Radiosensitivity and relative biological effectiveness based on a generalized target model

Formulation of Time-Dependent Cell Survival with Saturable Repairability of Radiation Damage

This study aims to provide a model that compounds historically proposed ideas regarding cell survival irradiated with X rays or particles. The parameters used in this model have simple meanings and are closely related to cell death-related phenomena. The model is adaptable to a wide range of doses and dose rates and thus can consistently explain previously published cell survival data. The formulas of the model were derived by using five basic ideas: 1. "Poisson's law"; 2. "DNA affected damage"; 3. "repair"; 4. "clustered affected damage"; and 5. "saturation of reparability". The concept of affected damage is close to but not the same as the effect caused by the double-strand break (DSB). The parameters used in the formula are related to seven phenomena: 1. "linear coefficient of radiation dose"; 2. "probability of making affected damage"; 3. "cell-specific repairability", 4. "irreparable damage by adjacent affected damage"; 5. "recovery of temporally changed repairability"; 6. "recovery of simple damage which will make the affected damage"; 7. "cell division". By using the second parameter, this model includes cases where a single hit results in repairable-lethal and double-hit results in repairable-lethal. The fitting performance of the model for the experimental data was evaluated based on the Akaike information criterion, and practical results were obtained for the published experiments irradiated with a wide range of doses (up to several 10 Gy) and dose rates (0.17 Gy/h to 55.8 Gy/h). The direct association of parameters with cell death-related phenomena has made it possible to systematically fit survival data of different cell types and different radiation types by using crossover parameters.

Optimization of Size of Nanosensitizers for Antitumor Radiotherapy Using Mathematical Modeling

The efficacy of antitumor radiotherapy can be enhanced by utilizing nonradioactive nanoparticles that emit secondary radiation when activated by a primary beam. They consist of small volumes of a radiosensitizing substance embedded within a polymer layer, which is coated with tumor-specific antibodies. The efficiency of nanosensitizers relies on their successful delivery to the tumor, which depends on their size. Increasing their size leads to a higher concentration of active substance; however, it hinders the penetration of nanosensitizers through tumor capillaries, slows down their movement through the tissue, and accelerates their clearance. In this study, we present a mathematical model of tumor growth and radiotherapy with the use of intravenously administered tumor-specific nanosensitizers. Our findings indicate that their optimal size for achieving maximum tumor radiosensitization following a single injection of their fixed total volume depends on the permeability of the tumor capillaries. Considering physiologically plausible spectra of capillary pore radii, with a nanoparticle polymer layer width of 7 nm, the optimal radius of nanoparticles falls within the range of 13-17 nm. The upper value is attained when considering an extreme spectrum of capillary pores.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

Modeling of ionizing radiation-induced chromosome aberration and tumor prevalence based on two classes of DNA double-strand breaks clustering in chromatin domains

There has been some controversy over the use of radiobiological models when modeling the dose-response curves of ionizing radiation (IR)-induced chromosome aberration and tumor prevalence, as those curves usually show obvious non-targeted effects (NTEs) at low doses of high linear energy transfer (LET) radiation. The lack of understanding the contribution of NTEs to IR-induced carcinogenesis can lead to distinct deviations of relative biological effectiveness (RBE) estimations of carcinogenic potential, which are widely used in radiation risk assessment and radiation protection. In this work, based on the initial pattern of two classes of IR-induced DNA double-strand breaks (DSBs) clustering in chromatin domains and the subsequent incorrect repair processes, we proposed a novel radiobiological model to describe the dose-response curves of two carcinogenic-related endpoints within the same theoretical framework. The representative experimental data was used to verify the consistency and validity of the present model. The fitting results indicated that, compared with targeted effect (TE) and NTE models, the current model has better fitting ability when dealing with the experimental data of chromosome aberration and tumor prevalence induced by multiple types of IR with different LETs. Notably, the present model without introducing an NTE term was adequate to describe the dose-response curves of IR-induced chromosome aberration and tumor prevalence with NTEs in low-dose regions. Based on the fitting parameters, the LET-dependent RBE values were calculated for three given low doses. Our results showed that the RBE values predicted by the current model gradually decrease with the increase of doses for the endpoints of chromosome aberration and tumor prevalence. In addition, the calculated RBE was also compared with those evaluated from other models. These analyses show that the proposed model can be used as an alternative tool to well describe dose-response curves of multiple carcinogenic-related endpoints and effectively estimate RBE in low-dose regions.

