1 THE ANATOMICAL RECORD 300: (2017) Sexual Dimorphism and Population Affinity in the Human Zygomatic Structure Comparing Surface to Outline Data STEFAN SCHLAGER* AND ALEXANDRA R UDELL Albert-Ludwigs-Universitat Freiburg Medizinische Fakultat, Biological Anthropology, Hebelstr. 29, Freiburg, Baden-W urttemberg 79104, Germany ABSTRACT The human zygomatic structure, consisting of the zygomatic bone and the zygomatic process of the temporal bone, is an essential part of the masticatory apparatus and has been shown to reflect population history and sexual dimorphism to varying degrees. In this study, we analyzed the predictive value of the outlines vs. the complete surface shape of the zygomatic bone in a sample of 98 Chinese (50 $, 48#) and 96 Germans (49 $, 47#). We first applied a surface registration process based on statistical shape modeling. A dense set of 1,480 pseudo-landmarks was then sampled automatically from the surface of the pooled mean shape and three curves were digitized manually along the outlines of the zygomatic bone. Both sets of pseudo-landmarks were automatically transferred to all specimens. Analysis of sex and population affinity showed both factors to be independently significant, but the interaction between them was not. Population affinity could be predicted quite accurately with correct classification of 97.9% using the surface data and 93.3% with the curve data. Sexual dimorphism was less distinct with 89.2% correct sex determination when using surface information compared with 77.8% when using the curve data. Population-related shape differences were captured primarily in the outlines, while sexual dimorphism is distributed more uniformly throughout the entire surface of the zygomatic structure. Anat Rec, 300: , VC 2016 Wiley Periodicals, Inc. Key words: zygoma; function; geometric morphometrics; statistical shape modeling The determination of ancestry and sex of unknown skeletal remains is an essential task in forensic anthropology. A vast amount of literature exists on different methods of determining sex and ancestry on basis of the human skull (Giles & Elliot, 1963; Jantz & Ousley, 2005; Sholts et al., 2011; Garvin & Ruff, 2012; Garvin et al., 2014). While most methods combine characteristics of different skull regions to reach best possible results (Giles & Elliot, 1963; Johnson et al., 1989; Ubelaker et al., 2002; Franklin et al., 2005; Jantz & Ousley, 2005; Ousley & Jantz, 2005; Kolatorowicz, 2006; Walker, 2008; Elliott & Collard, 2009; Guyomarc h & Bruzek, 2011; Fortes de Oliveira et al., 2012; Ogawa et al., 2013; Abdel Fatah et al., 2014), depending on the situation, only parts of the skull might be preserved. The zygomatic bone is part of most methods concerning the determination of sex and ancestry (Steyn & Iscan, 1998; Oskam *Correspondence to: Stefan Schlager, Albert-Ludwigs- Universitat Freiburg Medizinische Fakultat, Biological Anthropology, Hebelstr. 29 Freiburg 79117, Germany. Fax: Received 29 February 2016; Revised 4 May 2016; Accepted 6 June DOI /ar Published online in Wiley Online Library (wileyonlinelibrary. com). VC 2016 WILEY PERIODICALS, INC.
