlear models, mathematical and physical, with the shared goal of emulating nonlinear\nactive cochlear behavior, shed light on how the cochlea works if based on cochlear mi-\ncromechanics. Among the modeling efforts, silicon cochleae have promise in meeting the\nneed for real-time performance and low power consumption. Lyon and Mead developed\nthe \ufb01rst analog electronic cochlea [1], which employed a cascade of second-order \ufb01lters\nwith exponentially decreasing resonant frequencies. However, the cascade structure suf-\nfers from delay and noise accumulation and lacks fault-tolerance. Modeling the cochlea\nmore faithfully, Watts built a two-dimensional (2D) passive cochlea that addressed these\nshortcomings by incorporating the cochlear \ufb02uid using a resistive network [2]. This par-\nallel structure, however, has its own problem: response gain is diminished by interference\namong the second-order sections\u2019 outputs due to the large phase change at resonance [3].\n\nListening more to biology, our silicon cochlea aims to overcome the shortcomings of exist-\ning architectures by mimicking the cochlear micromechanics while including outer hair cell\n(OHC) electromotility. Although how exactly OHC motile forces boost the basilar mem-\nbrane\u2019s (BM) vibration remains a mystery, cochlear microanatomy provides clues. Based\non these clues, we previously proposed a novel mechanism, active bidirectional coupling\n(ABC), for the cochlear ampli\ufb01er [4]. Here, we report an analog VLSI chip that implements\nthis mechanism. In essence, our implementation is the \ufb01rst silicon cochlea that employs\nstimulus enhancement (i.e., active behavior) instead of undamping (i.e., high \ufb01lter Q [5]).\n\nThe paper is organized as follows. In Section 2, we present the hypothesized mechanism\n(ABC), \ufb01rst described in [4]. In Section 3, we provide a mathematical formulation of the\n\n\f\u0004L=\u0006\nME\u0006@\u0006M\n\n4\u0006K\u0006@\nME\u0006@\u0006M\n\nA\n\n\u0006HC=\u0006\n\u0006B\u0014+\u0006HJE\n\n*\u0004\n\n10+\n\n5JAHA\u0006?E\u0006E=\n\n@\n\n2D2\n\n4\u0004\n\n\u00040+\n\n,+\n\n*\u0004\n\n*=I=\u0006\n\ni -1\n\ni\n\ni+1\n\n)FE?=\u0006\n\nB\n\nFigure 1: The inner ear. A Cutaway showing cochlear ducts (adapted from [6]). B Longi-\ntudinal view of cochlear partition (CP) (modi\ufb01ed from [7]-[8]). Each outer hair cell (OHC)\ntilts toward the base while the Deiter\u2019s cell (DC) on which it sits extends a phalangeal pro-\ncess (PhP) toward the apex. The OHCs\u2019 stereocilia and the PhPs\u2019 apical ends form the\nreticular lamina (RL). d is the tilt distance, and the segment size. IHC: inner hair cell.\n\nmodel as the basis of cochlear circuit design. Then we proceed in Section 4 to synthesize\nthe circuit for the cochlear chip. Last, we present chip measurements in Section 5 that\ndemonstrate nonlinear active cochlear behavior.\n\n2 Active Bidirectional Coupling\n\nThe cochlea actively ampli\ufb01es acoustic signals as it performs spectral analysis. The move-\nment of the stapes sets the cochlear \ufb02uid into motion, which passes the stimulus energy\nonto a certain region of the BM, the main vibrating organ in the cochlea (Figure 1A). From\nthe base to the apex, BM \ufb01bers increase in width and decrease in thickness, resulting in an\nexponential decrease in stiffness which, in turn, gives rise to the passive frequency tuning\nof the cochlea. The OHCs\u2019 electromotility is widely thought to account for the cochlea\u2019s\nexquisite sensitivity and discriminability. The exact way that OHC motile forces enhance\nthe BM\u2019s motion, however, remains unresolved.