This research project aims at the development, analysis and computer implementation of mathematical models of the cardiovascular system. Our goal is to describe and simulate the anatomic structure and the physiological response of the human cardiovascular system in healthy or diseased states. This demands to address many fundamental issues. Blood flow interacts both mechanically and chemically with the vessel walls and tissue, giving rise to complex fluid-structure interaction problems. The mathematical analysis of these problems is complicated and the related numerical analysis difficult. We propose to extend the recently achieved results on blood flow simulations by directing our analysis in several new directions. Our goal is to encompass aspects of metabolic regulation, micro-circulation, the electrical and mechanical activity of the heart, and their interactions. Modelling and optimisation of drugs delivery in clinical diseases will be addressed as well. This requires the understanding of transport, diffusion and reaction processes within the blood and organs of the body. The emphasis of this project will be put on mathematical modelling, numerical analysis, algorithm implementation, computational efficiency, validation and verification. Our purpose is to set up a mathematical simulation platform eventually leading to the improvement of vascular diseases diagnosis, setting up of surgical planning, and cure of inflammatory processes in the circulatory system. This platform might also help physicians to construct and evaluate combined anatomic/physiological models to predict the outcome of alternative treatment plans for individual patients.
- sciences médicales et de la santémédecine cliniqueangiologiemaladies vasculaires
- sciences naturellesmathématiquesmathématiques puresanalyse mathématique
- sciences naturellessciences physiquesmécanique classiquemécanique des fluides
- sciences naturellesmathématiquesmathématiques appliquéesanalyse numérique
- sciences naturellesmathématiquesmathématiques appliquéesmodèle mathématique
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