Metabolic cost sets the shear stress profile of optimal vascular trees

Abstract

Vascular remodeling responds to local wall shear stress, but transport efficiency belongs to the network as a whole. We connect these scales by minimizing dissipation under a fixed maintenance budget, with vessel cost proportional to mass raised to an exponent b. At an optimum, dissipated power is proportional to vessel cost. This yields the shear set point |{tau} | {propto} r^(b-1){ell}^(b-1)/2 for radius r and length {ell}, with uniform shear recovered at b = 1. The associated local adaptation rule decreases the global functional, although the topology it reaches retains a memory of development. Simulations with 400 and 700 sinks show that staged growth improves transport mainly by allowing pruned connections to regrow. Fluctuating demand sustains loops without increasing the maintenance budget. The local condition fixes allocation on a given support, whereas growth and variable demand shape the topology that survives.