J Forensic Sci, January 2015, Vol. 60, No. 1 doi: 10.1111/1556-4029.12641 Available online at: onlinelibrary.wiley.com
PAPER ANTHROPOLOGY
Hana Brzobohat a,1,2 M.S.; V aclav Krajıcek,3 Ph.D.; Zdenek Hor ak,4 Ph.D.; and Jana Velemınska,1 Ph.D.
Sex Classification Using the Three-Dimensional Tibia Form or Shape Including Population Specificity Approach*
ABSTRACT: The aims of this study were to enable geometric morphometric sex classification using tibial proximal and distal sexual dimorphism and to evaluate the secular trend of tibial shape/form from the early 20th century to the present day. The study samples consisted of 61 adult tibias from an early 20th-century Czech population and 57 three-dimensional tibias from a 21st-century population. Discriminant function analysis with cross-validation was carried out to assess the accuracy of sex classification. Shape analysis revealed significant sex differences in both tibial extremities of the 21st-century sample and in the proximal tibia of the 20th-century population. Sex-based divergence varied between the analyzed samples, raising the issues of population specificity and diachronic change. Classification using tibial form was more successful than using tibial shape. The highest values of correct assignment (91.80% and 88.52%) were found using the form from the early 20th Czech population.
KEYWORDS: forensic science, geometric morphometrics, sexual dimorphism, optical scanning, computed tomography-derived models, tibia
Forensic anthropologists need to develop methods for estimating sex that are applicable to different skeletal elements in a complete or fragmentary state. Recently, a new technique combining both morphometric and meristic characteristics has become popular. Two-dimensional (2-D) and three-dimensional (3-D) geometric morphometric methods have exceeded evolutionary and clinical applications and offer an alternative method for identifying the sex of unknown skeletal remains (1,2). The application of these methods in forensic anthropology is still relatively new (3). In contrast to the intensively studied shape variability of cranium and pelvic bones (1,3,4), other components of the human skeleton are rather neglected from this point of view. Only a few geometric morphometric studies have been published on human long bones of the lower (5–12) and upper limbs (2,13). Generally, skeletal sexual dimorphism involves differences in size, shape, robusticity, and muscularity. Sex influences musculoskeletal health (14,15) and sex differences have also been identified at the tissue level in trabecular bone structures and in bone mineral content (16–18). Significant sexually dimorphic traits in
1 Department of Anthropology and Human Genetics, Faculty of Science, Charles University, Vinicna 7, 128 43 Prague, Czech Republic. 2 Institute of Archaeology of the Academy of Sciences, Letenska 4, 118 01, Prague, Czech Republic. 3 Department of Software and Computer Science Education, Faculty of Mathematics and Physics, Charles University, Malostranske namesti 25, 118 00, Prague, Czech Republic. 4 Laboratory of Biomechanics, Faculty of Mechanical Engineering, Czech Technical University, Technicka 4, 166 07, Prague, Czech Republic. *Supported by research grant number 613012 from The Charles University Grant Agency. Received 4 Nov. 2013; and in revised form 14 Feb. 2014; accepted 26 Feb. 2014.
© 2014 American Academy of Forensic Sciences
the tibia have been verified through biomechanics (19–21), traditional morphometrics (22–24), and by a recent geometric morphometric study (6). In addition, numerous clinical papers have described a relationship between proximal tibial morphology and sexual dimorphism (25). The clinical relevance of such results and the necessity of sex-specific knee implant design have been discussed within the orthopedic community (26–28). The sexbased differences in tibial plateau geometry found in these studies should be considered when assessing the risk of knee injury, susceptibility to osteoarthritis and success of total knee arthroplasty (29). Conventional classification procedures enable an evaluation of the effect of sex on the size and shape of the tibia, revealing that variations due to sex are profound enough to allow accurate determination but are limited by population specificity. Researchers using traditional approaches have shown that both proximal and distal tibial ends are sexually dimorphic (22,23,29–32). In a previous study, a detailed landmark-based geometric morphometric evaluation of these differences in an early medieval Czech sample was performed. Apart from the effect of sex, the results were discussed in terms of another two potential sources of variation in shape variability (age at death and social status of the individual). Our findings demonstrated that sex and age significantly influenced proximal shape, while distal tibial morphology was affected only by sex (33). The main objectives of this study were to extend the time range of the earlier study, detect any shape differences in proximal tibia in 20th-century and 21st-century populations, describe potential temporal changes, and define the regions where sexual dimorphism is most pronounced. Comparing two populations from different dates, we aimed to verify the relevance and appropriateness of commonly used osteological collection data. With 29
30
JOURNAL OF FORENSIC SCIENCES
this we intended to test the potential applicability of landmark techniques and the accuracy of sex determination from tibias for forensic investigations.
