Physics Linkages Between Arterial Morphology, Pulse Wave Reflection and Peripheral Flow

Abstract

Background: Previous physics-based analyses of arterial morphology in relation to pulsatile pressure and flow, with pulse wave reflection, focused on the large arteries and required assumptions about the relative thicknesses of arterial walls and the velocities of pulse waves in the arteries. A primary objective of this study was to analyze arterial morphology and pulse wave reflection, using physics-based wave propagation, which explicitly includes arterial stiffness, with potential autonomic flow regulation, for both large and small arteries. Methods: Pulse wave reflections that occur at arterial bifurcations, and their impact on macrocirculation and microcirculation pulse pressures and flows, are analyzed using the physics of wave propagation and impedance matching. Results: The optimum combinations of arterial dimensions and stiffnesses which minimize pulsatile reflections at arterial bifurcations are identified for both macrocirculation and microcirculation. The optimum ratio of arterial bifurcations’ branch-to-trunk luminal areas is predicted to have a value of 1.26, (with corresponding optimum stiffnesses) based on the principle that autonomic flow regulation minimizes pulsatile reflections. This newly predicted value of area ratio compares favorably with the Murray Scaling Law value of 1.26. For an area ratio of 1.26, the optimum bifurcation stiffness ratio is predicted to have a value of 1.12 for bifurcations in the macrocirculation and a value of 0.89 in the microcirculation. The analysis predicts that minimal pulsatile reflections may occur for area ratios not equal to 1.26, when vasodilation adjusts arterial stiffness to compensate for non-optimal arterial area ratios. The analysis predicts that the capillaries have about one-tenth the stiffness of the aorta, and the capillary bed possesses about one thousand times more total luminal area than the aorta. The analysis predicts there are about thirty generations, aorta to capillaries, of arterial bifurcations in an arterial tree. Conclusions: The optimum arterial morphologies predicted by this physics-based analysis correspond to those observed in human vascular physiology. The contributions that arterial stiffnesses and dimensions make to optimal pulsatile flow are relevant to the development of pharmaceuticals related to autonomic vasodilation, to the development of optimally designed stents and to surgical procedures related to vascular modification.