Biological adaptive radiotherapy for short-time dose compensation in lung SBRT patients

BACKGROUND

Conventional adaptive radiation therapy (ART) primarily focuses on adapting to anatomical changes during radiation therapy but does not account for biological effects such as changes in radiosensitivity and tumor response, particularly during treatment interruptions. These interruptions may allow sublethal damage repair in tumor cells, reducing the effectiveness of stereotactic body radiation therapy (SBRT).

PURPOSE

The aim of this study was to develop and evaluate a novel biological adaptive radiotherapy (BART) framework to compensate for the biological effects of radiation interruptions during SBRT for lung cancer.

METHODS

This study involved lung SBRT patients using volumetric modulated arc therapy. We evaluated the biological dose loss using a microdosimetric kinetic model during four interruption durations (30, 60, 90, and 120 min). The reduction in the biological dose due to interruptions was calculated. The physical dose was calculated from the decreased biological dose in the in-house software, which was incorporated into the TPS. The optimization process was conducted for dose compensation in the TPS. To quantitatively assess the impact of BART on dose distribution, we evaluated the differences in target dose coverage and organ-at-risk (OAR) exposure between the original plan (without interruption), the plan with interruption, the BART plan, and the plan summing the dose before the interruption and the physical dose after compensation (compensated PD plan). The compensated PD plan assumed no biological dose reduction before the interruption.

RESULTS

Without BART compensation, interruptions of 30, 60, 90, and 120 min resulted in biological dose reductions, ranging from 12.1% to 19.0% for D50% of the gross tumor volume (GTV) and from 16.4% to 24.9% for D98% of the PTV. After applying BART, the differences were minimized to -1.5% to -0.6% for D50% of the GTV and -0.1% to 0.9% for D98% of the PTV. In contrast, the compensated PD plan exhibited larger residual deviations, with dose differences ranging from -9.9% to -14.0% for D50% of the GTV and -12.3% to -7.3% for D98% of the PTV. The volume differences between the BART plan and the plan without interruption remained within -0.8% to -0.4% for V5Gy and -0.2% to 0.0% for V20Gy, while differences between the BART and compensated PD plans were similarly small. The maximum dose to the spinal cord (D0.1cc) also remained within -0.2 to 0.1 Gy for the BART plan relative to the plan without interruption and -0.1 to -0.5 Gy compared to the compensated PD plan. These results confirm that the OAR doses remained within clinically acceptable constraints across all evaluated plans.

CONCLUSION

This study demonstrated that the BART framework effectively compensates for the biological dose reduction caused by interruptions during lung cancer SBRT. BART successfully maintained target dose coverage and minimized biological dose loss for the target, while keeping OAR doses within safe limits, including for the lungs and spinal cord. The introduction of BART marks a significant advancement in adaptive radiotherapy, offering a comprehensive approach to managing interruptions and improving clinical outcomes.

Design of multi-ion therapy for head and neck cancers using carbon-, oxygen-, and neon-ion beams: potential efficacy against tumor hypoxia

Objective. In order to initiate multi-ion therapy for head and neck cancers, it is necessary to predetermine the target dose-averaged linear energy transfer (LETd) prescription to the gross tumor volume (GTV). This study investigated LETdoptimized treatment plans with carbon-, oxygen-, and neon-ion beams and demonstrated their potential efficacy against tumor hypoxia.Approach. Sixteen head and neck cancer patients with GTV sizes ranging from 5.5 to 143.1 cm3were selected for this retrospective planning study. Carbon, oxygen, and neon ions were used alone or in combination with two ion species. The treatment plans were optimized to increase LETdwithin the GTV and to make the LETddistribution uniform while maintaining the relative biological effectiveness weighted dose distributions of conventional intensity modulated carbon-ion therapy (IMIT). The effective dose improvement rate against IMIT was then estimated by changing oxygen partial pressure within the GTV to 0 mmHg because a substantial number of anoxic cancer cells is predicted to exist in a hypoxic tumor microenvironment.Main results. The target LETdof 90 keVμm-1was prescribable without deteriorating the dose distributions when: for example, carbon- and oxygen-ion beams were used for small tumors (around 20 cm3); oxygen-ion beams alone were used for medium tumors (around 50 cm3); and carbon- and neon-ion beams were used for large tumors (around 100 cm3). The uniformity of the LETddistributions within the GTV was about 10%. With the LETdprescription, the improvement rate of the effective dose covering 98% (i.e.D98%) of the GTV against anoxic cancer cells was about 30%.Significance. For the application to the first multi-ion therapy program, the target LETdprescription to the GTV was determined to be 90 keVμm-1. If tumor hypoxia contributes to the cause of recurrence, the proposed treatment may offer better local tumor control without compromising normal tissue sparing.

Dose compensation for decreased biological effective dose due to intrafractional interruption during radiotherapy: integration with a commercial treatment planning system

Objective.While the biological effective dose (BED) has been used to estimate the damage to tumor cells in radiotherapy, BED does not consider intrafractional interruption (IFI) occurring during irradiation. We aim to develop a framework to evaluate the decrease in BED [ΔBED] and to create a plan compensating for the decrease by IFI.Approach.ΔBEDwas calculated using a model based on the microdosimetric kinetic model (MKM) for four brain tumor cases treated using a volumetric-modulated arc therapy. Four biologically compensated plans (BCPs) were created in the treatment planning system by a single-time optimization using a base plan consideringΔBEDcreated in in-house software and optimization objectives for the original clinically delivered plan to achieve a homogeneous BED distribution within the planning target volume (PTV). The BED-volume histogram was evaluated for non-compensated plan and BCP with different timepoint of interruption, a percentage of gantry rotation angle (GRA) before interruption in planned GRA,ηand duration of interruptionτ. Characteristics of the dose accumulation were analyzed for different collimator angle sets, Plan A (10°, 85°) and Plan B (45° and 315°), for the first case.Main Results.Hot spots in theΔBEDdistribution forη= 25%, 50%, and 75% were observed at superior-and-interior ends, central region, and peripheral region in PTV, respectively. These behaviors could be understood by characteristics of the MKM-based model producing maximumΔBEDat 50% of the dose accumulation.ΔBED50%ranged 4.5%-6.6%, 5.0%-7.3%, and 5.3%-7.7% forτ= 60, 90, and 120 min, respectively. Plan A showed fast dose accumulation at superior and inferior edges while slow on peripheries in the lateral dose profile. Plan B showed more homogeneous PD distributions than Plan A during irradiation.Significance.The developed framework successfully evaluated and compensated for the decreased BED distribution.

Dosimetric analysis of six whole-breast irradiation techniques in supine and prone positions

In breast cancer radiation therapy, minimizing radiation-related risks and toxicity is vital for improving life expectancy. Tailoring radiotherapy techniques and treatment positions can reduce radiation doses to normal organs and mitigate treatment-related toxicity. This study entailed a dosimetric comparison of six different external beam whole-breast irradiation techniques in both supine and prone positions. We selected fourteen breast cancer patients, generating six treatment plans in both positions per patient. We assessed target coverage and organs at risk (OAR) doses to evaluate the impact of treatment techniques and positions. Excess absolute risk was calculated to estimate potential secondary cancer risk in the contralateral breast, ipsilateral lung, and contralateral lung. Additionally, we analyzed the distance between the target volume and OARs (heart and ipsilateral lung) while considering the treatment position. The results indicate that prone positioning lowers lung exposure in X-ray radiotherapy. However, particle beam therapies (PBTs) significantly reduce the dose to the heart and ipsilateral lung regardless of the patient's position. Notably, negligible differences were observed between arc-delivery and static-delivery PBTs in terms of target conformity and OAR sparing. This study provides critical dosimetric evidence to facilitate informed decision-making regarding treatment techniques and positions.

