Objectives: There is a need to optimise reduction of tooth tissue during preparation procedures to prevent pulpal injury and to minimise stresses on tooth and restoration. However, the physical and chemical requirements of the restorative material must also be met, whilst minimising unnecessary tooth tissue loss. The aim of this study was to use a mathematical modelling concept based on biological growth to optimise tooth reduction in an upper premolar. Methods: Three models of tooth reduction were investigated for structural shape optimisation using the finite element method. Three restorative materials (amalgam, composite and porcelain), three preparation shapes (conventional cavity, inlay and onlay) and a range of tooth-restoration contact conditions with coefficients of friction ranging from 0.01 to 0.50 were considered. The optimisation process was run for each preparation/material combination and the preparation form optimised to minimise the stresses at the tooth--restoration interface. Results: The restored tooth model using the optimised preparations exhibited significant reduction of the values of the stresses along the tooth-restoration interface regardless of the restorative material. For all restorative materials in all cavity shapes with a low coefficient of friction, the maximum stress value was reduced by fifty per cent or more. Conclusions: Mathematical modelling is a useful potential tool to provide sound scientific guidelines for the design of tooth preparation according to the material used.

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