L’imagerie par contraste de phase suscite un intérêt croissant dans le domaine biomédical, puisqu’il offre un contraste amélioré par rapport à l’imagerie d’atténuation conventionnelle. En effet, le décalage en phase induit par les tissus mous, dans la gamme d’énergie utilisée en imagerie, est environ mille fois plus important que leur atténuation. Le contraste de phase peut être obtenu, entre autres, en laissant un faisceau de rayons X cohérent se propager librement après avoir traversé un échantillon. Dans ce cas, les signaux obtenus peuvent être modélisés par la diffraction de Fresnel. Le défi de l’imagerie de phase quantitative est de retrouver l’atténuation et l’information de phase de l’objet observé, à partir des motifs diffractés enregistrés à une ou plusieurs distances. Ces deux quantités d’atténuation et de phase, sont entremêlées de manière non-linéaire dans le signal acquis. Dans ces travaux, nous considérons les développements et les applications de la micro- et nanotomographie de phase. D’abord, nous nous sommes intéressés à la reconstruction quantitative de biomatériaux à partir d’une acquisition multi-distance. L’estimation de la phase a été effectuée via une approche mixte, basée sur la linéarisation du modèle de contraste. Elle a été suivie d’une étape de reconstruction tomographique. Nous avons automatisé le processus de reconstruction de phase, permettant ainsi l’analyse d’un grand nombre d’échantillons. Cette méthode a été utilisée pour étudier l’influence de différentes cellules osseuses sur la croissance de l’os. Ensuite, des échantillons d’os humains ont été observés en nanotomographie de phase. Nous avons montré le potentiel d’une telle technique sur l’observation et l’analyse du réseau lacuno-canaliculaire de l’os. Nous avons appliqué des outils existants pour caractériser de manière plus approfondie la minéralisation et les l’orientation des fibres de collagènes de certains échantillons. L’estimation de phase, est, néanmoins, un problème inverse mal posé. Il n’existe pas de méthode de reconstruction générale. Les méthodes existantes sont soit sensibles au bruit basse fréquence, soit exigent des conditions strictes sur l’objet observé. Ainsi, nous considérons le problème inverse joint, qui combine l’estimation de phase et la reconstruction tomographique en une seule étape. Nous avons proposé des algorithmes itératifs innovants qui couplent ces deux étapes dans une seule boucle régularisée. Nous avons considéré un modèle de contraste linéarisé, couplé à un algorithme algébrique de reconstruction tomographique. Ces algorithmes sont testés sur des données simulées. / Phase contrast imaging has been of growing interest in the biomedical field, since it provides an enhanced contrast compared to attenuation-based imaging. Actually, the phase shift of the incoming X-ray beam induced by an object can be up to three orders of magnitude higher than its attenuation, particularly for soft tissues in the imaging energy range. Phase contrast can be, among others existing techniques, achieved by letting a coherent X-ray beam freely propagate after the sample. In this case, the obtained and recorded signals can be modeled as Fresnel diffraction patterns. The challenge of quantitative phase imaging is to retrieve, from these diffraction patterns, both the attenuation and the phase information of the imaged object, quantities that are non-linearly entangled in the recorded signal. In this work we consider developments and applications of X-ray phase micro and nano-CT. First, we investigated the reconstruction of seeded bone scaffolds using sed multiple distance phase acquisitions. Phase retrieval is here performed using the mixed approach, based on a linearization of the contrast model, and followed by filtered-back projection. We implemented an automatic version of the phase reconstruction process, to allow for the reconstruction of large sets of samples. The method was applied to bone scaffold data in order to study the influence of different bone cells cultures on bone formation. Then, human bone samples were imaged using phase nano-CT, and the potential of phase nano-imaging to analyze the morphology of the lacuno-canalicular network is shown. We applied existing tools to further characterize the mineralization and the collagen orientation of these samples. Phase retrieval, however, is an ill-posed inverse problem. A general reconstruction method does not exist. Existing methods are either sensitive to low frequency noise, or put stringent requirements on the imaged object. Therefore, we considered the joint inverse problem of combining both phase retrieval and tomographic reconstruction. We proposed an innovative algorithm for this problem, which combines phase retrieval and tomographic reconstruction into a single iterative regularized loop, where a linear phase contrast model is coupled with an algebraic tomographic reconstruction algorithm. This algorithm is applied to numerical simulated data.

