TITLE:
Assessment of Myogenic Power Expenditure Due to Arterial Wall Smooth Muscle Contraction Based upon the Fractal Nature of Vascular Trees
AUTHORS:
Akira Kamiya, Masahiro Shibata, Kimiko Yamamoto
KEYWORDS:
Myogenic Active Stress, Biomechanics, Fractal Integral, Oxygen Consumption, Allometric Law
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.12,
June
26,
2014
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.