Spatiotemporal lower-limb asymmetries during stair descent in athletes following anterior cruciate ligament reconstruction

PURPOSE

This study evaluated motor control recovery at different times following anterior cruciate ligament reconstruction (ACLR) by investigating lower-limb spatiotemporal symmetry during stair descent performances.

METHODS

We used a cross-sectional design to compare asymptomatic athletes (Controls, n = 18) with a group of people with ACLR (n = 49) divided into three time-from-ACLR subgroups (Early: <6 months, n = 17; Mid: 6-18 months, n = 16; Late: ≥18 months, n = 16). We evaluated: "temporal symmetry" during the stance subphases (single-support, first and second double-support) and "spatial symmetry" for hip-knee-ankle intra-joint angular displacements during the stance phase using a dissimilarity index applied on superimposed 3D phase plots.

RESULTS

We found significant between-group differences in temporal variables (p ≤ 0.001). Compared to Controls, both Early and Mid (p ≤ 0.05) showed asymmetry in the first double-support time (longer for their injured vs. non-injured leg), while Early generally also showed longer durations in all other phases, regardless of stepping leg. No statistically significant differences were found for spatial intra-joint symmetry between groups.

CONCLUSION

Temporal but not spatial asymmetry in stair descent is often present early after ACLR; it may remain for up to 18 months and may underlie subtle intra- and inter-joint compensations. Spatial asymmetry may need further exploration.

Principled and interpretable alignability testing and integration of single-cell data

Single-cell data integration can provide a comprehensive molecular view of cells, and many algorithms have been developed to remove unwanted technical or biological variations and integrate heterogeneous single-cell datasets. Despite their wide usage, existing methods suffer from several fundamental limitations. In particular, we lack a rigorous statistical test for whether two high-dimensional single-cell datasets are alignable (and therefore should even be aligned). Moreover, popular methods can substantially distort the data during alignment, making the aligned data and downstream analysis difficult to interpret. To overcome these limitations, we present a spectral manifold alignment and inference (SMAI) framework, which enables principled and interpretable alignability testing and structure-preserving integration of single-cell data with the same type of features. SMAI provides a statistical test to robustly assess the alignability between datasets to avoid misleading inference and is justified by high-dimensional statistical theory. On a diverse range of real and simulated benchmark datasets, it outperforms commonly used alignment methods. Moreover, we show that SMAI improves various downstream analyses such as identification of differentially expressed genes and imputation of single-cell spatial transcriptomics, providing further biological insights. SMAI's interpretability also enables quantification and a deeper understanding of the sources of technical confounders in single-cell data.

Statistical shape analysis of maxillary palatal morphology in patients with palatally displaced canines

OBJECTIVE

Maxillary morphology has long been a subject of interest due to its possible impact on palatally and labially displaced canines. This study aims to conduct a comparison of the palate morphology between individuals with palatal and labially displaced canines and control subjects using statistical shape analysis on a coronal cross-sectional of CBCT images.

MATERIALS AND METHODS

Patients aged between 12 and 43 years with palatally or labially displaced canines referred to Hamadan School of Dentistry between 2014 and 2019 were recruited for this retrospective study. The sample included 29 palatally displaced canines (PDC), 20 labially displaced canines (LDC), and 20 control groups (CG). Initially, the maxillary palate coronal section was acquired and landmarked in the region between the right and the left first molar. Procrustes and principal component analyses were used to identify the primary patterns of palatal shape variation. Statistical tests were then performed to examine both shape and size differences.

RESULTS

According to the results of Hotelling's T2 test, there is a significant difference between the mean shape of palate in PDC and CG (P = 0.009), while the difference between the PDC-LDC and LDC-CG groups is not significant. The longest full Procrustes distance was observed between PDC and CG (distance = 0.043), and the shortest full Procrustes distance was observed between LDC and CG (distance = 0.029). The first two principal components accounted for 84.47% of the total variance. The predictive accuracy of the discriminant analysis model showed that 72.46% of cases were correctly classified into the three study groups.

CONCLUSIONS

In terms of centroid size, there was no significant difference in the sectional area between the three groups, but the difference between the mean shape of palate in the PDC and CG groups was significant. The PDC group showed more prominent mid-palatal area in the molar region.

Scrutinising an inscrutable bark-nesting ant: Exploring cryptic diversity in the Rhopalomastix javana (Hymenoptera: Formicidae) complex using DNA barcodes, genome-wide MIG-seq and geometric morphometrics

Overlooking cryptic species diversity has grave implications on assessments of climate change impacts on biodiversity, ecosystems and organismal populations. Discriminating between cryptic species has long been challenging even for seasoned taxonomists, as interspecies morphological differences are often indiscernible by visual observation. Multi-disciplinary methods involving genetic analyses in conjunction with quantitative morphological data, should therefore be used to investigate boundaries between cryptic species. We adopted an integrated approach combining analyses of mitochondrial COI barcodes, a genome-wide dataset obtained via multiplexed inter-simple sequence repeats (ISSRs) genotyping by sequencing (MIG-seq), and geometric morphometrics to investigate species divergences in the inscrutable Rhopalomastix javana species complex. Objective clustering of COI suggested five putative molecular species units divergent from each other by thresholds within 4.2-10.6% uncorrected pairwise distance. Phylogenetic analyses based on concatenated MIG-seq data also recovered and strongly supported the monophyly of five major lineages in agreement with COI clusters. Co-ancestry analyses based on MIG-seq data using fineRADstructure resolved variable patterns of admixture linked to geography, and potential genetic drift within some putative species. Geometric morphometric analyses of specimen images further detected statistically significant differences in at least one of three anatomical aspects (Head, Meso, Profile) between all pairs of putative species. Head shape (full-face view) was determined to be the most informative character for species diagnosis, with relatively high classification accuracy. Thin-plate spline deformation grids highlighted areas of high variation between species in each shape for deeper taxonomic scrutiny. The presence of species from multiple distinct lineages existing in near-sympatry firmly demonstrates that R. javana comprises more than one closely-related species, but exact species boundaries are difficult to ascertain. Differences in elevation and its associated abiotic effects on ant adaptations and reproductive phenology may contribute to restricting gene flow and maintaining species boundaries between sympatric populations of the R. javana complex. We further assess the advantages and limitations of geometric morphometrics as a taxonomic tool. Despite its drawbacks, our combined approach has helped draw important insights on cryptic diversity in R. javana, and also identified gaps of knowledge that await address. Results from this study will inform and prime future in-depth taxonomic investigation on the R. javana complex, including formal descriptions and establishment of the five putative species.

