A common feature of morphogenesis is the formation of three-dimensional structures from the folding of two-dimensional epithelial sheets, aided by cell shape changes at the cellular-level. Changes in cell shape must be studied in the context of cell-polarised biomechanical processes within the epithelial sheet. In epithelia with highly curved surfaces, finding single-cell alignment along a biological axis can be difficult to automate in silico. We present 'Origami', a MATLAB-based image analysis pipeline to compute direction-variant cell shape features along the epithelial apico-basal axis. Our automated method accurately computed direction vectors denoting the apico-basal axis in regions with opposing curvature in synthetic epithelia and fluorescence images of zebrafish embryos. As proof of concept, we identified different cell shape signatures in the developing zebrafish inner ear, where the epithelium deforms in opposite orientations to form different structures. Origami is designed to be user-friendly and is generally applicable to fluorescence images of curved epithelia.

Osteoporosis is an age-associated disease characterised by low bone mineral density (BMD) and micro-architectural deterioration leading to enhanced fracture risk. Conventional dual-energy X-ray absorptiometry (DXA) analysis has facilitated our understanding of BMD reduction in specific regions of interest (ROIs) within the femur, but cannot resolve spatial BMD patterns nor reflect age-related changes in bone microarchitecture due to its inherent averaging of pixel BMD values into large ROIs. To address these limitations and develop a comprehensive model of involutional bone loss, this paper presents a fully automatic pipeline to build a spatio-temporal atlas of ageing bone in the proximal femur. A new technique, termed DXA region free analysis (DXA RFA), is proposed to eliminate morphological variation between DXA scans by warping each image into a reference template. To construct the atlas, we use unprocessed DXA data from Caucasian women aged 20-97 years participating in three cohort studies in Western Europe ( ,000). A novel calibration procedure, termed quantile matching regression, is proposed to integrate data from different DXA manufacturers. Pixel-wise BMD evolution with ageing was modelled using smooth quantile curves. This technique enables characterisation of spatially-complex BMD change patterns with ageing, visualised using heat-maps. Furthermore, quantile curves plotted at different pixel coordinates showed consistently different rates of bone loss at different regions within the femoral neck. Given the close relationship between spatio-temporal bone loss and osteoporotic fracture, improved understanding of the bone ageing process could lead to enhanced prognostic, preventive and therapeutic strategies for the disease.

Inferring a probability density function (pdf) for shape from a population of point sets is a challenging problem. The lack of point-to-point correspondences and the non-linearity of the shape spaces undermine the linear models. Methods based on manifolds model the shape variations naturally, however, statistics are often limited to a single geodesic mean and an arbitrary number of variation modes. We relax the manifold assumption and consider a piece-wise linear form, implementing a mixture of distinctive shape classes. The pdf for point sets is defined hierarchically, modeling a mixture of Probabilistic Principal Component Analyzers (PPCA) in higher dimension. A Variational Bayesian approach is designed for unsupervised learning of the posteriors of point set labels, local variation modes, and point correspondences. By maximizing the model evidence, the numbers of clusters, modes of variations, and points on the mean models are automatically selected. Using the predictive distribution, we project a test shape to the spaces spanned by the local PPCA's. The method is applied to point sets from: i) synthetic data, ii) healthy versus pathological heart morphologies, and iii) lumbar vertebrae. The proposed method selects models with expected numbers of clusters and variation modes, achieving lower generalization-specificity errors compared to state-of-the-art.

Computational fluid dynamics (CFD) is a valuable tool for studying vascular diseases, but requires long computational time. To alleviate this issue, we propose a statistical framework to predict the aneurysmal wall shear stress patterns directly from the aneurysm shape. A database of 38 complex intracranial aneurysm shapes is used to generate aneurysm morphologies and CFD simulations. The shapes and wall shear stresses are then converted to clouds of hybrid points containing both types of information. These are subsequently used to train a joint statistical model implementing a mixture of principal component analyzers. Given a new aneurysmal shape, the trained joint model is firstly collapsed to a shape only model and used to initialize the missing shear stress values. The estimated hybrid point set is further refined by projection to the joint model space. We demonstrate that our predicted patterns can achieve significant similarities to the CFD-based results. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Statistical shape models (SSM) are used to introduce shape priors in the segmentation of medical images. However, such models require large training datasets in the case of multi-object structures, since it is required to obtain not only the individual shape variations but also the relative position and orientation among objects. A solution to overcome this limitation is to model each individual shape independently. However, this approach does not take into account the relative position, orientations and shapes among the parts of an articulated object, which may result in unrealistic geometries, such as with object overlaps. In this article, we propose a new Statistical Model, the Statistical Interspace Model (SIM), which provides information about the interaction of all the individual structures by modeling the interspace between them. The SIM is described using relative position vectors between pair of points that belong to different objects that are facing each other. These vectors are divided into their magnitude and direction, each of these groups modeled as independent manifolds. The SIM was included in a segmentation framework that contains an SSM per individual object. This framework was tested using three distinct types of datasets of CT images of the spine. Results show that the SIM completely eliminated the inter-process overlap while improving the segmentation accuracy.

