Mathematical Sciences: Mathematical Modeling in Somatosensory Physiology

长期目标是发展对体感觉系统中机械到电转导的定量理解。本研究方案提出的模型系统为受体太平洋小体，主要是因为它是研究最广泛的皮肤受体。太平洋小体是包裹在皮肤和其他组织中的神经末梢。在先前的研究中，建立了菌株向受体膜传播的胶囊模型。本研究的目的是：(i)扩展胶囊模型，使其在解剖学上更真实；（ii）建立一个受体膜模型，包括一个应变敏感电导的转导电流模型，该模型解释了已知的细胞质延伸，并通过应变变量与胶囊模型耦合；（iii）启动具有受体的皮肤模型的开发；（iv）对为受体膜建立的广义索模型的溶液行为进行分析检验。这项研究是与生物力学建模专家M.H. Holmes和太平洋小体实验专家S. Bolanowski合作进行的。该研究的某些方面对其他机械感受器的分析应是有用的。与视觉和听觉系统相比，触觉系统还没有得到很好的理解，这种知识的缺乏阻碍了人工触觉系统的发展，而人工触觉系统在为老年人和残疾年轻人开发假肢装置方面非常有用，在机器人技术方面也有更明显的用途。其中一个有意义的部分是了解各种皮肤受体是如何工作的。从受体研究中提取的信息将用于未来研究中开发的触觉系统集成模型。建立触觉系统各个方面的定量模型的另一个目标是测试无法通过实验获得的关于触觉处理的各种假设。建模方法应该建议进行新的生理实验。

A long term goal is to develop a quantitative understanding of mechanical-to-electrical transduction in the somatosensory system. The model system proposed for this research proposal is the receptor Pacinian corpuscle, mainly because it is the most extensively studied skin receptor. The Pacinian corpuscle is an encapsulated nerve ending in the skin and other tissues. In a previous study a capsule model for the transmission of strain to the receptor membrane was developed. The aims of the proposed research are to: (i) extend the capsule model to make it more anatomically realistic; (ii) develop a receptor membrane model involving a transduction current model of a strain-sensitive conductance, which accounts for the known cytoplasmic extensions, and which is coupled to the capsule model through a strain variable; (iii) initiate development of a model for the skin with receptors; (iv) examine solution behavior analytically of the generalized cable model developed for the receptor's membrane. The research is in collaboration with M.H. Holmes, an expert in biomechanical modeling, and S. Bolanowski, Jr., a leading experimentalist in Pacinian corpuscles. Aspects of the research should be useful in analyzing other mechanoreceptors. The sense-of-touch, or tactile, system is not well understood in comparison to the vision and auditory systems, and that lack of knowledge hinders the development of artificial sense-of-touch systems that can be immensely useful in developing prosthetic devises for the old and handicapped young, as well as more obvious uses in robotics. A meaningful part of this is to understand how various skin receptors work. Information extracted out of studies of receptors will be used in an integrated model of the tactile system to be developed in future studies. Another goal in developing quantitative models of various aspects of the sense-of-touch system is to test various hypotheses about tactile processing that cannot be obtained experimentally. The modeling approach should suggest new physiological experiments to try.