  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.
