Murray's law for discrete and continuum models of biological networks

Jan Haskovec; Peter Markowich; Giulia Pilli

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arXiv · 1908.01197

Murray's law for discrete and continuum models of biological networks

Jan Haskovec·Peter Markowich·Giulia Pilli

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Abstract

We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray's law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray's law for its linearly stable steady states.

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Jan Haskovec, Peter Markowich, Giulia Pilli. 2019-08-03. Murray's law for discrete and continuum models of biological networks. https://arxiv.org/abs/1908.01197

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