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. 2014 Feb 18;9(2):e89033.
doi: 10.1371/journal.pone.0089033. eCollection 2014.

Modelling of human low frequency sound localization acuity demonstrates dominance of spatial variation of interaural time difference and suggests uniform just-noticeable differences in interaural time difference

Rosanna C G Smith  1 , Stephen R Price  2
Affiliations

Modelling of human low frequency sound localization acuity demonstrates dominance of spatial variation of interaural time difference and suggests uniform just-noticeable differences in interaural time difference

Rosanna C G Smith et al. PLoS One. .

Abstract

Sound source localization is critical to animal survival and for identification of auditory objects. We investigated the acuity with which humans localize low frequency, pure tone sounds using timing differences between the ears. These small differences in time, known as interaural time differences or ITDs, are identified in a manner that allows localization acuity of around 1° at the midline. Acuity, a relative measure of localization ability, displays a non-linear variation as sound sources are positioned more laterally. All species studied localize sounds best at the midline and progressively worse as the sound is located out towards the side. To understand why sound localization displays this variation with azimuthal angle, we took a first-principles, systemic, analytical approach to model localization acuity. We calculated how ITDs vary with sound frequency, head size and sound source location for humans. This allowed us to model ITD variation for previously published experimental acuity data and determine the distribution of just-noticeable differences in ITD. Our results suggest that the best-fit model is one whereby just-noticeable differences in ITDs are identified with uniform or close to uniform sensitivity across the physiological range. We discuss how our results have several implications for neural ITD processing in different species as well as development of the auditory system.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Model predictions for human ILDs and ITDs.
A, Model to determine ITD or ILD variation with azimuth angle θ for the experimental set up in Mills , Schmidt et al. and Kuhn . The human head is modelled as a solid sphere, radius a (8.75 cm) and the sound source is modelled as a point source, frequency f, and distance r from the centre of the head. Ears are positioned 100° away from the midline. B, Azimuthal variation of interaural level difference (ILD) for sound source at 0.5 m, 250 Hz, 500 Hz, 750 Hz or 1000 Hz, as predicted by our acoustic model for the experimental set up by Mills. C, Comparison of predicted curves for interaural phase differences (IPDs) and empirical data points from Mills , r = 0.5 m. D, Comparison of model interaural time differences (ITDs) with empirical data from Kuhn , r = 3.0 m.
Figure 2
Figure 2. Phase ambiguity frequency limit for varying head size.
This is the frequency at which interaural phase difference first reaches 180°. This model is for ears at 90° away from the midline. In this case the human phase ambiguity limit is 685 Hz (695 Hz for ears at 100°) for a head radius of 8.75 cm. As head size increases animals are restricted to using IPD as a non-ambiguous sound localization cue at lower frequencies. Animals with smaller heads have a greater range of frequencies in which IPD is a non-ambiguous cue.
Figure 3
Figure 3. Predicted values of ΔITD determined from acuity data.
A, Relationship between localization acuity (Δθ), just-noticeable difference in ITD identification (ΔITD) and the angular variation of ITD. B, Example of how ΔITDs are determined for each individual data point in an acuity data set. C, Candidate models for ΔITD distributions across ITD. Uniform distributions are described by parameter c0 and linear distributions are described by parameters cp and kp. D, Best-fit uniform or linear distributions for each acuity data set under consideration. Overall goodness of fit is similar for both distributions. Midline predictions of ΔITD are better for the linear distribution, but the proportionality constant is low in all cases and negative in one case (Schmidt data), making them close to the uniform case.
Figure 4
Figure 4. Best-fit acuity curves for uniform or linear ΔITD distributions.
Candidate uniform and linear ΔITD models used to find best-fit acuity (Δθ) distributions for five acuity data sets. Uniform distributions are described by parameter c0 and linear distributions are described by parameters cp and kp. As with the best-fit descriptions of ΔITD distributions, best-fit acuity distributions have low kp values for the linear ΔITD case, close to the uniform case. AICc values indicate that the majority of acuity data sets are more appropriately described by uniform ΔITD distribution as these have lower AICc values than for a linear ΔITD distribution (comparing the same data sets).
Figure 5
Figure 5. The effect of minimal available ΔITD on acuity.
Just-noticeable differences in ITD identification (ΔITDs) required to produce the same acuity (1°) at all angles, shown for the time domain (A) and angular domain (B). This is compared to an example of the minimum possible ΔITD available in the ITD identification system (across all ITDs). At some point across the range, the minimum ΔITD is greater than the ΔITD required for constant acuity, leading to poorer acuity laterally than at the midline (C). The crossover point depends both on the maximum sensitivity of the system (minimum ΔITD) and the value of constant acuity.
Figure 6
Figure 6. Probability distributions for a sound source in the angular and time domains.
Probability distributions in the angular (A) and time (B) domains for a distant pure tone 500 Hz sound with equal probability of originating at any azimuth angle. This results in a non-constant probability distribution across ITDs, with a greater probability of a sound having a long ITD.
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