Descriptive and Intuitive Population-Based Cardiac Motion Analysis via Sparsity Constrained Tensor Decomposition

International audienceAnalysing and understanding population-specific cardiac function is a challenging task due to the complex dynamics observed in both healthy and diseased subjects and the difficulty in quantitatively comparing the motion in different subjects. It was proposed to use affine parameters extracted from a Polyaffine motion model for a group of subjects to represent the 3D motion regionally over time for a group of subjects. We propose to construct from these parameters a 4-way tensor of the rotation, stretch, shear, and translation components of each affine matrix defined in an intuitive local coordinate system, stacked per region, for each affine component, over time, and for all subjects. From this tensor, Tucker decomposition can be applied with a constraint of sparsity on the core tensor in order to extract a few key, easily interpretable modes for each subject. Using this construction of a data tensor, the tensors of multiple groups can be stacked and collectively decomposed in order to compare and discriminate the motion in each group by analysing the different loadings of each combination of modes for each group. The proposed method was applied to study and compare left ventricular dynamics for a group of healthy adult subjects and a group of adults withrepaired Tetralogy of Fallot

Statistical analysis of organs' shapes and deformations: the Riemannian and the affine settings in computational anatomy

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and medicine that aims at analyzing and modeling the biological variability of organs' shapes at the population level. Shapes are equivalence classes of images, surfaces or deformations of a template under rigid body (or more general) transformations. Thus, they belong to non-linear manifolds. In order to deal with multiple samples in non-linear spaces, a consistent statistical framework on Riemannian manifolds has been designed over the last decade. We detail in this chapter the extension of this framework to Lie groups endowed with the affine symmetric connection, a more invariant (and thus more consistent) but non-metric structure on transformation groups. This theory provides strong theoretical bases for the use of one-parameter subgroups and diffeomorphisms parametrized by stationary velocity fields (SVF), for which efficient image registration methods like log-Demons have been developed with a great success from the practical point of view. One can further reduce the complexity with locally affine transformations , leading to parametric diffeomorphisms of low dimension encoding the major shape variability. We illustrate the methodology with the modeling of the evolution of the brain with Alzheimer's disease and the analysis of the cardiac motion from MRI sequences of images

Improving Understanding of Long-Term Cardiac Functional Remodelling via Cross-Sectional Analysis of Polyaffine Motion Parameters

International audienceChanges in cardiac motion dynamics occur as a direct result of alterations in structure, hemodynamics, and electrical activation. Abnormal ventricular motion compromises long-term sustainability of heart function. While motion abnormalities are reasonably well documented and have been identified for many conditions, the remodelling process that occurs as a condition progresses is not well understood. Thanks to the recent development of a method to quantify full ventricular motion (as opposed to 1D abstractions of the motion) with few comparable parameters, population-based statistical analysis is possible. A method for describing functional remodelling is proposed by performing statistical cross-sectional analysis of spatio-temporally aligned subject-specific polyaffine motion parameters. The proposed method is applied to pathological and control datasets to compare functional remodelling occurring as a process of disease as opposed to a process of ageing

Statistical Medial Model dor Cardiac Segmentation and Morphometry

In biomedical image analysis, shape information can be utilized for many purposes. For example, irregular shape features can help identify diseases; shape features can help match different instances of anatomical structures for statistical comparison; and prior knowledge of the mean and possible variation of an anatomical structure\u27s shape can help segment a new example of this structure in noisy, low-contrast images. A good shape representation helps to improve the performance of the above techniques. The overall goal of the proposed research is to develop and evaluate methods for representing shapes of anatomical structures. The medial model is a shape representation method that models a 3D object by explicitly defining its skeleton (medial axis) and deriving the object\u27s boundary via inverse-skeletonization . This model represents shape compactly, and naturally expresses descriptive global shape features like thickening , bending , and elongation . However, its application in biomedical image analysis has been limited, and it has not yet been applied to the heart, which has a complex shape. In this thesis, I focus on developing efficient methods to construct the medial model, and apply it to solve biomedical image analysis problems. I propose a new 3D medial model which can be efficiently applied to complex shapes. The proposed medial model closely approximates the medial geometry along medial edge curves and medial branching curves by soft-penalty optimization and local correction. I further develop a scheme to perform model-based segmentation using a statistical medial model which incorporates prior shape and appearance information. The proposed medial models are applied to a series of image analysis tasks. The 2D medial model is applied to the corpus callosum which results in an improved alignment of the patterns of commissural connectivity compared to a volumetric registration method. The 3D medial model is used to describe the myocardium of the left and right ventricles, which provides detailed thickness maps characterizing different disease states. The model-based myocardium segmentation scheme is tested in a heterogeneous adult MRI dataset. Our segmentation experiments demonstrate that the statistical medial model can accurately segment the ventricular myocardium and provide useful parameters to characterize heart function

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal