Spatio-Temporal Tensor Decomposition of a Polyaffine Motion Model for a Better Analysis of Pathological Left Ventricular Dynamics

International audienceGiven that heart disease can cause abnormal motion dynamics over the cardiac cycle, which can then affect cardiac function, understanding and quantifying cardiac motion can provide insight for clinicians to aid in diagnosis, therapy planning, as well as to determine the prognosis for a given patient. The goal of this paper is to extract population-specific cardiac motion patterns from 3D displacements in order to firstly identify the mean motion behaviour in a population and secondly to describe pathology-specific motion patterns in terms of the spatial and temporal aspects of the motion. Since there are common motion patterns observed in patients suffering from the same condition, extracting these patterns can lead towards a better understanding of a disease. Quantifying cardiac motion at a population level is not a simple task since images can vary widely in terms of image quality, size, resolution and pose. To overcome this, we analyse the parameters obtained from a cardiac-specific Polyaffine motion tracking algorithm, which are aligned both spatially and temporally to a common reference space. Once all parameters are aligned, different subjects and different populations can be compared and analysed in the space of Polyaffine transformations by projecting the transformations to a reduced-order subspace in which dominant motion patterns in each population can be extracted and analysed. Using tensor decomposition allows the spatial and temporal aspects to be decoupled in order to study the different components individually. The proposed method was validated on healthy volunteers and Tetralogy of Fallot patients according to known spatial andtemporal behaviour for each population. A key advantage of the proposed method is the ability to regenerate motion sequences from the respective models, thus the models can be visualised in terms of the full motion, which allows for better understanding of the motion dynamics of different populations

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 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

Indirect Image Registration with Large Diffeomorphic Deformations

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.Comment: 43 pages, 4 figures, 1 table; revise

Towards Hyper-Reduction of Cardiac Models using Poly-Affine Deformation

International audienceThis paper presents a method for frame-based finite element model in order to develop fast personalised cardiac electromechanical models. Its originality comes from the choice of the deformation model: it relies on a reduced number of degrees of freedom represented by affine transformations located at arbitrary control nodes over a tetrahedral mesh. This is motivated by the fact that cardiac motion can be well represented by such poly-affine transformations. The shape functions use then a geodesic distance over arbitrary Voronoï-like regions containing the control nodes. The high order integration of elastic energy density over the domain is performed at arbitrary integration points. This integration , which is associated to affine degrees of freedom, allows a lower computational cost while preserving a good accuracy for simple geometry. The method is validated on a cube under simple compression and preliminary results on simplified cardiac geometries are presented, reducing by a factor 100 the number of degrees of freedom

Fast left ventricle tracking using localized anatomical affine optical flow

Fast left ventricle tracking using localized anatomical affine optical flowIn daily clinical cardiology practice, left ventricle (LV) global and regional function assessment is crucial for disease diagnosis, therapy selection, and patient follow-up. Currently, this is still a time-consuming task, spending valuable human resources. In this work, a novel fast methodology for automatic LV tracking is proposed based on localized anatomically constrained affine optical flow. This novel method can be combined to previously proposed segmentation frameworks or manually delineated surfaces at an initial frame to obtain fully delineated datasets and, thus, assess both global and regional myocardial function. Its feasibility and accuracy were investigated in 3 distinct public databases, namely in realistically simulated 3D ultrasound, clinical 3D echocardiography, and clinical cine cardiac magnetic resonance images. The method showed accurate tracking results in all databases, proving its applicability and accuracy for myocardial function assessment. Moreover, when combined to previous state-of-the-art segmentation frameworks, it outperformed previous tracking strategies in both 3D ultrasound and cardiac magnetic resonance data, automatically computing relevant cardiac indices with smaller biases and narrower limits of agreement compared to reference indices. Simultaneously, the proposed localized tracking method showed to be suitable for online processing, even for 3D motion assessment. Importantly, although here evaluated for LV tracking only, this novel methodology is applicable for tracking of other target structures with minimal adaptations.The authors acknowledge funding support from FCT - Fundacao para a Ciência e a Tecnologia, Portugal, and the European Social Found, European Union, through the Programa Operacional Capital Humano (POCH) in the scope of the PhD grants SFRH/BD/93443/2013 (S. Queiros) and SFRH/BD/95438/2013 (P. Morais), and by the project ’PersonalizedNOS (01-0145-FEDER-000013)’ co-funded by Programa Operacional Regional do Norte (Norte2020) through the European Regional Development Fund (ERDF).info:eu-repo/semantics/publishedVersio

Incorporation of a deformation prior in image reconstruction

International audienceThis article presents a method to incorporate a deformation prior in image reconstruction via the formalism of deformation modules. The framework of deformation modules allows to build diffeomorphic deformations that satisfy a given structure. The idea is to register a template image against the indirectly observed data via a modular deformation, incorporating this way the deformation prior in the reconstruction method. We show that this is a well-defined regularization method (proving existence, stability and convergence) and present numerical examples of reconstruction from 2-D tomographic simulations and partially-observed images

Statistiques de forme, de structure et de déformation à l'échelle d'une population pour l'étude de la fibrillation auriculaire

Atrial fibrillation (AF) is the most common cardiac arrhythmia, characterized by chaotic electrical activation and unsynchronized contraction of the atria. This epidemic and its life-threatening complications and fast progression call for diagnosis and effective treatment as early as possible. Catheter ablation, an invasive procedure that establishes lesions to block the trigger points of AF and creates a barrier to the propagation of the arrhythmia, is an effective treatment for patients refractory to anti-arrhythmic drugs. However, the success rate of the first-time ablation may range from 30% to 75%, such that multiple ablation procedures may be recommended, and atrial mechanical function may be adversely affected. With evolving imaging and digital technologies, the objective of the study is to understand the underlying physiology of AF better and to provide tools to assist clinical decision-making. We analyze the correlations between recurrent arrhythmia and patient characteristics before ablation, including the left atrial shape extracted from computed tomography images. Non-invasive extraction of the anatomical structures of the heart is a crucial prerequisite. We first developed semi-automatic methods to segment the left atrium and the left atrial wall from images. Next, we achieved good segmentation results with a neural network model. Then, we studied markers of shape related to both global and local remodeling, and the quantification of adipose tissue, deploying diffeomorphometry and statistical analysis tools. Finally, we extended the work to the statistical analysis of temporal deformation. We proposed a symmetric reformulation of the pole ladder, which improves the numerical consistency and stability.La fibrillation auriculaire (FA) est le type d'arythmie cardiaque la plus commun, caractérisée par une activation électrique chaotique et une contraction non synchronisée des oreillettes. Cette maladie et ses complications potentiellement mortelles ainsi que sa progression rapide exigent de diagnostiquer et de mettre en place un traitement efficace dès que possible. L'ablation par cathéter, une procédure invasive qui établit des lésions pour bloquer les points de déclenchement de la FA et la propagation de l'arythmie, est un traitement efficace pour les patients réfractaires aux médicaments. Cependant, pour 30% des patients, la FA se redéveloppe, entraînant des interventions d'ablation multiples et affectant la fonction mécanique auriculaire. Le but de cette étude est de combiner l'expertise mathématique et informatique à la médecine afin de mieux comprendre la physiologie sous-jacente à la FA et de fournir des outils d'aide à la décision aux cliniciens. Nous analysons des corrélations entre l'arythmie récurrente et les caractéristiques du patient avant l'ablation, y compris la forme de l’oreillette gauche extraite d'images tomodensitométriques. Nous développons pour ce faire des méthodes semi-automatiques pour segmenter l’oreillette gauche et sa paroi à partir d’images. Ensuite, nous avons obtenu de bons résultats de segmentation avec un modèle de réseau de neurones artificiels. En outre, nous étudions des marqueurs de forme liés au remodelage global et local, et la quantification du tissu adipeux, en combinant une approche morphométrique difféomorphe à une analyse statistique. Enfin, le travail s’étend à l’analyse statistique de la déformation temporelle. Nous proposons une reformulation symétrique de l'échelle de perroquet qui améliore la cohérence et la stabilité numérique

Cardiac motion estimation in ultrasound images using a sparse representation and dictionary learning

Les maladies cardiovasculaires sont de nos jours un problème de santé majeur. L'amélioration des méthodes liées au diagnostic de ces maladies représente donc un réel enjeu en cardiologie. Le coeur étant un organe en perpétuel mouvement, l'analyse du mouvement cardiaque est un élément clé pour le diagnostic. Par conséquent, les méthodes dédiées à l'estimation du mouvement cardiaque à partir d'images médicales, plus particulièrement en échocardiographie, font l'objet de nombreux travaux de recherches. Cependant, plusieurs difficultés liées à la complexité du mouvement du coeur ainsi qu'à la qualité des images échographiques restent à surmonter afin d'améliorer la qualité et la précision des estimations. Dans le domaine du traitement d'images, les méthodes basées sur l'apprentissage suscitent de plus en plus d'intérêt. Plus particulièrement, les représentations parcimonieuses et l'apprentissage de dictionnaires ont démontré leur efficacité pour la régularisation de divers problèmes inverses. Cette thèse a ainsi pour but d'explorer l'apport de ces méthodes, qui allient parcimonie et apprentissage, pour l'estimation du mouvement cardiaque. Trois principales contributions sont présentées, chacune traitant différents aspects et problématiques rencontrées dans le cadre de l'estimation du mouvement en échocardiographie. Dans un premier temps, une méthode d'estimation du mouvement cardiaque se basant sur une régularisation parcimonieuse est proposée. Le problème d'estimation du mouvement est formulé dans le cadre d'une minimisation d'énergie, dont le terme d'attache aux données est construit avec l'hypothèse d'un bruit de Rayleigh multiplicatif. Une étape d'apprentissage de dictionnaire permet une régularisation exploitant les propriétés parcimonieuses du mouvement cardiaque, combinée à un terme classique de lissage spatial. Dans un second temps, une méthode robuste de flux optique est présentée. L'objectif de cette approche est de robustifier la méthode d'estimation développée au premier chapitre de manière à la rendre moins sensible aux éléments aberrants. Deux régularisations sont mises en oeuvre, imposant d'une part un lissage spatial et de l'autre la parcimonie des champs de mouvements dans un dictionnaire approprié. Afin d'assurer la robustesse de la méthode vis-à-vis des anomalies, une stratégie de minimisation récursivement pondérée est proposée. Plus précisément, les fonctions employées pour cette pondération sont basées sur la théorie des M-estimateurs. Le dernier travail présenté dans cette thèse, explore une méthode d'estimation du mouvement cardiaque exploitant une régularisation parcimonieuse combinée à un lissage à la fois dans les domaines spatial et temporel. Le problème est formulé dans un cadre général d'estimation de flux optique. La régularisation temporelle proposée impose des trajectoires de mouvement lisses entre images consécutives. De plus, une méthode itérative d'estimation permet d'incorporer les trois termes de régularisations, tout en rendant possible le traitement simultané d'un ensemble d'images. Dans cette thèse, les contributions proposées sont validées en employant des images synthétiques et des simulations réalistes d'images ultrasonores. Ces données avec vérité terrain permettent d'évaluer la précision des approches considérées, et de souligner leur compétitivité par rapport à des méthodes de l'état-del'art. Pour démontrer la faisabilité clinique, des images in vivo de patients sains ou atteints de pathologies sont également considérées pour les deux premières méthodes. Pour la dernière contribution de cette thèse, i.e., exploitant un lissage temporel, une étude préliminaire est menée en utilisant des données de simulation.Cardiovascular diseases have become a major healthcare issue. Improving the diagnosis and analysis of these diseases have thus become a primary concern in cardiology. The heart is a moving organ that undergoes complex deformations. Therefore, the quantification of cardiac motion from medical images, particularly ultrasound, is a key part of the techniques used for diagnosis in clinical practice. Thus, significant research efforts have been directed toward developing new cardiac motion estimation methods. These methods aim at improving the quality and accuracy of the estimated motions. However, they are still facing many challenges due to the complexity of cardiac motion and the quality of ultrasound images. Recently, learning-based techniques have received a growing interest in the field of image processing. More specifically, sparse representations and dictionary learning strategies have shown their efficiency in regularizing different ill-posed inverse problems. This thesis investigates the benefits that such sparsity and learning-based techniques can bring to cardiac motion estimation. Three main contributions are presented, investigating different aspects and challenges that arise in echocardiography. Firstly, a method for cardiac motion estimation using a sparsity-based regularization is introduced. The motion estimation problem is formulated as an energy minimization, whose data fidelity term is built using the assumption that the images are corrupted by multiplicative Rayleigh noise. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. Secondly, a fully robust optical flow method is proposed. The aim of this work is to take into account the limitations of ultrasound imaging and the violations of the regularization constraints. In this work, two regularization terms imposing spatial smoothness and sparsity of the motion field in an appropriate cardiac motion dictionary are also exploited. In order to ensure robustness to outliers, an iteratively re-weighted minimization strategy is proposed using weighting functions based on M-estimators. As a last contribution, we investigate a cardiac motion estimation method using a combination of sparse, spatial and temporal regularizations. The problem is formulated within a general optical flow framework. The proposed temporal regularization enforces smoothness of the motion trajectories between consecutive images. Furthermore, an iterative groupewise motion estimation allows us to incorporate the three regularization terms, while enabling the processing of the image sequence as a whole. Throughout this thesis, the proposed contributions are validated using synthetic and realistic simulated cardiac ultrasound images. These datasets with available groundtruth are used to evaluate the accuracy of the proposed approaches and show their competitiveness with state-of-the-art algorithms. In order to demonstrate clinical feasibility, in vivo sequences of healthy and pathological subjects are considered for the first two methods. A preliminary investigation is conducted for the last contribution, i.e., exploiting temporal smoothness, using simulated data

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information.The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations.Following the first edition of this workshop in 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions