Pseudo-spectral model of elastic-wave propagation through toothed-whale head anatomy, and implications for biosonar

The sound localization and biosonar system of toothed whales is exceptionally performant. What enables such precision, however, remains unclear, given that (i) toothed whales have no pinnae, and (ii) although their auditory pathways have been studied in detail, no specific feature that could functionally replace the pinna has been identified. We employ a pseudo-spectral time domain (PSTD) numerical scheme to model three-dimensional elastic wave propagation through a toothed-whale head including soft tissues. Computed tomography scans were used to build a velocity-density model of a bottlenose dolphin's head, parametrized on 1.11 mm voxels. We validate our wave propagation solver, identifying a range of frequencies and scale lengths where the PSTD scheme captures the complexities of wave propagation through anatomy. We next focus on the toothed whale's ability to determine the elevation of sound sources, where anatomy plays a crucial role. Sinusoidal bursts with 45 kHz central frequency, emitted by far-field sources at elevations from -90° to +90°, were recorded at the locations of left and right inner ear. We find that their elevation can be established, via correlation, solely based on the "coda" of the incoming signal, whose waveform is controlled by refraction through and reflection off multiple anatomical structures.