MUSCLE MECHANICS - Biomechanics and Motor Control of Human Movement - page 245

1971). However, research on muscles (Hill, 1953) showed that the time
course of the biochemical thermal events was impulsive in nature. Using
frog muscle at 0 ◦ C, the rate of heat production reaches a maximum 30 ms
after stimulation. If we recall that reaction rates increase 2 - 3 times every
10 ◦ C, we could predict an increase of 15 - 40 in the reaction rates at muscle
temperatures of 37 ◦ C. Therefore, the rate of heat production (indicating the
release of chemical energy at the cross-bridges) would be over in less than
2 ms. Thus, the associated mechanical energy release must also be assumed
to be a short-duration impulse. Fortunately, larger motor units also gener-
ate larger action potentials. Thus, the absolute value of the EMG is a series
of short-duration impulses that can be considered to represent the contrac-
tile element's impulsive force. Thus, a full-wave rectified EMG followed by
a nonlinearity (to model any nonlinearity between the EMG amplitude and
muscle force) is used to represent the relationship between the EMG and the
contractile element force.
Figure 9.18 shows the complete model, which incorporates the contractile
element, a linear damper B to model any viscous or velocity-dependent ele-
ments (in the contractile element and connective tissue), a linear spring K to
represent the series elastic elements (in the tendon, fascia, and cross-bridges),
and a mass element M to represent the effective mass of muscle tissue that
must be accelerated as the force impulse wave travels from the motor end
plate region toward both tendons. For an isometric contraction, the length
L 0 of the muscle remains constant, but x 2 shortens, causing a lengthening of
x 1 in the muscle's series elastic element. The impulsive contractile element
force F ce acts on the mass to accelerate it, but to do so the mass acts on the
Figure 9.18 Biomechanical model of a muscle during an isometric contraction of
varying tension. F ce is modeled as an impulsive contractile element force acting on an
equivalent mass M , a linear damping element B , and a series elastic element K . F ce as
input to the model is assumed to be the same shape as the full-wave rectified EMG with
an empirically curve-fitted nonlinearity. See the text for full details and justification for
the assumptions.