\n\nWe propose that the triangular mechanical unit formed by an OHC, a phalangeal process\n(PhP) extended from the Deiter\u2019s cell (DC) on which the OHC sits, and a portion of the\nreticular lamina (RL), between the OHC\u2019s stereocilia end and the PhP\u2019s apical tip, plays\nan active role in enhancing the BM\u2019s responses (Figure 1B). The cochlear partition (CP)\nis divided into a number of segments longitudinally. Each segment includes one DC, one\nPhP\u2019s apical tip and one OHC\u2019s stereocilia end, both attached to the RL. Approximating\nthe anatomy, we assume that when an OHC\u2019s stereocilia end lies in segment i \u2212 1, its\nbasolateral end lies in the immediately apical segment i. Furthermore, the DC in segment\ni extends a PhP that angles toward the apex of the cochlea, with its apical end inserted just\nbehind the stereocilia end of the OHC in segment i + 1.\nOur hypothesis (ABC) includes both feedforward and feedbackward interactions. On one\nhand, the feedforward mechanism, proposed in [9], hypothesized that the force resulting\nfrom OHC contraction or elongation is exerted onto an adjacent downstream BM segment\ndue to the OHC\u2019s basal tilt. On the other hand, the novel insight of the feedbackward\nmechanism is that the OHC force is delivered onto an adjacent upstream BM segment due\nto the apical tilt of the PhP extending from the DC\u2019s main trunk.\n\nIn a nutshell, the OHC motile forces, through the microanatomy of the CP, feed forward\nand backward, in harmony with each other, resulting in bidirectional coupling between\nBM segments in the longitudinal direction. Speci\ufb01cally, due to the opposite action of OHC\n\n\f\u0001\n\n\u0001\n\nx\n\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\u0001\n\nS\n\u0001\n\nM\n\nx\n\n\u0001\n\n\u0001\n\n\u0001\n\u0001\n\n\u0001\n\nm\nZ\n\ne\nR\n\n1\n\n0.5\n\n0\n-0.2\n\n0\n\nDistance from stapes\u0001mm\u0001\n\n15\n\n10\n\n5\n\n20\n\n25\n\nA\n\nB\n\nFigure 2: Wave propagation (WP) and basilar membrane (BM) impedance in the active\ncochlear model with a 2kHz pure tone (\u03b1 = 0.15, \u03b3 = 0.3). A WP in \ufb02uid and BM. B BM\n\nimpedance Zm (i.e., pressure divided by velocity), normalized bypS(x)M(x). Only the\n\nresistive component is shown; dot marks peak location.\n\nforces on the BM and the RL, the motion of BM segment i\u2212 1 reinforces that of segment i\nwhile the motion of segment i + 1opposes that of segment i, as described in detail in [4].\n\n3 The 2D Nonlinear Active Model\n\nTo provide a blueprint for the cochlear circuit design, we formulate a 2D model of the\ncochlea that includes ABC. Both the cochlea\u2019s length (BM) and height (cochlear ducts)\nare discretized into a number of segments, with the original aspect ratio of the cochlea\nmaintained. In the following expressions, x represents the distance from the stapes along\nthe CP, with x = 0at the base (or the stapes) and x = L (uncoiled cochlear duct length) at\nthe apex; y represents the vertical distance from the BM, with y = 0 at the BM and y = \u00b1h\n(cochlear duct radius) at the bottom/top wall.\n\nProviding that the assumption of \ufb02uid incompressibility holds, the velocity potential \u03c6\nof the \ufb02uids is required to satisfy 52\u03c6(x, y, t) = 0, where 52 denotes the Laplacian\noperator. By de\ufb01nition, this potential is related to \ufb02uid velocities in the x and y directions:\nVx = \u2212\u2202\u03c6/\u2202x and Vy = \u2212\u2202\u03c6/\u2202y.