  In 1926, Murray proposed the first law for the optimal design of blood
vessels. He minimized the power dissipation arising from the trade-off between
fluid circulation and blood maintenance. The law, based on a constant fluid
viscosity, states that in the optimal configuration the fluid flow rate inside
the vessel is proportional to the cube of the vessel radius, implying that wall
shear stress is not dependent on the vessel radius. Murray's law has been found
to be true in blood macrocirculation, but not in microcirculation. In 2005,
Alarc\'on et al took into account the non monotonous dependence of viscosity on
vessel radius - F{\aa}hr{\ae}us-Lindqvist effect - due to phase separation
effect of blood. They were able to predict correctly the behavior of wall shear
stresses in microcirculation. One last crucial step remains however: to account
for the dependence of blood viscosity on shear rates. In this work, we
investigate how viscosity dependence on shear rate affects Murray's law. We
extended Murray's optimal design to the whole range of Qu\'emada's fluids, that
models pseudo-plastic fluids such as blood. Our study shows that Murray's
original law is not restricted to Newtonian fluids, it is actually universal
for all Qu\'emada's fluid as long as there is no phase separation effect. When
phase separation effect occurs, then we derive an extended version of Murray's
law. Our analyses are very general and apply to most of fluids with shear
dependent rheology. Finally, we study how these extended laws affect the
optimal geometries of fractal trees to mimic an idealized arterial network.
