Biomedical Engineering Reference
In-Depth Information
in four different functional states where two are load-bearings and coupled through
seven reaction rates. The behavior of the active stress is proportional to the sum of
the fractions of the load-bearing myosin functional states and is, therefore, very de-
pendent on the behavior of the myosin kinetics model. However, it is not so trivial
to define the reaction rates in the Hai and Murphy model and also to validate the
simulated fraction values of attached cross-bridges. The Hai and Murphy kinetics
model is rather old; it suggests the existence of a slower latch state myosin, where
the myosin is dephosphorylated and attached, which has not been shown experimen-
tally. In the last years several advances have been proposed in the understanding of
myosin-actin kinetics so that an update of the myosin kinetics model would be a
very valuable task.
The mechanical model presented in this chapter is based on structural observa-
tions and has a relatively low number of material parameters which can be related to
the physical properties of the smooth muscle. For example, the physical parameter
μ
a
in the smooth muscle model (defined by the length of the contractile unit
L
CU
,
the elastic stiffness of a single cross-bridge
E
cb
, the average distance between the
cross-bridges
δ
and the contractile unit density
N
CU
) was investigated by comparing
it with experimental data of
L
CU
,
E
cb
,
δ
and
N
CU
. It was found that it corresponds
very well with the experimental data of the physical measurable units (Murtada et
al.,
2012
) supporting the description and the fitted value of
μ
a
. However, there are
still several items that can be improved such as an improved myosin kinetics model,
which is not dependent on a latch state, and a further developed filament sliding
evolution law.
With a realistic chemomechanical model of smooth muscle activity it is possible
to study more complex boundary-value problems that are clinically and pathophys-
iologically relevant by implementing the coupled model into a three-dimensional
finite element code. An implementation of the model into a finite element code also
allows to study the effects of time-dependent changes in Ca
2
+
for different inter-
nal pressures of an intact artery that are relevant for both short-term and long-term
changes in the vascular wall.
Acknowledgements
Financial support for SCM was provided through a Project Grant
(#20056167, #20094302) from the Swedish Research Council (VR) and the Swedish Heart-Lung
Foundation. This support is gratefully acknowledged.
References
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Fung YC (1970) Mathematical representation of the mechanical properties of the heart muscle.
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