Detailed segmentation of the vertebrae is an important pre-requisite in various applications of image-based spine assessment, surgery and biomechanical modeling. In particular, accurate segmentation of the processes is required for image-guided interventions, for example for optimal placement of bone grafts between the transverse processes. Furthermore, the geometry of the processes is now required in musculoskeletal models due to their interaction with the muscles and ligaments. In this paper, we present a new method for detailed segmentation of both the vertebral bodies and processes based on statistical shape decomposition and conditional models. The proposed technique is specifically developed with the aim to handle the complex geometry of the processes and the large variability between individuals. The key technical novelty in this work is the introduction of a part-based statistical decomposition of the vertebrae, such that the complexity of the subparts is effectively reduced, and model specificity is increased. Subsequently, in order to maintain the statistical and anatomic coherence of the ensemble, conditional models are used to model the statistical inter-relationships between the different subparts. For shape reconstruction and segmentation, a robust model fitting procedure is used to exclude improbable inter-part relationships in the estimation of the shape parameters. Segmentation results based on a dataset of 30 healthy CT scans and a dataset of 10 pathological scans show a point-to-surface error improvement of 20% and 17% respectively, and the potential of the proposed technique for detailed vertebral modeling.

Anatomical labeling of the cerebral arteries forming the Circle of Willis (CoW) enables inter-subject comparison, which is required for geometric characterization and discovering risk factors associated with cerebrovascular pathologies. We present a method for automated anatomical labeling of the CoW by detecting its main bifurcations. The CoW is modeled as rooted attributed relational graph, with bifurcations as its vertices, whose attributes are characterized as points on a Riemannian manifold. The method is first trained on a set of pre-labeled examples, where it learns the variability of local bifurcation features as well as the variability in the topology. Then, the labeling of the target vasculature is obtained as maximum a posteriori probability (MAP) estimate where the likelihood of labeling individual bifurcations is regularized by the prior structural knowledge of the graph they span. The method was evaluated by cross-validation on 50 subjects, imaged with magnetic resonance angiography, and showed a mean detection accuracy of 95%. In addition, besides providing the MAP, the method can rank the labelings. The proposed method naturally handles anatomical structural variability and is demonstrated to be suitable for labeling arterial segments of the CoW.

This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N(9) to N(6). The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N(3). In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N(4), while the previously proposed algorithm is of order N(6). The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.

A new automatic approach for saccular intracranial aneurysm isolation is proposed in this work. Due to the inter- and intra-observer variability in manual delineation of the aneurysm neck, a definition based on a minimum cost path around the aneurysm sac is proposed that copes with this variability and is able to make consistent measurements along different data sets, as well as to automate and speedup the analysis of cerebral aneurysms. The method is based on the computation of a minimal path along a scalar field obtained on the vessel surface, to find the aneurysm neck in a robust and fast manner. The computation of the scalar field on the surface is obtained using a fast marching approach with a speed function based on the exponential of the distance from the centerline bifurcation between the aneurysm dome and the parent vessels. In order to assure a correct topology of the aneurysm sac, the neck computation is constrained to a region defined by a surface Voronoi diagram obtained from the branches of the vessel centerline. We validate this method comparing our results in 26 real cases with manual aneurysm isolation obtained using a cut-plane, and also with results obtained using manual delineations from three different observers by comparing typical morphological measures.

This paper presents a technique to estimate and model patient-specific pulsatility of cerebral aneurysms over one cardiac cycle, using 3D rotational X-ray angiography (3DRA) acquisitions. Aneurysm pulsation is modeled as a time varying B-spline tensor field representing the deformation applied to a reference volume image, thus producing the instantaneous morphology at each time point in the cardiac cycle. The estimated deformation is obtained by matching multiple simulated projections of the deforming volume to their corresponding original projections. A weighting scheme is introduced to account for the relevance of each original projection for the selected time point. The wide coverage of the projections, together with the weighting scheme, ensures motion consistency in all directions. The technique has been tested on digital and physical phantoms that are realistic and clinically relevant in terms of geometry, pulsation and imaging conditions. Results from digital phantom experiments demonstrate that the proposed technique is able to recover subvoxel pulsation with an error lower than 10% of the maximum pulsation in most cases. The experiments with the physical phantom allowed demonstrating the feasibility of pulsation estimation as well as identifying different pulsation regions under clinical conditions.

Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid hemorrhage, which has significant morbidity and mortality. Although there is still controversy regarding the decision on which unruptured aneurysms should be treated, this is based primarily on their size. Nonetheless, many large lesions do not rupture whereas some small ones do. It is commonly accepted that hemodynamical factors are important to better understand the natural history of cerebral aneurysms. However, it might not always be practical to carry out a detailed computational analysis of such factors if a prompt assessment is required. Since shape is likely to be dependent on the balance between hemodynamic forces and the aneurysmal surrounding environment, an appropriate morphological 3-D characterization is likely to provide a practical surrogate to quickly evaluate the risk of rupture. In this paper, an efficient and novel methodology for 3-D shape characterization of cerebral aneurysms is described. The aneurysms are isolated by taking into account a portion of their adjacent vessels. Two methods to characterize the morphology of the aneurysms models using moment invariants have been considered: geometrical moment invariants (GMI) and Zernike moment invariants (ZMI). The results have been validated in a database containing 53 patients with a total of 31 ruptured aneurysms and 24 unruptured aneurysms. It has been found that ZMI indices are more robust than GMI, and seem to provide a reliable way to discriminate between ruptured and unruptured aneurysms. Correct rupture prediction rates of approximately equal to 80% were achieved in contrast to 66% that is found when the aspect ratio index is considered.