{"title": "A Silicon Model of Amplitude Modulation Detection in the Auditory Brainstem", "book": "Advances in Neural Information Processing Systems", "page_first": 741, "page_last": 750, "abstract": null, "full_text": "A Silicon Model of \n\nAmplitude Modulation Detection \n\nin the Auditory Brainstem \n\nAnd~ van Schaik, Eric Fragniere, Eric Vittoz \n\nMANIRA Center for Neuromimetic Systems \n\nSwiss Federal Institute of Technology \n\nCH-lOlS Lausanne \n\nemail: Andre.van_Schaik@di.epfl.ch \n\nAbstract \n\nDetectim of the periodicity of amplitude modulatim is a major step in \nthe  determinatim  of  the  pitch  of  a  SOODd.  In  this  article  we  will \npresent  a silicm model  that uses  synchrroicity of spiking neurms  to \nextract  the  fundamental  frequency  of  a  SOODd.  It  is  based  m  the \nobservatim that the so called  'Choppers'  in the mammalian  Cochlear \nNucleus  synchrmize well  for  certain  rates  of amplitude  modulatim, \ndepending  m  the  cell's  intrinsic  chopping  frequency.  Our  silicm \nmodel uses  three different circuits, i.e.,  an  artificial cochlea,  an  Inner \nHair Cell circuit, and a spiking neuron circuit \n\n1. INTRODUCTION \n\nOver  the  last  few  years,  we  have  developed  and  implemented  several  analog  VLSI \nbuilding blocks  that allow us  to model parts of the auditory pathway [1],  [2],  [3].  This \npaper  presents  me experiment  using  these  building  blocks  to create  a  model  for  the \ndetection of the fundamental  frequency of a harmroic complex.  The estimatim of this \nfundamental  frequency  by  the  model  shows  some  important  similarities  with  psycho(cid:173)\nacoustic  experiments  in  pitch  estimation  in  humans  [4].  A  good  model  of  pitch \nestimation  will  give  us  valuable  insights  in  the  way  the  brain  processes  sounds. \nFurthermore,  a practical  application  to  speech  recognition  can  be  expected,  either  by \nusing the pitch estimate as an element in the acoustic vector fed  to the recognizer, or by \nnormalizing the acoustic vector to the pitch. \n\n\f742 \n\nA.  van Schaik,  E.  Fragniere and E.  Wttoz \n\nAlthough  the model  doesn't yield  a complete model  of pitch  estimatim,  and explains \nprobably mly one of a few different mechanisms the brain uses for  pitch estimatim, it \ncan give us  a  better understanding of the physiological background of psycho-acoustic \nresults. An electrmic model can be especially helpful, when the parameters of the model \ncan be easily controlled, and when the model will operate in real time. \n\n2. THE MODEL \n\nThe model  was originally developed  by Hewitt  and Meddis  [4],  and  was  based  m  the \nobservatim that Chopper cells in the Cochlear Nucleus synchronize when the stimulus \nis modulated in amplitude within a particular modulation frequency range [5]. \n\nInferior ... Beahu \necJInddmee nil \n\nCoehl ........ ecIuudeaI \n\nIlierlug  lDaer IbIr \n\nA \nA \n\nn111 AN \n\ntil \n~ \n\nHair e4illllCldoi \n\nFig. 1. Diagram of the AM detection model. BMF=Best Modulation Frequency. \n\nThe diagram shown in figure  1 shows the elements of the model. The cochlea filters the \nincoming sound signal. Since the width of the pass-band of a cochlear band-pass filter is \nproportimal to its cut-off frequency,  the filters will not be able to resolve the individual \nharmooics  of a  high  frequency  carrier  (>3kHz)  amplitude  modulated  at  a  low  rate \n\u00ab500Hz). The outputs of the cochlear filters  that have their cut-off frequency  slightly \nabove the carrier frequency of the signal will therefm-e still be modulated in amplitude at \nthe  mginal  modulatim  frequency.  This  modulatim  compment  will  therefm-e \nsynchronize  a  certain  group  of  Chopper  cells.  The  synchronizatim  of this  group  of \nChopper  cells  can  be  detected  using  a  coincidence  detecting  neurm,  and  signals  the \npresence  of a  particular  amplitude  modulation  frequency.  