A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy

Math Biosci. 2000 Mar;164(1):17-38. doi: 10.1016/s0025-5564(99)00062-0.


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.

MeSH terms

  • Animals
  • Antineoplastic Agents / administration & dosage
  • Antineoplastic Agents / therapeutic use*
  • Cell Death / drug effects
  • Cell Division / drug effects
  • Computer Simulation
  • Drug Resistance, Neoplasm*
  • Humans
  • Mice
  • Mice, Nude
  • Models, Biological*
  • Vascular Neoplasms / blood supply
  • Vascular Neoplasms / drug therapy*


  • Antineoplastic Agents