Contraction dynamics in antagonist muscles

By taking into account the torque/angle and the torque/angular speed relationships of antagonist muscles acting across a joint it is possible to predict the contraction dynamics when they are simultaneously activated at a constant level. The simulation is displayed in a "phase-plane" where trajectories for each starting condition (angle--abscissa, angular speed--ordinate) represent the contraction dynamics. The results vary in the position of attractors, repulsors and trajectory shapes. Attractor points (at zero speed) have particular significance in joint stabilization. It was found that with certain reciprocal torque/angle relationships of antagonist muscles, a range of stable joint angles can be quickly reached just by selecting the proper group activation level. A given ratio between the activation levels selects the stable joint angle (attractor) while the overall amplitude will set the joint stiffness in that position. Thus a hypothesized control system should choose just two neural activation amplitudes (time-course considerations are unnecessary), with a reduction of the information needed to stiffen the joint. Furthermore, even ignoring the effects of joint friction, the trajectories toward attractors showed a tendency to cross the zero speed boundary no more than once, resembling the behaviour of an overdamped spring-dashpot system. A couple of testing simulations demonstrated that the combination of non-linear torque/angle and torque/speed relationships is essential to avoid tremor-like paths about the equilibrium and to quickly stiffen the joint. Other aspects related to co-contractions are discussed in the paper.