Modeling of the resensitization effect on carbon-ion radiotherapy for stage I non-small cell lung cancer

Objective. To investigate the effect of redistribution and reoxygenation on the 3-year tumor control probability (TCP) of patients with stage I non-small cell lung cancer (NSCLC) treated with carbon-ion radiotherapy.Approach. A meta-analysis of published clinical data of 233 NSCLC patients treated by carbon-ion radiotherapy under 18-, 9-, 4-, and single-fraction schedules was conducted. The linear-quadratic (LQ)-based cell-survival model incorporating the radiobiological 5Rs, radiosensitivity, repopulation, repair, redistribution, and reoxygenation, was developed to reproduce the clinical TCP data. Redistribution and reoxygenation were regarded together as a single phenomenon and termed 'resensitization' in the model. The optimum interval time between fractions was investigated for each fraction schedule using the determined model parameters.Main results.The clinical TCP data for 18-, 9-, and 4-fraction schedules were reasonably reproduced by the model without the resensitization effect, whereas its incorporation was essential to reproduce the TCP data for all fraction schedules including the single fraction. The curative dose for the single-fraction schedule was estimated to be 49.0 Gy (RBE), which corresponds to the clinically adopted dose prescription of 50.0 Gy (RBE). For 18-, 9-, and 4-fraction schedules, a 2-to-3-day interval is required to maximize the resensitization effect during the time interval. In contrast, the single-fraction schedule cannot benefit from the resensitization effect, and the shorter treatment time is preferable to reduce the effect of sub-lethal damage repair during the treatment.Significance.The LQ-based cell-survival model incorporating the radiobiological 5Rs was developed and used to evaluate the effect of the resensitization on clinical results of NSCLC patients treated with hypo-fractionated carbon-ion radiotherapy. The incorporation of the resensitization into the cell-survival model improves the reproducibility to the clinical TCP data. A shorter treatment time is preferable in the single-fraction schedule, while a 2-to-3-day interval between fractions is preferable in the multi-fraction schedules for effective treatments.

Investigation of the Impact of Temporal Dose Delivery Patterns of Ion Irradiation with the Local Effect Model

We present an extension of the Local Effect Model (LEM) to include time-dose relationships for predicting effects of protracted and split-dose ion irradiation at arbitrary LET. With this kinetic extension, the spatial and temporal induction and processing of DNA double strand breaks (DSB) in cellular nuclei can be simulated for a wide range of ion radiation qualities, doses and dose rates. The key concept of the extension is based on the joint spatial and temporal coexistence of initial DSB, leading to the formation of clustered DNA damage on the µm scale (as defined e.g., by the size scale of Mbp chromatin loops), which is considered to have an increased cellular lethality as compared to isolated, single DSB. By simulating the time dependent induction and repair of DSB and scoring of isolated and clustered DSB upon irradiation, the impact of dose rate and split dose on the cell survival probability can be computed. In a first part of this work, we systematically analyze the predicted impact of protraction in dependence of factors like dose, LET, ion species and radiosensitivity as characterized by the photon LQ-parameters. We establish links to common concepts that describe dose rate effects for low LET radiation. We also compare the model predictions to experimental data and find agreement with the general trends observed in the experiments. The relevant concepts of our approach are compared to other models suitable for predicting time effects. We investigate an apparent analogy between spatial and temporal concentration of radiation delivery, both leading to increased effectiveness, and discuss similarities and differences between the general dependencies of these clustering effects on their impacting factors. Finally, we conclude that the findings give additional support for the general concept of the LEM, i.e. the characterization of high LET radiation effects based on the distinction of just two classes of DSB (isolated DSB and clustered DSB).

Integrating microdosimetricin vitroRBE models for particle therapy into TOPAS MC using the MicrOdosimetry-based modeliNg for RBE ASsessment (MONAS) tool

Objective.In this paper, we present MONAS (MicrOdosimetry-based modelliNg for relative biological effectiveness (RBE) ASsessment) toolkit. MONAS is a TOPAS Monte Carlo extension, that combines simulations of microdosimetric distributions with radiobiological microdosimetry-based models for predicting cell survival curves and dose-dependent RBE.Approach.MONAS expands TOPAS microdosimetric extension, by including novel specific energy scorers to calculate the single- and multi-event specific energy microdosimetric distributions at different micrometer scales. These spectra are used as physical input to three different formulations of themicrodosimetric kinetic model, and to thegeneralized stochastic microdosimetric model(GSM2), to predict dose-dependent cell survival fraction and RBE. MONAS predictions are then validated against experimental microdosimetric spectra andin vitrosurvival fraction data. To show the MONAS features, we present two different applications of the code: (i) the depth-RBE curve calculation from a passively scattered proton SOBP and monoenergetic12C-ion beam by using experimentally validated spectra as physical input, and (ii) the calculation of the 3D RBE distribution on a real head and neck patient geometry treated with protons.Main results.MONAS can estimate dose-dependent RBE and cell survival curves from experimentally validated microdosimetric spectra with four clinically relevant radiobiological models. From the radiobiological characterization of a proton SOBP and12C fields, we observe the well-known trend of increasing RBE values at the distal edge of the radiation field. The 3D RBE map calculated confirmed the trend observed in the analysis of the SOBP, with the highest RBE values found in the distal edge of the target.Significance.MONAS extension offers a comprehensive microdosimetry-based framework for assessing the biological effects of particle radiation in both research and clinical environments, pushing closer the experimental physics-based description to the biological damage assessment, contributing to bridging the gap between a microdosimetric description of the radiation field and its application in proton therapy treatment with variable RBE.

Cell Survival Computation via the Generalized Stochastic Microdosimetric Model (GSM2); Part II: Numerical Results

In the present paper we numerically investigate, using Monte Carlo simulation, the theoretical results predicted by the Generalized Stochastic Microdosimetric Model (GSM2), as shown in the published companion paper. Taking advantage of the particle irradiation data ensemble (PIDE) dataset, we calculated GSM2 biological parameters of human salivary gland (HSG) and V79 cell lines. Further, exploiting the TOPAS-microdosimetric extension, we simulated the microdosimetric spectra of different radiation fields of therapeutic interest generated by four different ions (protons, helium-4, carbon-12 and oxygen-16) each at three different residual ranges. We investigated the properties of the initial damage distributions as well as the cell survival curve predicted by GSM2, focusing especially on the non-Poissonian effects naturally included in the model. GSM2 successfully computed cell survival curves, accurately describing experimental behavior even under challenging LET and dose conditions.

A spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation condition

In the present work, we develop a general spatial stochastic model to describe the formation and repair of radiation-induced DNA damage. The model is described mathematically as a measure-valued particle-based stochastic system and extends in several directions the model developed in Cordoni et al. (Phys Rev E 103:012412, 2021; Int J Radiat Biol 1-16, 2022a; Radiat Res 197:218-232, 2022b). In this new spatial formulation, radiation-induced DNA damage in the cell nucleus can undergo different pathways to either repair or lead to cell inactivation. The main novelty of the work is to rigorously define a spatial model that considers the pairwise interaction of lesions and continuous protracted irradiation. The former is relevant from a biological point of view as clustered lesions are less likely to be repaired, leading to cell inactivation. The latter instead describes the effects of a continuous radiation field on biological tissue. We prove the existence and uniqueness of a solution to the above stochastic systems, characterizing its probabilistic properties. We further couple the model describing the biological system to a set of reaction-diffusion equations with random discontinuity that model the chemical environment. At last, we study the large system limit of the process. The developed model can be applied to different contexts, with radiotherapy and space radioprotection being the most relevant. Further, the biochemical system derived can play a crucial role in understanding an extremely promising novel radiotherapy treatment modality, named in the community FLASH radiotherapy, whose mechanism is today largely unknown.

On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

In this paper, we study the system size expansion of a stochastic model for radiation-induced DNA damage kinetics and repair. In particular, we characterize both the macroscopic deterministic limit and the fluctuation around it. We further show that such fluctuations are Gaussian-distributed. In deriving such results, we provide further insights into the relationship between stochastic and deterministic mathematical models for radiation-induced DNA damage repair. Specifically, we demonstrate how the governing deterministic equations commonly employed in the field arise naturally within the stochastic framework as a macroscopic limit. Additionally, by examining the fluctuations around this macroscopic limit, we uncover deviations from a Poissonian behavior driven by interactions and clustering among DNA damages. Although such behaviors have been empirically observed, our derived results represent the first rigorous derivation that incorporates these deviations from a Poissonian distribution within a mathematical model, eliminating the need for specific ad hoc corrections.