2 TABLE 1. Landmark definitions. A visualization of landmark placement is given in Fig. 1 No. Landmark Description 1/2 Jugale (left/right) Angular point of zygomatic bone and superior margin of the temporal zygomatic process 3 Subspinale Transition of frontal downward edge of the spina nasalis anterior into the processus alveolaris 4 Rhinion In medial plane the most caudal point of the nasal bridge (as the sutura internasalis, traditionally used to define this landmark, is often not visible in CT-Scans) 5/6 Foramen supraorbitale (left/right) Placed at the orbital rim in same sagittal plane as the foramen supraorbitale, in case there is an incisura supraorbitalis, the point ist placed at the most medial part of it 7/8 Foramen infraorbitale (left/right) ANALYZING ZYGOMATIC SHAPE 227 on the orbital rim Placed at most superior point of foramen infraorbitale et al., 2009; Sholts et al., 2011; Fortes de Oliveira et al., 2012; Sholts & W arml ander, 2012; Abdel Fatah et al., 2014). It is an essential part of the masticatory apparatus and hence subject to strains and stresses induced by the masticatory muscles (Kupczik et al., 2007; R ohrle & Pullan, 2007; Davis et al., 2010; Wroe et al., 2010; Prado et al., 2013; Smith et al., 2015). Diet, climate and population history have been shown to influence the shape of the zygomatic bone (Gonzalez-Jose et al., 2005; von Cramon-Taubadel, 2009b; Paschetta et al., 2010; von Cramon-Taubadel, 2011b; von Cramon-Taubadel, 2014; Noback & Harvati, 2015a,b). Studies dealing with morphological and traditional anthropometric methods found the sex differences in the zygomatic structure to be statistically significant, but the variance of metrics of the sexes overlap in a way that valid sex determination is not possible (Monticelli & Graw, 2008). Also, the subjectivity of morphological methods has been highly criticized (Monticelli & Graw, 2008). Due to the complex shape of the zygomatic bone, traditional anthropometric measurements are challenging. During the past 20 years, the methods of Geometric Morphometrics (GM) have been more and more applied in physical anthropology (Rohlf & Marcus, 1993; Adams et al., 2004; Bookstein et al., 2004; Slice, 2005; Mitteroecker & Gunz, 2009; Adams et al., 2013; McNulty & Vinyard, 2015) and have been found to considerably improve the analysis of shape and the visualization of the results. Their application in forensic anthropologic studies concerning different parts of the human skeleton (Gonzales et al., 2009), especially the skull (Pretorius et al., 2006; Bigoni et al., 2007; Schlager et al., 2008; Oettle et al., 2009; Bigoni et al., 2010), has been widely spread since then. While especially early studies working with Geometric Morphometrics analyze 2D or 3D sets of anatomically or mathematically defined landmarks, even more geometric information can be taken into account when analyzing sets of so-called semi-landmarks capturing the shape of curves (Williams & Slice, 2010, 2014) or even surfaces, where no anatomical landmarks are available (Bookstein, 1997; Gunz et al., 2005; Adams et al., 2013; Gunz & Mitteroecker, 2013). The purpose of our study is to test how classification results differ when analyzing the contours of the zygomatic structure, consisting of the zygomatic bone and the zygomatic process of the temporal bone, compared with the geometric information of its surface. Our aim is to determine population specific shape variation and sexual dimorphism. As the zygomatic bone is devoid of distinct landmarks, we apply a semi-automatic surface registration approach to sample a dense set of corresponding 3D coordinates from all specimens. MATERIALS AND METHODS Sample The data under study consist of 194 anonymized CTscans taken in course of medical treatment in the Ninth Peoples Hospital, Shanghai (Chinese individuals) and the University Medical Center Freiburg (German individuals). Only individuals aged over 20 years with no signs of pathologies in the region of interest (ROI) were included. The sample is composed of 98 Chinese (50 $, 48 #) and 96 Germans (49 $, 47#). The average ages for Chinese males (45.6 years) and females (43.9 years) as well as European males (44.7 years) are fairly similar, with the European females being considerably older on average (55.8 years). Processing and analyses of patient related data were performed in compliance with the statutes of the ethics committee of the University Medical Center Freiburg. Data Acquisition After importing the medical images into the software VoximVR version 6.0, 1 the bone tissue was segmented based on a gray-value thresholding and exported as triangular surface mesh. In addition, eight anatomical landmarks were placed manually on the skull surface (Table 1 and Fig. 1). For analyzing the shape of the zygomatic structure, we used an approach based on densely sampled pseudolandmarks. Most studies on surface shape employ sliding semi-landmarks (Gunz & Mitteroecker, 2013) that are allowed to slide along the bone surface to minimize a specific metric, such as bending energy or Procrustes distance (Gunz et al., 2005; Perez et al., 2006). We found this approach to be unsuitable for analyzing the zygomatic structure, as the latter lacks reliable anatomical landmarks that could serve as cornerstones to keep the semi-landmarks from clustering together while trying to minimize the given metric. To tackle this problem we applied a surface registration based on statistical shape models (SSM) (see below and Fig. 2), wherein the eight cranio-facial landmarks were used only as priors to facilitate and guide the registration process. After extraction of surface/curve coordinates from within a defined ROI (Fig. 1), all shapes were aligned in 1
