Prospective in (Primate) dental analysis through tooth 3D topographical quantification

Abstract

The occlusal morphology of the teeth is mostly determined by the enamel-dentine junction morphology; the enamel-dentine junction plays the role of a primer and conditions the formation of the occlusal enamel reliefs. However, the accretion of the enamel cap yields thickness variations that alter the morphology and the topography of the enamel-dentine junction (i.e., the differential deposition of enamel by the ameloblasts create an external surface that does not necessarily perfectly parallel the enamel-dentine junction). This self-reliant influence of the enamel on tooth morphology is poorly understood and still under-investigated. Studies considering the relationship between enamel and dentine morphologies are rare, and none of them tackled this relationship in a quantitative way. Major limitations arose from: (1) the difficulties to characterize the tooth morphology in its comprehensive tridimensional aspect and (2) practical issues in relating enamel and enamel-dentine junction quantitative traits. We present new aspects of form representation based exclusively on 3D analytical tools and procedures. Our method is applied to a set of 21 unworn upper second molars belonging to eight extant anthropoid genera. Using geometrical analysis of polygonal meshes representatives of the tooth form, we propose a 3D dataset that constitutes a detailed characterization of the enamel and of the enamel-dentine junction morphologies. Also, for the first time, to our knowledge, we intend to establish a quantitative method for comparing enamel and enamel-dentine junction surfaces descriptors (elevation, inclination, orientation, etc.). New indices that allow characterizing the occlusal morphology are proposed and discussed. In this note, we present technical aspects of our method with the example of anthropoid molars. First results show notable individual variations and taxonomic heterogeneities for the selected topographic parameters and for the pattern and strength of association between enamel-dentine junction and enamel, the enamel cap altering in different ways the "transcription" of the enamel-dentine junction morphology.

Figure 1. Tridimensional orientation of the molars in the virtual space, example of aGorilla.

A1, alignment of the plane defined by the tip of the dentine horns at protocone (Pro), paracone (Par), metacone (Met) to the x, y plane (P1) of the virtual space; A2, aligned enamel-dentine junction surface; A3, aligned enamel surface. The lowermost point of each molar cervix is set to (x, y, 0) so that crown height is measured on a z-positive scale. The z axis is positively oriented from the cervix to the occlusal relief of the tooth. B1, the mesial axis (ma), a line joining the tip of the dentine horns at paracone and protocone is set parallel to the x-axis of the virtual space; B2, oriented enamel-dentine junction surface; B3, oriented enamel surface. Not to scale.

Figure 2. Patch identification for complexity assessment.

A, 3D view of a Gorilla second upper molar; B, detail of the paracone showing the surface polygonal grid; C, orientation of each polygonal element is coded using a chromatic scale, the contiguous triangles with comparable orientation range form a patch. Patch#1, P. #2 and P. #3 are three different patches of polygonal elements. Not to scale.

Figure 3. Tridimensional morphometric maps and associated chromatic color scales of the principal topographical parameters for OES and EDJ.

A, enamel thickness (mm); B, inclination (degree): enamel (B1), enamel-dentine junction (B2); C, orientation (degree): enamel (C1), enamel-dentine junction (C2); D, standardized curvature: enamel (D1), enamel-dentine junction (D2). The figured molars correspond to a subsample of eight individuals representative of the eight studied genera (from left to right): Homo, Pan, Gorilla, Hylobates, Cercocebus, Papio, Cercopithecus, Lagothrix. In order to improve the readability, the sizes of the molar representations have been modified in A to D; refer to the grey scale molars (first row) for relative and absolute size.

Figure 4. Enamel thickness variation.

A, occlusal enamel thickness (δ, whisker diagrams for mean and standard deviation in millimeter); B, enamel thickness distribution (within taxon average, mm) in hominoids (B1) and cercopithecoids/Lagothrix (B2) relative to the corresponding area of expression on the molars (mm²).

