How does tooth cusp radius of curvature affect brittle food item processing?

Abstract

Tooth cusp sharpness, measured by radius of curvature (RoC), has been predicted to play a significant role in brittle/hard food item fracture. Here, we set out to test three existing hypotheses about this relationship: namely, the Blunt and Strong Cusp hypotheses, which predict that dull cusps will be most efficient at brittle food item fracture, and the Pointed Cusp hypothesis, which predicts that sharp cusps will be most efficient at brittle food item fracture using a four cusp bunodont molar. We also put forth and test the newly constructed Complex Cusp hypothesis, which predicts that a mixture of dull and sharp cusps will be most efficient at brittle food item fracture. We tested the four hypotheses using finite-element models of four cusped, bunodont molars. When testing the three existing hypotheses, we assumed all cusps had the same level of sharpness (RoC), and gained partial support for the Blunt Cusp hypotheses. We found no support for the Pointed Cusp or Strong Cusp hypotheses. We used the Taguchi sampling method to test the Complex Cusps hypothesis with a morphospace created by independently varying the radii of curvature of the four cusps in the buccolingual and mesiodistal directions. The optimal occlusal morphology for fracturing brittle food items consists of a combination of sharp and dull cusps, which creates high stress concentrations in the food item while stabilizing the food item and keeping the stress concentrations in the enamel low. This model performed better than the Blunt Cusp hypothesis, suggesting a role for optimality in the evolution of cusp form.

Keywords: Taguchi; brittle food item fracture; finite-element analysis; occlusal morphology; radius of curvature; tooth biomechanics.

Figure 1.

Tension tests allow the user to calculate both the stress and strain of the material at any given point in time up to fracture (denoted by X). A stress–strain plot can be obtained by plotting stress on the y-axis and strain on the x-axis and can used to calculate several material properties of the specimen being tested. For example, the slope of the stress–strain curve in the linear, elastic region is Young's modulus. The elastic region of the stress–strain curve ends at the yielding point, which usually occurs after 0.2% strain. Brittle materials tend to fracture soon after the yielding point while ductile materials continue to deform in the plastic region until fracture occurs. (Online version in colour.)

Figure 2.

Correlations between RoC and energy, contact area, stresses in the food item and stresses in the enamel expected under the Blunt, Pointed and Strong Cusp hypotheses. (Online version in colour.)

Figure 3.

Cross section in the mesiodistal direction between two cusps, a and b, showing a number of the parameters that can be assigned to this parametric model. (Online version in colour.)

Figure 4.

One of the completed models, where all RoCs of the tooth are being held constant at 5 mm. (Online version in colour.)

Figure 5.

Six of the 23 models used to test the three existing hypotheses, ranging in RoC from 3 mm (left) to 7.6 mm (right). (Online version in colour.)

Figure 6.

Results depicting the changes in strain energy in the food item, contact area between the occlusal surface and the food item, tensile stress in the food item and tensile stress in the enamel as RoC increases. Numerical results can be found in the electronic supplementary material. (Online version in colour.)

Figure 7.

Occlusal view of the most optimal tooth (optimum, upper left), the least optimal tooth (T1, upper right), and three suboptimal teeth (SubOpt1–3, bottom) using the optimality criterion set forth in this paper. Short, green lines on the occlusal surface of the tooth depict sharp cusps, medium length, yellow line depicts a cusp with a medium level of sharpness, and long, red lines depict dull cusps. Cusp a is the lower, left hand cusp, cusp b is the lower right, cusp c is the upper left and cusp d is the upper right.

Figure 8.

Tensile stress distributions for the most optimal (upper left), least optimal (upper right), and suboptimal (bottom) teeth. The top contour plots are the tensile stress distributions on the underside of the food item, and the bottom are the tensile stress distributions along the EDJ. These are the stress distributions at a 2 kN bite force.