Biomedical Engineering Reference
In-Depth Information
Chapter 5
A Coupled Chemomechanical Model for Smooth
Muscle Contraction
Markus Böl and Andre Schmitz
Abstract
This manuscript presents a chemomechanically coupled three-
dimensional model, describing the contractile behavior of smooth muscles. It bases
on a strain-energy function, additively decomposed into passive parts and an ac-
tive calcium-driven part related to the chemical contraction of smooth muscle cells.
For the description of the calcium phase the four state cross-bridge model of Hai
and Murphy (Am. J. Physiol. 254:C99-106,
1988
) has been used. Before the fea-
tures and applicability of the proposed approach are illustrated in terms of three-
dimensional boundary-value problems, the model is validated by experiments on
porcine smooth muscle tissue strips.
5.1 Introduction
Many internal organs such as stomach, intestine, bronchia, urinary bladder, uterus,
airways, or blood vessels are composed by multiple layers of spindle-shaped smooth
muscle cells (SMCs). Focusing on vessel mechanics, vascular smooth muscle cells
are the key component in the vascular system regulating the diameter of vessels,
triggered by various neural, chemical and mechanical signals. Human arteries are
comprised of three distinct layers, the intima, the media, and the adventitia, in which
the proportion and structure of each varies with size and function of the particular
artery.
From the mechanical perspective, the media is the most significant layer in hu-
man healthy arteries. It is the middle layer and is characterized by a complex three-
dimensional network of smooth muscle cells embedded in a matrix of elastin and
collagen fibers (Fritsch and Kuehnel,
2007
). However, this architecture gives the
media high passive strength and the ability to resists loads in multiple directions.
Due to the existence of SMCs inside the media it is of particular interest related
to smooth muscle (SM) activation, too. Focusing at cell level, SM contraction is
M. Böl (
A. Schmitz
Institute of Solid Mechanics, Technische Universität Braunschweig, 38106 Braunschweig,
Germany
e-mail:
m.boel@tu-bs.de
)
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