Human mandibular shape is associated with masticatory muscle force

Understanding how and to what extent forces applied to the mandible by the masticatory muscles influence its form, is of considerable importance from clinical, anthropological and evolutionary perspectives. This study investigates these questions. Head CT scans of 382 adults were utilized to measure masseter and temporalis muscle cross-sectional areas (CSA) as a surrogate for muscle force, and 17 mandibular anthropometric measurements. Sixty-two mandibles of young individuals (20–40 years) whose scans were without artefacts (e.g., due to tooth filling) were segmented and landmarked for geometric morphometric analysis. The association between shape and muscle CSA (controlled for size) was assessed using two-block partial least squares analysis. Correlations were computed between mandibular variables and muscle CSAs (all controlled for size). A significant association was found between mandibular shape and muscle CSAs, i.e. larger CSAs are associated with a wider more trapezoidal ramus, more massive coronoid, more rectangular body and a more curved basal arch. Linear measurements yielded low correlations with muscle CSAs. In conclusion, this study demonstrates an association between mandibular muscle force and mandibular shape, which is not as readily identified from linear measurements. Retrodiction of masticatory muscle force and so of mandibular loading is therefore best based on overall mandibular shape.

The current study was therefore carried out to gain greater insight into the associations between muscle forces and mandibular morphology. Such a study requires living individuals and is best established using computerized tomography (CT) scans in which bone and soft tissue shadows are visible. More so, muscle cross-sectional areas (CSA) from CT, magnetic resonance imaging and ultrasound scans can be used as a surrogate for the peak forces that can be generated by the masticatory muscles 7,9,11,12,[27][28][29][30][31][32][33] .
The aims of this study were to identify associations between masticatory muscle force (as estimated by CSAs) and mandibular shape and to relate variations in specific muscle CSAs (masseter and temporalis) to specific aspects of mandibular shape and size variation. Two hypotheses were tested: H0 1 -no association exists between the CSAs of the masseter and temporalis muscles and mandibular shape; H0 2 -no associations exist between temporalis and masseter CSAs and anthropometric (linear and angular) measurements of the mandible. The first hypothesis was examined using shape variables derived from landmark data. The second hypothesis was tested using Pearson correlations to assess relationships between muscle CSAs and mandibular variables. The second analysis was carried out for practical reasons since archeological mandibles are sometimes too fragmented to readily allow shape analysis.

Material and Methods
The study included 382 individuals (193 males and 189 females) aged 18-80 years who had undergone a head and neck CT scan at Carmel Medical Center, Haifa (Brilliance 64, Philips Medical System, Cleveland, Ohio: slice thickness 0.9-3.0 mm, pixel spacing 0.3-0.5 mm, 120 kV, 250-500 mAs, number of slices 150-950 and Matrix 512*512), between the years 2000 and 2012. All CT scans were carried out for diagnostic purposes, where a CT scan was medically necessary. Inclusion criteria were as follows: age between 20 and 80 years, intact lower incisors, and at least two teeth of the posterior unit (premolars and/or molars) on each side. Exclusion criteria included the absence of the lower incisors; dental implants and metal restorations that interfere with imaging and so, measurement; prominent facial and mandibular asymmetry; craniofacial, temporomandibular joint, or muscular disorders; trauma; previous surgery on the head and neck region (based on medical files or signs on the skull); and technically aberrant CT scans. This study was approved by the ethical board of the Carmel Medical Center, Israel (number: 0066-11-CMC) and followed their guidelines.
Evaluating muscle areas (Force). CSAs of the masseter and temporalis muscles (which reflect peak force) were measured using the planar mode for sectioning CT stacks, and the 'region of interest' tool for tracing outlines and measuring areas available on the Brilliance Workspace Portal (Philips v. 2.6.1.5). Masticatory muscle CSAs were measured following the method of Weijs and Hillen 28 (Fig. 1). The muscle CSA was controlled for mandibular size using either mandibular centroid size (in GM analyses) or the geometric mean of the mandibular linear measurements (MGM -for analyses of anthropometric data; see statistical analysis section).
Evaluating mandibular shape using the geometric morphometrics. 62 mandibles (30 males and 32 females) were segmented and reconstructed from the CT stacks using Amira (v6.1). Semi-automated segmentation of CT sections was carried out based on grey level thresholds. Manual refinement of segmentation was carried out where needed. The inclusion criteria for this group were: age 20-40 years to control for age effect  (1)  on muscle CSAs and CT scans with no artefacts that may interfere with the segmentation (e.g., tooth filling and dental crown). The 3D form of the mandible was characterized using 35 landmarks and 60 curve semi-landmarks (representing 13 curves; Tables 1 and 2; Fig. 2). The landmarks, curves and curve semi-landmarks were placed on the mandibular surface mesh using the EVAN Toolbox software (v.1.71) and semi-landmark sliding was carried out to minimise bending energy 34 .
Evaluating mandibular shape and orientation using linear and angular measurements. 17 linear, CSA and angular measurements of the mandible were obtained. These include traditional measurements and non-standard ones that are feasible due to the use of CT scans 35 (Table 3; Fig. 3). All measurements were taken directly from CT scans using the Brilliance Workspace Portal (Philips v. 2.6.1.5). All linear measurements were controlled for mandibular size using the MGM (square roots of the CSA measurements of the mandible were divided by the MGM) following the principles presented in Jungers et al. 36 . This accounts for the effects of general size when assessing how the resulting indices covary with muscle CSAs, also scaled for MGM. Landmark based analyses. Reliability: Intra-and inter-observer variation in the shape of mandibular landmark configurations was assessed using five randomly selected mandibles. To assess intraobserver variation, one researcher (AP) placed the landmarks and curve semilandmarks twice on each mandible with a week-long interval between landmarking sessions. To assess inter-observer variation, the set of landmarks was placed by an additional independent researcher (GA). To examine variations in shape, Principal components analysis (PCA) was carried out following a General Procrustes Analysis (GPA) of the landmark data, which eliminates differences in orientation, location, and size 37 . The significances of Procrustes distances within and between repeated measurements of specimens and by researchers were assessed via permutation tests (1000 random permutations) 38 .
Mandibular shape and muscle CSAs. For the 3D shape analysis, Cartesian coordinates were converted into shape variables through GPA. PCA was carried out to examine shape variation in the general population. Since mandibular size affects shape variation [19][20][21] we controlled for allometry. Shape variables were regressed and standardized on centroid size (allometrically adjusted). A linear regression of log square roots of muscle CSAs on log centroid size (i.e., the independent variable) was used to allometrically adjust muscle CSAs.
Two-block Partial least squares (2B-PLS) analysis was carried out, separately for males and females, on allometrically adjusted muscle CSAs as one block and the adjusted shape variables as the second block, to examine the association between shape and muscle CSAs when allometry is accounted for. Visualization of shape changes along the PLS vector was carried out by warping the mean surface mesh using a triplet of thin plate splines (TPS) in the EVAN Toolbox (v. 1.71) 39 .  Analysis of linear measurements. Reliability. Anthropometric measurement reliability was assessed using 15 randomly selected mandibles. To assess intraobserver variation in the linear and angular dimensions, a single researcher (TST) carried out the measurements twice with a two-week interval between each attempt. To assess interobserver error, measurements were taken by an additional independent researcher (HM or VS). Intraclass correlation coefficient (ICC) analysis was carried out to examine the reproducibility of the measurements and was interpreted according to the categorization method of Cicchetti 40 .

