Sebastien Benzekry

Broschiertes Buch

Mathematical modeling and analysis of therapies for metastatic cancers

A short walk between anti-cancerous systemic therapies and mathematical analysis of structured population dynamics

Beschreibung

We introduce a mathematical model for the evolution of a cancer disease at the organism scale, taking into account for the metastases and their sizes as well as action of several therapies such as primary tumor surgery, chemotherapy and anti-angiogenic therapy. The mathematical problem is a renewal equation with bi-dimensional structuring variable. Mathematical analysis and functional analysis of an underlying Sobolev space are performed. Existence, uniqueness, regularity and asymptotic behavior of the solutions are proven in the autonomous case. A lagrangian numerical scheme is introduced and analyzed. Convergence of this scheme proves existence in the non-autonomous case. The effect of concentration of the boundary data into a Dirac mass is also investigated. Possible applications of the model are numerically illustrated for clinical issues such as the failure of anti-angiogenic monotherapies, scheduling of combined cytotoxic and anti-angiogenic therapies and metronomic chemotherapies. In order to give mathematical answers to these clinical problems an optimal control problem is formulated, analyzed and simulated.

Autor

Sebastien Benzekry is a mathematically trained scientist performing research in the fields of cancer biology and clinical oncology. He graduated from ENS of Paris in 2007, is a laureate of the mathematics agregation, obtained his PhD in Marseille, Fr in 2011, was a postdoctoral fellow in Boston, MA in 2012 and is now a junior researcher at inria.

Produktdetails

• Verlag: LAP Lambert Academic Publishing
• Seitenzahl: 280
• Erscheinungstermin: 5. Oktober 2013
• Englisch
• Abmessung: 220mm x 150mm x 17mm
• Gewicht: 435g
• ISBN-13: 9783659150357
• ISBN-10: 3659150355
• Artikelnr.: 39710273