Biomedical Engineering Reference
In-Depth Information
approximation solution for
V
max
from a fourth-order model, see the paper by [17], or [14].
It is more expedient, however, to simply simulate a solution for
x
1
(
) and then find
t
V
max
as a function of load.
Using a simulation to reproduce the isotonic experiment, elasticities estimated from the
length-tension curves as previously described, and data from rectus eye muscle, parameter
values for the viscous elements in the muscle model are found as
2 Nsm
1
B
1
¼
and
5 Nsm
1
as demonstrated by Enderle and coworkers in 1991
B
2
¼
0
:
.
The viscous element
B
1
is estimated from the time constant from the isotonic time course. The viscous element
B
2
is calculated by trial and error so the simulated force-velocity curve matches the experi-
mental force-velocity curve.
Figure 13.40 shows the force-velocity curves using the model described in Eq. (13.45)
(with triangles), plotted along with an empirical fit to the data (solid line). It is clear that
the force-velocity curve for the linear muscle model is hardly a straight line and that this
curve fits the data well.
The muscle lever model described by Eqs. (13.43) and (13.44) is a third-order linear
system and is characterized by three poles. Dependent on the values of the parameters,
the eigenvalues (or poles) consist of all real poles or a real and a pair of complex conjugate
poles. A real pole is the dominant eigenvalue of the system. Through a sensitivity analysis,
viscous element
B
1
is the parameter that has the greatest effect on the dominant eigenvalue
for this system, while viscous element
B
2
has very little effect on the dominant eigenvalue.
Thus, viscous element
B
1
is estimated so the dominant time constant of the lever system
model (approximately
B
1
K
lt
B
1
>
B
2
) matches the time constant from the isotonic experi-
mental data. For rectus eye muscle data, the duration of the isotonic experiment is
when
4000
3000
2000
1000
0
0
0.2
0.4
0.6
0.8
1.0
Load (P/P
o
)
FIGURE 13.40
Force-velocity curve derived from simulation studies with the linear muscle model with an end
stop. Shown with triangles indicating simulation calculation points and an empirical fit to the force-velocity data
(solid line), as described by Close and Luff [6].
Adapted from Enderle et al. [19].
