Biomedical Engineering Reference
In-Depth Information
T
x
K
pe
F
FIGURE 13.13
A muscle model consisting of an active-state tension generator,
F
, and a passive elastic element,
K
pe
. Upon stimulation of the active-state tension generator, a tension,
, is exerted by the muscle.
T
terminology is used so there is no confusion with the force created within the muscle when
the tension created by the muscle is discussed. The active tension generator is included
along with the passive elastic element in the muscle model as shown in Figure 13.13. The
relationship between tension,
T
, active-state tension,
F
, and elasticity is given by
T
¼
F
K
pe
x
ð
13
:
21
Þ
(constant length) experiments have been performed on humans over the years
to estimate the active tension generator at different levels of stimulation. These experiments
were usually performed in conjunction with strabismus surgery when muscles were
detached and reattached to correct crossed eyes. Consider the tension created by a muscle
when stimulated as a function of length as shown in Figure 13.14. The data were collected
from the lateral rectus muscle that was detached from one eyeball, while the other unoper-
ated eyeball fixated at different locations in the nasal (N) and temporal (T) directions from
Isometric
45
to 45
. This experiment was carried out under the assumption that the same neural
input is sent to each eyeball (Hering's Law of equal innervation), so the active-state tension
in the freely moving eyeball should be the same as that in the detached lateral rectus
muscle. At each fixation point, the detached lateral rectus muscle was stretched and tension
data was recorded at each of the points indicated on the graph. The thick line represents
the muscle tension at that particular eye position under normal conditions. The curve for
45
T is the zero stimulation case and represents the passive mechanical properties of
muscle. Note that the tension generated is a
function of the length of the muscle.
To compare the model in Figure 13.13 against the data in Figure 13.14, it is convenient to
subtract the passive elasticity in the data (represented by the 45
T curve) from each of the
data curves 30
T through 45
N, leaving only the hypothetical active-state tension. Shown
in the graph on the left in Figure 13.15 is one such calculation for 15
N with the active-state
tension given by the dashed line. The other curves in Figure 13.14 give similar results and
have been omitted because of the clutter. The dashed line should represent the active-state
tension, which appears to be a function of length. If this was a
nonlinear
active-state tension
element, the subtracted curve should be a horizontal line indicative of the size of the input.
One such input is shown for the active-state tension in the graph on the right in
Figure 13.15. The result in Figure 13.15 implies that either the active-state tension's effect
pure
