{"title": "A Passive Shared Element Analog Electrical Cochlea", "book": "Advances in Neural Information Processing Systems", "page_first": 662, "page_last": 670, "abstract": null, "full_text": "662 \n\nA  PASSIVE  SHARED  ELEMENT  ANALOG \n\nELECTRICAL  COCHLEA \n\nJoe Eisenberg \nBioeng. Group \nU.C. Berkeley \n\nEdwin Lewis \nDept Elect. Eng. \nU.C. Berkeley \n\nDavid Feld \nDept. Elect. Eng. \n207-30 Cory Hall \nU.C. Berkeley \nBerkeley, CA. 94720 \n\nABSTRACT \n\nWe present a  simplified model  of the  micromechanics of the human \ncochlea,  realized  with  electrical  elements.  Simulation  of the  model \nshows that it retains four signal processing features whose importance \nwe argue on the basis of engineering logic and evolutionary evidence. \nFurthermore, just as  the cochlea does,  the  model  achieves  massively \nparallel signal processing in a structurally economic way, by means of \nshared elements.  By extracting what we believe are the five essential \nfeatures of the cochlea, we hope to design a useful  front-end  filter to \nprocess  acoustic  images and to  obtain  a  better understanding  of the \nauditory system. \n\nINTRODUCTION \n\nResults of psychoacoustical and physiological experiments in humans indicate that \nthe auditory system  creates acoustic images via massively parallel neural computations. \nThese computations  enable the brain to perform voice detection, sound localization, and \nmany other complex taskS.  For example, by recording a random signal with a wide range \nof frequency  components, and playing this signal simultaneously through both channels \nof a stereo headset, one causes the brain to create an acoustical image of a \"shsh\" sound in \nthe center of the head.  Delaying the presentation of just one frequency component in the \nrandom  signal going  to  one ear and  simultaneously playing  the  original  signal  to the \nother ear, one would still have the image of a \"shsh\" in the center of the head; however if \none mentally searches the acoustical image space carefully, a clear tone can be found far \noff to one side of the head.  The frequency of this tone will be that of the component with \nthe time delay to one ear.  Both ears still are receiving wide-band random signals.  The \nisolated  tone  will not be perceptible from  the signal to  either ear alone;  but with both \nsignals together, the brain  has  enough data to isolate the delayed tone in an  acoustical \nimage.  The brain achieves this by massively parallel neural computation. \n\nBecause the acoustic front-end fIlter for the brain is the cochlea, people have proposed \nthat analogs of the cochlea might serve well as front-end fIlters  for man-made processors \nIf we  were  to  base a cochlear analog on \nof acoustical images  (Lyon,  Mead,  1988). \ncurrent biophysical models of this structure, it would be extraordinarily complicated and \nextremely difficult to  realize with  hardware.  Because of this, we want to start with a \ncochlear model  that incorporates a  minimum set of essential ingredients.  The ears of \nlower vertebrates, such as alligators and frogs, provide some clues to help identify those \ningredients.  These animals presumably have to compute acoustic images similar to ours, \n\n\fA Passive Shared Element Analog Electrical Cochlea \n\n663 \n\nbut they do not have cochleas.  The acoustic front-end filters in the ears of these animals \nevolved independently and in parallel to the evolution of the cochlea.  Nevertheless, those \nfront-end  filters  share  four  functional  properties  with  the part of the  cochlea which \nresponds to the lower 7 out of 10 octaves of hearing (20 Hz. to 2560 Hz.): \n\n1.  They are multichannel ftlters with each channel \n\ncovering a different part of the frequency spectrum. \n\n2.  Each channel is a relatively broad-band frequency \n\nfilter. \n\n3.  Each filter has an extremely steep high-frequency \n\nband edge (typically 60 to 200 db/oct). \n\n4.  Each filter has nearly linear phase shift as a function \n\nof frequency, within its passband. \n\nThe front-end acoustical filters of lower vertebrates also have at least one structural feature \nin  common with  the  cochlea:  namely,  the  various filter channels share their dynamic \ncomponents.  This is the fifth property we choose to include.  Properties 1 and 3 provide \ngood resolution in frequency;  properties 2 and 4 are what filter designers would add to \nprovide good resolution in time. \n\nIn order to compute acoustical images with the neural networks in our brain, we need \nboth kinds of resolution: time and frequency.  