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Resonance and anti-resonance in the design of chemotherapeutic protocols. (English) Zbl 0918.92017

Summary: 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 \(Z\)-Method) 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 vivo murine experiments, suggesting that intermittent delivery of cell-cycle phase-specific drugs at intervals equivalent to the mean cell-cycle time, might minimize harmful toxicity without compromising therapeutic effects on target cells.
A new implementation of the theory, to be denoted the anti-resonance 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 protocols. 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 resonance/anti-resonance relationship between the frequency of drug administration and those of the involved cell populations.

MSC:

92C50 Medical applications (general)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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