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Mathematical Analysis of Transport and Consumption of Molecules in Heterogeneous Brain Tissue (Methodology)

  • R. H. Kufahl
  • D. F. Bruley
  • N. A. Busch
  • J. H. HalseyJr.
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 169)

Abstract

A computer model of metabolite transport and consumption in heterogeneous brain tissue, using a combination of probabilistic and deterministic techniques is being developed. The metabolites are put into two separate classes: (I) those that have reached a membrane for the first time during a small time step, At, and (II) those that have not yet reached a cell membrane for the first time during that time step. The time dependent spatial distribution of class (I) molecules is determined using random walk theory, which takes into account the actual paths of the molecules. The variation of the spatial distribution of class (II) molecules with time is determined using the time dependent diffusion equation with a boundary condition of zero concentration on the enclosing membrane boundaries.

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References

  1. Chandrasekhar, S., 1943, Stochastic Problems in Physics and Astronomy, Rev. Mod. Phys., Vol. 15, No.1: 1.CrossRefGoogle Scholar
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  4. Spitzer, F., 1976, “Principles of Random Walk”, Springer, New York.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • R. H. Kufahl
    • 1
  • D. F. Bruley
    • 1
  • N. A. Busch
    • 1
  • J. H. HalseyJr.
    • 2
  1. 1.Louisiana Tech. UniversityRustonUSA
  2. 2.University of Alabama at BirminghamBirminghamUSA

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