Adherence of the Vascular Branching Geometry in the blue Crab, Callinectes Sapidus, to Murray's Cost-Optimized Model

Abstract

Murray's Law predicts that there will be a radius cubed relationship between the parent and daughter vessels of a branching system of vessels that minimize the cost per volumetric flow. This cost-optimizing model has proven to be a loose approximation of biological fluid transport systems as diverse as the trophic systems of sponges and the closed circulatory systems of mammals. This study examines this relationship in yet a third distinct group of animals, the phylum Arthropoda. Molds of the vascular system of blue crabs, Callinectes sapidus, were made by corrosion casting with modified Bateson's number 17. Diameters were measured from these molds and used to calculate a junction exponent for each branch point, which was then compared to the Murray's predicted value of three. The exponents in the blue crab circulatory system correspond well with Murray's ideal cost-optimized model. These findings are significant for a number of reasons. (1) This study is the first quantitative description of the branching geometry of an open circulatory system. (2) The phylogenetic distance of arthropods from the animals previously studied, sponges and mammals, as well as the distance between these two groups is evidence for three independent evolutions of this branching relationship in biological fluid transport systems. (3) The physiological characteristics of the blue crab vasculature, such as the lack of cells in direct contact with the fluid and the absence of arterial smooth muscle, raise questions as to the mechanism animals use to maintain a relatively constant branching geometry throughout their fluid transport system in the face of dynamic environmental conditions.