Biol Cybern (2007) 97:261–267DOI 10.1007/s00422-007-0178-9

LETTER TO THE EDITOR

Tuning bat LSO neurons to interaural intensity differencesthrough spike-timing dependent plasticity

Bertrand Fontaine · Herbert Peremans

Received: 31 May 2007 / Accepted: 20 August 2007 / Published online: 25 September 2007© Springer-Verlag 2007

Abstract Bats, like other mammals, are known to useinteraural intensity differences (IID) to determine azimuthalposition. In the lateral superior olive (LSO) neurons havefiring behaviors which vary systematically with IID. Thoseneurons receive excitatory inputs from the ipsilateral ear andinhibitory inputs from the contralateral one. The IID sensitiv-ity of a LSO neuron is thought to be due to delay differencesbetween the signals coming from both ears, differences due todifferent synaptic delays and to intensity-dependent delays.In this paper we model the auditory pathway until the LSO.We propose a learning scheme where inputs to LSO neu-rons start out numerous with different relative delays. Spiketiming-dependent plasticity (STDP) is then used to prunethose connections. We compare the pruned neuron responseswith physiological data and analyse the relationship betweenIID’s of teacher stimuli and IID sensitivities of trained LSOneurons.

1 Introduction

It is believed that bats use predominantly interaural inten-sity differences (IID) to determine the azimuth of a target(Fuzessery 1996; Aytekin et al. 2004). Due to the shadowingeffects of the head and the pinna, the intensity perceived bythe ear ipsilateral to the sound will be higher than the one onthe contralateral side. This shadowing effect changes alongwith the sound source position allowing the IID to code forthe latter.

B. Fontaine (B) · H. Peremans13, Prinsstraat, 2018 Antwerpen, Belgiume-mail: bertrand.fontaine@ua.ac.be

H. Peremanse-mail: herbert.peremans@ua.ac.be

In one of the first mammalian brain centers to processbinaural auditory information i.e., the LSO, the neurons showa firing rate dependent on IID (Tollin 2003; Park et al. 1996).The rate is maximum for IID values corresponding with thesound coming from the ipsilateral side and decreases as thesound becomes more centered to reach zero at a particularIID value. The shape of the IID firing curves of LSO neu-rons are thought to be caused by two mechanisms: the relativearrival times of the inputs from the two ears differ among cells(the latency hypothesis) and, to a lesser extent, firing thresh-olds between excitatory and inhibitory inputs are differentamong cells (the threshold hypothesis). Neurophysiologicalexperiments on bats (Park et al. 1997, 1996) have shownthat a majority of the neurons in the LSO behave in confor-mance to the latency hypothesis whereas only a minority fitthe threshold hypothesis.

Models for IID processing in the LSO have been describedbefore. In Reed and Blum (1990), the steady-state responseto long duration stimuli is considered. It is clear, however,that such stimuli are very different from the short durationecho signals processed by fm-bats like Eptesicus fuscus (Sur-lykke and Moss 2000). In Shi and Horiuchi (2007), a very-large-scale integration (VLSI) implementation is developedemphasizing the role of first spike latency and populationencoding in IID processing of short (2 ms) duration constantfrequency signals. None of these models, however, attemptto replicate the learning going on after birth in the LSO.

From neurophysiological measurements (Tollin 2003), itis known that LSO neurons receive excitatory inputs fromthe ipsilateral ear and inhibitory inputs from the contralat-eral one. Furthermore, it has been shown (Sanes and Friauf2000) that between birth and maturity the number of inputconnections, both excitatory and inhibitory, decreases withage suggesting that learning takes place by pruning connec-tions. In this paper we simulate the training of LSO neurons

123

262 Biol Cybern (2007) 97:261–267

-50 -40 -30 -20 -10 0 10 20 30 40 50-10

-5

0

5

10

15

20

azimuth [deg]

HR

TF

[dB

]

Left

RightIID

Fig. 1 HRTF and IID as a function of azimuth measured at both earsat 30 kHz and −10 elevation (Eptesicus fuscus)

using STDP (Gerstner and Kistler 2002). Because of their rel-ative importance we focus on neurons which conform to thelatency hypothesis. We compare the responses of the trainedneurons to those found in neurophysiological experiments.Finally, we investigate to what extent the IID of the teacherstimulus has an effect on the IID sensitivity of the trainedneurons. Other training parameters are also varied and theirvariations are related to the corresponding IID sensitivitychanges.