\nThe BM is driven by the \ufb02uid pressure difference across it. Hence, the BM\u2019s vertical motion\n(with downward displacement being positive) can be described as follows.\nPd(x) +F OHC(x) = S(x)\u03b4(x) +\u03b2 (x) \u02d9\u03b4(x) + M(x)\u00a8\u03b4(x),\n\n(1)\nwhere S(x) is the stiffness, \u03b2(x) is the damping, and M(x) is the mass, per unit area, of\nthe BM; \u03b4 is the BM\u2019s downward displacement. Pd = \u03c1 \u2202(\u03c6SV(x, y, t)\u2212 \u03c6ST(x, y, t))/\u2202t\nis the pressure difference between the two \ufb02uid ducts (the scala vestibuli (SV) and the scala\ntympani (ST)), evaluated at the BM (y = 0); \u03c1 is the \ufb02uid density.\nThe FOHC(x) term combines feedforward and feedbackward OHC forces, described by\n\nFOHC(x) = s0(cid:0) tanh(\u03b1\u03b3S(x)\u03b4(x \u2212 d)/s0) \u2212 tanh(\u03b1S(x)\u03b4(x + d)/s0)(cid:1),\n\n(2)\n\nwhere \u03b1 denotes the OHC motility, expressed as a fraction of the BM stiffness, and \u03b3 is\nthe ratio of feedforward to feedbackward coupling, representing relative strengths of the\nOHC forces exerted on the BM segment through the DC, directly and via the tilted PhP. d\ndenotes the tilt distance, which is the horizontal displacement between the source and the\nrecipient of the OHC force, assumed to be equal for the forward and backward cases. We\nuse the hyperbolic tangent function to model saturation of the OHC forces, the nonlinearity\nthat is evident in physiological measurements [8]; s0 determines the saturation level.\n\n\fWe observed wave propagation in the model and computed the BM\u2019s impedance (i.e., the\nratio of driving pressure to velocity). Following the semi-analytical approach in [2], we\nsimulated a linear version of the model (without saturation). The traveling wave transitions\nfrom long-wave to short-wave before the BM vibration peaks; the wavelength around the\ncharacteristic place is comparable to the tilt distance (Figure 2A). The BM impedance\u2019s\nreal part (i.e., the resistive component) becomes negative before the peak (Figure 2B). On\nthe whole, inclusion of OHC motility through ABC boosts the traveling wave by pumping\nenergy onto the BM when the wavelength matches the tilt of the OHC and PhP.\n\n4 Analog VLSI Design and Implementation\n\nBased on our mathematical model, which produces realistic responses, we implemented a\n2D nonlinear active cochlear circuit in analog VLSI, taking advantage of the 2D nature of\nsilicon chips. We \ufb01rst synthesize a circuit analog of the mathematical model, and then we\nimplement the circuit in the log-domain. We start by synthesizing a passive model, and\nthen extend it to a nonlinear active one by including ABC with saturation.\n\n4.1 Synthesizing the BM Circuit\n\nThe model consists of two fundamental parts: the cochlear \ufb02uid and the BM. First, we\ndesign the \ufb02uid element and thus the \ufb02uid network. In discrete form, the \ufb02uids can be\nviewed as a grid of elements with a speci\ufb01c resistance that corresponds to the \ufb02uid density\nor mass. Since charge is conserved for a small sheet of resistance and so are particles for\na small volume of \ufb02uid, we use current to simulate \ufb02uid velocity. At the transistor level,\nthe current \ufb02owing through the channel of a MOS transistor, operating subthreshold as a\ndiffusive element, can be used for this purpose. Therefore, following the approach in [10],\nwe implement the cochlear \ufb02uid network using a diffusor network formed by a 2D grid of\nnMOS transistors.