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Soft matter, here, liquids and polymers, have adaptability to a surrounding geometry. They intrinsically have advantageous characteristics from a mechanical perspective, such as flowing and wetting on surrounding surfaces, giving compliant, conformal and deformable behavior. From the behavior of soft matter for heterogeneous surfaces, compliant structures can be engineered as embedded liquid microstructures or patterned liquid microsystems for emerging compliant microsystems. Recently, skin electronics and soft robotics have been initiated as potential applications that can provide soft interfaces and interactions for a human-machine interface. To meet the design parameters, developing soft material engineering aimed at tuning material properties and smart processing techniques proper to them are to be highly encouraged. As promising candidates, Ga-based liquid alloys and silicone-based elastomers have been widely applied to proof-of-concept compliant structures. In this thesis, the liquid alloy was employed as a soft and stretchable electrical and thermal conductor (resistor), interconnect and filler in an elastomer structure. Printing-based liquid alloy patterning techniques have been developed with a batch-type, parallel processing scheme. As a simple solution, tape transfer masking was combined with a liquid alloy spraying technique, which provides robust processability. Silicone elastomers could be tunable for multi-functional building blocks by liquid or liquid-like soft solid inclusions. The liquid alloy and a polymer additive were introduced to the silicone elastomer by a simple mixing process. Heterogeneous material microstructures in elastomer networks successfully changed mechanical, thermal and surface properties. To realize a compliant microsystem, these ideas have in practice been useful in designing and fabricating soft and stretchable systems. Many different designs of the microsystems have been fabricated with the developed techniques and materials, and successfully evaluated under dynamic conditions. The compliant microsystems work as basic components to build up a whole system with soft materials and a processing technology for our emerging society.

La Tomographie à Emission de Positrons (TEP) permet d'obtenir une mesure dynamique et résolue en espace de la concentration d'un traceur radioactif injecté au patient. La quantification du débit sanguin cérébral par TEP repose sur l'utilisation d'un modèle cinétique le reliant à la variation spatio-temporelle de la concentration du traceur dans le cerveau. Différents modèles cinétiques sont proposés dans la littérature. Cependant, la majorité d'entre eux repose sur une modélisation compartimentale de l'organe observé. Dans ce cas, l'organe est subdivisé en un compartiment capillaire échangeant avec un compartiment tissulaire par une cinétique le plus souvent du premier ordre. Les résultats obtenus avec ce type de modèle sous-estiment le débit et ne permettent pas de prédire les premiers instants de la dynamique de répartition du traceur. Ces faiblesses ont été confirmées suite à l'amélioration de la résolution temporelle des tomographes, conduisant à l'élaboration de modèles incorporant plus de réalité physiologique. Cependant, tous ces modèles sont développés pour modéliser les échanges entre la micro-circulation et le tissu environnant à l'échelle d'un capillaire (échelle microscopique). Or la résolution spatiale des tomographes utilisés en clinique ne permet pas de distinguer la micro-circulation et le tissu. L'utilisation de ces modèles cinétiques avec des mesures de concentrations macroscopiques dépasse donc leur cadre théorique de validité et peut introduire des résultats faussés. Dans ce contexte, nous proposons un modèle cinétique basé sur le changement d'échelle (utilisant la méthode de prise de moyenne volumique). Ce changement d'échelle permet de remplacer l'ensemble micro-circulation/tissu par un volume fictif, homogène, dont les propriétés macroscopiques sont calculées à partir des propriétés microscopiques d'un Volume Elémentaire Représentatif (VER) du milieu. Dans un premier temps, afin de pouvoir comparer les résultats de ce modèle avec ceux du modèle compartimental standard, le VER considéré est constitué d'un capillaire unique et de son enveloppe de tissu, puis une complexité géométrique supplémentaire est introduite en considérant un réseau de capillaire isotrope à l'échelle de Darcy. Ces modèles sont utilisés pour identifier le débit à l'aide d'une méthode inverse. Pour cela, l'évolution temporelle du champ de concentration dans notre géométrie de référence, qui ne peut être mesurée par TEP en raison de sa faible résolution spatiale, est déterminée par des simulations numériques ainsi que par des mesures in vitro à l'aide d'un modèle expérimental, également développé au cours de ce travail, permettant de reproduire l'écoulement dans un canal traversant une matrice diffusante (gel d'alginate). / Positron Emission Tomography (PET) provides a dynamic and space-resolved measurement of the concentration field of a radioactive tracer previously injected to the patient. Quantification of cerebral blood flow by PET is based on the use of a kinetic model linking cerebral blood flow to the spatial and temporal variations of tracer concentration in the brain. Various kinetic models have been proposed in the literature. However, most of the mare based on a compartmental approach of the observed organ In this case, the organ is divided in two compartments, the capillary and the tissue, and the exchanges between these two compartments are often described by a first order kinetic model. Results obtained with this kind of model under estimate the flow rate and are notable to predict the first instants of the tracer dynamics distribution. With the continuous improvement of the temporal resolution of PET, these weaknesses have been confirmed, which led to the development of models incorporating more physiological reality. However, all these models have been developed to describe exchanges between micro-circulation and surrounding tissue at the scale of capillary vessels (microscopic scale). Because the spatial resolution of PET inclinical practice is insufficient to allow the distinction between micro-circulation and tissue, using of these models with kinetic measurement of macroscopic concentrations exceeds their theoretical validity and can introduce false results. In this context, we propose a kinetic model based on up-scaling (using the method of volume averaging). This up-scaling technique allows to replace the two previous compartments (tissue and micro-circulation) by an homogeneous fictive volume, whose macroscopic properties are calculated from the microscopic properties of are presentative elementary volume (REV) of the medium. First, in order to compare the results of this model with those of the standard compartmental model, the considered REV consists of a single capillary and its surrounding tissue. Second, additional geometric complexity is introduced by considering an isotropic capillary network at the Darcy scale. These models are used to identify the flow rate using an inverse method. For that purpose, the temporal evolution of concentration field in a geometry of reference, which can't be measured by PET due to its low spatial resolution, is determined by numerical simulations and by in vitro measurements. These measurements are performed using an experimental model developed during this work to reproduce the flow in a channel passing through a diffusive matrix (alginate gel).