Biomechanics of torsion in the human mandible

Abstract

Comparative investigations of mandibular function among primates have relied upon elementary structural models to estimate states of masticatory stress and strain. In these studies, mandibular corpus morphology is idealized as a homogeneous, isotropic symmetrical body of invariant geometry, and this morphological abstraction is used to infer relative levels of stress and strain in the jaw. In reality, none of the limiting conditions assumed by these models is satisfied; consequently, it is prudent to ask whether this "textbook" engineering approach is valid for the inference of biomechanical behavior. In this study, the predictions of various geometric representations of the mandibular corpus are evaluated against strains recorded in a sample of human jaws loaded in torsion. Symmetrical geometrical models (including various "robusticity" shape indices), although convenient, are probably not consistently reliable for predicting the distribution of strains in the corpus. The experimental data suggest that variations in cortical thickness within sections play a significant role in determining the profile of relative strains. For comparative applications, characterization of the corpus as an asymmetrical hollow ellipse (i.e., with differing thickness of medial and lateral cortical plates) may provide a reasonable portrayal of relative strains.

Morphometric estimation of torsional stiffness and strength in primate mandibles

“…Substitution of a dummy variable in lieu of corpus breadth (mandibular length) provides a test of whether this corpus dimension has a particularly strong functional link to the variable K that is independent of more Daegling and Hylander, 1998), from the location of the highest shear strains recorded in each specimen. The observed stresses were derived from surface strains and regionally specific estimates of shear modulus from human mandibular bone (Schwartz-Dabney and Dechow, 2003).…”

“…Conversely, when eccentricity is zero (i.e., a cylinder), the distinction between major and minor axes vanishes and the peripheral stress is uniform. Daegling and Hylander (1998) found no compelling relationship between eccentricity and observed strain gradients (if anything, the relationship appeared opposite to that of theory). The third problem is operational rather than theoretical: a formulaic solution to an asymmetrical hollow ellipse model (one that that is required by consideration of cortical geometry and circumstantially supported by the strain data) has yet to be developed.…”

“…Finally, the strain data and alternative model predictions for the experiments reported in Daegling and Hylander (1998) were compared to assess whether theoretical models were capable of predicting the rank-ordering of experimental specimens in terms of the maximum observed strains given applied loads. Corpus breadth, solid ellipse (derived from corpus breadth and height), hollow ellipse (using wall thickness values determined empirically), and thin tube models were evaluated.…”

“…The rationale for doing so is the correct observation that increases in transverse thickness serve to increase a section's polar moment of inertia and thereby improve its torsional stiffness and strength (Hylander, 1979). Theoretical considerations as well as experimental observation, however, establish that the polar moment of inertia is an inappropriate measure of torsional stiffness in the mandible (Daegling and Hylander, 1998). Still, Hylander's (1979) proxy is still widely utilized out of convenience, and on the grounds that large comparative samples yield higher statistical power (Taylor, 2002).…”

“…I argue here that corpus breadth is a misleading proxy for torsional stiffness or strength and appears to be informative in broad allometric comparisons only because it is likely to increase in rough proportion to torsional strength as a correlated artifact of somatic scaling. Daegling and Hylander (1998) identified two alternative models that were suitable for inferring structural competence of the mandible under torsional loads. Both the hollow elliptical and thin tube models require knowledge of cortical bone distribution, but the thin tube model makes no assumptions about cross-sectional geometry and is therefore well-suited for investigating how well corpus breadth relates to torsional strength (the hollow ellipse model utilizes the breadth dimension in its calculation and cannot be considered an independent measure).…”