Murray’s Law – Knowledge and References

Murray's Law

Murray's law is an optimization procedure proposed by Fung in 1997 for blood vessels that suggests a cost function which is the sum of the rate at which work is done to carry the flow of blood and the rate at which energy is used up by metabolism to maintain blood circulation. The law states that the arrangement of blood vessel networks should satisfy this cost function.From: Microfluidics and Nanofluidics Handbook [2019], Retinal micro-vascular network: data and model [2020]

Allometric Relationships

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Published in Arthur T. Johnson, Biology for Engineers, 2019

Arthur T. Johnson

Diameters of dichotomous branching vessel segments of the vasculature obey Murray’s law: () dparent3=dchild13+dchild23

Retinal micro-vascular network: data and model

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Published in Computer Methods in Biomechanics and Biomedical Engineering, 2020

L. Julien, J. Ventre, P.-Y Lagrée, A. Ramkhelawon, F. Rossant, M. Atlan, M. Paques, J.-M. Fullana

For blood vessels, an optimisation procedure, the Murray law, (Fung 1997) proposes a cost function that is the sum of the rate at work is done to carry the flow blood and the rate at which energy is used up by metabolism for maintain blood circulation. It follows in any junction involving three micro-vessels optimal relationships between radius (subscript 0 for incoming vessel and 1/2 for out coming vessels) and angles as sketched in the inset of Figure 1:

Murray's Law

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Allometric Relationships

Retinal micro-vascular network: data and model