Non-Invasive Electrocardiographic Imaging of Ventricular Activities: Data-Driven and Model-Based Approaches

Die vorliegende Arbeit beleuchtet ausgewählte Aspekte der Vorwärtsmodellierung, so zum Beispiel die Simulation von Elektro- und Magnetokardiogrammen im Falle einer elektrisch stillen Ischämie sowie die Anpassung der elektrischen Potentiale unter Variation der Leitfähigkeiten. Besonderer Fokus liegt auf der Entwicklung neuer Regularisierungsalgorithmen sowie der Anwendung und Bewertung aktuell verwendeter Methoden in realistischen in silico bzw. klinischen Studien

Bayesian Inference with Combined Dynamic and Sparsity Models: Application in 3D Electrophysiological Imaging

Data-driven inference is widely encountered in various scientific domains to convert the observed measurements into information that cannot be directly observed about a system. Despite the quickly-developing sensor and imaging technologies, in many domains, data collection remains an expensive endeavor due to financial and physical constraints. To overcome the limits in data and to reduce the demand on expensive data collection, it is important to incorporate prior information in order to place the data-driven inference in a domain-relevant context and to improve its accuracy. Two sources of assumptions have been used successfully in many inverse problem applications. One is the temporal dynamics of the system (dynamic structure). The other is the low-dimensional structure of a system (sparsity structure). In existing work, these two structures have often been explored separately, while in most high-dimensional dynamic system they are commonly co-existing and contain complementary information. In this work, our main focus is to build a robustness inference framework to combine dynamic and sparsity constraints. The driving application in this work is a biomedical inverse problem of electrophysiological (EP) imaging, which noninvasively and quantitatively reconstruct transmural action potentials from body-surface voltage data with the goal to improve cardiac disease prevention, diagnosis, and treatment. The general framework can be extended to a variety of applications that deal with the inference of high-dimensional dynamic systems

Invariant Reconstruction of Curves and Surfaces with Discontinuities with Applications in Computer Vision

The reconstruction of curves and surfaces from sparse data is an important task in many applications. In computer vision problems the reconstructed curves and surfaces generally represent some physical property of a real object in a scene. For instance, the sparse data that is collected may represent locations along the boundary between an object and a background. It may be desirable to reconstruct the complete boundary from this sparse data. Since the curves and surfaces represent physical properties, the characteristics of the reconstruction process differs from straight forward fitting of smooth curves and surfaces to a set of data in two important areas. First, since the collected data is represented in an arbitrarily chosen coordinate system, the reconstruction process should be invariant to the choice of the coordinate system (except for the transformation between the two coordinate systems). Secondly, in many reconstruction applications the curve or surface that is being represented may be discontinuous. For example in the object recognition problem if the object is a box there is a discontinuity in the boundary curve at the comer of the box. The reconstruction problem will be cast as an ill-posed inverse problem which must be stabilized using a priori information relative to the constraint formation. Tikhonov regularization is used to form a well posed mathematical problem statement and conditions for an invariant reconstruction are given. In the case where coordinate system invariance is incorporated into the problem, the resulting functional minimization problems are shown to be nonconvex. To form a valid convex approximation to the invariant functional minimization problem a two step algorithm is proposed. The first step forms an approximation to the curve (surface) which is piecewise linear (planar). This approximation is used to estimate curve (surface) characteristics which are then used to form an approximation of the nonconvex functional with a convex functional. Several example applications in computer vision for which the invariant property is important are presented to demonstrate the effectiveness of the algorithms. To incorporate the fact that the curves and surfaces may have discontinuities the minimizing functional is modified. An important property of the resulting functional minimization problems is that convexity is maintained. Therefore, the computational complexity of the resulting algorithms are not significantly increased. Examples are provided to demonstrate the characteristics of the algorithm

On Learning and Generalization to Solve Inverse Problem of Electrophysiological Imaging