Optimization of antitumor radiotherapy fractionation via mathematical modeling with account of 4 R's of radiobiology

A spatially-distributed continuous mathematical model of solid tumor growth and treatment by fractionated radiotherapy is presented. The model explicitly accounts for the factors, widely referred to as 4 R's of radiobiology, which influence the efficacy of radiotherapy fractionation protocols: tumor cell repopulation, their redistribution in cell cycle, reoxygenation and repair of sublethal damage of both tumor and normal tissues. With the use of special algorithm the fractionation protocols that provide increased tumor control probability, compared to standard clinical protocol, are found for various physiologically-based values of model parameters under the constraints of fixed overall normal tissue damage and maximum admissible fractional dose. In particular, it is shown that significant gain in treatment efficacy can be achieved for tumors of low malignancy by the use of protracted hyperfractionated protocols. The optimized non-uniform protocols are characterized by gradual escalation of fractional doses in their last parts, which start after the levels of oxygen and nutrients significantly elevate throughout the tumor and accelerated tumor proliferation manifests itself, which is a well-known experimental phenomenon.

Improved Asymptotic Expansions in High- and Low-Dose Ranges for Generalized Multi-Hit Model of Radiation-Induced Cell Survival

By considering an upper bound on the number of radiation-induced potential lethal damages that can be repaired in a cell, we have proposed the generalized multi-hit (GMH) model with a closed-form solution, which can better fit various radiation-induced cell survival curves. Recent analysis shows that the asymptotic expansions that we gave before can be used to approximate the generalized single-hit single-target (GSHST) model rather than the GMH model. To illustrate the asymptotic trends of radiation-induced cell survival curves, in this study, we improve the asymptotic expansions of the GMH model in low- and high-dose ranges based on the limit formula of the incomplete gamma function in the corresponding dose ranges. When the upper limit of the number of radiation-induced potential lethal damages is one, the improved expansions of the GMH model can be reduced to the previous expansions of the GSHST model, and the improved asymptotic expansions of the GMH model also indicate that the GMH model has the generalized linear-quadratic-linear (LQL) feature. The numerical simulations indicate that the improved asymptotic expansions in high- and low-dose ranges agree well with the non-linear fitting of the GMH model in six kinds of cell lines under the corresponding dose ranges. In addition, we analyze the relative errors of the improved expansions of the GMH model in high- and low-dose ranges to demonstrate the accuracy and effectiveness of the improved expansions. Based on the error analysis, we further give the reasonable ranges of radiation dose applicable to the improved asymptotic expansions of the GMH model.

The Determinant of DNA Repair Pathway Choices in Ionising Radiation-Induced DNA Double-Strand Breaks

Ionising radiation- (IR-) induced DNA double-strand breaks (DSBs) are considered to be the deleterious DNA lesions that pose a serious threat to genomic stability. The major DNA repair pathways, including classical nonhomologous end joining, homologous recombination, single-strand annealing, and alternative end joining, play critical roles in countering and eliciting IR-induced DSBs to ensure genome integrity. If the IR-induced DNA DSBs are not repaired correctly, the residual or incorrectly repaired DSBs can result in genomic instability that is associated with certain human diseases. Although many efforts have been made in investigating the major mechanisms of IR-induced DNA DSB repair, it is still unclear what determines the choices of IR-induced DNA DSB repair pathways. In this review, we discuss how the mechanisms of IR-induced DSB repair pathway choices can operate in irradiated cells. We first briefly describe the main mechanisms of the major DNA DSB repair pathways and the related key repair proteins. Based on our understanding of the characteristics of IR-induced DNA DSBs and the regulatory mechanisms of DSB repair pathways in irradiated cells and recent advances in this field, We then highlight the main factors and associated challenges to determine the IR-induced DSB repair pathway choices. We conclude that the type and distribution of IR-induced DSBs, chromatin state, DNA-end structure, and DNA-end resection are the main determinants of the choice of the IR-induced DNA DSB repair pathway.

