The mathematical modelling of adjuvant chemotherapy scheduling: incorporating the effects of protocol rest phases and pharmacokinetics

Abstract

In this paper the modelling objective is to determine the drug alternation time which minimises the formation of resistant tumour cells when delivering two non-cross resistant chemotherapeutics given such drugs cannot be delivered simultaneously and constraints due to pharmacokinetics and protocol rest phases. We initially consider cell cycle phase non-specific models, as investigated by Goldie and Coldman. By extending previous work, these models are generalised to consider chemotherapeutic S-phase specificity. We find with the cell cycle phase non-specific models that once the alternation time of the drugs is reduced below a critical threshold, a substantial improvement in protocol outcome is predicted. Extensive improvements are also observed for the S-phase specific investigation if the drugs can be alternated extremely rapidly. However, this is typically impossible due to pharmacokinetic constraints. Under such circumstances, the most appropriate choice of the alternation time can depend sensitively on the median and variance of the tumour cell cycle time in a complicated manner. For schedulings motivated by Capecitabine protocols, we find that switching the drugs only once, or at most twice, between rest phases gives the most reliable alternation time. The main and novel conclusion of this paper is the modelling prediction that one must be much more specific in the choice of the protocol alternation time if attempting to observe the improvements promised by Goldie and Coldman's alternation hypothesis for the rest phases, pharmacokinetics and delivery mechanisms typically encountered in cell cycle phase specific chemotherapy protocols.

The Worst Drug Rule Revisited: Mathematical Modeling of Cyclic Cancer Treatments

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On the Probability of Random Genetic Mutations for Various Types of Tumor Growth

“…This is a random event with a very small (yet nonzero) probability that modifies the cellular phenotype. These random genetic mutations are the main biological mechanism causing the development of drug resistance (Teicher 2006), together with genetic amplifications and kinetic resistance (Kimmel and Axelrod 1990; Harnevo and Agur 1991, 1993, Murray 1997; Panetta and Adam 1995; Gaffney 2005). Kinetic resistance refers to the reduction in effectiveness of a drug which is caused by the cell division cycle.…”

Modelling chemotherapy resistance in palliation and failed cure

“…Evidence supporting this hypothesis has been sought in numerous clinical trials (De Placido et al, 1995;Sieber et al, 2002;Siodlak et al, 1990), though it is typically refuted rather than validated. Gaffney (2004Gaffney ( , 2005 extended the Goldie and Coldman model to consider cell cycle phase specific drugs and the effects of drug delivery. It was shown that the Goldie and Coldman's alternation hypothesis often breaks down both due to the effects of pharmacokinetics and due to resonances between the application time of a cell cycle phase specific drug and the tumour cell cycle time.…”