Association of Murray's law with atherosclerosis risk: Numerical validation of a general scaling law of arterial tree.

Abstract

Atherogenesis is prone in medium and large-sized vessels, such as the aorta and coronary arteries, where hemodynamic stress is critical. Low and oscillatory wall shear stress contributes significantly to endothelial dysfunction and inflammation. Murray's law minimizes energy expenditure in vascular networks and applies to small arteries. However, its assumptions fail to account for the pulsatile nature of blood flow in larger, atherosclerosis-prone arteries. This study aims to numerically validate a novel general scaling law that extends Murray's law to incorporate pulsatile flow effects and demonstrate its applications in vascular health and artificial graft design. The proposed scaling law establishes an optimal relationship between arterial bifurcation characteristics and pulsatile flow dynamics, applicable throughout the vascular system. This work examines the relationship between deviations from Murray's law and the development of atherosclerosis in both coronary arteries and abdominal aorta bifurcations, explaining observed deviations from Murray's law in these regions. A finite volume method is applied to evaluate flow patterns in coronary arteries and aortoiliac bifurcations, incorporating in vivo pulsatile inflow and average outlet pressure. The results indicate that the proposed scaling law enhances wall shear stress distribution compared to Murray's law, which is characterized by higher wall shear stress and reduced oscillatory shear index. These findings suggest that vessels adhering to this scaling law are less susceptible to atherosclerosis. Furthermore, the results are consistent with clinical morphometric data, underscoring the potential of the proposed scaling law to optimize vascular graft designs, promoting favorable hemodynamic patterns and minimizing the occlusion risk in clinical applications.