Investigating Murray's law in the chick embryo

Abstract

According to the optimization principle known as Murray's law, the blood vessel geometry at a bifurcation satisfies the relation α=( D 1 3+ D 2 3)/ D 0 3=1, where D 0, D 1, and D 2 are the diameters of the parent and two daughter vessels, respectively. Previous investigations have shown that mature blood vessels adhere to this law fairly closely. The purpose of this study was to test Murray's law in the developing extraembryonic blood vessels of 2–4 day-old chick embryos. Vessel diameters were measured manually using image analysis software. The measurements for the group of all vessels at all studied stages ( n=449) gave α=1.01±0.34 (mean ± SD), and the value of α is similar at all stages. These results indicate that Murray's law holds in the chick embryo, even before medial smooth muscle becomes functional, suggesting that blood vessels follow the same basic morphogenetic rules throughout life.