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

Abstract

The sound-localization and, in particular, biosonar system of toothed whales is exceptionally performant. How this is achieved is not clear, given that: (i) toothed whales have no pinnae; (ii) while their auditory pathways have been studied in detail, no specific feature apparently replacing the pinna has been identified. In this study, 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 (CT) scans were utilized to build a three-dimensional velocity-density model of the specimen's head, parametrized on a high-resolution $1.11$ mm voxel grid. We first validate our wave propagation solver, identifying a range of frequencies and spatial scale lengths where the PSTD scheme captures the complexities of elastic wave propagation through toothed-whale anatomy. We next focus on the toothed whale's ability to locate sources on the median plane, where the role of anatomy is crucial. A 45 kHz central frequency burst (dolphin-like click) was modeled and directed at elevation angles from $-90^{\circ }$ to $+90^{\circ }$ in $5^{\circ }$ steps along the midsagittal plane. We find that the incoming sound can be localized, via correlation, from the reverberated portion of the time-domain waveforms recorded at the tympano-periotic complex locations.