Mathematical and numerical analysis for a model of growing metastatic tumors

Dominique Barbolosi (1) , Assia Benabdallah (2) , Florence Hubert (2) , Federico Verga (2)

1 Laboratoire de Toxicocinétique et Pharmacocinétique
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In cancer diseases, the appearance of metastases is a very pejorative forecast. Chemotherapies are systemic treatments which aims at the elimination of the micrometastases produced by a primitive tumour. The efficency of chemotherapies closely depends on the protocols of administration. Mathematical modeling is an invaluable tool to help in evaluating the best treatment strategy. Iwata and al proposed in 2000 a partial differential equation (PDE) that describes the metastatic evolution of an untreated tumour. We conducted in this article, a thorough mahematical analysis of this model. Particularly, we provide an explicit formula for the growth rate parameter, as well as a numerical resolution of this PDE. By increasing our understanding of the existing mode, this work is crucial for further extension and refinement of the model. It settle down the framework necessary for the consideration of drugs administration effects on tumour developpment.

Mots clés: Von Foerster equation; semigroup approach; asymptotic behaviour; characteristic scheme; metastatic tumors

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Cancer

Dominique Barbolosi, Assia Benabdallah, Florence Hubert, Federico Verga. Mathematical and numerical analysis for a model of growing metastatic tumors. Mathematical Biosciences, 2009, 218 (1), pp.1--14. ⟨10.1016/j.mbs.2008.11.008⟩. ⟨hal-00262335v3⟩