10 Spence and Pearson 
Ill 
The 
Computation of Sound Source 
the Barn Owl 
Elevation in 
Clay D. Spence 
John C. Pearson 
David Sarnoff Research Center 
CN5300 
Princeton, NJ 08543-5300 
ABSTRACT 
The midbrain of the barn owl contains a map-like representation of 
sound source direction which is used to precisely orient the head to- 
ward targets of interest. Elevation is computed from the interaural 
difference in sound level. We present models and computer simula- 
tions of two stages of level difference processing which qualitatively 
agree with known anatomy and physiology, and make several strik- 
ing predictions. 
I INTRODUCTION 
The auditory system of the barn owl constructs a map of sound direction in the 
external nucleus of the inferior colliculus (ICx) after several stages of processing the 
output of the cochlea. This representation of space enables the owl to orient its head 
to sounds with an accuracy greater than any other tested land animal [Knudsen, 
et al, 1979]. Elevation and azimuth are processed in separate streams before being 
merged in the ICx [Konishi, 1986]. Much of this processing is done with neuronal 
maps, regions of tissue in which the position of active neurons varies continuously 
with some parameters, e.g., the retina is a map of spatial direction. In this paper 
we present models and simulations of two of the stages of elevation processing 
that make several testable predictions. The relatively elaborate structure of this 
system emphasizes one difference between the sum-and-sigmoid model neuron and 
real neurons, namely the difficulty of doing subtraction with real neurons. We first 
briefly review the available data on the elevation system. 
The Computation of Sound Source Elevation in the Barn Owl 11 
LEFT RIGHT 
ICx ) ILD TUNED & 
INDEPENDENT 
I I ILD TUNED i '-- 
ICL ABI ? 
ILD SENSITIVE --- 
: ;? 
dorsal 
ILD & ABI 
SENSITIVE 
VLVp central 
ventral --- .-: 
ILD 
NA 
Intensit 
Figure 1: Overview of the Barn Owl's Elevation System. ABI: average binaural 
intensity. ILD' Interaural level difference. Graphs show cell responses as a function 
of ILD (or monaural intensity for NA). 
2 KNOWN PROPERTIES OF THE ELEVATION SYSTEM 
The owl computes the elevation to a sound source from the inter-aural sound pres- 
sure level difference (ILD). 1 Elevation is related to ILD because the owl's ears are 
asymmetric, so that the right ear is most sensitive to sounds from above, and the 
left ear is most sensitive to sounds from below [Moiseff, 1989]. 
After the cochlea, the first nucleus in the ILD system is nucleus angularis (NA) 
(Fig. 1). NA neurons are monaural, responding only to ipsilateral stimuli? Their 
outputs are a simple spike rate code for the sound pressure level on that side of the 
head, with firing rates that increase monotonically with sound pressure level over a 
rather broad range, typically 30 dB [Sullivan and Konishi, 1984]. 
] Azimuth is computed from the interaural time or phase delay. 
Neurons in all of the nuclei we will discuss except ICx have fairly narrow frequency tuning 
curves. 
12 Spence and Pearson 
Each NA projects to the contralateral nucleus ventralis lemnisci lateralis pars pos- 
terior (VLVp). VLVp neurons are excited by contralateral stimuli, but inhibited 
by ipsilateral stimuli. The source of the ipsilateral inhibition is the contralateral 
VLVp [Takahashi, 1988]. VLVp neurons are said to be sensitive to ILD, that is 
their ILD response curves are sigmoidal, in contrast to ICx neurons which are said 
to be tuned to ILD, that is their ILD response curves are bell-shaped. Frequency 
is mapped along the anterior-posterior direction, with slabs of similarly tuned cells 
perpendicular to this axis. Within such a slab, cell responses to ILD vary systemat- 
ically along the dorsal-ventral axis, and show no variation along the medio-lateral 
axis. The strength of ipsilateral inhibition s varies roughly sigmoidally along the 
dorsal-ventral axis, being nearly 100% dorsally and nearly 0% ventrally. The ILD 
threshold, or ILD at which the cell's response is half its maximum value, varies from 
about 20 dB dorsally to -20 dB ventrally. The response of these neurons is not in- 
dependent of the average binaural intensity (ABI), so they cannot code elevation 
unambiguously. As the ABI is increased, the ILD response curves of dorsal cells 
shift to higher ILD, those of ventral cells shift to lower ILD, and those of central 
cells keep the same thresholds, but their slopes increase (Fig. 1) [Manley, et al, 
1988]. 
