Finite Element Evaluation of Stress Distribution in Mature and Immature Teeth
INTRODUCTION: Traumatic injuries may affect the vitality and development of tooth. So divergence or parallelism of canal walls induces an open apex which is very susceptible to fracture. The aim of this study was to determine the stress distribution pattern in immature teeth and compare it with mature teeth. MATERIALS AND METHODS: In order to analyze stress distribution using finite element method, models were first designed according to actual samples by "ANSYS" software. Two models of the maxillary central incisors were designed, one mature and one with open apex. Mature tooth was designed as having undergone root canal therapy with gutta-percha and the immature one with both MTA plug and gutta-percha. Samples were loaded in seven stages and then, the stress distribution in each model was measured, using the "ANSYS" software. RESULTS: During gutta-percha condensation, the immature tooth transfers the stress directly to the external root surface where force is directly applied, whereas during masticatory occlusal forces, the stress is transferred to middle third of buccal and lingual surfaces and to buccal cervix in lunar shape. During traumatic forces, stress concentration was on the cervical region of buccal surface and middle third of buccal and lingual surfaces. MTA plug prevents stress distribution toward apical region and forces concentrate in dentin at the point where stress terminates. CONCLUSION: Within the limitations of this simulated mechanical analysis, it was confirmed that the pattern of stress distribution in mature and immature teeth is different. Cervical area of the buccal surface in immature teeth is one of the stress concentration areas, which contribute to the high rate of fracture in this area.
Biomechanical performance of an immature maxillary central incisor after revitalization: a finite element analysis.
AIM
To investigate the stress distribution in an immature maxillary incisor and the same tooth after simulated revitalization with deposition of tubular dentine or cementum by finite element analysis (FEA).


METHODOLOGY
A finite element model of a maxillary central incisor was developed on the basis of a µCT scan. The tooth was segmented in two parts: a part that represented a tooth in an immature state and an apical part that represented the tissue formed after revitalization. The apical part was given the mechanical properties of dentine or cementum. The immature tooth and the same tooth reinforced by either dentine or cementum underwent simulation of biting, trauma and orthodontic movement. Von Mises stress values were compared between the scenarios and tooth segments.


RESULTS
Maximum stress in the immature incisor developed apically; however, dentine- and cementum-reinforced teeth revealed the greatest stress in the external portion of the root decreasing towards the apex. Greatest mechanical stress was caused by dental trauma perpendicular to the long axis of the root followed by biting and orthodontic movement. Stress peaks were lower in the dentine-reinforced tooth compared with the cementum-reinforced tooth in all scenarios; however, median stress in the immature part was reduced irrespective of dentine or cementum deposition. Dentine reinforcement caused greater stress values in the apical segment due to absorbance of the applied force, whereas stress was not transferred towards deposited cementum.


CONCLUSIONS
Apposition of simulated hard tissue in a maxillary central incisor after revitalization reduced mechanical stress in the immature tooth. Formation of dentine was advantageous because, unlike cementum, it facilitated an even stress distribution throughout the root resulting in lower stress values.
Mahler functions and transcendence
Transcendence theory of mahler functions of one variable.- Transcendence theory of mahler functions of several variables.- Algebraic independence of mahler functions and their values.- Applications of elimination theory.- Regular sequences and mahler functions.