{"title": "The Computation of Sound Source Elevation in the Barn Owl", "book": "Advances in Neural Information Processing Systems", "page_first": 10, "page_last": 17, "abstract": "", "full_text": "10 \n\nSpence and Pearson \n\nThe Computation of Sound Source Elevation \n\n. \n'In \n\nthe Barn Owl \n\nClay D. Spence \nJohn C. Pearson \n\nDavid Sarnoff Research Center \n\nCN5300 \n\nPrinceton, NJ 08543-5300 \n\nABSTRACT \n\nThe midbrain of the barn owl contains a map-like representation of \nsound source direction which is used to precisely orient the head to(cid:173)\nward targets of interest. Elevation is computed from the interaural \ndifference in sound level. We present models and computer simula(cid:173)\ntions of two stages of level difference processing which qualitatively \nagree with known anatomy and physiology, and make several strik(cid:173)\ning predictions. \n\nINTRODUCTION \n\n1 \nThe auditory system of the barn owl constructs a map of sound direction in the \nexternal nucleus of the inferior colliculus (lex) after several stages of processing the \noutput of the cochlea. This representation of space enables the owl to orient its head \nto sounds with an accuracy greater than any other tested land animal [Knudsen, \net aI, 1979]. Elevation and azimuth are processed in separate streams before being \nmerged in the ICx [Konishi, 1986]. Much of this processing is done with neuronal \nmaps, regions of tissue in which the position of active neurons varies continuously \nwith some parameters, e.g., the retina is a map of spatial direction. In this paper \nwe present models and simulations of two of the stages of elevation processing \nthat make several testable predictions. The relatively elaborate structure of this \nsystem emphasizes one difference between the sum-and-sigmoid model neuron and \nreal neurons, namely the difficulty of doing subtraction with real neurons. We first \nbriefly review the available data on the elevation system. \n\n\fThe Computation of Sound Source Elc\\'ution in the Bam Owl \n\n11 \n\nC __ ICX_) \n\nICl \n\n_ iijj (!(,\\,\\ \\ \\ \\ '1'1? \n\n~. \ni If?' \n\n----- ~ \n\nIlD SENSITIVE \n\n-\n\ndorsal -\n\nIlD & ASI \nSENSITIVE \n\nVlVp \n\ncentral -\n\n+ \n\nventral -L' \n.... -------- .~ IlD \n\nNA \n\n( MONAURAL) - ~ ~ \n\nIntensity \n\nFigure 1: Overview of the Barn Owl's Elevation System. ABI: average binaural \nintensity. ILD: Inter aural level difference. Graphs show cell responses as a function \nof ILD (or monaural intensity for NA). \n\n2 KNOWN PROPERTIES OF THE ELEVATION SYSTEM \nThe owl computes the elevation to a sound source from the inter-aural sound pres(cid:173)\nsure level difference (ILD).l Elevation is related to ILD because the owl's ears are \nasymmetric, so that the right ear is most sensitive to sounds from above, and the \nleft ear is most sensitive to sounds from below [Moiseff, 1989]. \n\nAfter the cochlea, the first nucleus in the ILD system is nucleus angularis (NA) \n(Fig. 1). NA neurons are monaural, responding only to ipsilateral stimuli. 2 Their \noutputs are a simple spike rate code for the sound pressure level on that side of the \nhead, with firing rates that increase monotonically with sound pressure level over a \nrather broad range, typically 30 dB [Sullivan and Konishi, 1984]. \n\n1 Azimuth is computed from the interaural time or phase delay. \n2 Neurons in all of the nuclei we will discuss except rex have fairly narrow frequency tuning \n\ncurves. \n\n\f12 \n\nSpence and Pearson \n\nEach NA projects to the contralateral nucleus ventralis lemnisci lateralis pars pos(cid:173)\nterior (VLVp). VLVp neurons are excited by contralateral stimuli, but inhibited \nby ipsilateral stimuli. The source of the ipsilateral inhibition is the contralateral \nVLVp [Takahashi, 1988]. VLVp neurons are said to be sensitive to ILD, that is \ntheir ILD response curves are sigmoidal, in contrast to ICx neurons which are said \nto be tuned to ILD, that is their ILD response curves are bell-shaped. Frequency \nis mapped along the anterior-posterior direction, with slabs of similarly tuned cells \nperpendicular to this axis. Within such a slab, cell responses to ILD vary systemat(cid:173)\nically along the dorsal-ventral axis, and show no variation along the medio-Iateral \naxis. The strength of ipsilateral inhibition3 varies roughly sigmoidally along