Electro-Chemo-Mechanical Modeling of the Artery Myogenic Response
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Electro-Chemo-Mechanical Modeling of the Artery Myogenic Response Yali Li1 and Nakhiah Goulbourne1 1 Aerospace engineering department, University of Michigan, Ann Arbor, MI 48109, U.S.A. ABSTRACT Active contraction of smooth muscle results in the myogenic response and vasomotion of arteries, which adjusts the blood flow and nutrient supply of the organism. It involves coupled electrobiochemical and chemomechanical processes. This paper presents a new constitutive model to describe the myogenic response of the artery wall under different transmural pressures. The model includes two major components: a cell-level model for the electrobiochemical process, and a tissue-level model for the chemomechanical coupling. The electrochemical model is a lumped Hodgkin-Huxley-type cell membrane model for the nanoscopic ionic currents: calcium, sodium, and potassium. The calculated calcium concentration serves as input for the chemomechanical portion of the model; its molecular binding and the reactions with other enzymes cause the relative sliding of thin and thick filaments of the contractile unit. In the chemomechanical model, a new nonlinear viscoelastic model is introduced to describe the time varying behavior of the smooth muscle. Specifically, this model captures the filament overlap effect, active stress evolution, initial velocity, and elastic recoil in the media layer. Using the proposed constitutive model and a thin-walled equilibrium equation, the myogenic response is calculated for different transmural pressures. The integrated model is able to capture the pressure-diameter relationship incorporating fewer parameters than previous work and with clear physical meanings. INTRODUCTION Smooth muscle contraction involves a complex interaction of biological, electrical, biochemical and mechanical processes that occur at different length scales. Cell contraction can be initiated by a number of physiochemical agents (e.g. hormones, drugs, neurotransmitters), mechanical stimuli, and or electrical stimuli. The contractile apparatus is based on a molecular motor characterized by cross-bridge cycling and the relative sliding of thin and thick filaments [1-7]. The mechanism is set in motion by an increase in cytosolic calcium [8, 9]. The contractile units in smooth muscle can produce active force at a range of lengths. [3-5] Generally, there are two theoretical modeling approaches of modeling smooth muscle contraction: cell-based models and continuum models. Cell models are structural cross-bridge models, which are generally based on the sliding-filament theory of Huxley [3-5]. These models focus on the specifics of cross-bridge structure and the mechanics of myosin head cycling [9-12]. Continuum tissue models typically propose phenomenological constitutive formulations to describe smooth muscle contraction and whole artery deformation. [13-22] There appears to be a single mathematically tractable electro-chemo-mechanical model of the smooth muscle cell in cerebrovascular arteries [17]; it is a cell-level model. The model has sinc
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