The output frequency is thus the sum of two terms, one a function of spindle stretch, x2, and the other a function of the force, fi, generated by the intrafusal fiber when activated.

R2 (s) = Ko (X2-Xj) = X2(s)—P-+-.o i w/ . . 2.3-4

Polar regions Nuclear bag region t K t K

Polar regions Nuclear bag region t K t K

FIGURE 2.3-7 An oversimplified, lumped-parameter mechanical model for the static nuclear bag portion of a spindle. The polar regions of the IFM are represented by a dashpot (viscosity) in parallel with a linear elastic element in parallel with a force source activated by the frequency on the y motoneuron. These parallel elements, in turn, are in series with a linear elastic element representing the nuclear bag region of the IFM. The output instantaneous frequency on the model type II fiber is proportional to the stretch of the nuclear bag "spring."

FIGURE 2.3-7 An oversimplified, lumped-parameter mechanical model for the static nuclear bag portion of a spindle. The polar regions of the IFM are represented by a dashpot (viscosity) in parallel with a linear elastic element in parallel with a force source activated by the frequency on the y motoneuron. These parallel elements, in turn, are in series with a linear elastic element representing the nuclear bag region of the IFM. The output instantaneous frequency on the model type II fiber is proportional to the stretch of the nuclear bag "spring."

In the first case, let Fi be a constant, Thus,

The second term is a bias firing rate or "tone." Now let the input be a step stretch: X2(s) = X2o/s. The first term is of the form:

Thus, the time domain response of the model to a step stretch is r2(t) = [Ko X2o Kj/(Kj + K2)] {1 + (K2/K1)exp[-t(K1 + K^/D]}

Note that r2(t) cannot be negative. Figure 2.3-8 illustrates the model output fiber frequency given a step stretch of the spindle followed by a step return to zero stretch. Note that the initial overshoot in r, which indicates a degree of rate sensitivity, comes from the viscoelastic properties of the intrafusal fiber model.

Figure 2.3-9 illustrates the block diagram of a simple theoretical type 0 neuro-physiological control loop postulated to describe the CNS feedback mechanism

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