# Prediction of Force Sharing Among Synergistic Muscles

Gudrun Schappacher-Tilp^{*} and Walter Herzog

A primary research topic in biomechanics is the determination of forces generated by individual muscles during voluntary movements. Theoretically, force prediction models of synergistic muscle coordination are based on non-linear optimization of specific cost functions. The classical cost functions involve normalization of the muscle forces to the absolute force capacity of the target muscles (e.g. the cross-sectional area of the muscle or the maximal isometric force) [1, 2] leading to a functional relationship between moment arms and the predicted muscle forces [3]. However, experimental results provide strong evidence that the relationship between synergistic muscle forces is highly task-dependent [4]. Here, we investigated how task-dependent cost functions based on the instantaneous contractile conditions of muscles may improve predictions of synergistic force sharing and allow for realistic force sharing scenarios. \begin{thebibliography}{99} \bibitem{eins} Crowninshield, R.D., Brand R.A., 1981. A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14: 793-801 \bibitem{zwei}Dul, J., Johnson, G.E., Shiavi, R., Townsed, M.A. 1984. Muscular synergism. II. A minimum fatigue criterion for load sharing between synergistic muscles. J. Biomech. 17: 675-84 \bibitem{drei} Binding, P., Jinha, A., Herzog, W. 2000. Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models. J. Biomech. 33(11): 1423-32 \bibitem{vier} Herzog, W., Leonard, T.R., Guimaraes, A.C.S. 1993. Forces in gastrocnemius, soleus and plantaris tendons of the freely moving cat. J. Biomechanics 26: 945–953 \end{thebibliography}

Mathematics Subject Classification: 92B05

Keywords: force sharing, task-dependent cost function

Minisymposion: Modelling and Optimization in Mathematical Biology