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See also erratum DOI:10.1051/cocv/2011001; International audience; We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered. The algorithms are derived in discrete time as in the classical UKF formalism - well-adapted to time discretized dynamical equations - and then extended into consistent continuous-time versions. This reduced-order filtering approach can be used in particular for the estimation of parameters in large dynamical systems arising from the discretization of partial differential equations, when state estimation can be handled by an adequate Luenberger observer inspired from feedback control. In this case, we give an analysis of the joint state-parameter estimation procedure based on linearized error, and we illustrate the effectiveness of the approach using a test problem inspired from cardiac biomechanics.

International audience; In this paper we apply specific data assimilation methods in order to estimate regional contractility parameters in a biomechanical heart model, using as measurements real Cine MR images obtained in an animal experiment. We assess the effectiveness of this estimation based on independent knowledge of the controlled infarcted condition, and on late enhancement images. Moreover, we show that the estimated contractility values can improve the model behavior in itself, and that they can serve as an indicator of the local heart function, namely, to assist medical diagnosis for the post-infarct detection of hypokinetic or akinetic regions in the myocardial tissue

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.

A deeper understanding of finite element methods, and the development of improved finite element methods, can only be achieved with an appropriate mathematical and numerical assessment of the proposed techniques. The basis of such an assessment rests on identifying whether certain properties are satisfied by the finite element scheme and these properties depend on the framework within which the finite element method has been formulated.

The influence of the thickness in the finite element analysis of thin structures is a crucial issue, as it is deeply interrelated with the motivation of modeling a 3D continuum as a shell in engineering. Why, indeed, should we use shell models and finite elements – instead of 3D models – to analyze a given structure? The answer to this question seems obvious: firstly, the use of a shell model is to reduce the analysis cost, and secondly, the use of the shell model is to reduce the complexity of the analysis including the interpretation of the results for engineering design. Clearly, the motivation to use shell models rests upon the fact that shell mathematical models and finite elements incorporate kinematical assumptions pertaining to the displacement distribution across the thickness of the structure, see previous chapters.

Implicit in the concept of a “shell” is the idea that the thickness is “small” compared to the other two dimensions. In practice, it is not unusual to deal with structures for which the thickness is smaller by several orders of magnitude, in which case the shell is said to be “thin” (consider, for example, the shell body of a motor car). Considering the role of the thickness parameter t in the shell models that we presented in the previous chapter (see for example Eqs. (4.36) and (4.51)), with different powers of t in the bilinear terms on the left-hand side, it is essential to determine how the properties of the models are affected when this parameter becomes small. Likewise, it is important to know whether the model converges, in some sense to be specified, towards a limit model when the thickness t “tends to zero”, so that this possibly simpler model can be used instead of the original one when t is sufficiently small, i.e. we need to study the asymptotic behavior of the shell models. Of course, our goal is also to investigate the influence of the thickness on the convergence of finite element methods, as we want to be able to identify numerical procedures for which there is no deterioration of convergence when the thickness becomes small. To that purpose, the analysis of the asymptotic behaviors of mathematical shell models clearly also represents a crucial prerequisite on which we concentrate in this chapter, whereas the issues arising in the finite element solutions themselves are addressed in the next chapters.

In Chapter 7 we discussed the difficulties encountered in the formulation of reliable and effective shell elements. These difficulties are summarized in the synopsis of Figure 8.1 in correspondence with the various types of shell asymptotic behaviors that can be encountered, as addressed in Chapter 5. The objective of the present chapter is to propose some strategies to evaluate shell finite element discretizations in the search for improved schemes. With general analytical proofs not available for the convergence behavior, the numerical assessment is a key ingredient in these strategies. As an example we present the formulation of the MITC shell elements and demonstrate how the numerical assessment of these elements can be performed.

