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Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes. © 2023 The Authors. Advanced Materials published by Wiley-VCH GmbH.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes. © 2023 The Authors. Advanced Materials published by Wiley-VCH GmbH.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes. © 2023 The Authors. Advanced Materials published by Wiley-VCH GmbH.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Nanostructured surfaces have recently been established as a novel surface technology to alleviate health and industrial problems caused by bacterial biofilms. Whilst fundamental research has advanced, nanostructure arrays have generally only been developed on 2D, flat substrates, and evaluated by incubating bacteria parallel to nanostructure direction. These circumstances do not reflect real-world surfaces which are often curved and randomly oriented with respect to sedimentation direction. Titanium dioxide nanostructures on 3D, hemisphere-shaped substrates were fabricated using hydrothermal synthesis to investigate the effects of curvature and orientation on bactericidal performance. 3D surfaces were 91% more efficient at resisting Staphylococcus aureus adhesion compared to 2D surfaces, and cells that did attach were killed with the same or higher efficiency after 1 and 3 h exposure to nanostructured surfaces. This preliminary study establishes hydrothermal synthesis as a viable fabrication method of 3D bactericidal surfaces and provides insight into surface curvature and orientation impact on bactericidal efficiency.

Morphological characters play an important role in species descriptions and are essential for a better understanding of the function, evolution and plasticity of an organism’s shape. However, in complex-shaped organisms lacking characteristic features that can be used as landmarks, quantifying morphological traits, assessing their intra- and interspecific variation, and subsequently delineating phenotypically distinct groups continue to be problematic. For such organisms, three-dimensional morphological analysis might be a promising approach to differentiate morphogroups and potentially aid the delineation of species boundaries, though identifying informative features remains a challenge. Here, we assessed the potential of 3D-based quantitative morphology to delineate a priori and/or to discriminate a posteriori morphogroups of complex-shaped and taxonomically challenging organisms, such as corals from the morphologically diverse genus Acropora. Using three closely related coral taxa previously delimited using other lines of evidence, we extracted a set of variables derived from triangulated polygon meshes and medial axis skeletons of the 3D models. From the resulting data set, univariate and multivariate analyses of 3D-based variables quantifying overall shape including curvature, branching, and complexity were conducted. Finally, informative feature selection was performed to assess the discriminative power of the selected variables. Results revealed significant interspecific differences in the means of a set of 3D-based variables, highlighting potentially informative characters that provide sufficient resolution to discriminate morphogroups congruent with independent species identification based on other lines of evidence. A combination of representative features, remarkably represented by curvature, yielded measures that assisted in differentiating closely related species despite the overall morphospaces overlap. This study shows that a well-justified combinatio, SCOPUS: ar.j, info:eu-repo/semantics/published

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. Statement of significance: The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface cur, Biomaterials & Tissue Biomechanics

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. Statement of significance: The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface cur, Biomaterials & Tissue Biomechanics

Although much is known about the embryo during implantation, the architecture of the uterine environment in which the early embryo develops is not well understood. We employed confocal imaging in combination with 3D analysis to identify and quantify dynamic changes to the luminal structure of murine uterus in preparation for implantation. When applied to mouse mutants with known implantation defects, this method detected striking peri-implantation abnormalities in uterine morphology that cannot be visualized by histology. We revealed 3D organization of uterine glands and found that they undergo a stereotypical reorientation concurrent with implantation. Furthermore, we extended this technique to generate a 3D rendering of the cycling human endometrium. Analyzing the uterine and embryo structure in 3D for different genetic mutants and pathological conditions will help uncover novel molecular pathways and global structural changes that contribute to successful implantation of an embryo.

Although much is known about the embryo during implantation, the architecture of the uterine environment in which the early embryo develops is not well understood. We employed confocal imaging in combination with 3D analysis to identify and quantify dynamic changes to the luminal structure of murine uterus in preparation for implantation. When applied to mouse mutants with known implantation defects, this method detected striking peri-implantation abnormalities in uterine morphology that cannot be visualized by histology. We revealed 3D organization of uterine glands and found that they undergo a stereotypical reorientation concurrent with implantation. Furthermore, we extended this technique to generate a 3D rendering of the cycling human endometrium. Analyzing the uterine and embryo structure in 3D for different genetic mutants and pathological conditions will help uncover novel molecular pathways and global structural changes that contribute to successful implantation of an embryo.

Local solid shape applies to the surface curvature of small surface patches-essentially regions of approximately constant curvatures-of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution.

In this paper, we analyze the relation between the surface curvature of an isolated charged conductor and resultant electrostatic potential. The study will be performed for a long conductor with uniform cross section. It will be demonstrated by geometric arguments that a correlation between curvature and potential exists. This relation will be obtained for a set of polar coordinates that parameterize the surface of the isolated conductor. Two examples will be discussed based on quasi-circular conducting cylinders, whose cross sections are obtained firstly perturbing the equation of the circle by a cosine function and secondly by a more general function including a Fourier series expansion.

In this paper, we analyze the relation between the surface curvature of an isolated charged conductor and resultant electrostatic potential. The study will be performed for a long conductor with uniform cross section. It will be demonstrated by geometric arguments that a correlation between curvature and potential exists. This relation will be obtained for a set of polar coordinates that parameterize the surface of the isolated conductor. Two examples will be discussed based on quasi-circular conducting cylinders, whose cross sections are obtained firstly perturbing the equation of the circle by a cosine function and secondly by a more general function including a Fourier series expansion.

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used

In this paper it is described how to build a statistical shape model using a training set with a sparse of landmarks. A well defined model mesh is selected and fitted to all shapes in the training set using thin plate spline warping. This is followed by a projection of the points of the warped model mesh to the target shapes. When this is done by a nearest neighbour projection it can result in folds and inhomogeneities in the correspondence vector field. The novelty in this paper is the use and extension of a Markov random field regularisation of the correspondence field. The correspondence field is regarded as a collection of random variables, and using the Hammersley-Clifford theorem it is proved that it can be treated as a Markov Random Field. The problem of finding the optimal correspondence field is cast into a Bayesian framework for Markov Random Field restoration, where the prior distribution is a smoothness term and the observation model is the curvature of the shapes. The Markov Random Field is optimised using a combination of Gibbs sampling and the Metropolis-Hasting algorithm. The parameters of the model is found using a leave-one-out approach. The method leads to a generative model that produces highly homogeneous polygonised shapes with improved reconstruction capabilities of the training data. Furthermore, the method leads to an overall reduction in the total variance of the resulting point distribution model. The method is demonstrated on a set of human ear canals extracted from 3D-laser scans.