2 IID based localisation

As mentioned before, the shadowing effect of the head anddiffraction around the pinna causes the intensity of a reflectedecho to be different at both ears depending upon the positionof the reflector. In Fig. 1 we can see the HRTF measured onan Eptesicus fuscus (Aytekin et al. 2004) at 30 kHz and −10elevation. Within a certain azimuth range the IID is a mono-tonic function of azimuth e.g. in Fig. 1 this is the case between−30 and 50. Hence, azimuth can be inferred directly fromIID in this range. However, as can be seen in Fig. 2, theazimuth versus IID curves are different for different eleva-tions. Hence, IID information from multiple frequency chan-nels needs to be processed simultaneously to unambiguouslyestimate azimuth and elevation (Brainard et al. 1992; Walkeret al. 2003; Aytekin et al. 2004).

3 IID processing in the lateral superior olive

3.1 Physiological and experimental data

The LSO is located in the brainstem in the superior olivarycomplex. Most of its neurons receive their excitatory inputs

-25 -20 -15 -10 -5 0 5 10 15 20 25-25

-20

-15

-10

-5

0

5

10

15

20

25

azimuth [deg]

]g

ed[

noit

avel

e

contour plot HRTF at 30kHz

8dB

10dB

12dB14dB

9dB

11dB

13dB 15dB

Fig. 2 Contour plot of the HRTF gain measured at the right ear at30 kHz for different positions in space (Eptesicus fuscus)

contralateral ear ipsilateral ear

cochlea

CNANMNTB

LSO

cochlea

CN

AN

excitatory

inhibitory

Fig. 3 Auditory pathway until the LSO. AN auditory nerve, CNcochlear nucleus, MNTB medial nucleus of the trapezoidal body, LSOlateral superior olive

from the ipsilateral ear through bushy cells of the cochlearnucleus (CN) and inhibitory inputs from the contralateral ear.The contralateral pathway passes first through bushy cells ofthe contralateral CN and then through the ipsilateral medialnucleus of the trapezoid body (MNTB) which finally projectsto the LSO. The different connections can be seen in Fig. 3.

Neurons in the LSO have firing behaviors which dependon IID. In Park et al. (1996), firing rates of neurons in the LSOof Mexican free-tailed bats were measured. Earphones wereplaced in the funnel of each pinna. The acoustic stimuli were2 ms duration downward frequency-modulated (FM) sweepswith a rise–fall time of 0.2 ms. The frequency swept downfrom 5 kHz above to 5 kHz below the best frequency of theunit under measurement. The intensity at the ipsilateral earwas kept constant (20 dB SPL), while the contralateral inten-sity was varied between −10 and 50 dB in 5 dB steps. Everyneuron has a different IID-firing rate curve, but all resemblethe ones sketched in Fig. 4a. By convention we expressthe IID as the difference between ipsilateral intensity and

123

Biol Cybern (2007) 97:261–267 263

firin

g ra

te

IID [dB]

1

2

3

4

5

6

7

-30 -20 -10 0 10

ipsi

contra

ipsi contradB

30

IIDdB dB

10 20

30 20 10

30 30 0

30 40 10

postsynaptic potential

t

t

t

t

A B

Fig. 4 a Firing response of different LSO neurons when the IID is var-ied. b Mechanisms explaining the firing rate curve of an LSO neuronwith complete inhibition at 0 dB IID [adapted from Park et al. (1996)]

contralateral intensity. Although the responses are differ-ent they all have the same sigmoid shape shifted along theabscissa. A standard response feature allowing the character-isation of these IID-firing rate curves is the IID of completeinhibition (IIDCI). IIDCI denotes the IID value for which theneuron passes from a firing to a completely silent state.

3.2 Peripheral processing model

The peripheral auditory system model takes as input an acous-tic signal and gives as output a stream of spikes in a collec-tion of auditory nerve (AN) fibers. The joint time–frequencyanalysis performed on the incoming signal is modeled onthe transduction stage located in the inner ear. A simple butaccurate model is a dual-resonance non-linear filterbank(Sumner et al. 2003). The non-linearities allow the modelingof important properties like the broadening of the bandpassfilter bandwidth with increasing intensities. The inner haircells (IHC) and the spike generation in the spiral ganglioncells (SGC) of the AN are modeled as in Sumner et al. (2002).We consider a single frequency channel (30 kHz), which isrepresented by 20 AN fibers.

