Optimizing Cancer Chemotherapy: From Mathematical Theories to Clinical Treatment

Abstract

Cancer chemotherapy is much influenced by the “dose dense” paradigm, advocating maximally possible dose density early in treatment. This paradigm is based on a controversial mathematical model, assuming Gompertz tumor growth law. Alternatively, it has been suggested that for maximizing efficacy/toxicity ratio in cancer chemotherapy, the inter-dosing intervals should be determined according to the Resonance theory. This theory asserts that cell growth is maximal when the periodicity of drug administration is an integer or fractional multiple of the characteristic periodicity of the cell population. Model analysis and in vitro and in vivo experiments, suggest that differences in cell-cycle distributions of host and cancer cells canbe taken advantage of in chemotherapy by cell-cycle phase-specific drugs which use Resonance or Anti-Resonance (stochastic) drug pulsing. Mathematical proofs showing long-term prediction accuracy of cell population growth models under cell- cycle phase-specific drugs, enabled developing a heuristic optimization method for drug scheduling. Using this method in conjunction with personalized models of vascular tumor growth under chemotherapy by docetaxel and bevacizumab, an optimal combination regimen was tailored to a particular mesenchymal chondrosarcoma patient. The personalized regimen was prospectively validated, leading to increased longevity and quality of life of the patient. This patient's model was further simulated, suggesting that the relative advantage of “Dose Dense” drug therapy depends on personal cytokinetic and angiogenic parameters.