Muscle co-contraction modulates damping and joint stability in a three-link biomechanical limb

Computational models of neuromotor control require forward models of limb movement that can replicate the natural relationships between muscle activation and joint dynamics without the burdens of excessive anatomical detail. We present a model of a three-link biomechanical limb that emphasizes the dynamics of limb movement within a simplified two-dimensional framework. Muscle co-contraction effects were incorporated into the model by flanking each joint with a pair of antagonist muscles that may be activated independently. Muscle co-contraction is known to alter the damping and stiffness of limb joints without altering net joint torque. Idealized muscle actuators were implemented using the Voigt muscle model which incorporates the parallel elasticity of muscle and tendon but omits series elasticity. The natural force-length-velocity relationships of contractile muscle tissue were incorporated into the actuators using ideal mathematical forms. Numerical stability analysis confirmed that co-contraction of these simplified actuators increased damping in the biomechanical limb consistent with observations of human motor control. Dynamic changes in joint stiffness were excluded by the omission of series elasticity. The analysis also revealed the unexpected finding that distinct stable (bistable) equilibrium positions can co-exist under identical levels of muscle co-contraction. We map the conditions under which bistability arises and prove analytically that monostability (equifinality) is guaranteed when the antagonist muscles are identical. Lastly we verify these analytic findings in the full biomechanical limb model.