MATHEMATICAL SUBSTANTIATION OF BIOMECHANICAL BASES OF PATHOLOGICAL WEAR OF HARD TISSUES OF TEETH

Abstract

Using the Bernoulli principle, the muscles that raise, laterally shift, and advance the mandible were studied. The biomechanical component of the pathogenesis of pathological tooth abrasion was revealed. The role of "fast" and "strong" muscles in the process of excessive abrasion of hard tissues is revealed. Applying the Bernoulli principle to the study of muscles, the ratio of muscle length to its cross-sectional area was expressed mathematically in terms of coefficients. The average values of the coefficients of the same muscles in the control group on the priority and secondary sides differ insignificantly, which indicates a balanced work: the muscles are equally "fast" and equally "strong". Compared to the control group, the first group of patients showed a tendency to a more pronounced difference in the physical qualities of the muscles: strength begins to prevail in some, and speed in others. Clinically, this is manifested at the initial stage of abrasion of hard tooth tissues. A decrease in the temporalis and masseter muscle coefficients in the second group compared to the control group indicates a decrease in muscle length. The gradual increase in the ratios of the wing-shaped lateral muscle from the first to the second group on both the priority and secondary sides of chewing indicates its greater length relative to the cross-sectional area, and therefore, the acquisition of the quality of "speed". In patients of the third group, the difference in the ratio coefficients with the control group and between the priority and balancing sides is more pronounced. Increasingly, the temporalis and masseter muscles acquire the physical quality of "strength", and the wing-like muscles "speed". It is noteworthy that the coefficients of the wing-shaped muscles in patients of the second and third groups on the secondary side are increased compared to the priority side of chewing. Violation of the balance between the physical qualities of the muscles "strength" and "speed" affects the development of pathological tooth abrasion.