Murray’s law has been the subject of continual investigation since its derivation in 1926. In his original work Murray solved a simple analytical optimization problem to minimize power requirements, balancing flow rate and metabolic function to find the optimal relationship between the radius of a parent and daughter vessel in a bifurcation along with the bifurcation angle. The cost function used in his work was the sum of a pressure loss term and a metabolic cost term. Minimizing this cost function, Murray derived the following relationship between parent and daughter vessels,
and an angle between the branches of 37.5°.
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