Human tooth enamel is a hard, biocomposite material that is hierarchically structured at both the nanoscale and microscale. At the microscopic scale, the foundational structure is the enamel prism, or rod, while, at the nanoscale of organization, the prisms are composed of aggregates of hydroxyapatite crystallites (Boyde, 1997).

The alignment and structure of the prisms is dictated by the ameloblasts that secrete enamel matrix at two sites; the interameloblastic borders define the secretory pits, one of which relates to each cell, and the secretory pole (Tomes’) process serves to fill the pit. The prisms are surrounded by organic sheaths (Weber, 1973). As the enamel matrix mineralizes, hydroxyapatite crystallites form and are bound together by nanometer thin organic layers. These constitute the nanoscale structure of the prism (Wallwork et al., 2001). The ability of enamel to deform may be related to the unfolding behavior of macromolecules in this protein matrix (Zhou & Hsiung, 2006). The shape of the Tomes’ process largely determines the orientation of the hydroxyapatite crystallites, which appear to be principally aligned along the axis of the prism in its head but gradually diverge by as much as 60° in the tail (Habelitz et al., 2001, Poole and Brooks, 1961, White et al., 2001). While the crystallites are not necessarily co-oriented with one another or with the long axis of the prism, their orientation within the prism gradually changes with a spread that may vary between 30° and 90° (Beniash et al., 2019). This arrangement enhances energy dissipation while providing sufficient stiffness to promote fracture toughness (An et al., 2012).

The prism sheath differs in both nanohardness and elastic modulus from the prism itself (Ge et al., 2005, He et al., 2006), and this has been found to effectively reduce stress concentration on the prisms under both transverse and shear loading (Yoon et al., 2015). As enamel matures, however, the density differences between prisms and their sheaths may be reduced (Miake et al., 2016). As such, the structural matrix and arrangement of the hydroxyapatite crystallites that comprise the prisms together with the prism sheaths appear to contribute to the rather remarkable mechanical properties of tooth enamel (An et al., 2012, He and Swain, 2008, Yoon et al., 2015). There is good evidence to indicate that prisms tend to be larger near the outer enamel surface (OES) than closer to the enamel-dentine junction (EDJ) (Dean, 2004, Fosse, 1968, Risnes, 1998, Skobe and Stern, 1980). The arrangement of the prisms and the paths they follow from the EDJ to the OES are significant features relating to the ability of enamel to resist fatigue and fracture (e.g., Bajaj & Arola, 2009b).

Synchrotron imaging of a developing chimpanzee molar shows that enamel prisms follow a comparatively straight course with “irregular wave-like deviations” in 3D space, attaining path lengths that exceeded the straight-line distance of local enamel thickness by some 7 % (Tafforeau et al., 2012). Importantly, this study found that the prisms do not display movement with regular geometric properties (such as undulating sinusoidal curves) as had been proposed by previous workers (e.g., Jiang et al., 2003; Macho et al., 2003; Osborn, 1965, Osborn, 1990). Numerous investigations of human tooth enamel have been devoted to documenting the phenomenon of prism decussation, where the deviations of their paths result in adjacent groups of prisms with their long axes running at varying angles to one another (Boyde, 1969, Cui and Ge, 2007, Lynch et al., 2010, Mortell and Peyton, 1956, Osborn, 1965, Osborn, 1968bbb, Osborn, 1990, Radlanski et al., 2001, Skobe and Stern, 1980). The adjacent groups form the Hunter-Schreger Bands (HSBs) of alternating zones of prisms whose axes either approximate the plane of section through the enamel (parazones) or run at a distinct angle to it (diazones) (Fig. 1).

While the outermost layer of enamel may be prismless (Gwinnett, 1967, Kodaka et al., 1991, Ripa et al., 1966, Risnes and Li, 2018, Whittaker, 1982), the vast bulk of the enamel cap exhibits prismatic structure (Eisenmann, 1980, Gustafson and Gustafson, 1967, Nanci, 2017, Thompson, 2020). The presence of decussated prisms may vary depending upon location (Lynch et al., 2010, Thompson, 2020). Thus, there is commonly a very narrow zone immediately adjacent to the EDJ where the prisms run perpendicular to it before they begin to exhibit decussation (Bodier-Houllé et al., 2000, Kodaka et al., 1990). The outer quarter to third of the thickness of lateral enamel is generally devoid of decussation, where the prisms are more parallel to one another, approaching the OES at varying inclinations (Nanci, 2017, Radlanski and Renz, 2006, Thompson, 2020). The cervical portion of the enamel cap may exhibit marked variation in the orientation and sizes of the hydroxyapatite crystallites (Poole et al., 1981), which may be accompanied by considerable variation in prism shape, prism decussation and the presence of aprismatic enamel (Gašperšič, 1995). For example, the prisms in cervical enamel are poorly defined and follow a straight path from the EDJ to the OES (Osborn, 1968a), and the packing densities of HSBs are significantly lower in the cervical quarter than in the rest of the lateral enamel cap (Lynch et al., 2010). In the enamel that covers the cusp tips, the regular bands of parazones and diazones that characterize deep lateral enamel tend to be lost, and the prisms may form a gnarled structure (Eisenmann, 1980, Kodaka et al., 1996, Osborn, 1968aaa).