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.

Multiple levels of stochasticity accounted for in different radiation biophysical models: from physics to biology

PURPOSE

In the present paper we investigate how some stochastic effects are included in a class of radiobiological models with particular emphasis on how such randomnesses reflect into the predicted cell survival curve.

MATERIALS AND METHODS

We consider four different models, namely the Generalized Stochastic Microdosimetric Model GSM², in its original full form, the Dirac GSM² the Poisson GSM² and the Repair-Misrepair Model (RMR). While GSM² and the RMR models are known in literature, the Dirac and the Poisson GSM²  have been newly introduced in this work. We further numerically investigate via Monte Carlo simulation of four different particle beams, how the proposed stochastic approximations reflect into the predicted survival curves. To achieve these results, we consider different ion species at energies of interest for therapeutic applications, also including a mixed field scenario.

RESULTS

We show how the Dirac GSM², the Poisson GSM² and the RMR can be obtained from the GSM² under suitable approximations on the stochasticity considered. We analytically derive the cell survival curve predicted by the four models, characterizing rigorously the high and low dose limits. We further study how the theoretical findings emerge also using Monte Carlo numerical simulations.

CONCLUSIONS

We show how different models include different levels of stochasticity in the description of cellular response to radiation. This translates into different cell survival predictions depending on the radiation quality.

Modelling the HPRT-gene mutation induction of particle beams: systematic in vitro data collection, analysis and microdosimetric kinetic model implementation

Objective. Since the early years, particle therapy treatments have been associated with concerns for late toxicities, especially secondary cancer risk (SCR). Nowadays, this concern is related to patients for whom long-term survival is expected (e.g. breast cancer, lymphoma, paediatrics). In the aim to contribute to this research, we present a dedicated statistical and modelling analysis aiming at improving our understanding of the RBE for mutation induction ( RBE M ˜ ) for different particle species. Approach. We built a new database based on a systematic collection of RBE data for mutation assays of the gene encoding for the purine salvage enzyme hypoxanthine-guanine phosphoribosyltransferase from literature (105 entries, distributed among 3 cell lines and 16 particle species). The data were employed to perform statistical and modelling analysis. For the latter, we adapted the microdosimetric kinetic model (MKM) to describe the mutagenesis in analogy to lethal lesion induction. Main results. Correlation analysis between RBE for survival (RBES) and RBE M ˜ reveals significant correlation between these two quantities (ρ = 0.86, p < 0.05). The correlation gets stronger when looking at subsets of data based on cell line and particle species. We also show that the MKM can be successfully employed to describe RBE M ˜ , obtaining comparably good agreement with the experimental data. Remarkably, to improve the agreement with experimental data the MKM requires, consistently in all the analysed cases, a reduced domain size for the description of mutation induction compared to that adopted for survival. Significance. We were able to show that RBES and RBE M ˜ are strongly related quantities. We also showed for the first time that the MKM could be successfully applied to the description of mutation induction, representing an endpoint different from the more traditional cell killing. In analogy to the RBES, RBE M ˜ can be implemented into treatment planning system evaluations.

Impact of DNA Repair Kinetics and Dose Rate on RBE Predictions in the UNIVERSE

Accurate knowledge of the relative biological effectiveness (RBE) and its dependencies is crucial to support modern ion beam therapy and its further development. However, the influence of different dose rates of the reference radiation and ion beam are rarely considered. The ion beam RBE-model within our "UNIfied and VERSatile bio response Engine" (UNIVERSE) is extended by including DNA damage repair kinetics to investigate the impact of dose-rate effects on the predicted RBE. It was found that dose-rate effects increase with dose and biological effects saturate at high dose-rates, which is consistent with data- and model-based studies in the literature. In a comparison with RBE measurements from a high dose in-vivo study, the predictions of the presented modification were found to be improved in comparison to the previous version of UNIVERSE and existing clinical approaches that disregard dose-rate effects. Consequently, DNA repair kinetics and the different dose rates applied by the reference and ion beams might need to be considered in biophysical models to accurately predict the RBE. Additionally, this study marks an important step in the further development of UNIVERSE, extending its capabilities in giving theoretical guidance to support progress in ion beam therapy.

Biological Dose Optimization for Particle Arc Therapy using Helium and Carbon Ions

PURPOSE

To present biological dose optimization for particle arc therapy using helium and carbon ions.

METHODS

Treatment plan planning and optimization procedures were developed for spot-scanning hadron arc (SHArc) delivery using the RayStation TPS and a GPU-accelerated dose engine (^†TPS-XXX). The SHArc optimization algorithm is applicable for charged particle beams and determines angle-dependencies for spot/energy selection with three main initiatives: i) achieve standard clinical optimization goals and constraints for target and OARs, ii) target dose robustness and iii) increasing LET in the target volume. Three patient cases previously treated at the ^†INSTITUTION-XXX were selected for evaluation of conventional versus arc delivery for the two clinical particle beams (helium [⁴He] and carbon [¹²C] ions): glioblastoma, prostate-adenocarcinoma and skull-base chordoma. Biological dose and dose-averaged linear energy transfer (LET_d) distributions for SHArc were evaluated against conventional planning techniques (VMAT and IMPT_2F) applying the modified microdosimetric kinetic model (mMKM) for considering bio-effect with (α/β)_x=2Gy. Clinical viability and deliverability were assessed via evaluation of plan quality, robustness and irradiation time.

RESULTS

For all investigated patient cases, SHArc treatment optimizations met planning goals and constraints for target coverage and OARs, exhibiting acceptable target coverage and reduced normal tissue volumes with effective dose >10GyRBE compared to conventional 2F planning. For carbon ions, LET_d was increased in the target volume from ∼40-60keV/µm to ∼80-140keV/µm for SHArc compared to conventional treatments. Favorable LET_d distributions were possible with the SHArc approach, with maximum LET_d in CTV/GTV and potential reductions of high-LET regions in normal tissues and OARs. Compared to VMAT, SHArc affords substantial reductions in normal tissue dose (40-70%).

CONCLUSION

SHArc therapy offers potential treatment benefits such as increased normal tissue sparing from higher doses >10GyRBE, enhanced target LET_d, and potential reduction in high-LET components in OARs. Findings justify further development of robust SHArc treatment planning towards potential clinical translation.

Tumor radioresistance caused by radiation-induced changes of stem-like cell content and sub-lethal damage repair capability

Cancer stem-like cells (CSCs) within solid tumors exhibit radioresistance, leading to recurrence and distant metastasis after radiotherapy. To experimentally study the characteristics of CSCs, radioresistant cell lines were successfully established using fractionated X-ray irradiation. The fundamental characteristics of CSCs in vitro have been previously reported; however, the relationship between CSC and acquired radioresistance remains uncertain. To efficiently study this relationship, we performed both in vitro experiments and theoretical analysis using a cell-killing model. Four types of human oral squamous carcinoma cell lines, non-radioresistant cell lines (SAS and HSC2), and radioresistant cell lines (SAS-R and HSC2-R), were used to measure the surviving fraction after single-dose irradiation, split-dose irradiation, and multi-fractionated irradiation. The SAS-R and HSC2-R cell lines were more positive for one of the CSC marker aldehyde dehydrogenase activity than the corresponding non-radioresistant cell lines. The theoretical model analysis showed that changes in both the experimental-based ALDH (+) fractions and DNA repair efficiency of ALDH (-) fractions (i.e., sub-lethal damage repair) are required to reproduce the measured cell survival data of non-radioresistant and radioresistant cell lines. These results suggest that the enhanced cell recovery in SAS-R and HSC2-R is important when predicting tumor control probability in radiotherapy to require a long dose-delivery time; in other words, intensity-modulated radiation therapy is ideal. This work provides a precise understanding of the mechanism of radioresistance, which is induced after irradiation of cancer cells.

