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

TL;DR

A pseudo-spectral time domain (PSTD) numerical scheme is employed to model three-dimensional elastic wave propagation through a toothed-whale head including soft tissues, and it is found 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.

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.

Figures (11)

• Figure 1: Computed tomography (CT) scans of the dolphin’s head immersed in water, shown as grayscale CT slices in (a) axial, (b) sagittal, and (c) coronal planes. (d) Reconstructed model of the dolphin’s head in MATLAB, with labeled anatomical components: epidermis(1), bone(2), mandibular fat(3), air(4), melon(5), and connective tissue(6).
• Figure 2: Numerical simulation setup. Black dots on the top and left sides of the smaller box mark the virtual point sources used for generating the incoming plane wave. The red dashed lines the full extent of the box including the PML layers.
• Figure 3: Visualization of the voxel grid in the axial view of the dolphin’s head CT scan after down sampling to (a) 4 mm, (b) 2 mm, and (c) 1.11 mm voxel resolutions. (d) Input sinusoidal burst source used in the simulations. (e) Results of the convergence test, showing a comparison of recorded waveforms corresponding to (a), (b), and (c).
• Figure 4: Validation of the numerical model. (a) Schematic illustrating the positions of points X, and Y located in the specimen's head, at the tip of the jaw, and at the TPC, respectively. (b) Comparison of pressure waveforms recorded at positions Y and X, respectively. (c) Error difference calculated by subtracting the waveforms of the forward and reverse simulation.
• Figure 5: Normal and shear stresses on the x–y plane of the reverberant field at simulation time, T = 0.5 ms. (a)–(c) Normal stress distributions for Case 1, Case 2, and Case 3, respectively. (d)–(f) Corresponding shear stress distributions for the same cases.