Finite element modelling of sound transmission in the Weberian apparatus of zebrafish ( Danio rerio )

Abstract

Zebrafish, an essential vertebrate model, has greatly expanded our understanding of hearing. However, one area that remains unexplored is the biomechanics of the Weberian apparatus, crucial for sound conduction and perception. Using micro-computed tomography (μCT) bioimaging, we created three-dimensional finite element models of the zebrafish Weberian ossicles. These models ranged from the exact size to scaled isometric versions with constrained geometry (1 to 10 mm in ossicular chain length). Harmonic finite element analysis of all 11 models revealed that the resonance frequency of the zebrafish's Weberian ossicular chain is approximately 900 Hz, matching their optimal hearing range. Interestingly, resonance frequency negatively correlated with size, while the ratio of peak displacement and difference of resonance frequency between tripus and scaphium remained constant. This suggests the transmission efficiency of the ossicular chain and the homogeneity of resonance frequency at both ends of the chain are not size-dependent. We conclude that the Weberian apparatus's resonance frequency can explain zebrafish's best hearing frequency, and their biomechanical characteristics are not influenced by isometric ontogeny. As the first biomechanical modelling of atympanic ear and among the few non-human ear modelling, this study provides a methodological framework for further investigations into hearing mechanisms and the hearing evolution of vertebrates.