Using Geometric Morphometric Analysis of Magnetic Resonance Imaging to Assess the Anatomy of the Eustachian Tube in Children with and without Otitis Media

Otitis media (OM) is among the most common of childhood illnesses. It has long been hypothesized that children under age two are predisposed to OM due to differences in the anatomy of the Eustachian tube (ET), including the angle of the ET. OM in later childhood is less common but does occur, begging the question, are there shape differences in the ET that persist underlying later occurrences of OM? To answer this question, a novel method, which applied geometric and morphometric shape analysis to landmarks obtained from MRI data, was used. MRI scans were performed on 16 children (5 control, 3 cOME, and 8 rAOM) between 2011 and 2015. Sixteen landmarks representing the shape of the ET, cranial base, and palate were analyzed. The results of a Procrustes ANOVA indicate that the shape of the ET varies significantly (p < 0.01) between the OM and control groups. The shape differences between the OM group and the control are a medial and low attachment site of the tensor veli palatini (TVP) muscle, a posterior and high torus tubarius, and an anteriorly projected palate. These results support previous findings that a relatively horizontal ET is associated with a predisposition for OM. This study used a novel approach to examine anatomical differences in children with and without OM. First, the data set is unique in that it includes MRI scans of children with a confirmed OM diagnosis. Second, the use of MRI scans in craniofacial anatomy OM research is novel and allows for the collection of soft tissue landmarks and the visualization of soft tissue structures. Third, geometric morphometric shape analysis is a statistical method that captures shape differences, offering a more universal picture of nuanced changes within the entire set of landmarks, in contrast to more traditional linear and angular measurements used in prior OM studies examining craniofacial anatomy.

Exploring the trend effects of diffuse anthropogenic pollution in a large river passing through a densely populated area

The detection of non-point pollution in large rivers requires high-frequency sampling over a longer period of time, which, however presumably provides data with large spatial and temporal variance. Variability may mean that data sets recorded upstream and downstream from a densely populated area overlap, suggesting at first glance that the urban area did not affect water quality. This study presents a simple way to explore trend-like effects of non-point pollution in the Danube based on data that varied strongly in space and time. For one year, biweekly sampling was carried out upstream and downstream from a large city with negligible emission of untreated wastewater and the surrounding settlements, industrial and agricultural areas. Although most of the values of the 34 examined physicochemical characteristics fell within the range of data previously published for the Danube, and the mean values of all parameters indicated unpolluted surface water, different water quality was revealed upstream and downstream from the metropolitan area at each sampling time. Since the physicochemical characteristics causing the separation also differed from time to time, univariate tests and consensus ordination were used to determine which variables changed similarly during most of the examined period. With this evaluation method, several diffuse pollutants of anthropogenic origin contaminating the Danube in the long term were identified, such as nitrogen, phosphorus, sulphate, chloride, potassium and vanadium. The results demonstrated that trend-like effects of non-point pollution can be detected even in a large river, where physicochemical measurements can vary strongly in space and time.

Cross Sectional Analysis of Eurasian Skull Anatomy for 3D Cephalometry-Normative Data Reveal Four Different Skull Types

The unsolved problem in three-dimensional surgical planning for patients with facial deformity, dysgnathia, or asymmetry is the lack of a normative database of "norm skulls" that can be used as treatment objectives. A study was conducted on 90 Eurasian persons (46 male and 44 female adults) for whom cone beam-computed tomography images were available. Inclusion criteria were adult patients with a skeletal Class I pattern, proper interincisal relationship with normal occlusion, the absence of an open bite both in the anterior and posterior region, and a normal and balanced facial appearance; patients with dysgnathia and malformations were excluded. A total of 18 landmarks were digitized and 3D cephalometric measurements were performed and analyzed by means of proportions calculated from the landmarks. Male and female skulls were analyzed, as well as subdivisions revealed by cluster analysis. The data showed that four subtypes of skulls were distinguishable with statistical significance (p < 0.05). A male and a female type subdivided in a brachiocephalic and dolichocephalic phenotype could be identified. For each type, a mean shape was calculated by a Procrustes transformation, which, in turn, was used to create four template skulls from a male and a female skull. This was accomplished by fitting the polygon models of the two skulls to each of the two subtypes based on the landmarks marked on them using a thin plate spline transformation. The normative data of the subtypes can individually serve as a guide for orthodontic surgery in the Eurasian population, which is especially helpful in 3D planning and the execution of craniofacial operations.

Implementation of a personal identification system using alveolar bone images

OBJECTIVE

In recent years, personal identification has been performed using antemortem panoramic X-ray images and postmortem-CT images. Using these, we have developed a personal identification method that focuses on the alveolar bone. This study examined the effectiveness of this method and aimed to implement a reproducible system.

MATERIALS AND METHODS

For personal identification, a total of 633 CT images and panoramic X-ray images belonging to three groups with different conditions were used.　These images were 160 sets in the same person group and 96,820 in the other groups. The similarity of alveolar bone images was calculated using the landmark method of Procrustes analysis. The processes were system implemented and the methodology was validated.

RESULTS

The ability to identify between the same person group and other person groups showed 0.9769 as the area under the curve (AUC: ROC curve). At the cutoff value of 4.978, there was no false rejection rate, but false acceptance rate was slightly higher.

CONCLUSION

This method was useful as a screening method for personal identification. In addition, system implementation was efficient and reduced human error. In the future, we aim to realize a more efficient personal identification method using distortion-corrected images and including auto-detective landmarks using deep learning.

