The characterization of the mechanical behavior of soft living tissues is a big challenge in Biomechanics. The difficulty arises from both the access to the tissues and the manipulation in order to know their physical properties. Currently, the biomechanical characterization of the organs is mainly performed by testing ex-vivo samples or by means of indentation tests. In the first case, the obtained behavior does not represent the real behavior of the organ. In the second case, it is only a representation of the mechanical response of the indented areas. The purpose of the research reported in this thesis is the development of a methodology to in-vivo characterize the biomechanical behavior of two different organs: the breast and the cornea. The proposed methodology avoids invasive measurements to obtain the mechanical response of the organs and is able to completely characterize of the biomechanical behavior of them. The research reported in this thesis describes a methodology to in-vivo characterize the biomechanical behavior of the breast and the cornea. The estimation of the elastic constants of the constitutive equations that define the mechanical behavior of these organs is performed using an iterative search algorithm which optimizes these parameters. The search is based on the iterative variation of the elastic constants of the model in order to increase the similarity between a simulated deformation of the organ and the real one. The similarity is measured by means of a volumetric similarity function which combines overlap-based coefficients and distance-based coefficients. Due to the number of parameters to be characterized as well as the non-convergences that the solution may present in some regions, genetic heuristics were chosen to drive the search algorithm. In the case of the breast, the elastic constants of an anisotropic hyperelastic neo-Hookean model proposed to simulate the compression of the breast during an MRI-guided biopsy were estimated. Results from this analysis showed that the proposed algorithm accurately found the elastic constants of the proposed model, providing an average relative error below 10%. The methodology was validated using breast software phantoms. Nevertheless, this methodology can be easily transferred into its use with real breasts. In the case of the cornea, the elastic constants of a hyperelastic second-order Ogden model were estimated for 24 corneas corresponding to 12 patients. The finite element method was applied in order to simulate the deformation of the human corneas due to non-contact tonometry. The iterative search was applied in order to estimate the elastic constants of the model which approximates the most the simulated deformation to the real one. Results showed that these constants can be estimated with an error of about 5%. After the results obtained for both organs, it can be concluded that the iterative search methodology presented in this thesis allows the \textit{in-vivo} estimation the patient-specific elastic constants of the constitutive biomechanical models that govern the biomechanical behavior of these two organs. / Lago Ángel, MÁ. (2014). A new approach for the in-vivo characterization of the biomechanical behavior of the breast and the cornea [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/44116 / TESIS

L’épidémiologie des anévrismes de l’aorte est un problème de santé publique majeur dans les pays industrialisés. Cette pathologie peut engendrer la mort du patient en cas de rupture de l’anévrisme. Actuellement les critères d’intervention chirurgicale sont basés sur la morphologie de l’anévrisme et il existe des difficultés à évaluer correctement le risque de rupture pour chaque patient. L’objectif de cette thèse était de développer une méthode d’identification des propriétés mécaniques de la paroi artérielle de manière personnalisée permettant d’affiner les critères d’intervention chirurgicale. Des essais de gonflement utilisant des mesures de champs et le développement d’une méthodologie d’analyse ont permis de quantifier la distribution des contraintes des anévrismes de manière expérimentale et de mettre en évidence l’apparition des affaiblissements ponctuels dans la paroi afin de prédire la localisation de la rupture de l’anévrisme. Ensuite, une méthode d’identification de propriétés mécaniques a été mise en place pour mettre en évidence l’hétérogénéité du tissu artériel et pour localiser les endroits à l’origine de la rupture du tissu. L’identification des lois de comportement à partir de données expérimentales issues de patients permettra d’améliorer les modèles numériques artériels utilisées aujourd’hui. De plus, la méthodologie créée pour l’analyse de la rupture d’anévrismes pendant cette thèse ouvre la porte à une étape qui vise à développer la caractérisation mécanique in-vivo par l’utilisation de l’imagerie médicale. L’objectif final sera d’évaluer le risque de rupture de l’anévrisme de chaque patient de manière non-invasive. / Epidemiology of aortic aneurysms is a major public health issue that affects a significant proportion of the population in industrialized countries and can cause the death of the patient in case of rupture of the aneurysm.Currently the only criteria for surgery are based on the morphology of the aneurysm, and there are problems to accurately assess the risk of rupture for each patient.The aim of this thesis was to develop a method to identify the mechanical properties of the arterial wall in a personalized way to refine the criteria for surgery.Inflation tests, full-field measurements and a methodology developed were used in order to quantify experimentally the stress distribution of aneurysms. It was possible to highlight the appearance of localized weakening in the wall which will let us predict the location of the rupture on the aneurysm. Then a method was developed to identify the mechanical properties of the aortic tissue. It was possible to highlight the heterogeneity of arterial tissue and locate the places where the rupture of the tissue may occur.The identification of the aneurysm’s mechanical properties from experimental data will improved arterial numerical models used today. In addition, the methodology developed for the analysis of the rupture of aneurysms during this thesis opens the door to a step that aims to develop the in vivo mechanical characterization by the use of medical imaging. The ultimate goal will be to assess the risk of rupture of the aneurysm of each patient in a noninvasive manner.

