Abstract
Introduction: In this work, we develop a multi-scale model to calculate corrections to the prescription dose to predict compensation required for the DNA repair mechanism and the repopulation of the cancer cells due to the occurrence of patient scheduling variabilities and the treatment time-gap in fractionation scheme. Methods: A system of multi-scale, time-dependent birth-death Master equations is used to describe stochastic evolution of double-strand breaks (DSBs) formed on DNAs and post-irradiation intra and inter chromosomes end-joining processes in cells, including repair and mis-repair mechanisms in microscopic scale, with an extension appropriate for calculation of tumor control probability (TCP) in macroscopic scale. Variabilities in fractionation time due to systematic shifts in patient’s scheduling and randomness in inter-fractionation treatment time are modeled. For an illustration of the methodology, we focus on prostate cancer. Results: We derive analytical corrections to linear-quadratic radiobiological indices α and β as a function of variabilities in treatment time and shifts in patient’s scheduling. We illustrate the dependence of the absolute value of the compensated dose on radio-biological sensitivity, α/β, DNA repair half-time, T1/2, tumor cells repopulation rate, and the time-gaps among treatment fractions due to inter-patient variabilities. At a given tumor size, delays between fractions totaling 24 h over the entire course of treatment, in a typical prostate cancer fractionation scheme, e.g., 81 Gy, 1.8 Gy per fraction and 45 treatment days, require up to 10% compensation dose if the sublethal DNA repair half-time, T1/2, spans over 10 h. We show that the contribution of the fast DNA repair mechanisms to the total dose is negligible. Instead, any compensation to the total dose stems from the tumor cell repopulation that may go up to a significant fraction of the original dose for a time gap of up to one week. Conclusions: We recommend implementation of time irregularities in treatment scheduling in the clinic settings to be taken into account. To achieve a clinical endpoint, corrections to the prescription dose must be assessed, in particular, if modern external beam therapy techniques such as IMRT/VMAT are used for the treatment of cancer.