Arterial Wall Mechanics: Simulation Presentation O-40 S43

MYOGENIC RESPONSE IN ELASTIC ARTERIES: ELECTROMECHANICAL COUPLING

Horacio López (1), José F Rodríguez (1), Manuel Doblaré (1)

1. GEMM, Aragon Institute of Engineering Research. University of Zaragoza, Zaragoza, Spain

Introduction The myogenic response of an arterial vessel is referred to its pressure-dependent contraction, and was first proposed by [Bayliss 1902]. Myogenic response describes how a vessel adjusts its lumen diameter in response to the change of intravascular pressure. Arterial constriction is induced by pressure increase, while arterial dilation is due to a pressure decrease. However, this effects can also be induced by means of specific drugs. This mechanism starts within the smooth muscle cell present in blood vessels. Fundamental to the description of this active mechanism is the mathematical description of the contraction within the muscle cell. The smooth muscle cell developed by [Yang et al., 2003] and later modified by [Stalhand et al, 2007], has been incorporated in a finite strain three dimensional finite element code to study the myogenic response of anisotropic arteries. The model couples the electrophysiological activity occurring at cellular level with the mechanochemical mechanisms governing muscle contraction. The framework allows for studying the evolution of tissue properties, as well as a better understanding of the autoregulation of the vasculature. Methods The smooth muscle cell proposed by [Yang et al 2003] is taken to describe the electrophysiology of the cell, while the mechanochemical model proposed by [Stalhand et al, 2007] is used to describe muscle contractility. The electrophysiological model, through the stretch sensitive channels, allows to sense environmental changes (i.e., wall stress), which translates in changes in the membrane action potential and intracellular calcium concentration which modulates muscle contraction allowing for true myogenic response. The governing equations are given by

1

0,

12

jMN

M n

MNa MN

MN NM

V = I v,z + I C ,t

v = f V,v,z ,tz = g V,v,z ,t

xS =

X X

W WS = + + S C ,E E

(1)

where V is the membrane action potential, v are gating variables and z ion concentrations, S is the second Piola-Kirchoff stress tensor, W an anisotropic strain energy function and Sa the active component of the stress. The models have been implemented within a general purpose finite element code Results The integrated model is mimic published pressure-diameter results for cases of isolated resistance vessels. It also provides a valid framework for studying the biophysics of the myogenic mechanism responding to changes in transmural pressure, as well as biochemical changes occurring at cellular level.

References WM Bayliss, J Physiol, 28:220-231, 1902. J Yang et al, Med Eng Phys, 25:691-709, 2003. J. Stalhand et al., Prog. Biophys Mol Biol, in press

16th ESB Congress, Oral Presentations, Monday 7 July 2008 Journal of Biomechanics 41(S1)