Muscle activity determined by cosine tuning with a nontrivial preferred direction during isometric force exertion by lower limb

We investigated how the CNS selects a unique muscle activation pattern under a redundant situation resulting from the existence of bi-articular muscles. Surface electromyographic (EMG) activity was recorded from eight lower limb muscles while 11 subjects were exerting isometric knee and hip joint torque simultaneously (T-k and T-h, respectively. Extension torque was defined as positive). The knee joint was kept at either 90 degrees or 60 degrees. Various combinations of torque were imposed on both joints by pulling a cable attached to an ankle brace with approximately three levels of isometric force in 16 directions. The distribution of the data in the three-dimensional plot (muscle activation level quantified by the root mean squared value of EMG vs. T-k and T-h) demonstrates that the muscle activation level M can be approximated by a single model as M = [aT(k) + bT(h)] where [x] = max (x, 0) and a and b are constants. The percentage of variance explained by this model averaged over all muscles was 82.3 +/- 14.0% (mean +/- SD), indicating that the degree of fit of the data to the plane was high. This model suggests that the CNS uses a cosine tuning function on the torque plane (T-k, T-h) to recruit muscles. Interestingly, the muscle's preferred direction (PD) defined as the direction where it is maximally active on the torque plane deviated from its own mechanical pulling direction ( MD). This deviation was apparent in the mono-articular knee extensor (MD = 0 degrees, whereas PD = 14.1 +/- 3.7 degrees for vastus lateralis) and in the mono-articular hip extensor (MD = 90 degrees, whereas PD = 53.4 +/- 6.4 degrees for gluteus maximus). Such misalignment between MD and PD indicates that the mono-articular muscle's activation level depends on the torque of the joint that it does not span. Practical implications of this observation for the motor control studies were discussed. We also demonstrated that the observed shift from the MD to the PD is plausible in the configuration of our musculo-skeletal system and that the experimental results are likely to be explained by the CNS process to minimize the variability of the endpoint force vector under the existence of signal-dependent noise.