Shared elements, a structural feature, has \nobvious advantages  for economy of construction.  The fact that evolution has come  to \nthese  same  front-end  filter  properties repeatedly  suggests  that  these properties  have \ncompelling  advantages  with  respect to  an  animal's  survival.  We  submit that  we  can \nrealize all of these properties very well with the simplest of the modern cochlear models, \nthat  of Joseph  Zwislocki  (1965).  This  is  a  transmission  line  model  made \nnamely \nentirely of passive elements. \n\nFigure 1 - Drawing  of the ear with  the  cochlea represented  by  an \n\nelectrical  analog. \n\n\f664 \n\nFeld, Eisenberg and Lewis \n\nA  COCHLEAR MODEL \n\nIn  order  to  illustrate  Zwislocki's  model,  a  quick  review  of the  mechanics  of the \ncochlea is useful.  Figure 1 depicts the ear with  the cochlea  represented by an electrical \nanalog.  A sound pressure wave enters the outer ear  and strikes the ear drum  which, in \nturn, causes the three bones of the  middle ear to vibrate.  The last bone, known  as the \nstapes, is connected to the oval window (represented in figure  1 by the voltage source at \nthe  beginning of the  electrical analog), where  the acoustic energy  enters  the cochlea. \nAs  the  acoustic energy  is  transferred  to  the oval  window,  a  fluid-mechanical  wave  is \nformed  along  a  structure known  as  the  basilar  membrane  ([his  membrane  and  the \nsurrounding fluid is represented by the series and shunt circuit elements of figure 1).  As \nthe basilar membrane  vibrates,  the acoustical  signal is  transduced to  neural  impulses \nwhich travel along the auditory nerve, carrying the data used by the  nervous system  to \ncompute auditory  images.  Figure 2 is taken from  a paper by  Zweig et al.  (1976), and \ndepicts an uncoiled cochlea. As the fluid-mechanical wave travels through the cochlea: 1) \nThe wave gradually slows down, and 2) The higher-frequency components of the wave are \nabsorbed, leaving an increasingly narrower band of low-frequency components proceeding \non  toward  the  far  end  of the  cochlea.  If we  were  to  uncoil  and  enlarge  the  basilar \nmembrane  it would look  like  a  swim  fin  (figure  3).  If we now  were  to  push  on  the \nbasilar membrane, it would push back like a spring.  It is most compliant at the wide, \nthin end of the fin.  Thus as one moves  along  the  basilar membrane from  its basal to \napical end, its compliance increases.  Zwislocki's transmission-line model was tapered in \nthis same way. \n\nScala \nvestibuli \n\nHelicotrema \n\nFigure 2 - Uncoiled  cochlea  (Zweig.  1976). \n\n\fA Passive Shared Element Analog Electrical Cochlea \n\n665 \n\nBasal End \n\nFigure 3 - Simplified  uncoiled  and enlarged drawing  of the  basilar \n\nmembrane. \n\nZwislocki's  model  of the  cochlea  is  a  distributed  parameter  transmission  line. \nFigure 4 shows a lumped electrical analog of the model.  The series elements (L 1,,, .Lo) \nrepresent the local inertia of the cochlear fluid.  The shunt capacitive elements (CI, ... Co) \nrepresent the  local  compliance of the basilar membrane.  The  shunt resistive elements \n(R 1 , ... Rn) represent the local viscous resistance of the basilar membrane and associated \nfluid.  The  model  has  one  input  and  a  huge 'number of outputs.  The  input,  sound \npressure at the  oval window, is represented here  as  a voltage source.  The outputs are \neither the displacements or the velocities of the various regions of the basilar membrane. \n\nFigure 4 - Transmission line  model  of the  cochlea represented  as  an \n\nelectrical  circuit. \n\nIn the electrical analog, shown in figure 4, we have selected velocities as the outputs (in \norder to compare our data to real neural  tuning curves) and we have represented those \nvelocities  as  the  currents  (11 , .. .In).  The  original  analysis  of  Zwislocki's  tapered \ntransmission line  model  did not produce the  steep high  frequency  band edges that are \nobserved in  real cochleas. This deficiency  was a  major driving  force  behind the early \ndevelopment of more complex cochlear models.  Recently, it was found that the original \nanalysis placed the Zwislocki model in an inappropriate mode of operation (Lewis, 1984). \nIn this mode,determined by the relative parameter values, the high frequency band edges \nhad very gentle slopes.  