Three-dimensional mathematical analysis of the maximum stresses of the dentoalveolar segment under vertical and oblique loads

Abstract

Functional overload of teeth and implants is one of the most important reasons for their loosening and removal. Predicting the overload of teeth and implants is possible using digital technologies and special programs. Each study requires a basic study of functional stress indicators in an identical (preferably three-dimensional) mathematical model, as close as possible to clinical conditions.
 The aim of the study was to study the maximum stresses in the hard tissues of the tooth and in the alveolar socket under vertical and inclined functional loads using three-dimensional mathematical modeling.
 A differentiated analysis of the maximum integral stresses in a single-rooted tooth (mandibular canine) and the surrounding alveolar segment: enamel, dentin, cementum, cortical bone, spongy bone was carried out. A three-dimensional mathematical model of the segment was created, in which the fabrics corresponded to natural ones in their properties. A load of 150 N was applied to the cutting edge of the tooth in the vertical direction and at an angle of 45° from the buccal side. The maximum integral stresses according to Mises were analyzed.
 According to the results of three-dimensional mathematical modeling in the hard tissues of the tooth, the maximum stresses under vertical and inclined loads are most significant in magnitude in enamel, then in dentin and in cement (with an inclined load, respectively, up to 77.610 MPa, 56.469 MPa, 15.832 MPa). An oblique load significantly increases the stresses in the hard tissues of the tooth and the surrounding bone compared to a vertical load (by 77.4% in the case of enamel). With a vertical load, the zones of maximum stresses in enamel and dentin are localized in the zone of the cutting edge, in cement – in the cervical and apical parts of the root; oblique load concentrates stresses in the cervical part of the tooth and the upper third of the root.
 Stresses in the cortical bone tissue in the vertical direction of the load of the tooth are distributed along the tooth hole and along the outer surface of the jaw at the transition to the basal margin; with an oblique direction of the load, the stresses in the cortical bone are concentrated in the region of the neck of the tooth; maximum stresses under vertical and inclined loads 5.066 MPa and 27.909 MPa. Stresses in spongy bone tissue are recorded under the zones of maximum stresses in the adjacent cortical bone; maximum stresses under vertical and inclined loads 1.382 MPa and 4.375 MPa.