Murray's law for discrete and continuum models of biological networks
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Embargo End Date2020-01-01
Permanent link to this recordhttp://hdl.handle.net/10754/659074
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AbstractWe 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.
CitationHaskovec, J., Markowich, P., & Pilli, G. (2019). Murray’s law for discrete and continuum models of biological networks. Mathematical Models and Methods in Applied Sciences, 1–18. doi:10.1142/s0218202519500489
SponsorsGiulia Pilli acknowledges support from the Austrian Science Fund (FWF) through the grants F 65 and W 1245.
PublisherWorld Scientific Pub Co Pte Lt