A Threefold Deformation Decomposition in Shape Analysis for Medical Imaging: Spherical, Deviatoric and Non Affine Components

Chlamydoselachus anguineus, Garman 1884, commonly called the frilled shark, is a deep‐sea shark species occurring up to depths of 1300 m. It is assumed to represent an ancient morphotype of sharks (e.g., terminal mouth opening, more than five gill slits) and thus is often considered to represent plesiomorphic traits for sharks. Therefore, its early ontogenetic developmental traits are important for understanding the evolution of its particular phenotype. Here, we established six stages for prenatal embryos and used linear measurements and geometric morphometrics to analyse changes in shape and size as well as their timing during different embryonic stages. Our results show a change in head shape and a relocation of the mouth opening at a late stage of development. We also detected a negative allometric growth of the head and especially the eye compared to the rest of the body and a sexual dimorphism in total body length, which differs from the known data for adults. A multivariate analysis of covariance shows a significant interaction of shape related to the logarithm of centroid size and developmental stage. Geometric morphometrics results indicate that the head shape changes as a covariate of body size while not accounting for differences between sexes. The growth pattern of stages 32 and 33 indicates a shift in head shape, thus highlighting the moment in development when the jaws start to elongate anteriorly to finally achieve the adult condition of terminal mouth opening rather than retaining the early embryonic subterminal position as is typical for sharks. Thus, the antero‐terminal mouth opening of the frilled shark has to be considered a derived feature.

Comparative morphometrics of sharpsnout seabream ( Diplodus puntazzo Cetti, 1777), reared in different conditions

In this study we describe the development of the female femur based on the analysis of high-resolution radiographic images by means of geometric morphometrics, while assessing the usefulness of this method in these kinds of studies. The material analysed consisted of digital images in DICOM format (telemetries), corresponding to 184 left femora in anterior view, obtained from the database of the Hospital Sant Joan de Déu of Barcelona (Spain). Bones analysed corresponded to individuals from 9 to 14 years old. Size and shape variation of the entire femur was quantified by 22 two-dimensional landmarks. Landmark digitisation errors were assessed using Procrustes anova test. Centroid size (CS) variation with age was evaluated by an anova test. Shape variation was assessed by principal component analysis. A mancova test between the first five principal components and age, using the CS as covariable, was applied. Results indicated that both size and shape vary significantly with age. Several age-related shape changes remained significant after removing the allometric effect. In general, an increase in the robustness of the bone and noticeable phenotypic changes in certain areas of the femur were observed. During growth in the proximal region of the femur, the collo-diaphyseal angle decreases, the neck of the femur widens and the fovea moves to a lower position, standing more in line with the plane of the neck. Likewise, the size of the greater and lesser trochanters increase. In the distal region, a significant increase of epiphyseal dimensions was recorded, mainly in the medial condyle. The angular remodelling of the neck and the bicondylar region of the femur in females continues until 13 years old. The information provided in the present study increases our knowledge on the timing and morphology of the femur during development, and in particular the morphology of the different femoral ossification centres during development.

Editorial: Left ventricular dysfunction after open repair of simple confenital heart defects in infants and children

This paper presents a method for estimating the skeletal age of children based on the centroid size of their face and their basicranium, derived from the three-dimensional coordinates of anatomical landmarks. The sample consists of computed tomography scans of 127 children (54 boys, 73 girls) of mixed origin living in the area of Toulouse (France), ranging in age from a few days to 18 years. The purpose of the present investigation was, first, to increase the variety of age-related structures theoretically available for pediatric skeletal age estimation and, second, to devise a method that can be applicable from early postnatal age to the end of adolescence with a satisfactory accuracy independent of age and even a better accuracy with greater age. We examined the relationship between the chronological age and the centroid size, calculated by using geometric morphometric methods and a linear model. With the aid of cross-validations, the statistical analysis indicates that the centroid size of the facial skeleton can be used an age-related variable without any loss of accuracy with increased age, contrary to most of the methods of pediatric age estimation. The standard error was always lower or equal to 2.1 years (at the 95% confidence level) and decreased in our sub-sample of older children represented by a larger number of individuals.

