Biomedical Engineering Reference
In-Depth Information
Fig. 4.6
0
.
7
/
0
.
6by
using the model of Murtada et al. (
2010b
). By repeating this for different orientation density func-
tions
ρ(γ)
,where
γ
is a parameter describing the shape of the orientation density function, dif-
ferent behaviors of the predicted stress development at
λ
=
0
.
7
/
0
.
6 are obtained.
Right
: passive
length-tension behavior (Murtada et al.,
2010b
). Compare with the passive length-tension behavior
presented in Fig.
4.2
A
Left
: fitting results of the active stress developments at
λ
=
1
/
0
.
6and
λ
=
4.3.3.2 Filament Overlap and Sliding Behavior
One common explanation for the length-tension behavior is the variation in the fil-
ament overlap in a contractile unit. This hypothesis was studied by introducing a
filament overlap function
L
o
which defines the actin and myosin filament overlap
and thereby the number of maximum possible attached cross-bridges in a contrac-
tile unit (Murtada et al.,
2012
). The filament overlap depends on the lengths of
the actin and myosin filaments, and how these filaments slide with respect to each
other, which was described by the normalized filament sliding
u
fs
. An initial fil-
¯
x
0
and an average optimal filament sliding
u
opt
ament overlap
L
o
(u
fs
=
0
)
=
,for
fs
which optimal filament overlap is reached (
∂L
o
/∂u
fs
|
u
fs
=
u
opt
fs
=
0), were introduced.
Thus the optimal filament overlap
L
opt
was defined as
o
u
opt
fs
2
L
o
u
fs
=
fs
=
L
opt
u
opt
=
+
x
0
.
(4.15)
o
Together with the boundary conditions, a continuous parabolic function of the fila-
ment overlap
L
o
was expressed as
x
0
L
CU
,
u
fs
2
u
opt
fs
u
fs
L
o
=
u
fs
−
+
x
0
=
u
fs
−
¯
+¯
(4.16)
u
opt
fs
2
¯
u
opt
fs
u
opt
where
x
0
=
¯
x
0
/L
CU
and
¯
=
fs
/L
CU
, see Fig.
4.7
.
u
opt
fs
were defined
through two equations: the definition of the stretch of a contractile unit (
4.7
)at
The initial filament overlap
x
0
and the optimal filament overlap
¯
¯