\n\nSecond, we design the BM element and thus the BM. As current represents velocity, we\nrewrite the BM boundary condition (Equation 1, without the FOHC term):\n\n\u02d9Iin = S(x)R Imemdt+ \u03b2(x)Imem + M(x) \u02d9Imem,\n\n(3)\n\nwhere Iin, obtained by applying the voltage from the diffusor network to the gate of a\npMOS transistor, represents the velocity potential scaled by the \ufb02uid density. In turn, Imem\n\u02d9\u03b4. The FOHC\ndrives the diffusor network to match the \ufb02uid velocity with the BM velocity,\nterm is dealt with in Section 4.2.\n\nImplementing this second-order system requires two state-space variables, which we name\nIs and Io. And with s = j\u03c9, our synthesized BM design (passive) is\n\n\u03c41Iss + Is = \u2212Iin + Io,\n\u03c42Ios + Io = Iin \u2212 bIs,\n\n(4)\n(5)\n(6)\nwhere the two \ufb01rst-order systems are both low-pass \ufb01lters (LPFs), with time constants \u03c41\nand \u03c42, respectively; b is a gain factor. Thus, Iin can be expressed in terms of Imem as:\n\nIins2 =(cid:0)(b + 1)/\u03c41\u03c42 + ((\u03c41 + \u03c42)/\u03c41\u03c42)s + s2(cid:1) Imem.\n\nImem = Iin + Is \u2212 Io,\n\nComparing this expression with the design target (Equation 3) yields the circuit analogs:\n\nS(x) = (b + 1)/\u03c41\u03c42,\n\n\u03b2(x) = (\u03c41 + \u03c42)/\u03c41\u03c42,\n\nand M(x) = 1.\n\nNote that the mass M(x) is a constant (i.e., 1), which was also the case in our mathemat-\nical model simulation. These analogies require that \u03c41 and \u03c42 increase exponentially to\n\n\f0=\u0006B\n\u00042.\n\u0002\u001d\n\u001c\n\n8G\n\nA\n\n1E\u0006\u0002\n\n1E\u0006\u0002\n\nC\n\n1E\u0006\u0002\n\n1\u0006KJ\u0002\n\n1\u0006KJ\u0002\n\n1\u0006KJ\u0002\n\n1E\u0006\u0002\n\n1E\u0006\u0002\n\n+\u0002\n\nB\n\n1E\u0006\u0002\n\n\u0002\n\n\u0002\n\n\u0002 \u0002\n\n\u0002 \u0002\n\u0002 \u0002\n\n\u00042.\n1\u0006KJ\u0002\n\n1\u0006KJ\u0002\n\n*\u0004\n\n\u0002\n\n\u0002\n\n1I\u0002\n\n16\u0002\n\n>\n\n\u0002\n\n\u0002\n\n\u0002\n\n1\u0006\u0002\n\n\u0002\n\n\u0002\n\n\u0002 \u0002\n\n>\n\n\u0002\n\n1I\u0002\n\n16\u0002\n\n\u0002\n\n\u0002\n\n1\u0006\u0002\n\n6\u0006\u0014\u0006AECD>\u0006HI\n\n.H\u0006\u0006\u0014\u0006AECD>\u0006HI\n\n\u0002\n\n\u0002\n\n1\u0006A\u0006\u0002\n\n1\u0006A\u0006\u0002\n\nFigure 3: Low-pass \ufb01lter (LPF) and second-order section circuit design. A Half-LPF cir-\ncuit. B Complete LPF circuit formed by two half-LPF circuits. C Basilar membrane (BM)\ncircuit. It consists of two LPFs and connects to its neighbors through Is and IT.\n\nsimulate the exponentially decreasing BM stiffness (and damping); b allows us to achieve\na reasonable stiffness for a practical choice of \u03c41 and \u03c42 (capacitor size is limited by silicon\narea).\n\n4.2 Adding Active Bidirectional Coupling\n\nTo include ABC in the BM boundary condition, we replace \u03b4 in Equation 2 withR Imemdt\n\nFOHC = r\ufb00S(x)T(cid:0)R Imem(x \u2212 d)dt(cid:1) \u2212 rfbS(x)T(cid:0)R Imem(x + d)dt(cid:1) ,\n\nto obtain\n\nwhere r\ufb00 = \u03b1\u03b3 and rfb = \u03b1 denote the feedforward and feedbackward OHC motility\nfactors, and T denotes saturation. The saturation is applied to the displacement, instead\nof the force, as this simpli\ufb01es the implementation. We obtain the integrals by observing\n\nthat, in the passive design, the state variable Is = \u2212Imem/s\u03c41. Thus,RImem(x \u2212 d)dt =\n\u2212\u03c41f Isf andRImem(x + d)dt = \u2212\u03c41bIsb. Here, Isf and Isb represent the outputs of the \ufb01rst\n\nLPF in the upstream and downstream BM segments, respectively; \u03c41f and \u03c41b represent\ntheir respective time constants. To reduce complexity in implementation, we use \u03c41 to\napproximate both \u03c41f and \u03c41b as the longitudinal span is small.