Biomedical Engineering Reference
In-Depth Information
Fig. 4.7
Half contractile unit with the initial filament overlap
x
0
between the myosin and actin
filament. By introducing an optimal filament sliding distance
u
opt
fs
in a contractile unit, the filament
overlap function
L
o
can be described by a parabolic function with an optimal filament overlap
u
opt
fs
/
2
+
x
0
(Murtada et al.,
2012
)
optimal muscle length, i.e.
+
u
opt
fs
+
u
op
e
,
λ
opt
=
1
(4.17)
u
op
e
/L
CU
, and by assuming that the fraction of the active stress at
reference length
P
0
and at the optimal length
P
opt
is equal to the fraction of the
filament overlaps at the reference length and the optimal length, i.e.
u
opt
where
¯
=
e
P
0
P
opt
=
x
0
¯
.
(4.18)
u
opt
¯
fs
/
2
+¯
x
0
Hence, the active stress of a contractile unit with varying filament overlap was ex-
pressed as
μ
a
L
o
(
P
a
=
u
fs
)(n
AMp
+
¯
n
AM
)(λ
−¯
u
fs
−
1
),
(4.19)
L
o
(
¯
=
¯
where
u
fs
)/L
CU
.
One common way of studying the contractile mechanism in smooth muscle is to
measure the shortening velocity during isotonic quick-release. The relationship be-
tween the shortening velocity and the after-load during isotonic quick-release can be
described through a hyperbolic function, also known as Hill's equation (cf. Woledge
et al.,
1985
), i.e.
u
fs
)
L
o
(
+
+
=
(F
0
+
a)b,
(4.20)
where
F
is the isotonic after-load,
F
0
is the isometric force at which the quick-
release is performed,
v
is the muscle shortening velocity and
a,b
are fitting param-
eters. Based on the assumption that the velocity
v
reflects somewhat the behavior of
(F
a)(v
b)
