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Understanding of vascular organization is a long-standing problem inquantitative biology and biophysics and is essential for the growth of largecultured tissues. Approaches are needed that (1) make predictions of optimalarteriovenous networks in order to understand the natural vasculatures thatoriginate from evolution (2) can design vasculature for 3D printing of culturedtissues, meats, organoids and organs. I present a method for determining theglobally optimal structure of interlocking arterial and venous (arteriovenous)networks. The core physics is comprised of the minimization of total powerassociated with the whole vascular network, with penalties to stop arterial andvenous segments from intersecting. Specifically, the power needed forPoiseuille flow through vessels and the metabolic power cost for bloodmaintenance are optimized. Simultaneous determination of both arterial andvenous vasculatures is essential to avoid intersections between vessels thatwould bypass the capillary network. As proof-of-concept, I examine the optimalvascular structure for supplying square- and disk-like tissue shapes that wouldbe suitable for bioprinting in multi-well plates. Features in the trees aredriven by the bifurcation exponent and metabolic constant which affect whetherarteries and veins follow the same or different routes through the tissue. Theyalso affect the level of tortuosity in the vessels. The method could be used tounderstand the distribution of blood vessels within organs, to form the core ofsimulations, and combined with 3D printing to generate vasculatures forarbitrary volumes of cultured tissue and cultured meat.

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