Cell Survival Computation via the Generalized Stochastic Microdosimetric Model (GSM2); Part I: The Theoretical Framework

The current article presents the first application of the Generalized Stochastic Microdosimetric Model (GSM2) for computing explicitly a cell survival curve. GSM2 is a general probabilistic model that predicts the kinetic evolution of DNA damages taking full advantage of a microdosimetric description of a radiation energy deposition. We show that, despite the high generality and flexibility of GSM2, an explicit form for the survival fraction curve predicted by the GSM2 is achievable. We illustrate how several correction terms typically added a posteriori in existing radiobiological models to improve the prediction accuracy, are naturally included into GSM2. Among the most relevant features of the survival curve derived from GSM2 and presented in this article, is the linear-quadratic behavior at low doses and a purely linear trend for high doses. The study also identifies and discusses the connections between GSM2 and existing cell survival models, such as the Microdosimetric Kinetic Model (MKM) and the Multi-hit model. Several approximations to predict cell survival in different irradiation regimes are also introduced to include intercellular non-Poissonian behaviors.

Impact of a spatially dependent dose delivery time structure on the biological effectiveness of scanning proton therapy

PURPOSE

In the scanning beam delivery of protons, different portions of the target are irradiated with different linear energy transfer protons with various time intervals and irradiation times. This research aimed to evaluate the spatially dependent biological effectiveness of protracted irradiation in scanning proton therapy.

METHODS

One and two parallel opposed fields plans were created in water phantom with the prescribed dose of 2 Gy. Three scenarios (instantaneous, continuous, and layered scans) were used with the corresponding beam delivery models. The biological dose (physical dose × relative biological effectiveness) was calculated using the linear quadratic model and the theory of dual radiation action to quantitatively evaluate the dose delivery time effect. In addition, simulations using clinical plans (postoperative seminoma and prostate tumor cases) were conducted to assess the impact of the effects on the dose volume histogram parameters and homogeneity coefficient (HC) in targets.

RESULTS

In a single-field plan of water phantom, when the treatment time was 19 min, the layered-scan scenario showed a decrease of <0.2% (almost 3.3%) in the biological dose from the plan on the distal (proximal) side because of the high (low) dose rate. This is in contrast to the continuous scenario, where the biological dose was almost uniformly decreased over the target by approximately 3.3%. The simulation with clinical geometry showed that the decrease rates in D_99% were 0.9% and 1.5% for every 10 min of treatment time prolongation for postoperative seminoma and prostate tumor cases, respectively, whereas the increase rates in HC were 0.7% and 0.2%.

CONCLUSIONS

In protracted irradiation in scanning proton therapy, the spatially dependent dose delivery time structure in scanning beam delivery can be an important factor for accurate evaluation of biological effectiveness.

Adaptation of stochastic microdosimetric kinetic model to hypoxia for hypo-fractionated multi-ion therapy treatment planning

For hypo-fractionated multi-ion therapy (HFMIT), the stochastic microdosimetric kinetic (SMK) model had been developed to estimate the biological effectiveness of radiation beams with wide linear energy transfer (LET) and dose ranges. The HFMIT will be applied to radioresistant tumors with oxygen-deficient regions. The response of cells to radiation is strongly dependent on the oxygen condition in addition to radiation type, LET and absorbed dose. This study presents an adaptation of the SMK model to account for oxygen-pressure dependent cell responses, and develops the oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model. In the model, following assumptions were made: the numbers of radiation-induced sublethal lesions (double-strand breaks) are reduced due to lack of oxygen, and the numbers of oxygen-mediated lesions are reduced for radiation with high LET. The model parameters were determined by fitting survival data under aerobic and anoxic conditions for human salivary gland tumor cells and V79 cells exposed to helium-, carbon-, and neon-ion beams over the LET range of 18.5-654.0 keVμm^-1. The OSMK model provided good agreement with the experimental survival data of the cells with determination coefficients >0.9. In terms of oxygen enhancement ratio, the OSMK model reproduced the experimental data behavior, including slight dependence on particle type at the same LET. The OSMK model was then implemented into the in-house treatment planning software for the HFMIT to validate its applicability in clinical practice. A treatment plan with helium- and neon-ion beams was made for a pancreatic cancer case assuming an oxygen-deficient region within the tumor. The biological optimization based on the OSMK model preferentially placed the neon-ion beam to the hypoxic region, while it placed both helium- and neon-ion beams to the surrounding normoxic region. The OSMK model offered the accuracy and usability required for hypoxia-based biological optimization in HFMIT treatment planning.

Generalized stochastic microdosimetric model: The main formulation

The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (GSM^{2}), to describe biological damage induced by ionizing radiation. Starting from the microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by a given radiation to a cell nucleus. The resulting probability distribution is not required to satisfy any a priori conditions. After the initial assumption of instantaneous irradiation, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of GSM^{2}. Development of GSM^{2} can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities.

Radiobiological effects of the interruption time with Monte Carlo Simulation on multiple fields in photon beams

PURPOSE

The interruption time is the irradiation interruption that occurs at sites and operations such as the gantry, collimator, couch rotation, and patient setup within the field in radiotherapy. However, the radiobiological effect of prolonging the treatment time by the interruption time for tumor cells is little evaluated. We investigated the effect of the interruption time on the radiobiological effectiveness with photon beams based on a modified microdosimetric kinetic (mMK) model.

METHODS

The dose-mean lineal energy y_D (keV/µm) of 6-MV photon beams was calculated by the particle and heavy ion transport system (PHITS). We set the absorbed dose to 2 or 8 Gy, and the interruption time (τ) was set to 1, 3, 5, 10, 30, and 60 min. The biological parameters such as α_0, β_0, and DNA repair constant rate (a + c) values were acquired from a human non-small-cell lung cancer cell line (NCI-H460) for the mMK model. We used two-field and four-field irradiation with a constant dose rate (3 Gy/min); the photon beams were paused for interruption time τ. We calculated the relative biological effectiveness (RBE) to evaluate the interruption time's effect compared with no interrupted as a reference.

RESULTS

The y_D of 6-MV photon beams was 2.32 (keV/µm), and there was little effect by changing the water depth (standard deviation was 0.01). The RBE with four-field irradiation for 8 Gy was decreased to 0.997, 0.975, 0.900, and 0.836 τ = 1, 10, 30, 60 min, respectively. In addition, the RBE was affected by the repair constant rate (a + c) value, the greater the decrease in RBE with the longer the interruption time when the (a + c) value was large.

CONCLUSION

The ~10-min interruption of 6-MV photon beams did not significantly impact the radiobiological effectiveness, since the RBE decrease was <3%. Nevertheless, the RBE's effect on tumor cells was decreased about 30% by increasing the 60 min interruption time at 8 Gy with four-field irradiation. It is thus necessary to make the interruption time as short as possible.

The impact of dose delivery time on biological effectiveness in proton irradiation with various biological parameters

PURPOSE

The purpose of this study is to evaluate the sublethal damage (SLD) repair effect in prolonged proton irradiation using the biophysical model with various cell-specific parameters of (α/β)_x and T_1/2 (repair half time). At present, most of the model-based studies on protons have focused on acute radiation, neglecting the reduction in biological effectiveness due to SLD repair during the delivery of radiation. Nevertheless, the dose-rate dependency of biological effectiveness may become more important as advanced treatment techniques, such as hypofractionation and respiratory gating, come into clinical practice, as these techniques sometimes require long treatment times. Also, while previous research using the biophysical model revealed a large repair effect with a high physical dose, the dependence of the repair effect on cell-specific parameters has not been evaluated systematically.