This  model  is  biologically \nplausible,  because it is known  that the choppers  synchronize to a  particular  amplitude \nmodulatim frequency and that they project their output towards  the Inferim- Colliculus \n(ammgst others).  Furthermm-e,  neurms that can functim  as coincidence detectm-s  are \nshown to be present in the Inferim- Colliculus and the rate of firing of these neurms is a \n\n\fA Silicon Model of Amplitude Modulation Detection \n\n743 \n\nband-pass functiro of the amplitude modulatiro rate. It is not known  to date however if \nthe choppers actually project to these coincidence detectoc neurons. \nThe  actual  mechanism  that  synchrooizes  the chopper  cells  will  be  discussed  with  the \nmeasurements  in  sectim 4.  In the next sectim.  we  will first  present  the  circuits  that \nallowed us to build the VLSI implementation of this model. \n\n3. THE CIRCUITS \n\nAll  of the  circuits  used  in  our  model  have  already  been  presented  in  m(X'e  detail \nelsewhere.  but we  will  present them briefly f(X'  completeness.  Our  silicro cochlea has \nbeen  presented  in  detail  at  NlPS'95  [1].  and m(X'e  details  about  the  Inner  Hair  Cell \ncircuit and the spiking neuron circuit can be found in [2]. \n\n3.1 THE SILICON COCHLEA \n\nThe  silicro  cochlea crosists of a  cascade  of secmd (X'der  low-pass  filters.  Each  filter \nsectiro is biased using  Compatible Lateral Bipolar Transist(X's  (Q.BTs) which crotrol \nthe cut-off frequency  and the  quality fact(X'  of each  sectiro.  A  single  resistive  line is \nused  to bias  all  Q.BTs. Because of the exponential relatiro between  the Base-Emitter \nVoltage and the Collectoc current of the Q.BTs. the linear voltage gradient introduced \nby the resistive  line will yield a  filter cascade with an exponentially decreasing cut-off \nfrequency  of the  filters.  The  output  voltage  of each  filter  Vout  then  represents  the \ndisplacement of a basilar membrane sectiro.  In (X'der  to obtain  a  representatim of the \nbasilar membrane velocity.  we  take the difference between  Vout  and  the voltage m  the \ninternal node of the second order filter. \nWe have integrated this silicro cochlea using  104 filter  stages.  and the output of every \nsecond stage is connected to an output pin. \n\n3.2 THE INNER HAIR CELL MODEL \n\nThe inner  hair  cell  circuit  is used  to  half-wave  rectify  the  basilar  membrane velocity \nsignal  and to perf(I'm  some f(I'm  of temp<X'al  adaptatiro.  as can be  seen  in figure  2b. \nThe differential pair at the input is used to crovert the input voltage into a current with \na compressive relatim between input amplitude and the actual amplitude of the current. \n\n~Or---------------------~ \n\n~1.5 \n11.0 \n~ 0.5 \n\n0.0 . .  _NIl ... ..., ...... ..,.,.. ................. \n35 \n\n25 \n\n30 \n\n15 \n20 \ntlma (me) \n\no \n\n5 \n\n10 \n\nFig. 2. a) The Inner Hair Cell circuit. b) measured output current \n\nWe have integrated a small chip containing 4 independent inner hair cells. \n\n\f744 \n\nA.  van Schaik,  E.  Fragniere and E.  Vzttoz \n\n3.3 THE SPIKING NEURON MODEL \n\nThe spiking neuron circuit is given in figure 3. The membrane of a biological neuron is \nmodeled by a capacitance. Cmem.  and the membrane leakage current is coo.trolled by the \ngate  voltage.  VIeako  of an  NMOS  transiskX'.  In  the  absence  of  any  input  O\"ex=O).  the \nmembrane  voltage  will  be  drawn  to  its  resting  potential  (coo.trolled  by  V rest).  by  this \nleakage  current.  Excitatory  inputs  simply  add  charge  to  the  membrane  capacitance. \nwhereas inhibitory inputs  are simply modeled by a negative lex.  If an excitatory current \nlarger than the leakage current of the membrane is injected. the membrane potential will \nincrease from  its resting potential.  This membrane potential.  Vroom,  is COOlpared  with  a \ncoo.trollable threshold voltage V three.  using a basic transconductance amplifier driving  a \nhigh impedance load. If V mem exceeds V threa.  