Torque interaction among adjacent joints due to the action of biarticular muscles

In our musculoskeletal system, multiple muscles are involved in the generation of torque about a joint. Hence, an infinite number of combinations of muscle activities may exist in producing a certain amount of joint torque. Many studies have assumed that the level of muscle activity level depends on torque about the joint it spans. However, this assumption does not hold true in the presence of biarticular muscles. Here we show that the muscle activity level is modulated according to a scheme called "cosine tuning" based on our experiment on the isometric force exerted by the lower limb, that is, the muscle activity about the knee and the hip joints can be represented by a linear summation of the knee and hip joint torques. This way of modulation is very simple, but it is unintuitive on the point that the activation level of the monoarticular muscles explicitly depends on the torque of the adjacent joint that they do not span. It is demonstrated that such nontrivial cosine tuning can be mathematically explained by assuming that the muscle activity pattern is determined so as to minimize the variability of the end point force. Finally, the implications of the cosine tuning for muscle strength training and motor control are discussed.