Some Direct and Inverse Problems in Receptor Neurodynamics

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Bell 9706307 Mechanotransduction is a fundamental physiological process that is central for such diverse functions as hearing, touch, digestion, and balance. To understand mechanoreception in the somatosensory system, the investigator continues developing a detailed mathematical model of one receptor, the Pacinian corpuscle, an encapsulated nerve ending. One can not remove the capsule without damaging the nerve, so many questions about the voltage distribution along the nerve underneath the capsule can not be answered experimentally. Since one can only take neural measurements where the nerve emerges from the capsule after applying displacement stimuli to the capsule surface, how does voltage there depend on various neural parameters along the unexposed nerve? Does one need a nonlinear current-voltage relation to achieve a threshold voltage at the emerging end? Can one do extra recordings at the emerging end (overdetermined boundary conditions) and be able to recover the stimuli to the nerve? The project undertakes mathematical modeling to address these physiologically valuable questions. Our bodies receive mechanical stimuli continuously, but the stimuli must be processed into neural signals that the brain can interpret. This involves receptors called mechanoreceptors. Be they hair cells in the inner ear, or Pacinian corpuscles in the skin, there are properties that are nearly impossible to establish experimentally, so the investigator uses sophisticated mathematical models to help predict responses to given stimuli, as well as establish internal receptor properties. For example, the above mentioned skin receptor is a nerve ending which is protected by a bulb of membranes and fluid. Physiologically one can not separate the mechanical bulb (the capsule) from the nerve ending without sever damage to the nerve membrane. But with a good mathematical model one can determine respective contributions each component makes to response behavior. Also , the model can suggest ways of taking extra neural measurements outside the capsule which will aid in finding biologically unreachable parameter values inside the corpuscle. Analysis increases our understanding of the transduction process in the mammalian tactile system, and the analytic methodology transcends the particular model case considered here.