3 228 SCHLAGER AND R UDELL Fig. 1. Skull with landmarks (red, Nos. 2 and 7 not visible in this view); ROI (gray); curves C1 (red), C2 (yellow), C3 (green); and 1480 pseudo-landmarks (black). the same space by a Full Procrustes Analysis (Dryden & Mardia, 1998) using the R-package Morpho (Schlager, 2014a). Surface Registration Surface registration and statistical analyses were carried out using the statistical/mathematical computing environment R (R Core Team, 2015). Statistical shape models are generally calculated based on empirical data and describe the variability of a shape in a population (Cootes & Taylor, 1999, 2004; L uthi et al., 2012). Incorporating prior information about the variability of an anatomical structure, they can be of great help in regularizing the registration processes (Berendsen et al., 2013; Ciller et al., 2015): Seeking valid spatial correspondences between datasets, those possible correspondences that lead to invalid empirical shapes can easily be identified and discarded. In this study, a Gaussian Process Model (GPM a generalized version of an SSM) was first calculated based solely on the information of a template mesh and a set of B-spline kernels defining a synthetic covariance structure between the vertices of this mesh. This is based on the assumption that vertices close to each other show stronger covariance than those further apart (Williams & Rasmussen, 2006; L uthi et al., 2011), which induces a measure of smoothness in the fitting procedure. This first model incorporated no empirical data concerning variation and was only used as a preliminary SSM, regularizing the fitting of the template to 10 randomly selected specimens, using an elastic iteratively closest point (ICP) procedure. Our registration algorithm can be outlined as follows: 1. Align target rigidly to the SSM/GPM using landmarks (Fig. 2a). 2. Constrain the model based on the landmarks to ensure homology regarding these landmarks (Fig. 2b) (L uthi et al., 2011). 3. Starting with the mean of the constrained SSM/GPM, iteratively search for valid closest points (taking into account mesh topology).
4 Fig. 2. Intermediate steps in the registration process. (a) Two meshes aligned by landmarks (red: target mesh; gray: mean of SSM); (b) SSM constrained to landmarks (red: target mesh; gray: mean of constrained SSM); (c) smooth displacement field after three iterations; (d) final registration result (red: target mesh; gray wireframe: registered template); (e) heatmap of distances between registration result and target mesh.
5 230 SCHLAGER AND R UDELL Fig. 3. Curves C1 C3 transferred automatically to four randomly selected specimens using established mesh correspondences. 4. Calculate a smooth displacement field from the detected correspondences using a Gaussian smoothing kernel (Fig. 2c) (Moshfeghi et al., 1994). 5. Project the result back into model space to ensure valid deformations. 6. To allow for shapes outside the model, a weighted average between the shape suggested by the model and the deformed mesh is computed. Starting with a small weight on the deformed mesh, this weight increases with each iteration (Schlager & G opper, 2015). 7. Constrain the deformation by additionally penalizing mesh distortions as suggested by Amberg (2011) (Final result in Fig. 2d,e). The empirical covariance learned from the 10 random specimens was then added to the initial GPM, combining prior assumptions with empirical information about the midfacial morphology. The resulting SSM was then used to subsequently register the template mesh to all specimens in our sample using the algorithm outlined above. For establishing an initial spatial alignment and guiding the registration process, manually placed anatomical landmarks provide useful information (L uthi et al., 2011). In our case the landmarks were used to align the specimens to the SSM and to constrain the SSM to shapes with corresponding landmarks in a similar position (defined by a standard deviation for the assumed uncertainty due to measurement error) (L uthi et al., 2011; Gerig et al., 2014). This procedure leads to registration results that (a) incorporate anatomical information from landmarks and (b) exhibit a minimum of topological distortion of the template mesh, thereby producing reliable spatial correspondences. Visual inspection confirms this: after transferring the curve coordinates (see below) from the sample mean to all registered surfaces by using these correspondences, curves were placed accurately (Fig. 3). All these steps were carried out using the R-packages mesher (Schlager, 2015a) and