Sclerosteosis, a rare autosomal recessive genetic disorder caused by a mutation of the Sost gene, manifests in the facial skeleton by gigantism, facial distortion, mandibular prognathism, cranial nerve palsy, and, in extreme cases, compression of the medulla oblongata. Mice lacking sclerostin reflect some symptoms of sclerosteosis, but this is the first report of the effect on the facial skeleton. We used geometric morphometrics (GMM) to analyze the deformations of the murine facial skeleton from the wild‐type to the Sost gene knockout. Landmark coordinates were obtained by surface reconstructions from micro‐computed tomography. Centroid size, principal component scores in shape space and form space, and asymmetry were computed by the standard GMM formulas, and dental and skeletal jaw lengths were examined as ratios. We show here that, compared to wild type controls, mice lacking Sost have larger centroid size (effect size, p‐value: 4.59, <.001), higher mean asymmetry (1.14, .065), dental and skeletal mandibular prognathism (1.36, .010 and 5.92, <.001), a smaller foramen magnum (−1.71, .015), and calvaria that are more highly curved (form space p = 4.09, .002; shape space p = 12.82, .002). These features of mice lacking sclerostin largely correspond to the changes of the facial skeleton observed in sclerosteosis. This alignment further supports claims that the Sost gene plays a fundamental role in bony facial development in rodents and humans alike.

Geometric morphometric evaluation of cervical vertebrae shape and its relationship to skeletal maturation

The best insight into the development of Devonian phacopids has been obtained from Trimerocephalus lelievrei Crônier & Feist, 1997, a Famennian phacopine from Morocco, where changes in size and shape have been quantified. In this study, a morphometric approach has been used: (1) to retrodeform and then establish patterns of morphological variation in a well preserved but tectonically deformed assemblage belonging to another phacopine species Weyerites ensae (Richter & Richter, 1926), a Famennian phacopine from Thuringia, and (2) to establish patterns of developmental and evolutionary changes within two closely related species: Weyerites ensae and Trimerocephalus lelievrei. The method of retrodeformation using a set of discrete points presumed to be homologous on all studied individuals, has demonstrated that the next analyses are possible on the retrodeformed material as compared to the undeformed material. Morphometric analysis based on outline analysis has permitted demonstration of progressive shape change in agreement with ontogenetic ordination and a comparison of changes in size and shape in Weyerites ensae. The main changes in shape appear to occur in the meraspid period, whereas increase in size takes place mainly in the holaspid period. This pattern, already reported for Trimerocephalus lelievrei, can be generalized for phacopine trilobites from the Late Devonian. Moreover, the comparison of the two ontogenetic trajectories has shown that most of the differences are related to ‘structural’ changes, probably linked to a relative pre- post-displacement. The results suggest that ecological adaptation may be studied by examining the changes in development that occur within species through time and space.