\nWe obtain the active BM design by replacing Equation 5 with the synthesis result:\n\n\u03c42Ios + Io = Iin \u2212 bIs + rfb(b + 1)T (\u2212Isb) \u2212 r\ufb00(b + 1)T (\u2212Isf).\n\nNote that, to implement ABC, we only need to add two currents to the second LPF in\nthe passive system. These currents, Isf and Isb, come from the upstream and downstream\nneighbors of each segment.\n\n\f158\n\n*=IA\n\n156\n\n.\u0006KE@\n\n.\u0006KE@\n\nA\n\n*\u0004\n\n)FAN\n\n\u0002\n\u0002\n\n16\n16\n\u0002\n1I\n\u0002\n1I\n\n\u0002\n\n1E\u0006\n\u0002\n1I\n\u0002\n1I\n16\n16\n\n\u0002\n\u0002\n\n\u0002\n\n1E\u0006\n\n8I=J\n\n\u0002\n\u0002\n\n16\n16\n\u0002\n1I\n\u0002\n1I\n\n8I=J\n\n\u0002\n\n1\u0006A\u0006\n\n\u0002\n1I\n\u0002\n1I\n*\u0004\n\u0002\n16\n\u0002\n16\n\u0002\n\n1\u0006A\u0006\n\nB\n\nFigure 4: Cochlear chip. A Architecture: Two diffusive grids with embedded BM circuits\nmodel the cochlea. B Detail. BM circuits exchange currents with their neighbors.\n\n4.3 Class AB Log-domain Implementation\n\nWe employ the log-domain \ufb01ltering technique [11] to realize current-mode operation. In\naddition, following the approach proposed in [12], we implement the circuit in Class AB to\nincrease dynamic range, reduce the effect of mismatch and lower power consumption. This\ndifferential signaling is inspired by the way the biological cochlea works\u2014the vibration of\nBM is driven by the pressure difference across it.\n\nTaking a bottom-up strategy, we start by designing a Class AB LPF, a building block for\nthe BM circuit. It is described by\nout \u2212 I\n\n\u2212\nout)s + (I +\n\n\u2212\nin and \u03c4 I +\n\n\u2212\nouts + I +\n\n\u2212\nout) = I +\n\nin \u2212 I\n\n\u2212\nout = I 2\nq ,\n\noutI\n\n\u03c4(I +\n\nout \u2212 I\n\noutI\n\nwhere Iq sets the geometric mean of the positive and negative components of the output\ncurrent, and \u03c4 sets the time constant.\n\nCombining the common-mode constraint with the differential design equation yields the\nnodal equation for the positive path (the negative path has superscripts + and \u2212 swapped):\n\nout = I\u03c4(cid:0)(I +\nin \u2212 I\n\nC \u02d9V +\n\n\u2212\nin) + (I 2\n\nout \u2212 I +\n\nq /I +\n\nout)(cid:1) /(I +\n\nout + I\n\n\u2212\nout).\n\nThis nodal equation suggests the half-LPF circuit shown in Figure 3A. V +\nout, the voltage on\nthe positive capacitor (C +), gates a pMOS transistor to produce the corresponding current\n\u2212\nsignal, I +\nout are similarly related). The bias Vq sets the quiescent current Iq\nwhile V\u03c4 determines the current I\u03c4 , which is related to the time constant by \u03c4 = CuT/\u03baI\u03c4\n(\u03ba is the subthreshold slope coef\ufb01cient and uT is the thermal voltage). Two of these sub-\ncircuits, connected in push\u2013pull, form a complete LPF (Figure 3B).\n\n\u2212\nout and I\n\nout (V\n\nThe BM circuit is implemented using two LPFs interacting in accordance with the synthe-\nsized design equations (Figure 3C). Imem is the combination of three currents, Iin, Is, and\nIo. Each BM sends out Is and receives IT, a saturated version of its neighbor\u2019s Is. The\nsaturation is accomplished by a current-limiting transistor (see Figure 4B), which yields\nIT = T (Is) = IsIsat/(Is + Isat), where Isat is set by a bias voltage Vsat.\n\n4.4 Chip Architecture\n\nWe fabricated a version of our cochlear chip architecture (Figure 4) with 360 BM circuits\nand two 4680-element \ufb02uid grids (360\u00d713). This chip occupies 10.9mm2 of silicon area in\n0.25\u00b5m CMOS technology. Differential input signals are applied at the base while the two\n\ufb02uid grids are connected at the apex through a \ufb02uid element that represents the helicotrema.