Modeling the effects of cingula structure on strain patterns and potential fracture in tooth enamel

The mammalian cingulum is a shelf of enamel, which rings the base of the molar crown (fully or partially). Certain nonmammalian cynodonts show precursors of this structure, indicating that it may be an important dental character in the origins of mammals. However, there is little consensus as to what drove the initial evolution of the cingulum. Recent work on physical modeling of fracture mechanics has shown that structures which approximate mammalian dentition (hard enamel shell surrounding a softer/tougher dentine interior) undergo specific fracture patterns dependent on the material properties of the food items. Soft materials result in fractures occurring at the base of the stiff shell away from the contact point due to heightened tensile strains. These tensile strains occur around the margin in the region where cingula develop. In this article, we test whether the presence of a cingulum structure will reduce the tensile strains seen in enamel using basic finite element models of bilayered cones. Finite element models of generic cone shaped "teeth" were created both with and without cingula of various shapes and sizes. Various forces were applied to the models to examine the relative magnitudes and directions of average maximum principal strain in the enamel. The addition of a cingulum greatly reduces tensile strains in the enamel caused by "soft-food" forces. The relative shape and size of the cingulum has a strong effect on strain magnitudes as well. Scaling issues between shapes are explored and show that the effectiveness of a given cingulum to reducing tensile strains is dependent on how the cingulum is created. Partial cingula, which only surround a portion of the tooth, are shown to be especially effective at reducing strain caused by asymmetrical loads, and shed new light on the potential early function and evolution of mammalian dentitions.