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

Jan Haskovec, Peter A. Markowich, Giulia Pilli

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)2359-2376
Number of pages18
JournalMathematical Models and Methods in Applied Sciences
Volume29
Issue number12
DOIs
StatePublished - Sep 9 2019

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