Mathematical Sciences: Analysis of Biomathematical Models inSensory Physiology

动物中的机械感受器接受机械刺激，并将其转化为电反应。与这一提议相关的研究项目是由首席研究员对一种特殊的(触觉)感受器--太平洋小体--所做的研究推动的。太平洋小体在由许多层弹性膜组成的外囊上以位移的形式接收机械刺激，因此应力在这些层之间有流体。其中一个项目是分析在不同边界和初始条件下，通过均匀化技术得到的胶囊内压力场的模型方程。有证据支持这一假说，即通过包膜传递的压力对可兴奋的树突膜施加压力，树突膜可能具有应变激活的离子通道。通过将理论预测与观测结果进行比较，将改进数学模型。

Mechanoreceptors in animals receive mechanical stimuli which are transformed into electrical responses. Research projects associated with this proposal are motivated by the study the principal investigator has made on a particular (tactile) receptor, the Pacinian corpuscle. Pacinian corpuscles receive mechanical stimuli in the form of displacement, hence stress, on an outer capsule composed of many layers of elastic membrane with fluid between these layers. One project is to analyze a model equation for the pressure field in the capsule derived via homogenization techniques under various boundary and initial conditions. Evidence supports the hypothesis that pressure transmitted through the capsule puts stress on the excitable dendritic membrane, which may possess a strain-activated ionic channel. The mathematical models will be refined to by comparing theoretical predictions with observations.