an action potential will be generated. \n\nFig. 3. The Spiking Neuron circuit \n\nThe  generation  of the  actioo  potential  happens  in  a  similar  way  as  in  the  biological \nneuron. where an increased sodium coo.ductance creates the upswing of the spike. and a \ndelayed increase of the potassium coo.ductance creates the downswing. In the circuit this \nis modeled  as  follows.  H V mam  rises  above  Vthrea\u2022  the  output voltage of the  COOlparat<X\" \nwill rise to the positive power supply.  The output of the following  inverter will thus go \nlow. thereby allowing the \"sodium current\" INa  to pull Up the membrane potential. At the \nsame time however.  a second inverter will  allow the capacitance CK  to be charged at a \nspeed which can be coo.trolled by the current ~p. As soon  as the voltage on  CK  is high \nenough  to  allow  coo.ductioo  of  the  NMOS  to  which  it  is  connected.  the  \"potassium \ncurrent\" IK will be able to discharge the membrane capacitance. \nH V mam now drops below V threat  the output of the first inverter will become high. cutting \noff the current INa.  Furtherm<X\"e. the second inverter will then allow CK  to be discharged \nby the current IKdown. If IKdown  is small, the voltage on CK  will decrease only slowly.  and. \nas loog as this voltage stays high enough to allow IK  to discharge the membrane. it will \nbe  impossible to  stimulate the neuron if lex  is  smaller than  IK \u2022  Theref<X\"e  ~own can  be \nsaid to control the 'refractory period' of the neuron. \nWe have integrated a chip. coo.taining a group of 32 neurons. each having the same bias \nvoltages  and currents. The COOlponent mismatch  and  the noise ensure that we  actually \nhave 32 similar. but not completely equal neurons. \n\n4. TEST RESULTS \n\nMost neuro-physiological data coo.cerning low frequency amplitude modulation of high \nfrequency  carriers exists  f<X\"  carriers  at  about  5kHz  and  a modulation  depth  of about \n50%.  We  theref<X\"e  used  a 5 kHz  sinusoid in our tests  and  a 50%  modulatioo depth  at \nfrequencies below 550Hz. \n\n\fA Silicon Model of Amplitude Modulation Detection \n\n745 \n\n250 \n\n200 \n\ni 150 \n\n100 \n\n1-'-1 \n\n50 \n\n0 \n\n0 \n\n10 \n\n20 \n\n30 \nItn.~.) \n\n40 \n\n50 \n\n250 \n\n200 \n\nj  150 \n1 100 \n50 \n\n0 \n\n0 \n\n10 \n\n20 \n\n30 \nItn.~.) \n\n40 \n\n50 \n\nFig. 4. PSTH of the chopper chip for 2 different sound intensities \n\nFirst step in the elaboration of the model is to test if the group of spiking neurons on a \nsingle chip is capable of performing like a group of similar  Choppers.  Neurons  in the \nauditory  brainstem  are  often  characterized  with  a  Post  Stimulus  Time  Histogram \n(pSTH), which is a histogram of spikes in response to repeated stimulatien with a pure \ntone of short duratien. If the choppers en the chip are really similar, the PSTH of this \ngroup of choppers will be very similar to the PSTH of a  single chopper. In figure 4  the \nPSTH of the circuit is shown.  It is the result of the summed response of the 32 neurens \nen chip to 20 repeated  stimulatiens with  a 5kHz  tene burst.  This figure  shows that the \nresponse  of  the  Choppers  yields  a  PSTH  typical  of chopping  neurens,  and  that  the \nchopping  frequency,  keeping  all  other  parameters  constant,  increases  with  increasing \nsound  intensity.  The  chopping  rate  for  an  input  signal  of  given  intensity  can  be \ncontrolled by setting the refractory period of the spiking neurons,  and can thus be used \nto create the different groups of choppers shown  in figure  1.  The chopping rate of the \nchoppers in figure 4 is about 300Hz for a 29dB input signal. \n\n1..,..\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7,\u00b7_-\n\n0.5 \n\n0 \u2022 \u2022 \u2022  \n\no \n\n::>  (5 \n\n< \n::>( \u00bb  \nrefractory  charging  spkt \nperiod  w iclth \n\nperiod \n\n-Merrbrane \n\npotential \n\n10  time (rrs) \n\nStirrulation \nthreshoki \n\nFig. 5. Spike generation for a Chopper cell. \n\nTo understand why the Choppers  will  synchronize fix'  a certain  amplitude modulatien \nfrequency, one has to look at the signal envelope, which CCIltains  tempocal  information \nen a  time scale that can influence the spiking neurens. The 5kHz carrier itself will not \ncontain  any tempocal  informatien  that influences  the  spiking  neuren  in  an  impoctant \nway.  