A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy.
A mathematical model is developed that describes the reduction in volume of a vascular tumor in response to specific chemotherapeutic administration strategies. The model consists of a system of partial differential equations governing intratumoral drug concentration and cancer cell density. In the model the tumor is treated as a continuum of two types of cells which differ in their proliferation rates and their responses to the chemotherapeutic agent. The balance between cell proliferation and death within the tumor generates a velocity field which drives expansion or regression of the spheroid. Insight into the tumor's response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations.
Jackson
T L
TL
Department of Mathematics, Duke University, P.O. Box 90320, Durham, NC 27708-0320, USA. tjackson@math.duke.edu
Byrne
H M
HM
D000818:Animals; D000970:Antineoplastic Agents / Q000008:administration & dosage / Q000627:therapeutic use*; D016923:Cell Death / Q000187:drug effects; D002455:Cell Division / Q000187:drug effects; D003198:Computer Simulation; D019008:Drug Resistance, Neoplasm; D006801:Humans; D051379:Mice; D008819:Mice, Nude; D008954:Models, Biological; D019043:Vascular Neoplasms / Q000098:blood supply / Q000188:drug therapy*
D000970:Antineoplastic Agents