A mathematical analysis of the peripheral auditory system mechanics in the goldfish (Carassius auratus)

The dynamic response of the goldfish peripheral auditory system has been analyzed using lumped-parameter mechanical and fluid system models for the swimbladder, Weberian apparatus, and saccule. The swimbladder is treated as a two degree-of-freedom mechanical system consisting of two coupled mass-spring-damper arrangements. The swimbladder is coupled to the Weberian ossicles using a phenomenological analysis of the anterior swimbladder tunica externa which permits both stretching and sliding. Analysis of the saccule features only a single degree of freedom, corresponding to the direction of orientation of the ciliary bundles. Inputs to the saccule consist of the transverse canal fluid motion and the motion of the animal's head (assumed to match the local acoustic particle motion). Mechanical properties required for the system equations were estimated from published literature, direct measurements, and curve fits to experimental data for the motions of the swimbladders. The results indicate that the Weberian apparatus has a significant impact on hearing ability over the entire auditory bandwidth, not just at higher frequencies, and that the saccule functions as a displacement sensor above approximately 300 Hz.