RvtkStatismo (Schlager, 2015b), which is an R-implementation of the statistical shape modeling library statismo (L uthi et al., 2012). Extraction of the Zygomatic Structure We defined a ROI by selecting the structures belonging to the zygomatic bone and the processus temporalis. The selection was performed by cropping the mesh representing the sample s average using the Blender v software. As sutures were not visible in the CTdata and the extracted meshes, the medial border was defined by orbitale and the point of maximal curvature at the zygomatic process of the maxilla. The superior border of the region was set just above the incision indicating the fronto-zygomatic suture and the posterior border was set where the zygomatic process emerges from the temporal bone (Fig. 1). 1,480 3D coordinates were sampled within the ROI on the mesh representing the sample s mean shape using Poisson Disk sampling (Cook, 1986), resulting in a dense and evenly distributed point cloud. Exploiting the correspondence between vertices and surface topology throughout the sample, pseudo-homologous coordinates were obtained for each specimen. This was done by transferring the 1480 pseudo-landmarks to all registered meshes using barycentric coordinates (Meyer et al., 2002). Both steps were performed with the R-packages Rvcg (Schlager, 2014b) and mesher (Schlager, 2015a). Curve Extraction Analogous to the coordinates representing the surface geometry, we extracted 3 curves with 100 coordinates each that were sampled on the sample s mean shape and transferred to all specimens using barycentric coordinates (Fig. 1). The curves were placed manually on the mean shape using ISE-MeshTools (Lebrun, 2014). The first curve represents the part of the zygomatic bone which contributes to the orbital rim (C1). It starts at orbitale, the lowest point of the orbital rim, and ends at frontomalare orbitale, the cross point between orbital rim and the frontozygomatic suture. The second curve displays the course of the posterior part of the processus frontalis ossis zygomatici, including the angle between processus frontalis and processus temporalis, further following the superior border of the latter and of the processus zygomaticus ossis temporalis (C2). It starts at the anatomical landmark frontomalare temporale, the most lateral point of frontozygomatic suture, and ends superior to the point where the tuberculum auriculare dissolves posterior into the zygomatic arch. The third curve follows the inferior border of the processus maxillaris ossis zygomatici and of the processus zygomaticus ossis temporalis (C3). Its starting point is zygomaxillare, the most inferior point on the zygomaticomaxillary suture, and its end point is at the anterior point of the tuberculum auriculare, where it evolves from the zygomatic arch. Statistical Analyses To reduce dimensionality, Principal Component Analysis (PCA) was performed and the variables explaining 95% of the sample s variance were used to perform statistical testing sensitive to ill-posed covariance matrices (such as MANOVA and permutation testing based on 2
6 ANALYZING ZYGOMATIC SHAPE 231 TABLE 2. MANOVA of surface shape against population 3 sex Df Pillai Approx F Num Df Den Df Pr(>F) Pop Sex Pop:sex Residuals 190 TABLE 3. MANOVA of linear model curve shape population 3 sex Df Pillai Approx F Num Df Den Df Pr(>F) Pop Sex Pop:sex Residuals 190 The influence of the factors population and sex is significant, the interaction between the two is not significant. Mahalanobis-distances). These were the first 17 Principal Components (PCs) for the curve data and the first 25 PCs for the surface data. To test for significance of the factors population affinity and sex, we ran a MANOVA including an interaction term. The level of significance was set to 0.05 in all tests. To test for group differences, we used parametric MANOVAs, as well as permutation testing on both Mahalanobis-distances, based on the within-group covariance, and on Euclidean distances between group means. For assessing the effect size, we used a MANOVA approach (Langsrud et al., 2007; Langsrud & Mevik, 2012) that allows to avoid scaling by variance, thus displaying Type II Sums of Squares in an unscaled data space. Canonical Variate Analysis (CVA) (Albrecht, 1992) on PC-scores was performed using stepwise variable selection. Classification accuracy was assessed using a leaveone-out cross-validation procedure. For assessing sexual dimorphism the data were corrected for population by using the residuals from the linear model shape against population. To visualize the between group structure in an unscaled space, unlike CV-scores, we used scores from between-group PCAs (Boulesteix, 2005). Stepwise selection was performed using the R-package klar (Weihs et al., 2005) and the variables were selected based on their discriminatory power determined by leave-one-out cross-validation. For assessing population classification nine PCs (PCs 1 5, 7, 14, 19, 24) describing the surface data and 10 (PCs 1, 3 8, 10, 11, 16) for the curve data were selected as classifiers. For testing classification accuracy regarding sexual dimorphism nine variables