METHODS

Biological dose [relative biological effectiveness (RBE) × physical dose] calculation with repair included was carried out using the linear energy transfer (LET)-dependent linear-quadratic (LQ) model combined with the theory of dual radiation action (TDRA). First, we extended the dose protraction factor in the LQ model for the arbitrary number of different LET proton irradiations delivered sequentially with arbitrary time lags, referring to the TDRA. Using the LQ model, the decrease in biological dose due to SLD repair was systematically evaluated for spread-out Bragg peak (SOBP) irradiation in a water phantom with the possible ranges of both (α/β)_x and repair parameters ((α/β)_x  = 1-15 Gy, T_1/2  = 0-90 min). Then, to consider more realistic irradiation conditions, clinical cases of prostate, liver, and lung tumors were examined with the cell-specific parameters for each tumor obtained from the literature. Biological D_99% and biological dose homogeneity coefficient (HC) were calculated for the clinical target volumes (CTVs), assuming dose-rate structures with a total irradiation time of 0-60 min.

RESULTS

The differences in the cell-specific parameters resulted in considerable variation in the repair effect. The biological dose reduction found at the center of the SOBP with 30 min of continuous irradiation varied from 1.13% to 14.4% with a T_1/2 range of 1-90 min when (α/β)_x is fixed as 10 Gy. It varied from 2.3% to 6.8% with an (α/β)_x range of 1-15 Gy for a fixed value of T_1/2  = 30 min. The decrease in biological D_99% per 10 min was 2.6, 1.2, and 3.0% for the prostate, liver, and lung tumor cases, respectively. The value of the biological D_99% reduction was neither in the order of (α/β)_x nor prescribed dose, but both comparably contributed to the repair effect. The variation of HC was within the range of 0.5% for all cases; therefore, the dose distribution was not distorted.

CONCLUSION

The reduction in biological dose caused by the SLD repair largely depends on the cell-specific parameters in addition to the physical dose. The parameters should be considered carefully in the evaluation of the repair effect in prolonged proton irradiation.

Biological dose-enhancement analysis with Monte Carlo simulation for Lipiodol for photon beams

Background

Previously, the physical dose-enhancement factor (D_physEF) enhancement was introduced. However, the dose enhancement considering the biological effectiveness was not shown.

Purpose

The aim of the current study was to evaluate the biological dose-enhancement factor (D_bioEF) by the dose rate and to compare the D_physEF and the D_bioEF in Lipiodol for liver Stereotactic Body Radiation Therapy (SBRT).

Materials and methods

Flattening-filter-free (FFF) 6-MV (6MVX) and 10MVX beams were delivered by TrueBeam. A virtual inhomogeneity phantom and a liver SBRT patient-treatment plan were used. The D_physEF and lineal energy distribution ( y ) distribution was calculated from Monte Carlo simulations. Using a microdosimetric-kinetic (MK) model that is estimated based on the linear-quadratic formula for Lipiodol using human liver hepatocellular cells (HepG2), the biological dose and biological dose enhancement factor (D_bioEF) were calculated. The dose rate in the simulation was changed from 0.1 to 24 Gy/min.

Results

The D_bioEF (DR:2Gy/min) and D_physEF with 10MVX FFF beam were 23.2% and 19.1% at maximum and 12.8% and 11.1% on average in the Lipiodol. In the comparison of the D_bioEF between 0.1-24 Gy/min, the D_bioEF was 21.2% and 11.1% with 0.1 Gy/min for 6MVX and 10 MVX, respectively. The D_bioEF was larger than DEF for the 6MVX and 10MVX FFF beams. In clinical cases with the 10MVX FFF beam, the D_bioEF and D_physEF in the Lipiodol region can increase the in-tumor dose by approximately 11% and 10%, respectively, without increasing the dose to normal tissue.

Conclusions

The lower-energy and higher-dose-rate beams were contributed to the biological dose. The Lipiodol caused the enhancement of the physical dose and biological effectiveness.

Advances in knowledge

The biological dose enhancement (D_bioEF) should be considered in the high-density material such as the Lipiodol.

Dose compensation based on biological effectiveness due to interruption time for photon radiation therapy

OBJECTIVE

To evaluate the biological effectiveness of dose associated with interruption time; and propose the dose compensation method based on biological effectiveness when an interruption occurs during photon radiation therapy.

METHODS

The lineal energy distribution for human salivary gland tumor was calculated by Monte Carlo simulation using a photon beam. The biological dose (D_bio) was estimated using the microdosimetric kinetic model. The dose compensating factor with the physical dose for the difference of the D_bio with and without interruption (Δ) was derived. The interruption time (τ) was varied to 0.1, 0.2, 0.3, 0.4, 0.5, 1, 2, 3, 4, 5, 10, 20, 30, 40, 50, 75, and 120 min. The dose per fraction and dose rate varied from 2 to 8 Gy and 0.1 to 24 Gy/min, respectively.

RESULTS

The maximum Δ with 1 Gy/min occurred when the interruption occurred at half the dose. The Δ with 1 Gy/min at half of the dose was over 3% for τ >= 20 min for 2 Gy, τ = 10 min for 5 Gy, and τ = 10 min for 8 Gy. The maximum difference of the Δ due to the dose rate was within 3% for 2 and 5 Gy, and achieving values of 4.0% for 8 Gy. The dose compensating factor was larger with a high dose per fraction and high-dose rate beams.

CONCLUSION

A loss of biological effectiveness occurs due to interruption. Our proposal method could correct for the unexpected decrease of the biological effectiveness caused by interruption time.

ADVANCES IN KNOWLEDGE

For photon radiotherapy, the interruption causes the sublethal damage repair. The current study proposed the dose compensation method for the decrease of the biological effect by the interruption.

A Model for Estimating Dose-Rate Effects on Cell-Killing of Human Melanoma after Boron Neutron Capture Therapy

Boron neutron capture therapy (BNCT) is a type of radiation therapy for eradicating tumor cells through a ¹⁰B(n,α)⁷Li reaction in the presence of ¹⁰B in cancer cells. When delivering a high absorbed dose to cancer cells using BNCT, both the timeline of ¹⁰B concentrations and the relative long dose-delivery time compared to photon therapy must be considered. Changes in radiosensitivity during such a long dose-delivery time can reduce the probability of tumor control; however, such changes have not yet been evaluated. Here, we propose an improved integrated microdosimetric-kinetic model that accounts for changes in microdosimetric quantities and dose rates depending on the ¹⁰B concentration and investigate the cell recovery (dose-rate effects) of melanoma during BNCT irradiation. The integrated microdosimetric–kinetic model used in this study considers both sub-lethal damage repair and changes in microdosimetric quantities during irradiation. The model, coupled with the Monte Carlo track structure simulation code of the Particle and Heavy Ion Transport code System, shows good agreement with in vitro experimental data for acute exposure to ⁶⁰Co γ-rays, thermal neutrons, and BNCT with ¹⁰B concentrations of 10 ppm. This indicates that microdosimetric quantities are important parameters for predicting dose-response curves for cell survival under BNCT irradiations. Furthermore, the model estimation at the endpoint of the mean activation dose exhibits a reduced impact of cell recovery during BNCT irradiations with high linear energy transfer (LET) compared to ⁶⁰Co γ-rays irradiation with low LET. Throughout this study, we discuss the advantages of BNCT for enhancing the killing of cancer cells with a reduced dose-rate dependency. If the neutron spectrum and the timelines for drug and dose delivery are provided, the present model will make it possible to predict radiosensitivity for more realistic dose-delivery schemes in BNCT irradiations.

A theoretical cell-killing model to evaluate oxygen enhancement ratios at DNA damage and cell survival endpoints in radiation therapy

Radio-resistance induced under low oxygen pressure plays an important role in malignant progression in fractionated radiotherapy. For the general approach to predict cell killing under hypoxia, cell-killing models (e.g. the Linear-Quadratic model) have to be fitted to in vitro experimental survival data for both normoxia and hypoxia to obtain the oxygen enhancement ratio (OER). In such a case, model parameters for every oxygen condition needs to be considered by model-fitting approaches. This is inefficient for fractionated irradiation planning. Here, we present an efficient model for fractionated radiotherapy the integrated microdosimetric-kinetic model including cell-cycle distribution and the OER at DNA double-strand break endpoint (OER_DSB). The cell survival curves described by this model can reproduce the in vitro experimental survival data for both acute and chronic low oxygen concentrations. The OER_DSB used for calculating cell survival agrees well with experimental DSB ratio of normoxia to hypoxia. The important parameters of the model are oxygen pressure and cell-cycle distribution, which enables us to predict cell survival probabilities under chronic hypoxia and chronic anoxia. This work provides biological effective dose (BED) under various oxygen conditions including its uncertainty, which can contribute to creating fractionated regimens for multi-fractionated radiotherapy. If the oxygen concentration in a tumor can be quantified by medical imaging, the present model will make it possible to estimate the cell-killing and BED under hypoxia in more realistic intravital situations.