the \ndorsal-ventral axis, being nearly 100% dorsally and nearly 0% ventrally. The ILD \nthreshold, or ILD at which the cell's response is half its maximum value, varies from \nabout 20 dB dorsally to -20 dB ventrally. The response of these neurons is not in(cid:173)\ndependent of the average binaural intensity (ABI), so they cannot code elevation \nunambiguously. As the ABI is increased, the ILD response curves of dorsal cells \nshift to higher ILD, those of ventral cells shift to lower ILD, and those of central \ncells keep the same thresholds, but their slopes increase (Fig. 1) [Manley, et aI, \n1988]. \n\nEach VLVp projects contralaterally to the lateral shell of the central nucleus of the \ninferior colli cuI us (ICL) [T. T. Takahashi and M. Konishi, unpublished]. The ICL \nappears to be the nucleus in which azimuth and elevation information is merged \nbefore forming the space map in the ICx [Spence, et aI, 1989]. At least two kinds \nof ICL neurons have been observed, some with ILD-sensitive responses as in the \nVLVp and some with ILD-tuned responses as in the ICx [Fujita and Konishi, 1989]. \nManley, Koppl and Konishi have suggested that inputs from both VLVps could \ninteract to form the tuned responses [Manley, et aI, 1988]. The second model we \nwill present suggests a simple method for forming tuned responses in the ICL with \ninput from only one VLVp. \n\n3 A MODEL OF THE VLVp \nWe have developed simulations of matched iso-frequency slabs from each VLVp in \norder to investigate the consequences of different patterns of connections between \nthem. We attempted to account for the observed gradient of inhibition by using a \ngradient in the number of inhibitory cells. A dorsal-ventral gradient in the number \ndensity of different cell types has been observed in staining experiments [C. E. Carr, \net aI, 1989], with GABAergic cells4 more numerous at the dorsal end and a non(cid:173)\nGABAergic type more numerous at the ventral end. \n\nTo model this, our simulation has a \"unit\" representing a group of neurons at each \nof forty positions along the VLVp. Each unit has a voltage v which obeys the \nequation \n\n3 measured functionally, not actual synaptic strength. See [Manley, et al, 1988] for details. \n4 GABAergic cells are usually thought to be inhibitory. \n\n\fThe Computation or Sound Source Elevation in the Bam Owl \n\n13 \n\nSHELL \n\n~ .......... ,.,/ \nNA \n\n. ' \n..... \no \n\nInlensUy \n\n50 \n\n25 \n\n~\"\"/ \n\n.' \n..... \n\" \n.... \n\n,.' \n\no \n\n25 \n\n50 \n\nInlenslly \n\nLEFT \n\nRIGHT \n\nFigure 2: Models of Level Difference Computation in the VLVps and Generation \nof Tuned Responses in the ICL. Sizes of Circles represent the number density of \ninhibitory neurons, while triangles represent excitatory neurons. \n\nThis describes the charging and discharging ofthe capacitance C through the various \nconductances g, driven by the voltages VN, all of these being properties of the cell \nmembrane. The subscript L refers to passive leakage variables, E refers to excitatory \nvariables, and I refers to inhibitory variables. These model units have firing rates \nwhich are sigmoidal functions of v. The output on a given time step is a number \nof spikes, which is chosen randomly with a Poisson distribution whose mean is the \nunit's current firing rate times the length of the time step. gE and g[ obey the \nequation \n\nd2g \ndt 2 = -\"I dt - w g, \n\ndg \n\n2 \n\nthe equation for a damped harmonic oscillator. The effect of one unit's spike on \nanother unit is to \"kick\" its conductance g, that is it simply increments the conduc(cid:173)\ntance's time derivative by some amount depending on the strength of the connection. \n\n\f14 \n\nSpence and ~arson \n\nILD =\u00b720 dB \n\nILD=OdB \n\nILD = 20 dB \n\ndorsal \n\nventral \n\nLEFT ~ RATE ~RIGHT \n\nFigure 3: Output of Simulation of VLVps at Several ILDs. Position is represented \non the vertical axis. Firing rate is represented by the horizontal length of the black \nbars. \n\nInhibitory neurons increment dgI/dt, while excitatory neurons increment dgE/dt. 