were used for surface shape (PCs 2, 3, 8, 10, 13, 14, 16, 18, 21) and three for the curves (PCs 3, 11, 16). RESULTS For the surface data both predictors population affinity and sex were found to be highly significant (Table 2) with an insignificant interaction term MANOVA reports population to explain 7.7% of the overall variability and sex 3.0%. The curve data also results in an insignificant interaction term and 9.3% of the total variability explained by population affinity and 2.5% explained by sex, both being significant predictors (Table 3). The visualization of the between group structure of the surface data (Fig. 4) implies a distinct separation between populations and, to a lesser extent, a noticeable expression of sexual dimorphism. The curve data (Fig. 5) again shows a clear separation between populations, but sexes are far less distinct. Classification results (Table 4) based on the selected variables support this impression, providing almost perfect separation between populations with a cross-validated accuracy of 97.9% when using the surface data and still 93.3% when only regarding the outlines of the structure. Sexing accuracy is 89.2% when using surface information (Table 5), compared with 77.8% using curve information only. The visualizations of population averages (Figs. (6 and 7)) suggest the main differences to be located in the frontal process, which is wider in Chinese with a stronger expression of the posterior notch. In Europeans, there is a noticeable S-shape of the inferior rim of the temporal process which in Chinese runs almost straight. When viewed from superior, Chinese show a stronger arching in the lateral direction of the temporal process. The images of sex differences (Figs. (8 and 9)) show a wider angle at the orbital surface of the zygomatic bone in females as well as a more pronounced posterior notch in males. The inferior part of the zygomatic bone is also more pronounced in males in extending more into inferior and frontal directions than in females. The zygomatic arch is bowed stronger in males, leading to be laterally more pronounced in its middle part and forming a more acute angle to the temporal and zygomatic bone than in females. In addition, the male zygomatic arch has larger dimensions in vertical direction. When looking at the contours (Fig. 9), the main shape differences stand out distinctively. DISCUSSION Our results show considerable shape differences of the zygomatic bone and the zygomatic arch, which correlate with population affinity and sex. Classification of the surface data reached an accuracy of 97.9% using population affinity as classifier, with the curve data coming quite close with 93.3% correctly classified individuals. When predicting sex, the shape information contained in
7 232 SCHLAGER AND R UDELL Fig. 4. Scores of between-group PCA on surface shape with the first PC showing a clear separation between populations and the second a less distinct separation between sexes. the surface data performed considerably better (89.2% correct classifications) than the curve data (77.8% correctly classified). This indicates that the outline of the zygomatic region, as defined in this study, contains most of the geometric information relevant for distinguishing between the populations under investigation. Sexual dimorphism, on the contrary, is clearly better captured when taking the complete surface shape of the zygomatic structure into account. In both cases a larger portion of shape variation is explained by population affinity (7.7% in surface data and 9.3% in curve data) than by sex (3% in surface and 2.5% in curve data). The relatively low absolute values are due to the fact that in this case all dimensions are considered while the good classification results are based only on those PCs that contain relevant information concerning population affinity and sex. For both, surface and curve data, the interaction between population affinity and sex is insignificant, indicating a similar expression of sexual dimorphism in both populations. These findings confirm the results of Baab et al. (2010) who found in their study on cranial robusticity traits and shape of 14 geographically distinct populations that the robusticity between males and females differed consistently, with males reaching higher robusticity scores than females, but always on an intrapopulation level. Monticelli and Graw (2008) investigated the reliability of the zygomatic bone for sex estimation in a German sample with the morphological methods described in Ferembach et al. (1980) as well as metric analysis. They found the measurements to be highly reliable when compared with the results of purely qualitative morphological examination which is highly subjective and dependent on the experience of the examiner. Still, both methods lead to significant sex differentiation but relatively poor classification results (combined height and width of the left zygomaticum: 71.3%). Though we analyzed a slightly differently defined region, our results show that considering the entire geometric information of the zygomatic region leads to notably better sexing results than those based on