Intensity Modulated Radiation Fields Induce Protective Effects and Reduce Importance of Dose-Rate Effects

In advanced radiotherapy, intensity modulated radiation fields and complex dose-delivery are utilized to prescribe higher doses to tumours. Here, we investigated the impact of modulated radiation fields on radio-sensitivity and cell recovery during dose delivery. We generated experimental survival data after single-dose, split-dose and fractionated irradiation in normal human skin fibroblast cells (AGO1522) and human prostate cancer cells (DU145). The dose was delivered to either 50% of the area of a T25 flask containing the cells (half-field) or 100% of the flask (uniform-field). We also modelled the impact of dose-rate effects and intercellular signalling on cell-killing. Applying the model to the survival data, it is found that (i) in-field cell survival under half-field exposure is higher than uniform-field exposure for the same delivered dose; (ii) the importance of sub-lethal damage repair (SLDR) in AGO1522 cells is reduced under half-field exposure; (iii) the yield of initial DNA lesions measured with half-field exposure is smaller than that with uniform-field exposure. These results suggest that increased cell survival under half-field exposure is predominantly attributed not to rescue effects (increased SLDR) but protective effects (reduced induction of initial DNA lesions). In support of these protective effects, the reduced DNA damage leads to modulation of cell-cycle dynamics, i.e., less G₁ arrest 6 h after irradiation. These findings provide a new understanding of the impact of dose-rate effects and protective effects measured after modulated field irradiation.

Effect of Irradiation Time on Biological Effectiveness and Tumor Control Probability in Proton Therapy

PURPOSE

The biological effectiveness of proton beams may decrease with irradiation time because of sublethal damage repair (SLDR). The purpose of this study is to systematically evaluate this effect in hypofractionated proton therapy for various target sizes, depths, and prescribed doses per fraction.

METHODS AND MATERIALS

Plans with a single spread-out Bragg peak beam were created using a constant relative biological effectiveness (RBE) of 1.1 to cover targets of 6 different sizes located at 3 different depths in water. Biological doses of 2, 3, 5, 10, and 20 Gy (RBE) were prescribed to the targets. First, to investigate the depth variation of the biological effectiveness, the biological dose in instantaneous irradiation was recalculated based on the microdosimetric kinetic model. SLDR was then taken into account in the microdosimetric kinetic model during treatments to obtain the irradiation time-dependent biological effectiveness for irradiation time T of 5 to 60 minutes and beam interruption time τ of 0 to 60 minutes. The tumor control probabilities were calculated for single-fraction proton therapy fields of different Ts and τs, and the curative doses were evaluated at a tumor control probability of 90%.

RESULTS

The biological effectiveness decreased with longer T and τ and higher prescribed dose. The maximum decrease in the biological effectiveness was 21% with a 20 Gy (RBE) prescribed dose. In single-fraction proton therapy, the curative dose increased linearly by approximately 33% to 35% with the increase of T from 0 to 60 minutes.

CONCLUSIONS

The biological effectiveness varies largely with T and τ because of SLDR during treatments. This effect was pronounced for high prescribed doses per fraction. Thus, the effect of SLDR needs to be considered in hypofractionated and single-fraction proton therapies in relation to size and depth of the target.

DOSE-RATE AND CELL-KILLING SENSITIVITY OF HIGH-LINEAR ENERGY TRANSFER ION BEAM

It is believed that the dose-rate of radiation will have an influence on cell sensitivity. The dose-rate effects on cell survival can be expressed by the change of the β term in the linear quadratic model. The value at a high-dose-rate decreases below 60 Gy/h and reaches zero at 0.2 Gy/h or less for photons. However, the effect for a high-LET ion-beam is not well known. At HIMAC, cells were exposed to 70 keV/μm carbon-ion beams at different dose-rates between 0.5 and 600 Gy/h at room temperature. The β values for all survival curves show no significant differences among the dose-rates tested for HSG, V79 and CHO cells. Changing the ion-beam dose-rate had no effect on cell survival. This suggests that high-LET particle beams, such as galactic cosmic rays, may not exhibit a dose-rate effect on cell survival. Low-dose-rate radiation showed an effect similar to high-dose-rate radiation.

Report of the AAPM TG-256 on the relative biological effectiveness of proton beams in radiation therapy

The biological effectiveness of proton beams relative to photon beams in radiation therapy has been taken to be 1.1 throughout the history of proton therapy. While potentially appropriate as an average value, actual relative biological effectiveness (RBE) values may differ. This Task Group report outlines the basic concepts of RBE as well as the biophysical interpretation and mathematical concepts. The current knowledge on RBE variations is reviewed and discussed in the context of the current clinical use of RBE and the clinical relevance of RBE variations (with respect to physical as well as biological parameters). The following task group aims were designed to guide the current clinical practice: Assess whether the current clinical practice of using a constant RBE for protons should be revised or maintained. Identifying sites and treatment strategies where variable RBE might be utilized for a clinical benefit. Assess the potential clinical consequences of delivering biologically weighted proton doses based on variable RBE and/or LET models implemented in treatment planning systems. Recommend experiments needed to improve our current understanding of the relationships among in vitro, in vivo, and clinical RBE, and the research required to develop models. Develop recommendations to minimize the effects of uncertainties associated with proton RBE for well-defined tumor types and critical structures.

Report of a National Cancer Institute special panel: Characterization of the physical parameters of particle beams for biological research

PURPOSE

To define the physical parameters needed to characterize a particle beam in order to allow intercomparison of different experiments performed using different ions at the same facility and using the same ion at different facilities.

METHODS

At the request of the National Cancer Institute (NCI), a special panel was convened to review the current status of the field and to provide suggested metrics for reporting the physical parameters of particle beams to be used for biological research. A set of physical parameters and measurements that should be performed by facilities and understood and reported by researchers supported by NCI to perform pre-clinical radiobiology and medical physics of heavy ions were generated.

RESULTS

Standard measures such as radiation delivery technique, beam modifiers used, nominal energy, field size, physical dose and dose rate should all be reported. However, more advanced physical measurements, including detailed characterization of beam quality by microdosimetric spectrum and fragmentation spectra, should also be established and reported. Details regarding how such data should be incorporated into Monte Carlo simulations and the proper reporting of simulation details are also discussed.

CONCLUSIONS

In order to allow for a clear relation of physical parameters to biological effects, facilities and researchers should establish and report detailed physical characteristics of the irradiation beams utilized including both standard and advanced measures. Biological researchers are encouraged to actively engage facility staff and physicists in the design and conduct of experiments. Modeling individual experimental setups will allow for the reporting of the uncertainties in the measurement or calculation of physical parameters which should be routinely reported.

A comparison of mechanism-inspired models for particle relative biological effectiveness (RBE)

BACKGROUND AND SIGNIFICANCE

The application of heavy ion beams in cancer therapy must account for the increasing relative biological effectiveness (RBE) with increasing penetration depth when determining dose prescriptions and organ at risk (OAR) constraints in treatment planning. Because RBE depends in a complex manner on factors such as the ion type, energy, cell and tissue radiosensitivity, physical dose, biological endpoint, and position within and outside treatment fields, biophysical models reflecting these dependencies are required for the personalization and optimization of treatment plans.

AIM

To review and compare three mechanism-inspired models which predict the complexities of particle RBE for various ion types, energies, linear energy transfer (LET) values and tissue radiation sensitivities.

