Journal of Theoretical Medicine
Volume 1 (1998), Issue 3, Pages 237-245

Resonance and Anti-Resonance in the Design of Chemotherapeutic Protocols

Department of Cell Research and Immunology, Life Science Faculty, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv, Israel

Received 1 October 1996; Accepted 28 April 1998

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 improve the efficacy of cancer therapy. The underlying idea of the Z-method is to improve treatment efficacy by selecting treatment period 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 delivrey of cell-cycle phase-specific drugs at intervals equivalent to the man 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 cells 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 protocol. The algorithm is independent of the assumptions of the Z-Method. Itsupports 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.