Material and Methods Early 20th-Century Sample A series of 61 adult tibias of known age and sex from a central European population, obtained from the Pachner collection, was used for this study. This unique collection is housed in The Institute of Anatomy, 1st Faculty of Medicine, Charles University, Prague (Czech Republic), and comprises more than 300 postcranial skeletons with documentation (the data covering age at death, sex, and autopsy year). It originated in the first half of the 20th century for the purposes of studying the sexual dimorphism of the human skeleton. According to Pachner (34), the individuals represented are mostly of lower socioeconomic status. The material has often been used for studying and verifying methods of sex determination by means of both traditional (35) and geometric morphometrics (36). Only well-preserved left tibias without pathology from adult individuals were included in the study: 31 tibias from men ranging in age from 35 to 87 years, and 30 tibias from women ranging in age from 20 to 72 years (Table 1). 21st-Century Sample The bony surfaces of left tibias were extracted from clinical anonymized computed tomography (CT) scan sequences of 57 adult individuals who had undergone CT angiography (years 2010–2013) (30 were males ranging in age from 31 to 68 years, and 27 were females ranging in age from 33 to 91 years) (Table 1). We included only normal, nonpathological bones without any indication of injury or advanced degenerative and senescence characteristics in the analysis. Data Acquisition To digitize the early 20th-century tibias, a smartSCAN 3D-HE scanner (Breuckmann, GmbH, Meersburg, Germany) was used. This topometric system works on the basis of fringe projection on the physical model and recording of the modified patterns with two digital cameras with a resolution of 1.4 Mpix. Based on the system configuration (field of view (FOV) M-600, 480 mm 9 360 mm) used, the resolution in both the x and y axes was 360 lm. The resulting datasets, imaging the surface of the bone in four different positions, were processed and merged using OPTOCAT (Breuckmann, GmbH) software to make the final data object, which was exported in .stl format. Another 57 surface models of left tibias were created using reconstruction methods employing virtual 3-D modeling from the Digital Imaging and Communications in Medicine (DICOM) image sequence of CT outputs. The initial raw data were TABLE 1––Characteristics of the datasets by age and sex (N, number of individuals; M, males; F, females). All
20–40 years
40–60 years
60 + years
Population
N
M
F
N
M
F
N
M
F
N
M
F
20th century 21st century
61 57
31 30
30 27
11 3
1 2
10 1
30 17
18 14
12 3
20 37
12 14
8 23
acquired by scanning the lower limbs using a Siemens Definition AS+ (Siemens, Erlangen, Germany) tomograph. The slice increment was set at 0.5 mm, with an X-ray tube adjustment of 120 kV and 51.6 mAs. The FOV was defined by a matrix of 512 9 512 pixels in 12-bit gray-scale levels. These adjustments correspond to the usual settings for angiography examinations. The tomographic data underwent image processing, and then the bone surface was defined using a large number of polygons (.stl format). A 3-D model of the reconstructed tibial bony surface was created for a series of lower limb CT scans using the specialized software Mimics (Materialise, Leuven, Belgium). All areas of the CT scan with a specified range of gray values (GV) corresponding to bone tissue were recognized and manually thresholded in the first segmentation step. Then the 3-D geometric model was built according to a semi-automatically generated mask, which defined the boundaries of the osseous structure precisely and covered them with a triangular mesh surface. Computed tomography images can provide fairly accurate quantitative information on bone geometry (37). The accuracy of different acquisition, segmentation, and reconstruction tools has been evaluated in numerous studies identifying the average deviation between laser/optical scans and CT bone models (38–41). It is dependent on the resolution of the individual scans, pixel size, and slice distance. The appropriateness of including such data was justified in our study (41). The segmentation process has been proven to be reliable with an average deviation of 0.27 mm of registered surface models, indicating that landmark locations can be determined in CT-derived models with an acceptable degree of error (41). Geometric Morphometrics For each tibia, the 3-D coordinates of 21 landmarks (defined in Table 2) were registered on the polygonal model of the tibia using the Morphome3cs software (Fig. 1, Table 2). The long bones of the lower limbs are generally very poor in type I landmarks, according to the Bookstein classification (42), so it was necessary to determine most of them as extreme points of the structures/curvatures or as the points furthest away from the anatomical axes. At the same time, the condition of their absolute homology, in the sense of the homology of their position on the corresponding geometric structures of the various individuals that they represented, was met (43,44). Next, all the tibia models were averaged using a method called Procrustes imposition (45), to obtain a mean tibial shape. With this method, all the models are rotated and translated to minimize roto-translational discrepancies between them by minimizing the sum of the squared distances between homologous landmarks. Shape variability was analyzed using principal component analysis (PCA) to explore the relationships between groups. The PCA scatter plot represents the variation among the different individuals in the sample. The statistical significance of differences between the groups was assessed using a Hotelling test; to determine the number of components describing the common variance of the datasets, we used a broken-stick method (46). A significance level of a = 0.05 was used for all tests. Discriminant function analyses with cross-validation were carried out to assess the accuracy of the sex classification of the discriminant functions, first using the PCA scores from the Procrustes shape space and then using PCA scores from the generalized Procrustes analysis (GPA) residuals, including size. Size differences between males and females were assessed by measuring the centroid size. Its statistical significance was tested with a
ET AL. BRZOBOHATA TABLE 2––List of landmarks and landmark types according to Bookstein (42). Landmarks 5–8 were identified assuming the maximum width of the plateau was fixed in the horizontal position. Landmarks 10–13 were identified with the margo anterior fixed in the vertical position. Number
Type
1 2 3 4 5 6 7 8 9 10
I I III III II II II II III III
11
III
12
I
13
III
14
III
15 16 17 18 19 20
II II II II II II
21
II
.
SEX CLASSIFICATION USING 3D TIBIA FORM OR SHAPE
31
measure of shape sexual traits. The relationship between size and shape was evaluated using linear regression analysis (47). For statistical and geometrical analysis, Morphome3cs software (2013) was used (48).
Description Medial intercondylar tubercle Lateral intercondylar tubercle Maximum point of width of the tibial plateau (medial side) Maximum point of width of the tibial plateau (lateral side) Maximum anterior point of the medial facet Maximum posterior point of the medial facet Maximum anterior point of the lateral facet Maximum posterior point of the lateral facet Central point of oval formation of the tibial tuberosity Point on the inferior edge of the medial condyle vertically below point 3 Point on the inferior edge of the medial condyle vertically below point 6 Point on the inferior edge of the lateral condyle at the intersection with the edge of the fibular facet Point on the inferior edge of the lateral condyle vertically below point 4 Maximum distal point of the medial malleolus (computed as the most distant point from landmark 1) Medial anterior corner of the facies articularis inferior Lateral anterior corner of the facies articularis inferior Lateral posterior corner of the facies articularis inferior Medial posterior corner of the facies articularis inferior Maximum medial point of the medial malleolus Maximum anterior and lateral points over the fibular incisura Maximum posterior and lateral points over the fibular incisura
two-sample permutation t-test. Centroid size (42) is defined as the square root of the sum of the squared Euclidean distances from each landmark to the mean of the configuration of landmark coordinates: it is an expression of overall size of a morphological structure. Cross-validation score was used as a
Measurement Error To evaluate intra-observation error, all landmarks were digitized on three bones five times, with a time interval of at least 1 day between taking individual measurements. The measurement error was evaluated as the standard deviation of N measurements of an individual landmark (49): rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XN ððxi xÞ2 þ ðyi yÞ2 þ ðzi zÞ2 Þ=3N r¼ i¼1 The overall intra-observer measurement error was an average of all the measurement errors of the full landmark configuration.