In this dissertation, we are interested in solving a linear inverse problem: inverse electrophysiological (EP) imaging, where our objective is to computationally reconstruct personalized cardiac electrical signals based on body surface electrocardiogram (ECG) signals. EP imaging has shown promise in the diagnosis and treatment planning of cardiac dysfunctions such as atrial flutter, atrial fibrillation, ischemia, infarction and ventricular arrhythmia. Towards this goal, we frame it as a problem of learning a function from the domain of measurements to signals. Depending upon the assumptions, we present two classes of solutions: 1) Bayesian inference in a probabilistic graphical model, 2) Learning from samples using deep networks. In both of these approaches, we emphasize on learning the inverse function with good generalization ability, which becomes a main theme of the dissertation. In a Bayesian framework, we argue that this translates to appropriately integrating different sources of knowledge into a common probabilistic graphical model framework and using it for patient specific signal estimation through Bayesian inference. In learning from samples setting, this translates to designing a deep network with good generalization ability, where good generalization refers to the ability to reconstruct inverse EP signals in a distribution of interest (which could very well be outside the sample distribution used during training). By drawing ideas from different areas like functional analysis (e.g. Fenchel duality), variational inference (e.g. Variational Bayes) and deep generative modeling (e.g. variational autoencoder), we show how we can incorporate different prior knowledge in a principled manner in a probabilistic graphical model framework to obtain a good inverse solution with generalization ability. Similarly, to improve generalization of deep networks learning from samples, we use ideas from information theory (e.g. information bottleneck), learning theory (e.g. analytical learning theory), adversarial training, complexity theory and functional analysis (e.g. RKHS). We test our algorithms on synthetic data and real data of the patients who had undergone through catheter ablation in clinics and show that our approach yields significant improvement over existing methods. Towards the end of the dissertation, we investigate general questions on generalization and stabilization of adversarial training of deep networks and try to understand the role of smoothness and function space complexity in answering those questions. We conclude by identifying limitations of the proposed methods, areas of further improvement and open questions that are specific to inverse electrophysiological imaging as well as broader, encompassing theory of learning and generalization

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Advanced acquisition and reconstruction techniques in magnetic resonance imaging

