The emergence of vascular design in three dimensions

Nature shows that fluids bathe the animal body as trees matched canopy to canopy. The entering streams invade the body as river deltas and the reconstituted streams sweep and exit the body as river basins. Why should this be so? Why is animal vascularization not based on arrays of parallel channels, as in modern heat exchangers? In this paper, we rely on constructal theory to show that the flow architecture that provides greatest access from point to volume and from volume to point is the three-dimensional compounding of trees matched canopy to canopy. This three-dimensional tree architecture is deduced, not assumed. Its flow performance is evaluated at every step relative to the performance of equivalent architectures with parallel channels. This paper also shows that the dendritic design must become more complex (with more levels of branching) as the volume inhabited by the flow design increases. The transition from designs with p branching levels to p+1 levels occurs abruptly as the available flow volume increases. This fundamental development has implications not only in evolutionary animal design but also in animal tissue modeling and the design of new vascular (smart) materials with volumetric functionalities such as self-cooling and self-healing.