Solving the partial differential equations for the model with the \nhelp of a commonly  used simplification (the WKB  approximation), one finds  a second \nmode of operation.  In this mode, the  model produces all five of the properties that we \ndesire, including extraordinarily steep high-frequency band edges. \n\n\f666 \n\nFeld, Eisenberg and Lewis \n\nRESULTS \n\nWe were curious to know whether or not the newly-found mode of operation, with \nits very steep high-frequency band edges, could be found in a finite-element version of the \nmodel.  If so,  we should be able to realize a  lumped, analog  version  of the  Zwislocki \nmodel for use as a practical front-end filter for acoustical image formation and processing. \nWe  decided  to  implement  the  finite  element  model  in  SPICE.  SPICE  is  a  software \npackage  that is used  for  electrical circuit simulation.  Our  SPICE  model  showed  the \nfollowing:  As  long as the model was made up of enough segments,  and as long as the \nelements had  appropriate parameter values,  the  second mode  of operation indeed was \navailable.  Furthermore, it was the predominant mode of operation when the parameter \nvalues of the model were matched to biophysical data for the cochlea. \n\n\"~ \n\nCD \n:3 \nL\\.l \n:z: \n< Q: \nQ:I \n::E \n~ \nu \nZ \n~ \n1-0 < \n~ CI) \n\n~ ]/\\ \n\n,. \n\nL OG \n\n(FREQUENCY) \n\n100000 \n\nI  \" , \"  ,,,I \nU \n1.1 \n\nI \n\nI  \" ,  \",I \n\n\" \n, ... \n\nFREQUENCY  (kHz) \n\nFigure 5 - Frequency response  of \nthe  basilar membrane  velocity. \n\nFigure 6  - Inverted neural tuning curves \nfrom  three  afferent  fibers  of  a  cat cochlea \n(Kiang  and  Moxon,  1974). \n\nFigure  5  shows  the magnitude of the  electrical  analog's  response  plotted against \nfrequency on log-log coordinates.  The five curves correspond to five  different locations \nalong  our model.  The cutoff frequencies  span  approximately seven octaves.  Further \nadjustments of the parameters will be  needed in  order to shift these curves to span  the \nlower  seven  octaves  of human  audition.  For  comparison,  figure  6  shows  threshold \nresponse curves of a cat cochlea from a paper by Kiang and Moxon (1974).  These curves \nare  inverted  intentionally  because  Kiang  and  Moxon  plotted  stimulus  threshold  vs. \nfrequency  rather than  response  amplitude  vs.  frequency.  We use  these neural  tuning \ncurves  for  comparison because direct  observations  of cochlear  mechanics  have been \nlimited to the  basal  end.  Furthermore,  in  the realm  of single  frequencies  and  small \nsignals, Evans has produced compelling evidence that this is a valid comparison (Evans, \nin press).  These three  curves are  typical  of the  lower seven octaves of hearing.  One \nobvious discrepancy between Kiang and Moxon's data and our results is that our model \ndoes not exhibit the sharp corners occurring at the band edges.  The term sharp  corner \ndenotes the fact that the transition between the shallow rising edge and steep falling edge \nof a given curve is abrupt i.e. the corner is not rounded. \n\n\fA Passive Shared Element Analog Electrical Cochlea \n\n667 \n\nFigure 7  shows what happens to  the response curve at a single location along our \nmodel  as  the  number of stages  is  increased.  The curve on  the  right,  in  figure  7, was \nderived with 500 stages and does not change much as  we increase the number of stages \nindefinitely.  Thus  the  curve represents  a convergence of the solution  of the  lumped \nparameter Zwislocki  model  to the distributed parameter model.  The middle curve was \nderived with  100 stages and the left-hand curve was  derived with  50.  In  any lumped(cid:173)\nelement transmission line, there occurs an artifactual cutoff which occurs roughly at the \npoint where the given input wavelength exceeds the dimensions of the lumped elements. \nIf we do  not  lump  the stages in  our model  finely  enough,  we observe  this  artifactual \ncutoff as  opposed to  the true  cutoff of Zwislocki's distributed parameter model.  This \nphenomena is clearly  observed in the curve derived from 50 stages and may account for \nthe sharper comers in response curves from real cochleas.  However, in order to make our \nfinite element model operate in  a manner analogous to  that of the distributed parameter \nZwislocki model we need approximately 500 stages. \n\n~ \nc \n~ \n\"' 0 \n~ z \n\" .. ~ \n\n~ \n~ \n~ \n\"' 0 \n~ \n~ .. ~ \n\n10 \n\n10 0 00 0 \n\n10000 0 \n\nL OG \n\n!FREQUENCY ) \n\nIdB} \n\nL OG \n\n(FREQUENCY) \n\n(HZ) \n\nFigure 7 - Convergence  of cut(cid:173)\ntoff points  as  the  number of \nbranches  increase. \n\nFigure 8 - Frequency response  of the \nbasilar membrane  velocity  without \nthe  Heliocotrema. \n\nA critical element in  the Zwislocki model is a terminating resistor, representing the \nheliocotrema  (see  Rh  in  figure  3).  