The Determinant of DNA Repair Pathway Choices in Ionising Radiation-Induced DNA Double-Strand Breaks

Ionising radiation- (IR-) induced DNA double-strand breaks (DSBs) are considered to be the deleterious DNA lesions that pose a serious threat to genomic stability. The major DNA repair pathways, including classical nonhomologous end joining, homologous recombination, single-strand annealing, and alternative end joining, play critical roles in countering and eliciting IR-induced DSBs to ensure genome integrity. If the IR-induced DNA DSBs are not repaired correctly, the residual or incorrectly repaired DSBs can result in genomic instability that is associated with certain human diseases. Although many efforts have been made in investigating the major mechanisms of IR-induced DNA DSB repair, it is still unclear what determines the choices of IR-induced DNA DSB repair pathways. In this review, we discuss how the mechanisms of IR-induced DSB repair pathway choices can operate in irradiated cells. We first briefly describe the main mechanisms of the major DNA DSB repair pathways and the related key repair proteins. Based on our understanding of the characteristics of IR-induced DNA DSBs and the regulatory mechanisms of DSB repair pathways in irradiated cells and recent advances in this field, We then highlight the main factors and associated challenges to determine the IR-induced DSB repair pathway choices. We conclude that the type and distribution of IR-induced DSBs, chromatin state, DNA-end structure, and DNA-end resection are the main determinants of the choice of the IR-induced DNA DSB repair pathway.

Optimization of Dose Fractionation for Radiotherapy of a Solid Tumor with Account of Oxygen Effect and Proliferative Heterogeneity

A spatially-distributed continuous mathematical model of solid tumor growth and treatment by fractionated radiotherapy is presented. The model explicitly accounts for three time and space-dependent factors that influence the efficiency of radiotherapy fractionation schemes—tumor cell repopulation, reoxygenation and redistribution of proliferative states. A special algorithm is developed, aimed at finding the fractionation schemes that provide increased tumor cure probability under the constraints of maximum normal tissue damage and maximum fractional dose. The optimization procedure is performed for varied radiosensitivity of tumor cells under the values of model parameters, corresponding to different degrees of tumor malignancy. The resulting optimized schemes consist of two stages. The first stages are aimed to increase the radiosensitivity of the tumor cells, remaining after their end, sparing the caused normal tissue damage. This allows to increase the doses during the second stages and thus take advantage of the obtained increased radiosensitivity. Such method leads to significant expansions in the curative ranges of the values of tumor radiosensitivity parameters. Overall, the results of this study represent the theoretical proof of concept that non-uniform radiotherapy fractionation schemes may be considerably more effective that uniform ones, due to the time and space-dependent effects.

Generalized Multi-Hit Model of Radiation-Induced Cell Survival with a Closed-Form Solution: An Alternative Method for Determining Isoeffect Doses in Practical Radiotherapy

The standard linear-quadratic (LQ) model is currently the preferred model for describing the ionizing radiation-induced cell survival curves and tissue responses. And the LQ model is also widely used to calculate isoeffect doses for comparing different fractionated schemes in clinical radiotherapy. Despite its ubiquity, because the actual dose-response curve may appear linear at high doses in the semilogarithmic plot, the application of the LQ model is greatly challenged in the high-dose region, while the dose employed in stereotactic body radiotherapy (SBRT) is often in this area. Alternatively, the biophysical models of radiation-induced effects with a linear-quadratic-linear (LQL) characteristic can well fit the dose-survival curve of cells in vitro. However, most of these LQL models are phenomenological and have not fully considered the biophysical mechanism of radiation-induced damage and repair, and the fitting quality decreases in some high-dose ranges. In this work, to provide an alternative model to describe the cell survival curves in high-dose ranges and predict the biologically effective dose (BED) for SBRT, we propose a novel generalized multi-hit model with a closed-form solution by considering an upper bound on the number of lethal damages induced by radiation that can be repaired in a cell. This model has a clear biophysical basis and a simple expression, and also has the LQL characteristic under low- and high-dose approximate conditions. The experimental data fitting indicated that compared to the standard LQ model and our previously generalized target model, the current model can better fit the radiation-induced cell survival curves in the high-dose ranges (P < 0.05). The current model parameters and parameter ratios were determined from the fits in different kinds of cell lines irradiated with various dose rates and linear energy transfer (LET), which indicates that the model parameters significantly depend on the dose rate and LET. Based on the current model, we derived two equivalence formulae for the BED calculations in the low- and high-dose ranges, and then calculated the BED for the clinical data of SBRT from 17 selected studies. The correlation analysis showed that there were significant linear correlations between the BED at isocenter and planning target volume (PTV) edge calculated by this model and the LQ model (R > 0.86, P < 0.001). In conclusion, the generalized multi-hit model proposed in this work can be used as an alternative tool to handle in vitro radiation-induced cell survival curves in high-dose ranges, and calculate the in vivo BED for comparing the dose fractionation schemes in clinical radiotherapy.