Results Measurement Error The degree of inaccuracy in localizing landmarks was tested with five repeated digitizations of landmark configurations of three individuals and calculating the standard deviation of the full landmark configuration according to von Cramon-Taubadel et al. (49). The final average intra-observer error for all landmarks was 0.29 mm, with the highest deviation for landmark number 10 (0.48 mm) and the lowest one for landmark 14 (0.03 mm). As expected, type II and III landmarks were generally more difficult to identify than type I landmarks, according to the Bookstein classification (42). Landmark intra-observer error was one degree lower than average standard deviation of landmarks in the sample (7.36 mm), and the overall differences between repeatedly measured specimens were statistically significant (MANOVA,
FIG. 1––The landmark configuration used to describe the shape of the proximal (above) and distal (below) left tibia. The proximal articular end is presented in frontal, superior and dorsal views; the distal epiphysis is shown in lateral, medial and inferior views. Refer to Table 2 for the landmark descriptions employed.
32
JOURNAL OF FORENSIC SCIENCES
p < 0.0001). Therefore, the intra-observer error was acceptable and it had no influence on the results of the shape analyses even for the most problematic points. Shape Analysis In the early 20th-century sample, statistically significant shape differences were identified only for the proximal tibia (Table 3). The PCA performed on shape variables showed a large overlap between the sexes and the first principal component (PC1, accounting for 15.16% of the total variance) did not separate male and female proximal extremities very clearly (Fig. 2). However, it was obvious that female tibias had more negative values for PC2 (12.27% of the total variance), while males had more positive values. The frontal view showed the male lateral tibial condyle to be higher and narrower, the medial condyle to be relatively lower on the rear part, the medial tubercle to project more cranially and the tibial tuberosity to project more laterally than female proximal tibias. The lateral view showed that the tibial tuberosity was shifted more anteriorly and the line connecting the anterior edge of the medial facet with the tibial tuberosity was less precipitous in males. The anterior edge of the lateral articular facet was localized more superiorly, and the lower margin of the lateral condyle was closer to the front of the bone in the male tibias. The superior view showed a more noticeable lateral shift of the tuberosity and a relatively medio-laterally wider tibial plateau in male tibias (Fig. 3). Discriminant analysis with cross-validation yielded a 67.93% accuracy in sex determination using 17 PCA scores from the proximal end (Table 3). Sexual dimorphism represented by cross-validation score did not correlate with centroid size. In the 21st-century sample, permutation tests showed that both the proximal and distal tibia were sexually dimorphic in the shape space (Table 3). When size was removed from the analysis, the PCA was more sensitive to subtle shape differences, spreading over a large number of principal components (PC): in the proximal tibia, PC1 accounted for 16.93% and PC2 accounted for 14.32% of the total variance. Distally, the first two components explained 18.27% (PC1) and 14.81% (PC2) of the total variance. Male individuals had a tendency to cluster with negative values of PC1 (Fig. 2). Similar to the 20th-century sample, the height of the male lateral condyle was increased laterally, the medial tubercle was shifted more superiorly and medially, and tibial tuberosity was localized more anteriorly. The line connecting the anterior edge of the plateau with the tibial
tuberosity was less precipitous, and the articular surface was relatively antero-posteriorly wider in the superior view in males (Fig. 4). Other shape differences included a more medially facing tibial tuberosity in male proximal tibias and a slight lateral shift of the upper lateral edge of the lateral condyle in males when viewed frontally. Laterally, in males, we identified an anterior shift of the front edge of the medial facet, more superiorly localized landmarks defining the rear part of the lateral condyle, and a more anteriorly shifted point on the lower edge of the medial condyle. From the superior view, a noticeable elongation of the male lateral articular facet was observed together with the previously mentioned medial shift of the tibial tuberosity. The mean shape of the male distal tibia was distinguished by a slightly superiorly and anteriorly shifted apex of the medial malleolus, an antero-posteriorly wider articular facet and medial malleolus, an elongated and more forward-localized anterior margin of the facet and a narrower fibular incisura (Fig. 4). Consequently, the individuals were grouped according to their morphological affinity with an acceptable success rate for sex determination (using PC scores from the shape space) for both the upper (73.21%) and lower (76.79% accuracy) end of the tibia (Table 3). Sexual dimorphism was related to size both in proximal (R = 0.2789; R2 = 0.0778; p = 0.0373) and distal tibia (R = 0.3360; R2 = 0.1129; p = 0.0113). These findings show that sexual dimorphism represented by cross-validation score correlates with centroid size. Size was a substantial part of the sexual dimorphism in this sample and large proximal and distal tibias corresponded with more masculine traits and vice versa. After removing allometric trend from the data, there was no significant difference between the groups (p = 0.3245 proximally; p = 0.488 distally). Similar to the previous cases, in the pooled sample, a substantial part of the variability was scattered throughout a large number of components when size was normalized during GPA. The mean sex-based differences in shape were similar to those found in the early 20th century Czech population. Proximally, viewed frontally, the male lateral tibial condyle was higher, the medial tubercle was shifted superiorly, and the tibial tuberosity tended to locate more laterally than in female proximal tibias. Viewed laterally, the tibial tuberosity was more prominent frontally and the line connecting the anterior edge of the medial facet with the tibial tuberosity was less precipitous in males. Viewed superiorly, a slight lateral and noticeable anterior shift of the tuberosity was seen in the male tibia (Fig. 5). Sexual dimorphism represented by cross-validation score was not correlated with centroid size.
TABLE 3––Results of linear discriminant analysis with and without cross-validation using the PC scores from Procrustes shape space. The statistical significance of group differences (in bold, p < 0.05) was assessed using a nonparametric variant of Hotelling’s T2 test with 2000 permutations.
Sample 20th century
Tibia Proximal Distal
21st century
Proximal Distal
Pooled sample
Proximal Distal
N M F M F M F M F M F M F
31 30 31 30 30 27 30 27 61 57 61 57
Correctly classified without cross-validation (%)
Correctly classified with cross-validation (%)
p-value
p-value (permutation)
81.97
67.93
0.0543
0.0485
57.38
44.26
0.6629
0.6563
85.71
73.21
0.0033
0.0025
82.14
76.79
0.0059
0.0065
80.34
70.09
0.0217
0.0232
67.52
52.14
0.1931
0.2000
ET AL. BRZOBOHATA
.
