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On the pressure and flow-rate distributions in tree-like and arterial-venous networks

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Abstract

A solution algorithm yielding the pressure and flow-rate distributions for steady flow in an arbitrary, tree-like network is provided. Given the tree topology, the conductance of each segment and the pressure distribution at the boundary nodes, the solution is obtained from a simple recursion based on perfect Gauss elimination. An iterative solution method using this algorithm is suggested to solve for the pressure and flow-rate distributions in an arbitrary diverging-converging (arterial-venous) network consisting of two tree-like networks which are connected to each other at the capillary nodes. A number of special solutions for tree-like networks are obtained for which the general algorithm is either simplified or can be replaced by closed form solutions of the pressure and flow-rate distributions. These special solutions can also be obtained for each tree of diverging-converging networks having particular topologies and conductance distributions. Sample numerical results are provided.

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 216, Talbot Laboratory, 104 S. Wright Street, 61801, Urbana, IL, U.S.A.

    Stefan Mayer

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Mayer, S. On the pressure and flow-rate distributions in tree-like and arterial-venous networks. Bltn Mathcal Biology 58, 753–785 (1996). https://doi.org/10.1007/BF02459481

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  • DOI: https://doi.org/10.1007/BF02459481

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