The heliocotrema is a  small  hole at the end of the \nbasilar membrane.  Figure 8, shows the effects of removing  that resistor.  The irregular \nfrequency  characteristics are quite different from  the  experimental  data  and represent \npossibly wild excursions of the basilar membrane. \n\nFigure 9. shows phase data for the Zwislocki model, which is linear as a function of \n\nfrequency.  Anderson et aI (1971), show similar results in the squirrel monkey. \n\nWith lumped-element  analysis  we are able  to  obtain  temporal  as  well  as  spectral \nresponses.  For a temporal  waveform  such as an  acoustic pulse,  the linear relationship \nbetween  phase  and  frequency  guarantees  that  those  Fourier components  which  pass \nthrough  the spectral  filter  will  be reassembled  with proper phase relationships at the \noutput of the filter.  As  it travels  down  the basilar membrane.  the temporal  waveform \nwill simply be smoothed, due to loss of its higher-frequency components and delayed, due \nto  the linear phase shift.  Figure  10 shows the response of our electrical analog to a  1 \nmsec wide square pulse at the input.  The curves represent the  time courses of basilar \nmembrane displacement at four equally spaced locations along the cochlea.  The curve on \nthe right represents the  response at the apical end of the cochlea (the end farthest from the \ninput).  The curve on the left represents the response at a point 25 percent of the distance \n\n\f668 \n\nFeld, Eisenberg and Lewis \n\ninput end.  The impulse responses of mammalian cochleas and of the auditory filters of \nlower vertebrates all show a slight ringing,  again indicating a deficiency in our model. \n\nw \n\n~ \nd \n> \n\nLINEA.R  FREOUENCY  {HZ' \n\nTIfoilE \n\n(SECONDS) \n\n2000 \n\n04 \n\nApical  End \n\nFigure 9  - Phase response of the \nbasilar  membrane  velocity. \n\nFigure  10 - Traveling square wave \npulse  along  the  membrane  from  the \nbasal  to  apical  end. \n\nCONCLUSION \n\nResearch  activity  studying  the  function  of higher level  brain processing  is in  its \ninfancy and little is known about how the various features of the cochlea, such as linear \nphase, sharp band edges, as well as nonlinear features, such f1S  two-tone suppression and \ncubic  difference  tone  excitation,  are  used  by  the brain.  Therefore,  our approach,  in \ndeveloping a cochlear model, is to incorporate only the most essential ingredients.  We \nhave  incorporated  the  five  properties  mentioned  in  the  introduction  which  provide \nsimplicity of analysis, economy of hardware construction, and the preservation of both \ntemporal and spectral resolution. The inclusion of these properties is also consistent with \nthe fact that they are found in numerous species. \n\nWe have found  that in  the  correct  mode  of operation  a  tapered  transmission  line \nmodel  can  exhibit  these  five  important  cochlear  properties.  A  lumped-element \napproximation can be used to simulate this model as long as at least 500 stages are used. \nAs observed in figure 7, by decreasing the number of stages below 500, the solution to \nthe lumped-element model no longer adheres to the Zwislocki model.  In  fact, the output \nof the  coursely  lumped  model  more  closely  resembles  the  neural  tuning  data  of the \ncochlea in that it produces very sharp corners.  There is some evidence that indicates the \ncochlea is constructed of discrete components.  Indeed,  the hair cells  themselves  are \ndiscretized.  If this idea is valid, a model constructed of as little as 50 branches may more \naccurately represent the cochlear mechanics then the Zwislocki model. \n\nOur simple model has some drawbacks in that it does not replicate various properties \nof the cochlea.  For example, it does not span the full ten octaves of human audition, nor \ndoes it explain any of the experimentally observed nonlinear aspects seen in the cochlea. \nHowever, we take this approach because it provides us with a powerful analysis tool that \nwill enable us to study the behavior of lumped-element cochlear models.  