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Section: Application Domains

Estimation for complex and biological systems

Our main application for this line of investigation is the photodynamic therapy developed by T. Bastogne. We shall also focus on bacteriophage therapies and subdiffusion within molecules.

(i) Photodynamic therapy. One of the main application we have in mind for our identification problems is to model photodynamic therapy. This promising cancer treatment involves selective uptake and retention of a photosensitive drug in a tumor, followed by irradiation with light at an appropriate wavelength. Photosensitizers are photoactive compounds such as for instance porphyrins and chlorins. The activated photosensitizer is thought to produce singlet oxygen at high doses and thereby to initiate apoptotic and necrotic death of tumor. Due to the lack of response reproducibility, the complexity of interactions between physical, chemical and biological aspects and the high cost of experiments, there is a real demand in good mathematical and physical models which might help to better control and understand PDT responses. We are particularly concerned with modeling the drug uptake into cancer cells, the photoreactions induced by light exposition and tumor growth kinetics.

(ii) Bacteriophage systems. A collaboration between our team, the Mathematics and the Genetics and Microbiology Departments at the Universitat Autònoma de Barcelona (UAB) is being set up, focusing on probabilistic aspects of bacteriophage therapies for animal diseases like hemorrhagic septicemia in cattle or atrophic rhinitis in swine. This kind of therapy consists in inoculating a (benign) virus to animals in order to kill the bacteria known to be responsible of the disease. It was in use in the Soviet Union until the 80s, and is now re-emerging, still at an experimental level, due to the progressive slowdown in antibiotic efficiency.

Within this context, our analysis of a noisy predator-prey competition modeling the treatment helps to calibrate and to understand better the behavior of the system in terms of fluctuations around an equilibrium. Note that our preliminary contacts with the Genetics and Microbiology Departments at UAB also open the way to a particle model in order to represent the couple bacteria/virus living on a surface.