Analysis of Vestibular Hair Cell Bundle Mechanics Using Finite Element Modeling

Abstract

The vestibular system of vertebrates consists of the utricle, saccule, and the semicircular canals. Head movement causes deformation of hair cell bundles in these organs, which translate this mechanical stimulus into an electrical response sent to the nervous system. This study consisted of two sections, both utilizing a Fortran-based finite element program to study hair cell bundle response. In the first part, the effects of variations in geometry and material properties on bundle mechanical response were studied. Six real cells from the red eared slider turtle utricle were modeled and their response to a gradually increased point load was analyzed. Bundle stiffness and tip link tension distributions were the primary data examined. The cells fell into two groups based on stiffness. All cells exhibited an increase in stiffness as the applied load was increased, but cells in the stiffer group showed a greater increase. Tip link tensions in the compliant group were approximately 3 times as high as those in the stiffer group. Cells in the stiffer group were larger, with more cilia, and also had a higher stereocilia/kinocilium height ratio than the cells in the other group. The stereocilia/kinocilium height ratio was the most important geometric factor in influencing bundle stiffness. Modeling a bundle as just its middle row of stereocilia resulted in some decrease in stiffness, but more significantly, a stiffness that was virtually constant as applied load increased. Tip link tension distributions showed serial behavior in the core rows of stereocilia and parallel behavior in the outer rows; this trend intensified if the tip link elastic modulus was increased. It was demonstrated that full three-dimensional modeling of bundles is critical for obtaining complete and accurate results. In the second part of the study, tip link ion gates were modeled. Sufficient tension in a tip link caused that linkà ­s ion gate to open, increasing the length of the link and causing its tension to decrease or the link to go slack. The two parameters that were varied were tip link elastic modulus and tip link gating distance d (change in length of the link). Bundle stiffness drops of up to 25% were obtained, but only when tip links went slack after gate opening; tip link slackening was dependent on tip link gating distance. Higher tip link modulus resulted in higher stiffness drops. Variable tip link modulus and tip link pre-tensioning were modeled. Variable tip link modulus resulted in increased bundle stiffness, especially under high applied loads, and in some cases, resulted in greater bundle stiffness drops when ion gates opened. Tip link pre-tensioning had no noticeable effect on bundle response. No evidence against inclusion of pre-tensioning or variable tip link elastic modulus was found.