Modeling of Smooth Muscle Activation - Computer Models in Biomechanics - page 73

Chapter 6
Modeling of Smooth Muscle Activation

Jonas Stålhand, Anders Klarbring, and Gerhard A. Holzapfel

Abstract Smooth muscle contraction is governed by a complex chain of events in-
cluding both mechanical and electrochemical stimuli such as stretch and calcium ion
concentration. A homogeneous model for smooth muscle contraction is derived in
this paper by using a continuum thermodynamical framework. The model is based
on an additive decomposition of the deformation, and balance laws for the mechan-
ical and electrochemical scales are obtained using the principle of virtual power.
Constitutive equations are derived by applying the dissipation inequality, and a first-
order kinetic model for the chemical state of myosin and standard linear or nonlin-
ear mechanical models for the tissue are introduced. The constitutive equations also
provide couplings between the scales. The model includes experimentally observed
features like stretch dependent active force generation and hyperbolic relation be-
tween shortening velocity and afterload. The model is applied to an experimentally
relevant example to illustrate its potential.

6.1 Introduction

Smooth muscle cells are abundant throughout the human body and are found in
hollow organs like the arteries, iris of the eye, gastrointestinal tract, and the urinary
bladder. The main task for smooth muscles is to provide structural integrity and to

J. Stålhand ( A. Klarbring

Division of Mechanics, Linköping Institute of Technology, 581 83 Linköping, Sweden
e-mail: [e-mail]
A. Klarbring
e-mail: [e-mail]

) ·

G.A. Holzapfel
Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology,
Kronesgasse 5-I, 8010 Graz, Austria
e-mail: [e-mail]

G.A. Holzapfel
Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology
(KTH), Osquars Backe 1, 100 44 Stockholm, Sweden