This model is applied to the bat peripheral auditory systemby changing the parameters of the filterbank to values knownto apply for bats (Saillant et al. 1993). Neurophysiologicaldata on the CN and the AN of FM bats are not available tothe best of our knowledge. Therefore, missing parameters aretaken from the guinea-pig model. The guinea-pig is a wellstudied animal in auditory neuroscience and models existwhich parameters are easily available in the literature. Theparameters of the AN fibers are chosen to correspond withthe so-called high spontaneous rate fibers (Yost 2000).

The AN fibers project to neurons in the CN. We modelCN neurons using single-variable leaky integrate and fire(LIF) neurons (Burkitt 2006). We chose the membrane timeconstant so that the modeled neurons behave as coincidencedetectors (Joris et al. 1994). This enables our model to reli-ably detect the onset of a signal integrating the input from 20noisy AN fibers.

3.3 LSO model

A particular LSO neuron’s response is thought to be theresult of two processes (Park et al. 1996): the strength of theinput inhibition increases with contralateral intensity and thelatency of the input inhibition decreases with contralateralintensity. This is illustrated in Fig. 4b for a cell having com-plete inhibition at 0 db IID. When the contralateral intensityis lower than the ipsilateral intensity, the postsynaptic poten-tial caused by the contralateral input is lower and arriveslater, allowing the LSO neuron to fire. At 0 dB IID, both syn-apse contributions to the postsynaptic potential arrive simul-taneously and cancel each other. The neuron becomes silent.

The IID sensitivity curves vary greatly among cells andmost have IIDCI values different from zero. As mentionedbefore, for the LSO cells considered in the present analy-sis, the shaping of IID sensitivity is determined by latenciesexclusively (Park et al. 1996). The so-called latency hypoth-esis is based on two features of the input spike trains: (i) therelative arrival times of the inputs from the two ears differamong LSO cells and (ii) changes in the intensity of the stim-uli at the ear shift the latencies of the inputs. For example,if, for a particular LSO cell, the contralateral input arrivesafter the ipsilateral input when presented with identical stim-uli at both ears, the contralateral intensity must be increasedto achieve coincidence and thus the IIDCI is shifted towardsnegative values.

Relative arrival time between excitatory and inhibitoryinputs is due to numerous factors like different path lengths,different axonal diameters, etc. Mechanisms for intensity-dependent latency (IDL) are less well understood but it hasbeen established that neuron’s response latency along theauditory pathway typically shortens with increasing stimulusintensity (Klug et al. 2000). The IDL is already present at theAN where the decrease in latency with increasing intensityis of the order of 25 µs/dB (Heil and Irvine 1997). It has beenproposed (Krishna 2002) that the properties of the emissionof neurotransmitter in the synapse between IHC and SGC asa rare probabilistic event can explain the IDL encountered atthis stage. Using the peripheral processing model introducedbefore, the response latency changes with stimulus intensityas shown in Fig. 5. The CN response latency is taken as thearrival time of the first output spike of a CN neuron withrespect to stimulus onset.

4 Learning

4.1 Spike timing-dependent plasticity

The development of the LSO of a Gerbil is largely achievedduring the first 3 postnatal weeks (Sanes and Friauf 2000) inwhich period there is a structural change in the pathway. Inthe absence of more specific information about the develop-

123

264 Biol Cybern (2007) 97:261–267

55 60 65 70 75 80 85 90 95 1004

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

Sound intensity [dB]

Res

pons

e la

tenc

y [m

s]

Fig. 5 Intensity-dependent mean output latency function (length errorbars is equal to 2σ ) of a modeled CN neuron

ment of the bat LSO we will assume a similar developmentalprocess is at work in bats as well. Therefore both the refine-ment of the LSO–MNTB inhibitory as well as the excitatorynetwork result from elimination and strengthening of syn-apses driven by neural activity. This suggests that a learn-ing algorithm depending on relative firing times like STDP(Leibold and van Hemmen 2005, 2002) could be used forboth inhibitory and excitatory synapses.