'Y \nand ware chosen so that the oscillator is at least critically damped, and 9 remains \nnon-negative. This model gives a fairly realistic post-synaptic potential, and the \neffects of multiple spikes naturally add. The gradient of cell types is modeled by \nhaving a different maximum firing rate at each level in the VLVp. \n\nThe VLVp model is shown in figure 2. Here, central neurons of each VLVp project \nto central neurons of the other VLVp, while more dorsal neurons project to more \nventral neurons, and conversely. This forms a sort of \"criss-cross\" pattern ofprojec(cid:173)\ntions. In our simulation these projections are somewhat broad, each unit projecting \nwith equal strength to all units in a small patch. In order for the dorsal neurons to \nbe more strongly inhibited, there must be more inhibitory neurons at the ventral \nend of each VLVp, so in our simulation the maximum firing rate is higher there and \ndecreases linearly toward the dorsal end. A presumed second neuron type is used \nfor ouput, but we assumed its inputs and dynamics were the same as the inhibitory \nneurons and so we didn't model them. The input to the VLVps from the two NAs \nwas modeled as a constant input proportional to the sound pressure level in the \ncorresponding ear. We did not use Poisson distributed firing in this case because \nthe spike trains of NA neurons are very regular [Sullivan and Konishi, 1984]. NA \ninput was the same to each unit in the VLVp. \nFigure 3 shows spatial activity patterns of the two simulated VLVps for three dif(cid:173)\nferent ILDs, all at the same ABI. The criss-cross inhibitory connections effectively \ncause these bars of activity to compete with each other so that their lengths are \nalways approximately complementary. Figure 4 presents results of both models \ndiscussed in this paper for various ABIs and ILDs. The output of VLVp units \nqualitatively matches the experimentally determined responses, in particular the \nILD response curves show similar shifts with ABI. for the different dorsal-ventral \npositions in the VLVp (see Fig. 3 in [Manley, et aI, 1988]). Since the observed \nnon-GABAergic neurons are more numerous at the ventral end of the VLVp and \n\n\fThe Computation of Sound Source Elevation in the Barn Owl \n\n15 \n\nVLVp \n\nIeL \n\nDORSAL \n\nABI(dB) \n\nLIne Type \n.................... \n10 \n----\n20 \n40 - -\n3D \n._._ ... \nso \n\nDORSAL VLVp input \n\n~ 100 \n\n80 \n\n~ \n......... \nr..::I \n\n60 \n~ 40 \n~ 20 \nZ ...... \n~ \n\n0 -... ~ .. :=:. .. \"':':\" .... ~ .. ~,...-\n\nCENTRAL \n\nCENTRAL VLVp input \n\n80 \n\n~ ....,-\n\n60 \n\n~ 100 \n~ 40 \n~ 20 \nZ \n~ \n\n0 \n\n~ 100 ~~~~~ __ \u00a7-~--~ \n~ \n\n~.,. \n\n0 \n\n/,,-\n\n........... . \n\n8 \n\nVENTRAL VL Vp input \n\n..\u2022..\u2022...\u2022 \n\n...... . \n.' \n\n./ VENTRAL \n.: \n\n40 \n\n60 \n\n/ / / \nI \nI \nI \nI \n/ \n20 \n- / / \no ............... . \n-20 \n\n-10 \n\n........ .! \n\n..... / \n... \n\no \n\nILD (dB) \n\n10 \n\n20 \n\n-20 \n\n-10 \n\n0 \n\nILD (dB) \n\n10 \n\n20 \n\nFigure 4: ILD Response Curves of the VLVp and ICL models. Curves show percent \nof maximum firing rate versus ILD for several ABls. \n\n\f16 \n\nSpence and Pearson \n\nour model's inhibitory neurons are also more numerous there, this model predicts \nthat at least some of the non-GABAergic cells in the VLVp are the neurons which \nprovide the mutual inhibition between the VLVps. \n\n4 A MODEL OF ILD-TUNED NEURONS IN THE ICL \nIn this section we present a model to explain how leL neurons can be tuned to \nILD if they only receive input from the ILD-sensitive neurons in one VLVp. The \nmodel essentially takes the derivative of the spatial activity pattern in the VLVp, \nconverting the sigmoidal activity pattern into a pattern with a localized region of \nactivity corresponding to the end of the bar. \nThe model is shown in figure 2. The VLVp projects topographically to ICL neurons, \nexciting two different types. This would excite bars of activity in the ICL, except \none type of leL neuron inhibits the other type. Each inhibitory neuron projects \nto tuned neurons which represent a smaller ILD, to one side in the map. The \ninhibitory neurons acquire the bar shaped activity pattern from the VLVp, and \nare ILD-sensitive as a result. Of the neurons of the second type, only those which \nreceive input from the end of the bar are not also inhibited and prevented from \nfiring. \n\nOur simulation used the model neurons described above, with input to the ICL \ntaken from our model of the VLVp. Each unit in the VLVp projected to a patch \nof units in the leL with connection strengths