Each VLVp projects contralaterally to the lateral shell of the central nucleus of the 
inferior colliculus (ICL) [T. T. Takahashi and M. Konishi, unpublished]. The ICL 
appears to be the nucleus in which azimuth and elevation information is merged 
before forming the space map in the ICx [Spence, et al, 1989]. At least two kinds 
of ICL neurons have been observed, some with ILD-sensitive responses as in the 
VLVp and some with ILD-tuned responses as in the ICx [Fujita and Konishi, 1989]. 
Manley, KSppl and Konishi have suggested that inputs from both VLVps could 
interact to form the tuned responses [Manley, et al, 1988]. The second model we 
will present suggests a simple method for forming tuned responses in the ICL with 
input from only one VLVp. 
3 A MODEL OF THE VLVp 
We have developed simulations of matched iso-frequency slabs from each VLVp in 
order to investigate the consequences of different patterns of connections between 
them. We attempted to account for the observed gradient of inhibition by using a 
gradient in the number of inhibitory cells. A dorsal-ventral gradient in the number 
density of different cell types has been observed in staining experiments [C. E. Cart, 
et al, 1989], with GABAergic cells 4 more numerous at the dorsal end and a non- 
GABAergic type more numerous at the ventral end. 
To model this, our simulation has a "unit" representing a group of neurons at each 
of forty positions along the VLVp. Each unit has a voltage v which obeys the 
equation 
dv 
C- = -g(v - v) - gr(v - vr) - gI(v - vI). 
3rneasured functionally, not actual synaptic strength. See [Manley, et al, 1988] for details. 
4 GABAergic cells are usually thought to be inhibitory. 
The Computation of Sound Source Elevation in the Barn Owl 13 
SENSITIVE TUNED 
SHELL 
oA 
VLVp 
In lenslly I N A Inlenslly I 
LEFT RIGHT 
Figure 2: Models of Level Difference Computation in the VLVps and Generation 
of Tuned Responses in the ICL. Sizes of Circles represent the number density of 
inhibitory neurons, while triangles represent excitatory neurons. 
This describes the charging and discharging of the capacitance C through the various 
conductances g, driven by the voltages VN, all of these being properties of the cell 
membrane. The subscript L refers to passive leakage variables, E refers to excitatory 
variables, and I refers to inhibitory variables. These model units have firing rates 
which are sigmoidal functions of v. The output on a given time step is a number 
of spikes, which is chosen randomly with a Poisson distribution whose mean is the 
unit's current firing rate times the length of the time step. gz and g obey the 
equation 
d2g dg 
- - g' 
the equation for a damped harmonic oscillator. The effect of one unit's spike on 
another unit is to "kick" its conductance g, that is it simply increments the conduc- 
tance's time derivative by some amount depending on the strength of the connection. 
14 Spence and Pearson 
ILD -- -20 dB ILD -- 0 dB ILD = 20 dB 
dorsal 
ventral 
Figure 3: Output of Simulation of VLVps at Several ILDs. Position is represented 
on the vertical axis. Firing rate is represented by the horizontal length of the black 
bars. 
Inhibitory neurons increment dg/dt, while excitatory neurons increment dgz/dt. 7 
and w are chosen so that the oscillator is at least critically damped, and g remains 
non-negative. This model gives a fairly realistic post-synaptic potential, and the 
effects of multiple spikes naturally add. The gradient of cell types is modeled by 
having a different maximum firing rate at each level in the VLVp. 
The VLVp model is shown in figure 2. Here, central neurons of each VLVp project 
to central neurons of the other VLVp, while more dorsal neurons project to more 
ventral neurons, and conversely. This forms a sort of "criss-cross" pattern of projec- 
tions. In our simulation these projections are somewhat broad, each unit projecting 
with equal strength to all units in a small patch. In order for the dorsal neurons to 
be more strongly inhibited, there must be more inhibitory neurons at the ventral 
end of each VLVp, so in our simulation the maximum firing rate is higher there and 
decreases linearly toward the dorsal end. A presumed second neuron type is used 
for ouput, but we assumed its inputs and dynamics were the same as the inhibitory 
neurons and so we didn't model them. The input to the VLVps from the two NAs 
was modeled as a constant input proportional to the sound pressure level in the 
corresponding ear. We did not use Poisson distributed firing in this case because 
the spike trains of NA neurons are very regular [Sullivan and Konishi, 1984]. NA 
input was the same to each unit in the VLVp. 