However, most of the focus, experimental and computa-tional, has been directed towards excitatory synapses. Indeed,although a large proportion of the synapses in the brain areinhibitory, not that much is known about the learning mech-anisms of inhibitory synapses . Applying STDP to traininginhibitory networks is not straightforward. STDP follows amodified Hebb’s rule, such that weights are increased if theactivity between pre- and post-synaptic neurons is correlatedand the weights are decreased if this activity is uncorrelated.Unlike excitatory synapses, the activity of an inhibitory pre-synaptic neuron is negatively correlated with the activity ofits postsynaptic partner. We propose a modified learning win-dow to take this into account.

Experiments have shown that the contralateral inputs areactually excitatory at birth and become inhibitory afterwardsto be fully inhibitory at hearing onset (Sanes and Friauf2000). This divides the developmental period in two phases:(1) a contralateral early depolarizing stage which is linkedwith a growing of the LSO/MNTB connections and to ratherlong postsynaptic potentials (PSP) and (2) a contralateralhyperpolarizing stage which is linked with the refinement ofthe LSO/MNTB connections with much shorter PSP. Thisrefinement, which is what is modeled here, continues untilafter hearing onset. We assume that the MNTB, the CN andthe peripheral system are sufficiently mature to exhibit theproperties needed for our learning scheme.

The learning process is as follows: starting from an initialvalue, the synaptic weights wi (t) are updated at the end ofevery learning period TL:

wi (t + TL) = wi (t) + ∆wi (t). (1)

TL=20 ms is chosen to contain the interval between stim-ulus onset and the last LSO output spike elicited by this stim-ulus. The learning rule we used for the modification of thesynaptic weights w±

i of an LSO neuron consists of three parts(Kempter et al. 1999): (1) the arrival of an input spike froma synapse i changes wi by a certain amount cin, (2) whenan output spike is triggered, all the weights change by a cer-tain amount cout and (3) time differences between all pairs ofinput and output spikes influence a third change of weights:

∆w±i = η±

t+TL∫

t

[c±

in Sini (t

′) + c±

out Souti (t

′)]

dt′

+η±t+TL∫

t

t+TL∫

t

W ±(t′′ − t

′)Sin

i (t′)Sout(t

′′)dt

′dt

′′

= η±

⎡⎢⎣

′∑t fi

c±in +

′∑tn

c±out +

′∑t fi ,tn

W (t fi − tn)

⎤⎥⎦ . (2)

The ± sign denotes excitatory and inhibitory synapses. η±is the learning rate. Sin

i (t) = ∑t fi ∈Fi ;t f

i ≤tδ(t − t f

i ) denotes

a presynaptic spike train with t fi the arrival times at the syn-

apse and Fi stands for the set of all spike arrival times atsynapse i . Sout(t) is the output spike train. In the last partof Eq. 2 the prime indicates that only firing times t f

i and tn

in the time interval [t, t + TL] are to be taken into account.To avoid unlimited growth, we impose an upper and lowerbound on the weights: w±

i ∈ [0, wmax]. A synaptic changedue to the co-occurrence of an input and an output spike takesplace if presynaptic spike arrival time and postsynaptic firingtime both fall within some window. The window W used totrain excitatory synapses (Fig. 6a) has the same formulationas in Leibold and van Hemmen (2005). Let s be the differ-ence between an input spike arrival time and an output spiketriggering time, then for s < s∗

W +(s) = (A − B) exp[(

s − s∗) /τ0]

(3)

and, for s ≥ s∗,

W +(s) = A exp[− (

s − s∗) /τ1]

−B exp[− (

s − s∗) /τ2]. (4)

This window has a standard shape for STDP, which is a phe-nomenological model based on experimental data. The win-dow used for the inhibitory synapses W −(Fig. 6a) is a mir-rored version of the one used for the excitatory synapses W +

123

Biol Cybern (2007) 97:261–267 265

inhibitory

excitatory

-1 -0.5 0 0.5 1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

time difference [ms]

w(s

)

A

-40 -20 0 20

0.2

0.4

0.6

0.8

1

stimulus IID [dB]

LSO

spi

ke c

ount

B

40

0.1

0.3

0.5

0.7

0.9

0s*

Fig. 6 a Windows used for the STDP. b Firing rate when neuron ispresented with different IID’s. Neuron taught with a stimulus of 4.7 dBIID

which in addition is shifted towards a positive time offsets∗−. Mirroring guarantees anti-correlation between pre- andpost-synaptic activity after the learning. This way, inhibitoryinput neurons that have fired before or after an output spikewill have their synaptic weights decreased. Introducing theshift guarantees that the non-pruned contralateral inputs willbe trained to arrive later so that higher contralateral intensitiesare required to make them coincide with excitatory inputs.

4.2 Network setup

The pre-learning LSO cell is modeled by a LIF neuron con-nected with 50 CN neurons from the ipsilateral ear and 50CN neurons from the contralateral ear. The input synapsesdiffer in their delay which is taken linearly between 0 and3 ms. The weights are chosen randomly between 0 and wmax

for the ipsilateral synapses and between 0 and wmax/2 forthe contralateral synapses to ensure initial firing which willtrigger the learning process.

The different parameters were chosen as follows: LIF neu-ron: Rm = 1 MΩ , τm = 2 ms, Vthresh = −0.045 V, Vinit =−0.06 V, Vresting = −0.06 V, Vreset = −0.06 V, , Trefract =1 ms. Synapses: τContra = 0.5 ms, τIpsi = 0.1 ms, Wmax = 1e-6.Learning parameters: A+ = 2/3, B+ = 0.25, η+ = 1e-8,τ+

0 = 1/7 ms, τ+1 = 1/200 ms, τ+

2 = 1/2 ms, s∗+ = −1/80 ms,A− = 2/3, B− = 0.25, η− = 2e-8, τ−

0 = 1/5 ms, τ−1 = 1/200 ms,

τ−2 = 1/2 ms, s∗− = −0.3 ms, c+

out = 5/30, c+in = 2/75,

c−out = 5/180, c−

in = 1/45.The stimulus, average intensity 70 dB, is a 2 ms downward

FM sweep from 35 to 25 kHz. Due to the short duration ofthe signals used the CN neurons output between zero andtwo spikes per stimulus. The initial set of parameters for thewindows are taken from Leibold and van Hemmen (2005).

Then they have been tuned to the task at hand. As we said,W − must be a mirrored version of W + thus the parametersfor the two windows are similar. The width of the positivepart of W − is a bit larger to have more inhibitory synapsesthan excitatory after learning. That, together with the factthat the PSP for inhibition is longer than the excitatory one[τContra ≥ τIpsi (Sanes 1990)], ensure a complete inhibitioneven at very high contralateral intensities (when the inhibi-tion arrives before the excitation). The different time con-stants are chosen small enough to reach the expected timeprecision.

First, the system is presented with 1,000 stimuli corre-sponding to an azimuth of −5 (IID of 4.7 dB). Every outputspike triggers a weight update. After 1,000 stimulus presen-tations almost all weights are either zero or have reached theupper bound. The final weights of synapses of both typesare shown in Fig. 7. Note that the time reference is arbitrarywhich means that the first excitatory synapse need not bethe 0 ms delayed synapse. The only constraint that must holdafter learning is

DcSyn + Dc

IDL = DiSyn + Di

IDL + ∆s∗ (5)

where DcSyn and Di

Syn are, respectively, the contralateral and

ipsilateral synaptic delays and DcIDL and Di

IDL the contralat-eral and ipsilateral delays due to IDL. ∆s∗ = s∗−−s∗+ is thetime offset of the contralateral STDP window relative to theipsilateral one. The pruned network is then presented withstimuli whose IID’s range from −30 to +15 dB (with ipsilat-eral intensity kept constant) and the mean firing response iscomputed (Fig. 6b). The resulting responses have the sameshapes as the one measured in neurophysiological experi-ments (see Fig. 4).

4.3 Analysis of the resulting networks

Due to the probabilistic initialization of the learning phaseand the noise in the spike generation model, teaching multipleneurons with the same stimuli will not yield identical results.This can be seen in Fig. 8a, where each curve represents theestimated probability density function of the IID of completeinhibition (IIDCI) when multiple neurons are trained with thesame stimuli. The distributions are unimodal and well char-acterized by their mean.

If we now train multiple neurons with stimuli from dif-ferent positions, we can see an almost linear relationship(Fig. 8b) between the azimuth of the teacher stimulus andthe mean IIDCI of the trained neurons. Only azimuth val-ues corresponding to ipsilateral positions (IID≥0) have beenused as teacher values because neurons sensitive to ipsilateralsound are predominant in the ipsilateral LSO (Tollin 2003).