height and width alone. Interestingly, the analysis of curves did not perform much better than the measurements taken by Monticelli and Graw (2008). This suggests that sexual dimorphism is expressed in shape differences distributed over the entire surface structure, rather than being concentrated on specific regions. This finding is in contrast to the analysis of population differences where classification accuracy increases only slightly when taking the entire surface structure into account. The reasons for these differences in predicting sex and population affinity might be owed to the biological background of the shape differences. While population affinity might mainly be reflected in differences due to the morphological integration within the cranium and static demands, which can be recorded fairly comprehensively by the outlines, sexual dimorphism might be based on
8 ANALYZING ZYGOMATIC SHAPE 233 Fig. 5. Scores of between-group PCA on curve shape with the first PC showing a clear separation between populations and the second a much less distinct separation between sexes. more minute differences in muscle attachments, that spread throughout the surface and are less distinct. One limitation of our approach is the inability to evaluate subtle differences in the fine texture of the bone surface as described by morphological analysis (e.g., smooth, rough ). The muscle attachment sites, which are mostly described by morphological analysis surely provide additional information concerning sexual dimorphism, which could lead to even better classification results. Williams and Slice (2010, 2014) performed a 3D shape analysis on the outlines of the orbital apertures and the zygomatic arch of European- and African-American males and females. The outlines used in their studies are comparable with the ones analyzed in this study (Fig. 1), with C1 being part of the orbital outline in Williams and Slice (2010), C2 divided into two separate but connected curves, and C3, also split in two curves. Both, the 4 curves describing the zygomatic arch analyzed together and separately, as well as the orbital outline were found to be significantly influenced by ancestry and sex (Williams & Slice, 2014). As diet, climate, and the biomechanics of the masticatory apparatus strongly influence shape adaptations in the zygomatic structure, something should be said about these factors. A popular way to analyze the biomechanics of the human masticatory apparatus is Finite Element Analysis (FEA) (R ohrle & Pullan, 2007; Davis et al., 2010; Wroe et al., 2010; Prado et al., 2013). Prado et al. (2013) performed FEA of the human zygomatic pillar. Their results show that the lateral orbital rim is particularly subjected to physical stress, which is interesting when looking at the shape differences due to population affinity found in our study: The Chinese mean shape is clearly more pronounced in this region which could result from stronger strains and stresses applied here than in Europeans (Fig. 6). Further research could shed light on
9 234 SCHLAGER AND R UDELL TABLE 4. Cross-validated classification results for population affinity based on curve and surface data overall accuracy is 93.3% for the curves and 97.9% for the surface data Classified as Chinese curve/ surface Classified as German curve/ surface Chinese 93/ 97 5 /1 German 8/ 3 88 /93 TABLE 5. Cross-validated classification results for sexing based on curve and surface data overall accuracy is 77.8% for the curves and 89.2% for the surface data Classified as Chinese curve/ surface Classified as German curve/ surface Female 75 /90 24/ 9 Male 19 /12 76/ 83 the question how these differences are related to the overall skull morphology and associated strain and stress distributions. The results of Kupczik et al. (2007) should then be taken into account, as they found that the correct modeling of the zygomatico-temporal suture considerably improved the prediction of the Finite Element Model (FEM), thus generally recommending to include sutures when working with FEM (but see Wang et al. (2012)). Another promising aspect is the combination of GM and FEA, although one challenge is the possible creation of biologically non-existing bone features by statistical shape analysis which might skew subsequent FEAs (Weber, 2015). There are, however, approaches to overcome this limitation either by performing FEA for those individuals of a sample that lie closest to the extremes of the Principal Components (Smith et al., 2015) or by applying landmark point strains, which represent mean von-mises strain values of the surrounding bricks fixed at landmark points (Parr et al., 2012). Smith et al. (2015) found for their FEA of the masticatory forces of a sample of Pan troglodytes that the variation in cranial morphology results in different quantities of strains and stresses, but the distribution patterns of strains and stressess remain almost the same. These strains and stressess were mainly located at the zygomatic arch, the body of the zygoma and the lateral and inferior orbital margins. It is difficult to embed shape analyses on this bone region into a biological context, including