Modelling of forces in the human masticatory system with optimization of the angulations of the joint loads

Numerical models of the human masticatory system were constructed using algorithms which minimized non-linear functions of the muscle forces or the joint loads. However, the predicted solutions for isometric biting were critically dependent upon the modelled angular freedom of the joint loads. The most complete mathematical minimization of any objective function occurs when the joint load angles are predicted. However, the predictions have to be sensible in relation to the actual morphology of the joints. Therefore, the models were tested in terms of the angles of joint load predicted for a dry skull, using muscle vectors reconstructed from the geometry of the skull. The minimizations of muscle force were intrinsically incapable of predicting the angles of joint load. Such models must rely on constrained angles and this produces a restricted minimization and also an indeterminacy. In contrast, the minimizations of joint load predicted angles of joint load which varied appropriately with condylar position. The condylar movement was achieved with a positioning model which adjusted the angulation of the muscle vectors as the jaw was positioned. This model also generated the optimal sagittal shape of the articular eminence. Muscle predictions from the various models were not examined in detail, but the general nature of the predicted muscle force patterns was shown to be reasonable in some of the models and unreasonable in others. The results supported the hypothesis that the temporomandibular joint develops functionally to allow an approximate minimization of the joint loads during isomeric biting. This does not necessarily imply that the neurophysiological control is actually based on a minimization of joint load.