Simultaneous self-organization of arterial and venous networks driven by the physics of global power optimization

Understanding of vascular organization is a long-standing problem in quantitative biology and biophysics and is essential for the growth of large cultured tissues. Approaches are needed that (1) make predictions of optimal arteriovenous networks in order to understand the natural vasculatures that originate from evolution (2) can design vasculature for 3D printing of cultured tissues, meats, organoids and organs. I present a method for determining the globally optimal structure of interlocking arterial and venous (arteriovenous) networks. The core physics is comprised of the minimization of total power associated with the whole vascular network, with penalties to stop arterial and venous segments from intersecting. Specifically, the power needed for Poiseuille flow through vessels and the metabolic power cost for blood maintenance are optimized. Simultaneous determination of both arterial and venous vasculatures is essential to avoid intersections between vessels that would bypass the capillary network. As proof-of-concept, I examine the optimal vascular structure for supplying square- and disk-like tissue shapes that would be suitable for bioprinting in multi-well plates. Features in the trees are driven by the bifurcation exponent and metabolic constant which affect whether arteries and veins follow the same or different routes through the tissue. They also affect the level of tortuosity in the vessels. The method could be used to understand the distribution of blood vessels within organs, to form the core of simulations, and combined with 3D printing to generate vasculatures for arbitrary volumes of cultured tissue and cultured meat.