This thesis consists of a synthetized presentation of my research in order to get the French diploma“Habilitation à diriger des recherches”.It is organized into four chapters that constitute the four main topics I focused on since I got mypermanent position at Inria, in September 2008. These research axes have been developed within theframework of the Inria team MC2, leaded by T. Colin. This thesis is the result of collaborations withcolleagues of Bordeaux and elsewhere (Karlsruhe, Lyon, Rennes, Villejuif) as well as with Phd students andpostdoctoral fellows I co-supervised. Therefore I choose to use we to present the results.Chapter 1 is devoted to cell electropermeabilization modeling. Electropermeabilization (also calledelectroporation) is a significant increase in the electrical conductivity and permeability of cell membranethat occurs when pulses of large amplitude (a few hundred volts per centimeter) are applied to the cells:due to the electric field, the cell membrane is permeabilized, and then nonpermeant molecules can easilyenter the cell cytoplasm by transport (active and passive) through the electropermeabilized membranes. Ifthe pulses are too long, too numerous or if their amplitude is too high, the cell membrane is irreversiblydestroyed and the cells are killed. However, if the pulse duration is sufficiently short (a few milliseconds ora few microseconds, depending on the pulse amplitude), the cell membrane reseals within several tens ofminutes: such a reversible electroporation preserves the cell viability and is used in electrochemotherapy tovectorize the drugs into cancer cells. In Chapter 1, I present the modeling we derived in tight collaborationwith biologists, namely the L.M. Mir’s group at the IGR, which is one of the world’s leader in this field, aswell as the numerical schemes and the comparisons of the numerical simulations with the experimental data.Interestingly, our modeling that uncouples electric and permeable behaviours of the cell membrane makes itpossible to explain the strange observation of cell desensitization, that has been reported very recently by A.Silve et al. [100]. This desensitization consists of a less degree of cell permeabilization after a few successiveelectric pulses than for the same number of pulses but with a delay between each electric pulse delivery. Thisphenomenon is counter-intuitive and was not predictable by the previous models of the literature.Chapter II is devoted to cell migration modeling and more precisely to the endothelial cell migration onmicropatterned polymers. The goal is to provide models based on the experimental data in order to describethe cell migration on micropatterned polymers. The long–term goal is to provide tools for the optimizationof such a migration, which is crucial in tissue engineering. We develop a continuous model of Patlak-KellerSegeltype, which makes it possible to provide qualitative results in accordance with the experiments, andwe analyse the mathematical properties of this model. Then, we provide an agent-based model, based ona classical mechanics approach. Strikingly, this very simple model has been quantitatively fitted with theexperimental data provided by our colleagues of the biological institute IECB, in terms of cell orientationand cell migration. I conclude the chapter by on-going works on the invadopodia modeling, in collaborationwith T. Suzuki from Osaka University and M. Ohta from Tokyo University of Sciences. Chapter III is devoted to a very recent activity I started in 2013 on tumor growth models, thereforethis chapter is based on only one submitted preprint. I present the results on ductal carcinoma growthmodeling. Originally confined to the milk duct, these breast cancers may become invasive and agressive afterthe degradation of the duct membrane, and the main features of our model is to describe the membranedegradation thanks to a non-linear Kedem–Katchalsky condition that describes the jump of pressure acrossthe duct membrane. More precisely, the membrane permeability is given as a non-linear function of specificenzymes (MMPs) that degrade the membrane. We also provide some possible explanation of heterogeneityof tumor growth by modeling the influence of the micro-environment and the emergence of specific cell types.I eventually conclude by Chapter IV, which consists of a few advances in asymptotics analysis for domainsthat are singular or asymptotically singular, in the following of my PhD thesis. The results can be split intotwo parts: first I present approximate transmission conditions through a periodically rough thin layer, andhow we characterize the influence of such a layer on the polarization tensor in the sense of Capdeboscq andVoeglius [19]. Then I focus on the numerical treatment of the eddy current problem in domains with cornersingularity.Each chapter is organized into a description of the results, a few perspectives for forthcoming researchand a list of the published papers related to the topic of the chapter. Before presenting the results weobtained, I give in the next part a brief summary in French< Réduire