Biomedical Engineering Reference
In-Depth Information
Chapter 4
A Mathematical Approach for Studying
Ca
2
+
-Regulated Smooth Muscle Contraction
Saeil C. Murtada and Gerhard A. Holzapfel
Abstract
Smooth muscle is found in various organs. It has mutual purposes such
as providing mechanical stability and regulating organ size. To better understand
the physiology and the function of smooth muscle different experimental setups and
techniques are available. However, to interpret and analyze the experimental results
basic models of smooth muscle are necessary. Advanced mathematical models of
smooth muscle contraction further allow, to not, only investigate the experimental
behavior but also to simulate and predict behaviors in complex boundary conditions
that are not easy or even impossible to perform through
in vitro
experiments. In
this chapter the characteristic behaviors of vascular smooth muscle, specially those
relevant from a biomechanical point of view, and the mathematical models able to
simulate and mimic those behaviors are reviewed and studied.
4.1 Introduction
Smooth muscle has an important role in hollow organs where it determines the size
and the wall tension of the organ. In blood vessels the smooth muscle has a crit-
ical role in regulating the diameter and the flow resistance which affect the blood
pressure.
To increase the understanding of both basic and clinical/pathophysiological pro-
cesses of smooth muscle, well defined chemomechanical models which couple
S.C. Murtada (
)
Division Genetic Physiology, Department of Physiology and Pharmacology, Karolinska Institutet,
von Eulers väg 8, 177 71 Stockholm, Sweden
e-mail:
saeil.murtada@ki.se
G.A. Holzapfel
Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology,
Kronesgasse 5-I, 8010 Graz, Austria
e-mail:
holzapfel@tugraz.at
G.A. Holzapfel
Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology
(KTH), Osquars Backe 1, 100 44 Stockholm, Sweden