Theory and Methods: An Idiosyncratic History of Early Morphometrics R.A. Reyment. Multivariate Allometry C.P. Klingenberg. Data Acquisition: Introduction to Data Acquisition L.F. Marcus. Three-dimensional Data Capture and Acquisition D. Dean. Two-dimensional Imaging: An Update A. GarciaValdecasas. Imagina: A Direct Tool for Image Analysis in Systematics J.M. Becerra. Landmark Methods: Introduction to Landmark Methods D. Slice. Morphometric Spaces, Shape Components and the Effects of Linear Transformations F.J. Rohlf. Combining the Tools of Geometric Morphometrics F.L. Bookstein. Standard Formula for the Uniform Shape Component in Landmark Data F.L. Bookstein. Affine Transformations as a Modelof Virtual Form Change for Generating Morphospaces D. Russkin-Gutman, A.D. Buscalioni. Outlines: With and without Landmarks: Introduction to Outlines F.J. Rohlf. Eigenshape Analysis of Left Ventricular Outlines from Contrast Ventriculograms P.D. Sampson, et al. Chisquare Test of Biological Space Curve Affinities D. Dean, et al. Comparing Shapes of Organisms: Geographic Comparisons: Introduction to Geometric Morphometrics and Intraspecific Variation: A Fascinating Adventure A. Loy. Fluctuating Asymmetry in Mus musculus Subspecific Hybridization: Traditional and Procrustes Comparative Approach J.C. Auffray, et al. Wing Venation Variability in Monarthropalpus buxi (Diptera, Cecidomyiidae) and the Quaternary Coevolution of Box (Buxus sempervirens L.) and Its Midge: A Geometrical Morphometric Analysis M. Baylac, T. Daufresne. Size and Shape Variation in the Mandible of the Fossorial Rodent Spalax ehrenbergi: A Procrustes Analysis of Three Dimensions M. Corti, et al. Principal Components of Body Shape Variation within an Endemic Radiation of Threespine Stickleback J. Walker. Low Taxonomic Level and Intraspecific Comparisons: Introduction to Comparison of Similar Objects Whose Group Identity Is Known M. Corti. Identification of House Mice Musmusculus, and Mound Building Mice, M. spicilegus, Based on Distance and Landmark Data A. Demeter et al. Correspondence between Interlandmark Distances and Caliper Measurements S. Reig. Some Applications of Geometric Morphometrics to Ostracoda R.A. Reyment. Shape Changes during the Growth of the Sea Bass, Dicentrarchus labrax (Teleostea: Perciformes), in Relation to Different Rearing Conditions: An Application of Thinplate Spline Regression Analysis A. Loy, et al. Higher Taxonomic Level Comparisons: Introduction to Comparisons amongTaxa at the Level of Species, Genus and Family G. Naylor. The Evolution and Growth of the Hominid Pelvis: A Preliminary Thinplate Spline Study of Ilium Shape C. Berge. Stephanodonty in Fossil Murids: A Landmark based Morphometric Approach J. van Dam. 16 additional articles. Appendixes. Index.

This study investigates interspecific and intraspecific variation in patellar morphology among the examined species of ruminants and explores whether these differences are consistent with their reported locomotor ecology. While the patella functions as a crucial lever during locomotion, the extent to which this relatively small bone reflects adaptive variation across species remains uncertain. This research aims to characterize patellar shape diversity in five selected ruminant species and to explore its potential functional implications within this limited comparative framework. A total of 352 patellae representing five ruminant species (Bos taurus, Bison bonasus, Ovis aries, Capra hircus, and Capreolus capreolus) belonging to the families Bovidae and Cervidae were digitized as three-dimensional models and analyzed using geometric morphometrics. Morphospace distributions, shape variation, and allometric relationships were assessed. Distinct patellar morphologies were observed among the examined species. Bos taurus formed a distinct cluster, whereas European bison (Bison bonasus) largely overlapped with the sheep cluster in shape space. Nevertheless, Bovids tended to exhibit relatively more medio-lateral expansion and more developed cartilaginous processes, consistent with greater weight-bearing demands and joint stability. In contrast, Capreolus capreolus and Capra hircus displayed slender, elongated patellae with reduced projections, a morphology that may be associated with agility and speed-related locomotor demands. Ovis aries occupied an intermediate morphospace, overlapping partially with both large and small ruminants. Procrustes ANOVA confirmed significant shape differences among the examined species, excluding sheep and goats. Allometric analyses revealed a strong association between patellar shape and centroid size in this dataset of five species. These findings demonstrate that, in the studied species, patellar morphology reflects an intricate interplay of functional adaptation, phylogenetic relatedness, and allometric scaling. Despite its small size, the patella may serve as an informative morphological marker of ecological and functional differentiation among ruminant species within the comparative framework examined here, and the patterns observed in this study may help generate hypotheses for broader comparative analyses in other ruminant taxa.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-33370-3.

