Optimal occlusal force field of masticatory system under clenching by simplex method and principal component analysis

In the present paper, a method to evaluate the occlusal state and occlusal morphology that can integrate an optimal occlusal force field under clenching is proposed using simplex optimization and principal component analysis (PCA). The objective function of the optimization is taken as a sum of the weighted occlusal forces and reaction on temporomandibular joint (TMJ) to maximize the former and to minimize the latter. The optimized solutions in the region defined by the combination among three kinds of muscle forces were obtained by two-step simplex method, and the subregion with no reaction of TMJ was summarized as a ratio to the whole region, newly defined here as a good balance ratio. As a result of PCA of total 528 samples of the good balance ratios for 13 different muscle force combinations, two principal components (PCs) are enough to represent the optimized masticatory system. The first PC suggests the ideal state of occlusion and the second one implies the characterization of combination among muscles. From the consideration of PCA, with the wider equalizer angle, the easier it is to support the force of the temporalis muscle in an ideal occlusal position, and the more the occlusal contact point is shifted backward, the harder it is to support the force of the temporalis muscle. Comprehensively, the proposed good balance ratio becomes the effective quantity to evaluate the ideal masticatory system with the optimized occlusal force field for the statistically reduced indexes showing the combination of muscles.