SEX CLASSIFICATION USING 3D TIBIA FORM OR SHAPE
33
FIG. 2––Scatter plots (PC1 vs. PC2) based on shape variables for the proximal (left column) and distal (right column) tibia with 95% confidence ellipses (first row, 20th-century population sample; second row, 21st-century population sample; third row, pooled sample, black circles, females; white circles, males).
Form Analysis Unlike the first analysis, regarding shape–size space, both sexes of the 20th century sample were more differentiated along the PC1. The first two components explained more than 61% of the total variance, and statistically significant shape differences were identified in both the proximal and distal tibia (Table 4). The percentage of correct sex determination based on these variables reached 91.80% for proximal and 88.52% for distal ends. For the distal tibia, PC1 accounted for 53.91% and PC2 for 7.63% of the total variance (Fig. 6). Sexually dimorphic traits of the proximal tibia corresponded with those described in shape space. The male distal tibia was characterized by a more posteriorly and superiorly situated apex of the medial malleolus and a relatively wider fibular incisura and lateral margin of the lower articular facet. In contrast, the medial margin of the articular
facet was shorter in males than females. A slight anterior and superior shift was pronounced at the point defining the medial extremity of the medial malleolus (displayed as mean shapes to depict shifts in the landmarks better) (Fig. 3). The 21st century males and females were more grouped in the shape–size space, with the first two components explaining proximally 47.82% and 9.39%, respectively (Fig. 6). Distally, the first two components explained 48.93% (PC1) and 9.78% (PC2) of the total variance when size was included into the analysis. Male individuals had a tendency to cluster with negative values of PC1 (Fig. 6). When discriminant analysis was performed using shape and size, the percentage of correct determinations increased to 87.5% (proximally) and 85.71% (distally) (Table 4). When the pooled sample (118 individuals) of tibias was divided by sex, the accuracy obtained was 88.03% proximally and 87.18% distally (Table 4). The contributions of the first two
34
JOURNAL OF FORENSIC SCIENCES
FIG. 3––Visualization of proximal and distal tibial shape differences in the 20th-century sample. Wireframes representing the mean shapes are displayed in frontal, lateral and superior views (left column, proximal tibia) and in anterior, inferior and medial views (right column, distal tibia). Female, bold links; male, thin links. The displacement vectors are magnified three times to show the differences more clearly.
PC and distribution of the PCA scores are displayed in Fig. 6. PC1 discriminated between the two sexes to a considerable degree, but with an overlap; female tibias tended to cluster with positive values of PC1. Sexually dimorphic traits of the proximal tibia corresponded with those described in shape space. Distally, the apex of the medial malleolus was shifted superiorly and anteriorly in males. Moreover, the male lateral margin of the articular facet was elongated, while the medial margin was shifted anteriorly, the fibular incisura was narrower, and the point defining the medial extremity of the medial malleolus was localized more posteriorly (Fig. 5). Population Specificity By comparing these two samples, we identified a group of identical sex-based traits distinguishable in both a 20th- and 21st
century Czech population, that is, in males there was an increased height of the lateral condyle, superior shift of the medial tubercle, prominence of the tibial tuberosity, inclination of the line connecting the anterior edge of the plateau with the tuberosity, proportionality of the plateau, a superior shift of the apex of the medial malleolus, and elongated anterior and lateral margins of the lower articular facet, in comparison with the mean shape of the females (Figs 3, 4). However, sexual dimorphism was not uniformly expressed in the tibia and statistically significant differences were found between the pooled male and female groups separated by time period (regarding both shape and form). The tibias of 21st century individuals (males and females were evaluated independently) differed, with a more medial position of the tuberosity, a posterior shift of the anterior edge of the tibial plateau and the rear part of the proximal portion, a medio-laterally wider medial
ET AL. BRZOBOHATA
.
SEX CLASSIFICATION USING 3D TIBIA FORM OR SHAPE
35
FIG. 4––Visualization of proximal and distal tibial shape differences in the 21st-century sample. Wireframes representing the mean shapes are displayed in frontal, lateral and superior views (left column, proximal tibia) and in anterior, inferior and medial views (right column, distal tibia). Female, bold links; male, thin links. The displacement vectors are magnified three times to show the differences more clearly.
malleolus, a medio-laterally narrower lower articular facet and a more medially localized apex of the medial malleolus (not displayed). These temporal changes were found in both sexes. Eliminating the interference of size from the analysis revealed statistically significant differences between the sexes in both tibial extremities of the 21st century sample but only in the proximal tibial extremity in the 20th century sample. The percentage of individuals correctly classified using discriminant analysis, and shape variables did not reach appreciable levels (from 67.93% to 76.79%) (Table 3). Moreover, sex-based divergence varied between the samples analyzed, raising the issue of its population specificity, diachronic changes, and the need for appropriate reference data.
The comparison of centroid sizes showed that the 21st century proximal and distal tibias were markedly larger (p = 0.001) compared with the 20th century sample. Discussion and Conclusions In a previous study, we tested whether the shape of tibial extremities of adults is sex-specific, and whether it changes with senescence or with presumed social status in an early medieval population. The most significant differences in the morphology of the articular ends were found between the groups separated by sex (33). Based on this examination, we decided to verify the findings and describe the sexually dimorphic traits in 20th cen-
36
JOURNAL OF FORENSIC SCIENCES
FIG. 5––Visualization of proximal and distal tibial shape differences in the pooled sample. Wireframes representing the mean shapes are displayed in frontal, lateral and superior views (left column, proximal tibia) and in anterior, inferior and medial views (right column, distal tibia). Female, bold links; male, thin links. The displacement vectors are magnified three times to show the differences more clearly.
TABLE 4––Results of linear discriminant analysis with and without cross-validation using the PC scores of GPA residuals including size. The statistical significance of group differences (in bold, p < 0.05) was assessed using a nonparametric variant of Hotelling’s T2 test with 2000 permutations.
