Supplementary materials

Supplementary Figure 1: An overview of the four experiments selected for the purpose of demonstrating and validating the proposed framework. Experiment 1 and 2 simulate the localization (with HRIR) and lateralization (without HRIR) experiments in bilateral CI users, respectively. In addition, the effect of AGC was illustrated in experiment 1a and 1b (with and without AGC). Experiment 3 and 4 simulate the ITD just noticeable difference (JND) or ITD- and ILD-based lateralization, where single-electrode or multiple-electrode pairs were stimulated without a CI processing stage.

Supplementary Figure 2: Waveforms (column 1), spectrogram (column 2) and electrodograms (column 3-6) of these six acoustic stimuli (250 Hz sinusoidal tones, BB-, LP-, HP- noise bursts, clicks, and Chinese word ‘shui’) at 60 dB SPL. The electrodograms of four coding strategies are shown in column 3-6: 12-channel gammatone filter-bank based CIS (column3), FSx = 4 (column4), PP (column5), and the 8-of-22 channel FFT filter-bank based ACE* (column 6). The Matlab function for creating these plots is ‘plot_suppfig2.m’

Supplementary Figure 3: The electrodograms (A, C, within 60 ms, from 60°) and the ILD-azimuth functions (B, D) of the BB stimuli without (AGC = 0) and with AGC (AGC = 1) obtained from the 12-channel FSx = 4 coding strategies. The electrodogram of the right CI is shown in black behind the colored left electrodogram. The broadband ILDs before the CI processing were plotted as black dotted lines, while the ILDs of each individual electrode pair were plotted as colored solid lines. The simulated source level was 70 dB SPL. The corresponding Matlab function for plots is ‘plot_suppfig3’.

Supplementary Figure 4: Examples of the effects of different coding strategies (different colors represent 12-channel gammatone filter-bank based CIS, 8of22-channel CIS, FSx = 4, and PP without AGC) on the azimuthal localization performance with the six stimulus types (column 1-6) at 40 dB SPL: the spike pattern along the tonotopic axis for 0° azimuth (upper panels), response azimuth over target azimuth (lower panels) functions. The corresponding Matlab functions for generating the simulation and the plots are ‘gen_suppfig4.m, and ‘plot_subfig4.m’.

Supplementary Figure 5: Demonstration of the effect of AGC on the EI-outputs (localization) for the six stimuli at different levels with 12-channel FSx = 4 coding strategies. The first row shows the estimated direction vs the original direction without AGC, the second one with AGC. The corresponding Matlab functions for generating the simulation and the plots are ‘gen_suppfig5.m, and ‘plot_subfig5.m’.

Supplementary Figure 6: Example of an estimated psychometric ILD curve on the r_Δ scale (left y-axis) and the corresponding lateralization scale (right y-axis) after the mapping. The slope, width, and range are indicated by a, ω and range.

Supplementary Figure 7: The spike pattern along the tonotopic axis for ITD = 0 and ILD = 0 (upper panels), r_Δ-ITD (middle panels) and r_Δ-ILD (bottom panels) functions of the EI-outputs for the six stimuli types with a general 12-channel CIS coding strategy without AGC at 6 different levels (represented by different colors). The corresponding Matlab functions for generating the simulation and the plots are ‘gen_suppfig7.m’ and ‘plot_subfig7.m’.

Supplementary Figure 8: Effects of different coding strategies (different colors represent 12-channel gammatone filter-bank based CIS, FSx = 4, PP, and 8of22-channel FFT-based CIS; without AGC) on the ITD and ILD discrimination for the six stimuli types (column 1-6) at 60 dB SPL: the spike pattern along the tonotopic axis for ITD = 0 and ILD = 0 (upper panels), % right response-ITD (middle panels) and % right response-ILD (bottom panels) discrimination functions. The corresponding Matlab functions for generating the simulation and the plots are ‘gen_suppfig8.m’ and ‘plot_subfig8.m’.

Supplementary Figure 9: stimulation locations used in experiment 3 and 4. The marked red points are located at 5, 10, 15, 20, and 25 mm along the tonotopic axis.

Supplementary Figure 10: the normalized spike rate difference (r_Δ)-IPD functions (A, 380 µA; B, 600 µA) and the ITD JNDs-pulse rate functions (C, blue, 380 µA; purple, 600 µA) of single electrode stimulation at different pulse rates. The corresponding Matlab functions for the simulation and the generation of the plots are ‘gen_suppfig10.m’ and ‘plot_subfig10.m’.

Supplementary Figure 11: The average spike rate of the 35 EI-neurons along the tonotopic axis at ITD = 0 and ILD = 0 for 100 pps (A) and 1000 pps (B). On the y-axis, the spike rate is shown in spikes per second (sp/s), and the x-axis is the tonotopic location as well as the corresponding greenwood frequency. The normalized r_Δ-ITD (C, left y-axis) and r_Δ-ITD functions (D, left y-axis) and the corresponding lateralization results (right y-axis). The dotted lines in D are the corresponding results for the 1000 pps. The stimulation level is 480 µA. The corresponding Matlab functions for the simulation and generating the plots are ‘gen_suppfig11.m’ and ‘plot_subfig11.m’.

Supplementary Figure 12: The average spike rate of the 35 EI-neurons along the tonotopic axis for single-electrode pair stimulation located at 15 mm. Three pulse rates of 100 pps (A), 500 pps (B) and 1000 pps (C) were simulated for unmodulated pulses at eight different input levels with ITD = 0 and ILD = 0. On the y-axis the spike rate is shown in spikes per second (sp/s), and the x-axis is the location along the basilar membrane. Panel (D) shows the on-site (at 15 mm) EI neuron’s spike rate-level for these three pulse rates. The corresponding Matlab functions for the simulation and generating the plots are ‘gen_suppfig12.m’ and ‘plot_subfig12.m’.

© The Author(s), Published by EDP Sciences, 2023