Assessment of Myogenic Power Expenditure Due to Arterial Wall Smooth Muscle Contraction Based upon the Fractal Nature of Vascular Trees

Abstract

The purpose of this study is 1) to present a biomechanical model for evaluating the myogenic power expended in an arterial segment due to vascular smooth muscle contraction (VSMC) and 2) to assess the total power expenditure in the entire systemic arterial tree by utilizing the fractal nature of the branching architecture. The model is based on the mechanical equilibrium between the stretch stress exerted by blood pressure inside the vessel lumen and constricting stress elicited by VSMC in the vascular wall. An expression for myogenic power expenditure is formulated for a unit wall mass as a function of the internal vessel radius and extent of strain. This expression was then integrated over selected range of vessel radii, by taking into account of the fractal nature of the branching structure. When the total myogenic power expended in the systemic arterial tree in rat at the moderate strain level is converted to the oxygen consumption rate, it amounts to approximately 18% of the whole body oxygen consumption rate. This suggests that the mechanical power expenditure due to VSMC is a significant factor that should not be ignored in studies of vascular energetics.