Novel description for optimality principle of cerebral arteries within the circle of Willis: a Womersley number-based scaling law.

Deviation from the optimal bifurcation structure causes abnormal hemodynamic stress, increasing the risk of cerebral aneurysm initiation at the arterial bifurcation apexes of the Circle of Willis. Although Murray's law describes the optimal relationship between bifurcation calibers, major arterial bifurcations within the Circle of Willis show deviations from this law. This study introduces a novel scaling law that describes the optimum relationship between bifurcation characteristics based on pulsatile flow and the internal surface of vessels. The proposed scaling law applies to major intracranial arteries, such as the basilar, internal carotid and common carotid arteries, encompassing both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is its sole dependence on the Womersley number of parent vessels to determine bifurcation characteristics. The diameter ratios suggested by these relationships are in good agreement with available clinical morphometric data. Numerical simulations of pulsatile flow for several Womersley numbers indicate that the flow resistance and temperature stability of the proposed scaling law are preferable to those of Murray's law. That might be the reason this scaling law is the optimality principle governing the major cerebral arteries, particularly those arterial blood vessels responsible for the brain's thermoregulatory, because the brain's thermoregulatory and temperature stability are the physiological and anatomical constraints of the human brain. [ABSTRACT FROM AUTHOR]