METHODS

The review of models and mechanisms focuses on the Local Effect Model (LEM), the Microdosimetric-Kinetic (MK) model, and the Repair-Misrepair-Fixation (RMF) model in combination with the Monte Carlo Damage Simulation (MCDS). These models relate the induction of potentially lethal double strand breaks (DSBs) to the subsequent interactions and biological processing of DSB into more lethal forms of damage. A key element to explain the increased biological effectiveness of high LET ions compared to MV x rays is the characterization of the number and local complexity (clustering) of the initial DSB produced within a cell. For high LET ions, the spatial density of DSB induction along an ion's trajectory is much greater than along the path of a low LET electron, such as the secondary electrons produced by the megavoltage (MV) x rays used in conventional radiation therapy. The main aspects of the three models are introduced and the conceptual similarities and differences are critiqued and highlighted. Model predictions are compared in terms of the RBE for DSB induction and for reproductive cell survival.

RESULTS AND CONCLUSIONS

Comparisons of the RBE for DSB induction and for cell survival are presented for proton (¹ H), helium (⁴ He), and carbon (¹² C) ions for the therapeutically most relevant range of ion beam energies. The reviewed models embody mechanisms of action acting over the spatial scales underlying the biological processing of potentially lethal DSB into more lethal forms of damage. Differences among the number and types of input parameters, relevant biological targets, and the computational approaches among the LEM, MK and RMF models are summarized and critiqued. Potential experiments to test some of the seemingly contradictory aspects of the models are discussed.

Relative biological effectiveness study of Lipiodol based on microdosimetric-kinetic model

OBJECTIVES

We examine the contrast agent Lipiodol effect on the relative biological effectiveness (RBE) values for flattening filter free (FFF) and flattening filter (FF) beams of 6 MV-Xray (6 MVX) and 10 MVX.

METHODS

Lipiodol was placed at 5 cm depth in water. According to the microdosimetric kinetic model, the RBE values for killing the human liver hepatocellular cells were calculated from dose and lineal energy (yd(y)) from Monte Carlo simulations. RBE_200kVX and RBE_Co were defined as the ratios of dose using reference radiation (200 kVX, Co-ɤ) to the dose of test radiation (FFF and FF beams for 6 MV and 10 MV) to produce the same biological effects. The dose enhancement RBE (RBE_DE) was defined as the ratios of a dose without Lipiodol to with Lipiodol using to produce the same biological effects. The dose needed to achieve 10% (D_10%) and 1% cell survival (D_1%) was evaluated by cell surviving fraction (SF) formula.

RESULTS

The deviation of mean y‾_D values with and without Lipiodol were 3.9-4.8% for 6 MVX and 3.5-3.6% for 10 MVX. The RBE_200kVX and RBE_Co with Lipiodol were larger than that without Lipiodol. The RBE_DE was larger for FFF beam than for FF beam. The deviation of RBE_DE for FFF and FF beams of 6 MVX was larger than that of 10 MVX.

CONCLUSION

The presence of Lipiodol seemed to locally increase the absorbed dose and to also cause an enhancement of the relative biological effectiveness.

Investigation of dose-rate effects and cell-cycle distribution under protracted exposure to ionizing radiation for various dose-rates

During exposure to ionizing radiation, sub-lethal damage repair (SLDR) competes with DNA damage induction in cultured cells. By virtue of SLDR, cell survival increases with decrease of dose-rate, so-called dose-rate effects (DREs). Here, we focused on a wide dose-rate range and investigated the change of cell-cycle distribution during X-ray protracted exposure and dose-response curves via hybrid analysis with a combination of in vitro experiments and mathematical modelling. In the course of flow-cytometric cell-cycle analysis and clonogenic assays, we found the following responses in CHO-K1 cells: (1) The fraction of cells in S phase gradually increases during 6 h exposure at 3.0 Gy/h, which leads to radio-resistance. (2) Slight cell accumulation in S and G2/M phases is observed after exposure at 6.0 Gy/h for more than 10 hours. This suggests that an increase of SLDR rate for cells in S phase during irradiation may be a reproducible factor to describe changes in the dose-response curve at dose-rates of 3.0 and 6.0 Gy/h. By re-evaluating cell survival for various dose-rates of 0.186-60.0 Gy/h considering experimental-based DNA content and SLDR, it is suggested that the change of S phase fraction during irradiation modulates the dose-response curve and is possibly responsible for some inverse DREs.

Investigation of dose-rate effects and cell-cycle distribution under protracted exposure to ionizing radiation for various dose-rates

During exposure to ionizing radiation, sub-lethal damage repair (SLDR) competes with DNA damage induction in cultured cells. By virtue of SLDR, cell survival increases with decrease of dose-rate, so-called dose-rate effects (DREs). Here, we focused on a wide dose-rate range and investigated the change of cell-cycle distribution during X-ray protracted exposure and dose-response curves via hybrid analysis with a combination of in vitro experiments and mathematical modelling. In the course of flow-cytometric cell-cycle analysis and clonogenic assays, we found the following responses in CHO-K1 cells: (1) The fraction of cells in S phase gradually increases during 6 h exposure at 3.0 Gy/h, which leads to radio-resistance. (2) Slight cell accumulation in S and G₂/M phases is observed after exposure at 6.0 Gy/h for more than 10 hours. This suggests that an increase of SLDR rate for cells in S phase during irradiation may be a reproducible factor to describe changes in the dose-response curve at dose-rates of 3.0 and 6.0 Gy/h. By re-evaluating cell survival for various dose-rates of 0.186-60.0 Gy/h considering experimental-based DNA content and SLDR, it is suggested that the change of S phase fraction during irradiation modulates the dose-response curve and is possibly responsible for some inverse DREs.

Adaptation of stochastic microdosimetric kinetic model for charged-particle therapy treatment planning

The microdosimetric kinetic (MK) model underestimates the cell-survival fractions for high linear energy transfer (LET) and high dose irradiations. To address the issue, some researchers previously extended the MK model to the stochastic microdosimetric kinetic (SMK) model. In the SMK model, the radiation induced cell-survival fractions were estimated from the specific energies z _d and z _n absorbed by a microscopic subnuclear structure domain and a cell nucleus, respectively. By taking the stochastic nature of z _n as well as that of z _d into account, the SMK model could reproduce the measured cell-survival fractions for radiations with wide LET and dose ranges. However, treatment planning based on the SMK model was unrealistic in clinical practice due to its long computation time and huge memory space required for the computation. In this study, we modified the SMK model to shorten the computation time and to reduce the memory space required for the computation. By using the dose-averaged cell-nucleus specific energy per event [Formula: see text] in the SMK formalism, the stochastic nature of z _n was reflected onto the estimated cell-survival fractions. The accuracy of the modified SMK model was examined through the comparison between the estimated and the measured survival fractions of human salivary gland tumor cells and V79 cells. We then implemented the modified SMK model into the in-house treatment planning software for scanned charged-particle therapy to validate its applicability in clinical practice. As examples, treatment plans of helium-, carbon-, and neon-ion beams were made for an orbital tumor case. The modified SMK model could reproduce the measured cell-survival fractions more accurately compared to the MK model especially for high-LET and high-dose irradiations. In summary, the modified SMK model offers the accuracy and simplicity required in treatment planning of scanned charged-particle therapy for wide LET and dose ranges.

Integrated Modelling of Cell Responses after Irradiation for DNA-Targeted Effects and Non-Targeted Effects

Intercellular communication after ionizing radiation exposure, so-called non-targeted effects (NTEs), reduces cell survival. Here we describe an integrated cell-killing model considering NTEs and DNA damage along radiation particle tracks, known as DNA-targeted effects (TEs) based on repair kinetics of DNA damage. The proposed model was applied to a series of experimental data, i.e., signal concentration, DNA damage kinetics, cell survival curve and medium transfer bystander effects (MTBEs). To reproduce the experimental data, the model considers the following assumptions: (i) the linear-quadratic (LQ) function as absorbed dose to express the hit probability to emit cell-killing signals, (ii) the potentially repair of DNA lesions induced by NTEs, and (iii) lower efficiency of repair for the damage in NTEs than that in TEs. By comparing the model results with experimental data, we found that signal-induced DNA damage and lower repair efficiency in non-hit cells are responsible for NTE-related repair kinetics of DNA damage, cell survival curve with low-dose hyper-radiosensitivity (HRS) and MTBEs. From the standpoint of modelling, the integrated cell-killing model with the LQ relation and a different repair function for NTEs provide a reasonable signal-emission probability and a new estimation of low-dose HRS linked to DNA repair efficiency.

