Evaluating the effect of co-contraction in optimization models

The effect of co-contraction of antagonist muscles on spinal compression force is estimated using Karush-Kuhn-Tucker (K-K-T) multipliers. Co-contraction is modelled as an incremental increase in the lower bounds on the allowable muscle forces in an optimization model formation. The K-K-T multipliers associated with each lower bound provide an estimate of the partial derivate of the optimal objective function value with respect to a change in the lower bound. A model whose objective function is spinal compression force is analyzed to estimate the effect of co-contraction on spinal compression force. While the effect depends on the specific muscle and task under consideration, the marginal effect of co-contraction on spinal compression force can be as high as 5.52 N additional spinal compression force for every additional N of muscle force. Paradoxically, the co-contraction may slightly decrease predicted spinal compression in special circumstances.