Sample 20th century
Tibia Proximal Distal
21st century
Proximal Distal
Pooled sample
Proximal Distal
N M F M F M F M F M F M F
31 30 31 30 30 27 30 27 61 57 61 57
Correctly classified without cross-validation (%)
Correctly classified with cross-validation (%)
p-value
p-value (permutations)
91.80
91.80
PAPER ANTHROPOLOGY
Hana Brzobohat a,1,2 M.S.; V aclav Krajıcek,3 Ph.D.; Zdenek Hor ak,4 Ph.D.; and Jana Velemınska,1 Ph.D.
Sex Classification Using the Three-Dimensional Tibia Form or Shape Including Population Specificity Approach*
ABSTRACT: The aims of this study were to enable geometric morphometric sex classification using tibial proximal and distal sexual dimorphism and to evaluate the secular trend of tibial shape/form from the early 20th century to the present day. The study samples consisted of 61 adult tibias from an early 20th-century Czech population and 57 three-dimensional tibias from a 21st-century population. Discriminant function analysis with cross-validation was carried out to assess the accuracy of sex classification. Shape analysis revealed significant sex differences in both tibial extremities of the 21st-century sample and in the proximal tibia of the 20th-century population. Sex-based divergence varied between the analyzed samples, raising the issues of population specificity and diachronic change. Classification using tibial form was more successful than using tibial shape. The highest values of correct assignment (91.80% and 88.52%) were found using the form from the early 20th Czech population.
KEYWORDS: forensic science, geometric morphometrics, sexual dimorphism, optical scanning, computed tomography-derived models, tibia
Forensic anthropologists need to develop methods for estimating sex that are applicable to different skeletal elements in a complete or fragmentary state. Recently, a new technique combining both morphometric and meristic characteristics has become popular. Two-dimensional (2-D) and three-dimensional (3-D) geometric morphometric methods have exceeded evolutionary and clinical applications and offer an alternative method for identifying the sex of unknown skeletal remains (1,2). The application of these methods in forensic anthropology is still relatively new (3). In contrast to the intensively studied shape variability of cranium and pelvic bones (1,3,4), other components of the human skeleton are rather neglected from this point of view. Only a few geometric morphometric studies have been published on human long bones of the lower (5–12) and upper limbs (2,13). Generally, skeletal sexual dimorphism involves differences in size, shape, robusticity, and muscularity. Sex influences musculoskeletal health (14,15) and sex differences have also been identified at the tissue level in trabecular bone structures and in bone mineral content (16–18). Significant sexually dimorphic traits in
1 Department of Anthropology and Human Genetics, Faculty of Science, Charles University, Vinicna 7, 128 43 Prague, Czech Republic. 2 Institute of Archaeology of the Academy of Sciences, Letenska 4, 118 01, Prague, Czech Republic. 3 Department of Software and Computer Science Education, Faculty of Mathematics and Physics, Charles University, Malostranske namesti 25, 118 00, Prague, Czech Republic. 4 Laboratory of Biomechanics, Faculty of Mechanical Engineering, Czech Technical University, Technicka 4, 166 07, Prague, Czech Republic. *Supported by research grant number 613012 from The Charles University Grant Agency. Received 4 Nov. 2013; and in revised form 14 Feb. 2014; accepted 26 Feb. 2014.
© 2014 American Academy of Forensic Sciences
the tibia have been verified through biomechanics (19–21), traditional morphometrics (22–24), and by a recent geometric morphometric study (6). In addition, numerous clinical papers have described a relationship between proximal tibial morphology and sexual dimorphism (25). The clinical relevance of such results and the necessity of sex-specific knee implant design have been discussed within the orthopedic community (26–28). The sexbased differences in tibial plateau geometry found in these studies should be considered when assessing the risk of knee injury, susceptibility to osteoarthritis and success of total knee arthroplasty (29). Conventional classification procedures enable an evaluation of the effect of sex on the size and shape of the tibia, revealing that variations due to sex are profound enough to allow accurate determination but are limited by population specificity. Researchers using traditional approaches have shown that both proximal and distal tibial ends are sexually dimorphic (22,23,29–32). In a previous study, a detailed landmark-based geometric morphometric evaluation of these differences in an early medieval Czech sample was performed. Apart from the effect of sex, the results were discussed in terms of another two potential sources of variation in shape variability (age at death and social status of the individual). Our findings demonstrated that sex and age significantly influenced proximal shape, while distal tibial morphology was affected only by sex (33). The main objectives of this study were to extend the time range of the earlier study, detect any shape differences in proximal tibia in 20th-century and 21st-century populations, describe potential temporal changes, and define the regions where sexual dimorphism is most pronounced. Comparing two populations from different dates, we aimed to verify the relevance and appropriateness of commonly used osteological collection data. With 29
30
JOURNAL OF FORENSIC SCIENCES
this we intended to test the potential applicability of landmark techniques and the accuracy of sex determination from tibias for forensic investigations.
