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The kinetics of diffused substances in some biological systems

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Abstract

The purpose of this paper is to present a method for the determination of a solution for a coupled system of first order initial boundary-value problems arising from some biological systems. The physical problem is to determine the suspended and the superficial molecular concentrations of a traced substance passing through an organ containing a tangle of vessels, such as the kidney-ureter system. The approach to the problem is by successive approximation which leads to a recursion formula for the determination of the solution as well as error estimates for the approximations. The recursion formula involves only direct integration which indicates a promising possibility in obtaining numerical results by using a computer. In addition to the determination of a solution, some qualitative analysis of the solution is given. This includes the existence of a unique solution, the continuous dependency of the solution on the data, and the stability problem of a steady-state solution.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, 27607, Raleigh, North Carolina, USA

    C. V. Pao

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  1. C. V. Pao
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Pao, C.V. The kinetics of diffused substances in some biological systems. Bltn Mathcal Biology 40, 107–121 (1978). https://doi.org/10.1007/BF02463133

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  • DOI: https://doi.org/10.1007/BF02463133

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