A muscle spindle model for primary afferent firing based on a simulation of intrafusal mechanical events

Abstract

1. A muscle spindle model for primary afferent firing is presented that contains two components representing a gamma d-dependent (bag1) and gamma s-dependent (bag2/nuclear chain) intrafusal fiber. Each of the intrafusal fibers is composed of a linear elastic element representing the sensory part and a muscle fiber representing the muscular part. 2. The muscular part of the bag1 was modeled as a slow twitch, that of the bag2 as a fast twitch muscle fiber. 3. The sensory regions were linear length transducers, generating a rising depolarization on increasing stretch. The input of both bags was fused by taking the largest depolarization to determine a generator potential. The rate of primary afferent firing depended on this generator potential as well as on its rate of change. 4. To simulate the high sensitivity of muscle spindles to small amplitudes of stretching, a model analogue of cross-bridge fixation (or stiction) has been included in the muscular part of the bag1 fiber. This makes use of one hundred cross-bridge regions that release one after the other, provided a certain breaking force is exceeded. 5. The values of the mechanical parameters that defined the model were selected by a computerized search procedure. 6. The values found by means of this procedure allowed the model to provide an accurate simulation of experimental data on ramp-and-hold stretches (for 6 different stretch velocities under variable conditions of fusimotor activity). 7. On sinusoidal stretches at a frequency of 1 Hz the spindle model responded with about one-half the discharge modulation reported in experimental studies. Its phase advance tended to be slightly lower than that observed for real spindles. 8. Frequency response curves showed the same high sensitivities at high frequencies as those observed in real spindles. 9. Close evaluation of the model compared with experimental results in literature reveal its merits as well as its limitations. Because the model is structural rather than phenomenologic, it provides insight into how intrafusal events may contribute to observed firing properties of real muscle spindles.