Resonance and Anti‐Resonance in the Design of Chemotherapeutic Protocols

Abstract

Analytical and computational results suggest that one can control the growth of cell populations by exposing them to certain dosing frequencies of cell-cycle phase-specific cytotoxic agents. Thus, it has been shown theoretically that a resonance effect, manifesting itself in maximal population sizes, can be created, if the period of the drug pulse and that of the population are commensurable. Based on this theory a method (denoted The ZMethod) is suggested for improving the efficacy of cancer therapy. The underlying idea of the Z-method is to improve treatment efficacy by selecting treatment periods that create resonance for the limiting normal cell population, and by avoiding resonance for the cancer cells. These theoretical results are supported by in 11ivo murine experiments. mggesting that intermittent delivery of cell-cycle phase-specific drugs at intervals equivalent to the mean cell-cycle time, might minimize harmful toxicity without con~promising therapeutic effects on target cells. A new implementation of the theory, to be denoted the (intiresonance effect, is suggested in the present work. In essence, anti-resonance is a practical method of preventing resonance in systems where cancer cell kill needs to be maximized and toxicity to normal cells is marginal. The idea here is to reduce the effective number of cell lines whose period will resonate with the treatment period, by creating a stochastic treatment protocol. An algorithm has been developed for computing the efficacy of specific treatment protocols. The algorithm is independent of the assumptions of the Z-Method. It supports this method by showing theoretically that one can increase treatment success by generating a resonancekanti-resonance relationship between the frequency of drug administration and those of the involved cell populations.

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

“…This is evidenced in Fig. 5. (c) When the duration of an individual chemotherapy administration is greater than roughly two thirds of the S-phase duration, then use of resonance ideas (Dibrov et al, 1985;Agur et al, 1988Agur et al, , 1991Agur et al, , 1992Webb, 1990;Cojocaru and Agur, 1992;Webb, 1992a,b;Agur and Dvir, 1994;Ubezio et al, 1994;Webb and Johnson, 1996;Agur, 1998;Dibrov, 1998;Shochat et al, 1999;Anderson and Mackey, 2001) typically leads to an optimal or near optimal protocol given low values for the variance of the tumour cell cycle time. However, such resonance based timings are clearly inappropriate for larger, but nonetheless physiologically reasonable, values for the variance of the tumour cell cycle time, especially given larger rest phase durations.…”

“…In Anderson and Mackey (2001), Webb (1990), Dibrov et al (1985), Dibrov (1998), Agur et al (1988), Webb (1992a,b), Cojocaru and Agur (1992), Agur and Dvir (1994), Webb and Johnson (1996), Agur (1998), Shochat et al (1999), Agur et al (1991Agur et al ( , 1992 and Ubezio et al (1994) local maxima are observed when considering the mean toxicitylimiting cell cycle time, as particularly emphasised in Dibrov (1998) and Cojocaru and Agur (1992) for example. Here, we consider the median tumour cell cycle time.…”

“…The effects of the cell cycle and the most appropriate timing for the administration of cell cycle phase specific drugs have been investigated extensively in papers attempting to maximise cell kill or minimise toxicity (or both) (Dibrov et al, 1985;Agur et al, 1988Agur et al, , 1991Agur et al, , 1992Webb, 1990;Cojocaru and Agur, 1992;Webb, 1992a,b;Agur and Dvir, 1994;Ubezio et al, 1994;Webb and Johnson, 1996;Agur, 1998;Dibrov, 1998;Shochat et al, 1999;Anderson and Mackey, 2001) using the idea of resonances. In the author's previous work (Gaffney, 2004), a model for the development of drug resistance was constructed considering continuous infusions of S-phase specific chemotherapeutics in the adjuvant setting, as motivated by hepatic arterial infusion chemotherapy in liver and colorectal cancers.…”

Scheduling Chemotherapy: Catch 22 between Cell Kill and Resistance Evolution

“…1992, Agur 1998. Cojocaru and Agur (1992) developed a model leading to predictions that spiked doses separated by an interval that is an integer multiple of the host cell-cycle time can minimize host toxicity, while "pathogen elimination may not necessarily be hampered" (p.94), called the Z-method (Agur 1998). Clinical trials have not applied bolus treatments using the Z-method, so it is unclear whether CI or bolus following the Z-method would be less toxic.…”

“…Some theoretical studies and experiments on animal models, however, suggest that CI may be more toxic to the host, since dividing host cells, as well as tumor cells, are also killed in higher numbers (Skipper et al 1967, Ubezio et a / . 1992, Agur 1998. Cojocaru and Agur (1992) developed a model leading to predictions that spiked doses separated by an interval that is an integer multiple of the host cell-cycle time can minimize host toxicity, while "pathogen elimination may not necessarily be hampered" (p.94), called the Z-method (Agur 1998).…”