Mathematical models of proprioceptors. II. Structure and function of the Golgi tendon organ.

We developed a physiologically realistic mathematical model of the Golgi tendon organ (GTO) whose elements correspond to anatomical features of the biological receptor. The mechanical interactions of these elements enable it to capture all salient aspects of GTO afferent behavior reported in the literature. The model accurately describes the GTO's static and dynamic responses to activation of single motor units whose muscle fibers insert into the GTO, including the different static and dynamic sensitivities that exist for different types of muscle fibers (S, FR, and FF). Furthermore, it captures the phenomena of self- and cross-adaptation wherein the GTO dynamic response during motor unit activation is reduced by prior activation of the same or a different motor unit, respectively. The model demonstrates various degrees of nonlinear summation of GTO responses resulting from simultaneous activation of multiple motor units. Similarly to the biological GTO, the model suggests that the activation of every additional motor unit to already active motor units that influence the receptor will have a progressively weaker incremental effect on the GTO afferent activity. Finally, the proportional relationship between the cross-adaptation and summation recorded for various pairs of motor units was captured by the model, but only by incorporating a particular type of occlusion between multiple transduction regions that were previously suggested. This occlusion mechanism is consistent with the anatomy of the afferent innervation and its arrangement with respect to the collagen strands inserting into the GTO.