Tumour angiogenesis model with variable vessels' effectiveness

Volume 38 / 2011

Jan Poleszczuk, Iwona Skrzypczak Applicationes Mathematicae 38 (2011), 33-49 MSC: Primary 92C50; Secondary 34A12. DOI: 10.4064/am38-1-3

Abstract

We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties of the proposed model and present some numerical simulations.

Authors

  • Jan PoleszczukInstitute Applied Mathematics and Mechanics
    Faculty of Mathematics, Informatics and Mechanics
    University of Warsaw
    02-097 Warszawa, Poland
    e-mail
  • Iwona SkrzypczakCollege of Inter-faculty Individual Studies
    in Mathematics and Natural Sciences
    University of Warsaw
    02-089 Warszawa, Poland
    e-mail

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