Figure 5. Variations of orientation of enamel occlusal surface.

Each profile corresponds to the relative proportion of area expression (in percentage) of the eight orientation intervals. Since orientation is coded on 360°, the relative contribution of the orientation intervals is given in polar coordinates. The schematic drawing (lower right) indicates the direction of orientation for the considered surface according to the tooth orientation. Thus, for instance, polygons for which normal vector is in the 90–135° intervals correspond to a mesially oriented surface. Ms1, Ms2, mesial quadrants; Ds1, Ds2, distal quadrants; MB, DB, mesio- and distobuccal quadrants; ML, DL, mesio- and distolingual quadrants.

Figure 6. Variation of occlusal enamel and enamel dentine-junction inclination (λ^v).

Values for λ^v are reported for each specimen, for both EDJ and OES. λ^v is computed as the area of expression of polygons with inclination higher than 135° relative to the area of expression of polygon with inclination lower than 135°. The average λ^v is given for each taxon.

Figure 7. Inclination profiles of anthropoids molars.

The profile corresponds, for each taxon (average data), to the EDJ relative proportion of area of expression of inclination intervals (increment is 15°).

Figure 8. Standardized mean curvature values of enamel occlusal surface.

The position of each taxon on the graph corresponds to the area proportion of enamel occlusal non-curved surface (left axe, horizontal line is for within taxon average value). The bars illustrate the associate proportion of area of expression of convex (light green)/concave (light orange) to highly convex (green) and extremely concave (red) surfaces (average value, see right panel).

Figure 9. Maximum convexity index for enamel and enamel-dentine junction, comparison with occlusal enamel thickness in anthropoids.

Each specimen is represented by two circles, one for EDJ (φ^mci/EDJ) and one for OES (φ^mci/OES). The average occlusal enamel thickness (mm) is given for each taxon (horizontal line). Lx, Lagothrix; Cb, Cercocebus; Cc, Cercopithecus; Pp, Papio; Hy, Hylobates; Go, Gorilla; Pa, Pan; Ho, Homo.

Figure 10. Relationships between inclination of OES, minimum enamel thickness and inclination of EDJ.

Example of Cercocebus (A) and Gorilla (B). The correlations and their significance between λ^OES and δ, and between λ^OES and λ^EDJ have been computed for about 130 subsamples of 1000 inclination and thickness values (resample with replacement on the original data) for each specimen. The correlations are significant for all λ^OES and λ^EDJ comparisons in Cercocebus (A1, red profile) and Gorilla (B1, red profile). The OES inclination is significantly correlated to the enamel thickness (albeit negatively) in Cercocebus (A1, blue profile) while λ^OES and δ present significant positive correlation in 72.1% of the cases in gorillas (B1, blue profile; significant correlations are marked with a blue diamond). A simplified version of the observed relationship is given for Cercocebus (A2) and Gorilla (B2) from a subsample of 250 inclination and thickness values (resample with replacement on the original data). The surfaces of the dots in A2, B2 represent minimum enamel thickness value (scale *10).

Figure 11. Measuring the bilophodonty by the mean of polygon orientation distributions.

Example of a theoretical case of two cusps (outlined in green) showing various degrees of bilophodonty; a & b illustrate distinct lingual and buccal cusps, c development of buccal and lingual crests at lingual and buccal cusps, d, loph joining lingual and buccal cusps. The normal vector (red arrow) describing each point of the cusp outline (or polygons for tridimensional data) allows retrieving orientation values along the cusp contour. The cusp contour can be decomposed in different portions describing same orientation intervals (e.g. 0–45° or 90–135°, only mesial halves of the cusps is shown) numbered from 1 to 8. The distribution and the relative contribution of the orientation intervals to the shape of the cusp allow quantifying the development of bilophodonty. Hence for instance, complete bilophodonty is marked from c to d by the deletion of orientation classes 4 and 1 between cusps on their mesial side.