proportional to a gaussian function \nof distance from the center of the patch. (Equal strengths for the connections from \na given neuron worked poorly.) The results are shown in figure 4. The model \nshows sharp tuning, although the maximum firing rates are rather small. The ILD \nresponse curves show the same kind of ABI dependence as those of the VLVp model. \nThere is no published data to confirm or refute this, but we know that neurons in \nthe space map in the ICx do not show ABI dependence. There is a direct input \nfrom the contralateral NA to the ICL which may be involved in removing ABI \ndependence, but we have not considered that possibility in this work. \n\n5 CONCLUSION \nWe have presented two models of parts of the owl's elevation or interaural level \ndifference (ILD) system. One predicts a \"criss-cross\" geometry for the connections \nbetween the owl's two VLVps. In this geometry cells at the dorsal end of either \nVLVp inhibit cells at the ventral end of the other, and are inhibited by them. \nCells closer to the center of one VLVp interact with cells closer to the center of \nthe other, so that the central cells of each VLVp interact with each other (Fig. 2). \nThis model also predicts that the non-GABAergic cells in the VLVp are the cells \nwhich project to the other VLVp. The other model explains how the ICL, with \ninput from one VLVp, can contain neurons tuned to ILD. It does this essentially by \ncomputing the spatial derivative of the activity pattern in the VLVp. This model \npredicts that the ILD-sensitive neurons in the ICL inhibit the ILD-tuned neurons \nin the ICL. Simulations with semi-realistic model neurons show that these models \n\n\fThe Computation of Sound Source Elevation in the Barn Owl \n\n17 \n\nare plausible, that is they can qualitatively reproduce the published data on the \nresponses of neurons in the VLVp and the leL to different intensities of sound in \nthe two ears. \n\nAlthough these are models, they are good examples of the simplicity of information \nprocessing in neuronal maps. One interesting feature of this system is the elabo(cid:173)\nrate mechanism used to do subtraction. With the usual model of a neuron, which \ncalculates a sigmoidal function of a weighted sum of its inputs, subtraction would \nbe very easy. This demonstrates the inadequacy of such simple model neurons to \nprovide insight into some real neural functions. \n\nAcknowledgements \n\nThis work was supported by AFOSR contract F49620-89-C-0131. \n\nReferences \n\nC. E. Carr, I. Fujita, and M. Konishi. (1989) Distribution of GABAergic neurons \nand terminals in the auditory system of the barn owl. The Journal of Comparative \nNeurology 286: 190-207. \n\nI. Fujita and M. Konishi. (1989) Transition from single to multiple frequency chan(cid:173)\nnels in the processing of binaural disparity cues in the owl's midbrain. Society for \nNeuroscience Abstracts 15: 114. \n\nE. I. Knudsen, G. G. Blasdel, and M. Konishi. (1979) Sound localization by the barn \nowl measured with the search coil technique. Journal of Comparative Physiology \n133:1-11. \n\nM. Konishi. (1986) Centrally synthesized maps of sensory space. Trends in Neuro(cid:173)\nsciences April, 163-168. \nG. A. Manley, C. Koppl, and M. Konishi. (1988) A neural map of interaural in(cid:173)\ntensity differences in the brain stem of the barn owl. The Journal of Neuroscience \n8(8): 2665-2676. \n\n(1989) Binaural disparity cues available to the barn owl for sound \n\nA. Moiseff. \nlocalization. Journal of Comparative Physiology 164: 629-636. \nC. D. Spence, J. C. Pearson, J. J. Gelfand, R. M. Peterson, and W. E. Sullivan. \n(1989) Neuronal maps for sensory-motor control in the barn owl. In D. S. Touretzky \n(ed.), Advances in Neural Information Processing Systems 1, 748-760. San Mateo, \nCA: Morgan Kaufmann. \n\nW. E. Sullivan and M. Konishi. (1984) Segregation of stimulus phase and intensity \ncoding in the cochlear nucleus of the barn owl. The Journal of Neuroscience 4(7): \n1787-1799. \n\nT. T. Takahashi. (1988) Commissural projections mediate inhibition in a lateral \nlemniscal nucleus of the barn owl. Society for Neuroscience Abstracts 14: 323. \n\n\f", "award": [], "sourceid": 255, "authors": [{"given_name": "Clay", "family_name": "Spence", "institution": null}, {"given_name": "John", "family_name": "Pearson", "institution": null}]}