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Mathematical Medicine and Biology 1999 16(1):39-91; doi:10.1093/imammb/16.1.39
© 1999 by Institute of Mathematics and its Applications
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Modelling and simulation of chemotherapy of haematological and gynaecological cancers

FRANK K. NANI and M. NAMIK OGUZTÖRELI{dagger}

Department of Mathematics, University of Alberta Edmonton, Alberta, T6G 2G1, Canada

{dagger}Author to whom reprint requests should be addressed

In this paper elaborate mathematical models and investigative computer simulations for the chemotherapy of haematological and gynaecological cancers are presented. The pharmacodynamics of the actions of the antineoplastic drugs are described by multicompartmental models with the associated model equations taking into account the drug dosage, type of delivery, route of delivery, the intercompartmental drug-transition constants, degradation parameters, and leakage coefficients. The cell-cycle phase-specific six-compartmental cytokinetic tumour growth model presented here incorporates the cellcycle phase residence time, time lags associated with drug-induced cell-kill, or progression delays due to repair of cell damage. Investigative computer simulations are performed depicting the effects of cell-cycle phase-specific antineoplastic drugs on haematological and gynaecological cancer cells. The computer simulations are performed under various clinically plausible parametric configurations to elucidate the effects of certain critical variables such as tumour cell burden, mode of antineoplastic drug delivery, tumour cell loss and cell-cycle cytokinetic parameters.

Keywords: chemotherapy; haematological and gynaecological cancers; mathematical modelling and simulations; functional-differential equations


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