Mathematical Models of Proprioceptors. I. Control and Transduction in the Muscle Spindle

Abstract

. 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. I N T R O D U C T I O NThe muscle spindle is a sense organ found in most vertebrate skeletal muscles. In a typical mammalian lower limb muscle, several tens (or even hundreds) of muscle spindles can be found lying in parallel with extrafusal fibers and experiencing length changes representative of muscle length changes (Barker 1962;Eldred et al. 1962). The spindle has been found to play a dominant role both in kinesthesia and in reflexive adjustments to perturbations (Hulliger 1984;Matthews 1981). Its sensory transducers (primary and secondary afferents) provide the CNS with information about the length and velocity of the muscle in which the spindle is embedded. The spindle provides the main source of proprioceptive feedback for spinal sensorimotor regulation and servocontrol. At the same time that the spindle supplies the CNS with afferent information, it also receives continuous control through specialized fusimotor efferents (static and dynamic fusimotor efferents) whose task is to shift the spindle's relative sensitivities over the wide range of lengths and velocities that occur in various natural tasks (Banks 1994;Matthews 1962).The spindle consists of three types of intrafusal muscle fibers: long nuclear bag 1 and bag 2 fibers and shorter chain fibers ( Fig. 1A) (Boyd et al. 1977). Typically, one bag 1 , one bag 2 , and about four to 11 chain fibers lie in parallel within a spindle (Boyd and Smith 1984). The bag 1 ...

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