Material and Methods Early 20th-Century Sample A series of 61 adult tibias of known age and sex from a central European population, obtained from the Pachner collection, was used for this study. This unique collection is housed in The Institute of Anatomy, 1st Faculty of Medicine, Charles University, Prague (Czech Republic), and comprises more than 300 postcranial skeletons with documentation (the data covering age at death, sex, and autopsy year). It originated in the first half of the 20th century for the purposes of studying the sexual dimorphism of the human skeleton. According to Pachner (34), the individuals represented are mostly of lower socioeconomic status. The material has often been used for studying and verifying methods of sex determination by means of both traditional (35) and geometric morphometrics (36). Only well-preserved left tibias without pathology from adult individuals were included in the study: 31 tibias from men ranging in age from 35 to 87 years, and 30 tibias from women ranging in age from 20 to 72 years (Table 1). 21st-Century Sample The bony surfaces of left tibias were extracted from clinical anonymized computed tomography (CT) scan sequences of 57 adult individuals who had undergone CT angiography (years 2010–2013) (30 were males ranging in age from 31 to 68 years, and 27 were females ranging in age from 33 to 91 years) (Table 1). We included only normal, nonpathological bones without any indication of injury or advanced degenerative and senescence characteristics in the analysis. Data Acquisition To digitize the early 20th-century tibias, a smartSCAN 3D-HE scanner (Breuckmann, GmbH, Meersburg, Germany) was used. This topometric system works on the basis of fringe projection on the physical model and recording of the modified patterns with two digital cameras with a resolution of 1.4 Mpix. Based on the system configuration (field of view (FOV) M-600, 480 mm 9 360 mm) used, the resolution in both the x and y axes was 360 lm. The resulting datasets, imaging the surface of the bone in four different positions, were processed and merged using OPTOCAT (Breuckmann, GmbH) software to make the final data object, which was exported in .stl format. Another 57 surface models of left tibias were created using reconstruction methods employing virtual 3-D modeling from the Digital Imaging and Communications in Medicine (DICOM) image sequence of CT outputs. The initial raw data were TABLE 1––Characteristics of the datasets by age and sex (N, number of individuals; M, males; F, females). All
20–40 years
40–60 years
60 + years
Population
N
M
F
N
M
F
N
M
F
N
M
F
20th century 21st century
61 57
31 30
30 27
11 3
1 2
10 1
30 17
18 14
12 3
20 37
12 14
8 23
acquired by scanning the lower limbs using a Siemens Definition AS+ (Siemens, Erlangen, Germany) tomograph. The slice increment was set at 0.5 mm, with an X-ray tube adjustment of 120 kV and 51.6 mAs. The FOV was defined by a matrix of 512 9 512 pixels in 12-bit gray-scale levels. These adjustments correspond to the usual settings for angiography examinations. The tomographic data underwent image processing, and then the bone surface was defined using a large number of polygons (.stl format). A 3-D model of the reconstructed tibial bony surface was created for a series of lower limb CT scans using the specialized software Mimics (Materialise, Leuven, Belgium). All areas of the CT scan with a specified range of gray values (GV) corresponding to bone tissue were recognized and manually thresholded in the first segmentation step. Then the 3-D geometric model was built according to a semi-automatically generated mask, which defined the boundaries of the osseous structure precisely and covered them with a triangular mesh surface. Computed tomography images can provide fairly accurate quantitative information on bone geometry (37). The accuracy of different acquisition, segmentation, and reconstruction tools has been evaluated in numerous studies identifying the average deviation between laser/optical scans and CT bone models (38–41). It is dependent on the resolution of the individual scans, pixel size, and slice distance. The appropriateness of including such data was justified in our study (41). The segmentation process has been proven to be reliable with an average deviation of 0.27 mm of registered surface models, indicating that landmark locations can be determined in CT-derived models with an acceptable degree of error (41). Geometric Morphometrics For each tibia, the 3-D coordinates of 21 landmarks (defined in Table 2) were registered on the polygonal model of the tibia using the Morphome3cs software (Fig. 1, Table 2). The long bones of the lower limbs are generally very poor in type I landmarks, according to the Bookstein classification (42), so it was necessary to determine most of them as extreme points of the structures/curvatures or as the points furthest away from the anatomical axes. At the same time, the condition of their absolute homology, in the sense of the homology of their position on the corresponding geometric structures of the various individuals that they represented, was met (43,44). Next, all the tibia models were averaged using a method called Procrustes imposition (45), to obtain a mean tibial shape. With this method, all the models are rotated and translated to minimize roto-translational discrepancies between them by minimizing the sum of the squared distances between homologous landmarks. Shape variability was analyzed using principal component analysis (PCA) to explore the relationships between groups. The PCA scatter plot represents the variation among the different individuals in the sample. The statistical significance of differences between the groups was assessed using a Hotelling test; to determine the number of components describing the common variance of the datasets, we used a broken-stick method (46). A significance level of a = 0.05 was used for all tests. Discriminant function analyses with cross-validation were carried out to assess the accuracy of the sex classification of the discriminant functions, first using the PCA scores from the Procrustes shape space and then using PCA scores from the generalized Procrustes analysis (GPA) residuals, including size. Size differences between males and females were assessed by measuring the centroid size. Its statistical significance was tested with a
ET AL. BRZOBOHATA TABLE 2––List of landmarks and landmark types according to Bookstein (42). Landmarks 5–8 were identified assuming the maximum width of the plateau was fixed in the horizontal position. Landmarks 10–13 were identified with the margo anterior fixed in the vertical position. Number
Type
1 2 3 4 5 6 7 8 9 10
I I III III II II II II III III
11
III
12
I
13
III
14
III
15 16 17 18 19 20
II II II II II II
21
II
.
SEX CLASSIFICATION USING 3D TIBIA FORM OR SHAPE
31
measure of shape sexual traits. The relationship between size and shape was evaluated using linear regression analysis (47). For statistical and geometrical analysis, Morphome3cs software (2013) was used (48).
Description Medial intercondylar tubercle Lateral intercondylar tubercle Maximum point of width of the tibial plateau (medial side) Maximum point of width of the tibial plateau (lateral side) Maximum anterior point of the medial facet Maximum posterior point of the medial facet Maximum anterior point of the lateral facet Maximum posterior point of the lateral facet Central point of oval formation of the tibial tuberosity Point on the inferior edge of the medial condyle vertically below point 3 Point on the inferior edge of the medial condyle vertically below point 6 Point on the inferior edge of the lateral condyle at the intersection with the edge of the fibular facet Point on the inferior edge of the lateral condyle vertically below point 4 Maximum distal point of the medial malleolus (computed as the most distant point from landmark 1) Medial anterior corner of the facies articularis inferior Lateral anterior corner of the facies articularis inferior Lateral posterior corner of the facies articularis inferior Medial posterior corner of the facies articularis inferior Maximum medial point of the medial malleolus Maximum anterior and lateral points over the fibular incisura Maximum posterior and lateral points over the fibular incisura
two-sample permutation t-test. Centroid size (42) is defined as the square root of the sum of the squared Euclidean distances from each landmark to the mean of the configuration of landmark coordinates: it is an expression of overall size of a morphological structure. Cross-validation score was used as a
Measurement Error To evaluate intra-observation error, all landmarks were digitized on three bones five times, with a time interval of at least 1 day between taking individual measurements. The measurement error was evaluated as the standard deviation of N measurements of an individual landmark (49): rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XN ððxi xÞ2 þ ðyi yÞ2 þ ðzi zÞ2 Þ=3N r¼ i¼1 The overall intra-observer measurement error was an average of all the measurement errors of the full landmark configuration.
