Form and function of arterial bifurcations in various parts of the animal body
Branching patterns of arterial networks might influence vascular resistance and allow control of blood supply to peripheral tissues. Arterial casts from the brain, kidneys, and earlobes of cats and the chorioallantoic arteries of chick embryos were used for microscopic measurements of arterial geometry. From the measured diameters of parent and two daughter vessels at arterial bifurcations, we calculated the diameter exponent m. By applying the minimum work concept to blood flow through a cylindrical vessel, an optimal value m=3 has been derived (Murrays cubic law). The measured values of the diameter exponent were 2.59, 2.54, 2.58, and 2.49 for the brain, kidneys, earlobes, and chick embryos, respectively, exhibiting significant deviation from Murrays law. The physiological implication of the m values is discussed here.
arterial geometry blood flow murrays law optimal theory