Muscle Model
The maximum force or tension generated by a muscle varies with muscle length.
Figure
MM.1 shows the general shape of the lengthtension relationship.
60
80
100
120
140
160
180
0
10
20
30
40
50
60
70
80
90
100
% RESTING LENGTH
% MAXIMUM TENSION
Figure MM.1
Lengthtension curve for skeletal muscle
Note that a muscle will usually start at the resting length (100%) and shorten (< 100%).
Figure MM.1 depicts muscle response under isometric (constant length) conditions.
To
account for both forcevelocity and lengthtension properties a model is needed.
The
simplest model assumes linear curves as will now be considered.
The isometric forcelength and forcevelocity properties of muscle can be
idealized in a linear manner shown below:
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View Full DocumentFigure MM.2 Linear lengthtension and forcevelocity curves
If variable x is defined as changes in length from the resting length (positive sense to left
of resting length), muscle force F can be expressed as:
Fiso = Fmax – k1
x
Fmuscle = Fiso k2 dx/dt = Fmax – k1 x – k2 dx/dt
Note that k1 can be interpreted as a spring and k2 as a resistance.
In an electrical analog,
these elements are in series.
Constant k2 can be modeled as a resistance, but it is largely
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 '07
 Yamashiro
 Force, Tendon, Achilles tendon rupture

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