Results Measurement Error The degree of inaccuracy in localizing landmarks was tested with five repeated digitizations of landmark configurations of three individuals and calculating the standard deviation of the full landmark configuration according to von Cramon-Taubadel et al. (49). The final average intra-observer error for all landmarks was 0.29 mm, with the highest deviation for landmark number 10 (0.48 mm) and the lowest one for landmark 14 (0.03 mm). As expected, type II and III landmarks were generally more difficult to identify than type I landmarks, according to the Bookstein classification (42). Landmark intra-observer error was one degree lower than average standard deviation of landmarks in the sample (7.36 mm), and the overall differences between repeatedly measured specimens were statistically significant (MANOVA,
FIG. 1––The landmark configuration used to describe the shape of the proximal (above) and distal (below) left tibia. The proximal articular end is presented in frontal, superior and dorsal views; the distal epiphysis is shown in lateral, medial and inferior views. Refer to Table 2 for the landmark descriptions employed.
32
JOURNAL OF FORENSIC SCIENCES
p < 0.0001). Therefore, the intra-observer error was acceptable and it had no influence on the results of the shape analyses even for the most problematic points. Shape Analysis In the early 20th-century sample, statistically significant shape differences were identified only for the proximal tibia (Table 3). The PCA performed on shape variables showed a large overlap between the sexes and the first principal component (PC1, accounting for 15.16% of the total variance) did not separate male and female proximal extremities very clearly (Fig. 2). However, it was obvious that female tibias had more negative values for PC2 (12.27% of the total variance), while males had more positive values. The frontal view showed the male lateral tibial condyle to be higher and narrower, the medial condyle to be relatively lower on the rear part, the medial tubercle to project more cranially and the tibial tuberosity to project more laterally than female proximal tibias. The lateral view showed that the tibial tuberosity was shifted more anteriorly and the line connecting the anterior edge of the medial facet with the tibial tuberosity was less precipitous in males. The anterior edge of the lateral articular facet was localized more superiorly, and the lower margin of the lateral condyle was closer to the front of the bone in the male tibias. The superior view showed a more noticeable lateral shift of the tuberosity and a relatively medio-laterally wider tibial plateau in male tibias (Fig. 3). Discriminant analysis with cross-validation yielded a 67.93% accuracy in sex determination using 17 PCA scores from the proximal end (Table 3). Sexual dimorphism represented by cross-validation score did not correlate with centroid size. In the 21st-century sample, permutation tests showed that both the proximal and distal tibia were sexually dimorphic in the shape space (Table 3). When size was removed from the analysis, the PCA was more sensitive to subtle shape differences, spreading over a large number of principal components (PC): in the proximal tibia, PC1 accounted for 16.93% and PC2 accounted for 14.32% of the total variance. Distally, the first two components explained 18.27% (PC1) and 14.81% (PC2) of the total variance. Male individuals had a tendency to cluster with negative values of PC1 (Fig. 2). Similar to the 20th-century sample, the height of the male lateral condyle was increased laterally, the medial tubercle was shifted more superiorly and medially, and tibial tuberosity was localized more anteriorly. The line connecting the anterior edge of the plateau with the tibial
tuberosity was less precipitous, and the articular surface was relatively antero-posteriorly wider in the superior view in males (Fig. 4). Other shape differences included a more medially facing tibial tuberosity in male proximal tibias and a slight lateral shift of the upper lateral edge of the lateral condyle in males when viewed frontally. Laterally, in males, we identified an anterior shift of the front edge of the medial facet, more superiorly localized landmarks defining the rear part of the lateral condyle, and a more anteriorly shifted point on the lower edge of the medial condyle. From the superior view, a noticeable elongation of the male lateral articular facet was observed together with the previously mentioned medial shift of the tibial tuberosity. The mean shape of the male distal tibia was distinguished by a slightly superiorly and anteriorly shifted apex of the medial malleolus, an antero-posteriorly wider articular facet and medial malleolus, an elongated and more forward-localized anterior margin of the facet and a narrower fibular incisura (Fig. 4). Consequently, the individuals were grouped according to their morphological affinity with an acceptable success rate for sex determination (using PC scores from the shape space) for both the upper (73.21%) and lower (76.79% accuracy) end of the tibia (Table 3). Sexual dimorphism was related to size both in proximal (R = 0.2789; R2 = 0.0778; p = 0.0373) and distal tibia (R = 0.3360; R2 = 0.1129; p = 0.0113). These findings show that sexual dimorphism represented by cross-validation score correlates with centroid size. Size was a substantial part of the sexual dimorphism in this sample and large proximal and distal tibias corresponded with more masculine traits and vice versa. After removing allometric trend from the data, there was no significant difference between the groups (p = 0.3245 proximally; p = 0.488 distally). Similar to the previous cases, in the pooled sample, a substantial part of the variability was scattered throughout a large number of components when size was normalized during GPA. The mean sex-based differences in shape were similar to those found in the early 20th century Czech population. Proximally, viewed frontally, the male lateral tibial condyle was higher, the medial tubercle was shifted superiorly, and the tibial tuberosity tended to locate more laterally than in female proximal tibias. Viewed laterally, the tibial tuberosity was more prominent frontally and the line connecting the anterior edge of the medial facet with the tibial tuberosity was less precipitous in males. Viewed superiorly, a slight lateral and noticeable anterior shift of the tuberosity was seen in the male tibia (Fig. 5). Sexual dimorphism represented by cross-validation score was not correlated with centroid size.
TABLE 3––Results of linear discriminant analysis with and without cross-validation using the PC scores from Procrustes shape space. The statistical significance of group differences (in bold, p < 0.05) was assessed using a nonparametric variant of Hotelling’s T2 test with 2000 permutations.
Sample 20th century
Tibia Proximal Distal
21st century
Proximal Distal
Pooled sample
Proximal Distal
N M F M F M F M F M F M F
31 30 31 30 30 27 30 27 61 57 61 57
Correctly classified without cross-validation (%)
Correctly classified with cross-validation (%)
p-value
p-value (permutation)
81.97
67.93
0.0543
0.0485
57.38
44.26
0.6629
0.6563
85.71
73.21
0.0033
0.0025
82.14
76.79
0.0059
0.0065
80.34
70.09
0.0217
0.0232
67.52
52.14
0.1931
0.2000
ET AL. BRZOBOHATA
.