Procrustes Analysis for High-Dimensional Data

The Procrustes-based perturbation model (Goodall in J R Stat Soc Ser B Methodol 53(2):285-321, 1991) allows minimization of the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed matrices, and inapplicability in high-dimensional data. We provide an extension of the perturbation model focused on the high-dimensional data framework, called the ProMises (Procrustes von Mises-Fisher) model. The ill-posed and interpretability problems are solved by imposing a proper prior distribution for the orthogonal matrix parameter (i.e., the von Mises-Fisher distribution) which is a conjugate prior, resulting in a fast estimation process. Furthermore, we present the Efficient ProMises model for the high-dimensional framework, useful in neuroimaging, where the problem has much more than three dimensions. We found a great improvement in functional magnetic resonance imaging connectivity analysis because the ProMises model permits incorporation of topological brain information in the alignment's estimation process.

The formation of specific bacterial communities contributes to the enrichment of antibiotic resistance genes in the soil plastisphere

Soil serves as a major reservoir of both antibiotic resistance genes (ARGs) and microplastics. However, the characteristics of the antibiotic resistome in the soil plastisphere remain largely unknown. In this study, we used metagenomic approaches to reveal the changing patterns of ARGs and the bacterial community and their associations in response to three types of microplastics (light density polyethylene, LDPE; polypropylene, PP; polystyrene, PS) using particles 550 µm or 75 µm in diameter. The total ARG abundances significantly increased in the plastisphere and varied across plastic types. The LDPE plastisphere had the highest ARG total abundance and lowest Shannon diversity index, indicating that this plastic had the most severe negative impact on soil bacterial diversity. The PP plastisphere contained higher relative abundances of the pathogenic bacteria Acinetobacter johnsonii and Escherichia coli, demonstrating the higher pathogenic risk of the microbial communities enriched in the plastisphere. Specifically, multidrug resistance genes (ceoB and MuxB) co-existed with more than four microbial taxa, increasing the potential risk of ARG spread in pathogenic bacteria. These findings implied that the plastisphere acts as a hotspot for acquiring and spreading antibiotic resistance and may have long-term negative effects on the soil ecosystem and human health.

Individual variability in the nonlinear development of the corpus callosum during infancy and toddlerhood: a longitudinal MRI analysis

The human brain spends several years bootstrapping itself through intrinsic and extrinsic modulation, thus gradually developing both spatial organization and functions. Based on previous studies on developmental patterns and inter-individual variability of the corpus callosum (CC), we hypothesized that inherent variations of CC shape among infants emerge, depending on the position within the CC, along the developmental timeline. Here we used longitudinal magnetic resonance imaging data from infancy to toddlerhood and investigated the area, thickness, and shape of the midsagittal plane of the CC by applying multilevel modeling. The shape characteristics were extracted using the Procrustes method. We found nonlinearity, region-dependency, and inter-individual variability, as well as intra-individual consistencies, in CC development. Overall, the growth rate is faster in the first year than in the second year, and the trajectory differs between infants; the direction of CC formation in individual infants was determined within six months and maintained to two years. The anterior and posterior subregions increase in area and thickness faster than other subregions. Moreover, we clarified that the growth rate of the middle part of the CC is faster in the second year than in the first year in some individuals. Since the division of regions exhibiting different tendencies coincides with previously reported divisions based on the diameter of axons that make up the region, our results suggest that subregion-dependent individual variability occurs due to the increase in the diameter of the axon caliber, myelination partly due to experience and axon elimination during the early developmental period.

[Deep learning-assisted construction of three-demensional facial midsagittal plane]

OBJECTIVE

To establish a deep learning algorithm that can accurately determine three-dimensional facial anatomical landmarks, multi-view stacked hourglass convolutional neural networks (MSH-CNN) and to construct three-dimensional facial midsagittal plane automatically based on MSH-CNN and weighted Procrustes analysis algorithm.

METHODS

One hundred subjects with no obvious facial deformity were collected in our oral clinic. Three-dimensional facial data were scanned by three-dimensional facial scanner. Experts annotated twenty-one facial landmarks and midsagittal plane of each data. Eighty three-dimensional facial data were used as training set, to train the MSH-CNN in this study. The overview of MSH-CNN network architecture contained multi-view rendering and training the MSH-CNN network. The three-dimensional facial data were rendered from ninety-six views that were fed to MSH-CNN and the output was one heatmap per landmark. The result of the twenty-one landmarks was accurately placed on the three-dimensional facial data after a three-dimensional view ray voting process. The remaining twenty three-dimensional facial data were used as test set. The trained MSH-CNN automatically determined twenty-one three-dimensional facial anatomical landmarks of each case of data, and calculated the distance between each MSH-CNN landmark and the expert landmark, which was defined as position error. The midsagittal plane of the twenty subjects' could be automatically constructed, using the MSH-CNN and Procrustes analysis algorithm. To evaluate the effect of midsagittal plane by automatic method, the angle between the midsagittal plane constructed by the automatic method and the expert annotated plane was calculated, which was defined as angle error.

RESULTS

For twenty subjects with no obvious facial deformity, the average angle error of the midsagittal plane constructed by MSH-CNN and weighted Procrustes analysis algorithm was 0.73°±0.50°, in which the average position error of the twenty-one facial landmarks automatically determined by MSH-CNN was (1.13±0.24) mm, the maximum position error of the orbital area was (1.31±0.54) mm, and the minimum position error of the nasal area was (0.79±0.36) mm.

CONCLUSION

This research combines deep learning algorithms and Procrustes analysis algorithms to realize the fully automated construction of the three-dimensional midsagittal plane, which initially achieves the construction effect of clinical experts. The obtained results constituted the basis for the independent intellectual property software development.

[Deep learning-assisted construction of three-demensional facial midsagittal plane]

OBJECTIVE

To establish a deep learning algorithm that can accurately determine three-dimensional facial anatomical landmarks, multi-view stacked hourglass convolutional neural networks (MSH-CNN) and to construct three-dimensional facial midsagittal plane automatically based on MSH-CNN and weighted Procrustes analysis algorithm.