Innumerable studies of the deformation behavior and fracture toughness of enamel have provided ample evidence that the laminated and twisted structure (known as the Bouligand structure, Bouligand, 1972) of HSBs imparts significant resilience to an otherwise brittle entity. In particular, the HSBs impart anisotropy, which serves to dissipate the energy that is required to propagate a crack. In this case, cracks propagate preferentially along prisms, cleaving the protein-rich rod sheaths, rather than across the hydroxyapatite bundles that makeup the rods (Bechtle et al., 2010, Habelitz et al., 2001, Rasmussen et al., 1976, White et al., 2001, Yahyazadehfar et al., 2013). As such, diazonal and parazonal alterations in prism axes will serve to toughen the enamel block (Bajaj and Arola, 2009aa, Bajaj and Arola, 2009bbb, Bajaj et al., 2010, Bechtle et al., 2010, Chai et al., 2011, Chai et al., 2009, Lawn and Lee, 2009, Myoung et al., 2009, Rasmussen et al., 1976, Thompson, 2020, Yahyazadehfar et al., 2013). The energy required to propagate a crack increases significantly as it elongates (preferentially along prism sheaths) and when a crack encounters reorientation of the prism bundles that deflect it this causes its energy to dissipate. This R curve behavior of enamel, whereby the energy necessary to propagate a crack increases with crack depth, is attributable to decussation (Bajaj and Arola, 2009aa, Bajaj and Arola, 2009bbb, Lee et al., 2011). Toughness of the enamel cap may be as much as four times greater closer to the EDJ than the OES owing to decussation (Bajaj and Arola, 2009aa, Bajaj and Arola, 2009bbb). At the same time, the elastic modulus and hardness of enamel increase with distance from the EDJ (He et al., 2006, Park et al., 2008, Shen et al., 2020). This region of radial enamel has more limited potential for energy dissipation (i.e., a lower ability to resist fractures) than deeper enamel (An et al., 2012). The attendant interpretation of decussation is that it represents a functional adaptation of tooth enamel (He and Swain, 2009, Line and Novaes, 2005, Maas and Dumont, 1999, Popowics et al., 2004, Rensberger, 2000, von Koenigswald and Pfretzschner, 1991, Wilmers and Bargmann, 2020).

In light of the foregoing, it might be predicted that those regions of the enamel cap that experience the greatest masticatory forces (e.g., compression versus shear) will exhibit more decussation. This expectation would be in keeping with observations that primate molar enamel tends to be thicker over the ‘functional’ cusps with Phase II (crushing and grinding) facets than the ‘guiding’ cusps dominated by Phase I (shearing and guiding) facets. Thus, the lingual side of the protocone (mesiolingual cusp) in maxillary molars and the buccal sides of the protoconid and hypoconid (mesiobuccal and distobuccal cusps) in mandibular molars experience higher stress loading during mastication (Benazzi et al., 2011, Benazzi et al., 2016, Dejak et al., 2003, Kay and Hiiemäe, 1974, Lucas and Luke, 1984, Macho and Spears, 1999), and tend to have thicker enamel (Gantt et al., 2001, Grine et al., 2005, Grine, 2005, Kay, 1975, Kono et al., 2002, Mahoney, 2010, Molnar and Gantt, 1977, Schwartz, 2000aaa, Shillingburg and Grace, 1973). Differences in the mechanical properties of enamel between the buccal and lingual sides of a human maxillary molar have also been observed (Cuy et al., 2002). Such differences could be related to differences in enamel thickness and/or the degree to which it is decussated.

Similarly, some models of masticatory biomechanics suggest that there is a distalward increase in occlusal loading along the molar row (Janis and Fortelius, 1988, Koolstra et al., 1988, Molnar and Ward, 1977, Osborn and Baragar, 1985, Osborn, 1996). If these models are correct, enamel decussation might be expected to increase from the first molar (M1) to the third molar (M3). This expectation would be in accord with observations that the enamel cap tends to be thicker in the more distal molars (e.g., Grine, 2005; Macho and Berner, 1993, Macho and Berner, 1994; Schwartz, 2000a; Spears & Macho, 1995).

