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t

x (extrafusal muscle length)

x (extrafusal muscle length)

FIGURE 2.3-6 (A) Spindle type Ia afferent instantaneous frequency in response to extrafusal muscle length change (stretch) with and without open-loop, ys motor stimulation. (B) Spindle type II afferent instantaneous frequency in response to extrafusal muscle length change (stretch) with and without open-loop, ys motor stimulation.

dashpot symbol is used), in parallel with a linear elastic element, Kj. (In reality, the viscosity and elastic element are functions of the muscle state of activity; however, for simplicity, they are considered constants.) The polar regions of the intrafusal muscle fiber are in series with the purely elastic, center nuclear bag region in which the "flower spray" endings of a type II sensory neuron are attached. It is assumed that the firing frequency, r2, of the type II fiber is proportional to the stretch of the center region. That is, r2(t) = Ko(x2 - xj). Here x2 is the actual stretch of the spindle, and xj is the length change of the polar regions of the fiber. The system is shown in Figure 2.3-7.

Below is derived a mathematical model for the mechanical behavior of the simple spindle model. The Newtonian force equilibrium is fi + Dxj + KjXj = K2 (x2-xj )

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