METHODS

One hundred subjects with no obvious facial deformity were collected in our oral clinic. Three-dimensional facial data were scanned by three-dimensional facial scanner. Experts annotated twenty-one facial landmarks and midsagittal plane of each data. Eighty three-dimensional facial data were used as training set, to train the MSH-CNN in this study. The overview of MSH-CNN network architecture contained multi-view rendering and training the MSH-CNN network. The three-dimensional facial data were rendered from ninety-six views that were fed to MSH-CNN and the output was one heatmap per landmark. The result of the twenty-one landmarks was accurately placed on the three-dimensional facial data after a three-dimensional view ray voting process. The remaining twenty three-dimensional facial data were used as test set. The trained MSH-CNN automatically determined twenty-one three-dimensional facial anatomical landmarks of each case of data, and calculated the distance between each MSH-CNN landmark and the expert landmark, which was defined as position error. The midsagittal plane of the twenty subjects' could be automatically constructed, using the MSH-CNN and Procrustes analysis algorithm. To evaluate the effect of midsagittal plane by automatic method, the angle between the midsagittal plane constructed by the automatic method and the expert annotated plane was calculated, which was defined as angle error.

RESULTS

For twenty subjects with no obvious facial deformity, the average angle error of the midsagittal plane constructed by MSH-CNN and weighted Procrustes analysis algorithm was 0.73°±0.50°, in which the average position error of the twenty-one facial landmarks automatically determined by MSH-CNN was (1.13±0.24) mm, the maximum position error of the orbital area was (1.31±0.54) mm, and the minimum position error of the nasal area was (0.79±0.36) mm.

CONCLUSION

This research combines deep learning algorithms and Procrustes analysis algorithms to realize the fully automated construction of the three-dimensional midsagittal plane, which initially achieves the construction effect of clinical experts. The obtained results constituted the basis for the independent intellectual property software development.

ORTHOGONAL TRACE-SUM MAXIMIZATION: APPLICATIONS, LOCAL ALGORITHMS, AND GLOBAL OPTIMALITY

This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized canonical correlation analysis (CCA), Procrustes analysis, and cryo-electron microscopy of the Nobel prize fame. For these applications finding global solutions is highly desirable, but it has been unclear how to find even a stationary point, let alone test its global optimality. Through a close inspection of Ky Fan's classical result [Proc. Natl. Acad. Sci. USA, 35 (1949), pp. 652-655] on the variational formulation of the sum of largest eigenvalues of a symmetric matrix, and a semidefinite programming (SDP) relaxation of the latter, we first provide a simple method to certify global optimality of a given stationary point of OTSM. This method only requires testing whether a symmetric matrix is positive semidefinite. A by-product of this analysis is an unexpected strong duality between Shapiro and Botha [SIAM J. Matrix Anal. Appl., 9 (1988), pp. 378-383] and Zhang and Singer [Linear Algebra Appl., 524 (2017), pp. 159-181]. After showing that a popular algorithm for generalized CCA and Procrustes analysis may generate oscillating iterates, we propose a simple fix that provably guarantees convergence to a stationary point. The combination of our algorithm and certificate reveals novel global optima of various instances of OTSM.

[A method for constructing three-dimensional face symmetry reference plane based on weighted shape analysis algorithm]

OBJECTIVE

To establish a novel method based on three-dimensional (3D) shape analysis and weighted Procrustes analysis (WPA) algorithm to construct a 3D facial symmetry reference plane (SRP), automatically assigning weight to facial anatomical landmarks. The WPA algorithm suitability for commonly observed clinical cases of mandibular deviation were analysed and evaluated.

METHODS

Thirty patients with mandibular deviation were recruited for this study. The 3D facial SRPs were extracted independently based on original-mirror alignment method. Thirty-two anatomical landmarks were selected from the overall region by three times to obtain the mean coordinate. The SRP of experimental groups 1 and 2 were using the standard Procrustes analysis (PA) algorithm and WPA algorithm, respectively. A reference plane defined by experts based on regional iterative closest point (ICP) algorithm, served as the ground truth. Three experts manually selecting facial regions with good symmetry for original model, and common region was included in the study. The angle error values between the SRP of WPA algorithm in the experimental group 1 and the truth plane were evaluated in this study, and the SRP of PA algorithm of experimental group 2 was calculated in the same way. Statistics and measurement analysis were used to comprehensively evaluate the clinical suitability of the WPA algorithm to calculate the SRP. A paired t-test analysis (two-tailed) was conducted to compare the angles.

RESULTS

The average angle error between the SRP of WPA algorithm and the ground truth was 1.53°±0.84°, which was smaller than that between the SRP of PA and the ground truth (2.06°±0.86°). There were significant differences in the angle errors among the groups (P < 0.05). For the patients with severe mandibular deviation that the distance between pogonion and facial midline greater than 12 mm, the average angle error of the WPA algorithm was 0.86° smaller than that of the PA algorithm.

CONCLUSION

The WPA algorithm, based on weighted shape analysis, can provide a more adaptable SRP than the standard PA algorithm when applied to mandibular deviation patients and preliminarily simulate the diagnosis strategies of clinical experts.

A novel method for 3D face symmetry reference plane based on weighted Procrustes analysis algorithm

BACKGROUND

We aimed to establish a novel method, using the weighted Procrustes analysis (WPA) algorithm, which assigns weight to facial anatomical landmarks, to construct a three-dimensional facial symmetry reference plane (SRP) for mandibular deviation patients.

METHODS

Three-dimensional facial SRPs were independently extracted from 15 mandibular deviation patients using both our WPA algorithm and the standard PA algorithm. A reference plane was defined to serve as the ground truth. To determine whether the WPA SRP or the PA SRP was closer to the ground truth, we measured the position error of mirrored landmarks, the facial asymmetry index (FAI) error, and the angle error for the global face and each facial third partition.

RESULTS

The average angle error between the WPA SRP and the ground truth was 1.66 ± 0.81°, which was smaller than that between the PA SRP and the ground truth. The position error of the mirrored landmarks constructed using the WPA algorithm in the global face (3.64 ± 1.53 mm) and each facial partition was lower than that constructed using the PA algorithm. The average FAI error of the WPA SRP was - 7.77 ± 17.02 mm, which was smaller than that of the PA SRP.

CONCLUSIONS

This novel automatic algorithm, based on weighted anatomic landmarks, can provide a more adaptable SRP than the standard PA algorithm when applied to severe mandibular deviation patients and can better simulate the diagnosis strategies of clinical experts.

