Quantitative analysis of imprint shape and its relation to mechanical properties measured by microindentation in bone

Microindentation in bone is a micromechanical testing technique routinely used to extract material properties related to bone quality. As the analysis of microindentation data is based on assumptions about the contact between sample and surface, the aim of this study was to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topology was measured by atomic force microscopy. Statistical shape modeling of the residual imprint allowed to define a mean shape and to describe the variability in terms of 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was found to be highly consistent and free of any pile up while differing mostly by depth between species and direction. A few of the topological parameters, in particular depth, showed significant but rather weak and inconsistent correlations to variations in mechanical properties. The mechanical response of bone as well as the residual imprint shape was highly consistent within each category. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small deviations from an ideally flat surface.

Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

Estimating Particle Shape and Orientation Using Volume Tensors

We develop statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles. We focus on the case where particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle shape and orientation, and we derive stereological estimators of the tensors. These estimators are combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends on the orientation and shape of the particles. For instance, if the distribution of the typical particle is invariant under rotations, then the covariance matrix is proportional to the identity matrix. We develop a non-parametric test for such isotropy. A flexible Lévy-based particle model is proposed, which may be analysed using a generalized method of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex.

Automatic multi-resolution shape modeling of multi-organ structures.

Point Distribution Models (PDM) are among the most popular shape description techniques and their usefulness has been demonstrated in a wide variety of medical imaging applications. However, to adequately characterize the underlying modeled population it is essential to have a representative number of training samples, which is not always possible. This problem is especially relevant as the complexity of the modeled structure increases, being the modeling of ensembles of multiple 3D organs one of the most challenging cases. In this paper, we introduce a new GEneralized Multi-resolution PDM (GEM-PDM) in the context of multi-organ analysis able to efficiently characterize the different inter-object relations, as well as the particular locality of each object separately. Importantly, unlike previous approaches, the configuration of the algorithm is automated thanks to a new agglomerative landmark clustering method proposed here, which equally allows us to identify smaller anatomically significant regions within organs. The significant advantage of the GEM-PDM method over two previous approaches (PDM and hierarchical PDM) in terms of shape modeling accuracy and robustness to noise, has been successfully verified for two different databases of sets of multiple organs: six subcortical brain structures, and seven abdominal organs. Finally, we propose the integration of the new shape modeling framework into an active shape-model-based segmentation algorithm. The resulting algorithm, named GEMA, provides a better overall performance than the two classical approaches tested, ASM, and hierarchical ASM, when applied to the segmentation of 3D brain MRI.

PDB-Explorer: a web-based interactive map of the protein data bank in shape space

Background The RCSB Protein Data Bank (PDB) provides public access to experimentally determined 3D-structures of biological macromolecules (proteins, peptides and nucleic acids). While various tools are available to explore the PDB, options to access the global structural diversity of the entire PDB and to perceive relationships between PDB structures remain very limited. Methods A 136-dimensional atom pair 3D-fingerprint for proteins (3DP) counting categorized atom pairs at increasing through-space distances was designed to represent the molecular shape of PDB-entries. Nearest neighbor searches examples were reported exemplifying the ability of 3DP-similarity to identify closely related biomolecules from small peptides to enzyme and large multiprotein complexes such as virus particles. The principle component analysis was used to obtain the visualization of PDB in 3DP-space. Results The 3DP property space groups proteins and protein assemblies according to their 3D-shape similarity, yet shows exquisite ability to distinguish between closely related structures. An interactive website called PDB-Explorer is presented featuring a color-coded interactive map of PDB in 3DP-space. Each pixel of the map contains one or more PDB-entries which are directly visualized as ribbon diagrams when the pixel is selected. The PDB-Explorer website allows performing 3DP-nearest neighbor searches of any PDB-entry or of any structure uploaded as protein-type PDB file. All functionalities on the website are implemented in JavaScript in a platform-independent manner and draw data from a server that is updated daily with the latest PDB additions, ensuring complete and up-to-date coverage. The essentially instantaneous 3DP-similarity search with the PDB-Explorer provides results comparable to those of much slower 3D-alignment algorithms, and automatically clusters proteins from the same superfamilies in tight groups. Conclusion A chemical space classification of PDB based on molecular shape was obtained using a new atom-pair 3D-fingerprint for proteins and implemented in a web-based database exploration tool comprising an interactive color-coded map of the PDB chemical space and a nearest neighbor search tool. The PDB-Explorer website is freely available at www.​cheminfo.​org/​pdbexplorer and represents an unprecedented opportunity to interactively visualize and explore the structural diversity of the PDB.

Prediction of Trabecular Bone Anisotropy from Quantitative Computed Tomography using Supervised Learning and a Novel Morphometric Feature Descriptor

Patient-specific biomechanical models including local bone mineral density and anisotropy have gained importance for assessing musculoskeletal disorders. However the trabecular bone anisotropy captured by high-resolution imaging is only available at the peripheral skeleton in clinical practice. In this work, we propose a supervised learning approach to predict trabecular bone anisotropy that builds on a novel set of pose invariant feature descriptors. The statistical relationship between trabecular bone anisotropy and feature descriptors were learned from a database of pairs of high resolution QCT and clinical QCT reconstructions. On a set of leave-one-out experiments, we compared the accuracy of the proposed approach to previous ones, and report a mean prediction error of 6% for the tensor norm, 6% for the degree of anisotropy and 19◦ for the principal tensor direction. These findings show the potential of the proposed approach to predict trabecular bone anisotropy from clinically available QCT images.