Mención Internacional en el título de doctorMagnetic Resonance Imaging (MRI) is a biomedical imaging modality with outstanding features such as excellent soft tissue contrast and very high spatial resolution. Despite its great properties, MRI suffers from some drawbacks, such as low sensitivity and long acquisition times. This thesis focuses on providing solutions for the second MR drawback, through the use of compressed sensing methodologies. Compressed sensing is a novel technique that enables the reduction of acquisition times and can also improve spatiotemporal resolution and image quality. Compressed sensing surpasses the traditional limits of Nyquist sampling theories by enabling the reconstruction of images from an incomplete number of acquired samples, provided that 1) the images to reconstruct have a sparse representation in a certain domain, 2) the undersampling applied is random and 3) specific non-linear reconstruction algorithms are used. Cardiovascular MRI has to overcome many limitations derived from the respiratory and cardiac cycles, and has very strict requirements in terms of spatiotemporal resolution. Hence, any improvement in terms of reducing acquisition times or increasing image quality by means of compressed sensing will be highly beneficial. This thesis aims to investigate the benefits that compressed sensing may provide in two cardiovascular MR applications: The acquisition of small-animal cardiac cine images and the visualization of human coronary atherosclerotic plaques. Cardiac cine in small-animals is a widely used approach to assess cardiovascular function. In this work we proposed a new compressed sensing methodology to reduce acquisition times in self-gated cardiac cine sequences. This methodology was developed as a modification of the Split Bregman reconstruction algorithm to include the minimization of Total Variation across both spatial and temporal dimensions. We simulated compressed sensing acquisitions by retrospectively undersampling complete acquisitions. The accuracy of the results was evaluated with functional measurements in both healthy animals and animals with myocardial infarction. The method reached accelerations rates of 10-14 for healthy animals and acceleration rates of 10 in the case of unhealthy animals. We verified these theoretically-feasible acceleration factors in practice with the implementation of a real compressed sensing acquisition in a 7 T small-animal MR scanner. We demonstrated that acceleration factors around 10 are achievable in practice, close to those obtained in the previous simulations. However, we found some small differences in image quality between simulated and real undersampled compressed sensing reconstructions at high acceleration rates; this might be explained by differences in their sensitivity to motion contamination during acquisition. The second cardiovascular application explored in this thesis is the visualization of atherosclerotic plaques in coronary arteries in humans. Nowadays, in vivo visualization and classification of plaques by MRI is not yet technically feasible. Acceleration techniques such as compressed sensing may greatly contribute to the feasibility of the application in vivo. However, it is advisable to carry out a systematic study of the basic technical requirements for the coronary plaque visualization prior to designing specific acquisition techniques. On simulation studies we assessed spatial resolution, SNR and motion limits required for the proper visualization of coronary plaques and we proposed a new hybrid acquisition scheme that reduces sensitivity to motion. In order to evaluate the benefits that acceleration techniques might provide, we evaluated different parallel imaging algorithms and we also implemented a compressed sensing methodology that incorporates information from the coil sensitivity profile of the phased-array coil used. We found that, with the coil setup analyzed, acceleration benefits were greatly limited by the small size of the FOV of interest. Thus, dedicated phased-arrays need to be designed to enhance the benefits that accelerating techniques may provide on coronary artery plaque imaging in vivo.La Imagen por Resonancia Magnética (IRM) es una modalidad de imagen biomédica con notables características tales como un excelente contraste en tejidos blandos y una muy alta resolución espacial. Sin embargo, a pesar de estas importantes propiedades, la IRM tiene algunos inconvenientes, como una baja sensibilidad y tiempos de adquisición muy largos. Esta tesis se centra