Václav Krajíček

Skull shape asymmetry and the socioeconomic structure of an early medieval central european society

The socioeconomic structure of an early medieval society from the Mikulčice settlement (Czech Republic) was studied on the basis of an evaluation of the fluctuating and directional asymmetry (DA) of skulls. Two distinct inhabited regions, castle and sub-castle, were compared. Fluctuating asymmetry (FA) was used as a bioindicator of environmental stress, which is thought to have been different in the Mikulčice castle and sub-castle regions. DA is consistent with biomechanical loading, and it was expected to reflect different subsistence patterns. The material consisted of 129 crania from what was presumed to be a higher socioeconomic class (Mikulčice castle) and 71 crania from middle and lower socioeconomic classes (Mikulčice sub-castle). As a comparative sample, 138 crania from modern, lower socioeconomic classes (Pachner Collection) were used. The three-dimensional coordinates of 68 landmarks were digitized and analyzed using geometric morphometrics. In terms of DA, the highest values were recorded in the sub-castle sample and confirmed their lower socioeconomic position, with a grittier and lower protein diet compared with the castle sample. In terms of FA, distinctive differences between the sexes were found. In males, no differences were observed between castle and sub-castle, and the lowest FA values were recorded. In females, significantly higher values of FA were found, surprisingly in the castle sample, comparable with the more stressed Pachner Collection. We suspect that the FA reflects a more varied population of castle females as a consequence of patrilocality, although environmental stress remains a possibility.

Surface facial modelling and allometry in relation to sexual dimorphism

Sexual dimorphism is responsible for a substantial part of human facial variability, the study of which is essential for many scientific fields ranging from evolution to special biomedical topics. Our aim was to analyse the relationship between size variability and shape facial variability of sexual traits in the young adult Central European population and to construct average surface models of adult males and females. The method of geometric morphometrics allowed not only the identification of dimorphic traits, but also the evaluation of static allometry and the visualisation of sexual facial differences. Facial variability in the studied sample was characterised by a strong relationship between facial size and shape of sexual dimorphic traits. Large size of face was associated with facial elongation and vice versa. Regarding shape sexual dimorphic traits, a wide, vaulted and high forehead in combination with a narrow and gracile lower face were typical for females. Variability in shape dimorphic traits was smaller in females compared to males. For female classification, shape sexual dimorphic traits are more important, while for males the stronger association is with face size. Males generally had a closer inter-orbital distance and a deeper position of the eyes in relation to the facial plane, a larger and wider straight nose and nostrils, and more massive lower face. Using pseudo-colour maps to provide a detailed schematic representation of the geometrical differences between the sexes, we attempted to clarify the reasons underlying the development of such differences.

Variability in palatal shape and size in patients with bilateral complete cleft lip and palate assessed using dense surface model construction and 3D geometric morphometrics

Bilateral complete cleft lip and palate (BCLP) is the most severe of the common orofacial clefts and is associated with the greatest deformity during development. The aim of this study was to use geometric morphometrics to evaluate palatal shape and size variability in patients with BCLP in comparison to nonclefted Czech boys. The variability of palatal size and shape in BCLP patients was greater when compared with the nonclefted population. Though palate variability in BCLP was wide, nonclefted palatal shapes were generally different (a high, wide and vaulted palate) and fell almost outside the range of BCLP variability. The palatal size and shape of BCLP patients (range from 12.1 to 16.5 years) was not correlated with age. A comparison of the mean shapes of the clefted and nonclefted groups showed that the BCLP palate is flatter and narrower. The most notable size difference was found in the area between the maxilla and premaxilla. This phenomenon is associated with the persisting separation of the premaxilla from the rest of the palate. The shape of the palatal configuration of the premaxilla and adjacent area was concave in the nonclefted group and convex in BCLP patients.

Technical Note: Geometric Morphometrics and Sexual Dimorphism of the Greater Sciatic Notch in Adults From Two Skeletal Collections: The Accuracy and Reliability of Sex Classification

The greater sciatic notch (GSN) is one of the most important and frequently used characteristics for determining the sex of skeletons, but objective assessment of this characteristic is not without its difficulties. We tested the robustness of GSN sex classification on the basis of geometric morphometrics (GM) and support vector machines (SVM), using two different population samples. Using photographs, the shape of the GSN in 229 samples from two assemblages (documented collections of a Euroamerican population from the Maxwell Museum, University of New Mexico, and a Hispanic population from Universidad Nacional Autónoma de México, Mexico City) was segmented automatically and evaluated using six curve representations. The optimal dimensionality for each representation was determined by finding the best sex classification. The classification accuracy of the six curve representations in our study was similar but the highest and concurrently homologous cross-validated accuracy of 92% was achieved for a pooled sample using Fourier coefficient and Legendre polynomial methods. The success rate of our classification was influenced by the number of semilandmarks or coefficients and was only slightly affected by GSN marginal point positions. The intrapopulation variability of the female GSN shape was significantly lower compared with the male variability, possibly as a consequence of the intense selection pressure associated with reproduction. Males were misclassified more often than females. Our results show that by using a suitable GSN curve representation, a GM approach, and SVM analysis, it is possible to obtain a robust separation between the sexes that is stable for a multipopulation sample.

Changes in the sexual dimorphism of the human mandible during the last 1200 years in Central Europe.

