Hydrodynamics of the excitation of the cupula in the fish canal

Calculations on the dynamic behavior of the eupula in the fish lateral line canal are presented. The cupula is compared to a rigid half sphere that is sliding over an epithelium to which it is coupled elastically. The calculation of the hydrodynamic excitation of the cupula is based on a solution of the Navier-Stokes equation for a fluid flow past a vibrating sphere. No restrictions regarding the magnitude of the linear (ac) Reynolds number of the fluid flow are imposed on this solution. Cupular displacements calculated by the combination of hydrodynamics and mechanics of the eupula are compared to submicrometer displacements of the cupula of the ruff [Acerins cernua (L) ], which have been measured interferometrically [van Netten and Kroese, Hear. Res. 29, 55-61 ( 1987); van Netten, J. Acoust. Soc. Am. 83, 1667-1674 (1988) ]. A high degree of agreement is obtained between the calculations and the experimental data. By varying the relevant physical parameters of the model---eupular radius, the amount of elastic coupling, and viscosity of the fluid--their functional significance in lateral line transduction can be determined. From the theory, it appears that these physical parameters can be combined to only two independent dimensionless numbers, which completely determine the eupular frequency response. One number, the linear (ae) Reynolds number, is related to the hydrodynamics, whereas the second dimensionless number accounts for the interaction between hydrodynamics and mechanical properties of the organ.

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