\n\n\f5 Chip Measurements\n\nWe carried out two measurements that demonstrate the desired ampli\ufb01cation by ABC, and\nthe compressive growth of BM responses due to saturation. To obtain sinusoidal current as\nthe input to the BM subcircuits, we set the voltages applied at the base to be the logarithm\nof a half-wave recti\ufb01ed sinusoid.\n\nWe \ufb01rst investigated BM-velocity frequency responses at six linearly spaced cochlear posi-\ntions (Figure 5). The frequency that maximally excites the \ufb01rst position (Stage 30), de\ufb01ned\nas its characteristic frequency (CF), is 12.1kHz. The remaining \ufb01ve CFs, from early to later\nstages, are 8.2k, 1.7k, 905, 366, and 218Hz, respectively. Phase accumulation at the CFs\nranges from 0.56 to 2.67\u03c0 radians, comparable to 1.67\u03c0 radians in the mammalian cochlea\n[13]. Q10 factor (the ratio of the CF to the bandwidth 10dB below the peak) ranges from\n1.25 to 2.73, comparable to 2.55 at mid-sound intensity in biology (computed from [13]).\nThe cutoff slope ranges from -20 to -54dB/octave, as compared to -85dB/octave in biology\n(computed from [13]).\n\n\u0001\n\n\u0001\n\ny\nt\ni\nc\no\nl\ne\nV\n\nM\nB\n\nB\nd\n\ne\nd\nu\nt\ni\nl\np\nm\nA\n\nStage\n230\n\n50\n\n40\n\n30\n\n20\n\n10\n\n0\n-10\n\n0.1 0.2\n\n190\n\n150\n\n110\n\n70\n\n30\n\n\u0001\n\n0\n\n-2\n\ny\nt\ni\nc\no\nl\ne\nV\n\ns\nn\na\ni\nd\na\nr\n\u03a0\n\n\u0001\n\nM\nB\n\ne\ns\na\nh\nP\n\n-4\n\n10 20\n\n0.1 0.2\n\nFrequency\u0001kHz\u0001\n\n2\n\n5\n\n1\n\n0.5\n\nA\n\nFrequency\u0001kHz\u0001\n\n1\n\n2\n\n5\n\n0.5\n\nB\n\n10 20\n\nFigure 5: Measured BM-velocity frequency responses at six locations. A Amplitude.\nB Phase. Dashed lines: Biological data (adapted from [13]). Dots mark peaks.\n\nWe then explored the longitudinal pattern of BM-velocity responses and the effect of ABC.\nStimulating the chip using four different pure tones, we obtained responses in which a\n4kHz input elicits a peak around Stage 85 while 500Hz sound travels all the way to Stage\n178 and peaks there (Figure 6A). We varied the input voltage level and obtained frequency\nresponses at Stage 100 (Figure 6B). Input voltage level increases linearly such that the\ncurrent increases exponentially; the input current level (in dB) was estimated based on\nthe measured \u03ba for this chip. As expected, we observed linearly increasing responses at\nlow frequencies in the logarithmic plot. In contrast, the responses around the CF increase\nless and become broader with increasing input level as saturation takes effect in that region\n(resembling a passive cochlea). We observed 24dB compression as compared to 27 to 47dB\nin biology [13]. At the highest intensities, compression also occurs at low frequencies.\n\nThese chip measurements demonstrate that inclusion of ABC, simply through coupling\nneighboring BM elements, transforms a passive cochlea into an active one. This active\ncochlear model\u2019s nonlinear responses are qualitatively comparable to physiological data.