<div>The mechanical behaviors of different kinds of biological tissues, including muscle tissues, cortical bones, cancellous bones and skulls, were studied under various loading conditions to investigate their strain-rate sensitivities and loading-direction dependencies. Specifically, the compressive mechanical behaviors of porcine muscle were studied at quasi-static (<1/s) and intermediate (1/s─10^2/s) strain rates. Both the compressive and tensile mechanical behaviors of human muscle were investigated at quasi-static and intermediate strain rates. The effect of strain-rate and loading-direction on the compressive mechanical behaviors of human frontal skulls, with its entire sandwich structure intact, were also studied at quasi-static, intermediate and high (10^2/s─10^3/s) strain rates. The fracture behaviors of porcine cortical bone and cancellous bone were investigated at both quasi-static (0.01mm/s) and dynamic (~6.1 m/s) loading rates, with the entire failure process visualized, in real-time, using the phase contrast imaging technique. Research effort was also focused on studying the dynamic fracture behaviors, in terms of fracture initiation toughness and crack-growth resistance curve (R-curve), of porcine cortical bone in three loading directions: in-plane transverse, out-of-plane transverse and in-plane longitudinal. A hydraulic material testing system (MTS) was used to load all the biological tissues at quasi-static and intermediate loading rates. Experiments at high loading rates were performed on regular or modified Kolsky bars. Tomography of bone specimens was also performed to help understand their microstructures and obtain the basic material properties before mechanical characterizations. Experimental results found that both porcine muscle and human muscle exhibited non-linear and strain-rate dependent mechanical behaviors in the range from quasi-static (10^(-2)/s─1/s) to intermediate (1/s─10^2/s) loading rates. The porcine muscle showed no significant difference in the stress-strain curve between the along-fiber and transverse-to-fiber orientation, while it was found the human muscle was stiffer and stronger along fiber direction in tension than transverse-to fiber direction in compression. The human frontal skulls exhibited a highly loading-direction dependent mechanical behavior: higher ultimate strength, with an increasing ratio of 2, and higher elastic modulus, with an increasing ratio of 3, were found in tangential loading direction when compared with those in the radial direction. A transition from quasi-ductile to brittle compressive mechanical behaviors of human frontal skulls was also observed as loading rate increased from quasi-static to dynamic, as the elastic modulus was increased by factors of 4 and 2.5 in the radial and tangential loading directions, respectively. Experimental results also suggested that the strength in the radial direction was mainly depended on the diploë porosity while the diploë layer ratio played the predominant role in the tangential direction. For the fracture behaviors of bones, straight-through crack paths were observed in both the in-plane longitudinal cortical bone specimens and cancellous bone specimens, while the cracks were highly tortuous in the in-plane transverse cortical bone specimens. Although the extent of toughening mechanisms at dynamic loading rate was comparatively diminished, crack deflections and twists at osteon cement lines were still observed in the transversely oriented cortical bone specimens at not only quasi-static loading rate but also dynamic loading rate. The locations of fracture initiations were found statistical independent on the bone type, while the propagation direction of incipient crack was significantly dependent on the loading direction in cortical bone and largely varied among different types of bones (cortical bone and cancellous bone). In addition, the crack propagation velocities were dependent on crack extension over the entire crack path for all the three loading directions while the initial velocity for in-plane direction was lower than the other two directions. Both the cortical bone and cancellous bone exhibited higher fracture initiation toughness and steeper R-curves at the quasi-static loading rate than the dynamic loading rate. For cortical bone at a dynamic loading rate (5.4 m/s), the R-curves were steepest, and the crack surfaces were most tortuous in the in-plane transverse direction while highly smooth crack paths and slowly growing R-curves were found in the in-plane longitudinal direction, suggesting an overall transition from brittle to ductile-like fracture behaviors as the osteon orientation varies from in-plane longitudinal to out-of-plane transverse, and to in-plane transverse eventually.</div>