Sails are an example of fluid structure interaction (FSI), where the structural deformation, as well as the fluid dynamics, needs to be taken into account in order to analyse performances. The emphasis of this paper is placed on developing techniques that can study the dynamic behaviour of sails. This is necessary, especially when approaching downwind sails, where the nature of the flow is subjected to large separations and unsteady phenomena such as vortex shedding. Preliminary studies are presented about bluff body type flows, representative of spinnaker flows, and about typical Gennaker sections. From a structural perspective, the fabric is modelled with shells, rather than membranes. This approach shows considerable advantages, since these will capture buckling related phenomena such as wrinkling, which have to be treated with additional models for membrane based analysis. It is found that the unsteadiness and the presence of wrinkles can significantly alter the sail force

International audience; When establishing and analyzing model-parameter dependent mixed formulations, it is common to consider required ellipticity and inf-sup conditions for the continuous and discrete problems. However, in the modeling of some important categories of problems, like in the analysis of plates and shells, the ellipticity condition usually considered does not naturally hold, and the inf-sup condition can only be stated in an abstract form and can hardly be evaluated analytically. In this paper we present a new and practical ellipticity condition which together with the inf-sup condition guarantees that (i) when the model parameter goes to zero, the limit problem solution is uniformly approached, and (ii) an optimal finite element discretization has been established (for the interpolations used). In practice, a numerical test might be performed to see whether the proposed ellipticity condition is satisfied.

International audience; This paper is motivated by the modeling of blood flows through the beating myocardium, namely cardiac perfusion. As in other works, perfusion is modeled here as a flow through a poroelastic medium. The main contribution of this study is the derivation of a general poroelastic model valid for a nearly incompressible medium which experiences finite deformations. A numerical procedure is proposed to iteratively solve the porous flow and the nonlinear poroviscoelastic problems. Three-dimensional numerical experiments are presented to illustrate the model. The first test cases consist of typical poroelastic configurations: swelling and complete drainage. Finally, a simulation of cardiac perfusion is presented in an idealized left ventricle embedded with active fibers. Results show the complex temporal and spatial interactions of the muscle and blood, reproducing several key phenomena observed in cardiac perfusion.

International audience; Starting from the presentation of a unified perspective of segmentation with deformable models and data assimilation with images, we propose a data assimilation procedure designed to dynamically estimate 3D positions and velocities of the myocardium along the heart cycle, using data consisting of contours extracted from image sequences. We assess this procedure with a test problem based on a realistic computational heart model, and with synthetic data produced from reference simulations by creating binary images of the myocardium. The automatic meshing library CGAL is then employed to create contour meshes for each snapshot, and these meshes are directly used in the model measurement comparisons. This approach gives very satisfactory qualitativeand quantitative results.

International audience; Cardiac resynchronisation therapy (CRT) has been shown to be an effective adjunctive treatment for patients with dyssynchronous ventricular contraction and symptoms of the heart failure. However, clinical trials have also demonstrated that up to 30% of patients may be classified as non-responders. In this article, we present how the personalisation of an electromechanical model of the myocardium could help the therapy planning for CRT. We describe the four main components of our myocardial model, namely the anatomy, the electrophysiology, the kinematics and the mechanics. For each of these components we combine prior knowledge and observable parameters in order to personalise these models to patient data. Then the acute effects of a pacemaker on the cardiac function are predicted with the in silico model on a clinical case. This is a proof of concept of the potential of virtual physiological models to better select and plan the therapy.

International audience; We present numerical results obtained with a three-dimensional electromechanical model of the heart with a complete realistic anatomy. The electrical activity of the heart-torso domain is described by the bidomain equations in the heart and a Laplace equation in the torso. The mechanical model is based on a chemically-controlled contraction law of the myofibres integrated in a 3D continuum mechanics description accounting for large displacements and strains, and the main cardiovascular blood compartments are represented by simplified lumped models. We considered a normal case and a pathological condition and the medical indicators resulting from the simulations show physiological values, both for mechanical and electrical quantities of interest, in particular pressures, volumes and ECGs.

International audience; We propose an effective filtering methodology designed to perform estimation in a distributed mechanical system using position measurements. As in a previously introduced method, the filter is inspired from robust control feedback, but here we take full advantage of the estimation specificity to choose a feedback law that can act on displacements instead of velocities and still retain the same kind of dissipativity property which guarantees robustness. This is very valuable in many applications for which positions are more readily available than velocities, as in medical imaging. We provide an in-depth analysis of the proposed procedure, as well as detailed numerical assessments using a test problem inspired from cardiac biomechanics, as medical diagnosis assistance is an important perspective for this approach. The method is formulated first for measurements based on Lagrangian displacements, but we then derive a nonlinear extension allowing to instead consider segmented images, which of course is even more relevant in medical applications.

International audience; We present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an $H^\infty$ setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinite-dimensional mechanical system, the $H^\infty$ setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment - using a test problem inspired from cardiac biomechanics - demonstrates the effectiveness of our approach.

