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

Dynamic finite-strain modelling of the human left ventricle in health and disease using an immersed boundary-finite element method

Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and strain fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive elasticity of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a finite element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from end-diastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions

The estimation of patient-specific cardiac diastolic functions from clinical measurements.

An unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual active tension (AT) because of the impaired ventricular relaxation during diastole. To address this problem, this paper presents a method for estimating diastolic mechanical parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. Dynamic C1-continuous meshes are automatically built from the anatomy and deformation captured from dynamic MRI sequences. Diastolic deformation is simulated using a mechanical model that combines passive and active material properties. The problem of non-uniqueness of constitutive parameter estimation using the well known Guccione law is characterized by reformulation of this law. Using this reformulated form, and by constraining the constitutive parameters to be constant across time points during diastole, we separate the effects of passive constitutive properties and the residual AT during diastolic relaxation. Finally, the method is applied to two clinical cases and one control, demonstrating that increased residual AT during diastole provides a potential novel index for delineating healthy and pathological cases