Multidimensional scaling locus of memristor and fractional order elements

This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the "continuum" of fractional order elements (FOE). Each FOE is characterized by its behavior, either in the time or in the frequency domains, and the differences between the FOE are captured by a variety of distinct indices, such as the Arccosine, Canberra, Jaccard and Sørensen distances. The dissimilarity information is processed by the multidimensional scaling (MDS) computational algorithm to unravel possible clusters and to allow a direct pattern visualization. The MDS yields 3-dimensional loci organized according to the FOE characteristics both for linear and nonlinear elements. The new representation generalizes the standard Cartesian 2-dimensional periodic table of elements.

Urbanisation and wing asymmetry in the western honey bee (Apis mellifera, Linnaeus 1758) at multiple scales

Changes in the mean and variance of phenotypic traits like wing and head morphology are frequently used as indicators of environmental stress experienced during development and may serve as a convenient index of urbanization exposure. To test this claim, we collected adult western honey bee (Apis mellifera Linnaeus 1758, Hymenoptera, Apidae) workers from colonies located across an urbanization gradient, and quantified associations between the symmetries of both wing size and wing shape, and several landscape traits associated with urbanization. Landscape traits were assessed at two spatial scales (three km and 500 m) and included vegetation and anthropogenic land cover, total road length, road proximity and, population and dwelling density. We then used geometric morphometric techniques to determine two wing asymmetry scores-centroid size, a measure of wing size asymmetry and Procrustes distance, a measure of wing shape asymmetry. We found colony dependent differences in both wing size and shape asymmetry. Additionally, we found a negative association between wing shape asymmetry and road proximity at the three km buffer, and associations between wing shape asymmetry and road proximity, anthropogenic land cover and vegetation cover at the 500 m buffer. Whilst we were unable to account for additional variables that may influence asymmetry including temperature, pesticide presence, and parasitism our results demonstrate the potential usefulness of wing shape asymmetry for assessing the impact of certain landscape traits associated with urbanization. Furthermore, they highlight important spatial scale considerations that warrant investigation in future phenotypic studies assessing urbanization impact.

Erratum to: Morphometric analysis of Passiflora leaves: the relationship between landmarks of the vasculature and elliptical Fourier descriptors of the blade

Background

Leaf shape among Passiflora species is spectacularly diverse. Underlying this diversity in leaf shape are profound changes in the patterning of the primary vasculature and laminar outgrowth. Each of these aspects of leaf morphology—vasculature and blade—provides different insights into leaf patterning.

Results

Here, we morphometrically analyze >3300 leaves from 40 different Passiflora species collected sequentially across the vine. Each leaf is measured in two different ways: using 1) 15 homologous Procrustes-adjusted landmarks of the vasculature, sinuses, and lobes; and 2) Elliptical Fourier Descriptors (EFDs), which quantify the outline of the leaf. The ability of landmarks, EFDs, and both datasets together are compared to determine their relative ability to predict species and node position within the vine. Pairwise correlation of x and y landmark coordinates and EFD harmonic coefficients reveals close associations between traits and insights into the relationship between vasculature and blade patterning.

Conclusions

Landmarks, more reflective of the vasculature, and EFDs, more reflective of the blade contour, describe both similar and distinct features of leaf morphology. Landmarks and EFDs vary in ability to predict species identity and node position in the vine and exhibit a correlational structure (both within landmark or EFD traits and between the two data types) revealing constraints between vascular and blade patterning underlying natural variation in leaf morphology among Passiflora species.

Phenotypic and Genetic Analysis of the Leopard Complex Spotting in Noriker Horses

Genetic analyses of coat colors are frequently restricted to subjectively categorized phenotype information. The aim of this study was to develop a method to numerically quantify the variability of leopard complex (LP) spotting phenotypes introducing tools from image analysis. Generalized Procrustes analysis eliminates systematic errors due to imaging process. The binarization of normalized images and the application of principal component analysis (PCA) on the derived pixel matrices, transform pixel information into numerical data space. We applied these methods on 90 images to ascertain the specific leopard patterns within the Noriker breed. Furthermore, we genotyped a representative sample of 191 Noriker horses for the known LP spotting associated loci. Ninety-seven percentage of the genotyped leopard spotted horses were heterozygous for LP and had at least one copy of the PATN1 allele. However, the remaining pattern variation was great, indicating other genetic factors influencing the expression of LP spotting. Based upon this data, we estimated effect sizes of the modifier PATN1, and additional factors including sex, age, base color, and spotting phenotype of parents. The PCA of the pixel matrix resulted in 2 significant components accounting for 51% of the variation. Applying a linear model, we identified significant effects for age groups and base color on the first and second components, while for sex and parents' LP phenotype significant effects were found on 4 additional components.

Fluctuating asymmetry of the normal facial skeleton

The purpose of this study was to produce reliable estimations of fluctuating facial asymmetry in a normal population. Fifty-four computed tomography (CT) facial models of average-looking and symmetrical Chinese subjects with a class I occlusion were used in this study. Eleven midline landmarks and 12 pairs of bilateral landmarks were digitized. The repeatability of the landmark digitization was first evaluated. A Procrustes analysis was then used to measure the fluctuating asymmetry of each CT model, after all of the models had been scaled to the average face size of the study sample. A principal component analysis was finally used to establish the direction of the fluctuating asymmetries. The results showed that there was excellent absolute agreement among the three repeated measurements. The mean fluctuating asymmetry of the average-size face varied at each anthropometric landmark site, ranging from 1.0mm to 2.8mm. At the 95% upper limit, the asymmetries ranged from 2.2mm to 5.7mm. Most of the asymmetry of the midline structures was mediolateral, while the asymmetry of the bilateral landmarks was more equally distributed. These values are for the average face. People with larger faces will have higher values, while subjects with smaller faces will have lower values.

