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Bull Math Biol. 2018 Feb;80(2):283-293. doi: 10.1007/s11538-017-0371-5. Epub 2017 Dec 7.

Mathematical Modeling of the Effects of Tumor Heterogeneity on the Efficiency of Radiation Treatment Schedule.

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Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.
Department of Integrated Mathematical Oncology, Department of Radiation Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, 33647, USA.
Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.


Radiotherapy uses high doses of energy to eradicate cancer cells and control tumors. Various treatment schedules have been developed and tried in clinical trials, yet significant obstacles remain to improving the radiotherapy fractionation. Genetic and non-genetic cellular diversity within tumors can lead to different radiosensitivity among cancer cells that can affect radiation treatment outcome. We propose a minimal mathematical model to study the effect of tumor heterogeneity and repair in different radiation treatment schedules. We perform stochastic and deterministic simulations to estimate model parameters using available experimental data. Our results suggest that gross tumor volume reduction is insufficient to control the disease if a fraction of radioresistant cells survives therapy. If cure cannot be achieved, protocols should balance volume reduction with minimal selection for radioresistant cells. We show that the most efficient treatment schedule is dependent on biology and model parameter values and, therefore, emphasize the need for careful tumor-specific model calibration before clinically actionable conclusions can be drawn.


Cancer stem cell; Fractionation; Tumor control

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