en buscar soluciones para el segundo inconveniente mencionado a través del uso de metodologías de compressed sensing. Compressed sensing es una técnica novedosa que permite la reducción de los tiempos de adquisición y también la mejora de la resolución espacio-temporal y la calidad de las imágenes. La teoría de compressed sensing va más allá los límites tradicionales de la teoría de muestreo de Nyquist, permitiendo la reconstrucción de imágenes a partir de un número incompleto de muestras siempre que se cumpla que 1) las imágenes a reconstruir tengan una representación dispersa (sparse) en un determinado dominio, 2) el submuestreo aplicado sea aleatorio y 3) se usen algoritmos de reconstrucción no lineales específicos. La resonancia magnética cardiovascular tiene que superar muchas limitaciones derivadas de los ciclos respiratorios y cardiacos, y además tiene que cumplir unos requisitos de resolución espacio-temporal muy estrictos. De ahí que cualquier mejora que se pueda conseguir bien reduciendo tiempos de adquisición o bien aumentando la calidad de las imágenes resultaría altamente beneficiosa. Esta tesis tiene como objetivo investigar los beneficios que la técnica de compressed sensing puede proporcionar a dos aplicaciones punteras en RM cardiovascular, la adquisición de cines cardiacos de pequeño animal y la visualización de placas ateroscleróticas en arterias coronarias en humano. La adquisición de cines cardiacos en pequeño animal es una aplicación ampliamente usada para evaluar función cardiovascular. En esta tesis, proponemos una metodología de compressed sensing para reducir los tiempos de adquisición de secuencias de cine cardiaco denominadas self-gated. Desarrollamos esta metodología modificando el algoritmo de reconstrucción de Split-Bregman para incluir la minimización de la Variación Total a través de la dimensión temporal además de la espacial. Para ello, simulamos adquisiciones de compressed sensing submuestreando retrospectivamente adquisiciones completas. La calidad de los resultados se evaluó con medidas funcionales tanto en animales sanos como en animales a los que se les produjo un infarto cardiaco. El método propuesto mostró que factores de aceleración de 10-14 son posibles para animales sanos y en torno a 10 para animales infartados. Estos factores de aceleración teóricos se verificaron en la práctica mediante la implementación de una adquisición submuestreada en un escáner de IRM de pequeño animal de 7 T. Se demostró que aceleraciones en torno a 10 son factibles en la práctica, valor muy cercano a los obtenidos en las simulaciones previas. Sin embargo para factores de aceleración muy altos, se apreciaron algunas diferencias entre la calidad de las imágenes con submuestreo simulado y las realmente submuestreadas; esto puede ser debido a una mayor sensibilidad a la contaminación por movimiento durante la adquisición. La segunda aplicación cardiovascular explorada en esta tesis es la visualización de placas ateroscleróticas en arterias coronarias en humanos. Hoy en día, la visualización y clasificación in vivo de es te tipo de placas mediante IRM aún no es técnicamente posible. Pero no hay duda de que técnicas de aceleración, como compressed sensing, pueden contribuir enormemente a la consecución de la aplicación in vivo. Sin embargo, como paso previo a la evaluación de las técnicas de aceleración, es conveniente hacer un estudio sistemático de los requerimientos técnicos necesarios para la correcta visualización y caracterización de las placas coronarias. Mediante simulaciones establecimos los límites de señal a ruido, resolución espacial y movimiento requeridos para la correcta visualización de las placas y propusimos un nuevo esquema de adquisición híbrido que reduce la sensibilidad al movimiento. Para valorar los beneficios que las técnicas de aceleración pueden aportar, evaluamos diferentes algoritmos de imagen en paralelo e implementamos una metodología de compresed sensing que tiene en cuenta la información de los mapas de sensibilidad de las antenas utilizadas. En este estudio se encontró, que para la configuración de antenas analizadas, los beneficios de la aceleración están muy limitados por el pequeño campo de visón utilizado. Por tanto, para incrementar los beneficios que estas técnicas de aceleración pueden aportar la imagen de placas coronarias in vivo, es necesario diseñar antenas específicas para esta aplicación.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Elfar Adalsteinsson.- Secretario: Juan Miguel Parra Robles.- Vocal: Pedro Ramos Cabre