Divergent leaf shapes among Passiflora species arise from a shared juvenile morphology

Not only does leaf shape vary between Passiflora species, but between sequential nodes of the vine. The profound changes in leaf shape within Passiflora vines reflect the temporal development of the shoot apical meristem from which leaves are derived and patterned, a phenomenon known as heteroblasty. We perform a morphometric analysis of more than 3,300 leaves from 40 different Passiflora species using two different methods: homologous landmarks and Elliptical Fourier Descriptors (EFDs). Changes in leaf shape across the vine are first quantified in allometric terms; that is, changes in the relative area of leaf subregions expressed in terms of overall leaf area. Shape is constrained to strict linear relationships as a function of size that vary between species. Statistical analysis of leaf shape, using landmarks and EFDs, reveals that species effects (regardless of node) are the strongest, followed by interaction effects between species and heteroblasty (i.e., species-specific patterns in leaf shape across nodes) and that heteroblasty effects across nodes (regardless of species) are negligible. The ability of different nodes to predictively discriminate species and the variability of landmark and EFD traits at each node is then analyzed. Heteroblastic trajectories, the changes in leaf shape between the first and last measured leaves in a vine, are then compared between species in a multivariate space. Leaf shape diversity among Passiflora species is expressed in a heteroblastic-dependent manner, unique to each species. Leaf shape is constrained by linear, allometric relationships related to leaf size that vary between species. There is a strong species × heteroblasty interaction effect for leaf shape, suggesting that different leaf shapes between species arise through changes in shape across nodes specific to each species. The first leaves in the series are not only more like each other, but are also less variable across species. From this similar, shared leaf shape, subsequent leaves in the heteroblastic series follow divergent morphological trajectories. The disparate leaf shapes characteristic of Passiflora species arise from a shared, juvenile morphology.

Morphometric analysis of Passiflora leaves: the relationship between landmarks of the vasculature and elliptical Fourier descriptors of the blade

Background

Leaf shape among Passiflora species is spectacularly diverse. Underlying this diversity in leaf shape are profound changes in the patterning of the primary vasculature and laminar outgrowth. Each of these aspects of leaf morphology-vasculature and blade-provides different insights into leaf patterning.

Results

Here, we morphometrically analyze >3300 leaves from 40 different Passiflora species collected sequentially across the vine. Each leaf is measured in two different ways: using 1) 15 homologous Procrustes-adjusted landmarks of the vasculature, sinuses, and lobes; and 2) Elliptical Fourier Descriptors (EFDs), which quantify the outline of the leaf. The ability of landmarks, EFDs, and both datasets together are compared to determine their relative ability to predict species and node position within the vine. Pairwise correlation of x and y landmark coordinates and EFD harmonic coefficients reveals close associations between traits and insights into the relationship between vasculature and blade patterning.

Conclusions

Landmarks, more reflective of the vasculature, and EFDs, more reflective of the blade contour, describe both similar and distinct features of leaf morphology. Landmarks and EFDs vary in ability to predict species identity and node position in the vine and exhibit a correlational structure (both within landmark or EFD traits and between the two data types) revealing constraints between vascular and blade patterning underlying natural variation in leaf morphology among Passiflora species.

Geometric morphometric analysis reveals age-related differences in the distal femur of Europeans

Background

Few studies have looked into age-related variations in femur shape. We hypothesized that three-dimensional (3D) geometric morphometric analysis of the distal femur would reveal age-related differences. The purpose of this study was to show that differences in distal femur shape related to age could be identified, visualized, and quantified using three-dimensional (3D) geometric morphometric analysis.

Methods

Geometric morphometric analysis was carried out on CT scans of the distal femur of 256 subjects living in the south of France. Ten landmarks were defined on 3D reconstructions of the distal femur. Both traditional metric and geometric morphometric analyses were carried out on these bone reconstructions. These analyses were used to identify trends in bone shape in various age-based subgroups (<40, 40–60, >60).

Results

Only the average bone shape of the < 40-year subgroup was statistically different from that of the other two groups. When the population was divided into two subgroups using 40 years of age as a threshold, the subject's age was correctly assigned 80% of the time.

Discussion

Age-related differences are present in this bone segment. This reliable, accurate method could be used for virtual autopsy and to perform diachronic and interethnic comparisons. Moreover, this study provides updated morphometric data for a modern population in the south of France.

Conclusion

Manufacturers of knee replacement implants will have to adapt their prosthesis models as the population evolves over time.

Three-dimensional geometric morphometric analysis reveals ethnic dimorphism in the shape of the femur

Background

Ethnic dimorphism in the distal femur has never been studied in a three-dimensional analysis focused on shape instead of size. Yet, this dimorphism has direct implications in orthopedic surgery and in anthropology. The goal of this study was to show that differences in distal femur shape related to ethnic dimorphism could be identified, visualized, and quantified using 3D geometric morphometric analysis.

Methods

CT scans of the distal femur were taken from 482 patients who were free of any bone-related pathology: 240 patients were European (E) and 242 were Asian (A). Ten osteometric landmarks based on standard bone landmarks used in anthropometry were placed on these scans. Geometric morphometric analysis, principal component analysis (PCA), canonical variates analysis (CVA), and other discriminant analyses (Goodall’s F-test and Mahalanobis distance) were performed. A cross-validation analysis was carried out to determine the percentage of cases in which the ethnicity was correctly estimated.

Results

The shape of the E and A distal femur differed significantly (Goodall’s F = 94.43, P < 0.001 and Mahalanobis D2 distance = 1.85, P < 0.001). PCA identified a difference in distal femur shape between A and E. The CVA revealed that correct ethnicity was assigned in 82% of cases and the cross-validation revealed a 75% rate of correct ethnic group estimation.

Conclusion

The distal femur exhibits ethnic dimorphism. 3D geometric morphometric analysis made it possible to demonstrate these differences. The large number of subjects studied has helped modernize the references for certain bone measurements, with direct implication for orthopedic surgery and anthropology.

Concept mapping-An effective method for identifying diversity and congruity in cognitive style

This paper investigates the effects of cognitive style for decision making on the behaviour of participants in different phases of the group concept mapping process (GCM). It is argued that cognitive style should be included directly in the coordination of the GCM process and not simply considered as yet another demographic variable. The cognitive styles were identified using the Kirton Adaption-Innovation Inventory, which locates each person's style on a continuum ranging from very adaptive to very innovative. Cognitive style could explain diversity in the participants' behaviour in different phases of the GCM process. At the same time, the concept map as a group's common cognitive construct can consolidate individual differences and serves as a tool for managing diversity in groups of participants. Some of the results were that: (a) the more adaptive participants generated ideas that fit to a particular, well-established and consensually agreed paradigm, frame of reference, theory or practice; (b) the more innovative participants produced ideas that were more general in scope and required changing a settled structure (paradigm, frame of reference, theory or practice); and (c) the empirical comparison of the map configurations through Procrustes analysis indicated a strong dissimilarity between cognitive styles.