We propose a muscle chemo-mechanical model by which myosin heads - that can chemically bind to actin, thus creating so-called cross-bridges producing contraction forces in sarcomeres at the subcellular level - are considered as special chemical entities having internal mechanical variables pertaining to the actual geometric configuration. This provides a thermodynamical basis for modeling the complex interplay of chemical and mechanical phenomena at the sarcomere level. The resulting model is in the form of stochastic equations governing the dynamics of these microscopic mechanical variables in a Langevin framework. Equivalently, Fokker-Planck equations can be derived to describe the evolution of the associated probability densities. Under certain assumptions the corresponding moment equations can be closed, thus directly providing access to macroscopic quantities that can be incorporated in the overall constitutive equations of the muscle tissue. The underlying thermodynamical framework also enables the derivation of compatible numerical schemes, in particular in terms of energy balances. These modeling and discretization ingredients can be integrated in a global model of the cardiac system, to represent physiological and pathological phenomena in various medical applications.

We present a novel strategy to perform estimation for a mechanical system defined to feature the same essential characteristics as a heart model, using measurements of a type that is available in medical imaging. We adopt a sequential approach, and the joint state-parameter estimation procedure is constructed based on a robust and effective state estimator inspired from collocated feedback control. The convergence of the resulting joint estimator can be mathematically established, and we demonstrate its effectiveness by identifying localized contractility and stiffness parameters in a test problem representative of cardiac behavior and using synthetic - albeit realistic - measurements.

International audience; Effective triangular shell elements are of utmost interest in engineering practice, and the MITC6a element - a 6 node quadratic general shell element of the MITC family - has been shown to significantly reduce the locking phenomena arising in bending dominated behaviours. However, for some specific combinations of midsurface geometry and boundary conditions, the MITC6a element features some non-physical displacement modes with vanishing membrane strain energy. This phenomenon is thoroughly analyzed, and a remedy based on a stabilized bilinear form is proposed. Detailed numerical tests are included and the results demonstrate the good performance of the proposed method both for membrane and bending dominated problems.

In this paper, we overview the objectives and achievements of the CardioSense3D project dedicated to the construction of an electro-mechanical model of the heart.

International audience; We describe an approach that we propose to model the electromechanical behavior of the heart, and to use the model in a data assimilation procedure in order to perform an identification of the parameters and state. The modeling of the heart tissue is based on an electrically-activated contraction law formulated via multiscale considerations and is consistent with various physiological and thermomechanical key requirements. The global heart system also incorporates a simplified lumped modeling of the blood compartments. We report on numerical simulations and on validations of our model in reference and pathological conditions. Furthermore, the data assimilation procedure is intended to give access to quantities of interest for diagnosis purposes, and we present some promising results in this direction.

In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models.

International audience; The incompressible singularity found in 3D elasticity when Poisson's ratio approaches 1/2 is not present in classical shell models, nor in the limit models obtained from 3D elasticity when performing an asymptotic analysis with respect to the thickness parameter. However, some specific shell models - such as the 3D-shell model - do retain the incompressible singularity. These observations raise the issue of how adequately shell models can represent incompressible conditions, which this paper aims at investigating. We first perform a combined asymptotic analysis of 3D elasticity with respect to both the thickness parameter and Poisson's ratio and we obtain a commuting property, which is very valuable as a justification of the concept of an "incompressible shell", and substantiates the use of classical shell models with incompressible materials.We then show that the 3D-shell model does not enjoy a similar commuting property; nevertheless we propose a simple modification of this model for which commuting is obtained, hence consistency with incompressibility is recovered. We also illustrate our discussions with some numerical results.

International audience; We focus on a family of shell elements which are a direct generalization of the shell elements most commonly used in engineering practice. The elements in the family include the effects of the through-the-thickness normal stress and can be employed to couple directly with surrounding media on either surfaces of the shell. We establish the "underlying" mathematical model of the shell discretization scheme, and we show that this mathematical model features the same asymptotic behaviors "when the shell thickness becomes increasingly smaller" as classical shell models. The question of "locking" of the finite element discretization is also briefly addressed and we point out that, for an effective finite element scheme, the MITC approach of interpolation is available.

International audience; We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon - that we call ''pinching locking'' - is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account.

Publisher Summary In-vivo measurements of the cardiac activity are very valuable for clinical purposes, but some crucial biological quantities are hardly—or not at all—accessible, such as stresses/pressures or constitutive parameters that may reflect pathologies. To reach these quantities modeling is required. This chapter presents an electrically activated mechanical model of the myocardium by using an excitation-contraction model relying on a physiological basis and applied within a rheological model of Hill–Maxwell type. The chapter formulates data assimilation technique, and demonstrates the state and parameters of the model from experimental data. Some of these parameters are crucial for medical purposes to detect activation and contraction troubles, hence to diagnose heart pathologies. It is commonly admitted that the model of actin-myosin bridge dynamics because of Huxley allows to describe the muscle-contraction phenomena on the sarcomere scale. However, most modeling endeavours still rely on heuristic approaches and experimental testing, whether directly at the macroscopic level, or to identify the attachment and detachment rates of the bridges.

In this chapter we describe and analyse the linear shell models that we consider in this book. We first describe the fundamental shell kinematics used. Then we discuss the “basic shell model” which is implicitly employed in general finite element solutions and from which other classical shell and plate models can be derived. We summarize the shell models that we call the “shear-membrane-bending model” and the “membrane-bending model”, and introduce the proper mathematical framework in which they define well-posed problems. As special cases of these shell models we obtain well-known plate models.

The nonlinear analysis of shells is today clearly a very large field, in which much research and development has taken place, so that at present many nonlinear analyses can be performed with confidence in engineering practice, see for example (Bathe, 1999, 2001a; Ibrahimbegovic & Kratzig, 2002).

International audience; In general, shell structural problems can be identified to fall into one of the categories of membrane-dominated, bending-dominated and mixed shell problems. The asymptotic behaviour with a well-defined load-scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well-defined load-scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution using finite element analysis.

In this chapter, we describe and analyze the main strategies that have been proposed and used to formulate displacement-based finite element procedures for shells. By displacement-based we mean that the finite element solution is obtained by directly applying the variational principle in the finite element space which discretizes the space of admissible displacements for the structure. In particular, this implies that no “numerical trick” – such as reduced integration – is used in the formulation.

International audience; The formulation of nine-node mixed-interpolated shell elements based on a classical mathematical shell theory is presented, taking into account some fundamental considerations for the finite element analysis of shells. The elements are based on the Mixed Interpolation of Tensorial Components (MITC) approach, but the assumed covariant strain fields are applied only for the membrane and shear components. Two different types of elements are considered, depending on whether or not geometric approximations are included in the formulation. The performance of the proposed elements is illustrated with a well-established test problem - the Scordelis-Lo roof.

We present recent advances on a 3D numerical modeling of the myocardium which couples electrical and biomechanical models. The long-term objective is to simulate a realistic contraction of the heart from both electrical measurements (typically the ECG) and geometrical measurements (typically provided by medical imaging). This realistic contraction should provide useful quantitative parameters for the diagnosis and also for guiding some new forms of therapy. Our modeling is based on a multi- scale analysis ranging from microscopic to macroscopic scales, and integrates a priori information on the overall geometry and on the fiber directions extracted from specific medical imaging techniques (e.g. dtMRI). The FitzHugh-Nagumo equations are solved along with a constitutive law based on the Hill-Maxwell Rheological model, on which a data assimilation analysis is done. In medical image analysis, we believe that this new generation of physics-based deformable models will be useful to provide a more robust quantitative interpretation of temporal series of cardiac images. Resume. Nous presentons ici nos avancees sur la modelisation du myocarde couplant des modeles ´ et biomecaniques. L'objectiflong terme est de simuler la contraction du cœurpartir de mesures ECG et d'images medicales, afin de fournir des outils d'aide au diagnostic. Notre modele se base sur unemultiechelle des phenomenes et des donnees anatomiques extraites d'images medicales. La partierepose sur le modele de FitzHugh-Nagumo et la partie mecanique reprend le formalisme de Hill-Maxwell avec une nouvelle loi de comportement, sur laquelle de l'assimilation de donnees est realisee. En imagerie medicale, nous pensons que ce nouveau type de modeles devrait permettre une interpretation plus robuste des sequences temporelles.

We present a 3D numerical representation of the heart which couples the electrical and biomechanical models. To achieve this, the FitzHugh-Nagumo equations are solved along with a constitutive law based on the Hill-Maxwell rheological law. Ultimately, the parameters of this generic model will be adjusted by comparing the actual patient's ECG with computational results and the deformation of the biomechanical model with the geometric information extracted from the ultrasound images of the patient's heart.

This article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells.Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of ‘shell finite element’ is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements – such as the general shell elements – derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures.

We present a 3Dmec hanical model for the behaviour of the cardiac muscle, based on a recently proposed model of myofibre contraction. The construction of the 3D model involves a rheological model similar to that of Hill-Maxwell. We then introduce some discretisation techniques adapted to our mechanical model, and we report on some preliminary numerical results.

International audience; Based on fundamental considerations for the finite element analysis of shells, we evaluate in the present paper the performance of the MITC general shell elements. We give the results obtained in the analysis of judiciously selected test problems and conclude that the element are effective for general engineering applications.

SUMMARY We show that although no actual mathematical shell model is explicitly used in ‘general shell element’ formulations, we can identify an implicit shell model underlying these nite element procedures. This ‘underlying model’ compares well with classical shell models since it displays the same asymptotic behaviours|when the thickness of the shell becomes very small|as, for example, the Naghdi model. Moreover, we substantiate the connection between general shell element procedures and this underlying model by mathematically proving a convergence result from the nite element solution to the solution of the model. Copyright ? 2000 John Wiley & Sons, Ltd.

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.

International audience; We consider the design of finite element methods for the Naghdi shell model in the case when the deformation is bending dominated. Two formulations based on stabilizing techniques are introduced and it is proved that they are stable, hence free from locking. The theoretical estimates are confirmed by numerical benchmark studies.

In this paper, we present a framework to estimate local ventricular myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivisions. Then, this model is deformed to fit a clinical MRI, using a semi-automatic fuzzy segmentation, an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart is then presented and simulated. Finally, a data assimilation procedure is described, and applied to this model. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on fitting to patient-specific anatomy and assimilation with simulated data are very promising. Current work on model calibration and estimation of patient parameters opens up possibilities to apply this framework in a clinical environment.

This paper presents a first set of experiments to integrate a realistic electro-mechanical model of a beating heart into simulated real-time three-dimensional (RT3D) ultrasound data. A novel ultrasound simulation framework is presented, extended from the model of Meunier [12]. True three-dimensional transducer modeling was performed, using RT3D acquisition design. Myocardium and blood scattering parameters were defined in three dimensions. Ultrasound data sets were generated for a normal case and a pathological case, simulating left bundle branch block. Accuracy of an optical flow tracking method was evaluated on the simulated data to measure displacements on the myocardial surfaces and inside the myocardium over a cardiac cycle. The proposed simulation framework has important motivations in a cardiac modeling context as part of this project is focused on the design of effective parameter estimation methods, based on cardiac imaging.