Fitting the Generalized Target Model to Cell Survival Data of Proton Radiation Reveals Dose-Dependent RBE and Inspires an Alternative Method to Estimate RBE in High-Dose Regions

The imprecise estimation of the relative biological effectiveness (RBE) of proton radiation has been one of the main challenges for further calculating the biologically effective dose in proton therapy. Since dose levels can greatly influence the proton RBE, the relationship between the two should be clarified first. In addition, since the dose-response curves are usually too complex to readily assess RBE in high-dose regions, a reliable and simple method is needed to predict the RBE of proton radiation accurately in clinically relevant doses. The standard linear-quadratic (LQ) model is widely used to determine the RBE of particles for clinical applications. However, there has been some debate over its use when modeling the cell survival curves in high-dose regions, since those survival curves usually show linear behavior in the semilogarithmic plot. By considering both cellular repair effects and indirect effects of radiation, we have proposed a generalized target model with linear-quadratic linear (LQL) characteristics. For the more accurate evaluation of proton RBE in radiotherapy, here we used this generalized target model to fit the cell survival data in V79 and C3H 10T1/2 cells exposed to proton radiation with different LETs. The fitting results show that the generalized target model works as well as the LQ model in general. Based on the fitting parameters of the generalized target model, the RBE of six given doses D_T (RBE_T) could be calculated in the corresponding cell lines with different LETs. The results show that the RBE_T gradually decreases with increased dose in both cell types. In addition, inspired by the calculation method of the maximum values of RBE (RBE_M) in the low-dose region, a novel method was proposed for estimating the RBE in the high-dose region (RBE_H) based on the slope ratio of the dose-response curves in this region. Linear regression analysis indicated a significant linear correlation between the proposed RBE_H and the RBE_T in high-dose regions, which suggests that the current method can be used as an alternative tool, which is both simple and robust, to estimate RBE in high-dose regions.

Development of Dose-Response Calibration Curve for Dicentric Chromosome Induced by X-Rays

Chromosome aberration is a biomarker that has been used as a standard tool in biological dosimetry (biodosimetry) of individuals after exposure to ionizing radiation. It is based mainly on the induction of dicentric chromosomes - one of the radiation-induced biological effects, in order to correlate them with radiation dose. In this study, a dose calibration curve for X-rays was generated by using the dicentric assay and by fitting the data to both Chromosomal Aberration Calculation Software and Dose Estimate programs to compare the output of each method. Peripheral blood samples from four nonsmoker healthy donors were irradiated with various doses ranging from 0 to 4 Gy with 250 kV or 122 keV X-rays at a dose rate of 0.17 Gy/min. The irradiated blood was cultured, harvested, and analyzed according to the standard procedure as described by the International Atomic Energy Agency with slight modifications. The dose-response calibration data for dicentrics were fitted with the linear-quadratic model (Y_dic = 0.03987D² + 0.00651D). The dose-response calibration curve obtained in this research was comparable to other estimations with similar radiation quality and dose rates. The results in this research convinced us in sustaining a biodosimetry using a dose-response calibration curve in our laboratory.

Analysis of DNA methylation alterations in rice seeds induced by different doses of carbon-ion radiation

To investigate the mechanism underlying differences in biological effects induced by low- versus high-dose heavy-ion radiation (HIR) in rice plants, two-dimensional gel electrophoresis (2-DE) coupled with methylation-sensitive amplification polymorphism (MSAP) analysis were used to check the expression changes in rice leaf proteome profiles and the changes in DNA methylation after exposure of seeds to ground-based carbon-ion radiation at various cumulative doses (0, 0.01, 0.02, 0.1, 0.2, 1, 2, 5 or 20 Gy; 12C6+; energy, 165 MeV/u; mean linear energy transfer, 30 KeV/μm). In this study, principal component analysis (PCA) and gene ontology (GO) functional analysis of differentially expressed proteins of rice at tillering stage showed that proteins expressed in rice samples exposed to 0.01, 0.02, 0.1, 0.2 or 1 Gy differed from those exposed to 2, 5 or 20 Gy. Correspondingly, the proportion of hypermethylation was higher than that of hypomethylation at CG sites following low-dose HIR (LDR; 0.01, 0.2 or 1 Gy), whereas this was reversed at high-dose HIR (HDR; 2, 5 or 20 Gy). The hypomethylation changes tended to occur at CHG sites with both low- and high-dose HIR. Furthermore, sequencing of MSAP variant bands indicated that the plants might activate more metabolic processes and biosynthetic pathways on exposure to LDR, but activate stress resistance on exposure to HDR. This study showed that radiation induced different biological effects with low- and high-dose HIR, and that this may have been caused by different patterns of hyper- and hypomethylation at the CG sites.

A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells.