Figure 1.
Synchrony patterns induced by location-dependent filtering.
The left hand panels (A, B, D, F) show the signal pathway for a set of neurons tuned to the presented location of the sound, and the right hand panels (A, C, E, G) show the pathway for neurons not tuned to the presented location. (A) The sound source S propagates to the left ear (blue) and right ear (green) and is acoustically filtered by location-dependent HRTFs. (B, C) Signals resulting from filtering through the spectro-temporal receptive fields of two pairs of monaural neurons tuned at 1 kHz. The source location is in the synchrony receptive field of the first neuron pair (B). (D, E) Spike trains produced after neural filtering, for neurons tuned at frequencies between 150 Hz and 5 kHz. The signals shown in B and C correspond to the spike trains highlighted in yellow. The source location is in the synchrony receptive field of each frequency-specific neuron pair in panel D but not in panel E. (F, G) Spike trains from the left and right channels are reproduced here superimposed. Postsynaptic neurons that receive coincident inputs from their two presynaptic neurons produce spikes (red patches). The neural assembly in F is tuned to the presented location whereas the assembly in G is not.
Figure 2.
Relationship between synchrony receptive field and source location.
We represent each signal or filter by a set of columns, which can be interpreted as the level or phase of different frequency components (as in a graphic equalizer). In the first two columns, the sound source (pink) is acoustically filtered through the pairs of HRTFs corresponding to location X (green), then filtered through the receptive fields of neurons A and B (blue), and resulting signals are transformed into spike trains (red and blue traces). In this case, the two resulting signals are different and the spike trains are not synchronous. In the next two columns, the source is presented at location Y, corresponding to a different pair of HRTFs. Here the resulting signals match, so that the neurons fire in synchrony: location Y is in the synchrony receptive field of neuron pair (A,B). The next 4 columns show the same processing for locations X and Y but with a different pair of neurons (C,D). In this case, location X is in the synchrony receptive field of (C,D) but not location Y. When neural filters are themselves HRTFs, this matching corresponds to the maximum correlation in the localization algorithm described by MacDonald [16]. When neural filters are only phase and gain differences in a single frequency channel, the matching would correspond to the Equalisation-Cancellation model [18]–[20].
Figure 3.
(A) The source signal arrives at the two ears after acoustical filtering by HRTFs. The two monaural signals are transformed along the auditory pathway (decomposition into multiple frequency bands by the cochlea and further neural transformations) and transformed into spike trains by monaural neurons. These spike trains converge on neurons which fire preferentially when their inputs are coincident. Location-specific synchrony patterns are thus mapped to the activation of neural assemblies (shown here as (azimuth, elevation) pairs). (B) Detailed model architecture. Acoustical filtering (R,L) is simulated using measured HRTFs. The resulting signals are filtered by a set of gammatone filters γi with central frequencies between 150 Hz and 5 kHz, followed by additional transformations (“neural filtering” FjL/R). Spiking neuron models transform these filtered signals into spike trains, which converge from each side on a coincidence detector neuron (same neuron model). The neural assembly corresponding to a particular location is the set of coincidence detector neurons for which the synchrony field of their inputs contains that location (one pair for each frequency channel). (C) Model response to a sound played at a particular location. Colors represent the firing rate of postsynaptic neurons, vertically ordered by preferred frequency (the horizontal axis represents a dimension orthonogal to the tonotopical axis). The neural assembly that encodes the presented location is represented by white circles. (D) Same as in (C), but neurons are ordered by preferred interaural delay. (E) Total response of all neural assemblies to the same sound presentation, as a function of their assigned location. The most activated assembly encodes for the presented source location.
Figure 4.
Cochleograms of test sounds used in simulations: white noise; vowel-consonant-vowel (VCV); instruments; pure tones (between 150 Hz and 5 kHz, uniformly distributed in ERB scale).
The cochleograms show the output of the gammatone filters used in the model, half-wave rectified and low-pass filtered [56].
Figure 5.
Examples of neural filters in the ideal and approximate model, which are band-pass filtered HRTFs.
Each filter is 45 ms long. The central frequency varies between columns, while the HRTFs vary between rows in the first three rows. The resulting filters are similar to gammatone filters (shown in the last row), but not identical (see for example the differences in envelope within the first column, and within the last column).
Figure 6.
Estimation results in the ideal model.
(A) Left (blue) and right (green) head-related impulse responses (HRIR) for a particular location passed through a gammatone filter. (B, C) Activation of all location-specific neural assemblies for two particular source locations, represented as a function of their assigned location. The black+shows the sound location and the white x shows the model estimate (maximally activated assembly). (D–F) Spatial receptive fields of three neural assemblies, i.e., total activation as a function of source location. (G) Mean error in azimuth estimates for white noise (red), vowel-consonant-vowel (blue), musical instruments (green) and pure tones (magenta). Front/back confusions do not contribute to azimuth errors in this panel. (H) Mean error in elevation estimates. (I) Categorization performance discriminating left and right (L/R), front and back (F/B) and up and down (U/D).
Figure 7.
Illlustration of how the model can estimate both azimuth and elevation.
(A) ITD measured at 217 Hz as a function of source location. When the sound is presented at azimuth −45° and elevation −10°, the ITD is consistent with all locations shown by the solid curve. For a spherical head, this curve corresponds to the “cone of confusion”. (B) ITD measured at 297 Hz vs. source location. The pattern is similar but quantitatively different from ITDs measured at 217 Hz (A), because sound diffraction makes ITDs frequency-dependent [21]. The ITD at location (−45°,−10°) is consistent with all locations shown by the dashed curve. (C) When the sound includes frequency components at 217 Hz and 297 Hz and ITDs can be measured in both channels, source location is unambiguously signaled by the intersection of the two level lines (green cross), corresponding to the ITD measured at the two frequencies. The red circle shows that this intersection resolves a potential front-back confusion.
Figure 8.
Estimation results in the approximate model.
(A) Comparison of a gammatone-filtered HRIR (blue) and an approximate filter (green; gammatone with best delay and gain). (B, C) Activation of neural assemblies for two particular source locations, as in Figure 6. (C) shows a mistake of the model. (D) Spatial receptive field of a particular neural assembly, as in Figure 6. (E) Preferred interaural delay vs. preferred frequency for neurons in two assemblies tuned to locations differing only by a front-back reversion. (F) Interaural gain difference vs. preferred frequency for the same assemblies. (G–I) Performance of the model, as in Figure 6. (J–L) Estimation results as a function of the number of frequency channels used. Simulations were all performed using 240 channels. To obtain estimates of the error using a smaller number of channels while keeping the same frequency range, a randomly chosen subset of the 240 channels was chosen. Error estimates are averaged over many such random choices. (J) Mean error in azimuth estimates for white noise (red), vowel-consonant-vowel sounds (blue), instruments (green) and pure tones (magenta). (K) Mean error in elevation estimates. (L) Categorization performance discriminating left and right (solid), front and back (dashed) and up and down (dotted). For all classes of sounds except the pure tones, the left/right categorization performance is 100% for all points.
Figure 9.
(A) Mean error in azimuth (blue) and elevation (green) as a function of the level of intrinsic noise in the model, measured as the standard deviation of the membrane potential. (B) Mean error as a function of the membrane time constant of coincidence detector neurons. (C) Mean error as a function of the signal to noise ratio, with uncorrelated white noise in both ears. (D, E, F) Performance of the model using AdEx neurons in place of LIF neurons (as in Figure 6).
Figure 10.
(A, B) Response of a population of postsynaptic neurons with various preferred frequencies, interaural delays and gains to a long broadband sound (10 s) played at a particular location. (A) Maximum neural response (color-coded) over all the gains, for each frequency and relative delay. (B) Maximum neural response over all the delays, for each frequency and relative gain. In both (A) and (B), the white x symbols show the maximum response for each frequency, and the black+symbol shows the choice of best delay (A) and relative gain (B) for that location in the approximate model, based on the cross-correlation of HRIRs. (C, D, E) Performance of the approximate model (as in Figure 8) using delays and gains learned from hearing 7 example sounds of 1 s duration from each location.
Figure 11.
Simultaneous representation of two acoustical environments (two sets of HRTFs).
(A, B) Best delay and relative interaural gain for two assemblies (black and white circles) corresponding to the same location in the two different HRTF sets, as in Figure 8E and F. (C, D) Response of the postsynaptic neurons to a sound at a particular location with one HRTF set, as in Figure 3C and D. The black circles show the neurons tuned to the correct location for one set, the white for the other. (E) Summed responses of location-specific assemblies for the two HRTF sets (each assembly has a preferred location and set), for a particular location and HRTF set. The circles represent the source location in the correct (black) and incorrect (white) set. The maximally activated assembly encodes for both location and HRTF set. (F) Summed responses of neural assemblies as a function of preferred location, for both sets (sum of the two sets of responses in E).
Figure 12.
Mean error in estimates of elevation (A) and azimuth (B) of white noise in the approximate model as a function of the azimuth of the sound source.
The elevation error at zero azimuth is close to the chance level of 36 degrees.
Figure 13.
Performance of the model in low frequencies (under 3kHz).
(A, B, C) Performance of the approximate model, as in Fig. 5G–I, for low frequencies only (80 channels distributed on the ERB scale from 150Hz to 3kHz).
Figure 14.
Distribution of interaural phase differences (IPD) in the binaural signals and preferred IPDs of binaural neurons.
The color codes follow the conventions of Fig. 3 of Harper and McAlpine (2004). (A) Distribution of IPDs across all HRTFs (including all measured azimuths and elevations), as a function of frequency. The dark triangle corresponds to the physical limit of ITDs, which is smaller than half a period for low frequencies, while the light triangle corresponds to the situation when the maximum ITD is between π and 2π, which makes larger IPDs more represented than smaller ones (imagine folding a larger triangle at the vertical lines IPD = −π and IPD = π). (B) Distribution of best IPDs of neurons in the approximate model as a function of their preferred frequency. Best IPDs were measured using delayed white noise. The horizontal line at 400 Hz represents the frequency above which best delays should be continuously distributed, according to Harper and McAlpine (2004). A very similar distribution was obtained with the ideal model (not shown).
Table 1.
Neuron model parameters.