WorkshopsModels of tumor growth and therapy
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The growth of solid tumors can be described at a number of different scales from cell to the organ scale. For a large number of cells, the 'fluid mechanical' approach has been advocated recently by many authors in mathematics or biophysics. Several levels of mathematical descriptions are commonly used, inluding only elastic effects, or nutrients, or active movement and the solutions exhibit different qualitative behaviours. Another, more macroscopic, description is based on a free boundary problem close to the Hele-Shaw equation. Asymptotic analysis is a tool to derive these Hele-Shaw free boundary problems from cell density systems in the stiff pressure limit. This modeling also opens other questions as circumstances in which instabilities develop. This work is a collaboration with F. Quiros and J.-L. Vazquez (Universidad Autonoma Madrid), M. Tang (SJTU) and N. Vauchelet (LJLL).
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Benoît Perthame
2013-10-23
09:10:00 - 10:00:00
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The growth of solid tumors can be described at a number of different scales from cell to the organ scale. For a large number of cells, the 'fluid mechanical' approach has been advocated recently by many authors in mathematics or biophysics. Several levels of mathematical descriptions are commonly used, inluding only elastic effects, or nutrients, or active movement and the solutions exhibit different qualitative behaviours. Another, more macroscopic, description is based on a free boundary problem close to the Hele-Shaw equation. Asymptotic analysis is a tool to derive these Hele-Shaw free boundary problems from cell density systems in the stiff pressure limit. This modeling also opens other questions as circumstances in which instabilities develop. This work is a collaboration with F. Quiros and J.-L. Vazquez (Universidad Autonoma Madrid), M. Tang (SJTU) and N. Vauchelet (LJLL).
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