functional morphology and population history, as current research leads to diverging results. While some studies found the shape of the zygomatic bone to reflect mainly population history and climate adaptations rather than diet (Noback & Harvati, 2015a), others concluded the exact opposite (Gonzalez-Jose et al., 2005; von Cramon- Taubadel, 2009a,a,), or stated that the zygomatic region is as useful as other craniofacial regions for reconstructing phylogeny (von Cramon-Taubadel, 2009b,b). The diverging findings might be caused by methodological differences and concepts. First of all, to interpret Fig. 6. Template mesh warped onto the mean surface shape of population averages (a) lateral view; (b) viewed from superior. Yellow: Chinese; green: German. Fig. 7. Curve shapes of population averages (a) lateral view; (b) viewed from superior. Yellow: Chinese; green: German. functional aspects of the zygomatic shape, it should be analyzed in its size and position relative to other cranial modules, especially those included in the masticatory apparatus (Noback & Harvati, 2015b). Regional studies on populations changing their subsistence patterns in time found significant shape differences in the masticatory region (Gonzalez-Jose et al., 2005; Paschetta et al., 2010) supporting the assumption that the cranium, as a functional system, might respond differently to
10 ANALYZING ZYGOMATIC SHAPE 235 Fig. 8. Shape differences between male and female average shapes (exaggerated by factor 2; (a) lateral view; (b) viewed from superior. Blue: male; red: female. Fig. 9. Differences between male and female average curve shapes (exaggerated by factor 2; (a) lateral view; (b) viewed from superior. Blue: male; red: female. masticatory stresses varying by geographic region and population history respectively (Noback & Harvati, 2015a). In a recent study, Bastir and Rosas (2016) could show that a more anteriorly positioned middle cranial fossa lead to a flatter upper face and, remarkably, to more sharply angled and hence more laterally positioned zygomatics than in crania with more posteriorly placed middle cranial fossae. Here, the upper face exhibits a more pronounced topology and the zygomatics are only weakly angled, meaning that they are positioned more medially. While we did not include the cranial base topology in our sample, the findings on the upper face and the zygomatics are congruent with our findings on the surface data of European and Chinese individuals (Fig. 6) and those of a previous study on osseous nasal shape in the same sample (Schlager & R udell, 2015). Another factor leading to differing results might be the diverse sets of (sparsely placed) landmarks and the resulting differences in captured structures and superimposition effects. Because all approaches are based on minimizing Procrustes distances using a least-squares approach, differences in the spatial distribution of landmarks can lead to differing estimations of local shape variation. Our results show that the information contained in the outlines and surface of the zygomatic bone considerably improves capturing sexual dimorphism and population differences, compared with studies dealing with sets of sparsely placed anatomical landmarks. Hence, it is most likely that this approach, combined with information on possible influencing factors helps in further understanding the biological role of the zygomatic bone. CONCLUSION We could show conclusively that the shape of the human zygomatic structure differs significantly between sexes and populations included in this analysis. Taking into account the entire surface information leads in both cases to better classification results than only using the curves describing the outlines of the zygomatic structure. While the main shape differences between populations can be visualized as shape differences in the outlines, sexual dimorphism is distributed more uniformly throughout the surface of the zygoma. Thus, classification results for the factor sex can be significantly improved by incorporating information of the entire surface shape. Our method of registering all individuals using a regularized shape modeling approach allowed us to capture the shape of the zygomatic structure surface, despite its lack of reliable anatomical landmarks. OUTLOOK For future studies it would be enlightening to combine densely sampled shape information of the entire cranium with the influence of diet, climate, and geographic region and their intercorrelation. In this way, the knowledge of the biological role of the zygomatic bone as one cranial module among others can be further broadened. Ideally, this should also include FEA to directly model the biomechanical impact of shape changes associated with differences in the cranial modules. The registration procedure applied in this study could provide the additional benefit of extracting and analyzing any subset of the cranial bone structure, due to the corresponding mesh topology of the registered data. ACKNOWLEDGEMENTS We would like to thank Prof. Dr Dr Marc Metzger from the Department of Oral and Maxillofacial Surgery,
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