Relationship between arterial diameter and blood flow rate at major arterial bifurcations of the dog

Murray derived an optimum condition for avascular system by applying a concept of minimum work. Murray's law states that the diameter of a blood vessel is proportional to the cube root of the flow rate within it, and the cube of the diameter of the parent vessel is equal to the sum of the cubes of the diameter of the daughter vessels at an arterial bifurcation. We tested the applicability of Murray's law to our experimental data on the diameters of and flow rates in major arteries of four mongrel dogs in order to elucidate the physiological principles governing arterial architecture. It was found that our experimental data on major arterial bifurcations of the dog fitted Murray's law not exactly but reasonably well, and the relationship between the diameter of parent vessel and that of its daughter vessels at an arterial bifurcation was best expressed by a modified expression of Murray's law given by Sigma D-di(3) = 0.95 x D-p(3).