Article

Bulletin of Mathematical Biology

, Volume 65, Issue 5, pp 903-931

First online:

Regression and regrowth of tumour cords following single-dose anticancer treatment

  • Alessandro BertuzziAffiliated withIstituto di Analisi dei Sistemi ed Informatica del CNR “A. Ruberti” Email author 
  • , Alberto D’OnofrioAffiliated withDivision of Epidemiology and Biostatistics, European Institute of Oncology
  • , Antonio FasanoAffiliated withDipartimento di Matematica “U. Dini”, Università di Firenze
  • , Alberto GandolfiAffiliated withIstituto di Analisi dei Sistemi ed Informatica del CNR “A. Ruberti”

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Abstract

In this paper, the evolution of a tumour cord after treatment is investigated by extensive numerical simulations on the basis of a mathematical model developed by Bertuzzi et al. (submitted). The model is formulated in cylindrical symmetry adopting the continuum approach, and takes into account the influence of oxygen level on the proliferation and death rate of cells, the volume reduction due to disgregation of dead cells, and the cell killing effects of radiation and drugs. Some extensions of the model are proposed to represent more accurately the radioresistance of hypoxic cells and the cytotoxic action of anticancer drugs. The steady state of the cord, and the cord evolution from the steady state after the delivery of a single dose of an anticancer agent, are computed for various combinations of model parameters and for different choices of the functions describing the effects of treatments. The results of the numerical computations show that, in spite of its many simplifications, the model behaviour appears to be reasonable in view of the available experimental observations. The model allows having a better insight into some complex treatment-related events, such as cell reoxygenation and repopulation.