According to many investigations, changes in mandibular morphology can occur synchronously with changes in the environment, and sexual dimorphism of the mandible can be influenced by the environment. Sexual dimorphism during the last 1200 years was evaluated using geometric morphometric analysis of virtual cranial models. The method of geometric morphometrics allows differences in size and shape to be assessed separately. We analyzed groups of adult individuals dating to Early Middle Ages, High Middle Ages, Early Modern Ages and from a modern Czech population (21st century). Significant sexual dimorphism in mandibular size was found in all populations. A trend in the sexual dimorphism of size was seen, with differences between the sexes increasing gradually over time. Size changes in female mandibles were a better reflection of environmental conditions and climate than size changes in male mandibles. Regarding changes in the sexual dimorphism of shape, significant dimorphism was found in all four samples. However, the pattern of mandibular shape dimorphism was different and varied considerably between samples. There was only one stable shape trait showing sexual dimorphism across all four samples in our study: the gonion lies more laterally in male than in female mandibles and male mandibles are relatively wider than female mandibles. Sexual dimorphism of shape is not influenced by the climate; instead sexual selection might play a role. This research supports earlier studies that have found that the degree and pattern of sexual dimorphism is population-specific and the factors regulating sexual dimorphism today may not be the same as those in the past.

Development of facial sexual dimorphism in children aged between 12 and 15 years: a three‐dimensional longitudinal study

OBJECTIVES To evaluate sexual dimorphism of facial form and shape and to describe differences between the average female and male face from 12 to 15 years. SETTING AND SAMPLE POPULATION Overall 120 facial scans from healthy Caucasian children (17 boys, 13 girls) were longitudinally evaluated over a 4-year period between the ages of 12 and 15 years. MATERIALS AND METHODS Facial surface scans were obtained using a three-dimensional optical scanner Vectra-3D. Variation in facial shape and form was evaluated using geometric morphometric and statistical methods (DCA, PCA and permutation test). Average faces were superimposed, and the changes were evaluated using colour-coded maps. RESULTS There were no significant sex differences (p > 0.05) in shape in any age category and no differences in form in the 12- and 13-year-olds, as the female faces were within the area of male variability. From the age of 14, a slight separation occurred, which was statistically confirmed. The differences were mainly associated with size. Generally boys had more prominent eyebrow ridges, more deeply set eyes, a flatter cheek area, and a more prominent nose and chin area. CONCLUSION The development of facial sexual dimorphism during pubertal growth is connected with ontogenetic allometry.

Sex Classification Using the Three-Dimensional Tibia Form or Shape Including Population Specificity Approach*

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.

3-D shape analysis of palatal surface in patients with unilateral complete cleft lip and palate

Facial development of patients with unilateral complete cleft lip and palate (UCLP) is associated with many problems including deformity of the palate. The aim of this study was to evaluate palatal morphology and variability in patients with UCLP compared with Czech norms using methods of geometric morphometrics. The study was based on virtual dental cast analysis of 29 UCLP patients and 29 control individuals at the age of 15 years. The variability of palatal shape in UCLP patients was greater than that in nonclefted palates. Only 24% of clefted palates fell within the variability of controls. The palatal form of UCLP patients (range from 11.8 to 17.2 years) was not correlated with age. Compared with control palates, palates of UCLP patients were narrower, more anteriorly than posteriorly. Apart from the praemaxilla region, they were also shallower, and the difference increased posteriorly. The UCLP palate was characterised by the asymmetry of its vault. The maximum height of the palatal vault was anterior on the clefted side, whereas it was posterior on the nonclefted side. The slope of the UCLP palate was more inclined compared with the control group. The praemaxilla was therefore situated more inferiorly.

Low-rank matrix approximations for Coherent point drift

We test non-rigid Coherent point drift with different low-rank matrix approximations.We designed a clustering-based method of approximating eigenvectors.CPD preprocessing times have been decreased to about one third.Both precision of registration and robustness are sufficient for most applications. Coherent point drift (CPD) is a powerful non-rigid point cloud registration algorithm. A speed-up technique that allows it to operate on large sets in reasonable time, however depends on efficient low-rank decomposition of a large affinity matrix. The originally used algorithm for finding eigenvectors in this case is based on Arnoldis iteration which, though very precise, requires the calculation of numerous large matrix-vector products, which even with further speed-up techniques is computationally intensive. We use a different method of finding that approximation, based on Nystrom sampling and design a modification that significantly accelerates the preprocessing stage of CPD. We test our modifications on a variety of situations, including different point counts, added Gaussian noise, outliers and deformation of the registered clouds. The results indicate that using our proposed approximation technique the desirable qualities of CPD such as robustness and precision are only minimally affected, while the preprocessing times are lowered considerably.

Statistical Mesh Shape Analysis with Nonlandmark Nonrigid Registration

The analysis of shape represented as surface meshes is an important tool in anthropology and biomedicine for the study of aging, post-treatment development or sexual dimorphism. Most approaches rely on nonrigid registration using manually placed homologous landmarks, it is however often the case that some regions cannot be landmarked due to the lack of clear anatomical features. We therefore present a method of analyzing and visualizing the variability of a set of surface models that does not rely on landmarks for feature matching and uses coherent point drift (CPD), a nonrigid registration algorithm, instead. Our approach is based on the topology transfer of one arbitrarily selected base mesh to all other meshes with the use of CPD. The procedure ensures the identical meanings of corresponding vertices across the sample and allows the use of multivariate statistics even with shapes that would be difficult to process with methods that rely on landmarks for feature-matching.