Mathematical modeling of molar tooth preparations for complete crowns

Objectives: This study used both cone frustum and right truncated pyramids mathematical methods to evaluate and characterize molar tooth surface area. Previous mathematical modeling studies evaluated only the total surface area. We attempted to analyze both the top surface and lateral surface areas. Methods: The computations were performed according to the published formulas. The vertical heights of both models were assigned to be 3 and 4 mm and the horizontal base width chosen to be 9 and 10 mm for both models. Three total occlusal convergences: 10 degrees, 15 degrees, and 20 degrees were selected to be the tested parameters. Results: The calculated data revealed that the top surface area represented a relatively large proportion of the total surface area in both models. We also found that the effect of increasing the total occlusal convergence has a much greater effect on the overall top surface area than the lateral surface and total surface areas. Conclusions: The models previously used to report and compare surface areas of prepared natural teeth were found to be overestimating the overall surface area. More complex configurations including two-plane reductions, anatomy of cusps and retentive features such as slots and grooves need to be included in future modeling protocols.