Mandibular linear measurements and muscle CSAs.
A Kolmogorov-Smirnov test was carried out to test for the normality of distributions of the variables. Logarithmic transformation was carried out for variables that did not distribute normally. The association between muscle CSAs and mandibular measurements, both controlled for mandibular size (MGM), were assessed by calculating Pearson correlation coefficients. Data were controlled for sex (analyses were carried out separately for males and females) and age (using the partial correlation test).
Data availability. The datasets analyzed during the current study are available from the corresponding author on request.

Results
Reliability analysis. Permutation tests of Procrustes distances indicated that differences in shape among repeated measurements of specimens were significantly greater than those among specimens, when landmarks were placed by the same researcher (p < 0.01). No significant differences in shape distances between researchers were found (p > 0.05). ICC results for the reproducibility of the linear, CSA and angular measurements showed good to excellent agreement (0.84≤ICC≤0.995 for intraobserver variation and 0.71≤ICC≤0.996 for interobserver variation) 40 .
Mandibular shape variation. 37% of shape variation in the sample is explained by the first and second principal components of shape (PCs) (Fig. 4). Most female mandibles are located in the lower quadrants, whereas males are scattered mainly in the upper quadrants. The main aspect of shape variation represented by the first PC comprises changes in the shape of the mandibular body, which, warping along PC1, varies from being more triangular (right) to more rectangular (left). The main aspect of shape variation represented by the second PC relates  to the ascending ramus which varies in shape between an elongated narrow parallelogram (lower) to a wide low trapezoid (upper), with the coronoid process varying in shape between an elevated-narrow-pointed structure to a low-wide-rounded one (Fig. 4).
The association between mandibular shape and muscle CSA. 2B-PLS analyses between the first singular warps (SW1) of mandibular shape and the CSAs of the masseter and temporalis muscles, for both males

Measurement Definition
Bi-gonial breadth Distance between right and left gonion  Table 3. Linear, angular and cross-sectional area (CSA) measurements of the mandible.  Table 3 for definitions. and females, yielded high and significant correlations (r = 0.734, p < 0.001 and r = 0.697, p < 0.001, respectively) (Fig. 5). The visualization of the PLS for both males (Fig. 6) and females (Fig. 7) demonstrates that mandibles with large muscle CSAs manifest a wider more trapezoidal-shaped ramus, more massive coronoid, rectangular body and a curved basal arch. Mandibles with small CSA are characterized by a tall and narrow ramus (more like a parallelogram) with a pointed coronoid, triangular body and a more triangular basal arch. Table 4. Most mandibular measurements manifested either significant, small correlations or no significant correlations with muscle CSAs (Table 4). This analysis has yielded three types of parameters: 1. Parameters not associated with muscle CSAs: mandibular angle, mandibular angle width, coronoid width, coronoid width CSA, body length, body height at premolars and its CSA. 2. Parameters associated with muscle CSAs in either males or females. For females: bigonial breadth (with masseter CSA). For males: mandibular angle CSA (with both muscle CSAs), ramus width and its CSA (with temporalis CSA), body height at molar (with temporalis CSA), body height CSA at molar (with both muscle CSAs) and symphysis thickness (with temporalis CSA) and chin height (with masseter CSA). 3. Parameters associated with muscle CSAs for both males and females: ramus length (with masseter CSA) and coronoid height (with both muscle CSAs).

