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

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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
Issue number12
StatePublished - Sep 9 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Giulia Pilli acknowledges support from the Austrian Science Fund (FWF) through the grants F 65 and W 1245.


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