\n\n6 Conclusions\n\nWe presented an analog VLSI implementation of a 2D nonlinear cochlear model that uti-\nlizes a novel active mechanism, ABC, which we proposed to account for the cochlear am-\npli\ufb01er. ABC was shown to pump energy into the traveling wave. Rather than detecting\nthe wave\u2019s amplitude and implementing an automatic-gain-control loop, our biomorphic\nmodel accomplishes this simply by nonlinear interactions between adjacent neighbors. Im-\n\n\f\u0001\n\n\u0001\n\ny\nt\ni\nc\no\nl\ne\nV\n\nM\nB\n\nB\nd\n\ne\nd\nu\nt\ni\nl\np\nm\nA\n\n20\n\n10\n\n0\n\n-10\n\n0\n\nFrequency\n\n4k\n\n2k\n\n1k\n\n500 Hz\n\n60\n\n\u0001\n\n\u0001\n\ny\nt\ni\nc\no\nl\ne\nV\n\nM\nB\n\nB\nd\n\n40\n\ne\nd\nu\nt\ni\nl\np\nm\nA\n\n20\n\n0\n\n50\n\n100\n\n150\n\n200\n\n0.2\n\nStage Number\nA\n\nInput Level\n\n48 dB\n\nStage 100\n\n32 dB\n16 dB\n\n0 dB\n\nFrequency\u0001kHz\u0001\n\n1\n\n2\n\n5\n\n0.5\n\nB\n\n10 20\n\nFigure 6: Measured BM-velocity responses (cont\u2019d). A Longitudinal responses (20-stage\nmoving average). Peak shifts to earlier (basal) stages as input frequency increases from\n500 to 4kHz. B Effects of increasing input intensity. Responses become broader and show\ncompressive growth.\n\nplemented in the log-domain, with Class AB operation, our silicon cochlea shows enhanced\nfrequency responses, with compressive behavior around the CF, when ABC is turned on.\nThese features are desirable in prosthetic applications and automatic speech recognition\nsystems as they capture the properties of the biological cochlea.\n\nReferences\n\n[1] Lyon, R.F. & Mead, C.A. (1988) An analog electronic cochlea. IEEE Trans. Acoust. Speech\n\nand Signal Proc., 36: 1119-1134.\n\n[2] Watts, L. (1993) Cochlear Mechanics: Analysis and Analog VLSI . Ph.D. thesis, Pasadena, CA:\n\nCalifornia Institute of Technology.\n\n[3] Fragni`ere, E. (2005) A 100-Channel analog CMOS auditory \ufb01lter bank for speech recognition.\n\nIEEE International Solid-State Circuits Conference (ISSCC 2005) , pp. 140-141.\n\n[4] Wen, B. & Boahen, K. (2003) A linear cochlear model with active bi-directional coupling.\nThe 25th Annual International Conference of the IEEE Engineering in Medicine and Biology\nSociety (EMBC 2003), pp. 2013-2016.\n\n[5] Sarpeshkar, R., Lyon, R.F., & Mead, C.A. (1996) An analog VLSI cochlear model with new\ntransconductance ampli\ufb01er and nonlinear gain control. Proceedings of the IEEE Symposium on\nCircuits and Systems (ISCAS 1996) , 3: 292-295.\n\n[6] Mead, C.A. (1989) Analog VLSI and Neural Systems . Reading, MA: Addison-Wesley.\n[7] Russell, I.J. & Nilsen, K.E. (1997) The location of the cochlear ampli\ufb01er: Spatial representation\nof a single tone on the guinea pig basilar membrane. Proc. Natl. Acad. Sci. USA, 94: 2660-2664.\n[8] Geisler, C.D. (1998) From sound to synapse: physiology of the mammalian ear . Oxford Uni-\n\nversity Press.\n\n[9] Geisler, C.D. & Sang, C. (1995) A cochlear model using feed-forward outer-hair-cell forces.\n\nHearing Research , 86: 132-146.\n\n[10] Boahen, K.A. & Andreou, A.G. (1992) A contrast sensitive silicon retina with reciprocal\nsynapses. In Moody, J.E. and Lippmann, R.P. (eds.), Advances in Neural Information Pro-\ncessing Systems 4 (NIPS 1992) , pp. 764-772, Morgan Kaufmann, San Mateo, CA.\n\n[11] Frey, D.R. (1993) Log-domain \ufb01ltering: an approach to current-mode \ufb01ltering. IEE Proc. G,\n\nCircuits Devices Syst., 140 (6): 406-416.\n\n[12] Zaghloul, K. & Boahen, K.A. (2005) An On-Off log-domain circuit that recreates adaptive\n\ufb01ltering in the retina. IEEE Transactions on Circuits and Systems I: Regular Papers , 52 (1):\n99-107.\n\n[13] Ruggero, M.A., Rich, N.C., Narayan, S.S., & Robles, L. (1997) Basilar membrane responses\n\nto tones at the base of the chinchilla cochlea. J. Acoust. Soc. Am., 101 (4): 2151-2163.\n\n\f", "award": [], "sourceid": 2840, "authors": [{"given_name": "Bo", "family_name": "Wen", "institution": null}, {"given_name": "Kwabena", "family_name": "Boahen", "institution": null}]}