Three-dimensional model calculations for guinea pig cochlea.

Abstract

The WKB approximation was used for calculations of the pure tone response of a straight box model of the guinea pig cochlea with square scale cross sections and the fluid density and viscosity of water. Only one mode of elastic deformation of the partition was considered, corresponding to a flexible pectinate zone of the basilar membrane (BM) with rigid bony shelf, arches, and spiral ligament. Four distributions of pectinate zone transverse bending stiffness were considered, corresponding to volume compliances: (1) CB, measured by Békésy in the guinea pig post mortem, (2) CB/4, (3) CPL, deduced from Békésy's point load measurements in a human, with BM thickness inversely proportional to the width and rescaled for the guinea pig, and (4) 10CPL. We also considered various values of the relative longitudinal stiffness of the basilar membrane and the condition of drained or filled scala tympani. When compared to in vivo and post-mortem measurements of the guinea pig, the model results lead to the conjecture that the transverse fibers of the basilar membrane decrease in stiffness with time post mortem, while the ground substance increases in stiffness. Calculations using the compliance CB/4, with the ST drained with zero longitudinal BM stiffness give a response similar in location, peak shape, and phase to the in vivo capacitance probe measurements of Wilson and Johnstone [J., Acoust. Soc. Am 57, 705--23 (1975)]. Calculations for the ST filled and closed show a BM amplitude similar in location and shape to the spiral ganglion cell threshold curves obtained by Robertson and Johnstone [J. Acoust. Soc. Am. 57, 466--469 (1979)] from abnormal cochleas without outer hair cells. This indicates that the normal peak neural stimulation occurs about 1 mm apical of the BM peak amplitude. Naturally, the discrepancies between the postulated physical model and the cochlea prevent firm conclusions about cochlear function.