L’élastographie est une technique d’imagerie qui vise à cartographier in vivo les propriétés mécaniques des tissus biologiques dans le but de fournir des informations diagnostiques additionnelles. Depuis son introduction en imagerie ultrasonore dans les années 1990, l’élastographie a trouvé de nombreuses applications. Cette modalité a notamment été utilisée pour l’étude du sein, du foie, de la prostate et des artères par imagerie ultrasonore, par résonance magnétique ou en tomographie par cohérence optique. Dans le contexte des maladies cardiovasculaires, cette modalité a un fort potentiel diagnostique puisque l’athérosclérose modifie la structure des tissus biologiques et leurs propriétés mécaniques bien avant l’apparition de tout symptôme. Quelle que soit la modalité d’imagerie utilisée, l’élastographie repose sur : l’excitation mécanique du tissu (statique ou dynamique), la mesure de déplacements et de déformations induites, et l’inversion qui permet de recouvrir les propriétés mécaniques des tissus sous-jacents. Cette thèse présente un ensemble de travaux d’élastographie dédiés à l’évaluation des tissus de l’appareil cardiovasculaire. Elle est scindée en deux parties. La première partie intitulée « Élastographie vasculaire » s’intéresse aux pathologies affectant les artères périphériques. La seconde, intitulée « Élastographie cardiaque », s’adresse aux pathologies du muscle cardiaque. Dans le contexte vasculaire, l’athérosclérose modifie la physiologie de la paroi artérielle et, de ce fait, ses propriétés biomécaniques. La première partie de cette thèse a pour objectif principal le développement d’un outil de segmentation et de caractérisation mécanique des composantes tissulaires (coeur lipidique, tissus fibreux et inclusions calciques) de la paroi artérielle, en imagerie ultrasonore non invasive, afin de prédire la vulnérabilité des plaques. Dans une première étude (Chapitre 5), nous présentons un nouvel estimateur de déformations, associé à de l’imagerie ultrarapide par ondes planes. Cette nouvelle méthode d’imagerie permet d’augmenter les performances de l’élastographie non invasive. Dans la continuité de cette étude, on propose une nouvelle méthode d’inversion mécanique dédiée à l’identification et à la quantification des propriétés mécaniques des tissus de la paroi (Chapitre 6). Ces deux méthodes sont validées in silico et in vitro sur des fantômes d’artères en polymère. Dans le contexte cardiaque, les ischémies et les infarctus causés par l’athérosclérose altèrent la contractilité du myocarde et, de ce fait, sa capacité à pomper le sang dans le corps (fonction myocardique). En échocardiographie conventionnelle, on évalue généralement la fonction myocardique en analysant la dynamique des mouvements ventriculaires (vitesses et déformations du myocarde). L’abscence de contraintes physiologiques agissant sur le myocarde (contrairement à la pression sanguine qui contraint la paroi vasculaire) ne permet pas de résoudre le problème inverse et de retrouver les propriétés mécaniques du tissu. Le terme d’élastographie fait donc ici référence à l’évaluation de la dynamique des mouvements et des déformations et non à l’évaluation des propriétés mécanique du tissu. La seconde partie de cette thèse a pour principal objectif le développement de nouveaux outils d’imagerie ultrarapide permettant une meilleure évaluation de la dynamique du myocarde. Dans une première étude (Chapitre 7), nous proposons une nouvelle approche d’échocardiographie ultrarapide et de haute résolution, par ondes divergentes, couplée à de l'imagerie Doppler tissulaire. Cette combinaison, validée in vitro et in vivo, permet d’optimiser le contraste des images mode B ainsi que l’estimation des vitesses Doppler tissulaires. Dans la continuité de cette première étude, nous proposons une nouvelle méthode d’imagerie des vecteurs de vitesses tissulaires (Chapitre 8). Cette approche, validée in vitro et in vivo, associe les informations de vitesses Doppler tissulaires et le mode B ultrarapide de l’étude précédente pour estimer l’ensemble du champ des vitesses 2D à l’intérieur du myocarde. / Elastography is an imaging technique that aims to map the in vivo mechanical properties of biological tissues in order to provide additional diagnostic information. Since its introduction in ultrasound imaging in the 1990s, elastography has found many applications. This method has been used for the study of the breast, liver, prostate and arteries by ultrasound imaging, magnetic resonance imaging (MRI) or optical coherence tomography (OCT). In the context of cardiovascular diseases (CVD), this modality has a high diagnostic potential as atherosclerosis, a common pathology causing cardiovascular diseases, changes the structure of