Morphometric analysis of Passiflora leaves: the relationship between landmarks of the vasculature and elliptical Fourier descriptors of the blade

BACKGROUND

Leaf shape among Passiflora species is spectacularly diverse. Underlying this diversity in leaf shape are profound changes in the patterning of the primary vasculature and laminar outgrowth. Each of these aspects of leaf morphology-vasculature and blade-provides different insights into leaf patterning.

RESULTS

Here, we morphometrically analyze >3300 leaves from 40 different Passiflora species collected sequentially across the vine. Each leaf is measured in two different ways: using 1) 15 homologous Procrustes-adjusted landmarks of the vasculature, sinuses, and lobes; and 2) Elliptical Fourier Descriptors (EFDs), which quantify the outline of the leaf. The ability of landmarks, EFDs, and both datasets together are compared to determine their relative ability to predict species and node position within the vine. Pairwise correlation of x and y landmark coordinates and EFD harmonic coefficients reveals close associations between traits and insights into the relationship between vasculature and blade patterning.

CONCLUSIONS

Landmarks, more reflective of the vasculature, and EFDs, more reflective of the blade contour, describe both similar and distinct features of leaf morphology. Landmarks and EFDs vary in ability to predict species identity and node position in the vine and exhibit a correlational structure (both within landmark or EFD traits and between the two data types) revealing constraints between vascular and blade patterning underlying natural variation in leaf morphology among Passiflora species.

Preliminary Study to Determine the Reference Plane of Patients With a Unilateral Cleft Lip and Palate

OBJECTIVE

The objective of this study was to determine the three-dimensional midsagittal reference planes for unilateral cleft lip and palate (UCLP) patients that can be easily applied in a clinical setting.

DESIGN

This was a retrospective analysis.

PATIENTS

There were 35 UCLP patients (25 men, 10 women; 28.1 ± 6.9 years old) in this study.

METHODS

With landmark's three-dimensional coordinates obtained from cone-beam computed tomography, the symmetric midsagittal reference planes were calculated by applying the ordinary Procrustes superimposition method using the original and mirror images. Procrustes analysis was also used to find the closest landmarks to the calculated symmetric midsagittal reference plane and test its compatibility with the symmetrical midsagittal reference plane.

MAIN OUTCOME MEASURE

The three nearest landmarks to the symmetric midsagittal reference plane were Opisthion, Basion, and Nasion.

RESULTS

The averages of the sums of the squared Euclidean distance and squared Procrustes distance differences between the two configurations and shapes fabricated by the symmetrical and landmark-based midsagittal reference planes, respectively, were calculated as 1.836 ± 3.295 and 1.519 × 10^-5 ± 2.351 × 10^-5.

CONCLUSION

It was confirmed that the midsagittal reference planes from these selected landmarks for UCLP patients were compatible with symmetric midsagittal reference planes from the Procrustes analysis and the asymmetric measurements.

The Inappropriate Symmetries of Multivariate Statistical Analysis in Geometric Morphometrics

In today's geometric morphometrics the commonest multivariate statistical procedures, such as principal component analysis or regressions of Procrustes shape coordinates on Centroid Size, embody a tacit roster of symmetries-axioms concerning the homogeneity of the multiple spatial domains or descriptor vectors involved-that do not correspond to actual biological fact. These techniques are hence inappropriate for any application regarding which we have a-priori biological knowledge to the contrary (e.g., genetic/morphogenetic processes common to multiple landmarks, the range of normal in anatomy atlases, the consequences of growth or function for form). But nearly every morphometric investigation is motivated by prior insights of this sort. We therefore need new tools that explicitly incorporate these elements of knowledge, should they be quantitative, to break the symmetries of the classic morphometric approaches. Some of these are already available in our literature but deserve to be known more widely: deflated (spatially adaptive) reference distributions of Procrustes coordinates, Sewall Wright's century-old variant of factor analysis, the geometric algebra of importing explicit biomechanical formulas into Procrustes space. Other methods, not yet fully formulated, might involve parameterized models for strain in idealized forms under load, principled approaches to the separation of functional from Brownian aspects of shape variation over time, and, in general, a better understanding of how the formalism of landmarks interacts with the many other approaches to quantification of anatomy. To more powerfully organize inferences from the high-dimensional measurements that characterize so much of today's organismal biology, tomorrow's toolkit must rely neither on principal component analysis nor on the Procrustes distance formula, but instead on sound prior biological knowledge as expressed in formulas whose coefficients are not all the same. I describe the problems of the standard techniques, discuss several examples of the alternatives, and draw some conclusions.

Examining the Efficiency of Models Using Tangent Coordinates or Principal Component Scores in Allometry Studies

Most of the studies in medical and biological sciences are related to the examination of geometrical properties of an organ or organism. Growth and allometry studies are important in the way of investigating the effects of diseases and the environmental factors effects on the structure of the organ or organism. Thus, statistical shape analysis has recently become more important in the medical and biological sciences. Shape is all geometrical information that remains when location, scale and rotational effects are removed from an object. Allometry, which is a relationship between size and shape, plays an important role in the development of statistical shape analysis. The aim of the present study was to compare two different models for allometry which includes tangent coordinates and principal component scores of tangent coordinates as dependent variables in multivariate regression analysis. The results of the simulation study showed that the model constructed by taking tangent coordinates as dependent variables is more appropriate than the model constructed by taking principal component scores of tangent coordinates as dependent variables, for all sample sizes.