Consider  the  case  when  the  modulation  frequency  is  similar  to  the  chopping \nfrequency (figure 5). If a Chopper then spikes during the rising flank of the envelope, it \nwill come out of its refractory period just before the next rising flank of the envelope. If \nthe  driven  chopping  frequency  is  a  bit  too  low,  the  Chopper  will  come  out  of  its \nrefractory period  a  bit  later,  therefix'e  it  receives  a  higher  average  stimulation  and  it \nspikes  a  little  higher  en  the  rising  flank  of the  envelope.  This  in  turn  increases  the \nchopping  frequency  and  thus  provides  a  form  of negative  feedback  on  the  chopping \nfrequency.  This  theref(X'e  makes  spiking  en a  certain  point  en the rising flank  of the \nenvelope a  stable situatien. With the same reasening one can show that spiking en the \nfalling flank is theref(X'e an unstable situatien. Furthermore, it is not possible to stabilize \na cell driven above its maximum chopping rate, n(X'  is it possible to stabilize a cell that \nfires  m(X'e  than  ence  per modulatien  period.  Since  a  group  of  similar  choppers  will \n\n\f746 \n\nA. van Schaik, E. Fragniere and E.  Vittoz \n\nstabilize at about the same point on the rising flank. their spikes will thus coincide when \nthe modulation frequency allows them to. \n\n250200 \n\n........................................ m \u00b7\u00b7 ... \u2022\u00b7 .. \u00b7\u00b7\u00b7 .... i~4&;i3\"li:\u00b7 \n\n..... \u00b7\u00b7\u00b7\u2022 ........... \u2022\u2022 ...... \u2022 .. \u00b7\u2022\u2022 .. \u2022\u2022 .. \u00b7\u2022\u2022\u2022\u00b7\u2022 ... \u00b7\u00b7 .... \u2022 .. I==\u00b7[! \n\nl \n\n2SO \n\n200 \n\nmodllllllDn .... (HI) \n\no \n\n100 \n\n200 \n\n300 \n\n400 \n\n500 \n\n600 \n\nmodulldon .... (HI) \n\nFig. 6. AM sensitivity of the coincidence detecting neuron. \n\nAnother  free  parameter  of  the  model  is  the  threshold  of  the  coincidence  detecting \nneuron. If this parameter is  set so that at least 60% of the choppers must spike within \nIms to be considered  a coincidence.  we obtain  the output of figure 6.  We can see  that \nthis  yields  the expected  band-pass  Modulation Transfer Function  (MTF).  and  that  the \nbest  modulation  frequency  f(X'  the  29dB  input  signal  caTesponds  to  the  intrinsic \nchopping rate of the group of neuroo.s.  Figure 6  also shows  that  the  best  modulatioo. \nfrequency  (BMF). just as  the chopping rate.  increases  with  increasing  sound  intensity. \nbut  that  the  maximum  number  of spikes  per  second  actually  decreases.  This  second \neffect is caused by the fact  that the stabilizing effect of the positive flank  of the signal \nenvelope  only  influences  the  time  during  which  the  neuron  is  being  charged.  which \nbecomes  a  smaller part of the  total  spiking  period  at  higher  intensities.  The negative \nfeedback thus has less influence on the total chopping period and therefore synchronizes \nthe choppers less. \n\n25O~ \n200~ \n\n250 \n\n.\u2022\u2022...\u2022\u2022\u2022...\u2022. .\u2022\u2022...........\u2022.........\u2022.\u2022..\u2022\u2022.\u2022\u2022\u2022.\u2022\u2022\u2022\u2022 .\u2022.\u2022..\u2022. .\u2022.........\u2022\u2022 \n---.15.5c1! \n\n200 f------' \n\no \n\n100 \n\n200 \n\n300 \n\n400 \n\n500 \n\n600 \n\n100 \n\n200 \n\n300 \n\n400 \n\n500 \n\n600 \n\nmoduWlon .... (HI) \n\na \n\nmodllllllDn .... (HE) \n\nb \n\nFig. 7. AM sensitivity of the coincidence detecting neuron. \n\nWhen  the coincidence threshold  is  lowered  to 50%.  we  can  see  in figure  7a  that  the \nmaximum  number  of  spikes  goes  up.  because  this  threshold  is  m(X'e  easily  reached. \nFurthermore.  a  second  pass-band  shows  up  at  double  the  BMF.  This  is  because  the \nchoppers fire only every second amplitude modulation period.  