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International audience; In this paper, we adapt a previously developed poromechanical formulation to model the perfusion of myocardium during a cardiac cycle. First, a complete model is derived in 3D. Then, we perform a dimensional reduction under the assumption of spherical symmetry and propose a numerical algorithm that enables us to perform simulations of the myocardial perfusion throughout the cardiac cycle. These simulations illustrate the use of the proposed model to represent various physiological and pathological scenarios, specifically the vasodilation in the coronary network (to reproduce the standard clinical assessment of myocardial perfusion and perfusion reserve), the stenosis of a large coronary artery, an increased vascular resistance in the microcirculation (microvascular disease) and the consequences of inotropic activation (increased myocardial contractility) particularly at the level of the systolic flow impediment. Our results show that the model gives promising qualitative reproductions of complex physiological phenomena. This paves the way for future quantitative studies using clinical or experimental data.

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. In this article, 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. In this paper the personalisation of the anatomy, the electrophysiology, the kinematics and the mechanics are described. 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 mm Hg s−1, less than 5% error. These promising results demonstrate the potential of physiological models personalised from images and electrophysiology signals to improve patient selection and plan CRT.

International audience; Parameter estimation from non-invasive measurements is a crucial step in patient-specific cardiac modeling. It also has the potential to provide sig- nificant assistance in the clinical diagnosis of cardiac diseases through the quantification of myocardial material heterogeneity. In this paper, we for- mulate a novel Reduced-order Unscented Kalman Filter (rUKF) applied to the left ventricular (LV) nonlinear mechanical model based on cubic-Hermite finite elements. Material parameters in the widely-employed transversely isotropic Guccione's constitutive law are successfully identified for both ho- mogeneous and heterogeneous cases. We conclude that the four parameters in Guccione's law can be uniquely and correctly determined in silico from noisy displacement measurements of material points located on the myocar- dial surfaces. The future application of this novel and effective approach to real clinical measurements is thus promising.

International audience; Effective shell finite elements are of utmost interest in engineering practice, and more particularly triangular shell elements are often needed to handle complex geometries. The quadrilateral elements of the MITC family have been shown to be effective for general asymptotic behaviors, but a triangular MITC shell finite element of comparable performance remains to be found. The main difficulty is to reduce the locking phenomenon arising in bending dominated situations without destroying the ability of the procedure to accurately capture membrane dominated and mixed behaviors. In this context, we have designed a simple numerical rank test aimed at assessing the reliability of MITC triangular elements. This test led to selecting some specific MITC6 tying schemes, which have been further assessed using some meaningful test problems. The assessment results showed that the MITC6a shell element is a most promising candidate, although it may feature some non-physical membrane spurious modes in some specific shell problems.

We present a novel strategy to perform estimation for a dynamical mechanical system in standard operating conditions, namely, without ad hoc experimental testing. We adopt a sequential approach, and the joint state-parameter estimation procedure is based on a state estimator inspired from collocated feedback control. This type of state estimator is chosen due to its particular effectiveness and robustness, but the methodology proposed to adequately extend state estimation to joint state-parameter estimation is general, and - indeed -applicable with any other choice of state feedback observer. The convergence of the resulting joint estimator is mathematically established. In addition, we demonstrate its effectiveness with a biomechanical test problem defined to feature the same essential characteristics as a heart model, in which we identify localized contractility and stiffness parameters using measurements of a type that is available in medical imaging.

Resume La plupart des methodes de simulation numerique du tombe de tissus sont basees sur un modele mecanique s'appuyant, en general, sur un maillage surfacique uniforme. Le tissu etant un materiau tres souple, de nombreux plis peuvent se former sur sa surface lorsque celui-ci est en mouvement libre ou contraint (collisions, points d'arrimage, etc.). Le probleme de la simulation est de faire evoluer le systeme mecanique tout en ayant une representation geometrique realiste de la surface. Il se pose alors un probleme de discretisation adequate de la surface. Pour remedier, a ce probleme, nous proposons une methode basee sur un maillage adaptatif permettant au modele mecanique d'evoluer sans la contrainte d'un maillage uniforme. Nous decrivons aussi un nouveau modele mecanique adapte ainsi que notre methode de raffinement local du maillage. Un exemple numerique vient illustrer l'interet de notre methode. Pour citer cet article : J. Villard et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 561–566.

We obtain estimates for the consistency errors arising in general shell element procedures, which are widely used in engineering practice. These estimates improve a previous result by the same authors. Moreover, numerical experiments indicate that these new estimates are optimal. Further, we introduce a modified procedure for which nominal convergence is recovered. These results are of much practical significance.

International audience; We present an inf-sup test for general mixed shell finite element discretizations. The test is useful in the thorough evaluation of a shell finite element discretization scheme. We apply the test to the MITC shell elements and find that these elements pass the test.

The objective in this paper is to present fundamental considerations regarding the finite element analysis of shell structures. First, we review some well-known results regarding the asymptotic behaviour of a shell mathematical model. When the thickness becomes small, the shell behaviour falls into one of two dramatically different categories; namely, the membrane-dominated and bending-dotninated cases. The shell geometry and boundary conditions decide into which category the shell structure falls, and a seemingly small change in these conditions can result into a change of category and hence into a dramatically different shell behaviour. An effective finite element scheme should be applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal and independent of the shell thickness. Such a finite element scheme is difficult to achieve but it is important that existing procedures be analysed and measured with due regard to these considerations. To this end, we present theoretical considerations and we propose appropriate shell analysis test cases for numerical evaluations.

We briefly review the inf-sup condition for the finite element solution of problems in incompressible elasticity, and then propose a numerical test on whether the inf-sup condition is passed. The evaluation of elements with this test is simple, and various results are presented. This inf-sup test will prove useful for many discretizations of constrained variational problems.

Objectifs Connaitre l’anatomie cardiaque et la physiologie de la contraction myocardique. Connaitre les sequences permettant d’etudier la contraction myocardique. Savoir analyser une sequence de perfusion au repos et sous stress pharmacologique. Points cles La contraction myocardique associe un double raccourcissement (circonferentiel et longitudinal), un epaississement radial et une rotation du ventricule gauche. Les sequences b SSFP apprecient essentiellement l’epaississement radial. Les sequences de tagging permettent d’etudier les autres composantes de la contraction. L’etude de la perfusion necessite des sequences ultrarapides qui peuvent etre couplees a l’injection d’agents pharmacologiques. Resume La systole myocardique s’accompagne d’un mouvement de torsion du ventricule gauche qui accroit l’efficacite hemodynamique de la contraction. Ce mouvement de torsion est lie en partie a la disposition en double helice des fibres myocardiques. L’analyse incomplete de la contraction sur les sequences b SSFP peut etre affinee avec des sequences de tagging qui etudient la deformation de bandes de saturation intramyocardiques au cours du cycle cardiaque. D’autres sequences sont en developpement comme l’imagerie en tenseur de diffusion qui exploite le caractere anisotropique des cardiomyocytes. L’etude de la perfusion beneficie souvent de l’injection d’agents vasodilatateurs afin de detecter la baisse de la reserve coronaire. Des sequences ultrarapides type EPI sont les plus adaptees pour etudier la perfusion. Leur analyse est le plus souvent visuelle. Les images de perfusion doivent etre comparees aux resultats des sequences de rehaussement tardif.