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Purpose: to determine optimal fractionation schedule which provides maximum biologically effective dose (BED) in the targeted tumor in the case of heterogeneous radiosensitivity of malignant cells in combination with a spatially varying sparing factor for the organ at risk., Methods: the mathematical framework used in the current study is based on the linear-quadratic (LQ) model with heterogeneous parameters alpha and beta for malignant cells. To determine optimal fractionation, we consider changes in BED in the treatment target (BED tar ) under the condition of fixed BED in the affected normal tissue (BED nt )., Results: we demonstrate both analytically and via numerical calculations that there exists an optimal number of fractions for which biologically effective dose in the uniformly irradiated target is at maximum. It is also shown that dependence of BED tar on number of fractions is generally non-monotonic and is affected by the variances σ α and σ β of the alpha and beta radiosensitivities, respectively. In a particular case when σ α and σ β are sufficiently small, expression for the optimal target dose which maximizes BED tar was derived analytically., Conclusion: the obtained results demonstrate that in the presence of heterogeneous alpha and beta in the tumor, hypofractionation can either increase or decrease BED tar depending on the variances σ α and σ β . Consequently, intratumor heterogeneity is an important factor which can affect radiobiological comparison of different fractionation regimens., (Copyright © 2019 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.)

Purpose: To assess the role of reoxygenation of hypoxic tumor cells in hypofractionated radiotherapy of prostate cancer. Methods: The considered radiobiological model is based on the assumption of two populations (compartments) of cells: oxygenated (aerobic) cells and hypoxic cells. After each fraction of radiation, some of the hypoxic cells reoxygenate while a fraction of initially aerobic cells becomes hypoxic. The kinetics of this process between successive treatments is described by coupled, first‐order differential equations. To determine the effect of reoxygenation on cell kill in the treatment target, we utilize the linear‐quadratic (LQ) model assuming different radiosensitivities for the aerobic and hypoxic cells. Results: Analytical solutions for the number of surviving malignant cells are obtained for special cases of slow and fast reoxygenation. The radiobiological effect of reoxygenation for different fractionation regimens is also evaluated numerically. Conclusions: In this study, a radiobiological model for kinetics of reoxygenation in tumors is used to evaluate different fractionation schedules in radiotherapy of prostate cancer. The obtained results indicate that in the case of low alpha/beta ratio for malignant cells (e.g., α/β = 1.5 Gy), treatment schedule with 4–10 fractions and dose per fraction >4–5 Gy can result in increased cell kill in the treatment target at the same level of rectal toxicity as compared to conventional fractionation. The findings of this study also suggest that radiotherapy of the prostate with 1–3 fractions can be radiobiologically inferior to treatments with greater number of fractions. [ABSTRACT FROM AUTHOR]

Purpose: To investigate the effect of radiation protraction on biologically effective dose (BED) in the case when dose per fraction is significantly greater than the standard dose of 2 Gy. Methods: By using the modified linear-quadratic model with monoexponential repair, the authors investigate the effect of long treatment times combined with dose escalation. Results: The dependences of the protraction factor and the corresponding BED on fraction time were determined for different doses per fraction typical for stereotactic radiosurgery (SRS) and stereotactic body radiation therapy (SBRT). In the calculations, the authors consider changes in the BED to the normal tissue under the condition of fixed BED to the target. Conclusion: The obtained results demonstrate that simultaneous increase in fraction time and dose per fraction can be beneficial for SRS and SBRT because of the related decrease in BED to normal structures while BED to the target is fixed. [ABSTRACT FROM AUTHOR]