Modeling Human Atrial Patho-Electrophysiology from Ion Channels to ECG - Substrates, Pharmacology, Vulnerability, and P-Waves

Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This thesis presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF

Caractérisation des propriétés élastiques de la paroi artérielle par ultrasonographie endovasculaire

RÉSUMÉ Dans le cadre de ce projet, on présente une nouvelle technique d'imagerie ultrasonore de l'élasticité du tissu artériel: l'élastographie endovasculaire (EEV). Le changement de la rigidité du tissu artériel est souvent un indice d'état pathologique. Il en est ainsi de l'athérosclérose qui est une pathologie au cours de laquelle la paroi artérielle s'épaissit et perd graduellement son élasticité. Cette pathologie se caractérise par la formation de plaques d'athéromes constituées de dépôts de nature variée (lipidiques, fibreux ou calcifiés) qui induisent des changements localisés des propriétés élastiques du tissu artériel et un rétrécissement de la lumière artérielle. L'objectif de ce projet de recherche est de développer un outil capable de caractériser et de quantifier les propriétés élastiques de la paroi artérielle afin de permettre le diagnostic de pathologies artérielles comme l'athérosclérose. Il existe diverses techniques d'exploration vasculaire. L'ultrasonographie intravasculaire (USIV), par exemple, fournit une visualisation tomographique de la paroi artérielle qui permet l'étude de son comportement. Les estimations de déplacement et de déformation, issues de l'USIV, sont utilisées pour la caractérisation des propriétés élastiques de la paroi artérielle. Dans l'élastographie endovasculaire (EEV), les mesures de déplacements internes issus de l'USIV sont utilisées pour obtenir l'information relative aux propriétés élastiques de la paroi artérielle. L'EEV permettrait une visualisation précise de l'étendue de la pathologie et du niveau de son infiltration dans la paroi. De plus, certaines plaques sont plus instables que d'autres et, grâce à l'EEV, il serait possible de prédire les sites qui sont propices à la rupture. Ces sites correspondraient aux points de concentration de contraintes. Généralement, c'est à ces endroits que les plaques se disloquent et conduisent à la formation de thromboses qui provoquent le plus souvent l'arrêt de la circulation sanguine. L'EEV, par sa capacité de différencier les types de plaques et de caractériser leur rigidité, pourrait servir à raffiner le diagnostic ainsi que les interventions thérapeutiques. En utilisant le modèle théorique de l'EEV, il serait possible de prédire la réponse du tissu à une intervention comme l'angioplastie. Ceci permettrait d'anticiper toute complication, comme la déchirure intimale, et ainsi de choisir une autre modalité d'intervention plus appropriée. Nous verrons, au chapitre 3, la formulation du problème direct (PD) en EEV. La résolution du PD est basée sur l'utilisation d'un modèle théorique qui décrit l'équilibre mécanique du tissu artériel suite à l'application d'un faible échelon de pression intraluminale. La pression intraluminale est appliquée au moyen d'un dispositif composé d'un ballonnet et d'un transducteur ultrasonore. Ce dispositif, en plus de fournir les images échographiques de l'opération de compression, stabilise le système d'imagerie, offrant ainsi des conditions quasi statiques. Le tissu artériel est modélisé comme un milieu élastique, linéaire, isotopique et quasi incompressible (v = 0.497). Dans ces conditions, seul le module de Young est requis pour une caractérisation complète du comportement du tissu artériel. D'autre part, puisque seules les composantes du déplacement qui sont dans le plan de propagation des ultrasons sont mesurables, le modèle est considéré comme en état plan de déformation. Cette hypothèse ne représente pas une limitation excessive, puisque l'artère est dans un état d'étirement longitudinal qui minimise sa déformation dans cette orientation. L'image de la distribution de déformation interne, dérivée du champ de déplacement induit par la compression du tissu artériel, est appelée «élastogramme endovasculaire». Sous l'hypothèse de l'uniformité du champ de contrainte issu de cette compression, la distribution de déformation est interprétée comme la distribution du module d'élasticité du tissu artériel. Le champ de contrainte est fonction des conditions aux frontières et de la distribution d'élasticité. Puisque cette distribution d'élasticité n'est pas uniforme, la distribution de contrainte ne l'est pas non plus. Cette inhomogénéité du champ de contrainte se traduit par une manifestation artefactuelle. Cette manifestation est directement liée à la complexité structurale des plaques, et la structure des plaques influence considérablement le patron de déformation. Comme les mesures de déplacement sont estimées à partir des sonogrammes intravasculaires, un modèle de formation d'images échographiques endovasculaires est proposé pour permettre une éventuelle étude qui se penchera sur les artefacts reliés à ce type d'imagerie échographique de révolution. Dans le but de réduire l'effet des artefacts et d'obtenir une représentation quantitative de la vraie distribution d'élasticité et, donc, de pouvoir déterminer la distribution de contraintes, on considère l'EEV dans le cadre de résolution d'un problème inverse (PI). La solution du PI est celle qui minimise l'erreur quadratique, au sens des moindres carrés, entre le champ de déplacement axial mesuré et celui prédit. Le champ de déplacement prédit est calculé, en utilisant la méthode des éléments finis, à partir des équations d'élasticité pour une distribution d'élasticité et des conditions aux frontières données. La résolution du PI en EEV est étudiée au chapitre 4. Dans un premier temps, les composantes axiale et latérale du champ de déplacement sont utilisées pour la reconstruction de la distribution d'élasticité. Utilisant la méthode de Gauss-Newton dans des conditions idéales, la distribution d'élasticité injectée est récupérée exempte de toute manifestation artefactuelle, comme celle vue dans l'image de déformation. Dans un deuxième temps, seule la composante axiale est utilisée, puisque la variance dans l'estimation de la composante latérale du champ de déplacement est plus grande que celle de la composante axiale. Pour stabiliser la solution du PI et accéder à une solution unique, la méthode de Levenberg-Marquardt est utilisée. Le problème étant mal posé, une étape essentielle pour la convergence vers la solution est celle de la détermination du paramètre d'amortissement (régularisation) optimal qui sert à adoucir les rebondissements de la solution. Pour le choix de ce facteur d'amortissement, une méthode utilisant la décomposition en valeurs singulières est utilisée. La résolution du PI nous permet de récupérer la distribution d'élasticité même dans le cas où une composante de bruit est ajoutée à l'information de déplacement. Toutefois, lorsque le rapport signal sur bruit est supérieur à 30 dB, la reconstruction est acceptable. En dessous de ce seuil, les artefacts prédominent.