Microdosimetric Modeling of Biological Effectiveness for Boron Neutron Capture Therapy Considering Intra- and Intercellular Heterogeneity in 10B Distribution

We here propose a new model for estimating the biological effectiveness for boron neutron capture therapy (BNCT) considering intra- and intercellular heterogeneity in 10B distribution. The new model was developed from our previously established stochastic microdosimetric kinetic model that determines the surviving fraction of cells irradiated with any radiations. In the model, the probability density of the absorbed doses in microscopic scales is the fundamental physical index for characterizing the radiation fields. A new computational method was established to determine the probability density for application to BNCT using the Particle and Heavy Ion Transport code System PHITS. The parameters used in the model were determined from the measured surviving fraction of tumor cells administrated with two kinds of 10B compounds. The model quantitatively highlighted the indispensable need to consider the synergetic effect and the dose dependence of the biological effectiveness in the estimate of the therapeutic effect of BNCT. The model can predict the biological effectiveness of newly developed 10B compounds based on their intra- and intercellular distributions, and thus, it can play important roles not only in treatment planning but also in drug discovery research for future BNCT.

Validation of the physical and RBE-weighted dose estimator based on PHITS coupled with a microdosimetric kinetic model for proton therapy

The microdosimetric kinetic model (MKM) is widely used for estimating relative biological effectiveness (RBE)-weighted doses for various radiotherapies because it can determine the surviving fraction of irradiated cells based on only the lineal energy distribution, and it is independent of the radiation type and ion species. However, the applicability of the method to proton therapy has not yet been investigated thoroughly. In this study, we validated the RBE-weighted dose calculated by the MKM in tandem with the Monte Carlo code PHITS for proton therapy by considering the complete simulation geometry of the clinical proton beam line. The physical dose, lineal energy distribution, and RBE-weighted dose for a 155 MeV mono-energetic and spread-out Bragg peak (SOBP) beam of 60 mm width were evaluated. In estimating the physical dose, the calculated depth dose distribution by irradiating the mono-energetic beam using PHITS was consistent with the data measured by a diode detector. A maximum difference of 3.1% in the depth distribution was observed for the SOBP beam. In the RBE-weighted dose validation, the calculated lineal energy distributions generally agreed well with the published measurement data. The calculated and measured RBE-weighted doses were in excellent agreement, except at the Bragg peak region of the mono-energetic beam, where the calculation overestimated the measured data by ~15%. This research has provided a computational microdosimetric approach based on a combination of PHITS and MKM for typical clinical proton beams. The developed RBE-estimator function has potential application in the treatment planning system for various radiotherapies.

Markov chain Monte Carlo analysis for the selection of a cell-killing model under high-dose-rate irradiation

PURPOSE

High-dose-rate irradiation with 6 MV linac x rays is a wide-spread means to treat cancer tissue in radiotherapy. The treatment planning relies on a mathematical description of surviving fraction (SF), such as the linear-quadratic model (LQM) formula. However, even in the case of high-dose-rate treatment, the repair kinetics of DNA damage during dose-delivery time plays a function in predicting the dose-SF relation. This may call the SF model selection into question when considering the dose-delivery time or dose-rate effects (DREs) in radiotherapy and in vitro cell experiments. In this study, we demonstrate the importance of dose-delivery time at high-dose-rate irradiations used in radiotherapy by means of Bayesian estimation.

METHODS

To evaluate the model selection for SF, three types of models, the LQM and two microdosimetric-kinetic models with and without DREs (MKM_DR and MKM) were applied to describe in vitroSF data (our work and references). The parameters in each model were evaluated by a Markov chain Monte Carlo (MCMC) simulation.

RESULTS

The MCMC analysis shows that the cell survival curve by the MKM_DR fits the experimental data the best in terms of the deviance information criterion (DIC). In the fractionated regimen with 30 fractions to a total dose of 60 Gy, the final cell survival estimated by the MKM_DR was higher than that by the LQM. This suggests that additional fractions are required for attaining the total dose equivalent to yield the same effect as the conventional regimen using the LQM in fractionated radiotherapy.

CONCLUSIONS

Damage repair during dose-delivery time plays a key role in precisely estimating cell survival even at a high dose rate in radiotherapy. Consequently, it was suggested that the cell-killing model without repair factor during a short dose-delivery time may overestimate actual cell killing in fractionated radiotherapy.

Modeling cell survival and change in amount of DNA during protracted irradiation

Hyper-radiosensitivity (HRS) is a well-known bioresponse under low-dose or low-dose-rate exposures. Although disorder of the DNA repair function, non-targeted effects and accumulation of cells in G2 have been experimentally observed, the mechanism for inducing HRS by long-term irradiation is still unclear. On the basis of biological experiments and a theoretical study, we have shown that change in the amount of DNA associated with accumulation of cells in G2 enhances radiosensitivity. To demonstrate continuous irradiation with 250 kVp X-rays, we adopted a fractionated regimen of 0.186 or 1.00 Gy per fraction at intervals of 1 h (i.e. 0.186 Gy/h, 1.00 Gy/h on average) to Chinese Hamster Ovary (CHO)-K1 cells. The change in the amount of DNA during irradiation was quantified by flow cytometric analysis with propidium iodide (PI). Concurrently, we attempted a theoretical evaluation of the DNA damage by using a microdosimetric-kinetic (MK) model that was modified to incorporate the change in the amount of DNA. Our experimental results showed that the fraction of the cells in G2/M phase increased by 6.7% with 0.186 Gy/h and by 22.1% with 1.00 Gy/h after the 12th irradiation. The MK model considering the change in amount of DNA during the irradiation exhibited a higher radiosensitivity at a high dose range, which could account for the experimental clonogenic survival. The theoretical results suggest that HRS in the high dose range is associated with an increase in the total amount of DNA during irradiation.

A Simpler Energy Transfer Efficiency Model to Predict Relative Biological Effect for Protons and Heavier Ions

The aim of this work is to predict relative biological effectiveness (RBE) for protons and clinically relevant heavier ions, by using a simplified semi-empirical process based on rational expectations and published experimental results using different ion species. The model input parameters are: Z (effective nuclear charge) and radiosensitivity parameters α_L and β_L of the control low linear energy transfer (LET) radiation. Sequential saturation processes are assumed for: (a) the position of the turnover point (LET_U) for the LET–RBE relationship with Z, and (b) the ultimate value of α at this point (α_U) being non-linearly related to α_L. Using the same procedure for β, on the logical assumption that the changes in β with LET, although smaller than α, are symmetrical with those of α, since there is symmetry of the fall off of LET–RBE curves with increasing dose, which suggests that LET_U must be identical for α and β. Then, using iso-effective linear quadratic model equations, the estimated RBE is scaled between α_U and α_L and between β_U and β_L from for any input value of Z, α_L, β_L, and dose. The model described is fitted to the data of Barendsen (alpha particles), Weyrather et al. (carbon ions), and Todd for nine different ions (deuterons to Argon), which include variations in cell surviving fraction and dose. In principle, this new system can be used to complement the more complex methods to predict RBE with LET such as the local effect and MKM models which already have been incorporated into treatment planning systems in various countries. It would be useful to have a secondary check to such systems, especially to alert clinicians of potential risks by relatively easy estimation of relevant RBEs. In clinical practice, LET values smaller than LET_U are mostly encountered, but the model extends to higher values beyond LET_U for other purposes such as radiation, protection, and astrobiology. Considerable further research is required, perhaps in a dedicated international laboratory, using a basket of different models to determine what the best system or combination of systems will be to make proton and ion beam radiotherapy as safe as possible and to produce the best possible clinical results.