Mathematical models of proprioceptors. I. Control and transduction in the muscle spindle.

We constructed a physiologically realistic model of a lower-limb, mammalian muscle spindle composed of mathematical elements closely related to the anatomical components found in the biological spindle. The spindle model incorporates three nonlinear intrafusal fiber models (bag(1), bag(2), and chain) that contribute variously to action potential generation of primary and secondary afferents. A single set of model parameters was optimized on a number of data sets collected from feline soleus muscle, accounting accurately for afferent activity during a variety of ramp, triangular, and sinusoidal stretches. We also incorporated the different temporal properties of fusimotor activation as observed in the twitchlike chain fibers versus the toniclike bag fibers. The model captures the spindle's behavior both in the absence of fusimotor stimulation and during activation of static or dynamic fusimotor efferents. In the case of simultaneous static and dynamic fusimotor efferent stimulation, we demonstrated the importance of including the experimentally observed effect of partial occlusion. The model was validated against data that originated from the cat's medial gastrocnemius muscle and were different from the data used for the parameter determination purposes. The validation record included recently published experiments in which fusimotor efferent and spindle afferent activities were recorded simultaneously during decerebrate locomotion in the cat. This model will be useful in understanding the role of the muscle spindle and its fusimotor control during both natural and pathological motor behavior.