This PhD thesis is an interdisciplinary research that deals with applied biomechanical modeling of the cardiovascular system in patients with congenital heart diseases . The aim is to explore the potential of biomechanical modeling to assist in clinical decision-making.First, we explored the ability of a previously developed biomechanical model to augment the interpretation of clinical data for patients with tetralogy of Fallot after repair (rTOF) prior to and after pulmonary valve replacement (PVR). Patient-specific models of the right ventricle (RV) and pulmonary circulation were built for 20 subjects pre- and post-PVR using cardiovascular magnetic resonance (CMR) and pressure catheter data. These models were subjected to the effects of pulmonary valve (PV) regurgitation and/or RV outflow tract (RVOT) obstruction. The models provided patient-specific indices of myocardial contractility pre- and post-PVR. The results showed a decrease of contractility in all patients post-PVR. Patients with predominantly RVOT obstruction experienced a higher level of contractility decrease whereas ceasing the regurgitation itself did not lead to a significant reduction in contractility. After this detailed study of pathophysiology of the overloaded RVs pre- and post-PVR, we explored the ability of the model to predict the response of ventricular mechanics when progressively decreasing the afterload of the RVs in patients with rTOF. Pre-PVR patient-specific models were used and cessation of PV regurgitation and progressive decrease of RVOT resistance were assumed. The resulting in silico relationships between the contractility and RVOT resistance post-PVR appeared to be linear, and consistent with that given by the patient-specific post-PVR models.For patients with single-ventricle hearts undergoing CMR combined with a pressure catheter (as part of planning for complex surgery), the model was used to synchronize in time the catheter-pressure data and the ventricular volumes obtained by CMR. This model-assisted time-synchronization produces high quality P-V loops that yield more accurate indices of myocardial energetics (maximum value of time-varying elastance (E_max) and stroke work) and hence could be used to ameliorate the clinical interpretation.Finally, we compared the indices of E_max and maximum time derivative of ventricular pressure, max(dP/dt), when obtained directly from the clinical measurements vs. model-derived contractility and max(dP/dt). All data- and model-derived indices showed a good agreement. In addition, a potential application of model-derived max⁡(dP/dt) as a model-based data filter was emphasized.Overall, this thesis demonstrated (1) an ability of biomechanical modeling to provide additional mechanical indices of ventricular function and their evolution under different loading conditions, which has the potential to contribute into the planning of optimal therapy; (2) an application of the model to provide robust clinical data processing of a variety of data acquisition protocols; and (3) a correspondence of model-derived indices with clinically accepted surrogate measures of contractility. In conclusion, this thesis showed that biomechanical modeling could be deployed in a clinical environment to address various types of problems towards the delivery of personalized healthcare solutions.; Cette thèse de doctorat est une recherche interdisciplinaire qui porte sur la modélisation biomécanique appliquée du système cardiovasculaire chez les patients atteints de cardiopathies congénitales. L'objectif est d'explorer le potentiel de la modélisation biomécanique pour aider à la prise de décision clinique.Tout d'abord, nous avons exploré la capacité d'un modèle biomécanique précédemment développé à améliorer l'interprétation des données cliniques pour les patients atteints de tétralogie de Fallot après réparation (TOFr) avant et après le remplacement de la valve pulmonaire (RVP). Des modèles personnalisés du ventricule droit (VD) et de la circulation pulmonaire ont été construits pour 20 sujets avant et après le RVP à l'aide de données obtenues par résonance magnétique cardiovasculaire (RMC) et par cathéter de pression. Ces modèles ont été soumis aux effets de la régurgitation de la valve pulmonaire (VP) et/ou de l'obstruction du canal de sortie du VD (RVOT). Les modèles ont fourni des indices de contractilité myocardique personnalisés avant et après la RPV. Les résultats ont montré une diminution de la contractilité chez tous les patients après la RVP. Les patients présentant une obstruction prédominante de l'RVOT ont connu une diminution plus importante de la contractilité, alors que l'arrêt de la régurgitation elle-même n'a pas entraîné de réduction significative de la contractilité. Après cette étude détaillée de la pathophysiologie des VD surchargés avant et après la RVP, nous avons exploré la capacité du modèle à prédire la réponse de la mécanique ventriculaire lors de la diminution progressive de la post-charge des VD chez les patients atteints de TOFr. Des modèles pré-PVR personnalisés ont été utilisés et l'arrêt de la régurgitation PV et la diminution progressive de la résistance RVOT ont été supposés. Les relations in silico résultantes entre la contractilité et la résistance de l'RVOT après la RVP sont apparues linéaires et cohérentes avec celles données par les modèles post-RVP spécifiques aux patients.Pour les patients dont le cœur est constitué d'un seul ventricule et qui subissent une RMC combinée à un cathéter de pression (dans le cadre de la planification d'une chirurgie complexe), le modèle a été utilisé pour synchroniser dans le temps les données de pression du cathéter et les volumes ventriculaires obtenus par RMC. Cette synchronisation temporelle assistée par le modèle produit des boucles P-V de haute qualité qui donnent des indices plus précis de l'énergétique cardiaque (valeur maximale de l'élastance variable dans le temps (E_max) et du travail systémique) et qui pourraient donc être utilisés pour améliorer l'interprétation clinique.Enfin, nous avons comparé les indices de E_max et de la dérivée temporelle maximale de la pression ventriculaire, max(dP/dt), obtenus directement à partir des mesures cliniques, avec la contractilité et le max(dP/dt) dérivés du modèle. Tous les indices dérivés des données et du modèle ont montré une bonne concordance. De plus, une application potentielle du max(dP/dt) dérivé du modèle comme filtre de données basé sur le modèle a été soulignée.Dans l'ensemble, cette thèse a démontré (1) la capacité de la modélisation biomécanique à fournir des indices mécaniques supplémentaires de la fonction ventriculaire et leur évolution dans différentes conditions de charge, ce qui pourrait contribuer à la planification d'une thérapie optimale ; (2) une application du modèle pour fournir un traitement robuste des données cliniques d'une variété de protocoles d'acquisition de données ; et (3) une correspondance des indices dérivés du modèle avec des mesures de substitution de la contractilité acceptées cliniquement. En conclusion, cette thèse a montré que la modélisation biomécanique pouvait être déployée dans un environnement clinique pour résoudre divers types de problèmes en médecine personnalisée.