Climate change may force organisms to adapt genetically or plastically to new environmental conditions. Invasive species show remarkable potential for rapid adaptation. The ovoviviparous New Zealand mud snail (NZMS), Potamopyrgus antipodarum, has successfully established across Europe with two clonally reproducing mitochondrial lineages since its arrival in the first half of the 19th century. Its remarkable variation in shell morphology was shown to be fitness relevant. We investigated the effects of temperature on shell morphology across 11 populations from Germany and the Iberian Peninsula in a common garden across three temperatures. We analyzed size and shape using geometric morphometrics. For both, we compared reaction norms and estimated heritabilities. For size, the interaction of temperature and haplotype explained about 50% of the total variance. We also observed more genotype by environment interactions indicating a higher degree of population differentiation than in shape. Across the three temperatures, size followed the expectations of the temperature‐size rule, with individuals growing larger in cold environments. Changes in shape may have compensated for changes in size affecting space for brooding embryos. Heritability estimates were relatively high. As indicated by the very low coefficients of variation for clonal repeatability (CV A ), they can probably not be compared in absolute terms. However, they showed some sensitivity to temperature, in haplotype t more so than in z, which was only found in Portugal. The low CV A values indicate that genetic variation among European populations is still restricted with a low potential to react to selection. A considerable fraction of the genetic variation was due to differences between the clonal lineages. The NZMS has apparently not been long enough in Europe to accumulate significant genetic variation relevant for morphological adaptation. As temperature is obviously not the sole factor influencing shell morphology, their interaction will probably not be a factor limiting population persistence under a warming climate in Europe.

Traditionally, the distinction between meraspis and holaspis among trilobites has been based on the achievement of the full adult complement of thoracic segments. Using a large sample (over 700 specimens collected from a single bed) we explore the utility of employing the ontogenetic trajectory of the cranidium as an alternative means to differentiate trilobite growth stages. This method is particularly useful for species represented solely by exuviae and disarticulated individuals. We use geometric morphometrics to examine shape change among cranidia ranging in size from 0.9 mm to 11.6 mm in cephalic length. The 114 measured specimens exhibit a rather continuous gradation in size in which no distinct instars are evident.The meraspid and holaspid specimens exhibit allometry when partial warp scores and uniform components of shape derived from thin-plate spline analysis are regressed onto log centroid size. To describe allometric shape change, deformation vectors from the smallest to the largest specimen in both ontogenetic stages are presented in three different superimposition settings by using a new software program. We have concluded that a new superimposition method (the Sliding Baseline Registration) is a useful tool for visualizing allometry in organisms that contain an axis of symmetry. As a result, we conclude that allometry is evident in meraspides and holaspides, but the degree of allometry in holaspides is very small relative to that in meraspides. The boundary between meraspis and holaspis in Triarthrus becki appears to correspond to a large change in the rate of ontogenetic change, but neither to a change in the direction of that trajectory nor to a cessation of ontogenetic change. This boundary also corresponds to a cranidium centroid size that matches well previous determinations that holaspis begins at about 2.8 mm in cephalic length.

BackgroundConsidering the practicality of geometric morphometrics which could discriminate insect species, this application was extended to the analysis of blow fly larval growth based on cephalopharyngeal skeleton. In forensic entomology, cephalopharyngeal skeleton plays a crucial role in species identification but the morphometric information of this part is scarce. In this study, Chrysomya megacephala (Fabricius, 1794) was reared in two study replicates in natural conditions and samplings were conducted at fixed daily intervals. Cephalopharyngeal skeletons were removed from larvae and mounted on glass slides. Images were obtained from the specimens; digitized and geometric morphometric analysis on C. megacephala cephalopharyngeal skeletons was performed with MorphoJ software based on the ordination of five landmarks. The assessments of this analysis were based on centroid size measurements, visualization on the landmarks displacements, classification of the relative landmarks by using canonical variate analysis, and ontogenetic allometry determination.FindingsCentroid size was strongly correlated with developmental time (p < 0.05) and significantly different between daily intervals (p < 0.05). Ontogenetic allometric effect based on multivariate regression on Procrustes coordinates and centroid size was significant (p < 0.0001), indicating that shape was influenced by growth (60.3%). Disposition occurred on all landmarks during development and was further discriminated based on age groups.ConclusionsOther than discriminating between species, geometric morphometrics was found to be practical to visualize larval growth based on cephalopharyngeal skeletons which can be useful in forensic entomology.