Other direct relationships can be found between meanIIDCI and, for instance, particular parameters of the learn-

123

266 Biol Cybern (2007) 97:261–267

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5 3

final contralateral weight

final ipsilateral weight

synaptic delay [ms]

synaptic delay [ms]

1

0.5

0

1

0.5

0

A

B

Fig. 7 Learning with a stimulus at −5. a weights of the ipsilateralsynapses (x for initial values, O for final values). b weights of thecontralateral synapses (x for initial values, O for final values)

-20 -15 -10 -5 0 5

-20

-15

-10

-5

-30 -20 -10 0 100

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

azimuth teacher stimulus [degr]IID [dB]CI

prob

abili

ty d

ensi

ty

DIIn

ae

m[d

B]

CI

-20

1

-10

5

A B

Fig. 8 a Estimation of the probability density function of the IIDCIwith four teacher azimuth values(−20, −10, 1, 5). b mean IIDCIas a function of the teacher azimuth

ing window. For example, ∆s∗, the time offset of the inhibi-tory window with respect to W +, can be adjusted to reach adesired shift in the mean IIDCI for a fixed teacher IID valueFig. 9. A larger ∆s∗ favors inhibitory synapses with longerdelays (thus shifting the group of synapses in Fig. 7b to theright). Hence, the inhibitory inputs need a higher intensityto compensate for this delay and arrive simultaneously withthe excitatory input. As a consequence, the IIDCI is shiftedtowards more negative values.

0 0.2 0.4 0.6 0.8 1 1.2 1.4-25

-20

-15

-10

-5

0

[dB

]DII

CI

s* [ms]

Fig. 9 Mean IIDCI as a function of the time offset s∗ of the inhibitorywindow

5 Conclusion

We have shown that it is possible to tune LIF neurons forIID using STDP. Our pre-learning architecture contains inputneurons with deterministically increasing synaptic delays.This allows us to relate certain parameters of the training tothe shape of the resulting response as characterized by IIDCI.The azimuth of the teacher, for instance, was shown to influ-ence the IID firing rate curve of the trained neuron. As isthe case for particular parameters of the learning windowse.g., the time offset of the inhibitory window. This controlover the resulting IID sensitives is interesting if one wants tofurther process the output of a population of LSO neurons todo azimuth estimation. Indeed, it presents a means to forcethe IID sensitivities of the LSO neurons to cover a particularIID range of interest with a minimum number of neurons.

It is clear that a biologically more plausible IID estimationscheme would have less control (if any at all) over the learn-ing parameters and would have to rely on a larger populationto ensure that random variations of the relevant neuron prop-erties would allow the population to cover the whole rangeof IID’s. For instance, to cover a broader range of IID valuesthe IIDCI’s after learning should also have a broader distribu-tion around a mean IIDCI. This can be arranged by changingour pre-learning architecture into one that resembles morethe biological one. Indeed, as shown in Klug et al.(2000),inputs reaching the LSO have different IDL functions. Wecan thus use input neurons which have different IDL func-tions and random relative synaptic delays. We are currentlyinvestigating to what extent this more realistic distribution ofthe network parameters affects the resulting IID sensitivitiesby teaching such a population of LSO neurons using teacherstimuli corresponding with azimuthal positions drawn from arealistic distribution. We conjecture that although the result-

123

Biol Cybern (2007) 97:261–267 267

ing IID-firing rate curves would be less sharp, the output ofthose networks i.e., the number of spikes and the responsedelay, would be enough to estimate the IID at a particular fre-quency. Integrating this information along frequency chan-nels would allow us to estimate the azimuth and the elevationof a target.

Acknowledgments This work is sponsored by the EU as part ofthe CILIA project. The authors would like to thank M. Aytekin andC. Moss for having made available their Big Brown bat HRTF measure-ments. The peripheral system was modeled using the DSAM modelingsoftware http://www.pdn.cam.ac.uk/groups/dsam/. The spiking neuronnetwork was simulated using the Csim Toolbox http://www.lsm.tugraz.at/csim.

