Perturbation approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation |
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Authors: | Donald A French David A Edwards |
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Institution: | (1) Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH 45221-0025, USA;(2) Department of Mathematical Sciences, University of Delaware, 511 Ewing Hall, Newark, DE 19716, USA |
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Abstract: | In this paper, a mathematical model of the diffusion of cAMP into olfactory cilia and the resulting electrical activity is
presented. The model, which consists of two nonlinear differential equations, is studied using perturbation techniques. The
unknowns in the problem are the concentration of cAMP, the membrane potential, and the quantity of most interest in this work:
the distribution of CNG channels along the length of a cilium. Experimental measurements of the total current during this
diffusion process provide an extra boundary condition which helps determine the unknown distribution function. A simple perturbation
approximation is derived and used to solve this inverse problem and thus obtain estimates of the spatial distribution of CNG
ion channels along the length of a cilium. A one-dimensional computer minimization and a special delay iteration are used
with the perturbation formulas to obtain approximate channel distributions in the cases of simulated and experimental data.
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Keywords: | Olfaction Inverse problem Cilia Perturbation analysis Computational neuroscience |
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