BackgroundThere is currently no method that can predict whether or under what condition hypopnea, even obstructive sleep apnea (OSA), will occur during sleep for individuals based on credible parameters measured under waking condition. We propose a threshold concept based on the narrowest cross-sectional area of the upper airway (CSA-UA) and aim to prove our hypothesis on the threshold of the area for hypopnea onset (TAHO), which can be used as an indicator of hypopnea onset during sleep and measured while awake.MethodsWe performed magnetic resonance imaging for 20 OSA patients to observe CSA-UA changes during fluid accumulation in the neck caused by elevating their legs, and identified TAHO by capturing the sudden enlargement in CSA-UA. Correlation analyses between TAHO and the body mass index (BMI), and between the reduction in CSA-UA and the increase in the neck circumference (NC) with fluid accumulation were performed. Logistic regression analysis was performed for identifying OSA patients based on the behaviors of their CSA-UA changes during leg raising. Shape changes of airway cross-section were also investigated.ResultsFour CSA-UA change patterns after fluid redistribution were identified. Six patients had similar CSA-UA variation behaviors observed in healthy subjects. From the other three change patterns involving 14 patients, a threshold value of CSA-UA 0.63 ± 0.21 cm2 was identified for normal breathing. Data showed a positive correlation between TAHO and BMI (r = 0.681, p = 0.0007), and a negative correlation between the reduction in CSA-UA and the increase in NC (r = − 0.513, p = 0.051) with fluid accumulation. A sigmoid function for the probability of being a OSA patient p = 1/[1 + exp. (4.836 + 3.850 t-8.4 h)] was obtained to effectively separate OSA patients from normal subjects. The upper airway narrowing occurred in anteroposterior, lateral, or both directions, suggesting different tendencies of upper airway collapse in patients. Three types of shape changes in the cross-section of the upper airway, which had different effects on airway resistance, were measured.ConclusionsOur findings prove TAHO hypothesis. The threshold measured while awake for normal breathing can be used clinically as the indicator of hypopnea onset during sleep, and therefore to identify OSA patients under waking condition and design effective personalized treatments for OSA patients. Both shape and size changes in the cross-section of the upper airway affect airway resistance significantly. Shape change in the cross-section of the upper airway can provide key clinical information on the collapse patterns of the upper airway for individuals.

