Séminaire OrléansIdentification de paramètres pour la modélisation de la croissance de tumeurs.
Thierry Colin (Bordeaux)
Thursday 24 February 2011 14:00 - Orléans - Salle de Séminaire
Mathematical modelling of tumor growth can be a useful tool to improve the under- standing of cancer treatment in terms, for example, of prognosis, drug effect modelling and clinical protocols definition. In this work we consider first stages of tumour development that correspond to avascular growth. We consider continuous-type models based on mixture theory. They rely on a sys- tem of non-linear coupled parametric partial differential equations, in which a set of parameters accounts for the complexity of the different tissues attacked by the tumour as well as for the differences between the same tissues of different individuals. The tumour growth is investigated at a macroscopic scale and therefore all the microscopic and mesoscopic scale phenomena that we do not model directly are lumped in such parameters. In order to apply such models in practical situations these parameters need to be identified, i.e., a realistic value has to be estimated. One way to determine their values is by means of inverse problems, exploiting data coming from medical imagery The main difficulty is that the amount of data for system identification is scarce. Although medical scans allow a quite accurate localization of the tumor in space, little information can be inferred about its cellular nature or nutrient distribution. In addition, only two scans are usually available before treatment making estimation of time evolution a challenging problem. The aim of this presentation is to explain an efficient identification procedure that allows the parameter estimation of a two-dimensional tumor growth model, with the final objective of obtaining a prognostic model. In particular the results of several classes of inverse problems are discussed: we progressively increase the model complexity while decreasing the amount of available data, in order to approach realistic applications.