Biomedical Engineering Reference
In-Depth Information
the number of load-bearing cross-bridges have been modeled through different ap-
proaches, see, e.g., Peterson (
1982
); Kato et al. (
1984
); Hai and Murphy (
1988
). In
the myosin kinetics model by Hai and Murphy (
1988
) the latched cross-bridge was
incorporated, and the myosin is described in four different functional states: (M)
unattached and dephosphorylated, (Mp) unattached and phosphorylated, (AMp) at-
tached and phosphorylated, (AM) attached and dephosphorylated. The two states
where the myosin forms a cross-bride between the actin filament which can carry
load are the attached states, AMp and AM. These functional states are coupled
through different rate constants, where some can be related to the phosphorylating
MLCK activity and some to dephosphorylating MLCP activity.
The average elastic elongation of the attached cross-bridges in the smooth mus-
cle contractile unit is a key parameter to model the tension development in smooth
muscle. It corresponds to the elastic serial element in the Hill muscle model. The
average elastic elongation of the attached cross-bridges depends on the total defor-
mation applied on the smooth muscle contractile unit and the sliding of actin and
myosin filaments, which could be related to the contractile element in the Hill mus-
cle model. It is necessary to model both the filament sliding and the average elastic
elongation of the attached cross-bridges to simulate the length change and the ten-
sion development during muscle contraction. Among the smooth muscle models
available in the literature there are some that also considers the filament sliding be-
havior to describe the active tension development and the total deformation of the
smooth contractile unit (cf. Stålhand et al.,
2008
; Murtada et al.,
2010a
).
4.3 The Chemomechanical Response in Smooth Muscle—Results
In this section the modeling approach by Murtada et al. (
2010a
,
2010b
,
2012
)is
briefly reviewed. This is an approach that is able to simulate both the length-tension
and the force-velocity behavior of smooth muscle in addition to muscle contraction
and relaxation regulated by
Ca
2
+
]
i
.
In the work by Murtada et al. (
2010a
,
2010b
,
2012
), the model by Hai and Mur-
phy (
1988
) was used to simulate the kinetics of the myosin functional states and the
fraction of attached cross-bridges.
[
4.3.1 Cross-Bridge Kinetics Model
The active force produced by the smooth muscle is dependent on the number of
attached cross-bridges in a smooth muscle contractile unit. The kinetics of attached
cross-bridges is regulated by the MLCK and MLCP activity, which can be described
by the cross-bridge kinetics model by Hai and Murphy (
1988
). Chemical kinetics
