The effects of relative food item size on optimal tooth cusp sharpness during brittle food item processing

Abstract

Teeth are often assumed to be optimal for their function, which allows researchers to derive dietary signatures from tooth shape. Most tooth shape analyses normalize for tooth size, potentially masking the relationship between relative food item size and tooth shape. Here, we model how relative food item size may affect optimal tooth cusp radius of curvature (RoC) during the fracture of brittle food items using a parametric finite-element (FE) model of a four-cusped molar. Morphospaces were created for four different food item sizes by altering cusp RoCs to determine whether optimal tooth shape changed as food item size changed. The morphospaces were also used to investigate whether variation in efficiency metrics (i.e. stresses, energy and optimality) changed as food item size changed. We found that optimal tooth shape changed as food item size changed, but that all optimal morphologies were similar, with one dull cusp that promoted high stresses in the food item and three cusps that acted to stabilize the food item. There were also positive relationships between food item size and the coefficients of variation for stresses in food item and optimality, and negative relationships between food item size and the coefficients of variation for stresses in the enamel and strain energy absorbed by the food item. These results suggest that relative food item size may play a role in selecting for optimal tooth shape, and the magnitude of these selective forces may change depending on food item size and which efficiency metric is being selected.

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

Figure 1.

An ant (length = 2.0 mm) being shown relative to a theoretical cross section of a tooth being isometrically scaled to the width of E. patas (left), P. troglodytes (centre) and G. gorilla (right) teeth. Note how the cusps of the tooth on the left look sharper relative to the ant than the cusps of the tooth on the right.

Figure 2.

Cross section between two of the cusps (a,b) showing some of the parameters that can be varied in the model. a, height of cusp a; b, height of cusp b; c, enamel thickness; d, RoC of cusp a; e, RoC of cusp b; f, distance between cusps a and b; g, height of valley between cusps a and b. The blue panels on the outside depict two cusps, the green panel in the centre represents a valley, and the red panels represent two transitional zones, where the food item would interact equally with the cusps and valleys. (Online version in colour.)

Figure 3.

Four hollow, hemispherical, food items shown with the parametric molar. (Online version in colour.)

Figure 4.

Three optimal morphologies for the small (a), medium (b), large (b) and x-large (c) food items. Sharp cusps are denoted by short, green lines, medium cusps are denoted by medium length, yellow lines and dull cusps are represented by long, red lines. (Online version in colour.)

Figure 5.

Tensile stress distributions along the EDJ (top) and inner surface of the hollow, hemispherical food item (bottom). (Online version in colour.)

Figure 6.

Averages for the efficiency metrics with 95% confidence intervals.