Shaping static elbow torque-angle relationships by spinal cord circuits: a theoretical study.

Abstract

Static torque-angle relationships (invariant characteristics) as measured by Feldman [Feldman A. G. (1980) Neuroscience 5, 81-90] at the human elbow joint for constant descending excitatory drive have a monotonic convex shape determining joint angle-dependent stiffness. In contrast, for constant activation of elbow flexors, the torque increases, peaks and decreases again with increasing angle because of related moment arm alterations [Hasan Z. and Enoka R. M. (1985) Expl Brain Res. 59, 441-450]. Conversion of such constant-excitation torque-angle shapes into an invariant characteristic might result from action of the stretch reflex which adds excitation with increasing joint angle. To test whether a simple linear model of the stretch reflex could convert constant excitation torque-angle relationships into invariant characteristics, the following assumptions were made. (1) Muscle fibre length increases linearly with joint angle. (2) Reflex muscle excitation (electromyogram) is linearly related to muscle (fibre) length. With these assumptions, invariant characteristic shape cannot be derived from constant excitation torque-angle relationships because it would be sigmoid at low and nearly straight at large joint angles, whilst real flexor invariant characteristics are more convex at large than small angles. It is suggested that recurrent inhibition via Renshaw cells contributes to bend the invariant characteristics into their right shape. Renshaw cells show a nonlinear saturating dependence on motor axon input rate and amount of excitation, i.e. number of active axon collateral synapses. These relationships can contribute to shape motoneuron output so as to yield convex invariant characteristics. Whilst it is not quite clear whether the gain of recurrent inhibition from and to skeleto-motoneurons is high enough to co-determine the invariant characteristic shape significantly, recurrent inhibition of Ia inhibitory interneurons mediating reciprocal inhibition between antagonists is supposed to be quite strong and may influence joint stiffness by interacting with reciprocal inhibition. The arguments presented here extend those of Feldman and co-workers concerning the role of recurrent inhibition and in addition provide a possible explanation for the functional role of mutual inhibition between Renshaw cells. Together with reflex feedback, recurrent inhibition thus contributes to fine-regulate force output and joint stiffness. To account for this cooperation and to make another step towards a general theory of spinal cord circuits, major traits of a new concept are briefly outlined.