Spindle model responsive to mixed fusimotor inputs and testable predictions of beta feedback effects

Skeletofusimotor (beta) motoneurons innervate both extrafusal muscle units and muscle fibers within muscle spindle stretch receptors. By receiving excitation from group Ia muscle spindle afferents and driving the muscle spindle afferents that excite them, they form a positive feedback loop of unknown function. To study it, we developed a computationally efficient model of group Ia afferent behavior, capable of responding to multiple fusimotor inputs, that matched experimental data. This spindle model was then incorporated into a simulation of group Ia feedback during ramp/hold and triangular stretches with and without closure of the beta loop, assuming that gamma and beta fusimotor drives of the same type (static or dynamic) have identical effects on spindle afferent firing. The effects of beta feedback were implemented by driving a fusimotor input with a delayed and filtered fraction of the spindle afferent output. During triangular stretches, feedback through static beta motoneurons enhanced Ia afferent firing during shortening of the spindle. In contrast, closure of a dynamic beta loop increased Ia firing during lengthening. The strength of beta feedback, estimated as a "loop gain" was comparable to experimental estimates. The loop gain increased with velocity and amplitude of stretch but decreased with increased superimposed gamma fusimotor rates. The strongest loop gains were seen when the beta loop and the gamma bias were of different types (static vs. dynamic).