title: Mathematical and numerical analysis for a model of growing metastatic tumors.
abstract: In cancer diseases, the appearance of metastases is a very pejorative forecast. Chemotherapies are systemic treatments which aim at the elimination of the micrometastases produced by a primitive tumour. The efficiency of chemotherapies closely depends on the protocols of administration. Mathematical modeling is an invaluable tool to help in evaluating the best treatment strategy. Iwata et al. [K. Iwata, K. Kawasaki, N. Shigesad, A dynamical model for the growth and size distribution of multiple metastatic tumors, J. Theor. Biol. 203 (2000) 177.] proposed a partial differential equation (PDE) that describes the metastatic evolution of an untreated tumour. In this article, we conducted a thorough mathematical 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 model, this work is crucial for further extension and refinement of the model. It settles down the framework necessary for the consideration of drugs administration effects on tumour development.
authors.affiliation: Université de la Méditerranée - UPRES EA 3286 - IFR 125, Physiopathologie Humaine de Marseille, 27, Boulevard Jean Moulin, 13385 Marseille Cedex 5, France. dominique.barbolosi@univ-cezanne.fr
authors.forename: Dominique
authors.initials: D
authors.lastname: Barbolosi
authors.forename: Assia
authors.initials: A
authors.lastname: Benabdallah
authors.forename: Florence
authors.initials: F
authors.lastname: Hubert
authors.forename: Federico
authors.initials: F
authors.lastname: Verga
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use*; D048708:Cell Growth Processes / Q000502:physiology; D006801:Humans; D008954:Models, Biological; D009362:Neoplasm Metastasis; D009369:Neoplasms / Q000188:drug therapy / Q000473:pathology*
chemical_list: D000970:Antineoplastic Agents