Preface. Acknowledgments. Introduction. 1. Virtual Reconstruction. 1.1 A Virtual Reality Contest. 1.2 Virtual Reconstruction. 1.3 Computer-Assisted Paleontology. 1.3.1 Data Acquisition. 1.3.2 Data Segmentation and Three-Dimensional Reconstruction. 1.3.3 Virtual Fossil Reconstruction. 1.3.4 From Virtual Reality to Real Virtuality. 1.3.5 Databases and Morphometry. 1.3.6 Virtual Reconstruction in Space and Time. 1.4 Computer-Assisted Surgery. 1.5 Further Reading. 2. Data Representation. 2.1 World Food on a Chessboard. 2.2 Facts About Data to Get Data About Facts. 2.2.1 Analog and Digital Data. 2.2.2 Bits, Bytes, and Words. 2.2.3 Characters, Numbers, Pixels, and Voxels. 2.2.4 Representing Gray Tones and Colors. 2.2.5 Data Compression. 2.2.6 Some Common Image File Formats. 2.2.7 Implicit Versus Explicit Representation of Object Data. 2.2.8 Modeling Three-Dimensional Objects. 2.3 A Taxonomy of Biomedical Data. 2.3.1 Perspectives on Data. 2.3.2 Volume Data. 2.3.3 Surface Data. 2.3.4 Landmark Data. 2.3.5 Extent-Based Data. 2.3.6 Relational Data. 2.4 Further Reading. 3. Data Acquisition. 3.1 Data and the Physical World. 3.2 Vision and Photography as Data Acquisition: Performance Considerations. 3.3 Computed Tomography. 3.3.1 Frau RAntgena s Wedding Ring. 3.3.2 Radiographic Projections. 3.3.3 Reconstructing CT Images. 3.3.4 CT Scanning: Technical Considerations. 3.3.5 Limitations of CT Data Acquisition. 3.3.6 Slice-to-Slice, Helical, and Multislice CT. 3.3.7 Industrial and Micro Computed Tomography. 3.3.8 Three-Dimensional Data Acquisition with a Medical Scanner. 3.4 Magnetic Resonance Imaging. 3.5 Surface Scanners. 3.6 3D Digitizers. 3.7 Further Reading. 4. Image Data Processing. 4.1 Recovering Objects from Images. 4.2 Converting a CT Image into a Screen Image. 4.3 Filtering Images. 4.3.1 Coffee and Kernels. 4.3.2 Convolution and Fourier Analysis. 4.3.3 Statistical Filters. 4.3.4 Edge Detection Filters. 4.4 Extracting Isosurfaces. 4.4.1 Determining Boundaries in CT Images. 4.4.2 From Edges to Isocontours and Isosurfaces. 4.5 Interactive Segmentation. 4.6 Further Reading. 5. Visualization and Interaction. 5.1 Visualizing Data in Two and More Dimensions. 5.2 Interaction with Virtual Worlds. 5.3 The Graphics Rendering Pipeline. 5.4 Setting Up a Virtual Environment. 5.4.1 Object Materials, Lighting, and Shading. 5.4.2 Setting Up the Camera. 5.4.3 Object Manipulation and Interaction. 5.5 Volume Rendering. 5.6 Further Reading. 6. Virtual Fossil Reconstruction. 6.1 A Baroque Puzzle. 6.2 Principles of Reconstruction. 6.3 Physical and Virtual Reconstruction. 6.4 Preparing and Restoring Fossils on the Computer Screen. 6.5 Reconstructing Fossil Morphologies. 6.5.1 Recovering Implicit Anatomic Information. 6.5.2 Combining Computer Graphics and Anatomy: The Globe Paradigm. 6.5.3 Inferring Missing Information. 6.5.4 Interpolation and Extrapolation. 6.6 Correcting Fossil Deformation. 6.6.1 Taphonomic Scenarios. 6.6.2 Correcting Plastic Deformation. 6.7 Validating Virtual Reconstructions. 6.8 Paleodiagnostics and Paleoforensics. 6.9 Inferring Soft Tissue Structures. 6.9.1 Motivation. 6.9.2 Fossil Soft Tissue Reconstruction: Classic and Virtual Approaches. 6.9.3 What Shall Be Reconstructed? 6.9.4 Soft Tissue Reconstruction and Measurement. 6.10 Virtual Surgery: A Paleoanthropologista s Eye View. 6.10.1 Motivation. 6.10.2 Virtual Planning and Simulation of Surgical Interventions. 6.10.3 Custom Implant Design. 6.10.4 Soft Tissue Reconstruction. 6.11 Further Reading. 7. From Virtual Reality to Real Virtuality. 7.1 Reifying Virtual Objects. 7.2 Principles of Rapid Prototyping. 7.3 Combining Virtual Reality and Real Virtuality. 7.4 Further Reading. 8. Morphometric Analysis. 8.1 Morphometry as Reconstruction. 8.2 Morphometry and Geometry. 8.2.1 The Role of Geometry. 8.2.2 The Role of Size and Shape. 8.2.3 Multivariate Morphometry. 8.2.4 Principal Components Analysis and Dimension Reduction. 8.2.5 Classic Multivariate Morphometry: Geometry Lost. 8.2.6 Geometric Morphometrics: Geometry Recovered. 8.3 Shape Space Analysis. 8.3.1 From Da Arcy Thompson to Kendall. 8.3.2 The Workflow of Shape Space Analysis. 8.3.3 Determining a Reference Shape. 8.3.4 Analyzing Data in Shape Space. 8.3.5 Visualizing Patterns of Shape Difference and Shape Change. 8.3.5 Visualizing Patterns of Shape Difference and Shape Change. 8.4 Euclidean Distance Matrix Analysis. 8.4.1 In Search of the Golden Mean. 8.4.2 Exploring Form Variability with EDMA. 8.5 Outline Analysis. 8.6 A Comparison of Geometric Morphometric Methods. 8.6.1 Criteria for Comparison. 8.6.2 From Pattern to Process. 8.7 Exploring Morphometric Patterns. 8.8 Further Reading. Appendix A. Image Data Acquisition Systems: Performance Considerations. Appendix B. Parameters Influencing the Quality of CT Image Data. Appendix C. CT Scanning of Fossil Specimens and Recent Skeletal Specimens: How to Proceed? Appendix D. Object Manipulation in Virtual Space. Appendix E. A Parsimonious Approach to Correction of Taphonomic Deformation. Appendix F. Morphometry. References. Index.