3D-Geomorphometrics tooth shape analysis in hypodontia

Assessment of tooth morphology is an important part of the diagnosis and management of hypodontia patients. Several techniques have been used to analyze tooth form in hypodontia patients and these have shown smaller tooth dimensions and anomalous tooth shapes in patients with hypodontia when compared with controls. However, previous studies have mainly used 2D images and provided limited information. In the present study, 3D surface-imaging and statistical shape analysis were used to evaluate tooth form differences between hypodontia and control patients. Eighteen anatomical landmarks were recorded on the clinical crown of the lower left first permanent molar of 3D scanned study models of hypodontia and control subjects. The study sample group comprised of 120 hypodontia patients (40 mild, 40 moderate, and 40 severe hypodontia patients) and 40 age- and sex-matched controls. Procrustes coordinates were utilized to scale and superimpose the landmark coordinate data and then were subjected to principal component analysis (PCA). Subsequently, differences in shape as well as size were tested statistically using allometric analysis and MANOVA. Significant interaction was found between the two factor variables “group” and “sex” (p < 0.002). Overall expected accuracies were 66 and 56% for females and males, respectively, in the cross-validated discriminant-analysis using the first 20 PCs. Hypodontia groups showed significant shape differences compared with the control subjects (p < 0.0001). Significant differences in tooth crown shape were also found between sexes (p < 0.0001) within groups. Furthermore, the degree of variation in tooth form was proportional to the degree of the severity of the hypodontia. Thus, quantitative measurement of tooth shape in hypodontia patients may enhance the multidisciplinary management of those patients.

Axial cervical vertebrae-based multivariate regression model for the estimation of skeletal-maturation status

OBJECTIVES

This study aimed to determine the viability of using axial cervical vertebrae (ACV) as biological indicators of skeletal maturation and to build models that estimate ossification level with improved explanatory power over models based only on chronological age.

MATERIALS AND METHODS

The study population comprised 74 female and 47 male patients with available hand-wrist radiographs and cone-beam computed tomography images. Generalized Procrustes analysis was used to analyze the shape, size, and form of the ACV regions of interest. The variabilities of these factors were analyzed by principal component analysis. Skeletal maturation was then estimated using a multiple regression model.

RESULTS

Separate models were developed for male and female participants. For the female estimation model, the adjusted R(2) explained 84.8% of the variability of the Sempé maturation level (SML), representing a 7.9% increase in SML explanatory power over that using chronological age alone (76.9%). For the male estimation model, the adjusted R(2) was over 90%, representing a 1.7% increase relative to the reference model.

CONCLUSIONS

The simplest possible ACV morphometric information provided a statistically significant explanation of the portion of skeletal-maturation variability not dependent on chronological age. These results verify that ACV is a strong biological indicator of ossification status.

Reproducibility of 3D chromatin configuration reconstructions

It is widely recognized that the three-dimensional (3D) architecture of eukaryotic chromatin plays an important role in processes such as gene regulation and cancer-driving gene fusions. Observing or inferring this 3D structure at even modest resolutions had been problematic, since genomes are highly condensed and traditional assays are coarse. However, recently devised high-throughput molecular techniques have changed this situation. Notably, the development of a suite of chromatin conformation capture (CCC) assays has enabled elicitation of contacts-spatially close chromosomal loci-which have provided insights into chromatin architecture. Most analysis of CCC data has focused on the contact level, with less effort directed toward obtaining 3D reconstructions and evaluating the accuracy and reproducibility thereof. While questions of accuracy must be addressed experimentally, questions of reproducibility can be addressed statistically-the purpose of this paper. We use a constrained optimization technique to reconstruct chromatin configurations for a number of closely related yeast datasets and assess reproducibility using four metrics that measure the distance between 3D configurations. The first of these, Procrustes fitting, measures configuration closeness after applying reflection, rotation, translation, and scaling-based alignment of the structures. The others base comparisons on the within-configuration inter-point distance matrix. Inferential results for these metrics rely on suitable permutation approaches. Results indicate that distance matrix-based approaches are preferable to Procrustes analysis, not because of the metrics per se but rather on account of the ability to customize permutation schemes to handle within-chromosome contiguity. It has recently been emphasized that the use of constrained optimization approaches to 3D architecture reconstruction are prone to being trapped in local minima. Our methods of reproducibility assessment provide a means for comparing 3D reconstruction solutions so that we can discern between local and global optima by contrasting solutions under perturbed inputs.

Articulatory distinctiveness of vowels and consonants: a data-driven approach

PURPOSE

To quantify the articulatory distinctiveness of 8 major English vowels and 11 English consonants based on tongue and lip movement time series data using a data-driven approach.

METHOD

Tongue and lip movements of 8 vowels and 11 consonants from 10 healthy talkers were collected. First, classification accuracies were obtained using 2 complementary approaches: (a) Procrustes analysis and (b) a support vector machine. Procrustes distance was then used to measure the articulatory distinctiveness among vowels and consonants. Finally, the distance (distinctiveness) matrices of different vowel pairs and consonant pairs were used to derive articulatory vowel and consonant spaces using multidimensional scaling.

RESULTS

Vowel classification accuracies of 91.67% and 89.05% and consonant classification accuracies of 91.37% and 88.94% were obtained using Procrustes analysis and a support vector machine, respectively. Articulatory vowel and consonant spaces were derived based on the pairwise Procrustes distances.

CONCLUSIONS

The articulatory vowel space derived in this study resembled the long-standing descriptive articulatory vowel space defined by tongue height and advancement. The articulatory consonant space was consistent with feature-based classification of English consonants. The derived articulatory vowel and consonant spaces may have clinical implications, including serving as an objective measure of the severity of articulatory impairment.

How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test

The Mantel test provides a means to test the association between distance matrices and has been widely used in ecological and evolutionary studies. Recently, another permutation test based on a Procrustes statistic (PROTEST) was developed to compare multivariate data sets. Our study contrasts the effectiveness, in terms of power and type I error rates, of the Mantel test and PROTEST. We illustrate the application of Procrustes superimposition to visually examine the concordance of observations for each dimension separately and how to conduct hypothesis testing in which the association between two data sets is tested while controlling for the variation related to other sources of data. Our simulation results show that PROTEST is as powerful or more powerful than the Mantel test for detecting matrix association under a variety of possible scenarios. As a result of the increased power of PROTEST and the ability to assess the match for individual observations (not available with the Mantel test), biologists now have an additional and powerful analytical tool to study ecological and evolutionary relationships.