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The objective of this study is to investigate the effect of the tensile force ratio between the two extensor muscles for the hip joint on the forces acting on the knee joint. We have created a mathematical model of lower limb and have performed some simulations to introduce the forces acting on the knee joint for various daily activities. With only one exception, our results for knee joint forces were in good or close agreement involving all range of knee flexion either with the in vivo data or other literature data. The exception was that, at high knee flexion angle (knee bend), the tangential components of knee joint force became pretty larger than those from the in vivo data, while the normal components did not differ much with each other though as shown in Fig. 1. We considered that the above mentioned discrepancy was attributed to the fact that in order to solve an indeterminate problem, we had assumed the hamstrings and the gluteus maximus work together with the same force with each other, thereby introducing the hamstrings force too great. Then we expected that the above discrepancy could be eliminated if we change the tensile force ratio between the hamstrings and the gluteus maximus basing upon a certain biomechanical criterion, for example the biological cross-sectional areas. Thus we modified our model so that we could introduce the knee joint forces as a function of the tensile force ratio. Simulation was performed for the various tensile ratio values and it was found that the knee joint force was sensitively affected by the tensile ratio and the above mentioned discrepancy between the simulation results and the in vivo data could be eliminated if the ratio value was appropriately chosen. Figure 2 shows the situation; Variations of F n and F t as a function of knee angle q for the various tensile force ratio r between the hamstrings and the gluteus maximus. Where, r=1.56 was determined from the biological cross-sectional areas of the hamstrings and the gluteus maximus and r=4.5 was determined so that the simulation results best fit to the in vivo data. It has been criticized that there exist large variations of knee joint forces obtained from model analyses. And the reasons for this have been attributed to for example such facts that the model is 2D and the parameter values are incorrect. Yet, another important issue may be to find out the way how to determine the value of the synergetic muscles9 force ratio with reflecting a biological rationality.

Effect of the Tensile Force Ratio of Gluteus Maximus and Hamstrings on the Knee Joint Force