Mixture of Probabilistic Principal Component Analyzers for Shapes from Point Sets.

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.

Intervertebral disc classification by its degree of degeneration from T2-weighted magnetic resonance images.

PURPOSE: The primary goal of this article is to achieve an automatic and objective method to compute the Pfirrmann's degeneration grade of intervertebral discs (IVD) from MRI. This grading system is used in the diagnosis and management of patients with low back pain (LBP). In addition, biomechanical models, which are employed to assess the treatment on patients with LBP, require this grading value to compute proper material properties. MATERIALS AND METHODS: T2-weighted MR images of 48 patients were employed in this work. The 240 lumbar IVDs were divided into a training set (140) and a testing set (100). Three experts manually classified the whole set of IVDs using the Pfirrmann's grading system and the ground truth was selected as the most voted value among them. The developed method employs active contour models to delineate the boundaries of the IVD. Subsequently, the classification is achieved using a trained Neural Network (NN) with eight designed features that contain shape and intensity information of the IVDs. RESULTS: The classification method was evaluated using the testing set, resulting in a mean specificity (95.5 %) and sensitivity (87.3 %) comparable to those of every expert with respect to the ground truth. CONCLUSIONS: Our results show that the automatic method and humans perform equally well in terms of the classification accuracy. However, human annotations have inherent inter- and intra-observer variabilities, which lead to inconsistent assessments. In contrast, the proposed automatic method is objective, being only dependent on the input MRI.

A multi-center milestone study of clinical vertebral CT segmentation.

A multiple center milestone study of clinical vertebra segmentation is presented in this paper. Vertebra segmentation is a fundamental step for spinal image analysis and intervention. The first half of the study was conducted in the spine segmentation challenge in 2014 International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) Workshop on Computational Spine Imaging (CSI 2014). The objective was to evaluate the performance of several state-of-the-art vertebra segmentation algorithms on computed tomography (CT) scans using ten training and five testing dataset, all healthy cases; the second half of the study was conducted after the challenge, where additional 5 abnormal cases are used for testing to evaluate the performance under abnormal cases. Dice coefficients and absolute surface distances were used as evaluation metrics. Segmentation of each vertebra as a single geometric unit, as well as separate segmentation of vertebra substructures, was evaluated. Five teams participated in the comparative study. The top performers in the study achieved Dice coefficient of 0.93 in the upper thoracic, 0.95 in the lower thoracic and 0.96 in the lumbar spine for healthy cases, and 0.88 in the upper thoracic, 0.89 in the lower thoracic and 0.92 in the lumbar spine for osteoporotic and fractured cases. The strengths and weaknesses of each method as well as future suggestion for improvement are discussed. This is the first multi-center comparative study for vertebra segmentation methods, which will provide an up-to-date performance milestone for the fast growing spinal image analysis and intervention.

Statistical Interspace Models (SIMs): Application to Robust 3D Spine Segmentation.

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.

Accurate Segmentation of Vertebral Bodies and Processes Using Statistical Shape Decomposition and Conditional Models.

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.

On the relative relevance of subject-specific geometries and degeneration-specific mechanical properties for the study of cell death in human intervertebral disk models.

Capturing patient- or condition-specific intervertebral disk (IVD) properties in finite element models is outmost important in order to explore how biomechanical and biophysical processes may interact in spine diseases. However, disk degenerative changes are often modeled through equations similar to those employed for healthy organs, which might not be valid. As for the simulated effects of degenerative changes, they likely depend on specific disk geometries. Accordingly, we explored the ability of continuum tissue models to simulate disk degenerative changes. We further used the results in order to assess the interplay between these simulated changes and particular IVD morphologies, in relation to disk cell nutrition, a potentially important factor in disk tissue regulation. A protocol to derive patient-specific computational models from clinical images was applied to different spine specimens. In vitro, IVD creep tests were used to optimize poro-hyperelastic input material parameters in these models, in function of the IVD degeneration grade. The use of condition-specific tissue model parameters in the specimen-specific geometrical models was validated against independent kinematic measurements in vitro. Then, models were coupled to a transport-cell viability model in order to assess the respective effects of tissue degeneration and disk geometry on cell viability. While classic disk poro-mechanical models failed in representing known degenerative changes, additional simulation of tissue damage allowed model validation and gave degeneration-dependent material properties related to osmotic pressure and water loss, and to increased fibrosis. Surprisingly, nutrition-induced cell death was independent of the grade-dependent material properties, but was favored by increased diffusion distances in large IVDs. Our results suggest that in situ geometrical screening of IVD morphology might help to anticipate particular mechanisms of disk degeneration.

3D segmentation of annulus fibrosus and nucleus pulposus from T2-weighted magnetic resonance images.

Computational medicine aims at employing personalised computational models in diagnosis and treatment planning. The use of such models to help physicians in finding the best treatment for low back pain (LBP) is becoming popular. One of the challenges of creating such models is to derive patient-specific anatomical and tissue models of the lumbar intervertebral discs (IVDs), as a prior step. This article presents a segmentation scheme that obtains accurate results irrespective of the degree of IVD degeneration, including pathological discs with protrusion or herniation. The segmentation algorithm, employing a novel feature selector, iteratively deforms an initial shape, which is projected into a statistical shape model space at first and then, into a B-Spline space to improve accuracy.The method was tested on a MR dataset of 59 patients suffering from LBP. The images follow a standard T2-weighted protocol in coronal and sagittal acquisitions. These two image volumes were fused in order to overcome large inter-slice spacing. The agreement between expert-delineated structures, used here as gold-standard, and our automatic segmentation was evaluated using Dice Similarity Index and surface-to-surface distances, obtaining a mean error of 0.68 mm in the annulus segmentation and 1.88 mm in the nucleus, which are the best results with respect to the image resolution in the current literature.

Statistical shape and appearance models in osteoporosis.

Statistical models (SMs) of shape (SSM) and appearance (SAM) have been acquiring popularity in medical image analysis since they were introduced in the early 1990s. They have been primarily used for segmentation, but they are also a powerful tool for 3D reconstruction and classification. All these tasks may be required in the osteoporosis domain, where fracture detection and risk estimation are key to reducing the mortality and/or morbidity of this bone disease. In this article, we review the different applications of SSMs and SAMs in the context of osteoporosis, and it concludes with a discussion of their advantages and disadvantages for this application.