References

1. Aytekin M, Grassi E, Sahota M, Moss CF (2004) The bat head-related transfer function reveals binaural cues for sound localiza-tion in azimuth and elevation. J Acoust Soc Am 116(6):3594–3605

2. Brainard MS, Knudsen EI, Esterly SD (1992) Neural derivation ofsound source location: resolution of spatial ambiguities in binauralcues. J Acoust Soc Am 91(2):1015–1027

3. Burkitt AN (2006) A review of the integrate-and-fire neuronmodel: II. inhomogeneous synaptic input and network properties.Biol Cybern 95(2):97–112

4. Fuzessery ZM (1996) Monaural and binaural spectral cues createdby the external ears of the pallid bat. Hear Res 95(1):1–17

5. Gerstner W, Kistler WM (2002) Spiking neuron models: sin-gle neurons, populations, plasticity. Cambridge University Press,Cambridge

6. Heil P, Irvine DRF (1997) First-spike timing of auditory-nervefibers and comparison with auditory cortex. J Neurophysiol78(5):2438–2454

7. Joris PX, Smith PH, Yin TC (1994) Enhancement of neural syn-chronization in the anteroventral cochlear nucleus. II. responsesin the tuning curve tail. J Neurophysiol 71(3):1037–1051

8. Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learningand spiking neurons. Phys Rev E 59(4):4498–4514

9. Klug A, Khan A, Burger RM, Bauer EE, Hurley LM, Yang L,Grothe B, Halvorsen MB, Park TJ (2000) Latency as a functionof intensity in auditory neurons: influences of central processing.Hear Res 148(1-2):107–123

10. Krishna BS (2002) An unified mechanism for spontaneous-rateand first-spike timing in the auditory nerve. J Comput Neurosci13(2):71–91

11. Leibold C, van Hemmen JL (2002) Mapping time. Biol Cybern87(5-6):428–439

12. Leibold C, van Hemmen JL (2005) Spiking neurons learning phasedelays: how mammals may develop auditory time difference sen-sitivity. Phys Rev Lett 94(16):168102

13. Park TJ, Grothe B, Pollak GD, Schuller G, Koch U (1996) Neuraldelays shape selectivity to interaural intensity differences in thelateral superior olive. J Neurosci 16(20):6554–6566

14. Park TJ, Monsivais P, Pollak GD (1997) Processing of interauralintensity differences in the lso: role of interaural threshold differ-ences. J Neurophysiol 77(6):2863–2878

15. Reed MC, Blum JJ (1990) A model for the computation and encod-ing of azimuthal information by the lateral superior olive. J AcoustSoc Am 88(3):1442–1453

16. Saillant PA, Simmons JA, Dear SP, McMullen TA (1993) A com-putational model of echo processing and acoustic imaging in fre-quency-modulated echolocating bats: the spectrogram correlationand transformation receiver. J Acoust Soc Am 94(5):2691–2712

17. Sanes DH (1990) An in vitro analysis of sound localization mecha-nisms in the gerbil lateral superior olive. J Neurosci 10:3494–3506

18. Sanes DH, Friauf E (2000) Development and influence of inhibi-tion in the lateral superior olivary nucleus. Hear Res 147(1):46–58

19. Shi RZ, Horiuchi TK (2007) A neuromorphic VLSI model of batinteraural level difference processing for azimuthal echolocation.IEEE Trans Circuits Syst 54(1):74–88

20. Sumner CJ, Lopez-Poveda EA, O’Mard LP, Meddis R (2002) Arevised model of the inner-hair cell and auditory-nerve complex.J Acoust Soc Am 111(5):2178–2188

21. Sumner CJ, O’Mard LP, Lopez-Poveda EA, Meddis R (2003) Anon-linear filter-bank model of the guinea-pig cochlear nerve: ratesresponses. J Acoust Soc Am 113(6):3264–3274

22. Surlykke A, Moss CF (2000) Echolocation behavior of big brownbats, Eptesicus fuscus, in the field and the laboratory. J Acoust SocAm 108(5):2419–2429

23. Tollin DJ (2003) The lateral superior olive: a functional role insound source localization. Neuroscientist 9(2):127–143

24. Walker VA, Peremans H, Hallam JCT (2003) An investigation ofactive reception mechanisms for echolocators. In: Thomas JA,Moss CF, Vater M (eds) Echolocation in bats and dolphins.University of Chicago Press, Chicago, pp 507–514

25. Yost WA (2000) Fundamentals of hearing: an introduction, 4th edn,Academic, San Diego

123