Discussion
The current study shows that mandibular shape varies to a certain extent as a function of the forces applied to it by the temporalis and masseter muscles (Fig. 5). This is anticipated based on prior studies; "…the size and shape …of the jaws should reflect muscle size and activity" 13 (p. 136). The major aspects of mandibular shape that covary with muscle CSAs, independent of sex, are, with larger CSAs, a wider trapezoidal ramus, a massive coronoid, a more rectangular body and curved basal arch. In contrast, mandibles with a tall and narrow ramus    (parallelogram-like), a more pointed coronoid, a more triangular body and a more triangular basal arch were associated with smaller muscle CSA (Figs 6 and 7). In the absence of studies that directly measure the association between mandibular shape and masticatory muscle CSAs, our discussion is largely based on circumstantial evidence, namely, the associations between mandibular morphology and dental attrition (i.e., indicating extensive function of the masticatory muscles) and mandibular morphology and subsistence economy (i.e., softer diet requires less mastication force). For example, several anthropological studies have reported an association between excessive attrition and broad mandibles [41][42][43][44] . It has been shown that agriculturalists (softer diet) had relatively short and broad mandibles with a tall, angled ramus and coronoid process, whereas hunter-gatherer populations (harder diet) have relatively long and narrow mandibles with a short, upright ramus and coronoid process 24 . These results are in agreement with our observations. Modern population studies offer similar insights. For example, individuals suffering from bruxism manifest broad mandibles [45][46][47] ; subjects with strong bite forces tend to have a low mandibular plane angle and wide mandible, whereas those with weak bite force tend to have a high mandibular plane angle and narrow mandible 1,48,49 .
Direct evidence for an association between mandibular morphology and masticatory muscle force comes from clinical studies. For example, in individuals suffering from myotonic dystrophy of the masticatory muscles a greater mandibular angle and excessive vertical growth of the mandible was reported (e.g. 6,50 ); and enlargement of the coronoid process was observed in individuals with temporalis muscle hyperactivity 51 .
Several animal experimental studies provide further support for this association. For example, pigs raised on a soft rather than a normal diet, manifested changes in jaw morphology and dental arch dimensions 52 ; and reduced function of the masticatory system in rats caused changes in the width, height and thickness of the alveolar process and smaller cross-sectional area of the bone 16,17,53,54 .
Of the 17 linear parameters used in our study, 10 manifested significant low associations with muscle CSAs. Yet, these associations varied with sex and muscle (temporalis and/or masseter). Only two linear measurements (coronoid height and ramus length) showed significant, but weak, associations with muscle CSAs in both males and females when controlled for size. These results coincide with our shape analysis and highlight some of the biomechanical factors involved in mandibular design. For example, the anterior ramal border, from coronoid process downward, is under considerable tension during mastication 55 , potentially explaining the involvement of the temporalis and masseter muscles in shaping the ramus and coronoid. The increase in mandibular CSAs at the ramus, mandibular angle and body at the molar region, with muscle CSAs is in accordance with previous studies suggesting that the thickening and increase in height of the posterior part of the mandibular body with increased muscle strain is to enable the mandible to resist the parasagittal and transverse bending stresses, which are concentrated in these regions [56][57][58][59] . The idea of bone apposition over areas with increased demand to withstand bending force has been demonstrated in several human and animal studies (e.g. 16,17,60 ).
Finally, all linear measurements in our study show, after correction for size, low correlations with muscle CSAs. This raises the question of why our findings do not support those of previous studies (e.g. 14,28,49 ) that found high correlations. This might be because studies suggesting much higher correlations between mandibular linear measures and mastication force (e.g. 28,49 ) did not correct their data for mandibular size. It is noteworthy that very few allometrically adjusted anthropometric variables show significant correlations with muscle CSAs. Those that do, largely reflect the findings of the PLS analyses of Figs 5-7 in that they measure ramus and coronoid form. However, given the strength of these associations they are likely useful only to predict the strength of masticatory  muscle action among sample means rather than individuals. Indeed, the weak correlations shown by all variables stand in contrast to the PLS analyses of landmark data which find significant overall associations. This finding emphasizes the need to take a multivariate or landmark based approach to dietary retrodiction in archaeological populations. Even with such an approach, population loading history is most reliably inferred, rather than the diet or masticatory muscle force of any one individual.