A mathematical model for mechanical activation and compound action potential generation by the utricle in response to sound and vibration.

Introduction: Calyx bearing vestibular afferent neurons innervating type I hair cells in the striolar region of the utricle are exquisitely sensitive to auditory-frequency air conducted sound (ACS) and bone conducted vibration (BCV). Here, we present experimental data and a mathematical model of utricular mechanics and vestibular compound action potential generation (vCAP) in response to clinically relevant levels of ACS and BCV. Vibration of the otoconial layer relative to the sensory epithelium was simulated using a Newtonian two-degree-of-freedom spring-mass-damper system, action potential timing was simulated using an empirical model, and vCAPs were simulated by convolving responses of the population of sensitive neurons with an empirical extracellular voltage kernel. The model was validated by comparison to macular vibration and vCAPs recorded in the guinea pig, in vivo. Results: Transient stimuli evoked short-latency vCAPs that scaled in magnitude and timing with hair bundle mechanical shear rate for both ACS and BCV. For pulse BCV stimuli with durations <0.8 ms, the vCAP magnitude increased in proportion to temporal bone acceleration, but for pulse durations >0.9 ms the magnitude increased in proportion to temporal bone jerk. Once validated using ACS and BCV data, the model was applied to predict blast-induced hair bundle shear, with results predicting acute mechanical damage to bundles immediately upon exposure. Discussion: Results demonstrate the switch from linear acceleration to linear jerk as the adequate stimulus arises entirely from mechanical factors controlling the dynamics of sensory hair bundle deflection. The model describes the switch in terms of the mechanical natural frequencies of vibration, which vary between species based on morphology and mechanical factors.