Some Direct and Inverse Problems in Receptor Neurodynamics

机械转导是一种基本的生理过程，对听觉、触觉、消化和平衡等多种功能起着中心作用。为了理解体感觉系统中的机械感受，研究者继续开发一种受体的详细数学模型，Pacinian小体，一种包裹的神经末梢。人们不可能在不损伤神经的情况下取出胶囊，因此关于胶囊下沿神经的电压分布的许多问题无法通过实验来回答。由于人们只能在对胶囊表面施加位移刺激后对神经从胶囊中出现的地方进行神经测量，那么沿着未暴露的神经，那里的电压如何依赖于各种神经参数？是否需要一个非线性的电流-电压关系来达到新兴端的阈值电压？是否可以在出现的末端（超确定的边界条件）做额外的记录，并能够恢复对神经的刺激？该项目采用数学建模来解决这些生理学上有价值的问题。我们的身体不断地接受机械刺激，但这些刺激必须被处理成大脑可以解释的神经信号。这涉及到一种叫做机械感受器的受体。无论是内耳中的毛细胞，还是皮肤中的太平洋小体，都有一些几乎不可能通过实验建立的特性，因此研究人员使用复杂的数学模型来帮助预测对给定刺激的反应，以及建立内部受体的特性。例如，上面提到的皮肤受体是一个神经末梢，它被一层膜和液体所保护。从生理学上讲，人们不能在不严重损伤神经膜的情况下将机械球（囊）与神经末梢分离。但是，有了一个好的数学模型，就可以确定每个组件对响应行为的各自贡献。此外，该模型还可以提出在胶囊外进行额外神经测量的方法，这将有助于找到生物上无法到达的微粒内参数值。分析增加了我们对哺乳动物触觉系统转导过程的理解，分析方法超越了这里考虑的特定模型案例。

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.