Reflex regulation of antagonist muscles for control of joint equilibrium position

A systems model of spinal neuro-musculo-skeletal system (α-γ model) is developed to investigate the plausible roles of spinal proprioceptive feedback in movement control. The model is composed of a joint, a pair of antagonist muscles, length and velocity feedback from muscle spindle, as well as spinal stretch reflex, reciprocal inhibition and recurrent inhibition of Renshaw cells. A descending command modulates the background activation of α motoneuron pools in combination with these reflex activities. A static γ command controls the fusimotor contraction of the spindle. Simulation results reveal that the equilibrium joint angle is linearly correlated to the level of static γ fusimotor activity of the spindle for a wide range of external loading conditions and reflex gains, suggesting that these spinal reflexes may contribute to regulate the equilibrium position of the joint. Sensitivity analysis further shows that reflex gains and other central commands alter the quasi-linear relation in regular fashions. The reciprocal inhibition gain changes the slope of the linear θ_eq-γ curve; and the descending α excitation, the stretch reflex gain, and the external load all shift the θ_eq-γ curve in parallel. These results imply that reflex gains and descending α commands may be coordinated to maintain a unique θ_eq-γ curve while providing the flexibility to counteract external loads, to execute a movement, or to regulate additional muscle variables. Dynamic simulation suggests that control of a class of movements can be achieved with a triphasic, α pulse and a continuous γ signal. The model study supports the notion of a dual strategy for controlling trajectories via a feedforward α command and for regulating the final equilibrium positions via a feedback γ command.