Computational Investigation on the Empirical Relation of Murray’s Law

The human circulatory system is complex, and about one-sixth of the resting metabolic rate is consumed for keeping the blood flowing through the system. It consists of geometrical complications such as tapering, branching, channel bifurcations and curvatures. For minimizing the biological work accounting for the blood flow at the bifurcations, Murray’s law was formulated by Cecil D. Murray. The work done in overcoming the viscous drag and the maintenance of the vessel is considered for deriving the empirical relation of Murray’s law. The empirical relation states that the volumetric flow rate is proportional to the cube of the vessel radius. Here, in this study, we have computationally investigated the above stated empirical relation.