Biomedical Engineering Reference
In-Depth Information
Tension (g)
30
Data
20
Linear Approx.
10
−
2
2
4
6
8
Change in Length (mm)
FIGURE 13.12
The tension-displacement curve for unexcited muscle. The slope of the linear approximation to
the data is muscle passive elasticity,
K
pe
.
to stretch a muscle is a
function of distance. Thus, in order to precisely model this
element, a nonlinear spring element should be used. Note that the change in length at
0 refers to the length of the muscle at primary position (looking straight ahead). Thus, the
eye muscles are stretched, approximately 3 mm
nonlinear
when the eye movement system is at rest
in primary position. At rest, the muscle length is approximately 37 mm.
To be useful in a linear model of muscle, Figure 13.12 should be linearized in the vicinity
of an operating point. The operating point should be somewhat centered in the region in
which the spring operates. In Figure 13.12, a line tangent to the curve at primary position
provides a linear approximation to the spring's behavior in this region as done historically.
For ease in analysis, the following relationships hold for a sphere representing the eyeball
radius of 11 mm.
,
10
3
N
1g
¼
9.806
10
4
m
1
¼
0.192 mm
¼
1.92
The slope of the line,
K
pe
, is approximately
10
3
N
1g
1
2
g
2
g
9
:
806
2
N
m
K
pe
¼
0
:
¼
0
:
10
4m
¼
10
:
1
:
92
and represents the elasticity of the passive elastic element.
The choice of the operating region is of vital importance concerning the slope of the
curve. At this time, a point in the historical operating region of rectus muscle is used. In
most of the oculomotor literature, the term
is typically subtracted out of the analysis
and is not used. The operating point will be revisited in Section 13.7, and this element will
be completely removed from the model.
K
pe
13.5.2 Active-State Tension Generator
In general, a muscle produces a force in proportion to the amount of stimulation. The ele-
ment responsible for the creation of force is the active-state tension generator
.
Note that this