--------------------ABSTRACT This thesis deals with the endovascular elastography (EVE) which is a new ultrasonic imaging technique to characterize the elastic properties of the arterial wall tissue. These arterial wall elastic properties are derived from ultrasonically estimated displacements induced by an intraluminal pressure push. The pathological state of arterial tissue is generally correlated with a local change in its mechanical perperties. The objective of this research is to develop a method able to characterize and quantify the arterial elastic properties, allowing the diagnosis of arterial pathologies. Atherosclerosis is this arterial pathology characterized by arterial wall thickening and loss of elasticity. It begins with the accumulation of atheroma (plaque) leading to the narrowing of the arterial lumen. These plaques are often structurally complex, with varying amounts of lipid, fibrous tissue, and calcium deposits. These changes lead to a localized modification of the elastic distribution of the arterial wall tissue. Intravascular ultrasound (IVUS) is this catheter based modality with the ability to provide a tomographic image of the vascular allowing the study of its behavior. The IVUS estimate of the displacement filed is used to characterize the elastic properties of the arterial wall. EVE would allow an accurate visualization of the spread out of the pathology and the depth of its infiltration into the arterial wall. Also, since some plaques are more unstable than others, it would be possible to predict the locations of plaque rupture through the points of stress concentration. Generally, if failure is expected to occur it will be at these points of stress concentration. EVE, by its capacity to distinguish between plaque types and characterize their hardness, would refine the diagnosis and the remedial interventions. It would be possible, with the theoretical model of EVE, to predict the response of the tissue to a procedure such as angioplasty. This would allow to predict any complication, as intimale tearing, assisting in the choice of an other more appropriate modality. In chapter 3, we will see the formulation of the forward problem (FP) in EVE. Its resolution is based on a theoretical model that describes the mechanical balance of the arterial tissue when excited by a small step of intraluminal pressure. This intraluminal pressure is induced by a combined angioplasty balloon and an ultrasound catheter system. In addition to image the inflation procedure, the combined system stabilizes the artery and the imaging system, and the applied pressure imposes a quasi-static condition. As a first approximation, the arterial wall tissue, including plaques, is modeled as isotropic, incompressible and linearly elastic material. In these circumstances, only Young's modulus is needed to fully characterize the behavior of the arterial tissue. Furthermore, since only the component of the displacement in the acoustical scanning plane is assessable, the model is considered in a plane strain state. This assumption does not represent an extreme restriction, considering the artery is in a state of longitudinal stretching that minimizes its deformation in this direction. The strain image, derived from the displacement field obtained after compressing the arterial tissue, is called the endovascular elastogram. With the assumption of constant stress field at the inner wall boundary, the strain field is considered as a relative measure of the elasticity distribution of the arterial wall. The stress distribution is dependent on the boundary conditions and the elasticity distribution. The non-uniformity of the elasticity distribution implies the non-uniformity of the stress distribution. This inhomogeneity of the stress field conveys to an artifactual exhibition. This artifactual exhibition is directly associated with the structural complexity of plaques. The composition of plaques affects greatly the deformation pattern. While the displacement measures are estimated from intravascular sonograms, an echographic endovascular image formation model is proposed to study the artifact surrounding this kind of imaging system. To reduce the consequence of these artifacts and to obtain a quantitative representation of the elasticity distribution, we consider the EVE in the framework of an inverse problem (IP) solution. The solution of the IP is the one that minimizes the least squares error between the observed and predicted displacement field. The predicted displacement field is computed using the finite element method, to numerically solve the elasticity equations, for a given set of elasticity distribution and boundary conditions. The IP is first solved using both the axial and lateral component of the displacement field. Using the Gauss-Newton method, in an ideal condition, the reconstruction of the elasticity distribution was successful. This elasticity distribution was clear of any artifactual presence as in the strain image. Subsequently, since in practice only the component of the displacement in the acoustical scanning plane can be measured, we use only the axial component of the displacement field to solve the IP. To solve the IP and single out a stable solution, Levenberg-Marquardt method is used. The IP being ill-posed, a fundamental step to get the solution is to regularize the problem and to estimate the optimal damping factor used to damp the solution oscillations. This damping factor is obtained using the singular value decomposition. In this IP solving, we were able to retrieve an acceptable solution even in the case where we add a noise in the displacement data. When the signal to noise ratio (SNR) is greater than 30 dB the solution is admissible. Beyond this threshold the artifacts dominate.-----------CONTENU Physiologie vasculaire -- Athérosclérose et thrombose -- Traitement de l'athérosclérose -- Modalités d'imagerie vasculaire -- Étude de l'élasticité artérielle -- USIV dans la caractérisation du tissu vasculaire -- Estimation du mouvement -- Elastographie endovasculaire -- Endovascular elastography : the forward problem -- The forward problem formulation -- Polar image formation model -- Endovascular elastography : the inverse problem -- The Inverse problem in endovascular elastography