Biomedical Engineering Reference
In-Depth Information
T
T
x
1
x
1
K
se
K
se
K
pe
x
2
x
2
K
lt
F
K
lt
F
FIGURE 13.19
Diagram on left illustrates a muscle model consisting of an active-state tension generator
F
in
parallel to a length-tension elastic element
K
lt
, connected to a series elastic element
K
se,
all in parallel with the
passive elastic element
K
pe
. Upon stimulation of the active-state tension generator
F
, a tension
T
is exerted by
the muscle. The diagram on the right is the same muscle model except that
K
pe
has been removed.
T
¼
K
se
x
2
x
1
ð
Þ
ð
13
:
23
Þ
¼
F
þ
K
se
x
1
K
se
þ
K
lt
F
¼
K
lt
x
þ
K
se
x
ð
x
Þ !
x
ð
13
:
24
Þ
2
2
1
2
Substituting
x
2
from Eq. (13.24) into (13.23) gives
K
se
K
se
þ
K
lt
K
se
K
se
þ
K
lt
F
K
se
K
lt
K
se
þ
K
lt
x
T
¼
ð
F
þ
K
se
x
Þ
K
se
x
¼
ð
13
:
25
Þ
1
1
1
K
se
K
se
þ
K
lt
F
Equation (13.25) is an equation for a straight line with y-intercept
and slope
K
se
K
lt
K
se
þ
K
lt
:
0.8 g/
¼
The slope of the length-tension curve in Figure 13.14 is given by
K
¼
40.86 N/m. Therefore,
K
se
K
lt
K
se
þ
K
lt
¼
86
N
m
K
¼
40
:
ð
13
:
26
Þ
Solving Eq. (13.26) for
K
lt
yields
K
se
K
K
se
K
¼
7
N
m
K
lt
¼
60
:
ð
13
:
27
Þ
13.5.4 The Force-Velocity Relationship
Early experiments indicated that muscle had elastic as well as viscous properties. Muscle
was tested under isotonic (constant force) experimental conditions as shown in Figure 13.20
to investigate muscle viscosity. The muscle and load were attached to a lever with a high
lever ratio. The lever reduced the gravity force (mass
gravity) of the load at the muscle by
one over the lever ratio, and the inertial force (mass
acceleration) of the load by one over
the lever ratio squared. With this arrangement, it was assumed that the inertial force
exerted by the load during isotonic shortening could be ignored. The second assumption
