Mathematical Sciences: Mathematical Modeling in Somatosensory Physiology

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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.