and part of the group of \nchoppers  will  synchronize  during  the  odd  periods.  whereas  others  during  the  even \nperiods. The division of the group of choppers will typically be close to.  but hardly ever \nexactly 50-50.  so that either during the odd  or  during  the even  modulation period the \n50% coincidence threshold is exceeded.  The 60%  threshold of figure 6 will only rarely \nbe exceeded. explaining the weak second peak seen around 500Hz in this figure. \n\n\fA Silicon Model of Amplitude Modulation Detection \n\n747 \n\nFigure 7b.  shows the MIF f<X\"  low intensity signals with  a SO%  coincidence threshold. \nAt  low  intensities  the  effect  of an  additional  non-linearity,  the  stimulation  threshold, \nshows  up.  Whenever  the  instantaneous  value  of  the  envelope  is  lower  than  the \nstimulatioo threshold, the spiking neuroo will not be stimulated because its input current \nwill be lower than the cell's leakage current. At these low intensities the activity during \nthe valleys of the modulatioo envelope will thus not be enough to stimulate the Choppers \n(see figure 5). F<X\"  stimuli with  a lower modulatioo frequency than the group's chopping \nfrequency,  the Choppers will come out of their refract<X\"y period in such a valley. These \nchoppers  theref<X\"e  will  have  to  wait  f<X\"  the  envelope  amplitude  to  increase  above  a \ncertain value,  bef<X\"e  they receive  anew  a stimulatioo. This waiting period nullifies the \neffect of the variatioo of the refractory period of the Choppers, and thus synchronizes the \nChoppers for low modulatioo frequencies.  A secoo.d effect of this waiting period is that \nin this case the firing rate of the Choppers matches the modulation frequency.  When the \nmodulation  frequency  becomes  higher  than  the  maximum  chopping  frequency,  the \nChoppers  will  fire  only every  secood  period,  but  will  still  be  synchronized,  as  can  be \nseen between 300Hz and 500Hz in figure 7b. \n\n5. CONCLUSIONS \n\nIn this  article  we have  shown  that it is  possible  to use  our  building blocks  to build  a \nmulti-chip system  that models  part of the  audit(X\"y  pathway.  Furtherm<X\"e,  the fact  that \nthe spiking neuron chip can be easily biased to function as  a group of similar Choppers, \ncombined  with  the  relative  simplicity  of the  spike  generation  mechanism  of a  single \nneuroo 00 chip, allowed us to gain insight in the process by which chopping neurons in \nthe  mammalian  Cochlear  Nucleus  synchronize  to  a  particular  range  of  amplitude \nmodulation frequencies. \n\nReferences \n\n[1]  A.  van  Schaik,  E.  Fragniere,  &  E.  Vittoz,  \"Improved  silicm  cochlea  using \ncompatible lateral bipolar transist<X\"s,\"  Advances in Neural Information Processing \nSystems 8, MIT Press, Cambridge, 1996. \n\n[2]  A.  van Schaik, E.  Fragniere, &  E. Vittoz,  \"An analoge electronic model of ventral \ncochlear  nucleus  neurons,\"  Proc.  Fifth  Int. Con!  on  Microelectronics for  Neural \nNetworks  and Fuzzy  Systems,  IEEE  Computer Society Press,  Los  Alamitos,  1996, \npp. S2-59. \n\n[3]  A.  van  Schaik  and  R  Meddis,  \"The  electronic  ear;  towards  a  blueprint,\" \n\nNeurobiology, NATO ASI series, Plenum Press, New York, 1996. \n\n[4]  MJ. Hewitt and R  Meddis, \"A computer model of amplitude-modulatioo sensitivity \n\nof single units in the inferior colliculus,\" 1. Acoust. Soc. Am., 9S, 1994, pp.  I-IS. \n\n[S]  MJ.  Hewitt,  R  Meddis,  & T.M.  Shackletoo,  \"A  computer  model  of a  cochlear(cid:173)\nnucleus  stellate cell:  respooses  to  amplitude-modulated  and  pure  tone  stimuli,\" 1. \nAcoust. Soc. Am., 91. 1992, pp. 2096-2109. \n\n\f\fPART VI \n\nSPEECH, HANDWRITING AND  SIGNAL \n\nPROCESSING \n\n\f\f", "award": [], "sourceid": 1265, "authors": [{"given_name": "Andr\u00e9", "family_name": "van Schaik", "institution": null}, {"given_name": "Eric", "family_name": "Fragni\u00e8re", "institution": null}, {"given_name": "Eric", "family_name": "Vittoz", "institution": null}]}