Fast Prediction of Femoral Biomechanics Using Supervised Machine Learning and Statistical Shape Modeling

Finite element (FE) analysis is an important computational tool in biomechanics. However, its adoption into clinical practice has been hampered by its computational complexity and required high technical competences for clinicians. In this paper we propose a supervised learning approach to predict the outcome of the FE analysis. We demonstrate our approach on clinical CT and X-ray femur images for FE predictions ( FEP), with features extracted, respectively, from a statistical shape model and from 2D-based morphometric and density information. Using leave-one-out experiments and sensitivity analysis, comprising a database of 89 clinical cases, our method is capable of predicting the distribution of stress values for a walking loading condition with an average correlation coefficient of 0.984 and 0.976, for CT and X-ray images, respectively. These findings suggest that supervised learning approaches have the potential to leverage the clinical integration of mechanical simulations for the treatment of musculoskeletal conditions.

Enhanced associative memory for colour (but not shape or location) in synaesthesia

People with grapheme-colour synaesthesia have been shown to have enhanced memory on a range of tasks using both stimuli that induce synaesthesia (e.g. words) and, more surprisingly, stimuli that do not (e.g. certain abstract visual stimuli). This study examines the latter by using multi-featured stimuli consisting of shape, colour and location conjunctions (e.g. shape A + colour A + location A; shape B + colour B + location B) presented in a recognition memory paradigm. This enables distractor items to be created in which one of these features is ‘unbound’ with respect to the others (e.g. shape A + colour B + location A; shape A + colour A + location C). Synaesthetes had higher recognition rates suggesting an enhanced ability to bind certain visual features together into memory. Importantly, synaesthetes’ false alarm rates were lower only when colour was the unbound feature, not shape or location. We suggest that synaesthetes are “colour experts” and that enhanced perception can lead to enhanced memory in very specific ways; but, not for instance, an enhanced ability to form associations per se. The results support contemporary models that propose a continuum between perception and memory.

Stereological estimation of particle shape and orientation from volume tensors

In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with CVs of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat.

Shape model, reference system definition, and cartographic mapping standards for comet 67P/Churyumov-Gerasimenko Stereo-photogrammetric analysis of Rosetta/OSIRIS image data

We analyzed more than 200 OSIRIS NAC images with a pixel scale of 0.9-2.4 m/pixel of comet 67P/Churyumov-Gerasimenko (67P) that have been acquired from onboard the Rosetta spacecraft in August and September 2014 using stereo-photogrammetric methods (SPG). We derived improved spacecraft position and pointing data for the OSIRIS images and a high-resolution shape model that consists of about 16 million facets (2 m horizontal sampling) and a typical vertical accuracy at the decimeter scale. From this model, we derive a volume for the northern hemisphere of 9.35 km(3) +/- 0.1 km(3). With the assumption of a homogeneous density distribution and taking into account the current uncertainty of the position of the comet's center-of-mass, we extrapolated this value to an overall volume of 18.7 km(3) +/- 1.2 km(3), and, with a current best estimate of 1.0 X 10(13) kg for the mass, we derive a bulk density of 535 kg/m(3) +/- 35 kg/m(3). Furthermore, we used SPG methods to analyze the rotational elements of 67P. The rotational period for August and September 2014 was determined to be 12.4041 +/- 0.0004 h. For the orientation of the rotational axis (z-axis of the body-fixed reference frame) we derived a precession model with a half-cone angle of 0.14 degrees, a cone center position at 69.54 degrees/64.11 degrees (RA/Dec J2000 equatorial coordinates), and a precession period of 10.7 days. For the definition of zero longitude (x-axis orientation), we finally selected the boulder-like Cheops feature on the big lobe of 67P and fixed its spherical coordinates to 142.35 degrees right-hand-rule eastern longitude and -0.28 degrees latitude. This completes the definition of the new Cheops reference frame for 67P. Finally, we defined cartographic mapping standards for common use and combined analyses of scientific results that have been obtained not only within the OSIRIS team, but also within other groups of the Rosetta mission.

Effects of shape Rosmarinus officinalis neighbors on resprouting of shape Erica multiflora individuals

To study the effects of competition in Mediterranean shrubland regeneration following disturbance, we used a neighborhood approach to assess the influence of mature Rosmarinus officinalis neighbors on the resprouting of Erica multiflora individuals after clipping. Sprout biomass of target plants 2 years after clipping was regressed against various measures of neighbor abundance within a 2 m radius around target E. multiflora individuals in which all vegetation except R. officinalis had been removed. The largest single influence on the biomass of sprouts produced was the previous biomass of the resprouting plant. The abundance of R. officinalis neighbors had a weak but detectable effect on resprouting of E. multiflora. Abundance of neighbors within 60 cm from target plants was the best predictor of regrowth. At this distance, two simple measures of neighbor abundance within the neighborhood, the number of neighbors and the sum of their heights, were significant in accounting for variation in resprouted biomass. None of the combinations of neighbor variables performed significantly better than single variables. The best models accounted for around 24 percent of the variation in resprout biomass. As in other studies, angular dispersion of neighbors never had a significant effect on performance of target plants. The weak but significant response of resprouting to variation in R. officinalis abundance suggests that the intensity of competition in the experiment was low because of the removal of other species.

How to be in a good shape? The influence of clone morphology on cell competition

Cell competition is a conserved mechanism where slow proliferating cells (so called losers) are eliminated by faster proliferating neighbors (so called winners) through apoptosis.(1) It is an important process which prevents developmental malformations and maintains tissue fitness in aging adults.(2) Recently, we have shown that the probability of elimination of loser cells correlates with the surface of contact between losers and winners in Myc-induced competition.(3) Moreover, we have characterized an active mechanism that increases the surface of contact between losers and winners, hence accelerating the elimination of loser cells. This is the first indication that cell shape and mechanics can influence cell competition. Here, we will discuss the consequence of the relationship between shape and competition, as well as the relevance of this model for other modes of competition.