If there are differences in the HSB configurations between ‘functional’ and ‘guiding’ cusps, or along the molar row, these could have implications for the interpretation of enamel chipping frequencies in relation to behaviors, including the inference of dietary regimens (e.g., Constantino et al., 2010; Constantino et al., 2012; Fannin et al., 2020; Lee et al., 2011; Robinson, 1956; Towle et al., 2017; Wallace, 1973; but see Ziscovici et al., 2014). While several studies have reported that ‘guiding’ cusps exhibit more enamel chipping than ‘functional’ cusps (e.g., Bader et al., 2001; Cavel et al., 1985; Eakle et al., 1986; Towle & Loch, 2021; Towle et al., 2021), the potential impact of underlying enamel structure on fracture/chip locations has received little attention. In this regard, if the Phase I cusps display weaker patterns of enamel decussation than Phase II cusps, they may be intrinsically more susceptible to chipping. Similarly, if more mesial molars display weaker patterns of enamel decussation, they may be intrinsically more susceptible to chipping than more distal molars. If susceptibility to chipping is not distributed evenly between the cusps or along the molar row, additional factors such as the location of the chip would better be considered when interpreting dental chipping frequencies.

While numerous studies have documented overall patterns of enamel decussation in human teeth, little attention has been paid to examining potential differences in HSB distributions between the cusps that support Phase II facets and those with Phase I facets. This may be owing to the difficulty in identifying methods by which to quantify decussation that would enable such comparisons. To date, five different approaches have been employed in attempts to quantify aspects of enamel decussation.

Beynon and Wood (1986) employed linear and angular measures of HSBs and a measure of their curvature in the lateral enamel with a view to characterizing decussation in the teeth of East African hominin fossils. They recorded HSB Width, HSB Prism Angle and HSB Curvature, where HSB Width was defined as the diameter across “at least ten alternating parazones and diazones” (Beynon & Wood, 1986: 181), but it is unclear how many pairs could be included beyond ten. While HSB Prism Angle and HSB Curvature might be morphologically relevant to identifying hominin fossil teeth, they do not seem to address functional aspects of HSBs. To our knowledge, these parameters have not been employed by any other worker.

Jiang et al. (2003) created a computer model of decussation based on images recorded from fractured human teeth in which a regular, geometric sinusoidal course was imposed from shading algorithms relating to the inferred of prism paths from the DEJ to the OES. However, as noted above, Dean (2004) and Tafforeau et al. (2012) have demonstrated that prisms do not display regular geometric properties such as undulating sinusoidal curves as required by the model of Jiang et al. (2003).

Mostafiz et al. (2007) employed a mathematical algorithm that transformed images of prisms obtained by SEM from serially ground enamel blocks into linear features whose length aspect ratios were then measured. While this provided a measure of prism anisotropy, the technique is wholly destructive of the enamel cap. As such, this method of quantification has not been implemented beyond the initial demonstration of its potential.

Hogg and Richardson (2019) used an image compression ratio (ICR) algorithm to analyze thin section enamel photomicrographs, where compression values were treated as proxies for enamel complexity. Although this method holds promise for images recorded at comparatively low magnification (where an abundance of HSBs can be visualized), and where the differences in complexity are rather striking, it is unclear whether subtle differences in decussation can be recognized by ICR.

Lynch et al. (2010) examined HSB packing densities micrographs of sectioned human molars by counting the number of light and dark bands between the EDJ and OES in four regions of lateral enamel, where an HSB was defined as a single light or dark band. The HSB packing density of each segment was calculated by dividing the total number of HSBs by the length of the EDJ of that segment. Despite the relatively large number of M1s examined by Lynch et al. (2010), no data are available on the second or the third molars.

While HSB packing density undoubtedly reflects a significant component of enamel structure, this only documents anisotropy in the vertical dimension. The relative lengths of the HSBs also comprise an important element of enamel, as this relates to the thickness of decussated vs radial enamel. This feature compliments HSB packing density in characterizing the anisotropy of enamel prism orientation within the enamel cap. To our knowledge, relative HSB length has not been investigated as an intrinsic feature in the context of the functional differences between the cusps. In this study, we adopt the HSB packing density developed by Lynch et al. (2010) and also consider relative HSB length as they provide quantitative assessments of enamel decussation in lateral molar enamel.

Given the functional implications of enamel decussation discussed above, the objectives of this study are to examine the configuration of enamel decussation as represented by HSB packing density and relative HSB length 1) between the ‘functional’ and ‘guiding’ cusps of human molars; and 2) along the upper and lower molar rows from M1 to M3.