Biomedical Engineering Reference
In-Depth Information
Fig. 4.4
Left
: fitting results of the active stress development (
P
f
=
P
a
) using the model of Mur-
tada et al. (
2010a
), with parameter values
μ
a
L
o
0
.
93 MPa and
μ
p
=
0
.
90 MPa.
Right
: isotonic stretch behavior (
λ
f
=
λ
) for different isotonic after-loads. The plot
at the
top right corner
is an enlargement of the
encircled region
for a certain after-load (Murtada
et al.,
2010a
). Compare with the experimental results presented in Figs.
4.2
Band
4.2
C
=
4
.
5MPa,
η
=
60
.
0MPas,
κ
=
muscle relaxation (extension),
u
fs
is driven by the resulting force of the external
force acting on the contractile unit, and the internal force from all the attached cross-
bridges (AMp, AM). The evolution law of
u
fs
is summarized as an active dashpot
where the normalized filament sliding velocity
u
fs
is proportional to the difference
of the internal force
P
c
and the external active force
P
a
such as
η
¯
u
fs
=
P
c
−
P
a
,
(4.10)
with
⎧
⎨
κn
AMp
,
for
P
a
<κn
AMp
,
P
c
=
P
a
,
for
κn
AMp
≤
P
a
≤
κ(n
AMp
+
n
AM
),
(4.11)
⎩
κ(n
AMp
+
n
AM
),
for
P
a
>κ(n
AMp
+
n
AM
),
where
η
is a positive material parameter and
κ
is a parameter related to the average
driving/resisting force of the attached cycling and non-cycling cross-bridges (AMp,
AM).
The material parameters were fitted to isometric and isotonic contraction data
performed on intact smooth muscle taenia coli (Arner,
1982
), resulting to
μ
a
L
o
=
4
.
5MPa,
η
0
.
90 MPa (the parameter
μ
p
is
the shear modulus of the passive matrix material of the smooth muscle cells and the
intermixed fibrous components).
The model was able to predict the active tension development during isometric
contraction and a realistic behavior of the muscle length change during isotonic con-
traction for different after-loads, see Fig.
4.4
. However, with the current description
of the
=
60
.
0MPas,
κ
=
0
.
93 MPa and
μ
p
=
u
fs
evolution law and the constant filament overlap, the model is not able
to predict the nonlinear behavior of the length-tension and the force-(shortening)
velocity behavior.
¯