biological tissues and their mechanical properties well before any symptoms appear. Whatever the imaging modality, elastography is based on: the mechanical excitation of the tissue (static or dynamic), the measurement of induced displacements and strains, and the inverse problem allowing the quantification of the mechanical properties of underlying tissues. This thesis presents a series of works in elastography for the evaluation of cardiovascular tissues. It is divided into two parts. The first part, entitled « Vascular elastography » focuses on diseases affecting peripheral arteries. The second, entitled « Cardiac elastography » targets heart muscle pathologies. In the vascular context, atherosclerosis changes the physiology of the arterial wall and thereby its biomechanical properties. The main objective of the first part of this thesis is to develop a tool that enables the segmentation and the mechanical characterization of tissues (necrotic core, fibrous tissues and calcium inclusions) in the vascular wall of the peripheral arteries, to predict the vulnerability of plaques. In a first study (Chapter 5), we propose a new strain estimator, associated with ultrafast plane wave imaging. This new imaging technique can increase the performance of the noninvasive elastography. Building on this first study, we propose a new inverse problem method dedicated to the identification and quantification of the mechanical properties of the vascular wall tissues (Chapter 6). These two methods are validated in silico and in vitro on polymer phantom mimicking arteries. In the cardiac context, myocardial infarctions and ischemia caused by atherosclerosis alter myocardial contractility. In conventional echocardiography, the myocardial function is generally evaluated by analyzing the dynamics of ventricular motions (myocardial velocities and deformations). The abscence of physiological stress acting on the myocardium (as opposed to the blood pressure which acts the vascular wall) do not allow the solving the inverse problem and to find the mechanical properties of the fabric. Elastography thus here refers to the assessment of motion dynamics and deformations and not to the evaluation of mechanical properties of the tissue. The main objective of the second part of this thesis is to develop new ultrafast imaging tools for a better evaluation of the myocardial dynamics. In a first study (Chapter 7), we propose a new approach for ultrafast and high-resolution echocardiography using diverging waves and tissue Doppler. This combination, validated in vitro and in vivo, optimize the contrast in B-mode images and the estimation of myocardial velocities with tissue Doppler. Building on this study, we propose a new velocity vector imaging method (Chapter 8). This approach combines tissue Doppler and ultrafast B-mode of the previous study to estimate 2D velocity fields within the myocardium. This original method was validated in vitro and in vivo on six healthy volunteers.

The purpose of this research was to study the synthesis and remodeling of extracellular matrix (ECM) by fibroblasts with special emphasis on the culture environment (media composition and initial ECM composition) and the resulting mechanical integrity of the ECM. This was investigated by culturing fibroblasts for 3 weeks in a variety of culture conditions consisting of collagen gels, fibrin gels, or media permissive to the self-production of ECM (Cell-Derived Matrix), and quantifying the mechanics of the resulting ECM. The mechanical characteristics were related to the biochemistry of the resulting ECM, notably in terms of collagen accumulation and collagen fibril diameters. The ultimate tensile strength (UTS) of the collagen gels and fibrin gels at the end of the 3-week period was 168.5 ± 43.1 kPa and 133.2 ± 10.6 kPa, respectively. The ultimate tensile strength of the cell-derived matrices was 223.2 ± 9 kPa, and up to 697.1 ± 36.1 kPa when cultured in a chemically-defined medium that was developed for the rapid growth of matrix in a more defined environment. Normalizing the strength to collagen density resulted in a UTS / Collagen Density in these groups of 6.4 ± 1.9 kPa/mg/cm3, 25.9 ± 2.4 kPa/mg/cm3, 14.5 ± 1.1 kPa/mg/cm3, and 40.0 ± 1.9 kPa/mg/cm3, respectively. Cells were synthetically more active when they produced their own matrix than when they were placed within gels. The resulting matrix was also significantly stronger when it was self-produced than when the cells rearranged the matrix within gels that corresponded to a significantly larger fraction of non-acid and pepsin extractable collagen. These studies indicate that cell-derived matrices have potential both as in vitro wound healing models and as soft connective tissue substitutes.