SEX CLASSIFICATION USING 3D TIBIA FORM OR SHAPE
33
FIG. 2––Scatter plots (PC1 vs. PC2) based on shape variables for the proximal (left column) and distal (right column) tibia with 95% confidence ellipses (first row, 20th-century population sample; second row, 21st-century population sample; third row, pooled sample, black circles, females; white circles, males).
Form Analysis Unlike the first analysis, regarding shape–size space, both sexes of the 20th century sample were more differentiated along the PC1. The first two components explained more than 61% of the total variance, and statistically significant shape differences were identified in both the proximal and distal tibia (Table 4). The percentage of correct sex determination based on these variables reached 91.80% for proximal and 88.52% for distal ends. For the distal tibia, PC1 accounted for 53.91% and PC2 for 7.63% of the total variance (Fig. 6). Sexually dimorphic traits of the proximal tibia corresponded with those described in shape space. The male distal tibia was characterized by a more posteriorly and superiorly situated apex of the medial malleolus and a relatively wider fibular incisura and lateral margin of the lower articular facet. In contrast, the medial margin of the articular
facet was shorter in males than females. A slight anterior and superior shift was pronounced at the point defining the medial extremity of the medial malleolus (displayed as mean shapes to depict shifts in the landmarks better) (Fig. 3). The 21st century males and females were more grouped in the shape–size space, with the first two components explaining proximally 47.82% and 9.39%, respectively (Fig. 6). Distally, the first two components explained 48.93% (PC1) and 9.78% (PC2) of the total variance when size was included into the analysis. Male individuals had a tendency to cluster with negative values of PC1 (Fig. 6). When discriminant analysis was performed using shape and size, the percentage of correct determinations increased to 87.5% (proximally) and 85.71% (distally) (Table 4). When the pooled sample (118 individuals) of tibias was divided by sex, the accuracy obtained was 88.03% proximally and 87.18% distally (Table 4). The contributions of the first two
34
JOURNAL OF FORENSIC SCIENCES
FIG. 3––Visualization of proximal and distal tibial shape differences in the 20th-century sample. Wireframes representing the mean shapes are displayed in frontal, lateral and superior views (left column, proximal tibia) and in anterior, inferior and medial views (right column, distal tibia). Female, bold links; male, thin links. The displacement vectors are magnified three times to show the differences more clearly.
PC and distribution of the PCA scores are displayed in Fig. 6. PC1 discriminated between the two sexes to a considerable degree, but with an overlap; female tibias tended to cluster with positive values of PC1. Sexually dimorphic traits of the proximal tibia corresponded with those described in shape space. Distally, the apex of the medial malleolus was shifted superiorly and anteriorly in males. Moreover, the male lateral margin of the articular facet was elongated, while the medial margin was shifted anteriorly, the fibular incisura was narrower, and the point defining the medial extremity of the medial malleolus was localized more posteriorly (Fig. 5). Population Specificity By comparing these two samples, we identified a group of identical sex-based traits distinguishable in both a 20th- and 21st
century Czech population, that is, in males there was an increased height of the lateral condyle, superior shift of the medial tubercle, prominence of the tibial tuberosity, inclination of the line connecting the anterior edge of the plateau with the tuberosity, proportionality of the plateau, a superior shift of the apex of the medial malleolus, and elongated anterior and lateral margins of the lower articular facet, in comparison with the mean shape of the females (Figs 3, 4). However, sexual dimorphism was not uniformly expressed in the tibia and statistically significant differences were found between the pooled male and female groups separated by time period (regarding both shape and form). The tibias of 21st century individuals (males and females were evaluated independently) differed, with a more medial position of the tuberosity, a posterior shift of the anterior edge of the tibial plateau and the rear part of the proximal portion, a medio-laterally wider medial
ET AL. BRZOBOHATA
.
SEX CLASSIFICATION USING 3D TIBIA FORM OR SHAPE
35
FIG. 4––Visualization of proximal and distal tibial shape differences in the 21st-century sample. Wireframes representing the mean shapes are displayed in frontal, lateral and superior views (left column, proximal tibia) and in anterior, inferior and medial views (right column, distal tibia). Female, bold links; male, thin links. The displacement vectors are magnified three times to show the differences more clearly.
malleolus, a medio-laterally narrower lower articular facet and a more medially localized apex of the medial malleolus (not displayed). These temporal changes were found in both sexes. Eliminating the interference of size from the analysis revealed statistically significant differences between the sexes in both tibial extremities of the 21st century sample but only in the proximal tibial extremity in the 20th century sample. The percentage of individuals correctly classified using discriminant analysis, and shape variables did not reach appreciable levels (from 67.93% to 76.79%) (Table 3). Moreover, sex-based divergence varied between the samples analyzed, raising the issue of its population specificity, diachronic changes, and the need for appropriate reference data.
The comparison of centroid sizes showed that the 21st century proximal and distal tibias were markedly larger (p = 0.001) compared with the 20th century sample. Discussion and Conclusions In a previous study, we tested whether the shape of tibial extremities of adults is sex-specific, and whether it changes with senescence or with presumed social status in an early medieval population. The most significant differences in the morphology of the articular ends were found between the groups separated by sex (33). Based on this examination, we decided to verify the findings and describe the sexually dimorphic traits in 20th cen-
36
JOURNAL OF FORENSIC SCIENCES
FIG. 5––Visualization of proximal and distal tibial shape differences in the pooled sample. Wireframes representing the mean shapes are displayed in frontal, lateral and superior views (left column, proximal tibia) and in anterior, inferior and medial views (right column, distal tibia). Female, bold links; male, thin links. The displacement vectors are magnified three times to show the differences more clearly.
TABLE 4––Results of linear discriminant analysis with and without cross-validation using the PC scores of GPA residuals including size. The statistical significance of group differences (in bold, p < 0.05) was assessed using a nonparametric variant of Hotelling’s T2 test with 2000 permutations.
Sample 20th century
Tibia Proximal Distal
21st century
Proximal Distal
Pooled sample
Proximal Distal
N M F M F M F M F M F M F
31 30 31 30 30 27 30 27 61 57 61 57
Correctly classified without cross-validation (%)
Correctly classified with cross-validation (%)
p-value
p-value (permutations)
91.80
91.80