This tool will \nallow us to proceed to the next step; the building of a hardware analog of the cochlea. \n\n\fA Passive Shared Element Analog Electrical Cochlea \n\n669 \n\nallow US to proceed to the next step; the building of a hardware analog of the cochlea. \n\nRESEARCH  DIRECTIONS \n\nIn and of itself, the tapered shared element travelling wave structure we have chosen is \ninteresting to analyze.  In order to get even further insight into how this filter works and \nto  aid  in  the  building  of a  hardware  version  of such  a  filter,  we  plan  to  study  the \nplacement of the poles and zeroes of the transfer function at each tap along the structure. \nIn a travelling wave transmission line we expect that the transfer function at each tap will \nhave  the  same  denominator.  Therefore,  it  must  be  the  numerators  of the  transfer \nfunctions  which  will change,  i.e.  the  zeroes will change from  tap to tap.  It will be of \ninterest to see what role the zeroes play in such a ladder structure.  Furthennore, it will be \nof great interest  to  us  to  study  what happens  to  the  poles  and  zeroes  of the  transfer \nfunction  at each tap  as the number of stag~s is increased  (approaching  the  distributed \nparameter ftlter), or  decreased (apprpaching the lumped-element cutoff version of the filter \nwith sharper corners).  We should emphasize that our circuit is bi-directional, i.e. there is \nloading from the stages before and after each tap, as in the real cochlea.  For this reason, \nwe must consider carefully the options for hardware realization of our circuit.  We might \nchoose to  make a  mechanical  structure on silicon or some oilier medium, or we could \nconvert our  structure  into  a  uni-directional  circuit  and  build  it as  a  digital  or  analog \ncircuit \n\nUsing this design we plan to build an  acoustic imaging device that will enable us to \nexplore  various  signal  processing  tasks.  One  such  task  would  be to  extract acoustic \nsignals from  noise. \n\nAll species need to cope with two types of noise, internal sensor and amplifier noise, \nand external noise such as that generated by wind.  Spectral decomposition is on effective \nway to deal with internal noise.  For example, the amplitudes of the spectral components \nin the passband of a filter are largely undiminished, whereas the broadband noise, passed \nby the filter, is proportional to the square root of the bandwidth.  External noise reduction \ncan be accomplished by spatial decomposition.  When temporal resolution is preserved in \nsignals, spatial decomposition can be achieved by cross correlation of the signals from \ntwo ears.  Therefore, from these two properties, spectral and temporal resolution, one can \nconstruct an  acoustic imaging system  in  which signals buried in  a  sea of noise can be \nextracted. \n\nAcknowledgments \n\nWe would like  to  thank Thuan  Nguyen  for  figure  1,  Eva Poinar who  helped  with  the \nfigures,  Michael  Sneary  for  valuable  discussion,  and  Bruce  Parnas  for  help  with \nprogramming. \n\n\f670 \n\nFeld, Eisenberg and Lewis \n\nReferences \n\nAnderson, DJ., Rose, I.E., Hind, I.E .\u2022  Brugge I.F.. Temporal Position of Discharges in \nSingle Auditory Nerve Fibers Within the Cycle of a Sine-Wave Stimulus: Frequency and \nIntensity Effects, J. Acoust.  Soc.  A~z.., 49.  1131-1139,  1971. \n\nEvans, E.F .\u2022 Cochlear Filtering:  A View Seen Through the Temporal Discharge Patterns \nof Single Cochlear Nerve Fibers.  A talk given at the 1988 NATO advanced workshop. to \nbe published as  (J.P.  Wilson,  D.T.  Kemp,  eds.)  Mechanics of Hearing. Plenum  Press. \nN.Y. \n\nKiang,  N.Y.S .\u2022  Moxon,  E.C .\u2022  Tails  of Tuning  Curves  of Auditory-Nerve  Fibers,  J. \nAcoust.  Soc.  Am.,  55,  620-630.  1974. \n\nLewis.  E.R.,  High  Frequency  Rolloff  in  a  Cochlear  Model  Without  critical-layer \nresonance. J. Acoust.  Soc.  Am .\u2022 76 (3) September, 1984. \n\nLyon, R.F., Mead, C.A .\u2022 An Analog Electronic Cochlea, IEEE  Trans.-ASSP,  36. 1119-\n1134.  1988. \n\nZweig.  G., Lipes.  R..  Pierce.  I.R..  The  Cochlear  Compromise,  J.  Acoust.  Soc.  Am., \n59, 975-982. 1976. \n\nZwislocki.I., Analysis of Some Auditory Characteristics, in Handbook of Mathematical \nPsychology,  Vol.  3. (Wiley. New York), pp.  1-97, 1965. \n\n\f", "award": [], "sourceid": 144, "authors": [{"given_name": "David", "family_name": "Feld", "institution": null}, {"given_name": "Joe", "family_name": "Eisenberg", "institution": null}, {"given_name": "Edwin", "family_name": "Lewis", "institution": null}]}