Figure 3 shows spatial activity patterns of the two simulated VLVps for three dif- 
ferent ILDs, all at the same ABI. The criss-cross inhibitory connections effectively 
cause these bars of activity to compete with each other so that their lengths are 
always approximately complementary. Figure 4 presents results of both models 
discussed in this paper for various ABIs and ILDs. The output of VLVp units 
qualitatively matches the experimentally determined responses, in particular the 
ILD response curves show similar shifts with ABI. for the different dorsal-ventral 
positions in the VLVp (see Fig. 3 in [Manley, et al, 1988]). Since the observed 
non-GABAergic neurons are more numerous at the ventral end of the VLVp and 
The Computation of Sound Source Elevation in the Barn Owl 15 
VLVp ICL 
lOO 
8o 
6o 
40 
2o 
o 
I I I 
DORSAL .-7 
n() Llrn B'P ,- ..... / __ 
o .............. .. / 
20 i / 
40 ;': / -- 
,o ...... !,,/ 
----:--:---- ...... t"-- I 
I I I 
DORSAL VLVp input 
lOO 
80 
6o 
40 
2o 
o 
,, 
CENTRAL VLVp input 
100 
80 
60 
 o 
20 
o 
-20 
II I/// ?,,,/..,.,,.'"'- -- 
/ :"" VENTRAL -- 
-'-':- .......... t o-" I 
--10 0 10 20 
mD (dB) 
-20 
I I I 
VENTRAL VLVp input -- 
Figure 4: ILD Response Curves of the VLVp and ICL models. Curves show percent 
of maximum firing rate versus ILD for several ABIs. 
16 Spence and Pearson 
our model's inhibitory neurons are also more numerous there, this model predicts 
that at least some of the non-GABAergic cells in the VLVp are the neurons which 
provide the mutual inhibition between the VLVps. 
4 A MODEL OF ILD-TUNED NEURONS IN THE ICL 
In this section we present a model to explain how ICL neurons can be tuned to 
ILD if they only receive input from the ILD-sensitive neurons in one VLVp. The 
model essentially takes the derivative of the spatial activity pattern in the VLVp, 
converting the sigmoidal activity pattern into a pattern with a localized region of 
activity corresponding to the end of the bar. 
The model is shown in figure 2. The VLVp projects topographically to ICL neurons, 
exciting two different types. This would excite bars of activity in the ICL, except 
one type of ICL neuron inhibits the other type. Each inhibitory neuron projects 
to tuned neurons which represent a smaller ILD, to one side in the map. The 
inhibitory neurons acquire the bar shaped activity pattern from the VLVp, and 
are ILD-sensitive as a result. Of the neurons of the second type, only those which 
receive input from the end of the bar are not also inhibited and prevented from 
firing. 
Our simulation used the model neurons described above, with input to the ICL 
taken from our model of the VLVp. Each unit in the VLVp projected to a patch 
of units in the ICL with connection strengths proportional to a gaussian function 
of distance from the center of the patch. (Equal strengths for the connections from 
a given neuron worked poorly.) The results are shown in figure 4. The model 
shows sharp tuning, although the maximum firing rates are rather small. The ILD 
response curves show the same kind of ABI dependence as those of the VLVp model. 
There is no published data to confirm or refute this, but we know that neurons in 
the space map in the ICx do not show ABI dependence. There is a direct input 
from the contralateral NA to the ICL which may be involved in removing ABI 
dependence, but we have not considered that possibility in this work. 
5 CONCLUSION 
We have presented two models of parts of the owl's elevation or interaural level 
difference (ILD) system. One predicts a "criss-cross" geometry for the connections 
between the owl's two VLVps. In this geometry cells at the dorsal end of either 
VLVp inhibit cells at the ventral end of the other, and are inhibited by them. 
Cells closer to the center of one VLVp interact with cells closer to the center of 
the other, so that the central cells of each VLVp interact with each other (Fig. 2). 
This model also predicts that the non-GABAergic cells in the VLVp are the cells 
which project to the other VLVp. The other model explains how the ICL, with 
input from one VLVp, can contain neurons tuned to ILD. It does this essentially by 
computing the spatial derivative of the activity pattern in the VLVp. This model 
predicts that the ILD-sensitive neurons in the ICL inhibit the ILD-tuned neurons 
in the ICL. Simulations with semi-realistic model neurons show that these models 
The Computation of Sound Source Elevation in the Barn Owl 17 
are plausible, that is they can qualitatively reproduce the published data on the 
responses of neurons in the VLVp and the ICL to different intensities of sound in 
the two ears. 
Although these are models, they are good examples of the simplicity of information 
processing in neuronal maps. One interesting feature of this system is the elabo- 
rate mechanism used to do subtraction. With the usual model of a neuron, which 
calculates a sigmoidal function of a weighted sum of its inputs, subtraction would 
be very easy. This demonstrates the inadequacy of such simple model neurons to 
provide insight into some real neural functions. 
A cknowle dgement s 
This work was supported by AFOSR contract F49620-89-C-0131. 
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