Relating PDEs in cylindrical coordinates and CTMCs with levels of concentration

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Abstract

We present the derivation of a CTMC with levels model of diffusion in cylindrical coordinates from the partial differential equation for Fick's law. The resulting model abstracts both molar concentration, by discrete levels, and spatial location, by discrete compartments. We apply the results to the diffusion of nitric oxide in human vessels and illustrate with simulations in the PRISM tool. © 2010 Elsevier B.V. All rights reserved.

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Degasperi, A., & Calder, M. (2010). Relating PDEs in cylindrical coordinates and CTMCs with levels of concentration. In Electronic Notes in Theoretical Computer Science (Vol. 268, pp. 49–59). https://doi.org/10.1016/j.entcs.2010.12.005

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