Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart

Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model

International audienceThe objective of this paper is to propose and assess an estimation procedure - based on data assimilation principles - well-suited to obtain some regional values of key biophysical parameters in a beating heart model, using actual Cine-MR images. The motivation is twofold: (1) to provide an automatic tool for personalizing the characteristics of a cardiac model in order to achieve predictivity in patient-specific modeling, and (2) to obtain some useful information for diagnosis purposes in the estimated quantities themselves. In order to assess the global methodology we specifically devised an animal experiment in which a controlled infarct was produced and data acquired before and after infarction, with an estimation of regional tissue contractility - a key parameter directly affected by the pathology - performed for every measured stage. After performing a preliminary assessment of our proposed methodology using synthetic data, we then demonstrate a full-scale application by first estimating contractility values associated with 6 regions based on the AHA subdivision, before running a more detailed estimation using the actual AHA segments. The estimation results are assessed by comparison with the medical knowledge of the specific infarct, and with late enhancement MR images. We discuss their accuracy at the various subdivision levels, in the light of the inherent modeling limitations and of the intrinsic information contents featured in the data

Coopération entre segmentation et mouvement pour l'estimation conjointe des déplacements pariétaux et des déformations myocardiaques

The work done in this thesis is related to the project 3DStrain the overall objective of which is to develop a generic framework for the parietal and regional tracking of the left ventricle and to adapt it the 3D + t cardiac imaging modalities used in clinical routine (3D ultrasound, SPECT, cine MRI). We worked on the parietal motion and myocardial deformation. We made the state-of-the-art on motion estimation approaches in general and on methods applied to imaging modalities in clinical practice to quantify myocardial deformation taking into account their specificities and limitations. We focused on tracking methods that optimize the similarity between the intensities between consecutive images of a sequence to estimate the spatial velocity field. They are based on the assumption of the invariance of image gray level (or optical flow) and regularization terms are used to solve the aperture problem. We proposed a regularization term well suited to physical and physiological properties of myocardial motion. The advantage of the proposed approach relies on its flexibility to estimate the dense field of myocardial motion on image sequences over the cardiac cycle. Motion is estimated while preserving myocardial wall discontinuities. However, the data similarity term used in our method is based only on the intensity of the image. It properly estimates the displacement field especially in the radial direction as the movement of circumferential twist is hardly visible on cine MRI in short axis view, the data we used for performing the experiments. To make the estimation more robust, we proposed a dynamic evolution model for the cardiac contraction and relaxation to introduce the temporal constraint ofthe dynamics of the heart. This model helps to estimate not only the dense field of myocardial displacement, but also other parameters of myocardial contractility (the contraction phase and asymmetry between systole and diastole) in variational data assimilation formalism. Automatic estimation of deformation and myocardial contractibility (the strain, phase and asymmetry) was validated against the cardiological and radiological expertise (Dr Elisabeth Coupez and Dr Lucie Cassagnes, CHU Clermont-Ferrand) through semi-quantitative scores of contraction called Wall Motion Score (WMS) and Wall Thickening Index (WTI). The proposed method provides promising results for both motion estimation results and the diagnosis indices for evaluation of myocardial dyskinesia. In order to gain in robustness and accuracy, it is necessary to perform the measurement of strain and indices of myocardial contraction precisely inside endocardial and epicardial walls. Therefore, we conducted a collaborative work with Kevin Bianchi, another PhD student on the project 3DStrain and we proposed a method of coupling of myocardial segmentation by deformable models and estimation of myocardial motion in a variational data assimilation framework.Pas de résumé disponibl

Apprentissage statistique pour la personnalisation de modèles cardiaques à partir de données d’imagerie

This thesis focuses on the calibration of an electromechanical model of the heart from patient-specific, image-based data; and on the related task of extracting the cardiac motion from 4D images. Long-term perspectives for personalized computer simulation of the cardiac function include aid to the diagnosis, aid to the planning of therapy and prevention of risks. To this end, we explore tools and possibilities offered by statistical learning. To personalize cardiac mechanics, we introduce an efficient framework coupling machine learning and an original statistical representation of shape & motion based on 3D+t currents. The method relies on a reduced mapping between the space of mechanical parameters and the space of cardiac motion. The second focus of the thesis is on cardiac motion tracking, a key processing step in the calibration pipeline, with an emphasis on quantification of uncertainty. We develop a generic sparse Bayesian model of image registration with three main contributions: an extended image similarity term, the automated tuning of registration parameters and uncertainty quantification. We propose an approximate inference scheme that is tractable on 4D clinical data. Finally, we wish to evaluate the quality of uncertainty estimates returned by the approximate inference scheme. We compare the predictions of the approximate scheme with those of an inference scheme developed on the grounds of reversible jump MCMC. We provide more insight into the theoretical properties of the sparse structured Bayesian model and into the empirical behaviour of both inference schemesCette thèse porte sur un problème de calibration d'un modèle électromécanique de cœur, personnalisé à partir de données d'imagerie médicale 3D+t ; et sur celui - en amont - de suivi du mouvement cardiaque. A cette fin, nous adoptons une méthodologie fondée sur l'apprentissage statistique. Pour la calibration du modèle mécanique, nous introduisons une méthode efficace mêlant apprentissage automatique et une description statistique originale du mouvement cardiaque utilisant la représentation des courants 3D+t. Notre approche repose sur la construction d'un modèle statistique réduit reliant l'espace des paramètres mécaniques à celui du mouvement cardiaque. L'extraction du mouvement à partir d'images médicales avec quantification d'incertitude apparaît essentielle pour cette calibration, et constitue l'objet de la seconde partie de cette thèse. Plus généralement, nous développons un modèle bayésien parcimonieux pour le problème de recalage d'images médicales. Notre contribution est triple et porte sur un modèle étendu de similarité entre images, sur l'ajustement automatique des paramètres du recalage et sur la quantification de l'incertitude. Nous proposons une technique rapide d'inférence gloutonne, applicable à des données cliniques 4D. Enfin, nous nous intéressons de plus près à la qualité des estimations d'incertitude fournies par le modèle. Nous comparons les prédictions du schéma d'inférence gloutonne avec celles données par une procédure d'inférence fidèle au modèle, que nous développons sur la base de techniques MCMC. Nous approfondissons les propriétés théoriques et empiriques du modèle bayésien parcimonieux et des deux schémas d'inférenc