Section: New Results

Modeling and estimation in biomechanics

Patient-Specific Electromechanical Models of the Heart for the Prediction of Pacing Acute Effects in CRT: a Preliminary Clinical Validation

In collaboration with Project-Team Asclepios from INRIA Sophia-Antipolis-Méditerranée and the Division of Imaging Sciences of St Thomas’ Hospital, King's College London we demonstrated the benefits of using patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT, see [5] .

Cardiac resynchronisation therapy (CRT) is an effective treatment for patients with congestive heart failure and a wide QRS complex. However, up to 30% of patients are non-responders to therapy in terms of exercise capacity or left ventricular reverse remodelling. A number of controversies still remain surrounding patient selection, targeted lead implantation and optimisation of this important treatment. The development of biophysical models to predict the response to CRT represents a potential strategy to address these issues. We present how the personalisation of an electromechanical model of the myocardium can predict the acute haemodynamic changes associated with CRT. In order to introduce such an approach as a clinical application, we needed to design models that can be individualised from images and electrophysiological mapping of the left ventricle. We performed the personalisation of the anatomy, the electrophysiology, the kinematics and the mechanics. The acute effects of pacing on pressure development were predicted with the in silico model for several pacing conditions on two patients, achieving good agreement with invasive haemodynamic measurements: the mean error on dP/dtmax is 47.5 ± 35 mmHg.s−1, less than 5% error.

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

Participants : Radomir Chabiniok, Dominique Chapelle, Alexandre Imperiale, Philippe Moireau.

In collaboration with P.-F. Lesault, A. Rahmouni and J.-F. Deux from Hospital H. Mondor, Créteil we proposed and assessed 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, see [8] , [1] . 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.

We are now working on improving these results by the use of Tagged-MRI, see [9] . The first approach consists in assuming that the image data is processed in the form of deforming tag planes, which we employ to obtain a discrepancy between the model and the data by computing distances to these surfaces. We assess our procedure using synthetic measurements produced with a model representing an infarcted heart as observed in an animal experiment, and the estimation results are found to be of superior accuracy compared to assimilation based on segmented endo- and epicardium surfaces. Then we extend this strategy to tagged lines instead of tagged planes or even directly with apparent displacements extracted from tagged images by optical flow methods.

Convergence of observers based on partial field measurements for the wave equation

Participants : Dominique Chapelle, Nicolae Cîndea, Maya de Buhan, Philippe Moireau.

We analyzed an observer strategy based on partial – i.e. in a subdomain – measurements of the solution of a wave equation, in order to compensate for unknown initial conditions, see [17] , [18] . We proved the exponential convergence of this observer under a non-standard observability condition, whereas using measurements of the time-derivative of the solution would lead to a standard observability condition arising in stabilization and exact controlability. Nevertheless, we directly related our specific condition to the classical geometric control condition. This results justify in a linear framework the use of our observer-based filter in cardiac modeling.

Reduced nonlinear optimal filtering

Participants : Dominique Chapelle, Akos Matszangosz, Philippe Moireau.

We investigated some issues pertaining to reduced-order considerations in nonlinear optimal filtering. Classically, optimal filtering formulations lead to Hamilton-Jacobi-Bellman (HJB) equations posed in the complete “space of uncertainty”, namely, including the state space. This makes such methods generally untractable for PDE-based models. However, under certain assumptions pertaining to reduced uncertainties we can transform the HJB equations into a form posed in the reduced uncertainty space, and with only time derivatives involved. This form can be solved for – including with PDEs – provided this reduced space is of limited size, and then gives a reference “optimal” method to which other filtering procedures can be compared. The subject of Akos Matszangosz' internship (from “Ecole des Mines de Paris”, duration 4 months) was to design and perform an adequate implementation of this reduced-order optimal filter, based on a sparse-grid discretization of the uncertainty space. In addition, we are currently working on discrete-time optimal filtering formulations, which are distinct – and preferable in principle – to discretizing the continuous forms.