Linear-quadratic Model Research Articles

An empirical model of carbon-ion relative biological effectiveness based on the linear correlation between radiosensitivity to photons and carbon ions.

To develop an empirical model to predict carbon ion (C-ion) relative biological effectiveness (RBE). 

Approach. We used published cell survival data comprising 360 cell line/energy combinations to characterize the linear energy transfer (LET) dependence of cell radiosensitivity parameters describing the dose required to achieve a given survival level, e.g. 5% (D5%), which are linearly correlated between photon and C-ion radiations. Based on the LET response of the metrics D5% and D37%, we constructed a model containing four free parameters that predicts cells' linear quadratic model (LQM) survival curve parameters for C-ions, αCand βC, from the reference LQM parameters for photons, αXand βX, for a given C-ion LET value. We fit our model's free parameters to the training dataset and assessed its accuracy via leave-one out cross-validation. We further compared our model to the local effect model (LEM) and the microdosimetric kinetic model (MKM) by comparing its predictions against published predictions made with those models for clinically relevant LET values in the range of 23-107 keV/μm. 

Main Results. Our model predicted C-ion RBE within ±7%-15% depending on cell line and dose which was comparable to LEM and MKM for the same conditions. 

Significance. Our model offers comparable accuracy to the LEM or MKM but requires fewer input parameters and is less computationally expensive and whose implementation is so simple we provide it coded into a spreadsheet. Thus, our model can serve as a pragmatic alternative to these mechanistic models in cases where cell-specific input parameters cannot be obtained, the models cannot be implemented, or for which their computational efficiency is paramount.

Equilibrium Control in Uncertain Linear Quadratic Differential Games with V-Jumps and State Delays: A Case Study on Carbon Emission Reduction

Uncertainty, time delays, and jumps often coexist in dynamic game problems due to the complexity of the environment. To address such issues, we can utilize uncertain delay differential equations with jumps to depict the dynamic changes in differential game problems that involve uncertain noise, delays, and jumps. In this paper, we first examine a linear quadratic differential game optimistic value problem within an uncertain environment characterized by jumps and delays. By applying the Z(x,y) transform, we convert the infinite-dimensional problem into a finite-dimensional one. We then demonstrate that the condition for the existence of a Nash equilibrium strategy is equivalent to the existence of solutions to two cross-coupled matrix Riccati equations. Furthermore, we explore the saddle point equilibrium strategy of the linear quadratic differential game optimistic value model and derive the corresponding saddle point equilibrium solution. Finally, we apply our results to solve a carbon emission reduction game problem.

Elevated α/β ratio after hypofractionated radiotherapy correlated with DNA damage repairment in an experimental model of prostate cancer.

Our previous study demonstrated that the linear quadratic model appeared to be not well-suited for high dose per fraction due to an observed increase in α/β ratio as the dose per fraction increased. To further validate this conclusion, we draw the cell survival curve to calculate the α/β ratio by the clone formation experiment and then convert the fractionated radiation dose into an equivalent single hypofractionated radiation dose comparing with that on the survival curve. Western Blot and laser confocal immunofluorescence were used to detect the expression of γ-H2AX and RAD51 after different fractionated modes of radiation. We constructed a murine xenograft model, and changes in transplanted tumor volume were used to evaluate the biological effects after different fractionated radiation. The results demonstrated that when fractionated radiation dose was converted into equivalent single hypofractionated radiation dose, the effectiveness of hypofractionated radiation was overestimated. If a larger α/β ratio was used, the discrepancy tended to become smaller. γ-H2AX was higher in 24h after a single high dose radiation than the continuous expression of the DNA repair marker RAD51. This implies more irreparable damage in a single high dose radiation compared with fractionated radiation. In the murine xenograft model, the effectiveness of hypofractionated radiation was also overestimated, and additional fractions of irradiation may be required. The conclusion is that after single hypofractionated radiation, the irreparable damage in cells increased (α value increased) and some repairable sublethal damage (β value) was converted into irreparable damage (α value). When α value increased and β value decreased, the ratio increased.

Breast cancer radiobiology: The renaissance of whole breast radiation fractionation (Review).

Breast cancer radiotherapy has evolved significantly, driven by decades of research into fractionation schedules aimed at optimizing treatment efficacy and minimizing toxicity. Initial trials such as NSABP B-06 and EBCTCG meta-analyses established the benefits of adjuvant whole-breast irradiation in reducing local recurrence and improving survival rates. The linear-quadratic (LQ) model provided a framework to understand tissue response to radiation, highlighting the importance of the α/β ratio in determining fractionation sensitivity. The present scoping review aimed to identify and describe hypofractionation regimens for whole breast radiotherapy and evaluate dose differences using the LQ model across proposed α/β ratios. A comprehensive PubMed search for clinical trials published since 2010 on hypo-fractionated regimens was performed. Studies discussing α/β ratios for breast cancer have been also searched. Data on dose, fractions and α/β ratios were collected, and biologically effective dose (BED) and equivalent dose in 2 Gy fractions were calculated. The coefficient of variation for BED varied with α/β ratios, showing the lowest variability for an α/β ratio of ~3 without tumor repopulation and increased with repopulation (BED-kT; k is a constant that depends on the repopulation rate of the tumor, and T is the total treatment time in days). Significant differences in BED variances were observed across α/β ratios (F-statistic 219.6, P<0.0001). START trials (P, A, and B) established α/β ratios of 3-4 Gy for breast cancer and normal tissues, confirming that hypofractionation is as effective as standard fractionation with potentially fewer late toxicities. Subsequent trials, such as FAST and FAST-Forward, demonstrated that ultra-hypofractionation is equivalent in tumor compared with conventional regimens. Further research is needed to gain a stronger understanding of radiobiological properties of breast cancer cells. Advances in radiotherapy technologies and the integration of biomarkers, radiomics and genomics are transforming treatment, moving towards precision medicine.

An in-silico study of conventional and FLASH radiotherapy iso-effectiveness: potential impact of radiolytic oxygen depletion on tumor growth curves and tumor control probability

Objective. This work aims to investigate the iso-effectiveness of conventional and FLASH radiotherapy on tumors through in-silico mathematical models. We focused on the role of radiolytic oxygen depletion (ROD), which has been argued as a possible factor to explain the FLASH effect.Approach. We used a spatiotemporal reaction-diffusion model, including ROD, to simulate tumor oxygenation and response. From those oxygen distributions we obtained surviving fractions (SFs) using the linear-quadratic (LQ) model with the oxygen enhancement ratios (OERs). We then employed the calculated SFs to describe the evolution of preclinical tumor volumes through a mathematical model of tumor response, and we also extrapolated those results to calculate tumor control probabilities (TCPs) using the Poisson-LQ approach.Main results. Our study suggests that the ROD effect may cause differences in SF between FLASH and conventional radiotherapy, especially in lowα/βandpoorly oxygenatedcells. However, a statistical analysis showed that these changes in SF generally do not result in significant differences in the evolution of preclinical tumor growth curves when the sample size is small, because such differences in SF may not be noticeable in the heterogeneity of the population of animals. Nonetheless, when extrapolating this effect to TCP curves, we observed important differences between both techniques (TCP is lower in FLASH radiotherapy). When analyzing the response of tumors with heterogeneous oxygenations, differences in TCP are more important forwell oxygenatedtumors. This apparent contradiction with the results obtained for homogeneously oxygenated cells is explained by the complex interplay between the heterogeneity of tumor oxygenation, the OER effect, and the ROD effect.Significance. This study supports the experimentally observed iso-effectiveness of FLASH and conventional radiotherapy when analyzing the volume evolution of preclinical tumors (that are far from control). However, this study also hints that tumor growth curves may be less sensitive to small variations in SF than tumor control probability: ROD may lead to increased SF in FLASH radiotherapy, which while not large enough to cause significant differences in tumor growth curves, could lead to important differences in clinical TCPs. Nonetheless, it cannot be discarded that other effects not modeled in this work, like radiation-induced immune effects, can contribute to tumor control and maintain the iso-effectiveness of FLASH radiotherapy. The study of tumor growth curves may not be the ideal experiment to test the iso-effectiveness of FLASH, and experiments reporting TCP orD50may be preferred.

Cancer mortality risk in the Urals Cohort of Exposed Population Offspring

The objective of the study is to analyze solid cancer mortality and estimate the risk value of solid cancer mortality in the offspring of parents irradiated in the Southern Urals, depending on the dose to the parents' gonads as well as to conduct a preliminary assessment of the mortality risk from cancer of individual locations depending on the gonadal dose. The issue of the transgenerational effects of the human gonad exposure is still very important. There exists conclusive evidence of the presence of such effects in experimental animals. However, there is no proof of the existence of these effects in humans despite a great number of research on this subject. International scientific community and international organizations, UNSCEAR and ICRP being among them, regard this issue as the one that has not been solved yet and requires further studies. Urals Cohort of offspring of the population exposed on the Techa River and on the territory of the East Ural radioactive trace was established in the Urals research Center for Radiation medicine in 2022. The key feature of the cohort is the exclusion of the offspring with postnatal exposure. The size of the cohort as of September 2023 is 31,154 persons. The number of person-years over the whole follow-up period from 1950 through 2020 is 1 226 380. Mean dose to the gonads of mothers of all the cohort members is 41 mGy, to those of the fathers' — 35 mGy, mean combined gonad dose is 76 mGy. Over the whole follow-up period 3,774 deaths from all causes including 284 deaths from solid cancers were registered in the cohort. The mean age of the cohort members at the end of the follow-up period was 42 years. The risk of death was analyzed using Poisson regression by the programs of the EPICURE statistical software package. Three models of dose dependence were tested: linear, quadratic, and linear-quadratic models of paternal gonadal dose, maternal gonadal dose, and total gonadal dose. Mortality risk analysis of all solid cancers in the offspring cohort showed no statistically significant effect with parental gonadal dose (we have obtained positive although statistically insignificant values of solid cancers mortality risk) which is consistent with the results of other studies in human populations. At the same time, the analysis for the first time obtained a statistically significant linear dependence of the solid cancer mortality risk in offspring with father's age over 45 years depending on the dose to the father's gonads. The excess relative risk of death was 8.09/Gy, (0.51-22.93), p &lt; 0.05. Also, for the first time, evidence of dose dependence of the mortality risk of lung cancer in male offspring on maternal gonadal dose, paternal gonadal dose, and combined gonadal dose was obtained. The values of excess relative risk of lung cancer and 95% confidence intervals according to the linear model were 5.39/Gy (0.46; 15.56) from paternal gonad dose, 4.36/Gy (0.15; 13.48) from maternal gonad dose, and - 3.95/Gy (0.55; 12.14) from combined gonad dose. Point risk estimates of lung cancer at this stage are characterized by wide confidence intervals and require additional studies to assess the influence of possible effect modifiers, but with a high degree of probability indicate the presence of dose dependence of this effect. Increasing the follow-up period and attained age, will increase the number of cancers in the future and will reduce dose response uncertainties and provide more accurate estimates of the risk of death in the offspring cohort.

Relative biological effectiveness of clinically relevant photon energies for the survival of human colorectal, cervical, and prostate cancer cell lines

Objective.Relative biological effectiveness (RBE) differs between radiation qualities. However, an RBE of 1.0 has been established for photons regardless of the wide range of photon energies used clinically, the lack of reproducibility in radiobiological studies, and outdated reference energies used in the experimental literature. Moreover, due to intrinsic radiosensitivity, different cancer types have different responses to radiation. This study aimed to characterize the RBE of clinically relevant high and low photon energiesin vitrofor three human cancer cell lines: HCT116 (colon), HeLa (cervix), and PC3 (prostate).Approach.Experiments were conducted following dosimetry protocols provided by the American Association of Physicists in Medicine. Cells were irradiated with 6 MV x-rays, an192Ir brachytherapy source, 225 kVp and 50 kVp x-rays. Cell survival post-irradiation was assessed using the clonogenic assay. Survival fractions were fitted using the linear quadratic model, and survival curves were generated for RBE calculations.Main results.Cell killing was more efficient with decreasing photon energy. Using 225 kVp x-rays as the reference, the HCT116 RBESF0.1for 6 MV x-rays,192Ir, and 50 kVp x-rays were 0.89 ± 0.03, 0.95 ± 0.03, and 1.24 ± 0.04; the HeLa RBESF0.1were 0.95 ± 0.04, 0.97 ± 0.05, and 1.09 ± 0.03, and the PC3 RBESF0.1were 0.84 ± 0.01, 0.84 ± 0.01, and 1.13 ± 0.02, respectively. HeLa and PC3 cells had varying radiosensitivity when irradiated with 225 and 50 kVp x-rays.Significance.This difference supports the notion that RBE may not be 1.0 for all photons through experimental investigations that employed precise dosimetry. It highlights that different cancer types may not have identical responses to the same irradiation quality. Additionally, the RBE of clinically relevant photons was updated to the reference energy of 225 kVp x-rays.

Risks of Circulatory Diseases among Korean Radiation Workers Exposed to Low-dose Radiation.

High-dose radiation has been widely recognized as a risk factor for circulatory diseases. There is increasing evidence for risk of circulatory diseases in response to low and moderate radiation doses in recent years, but the results are not always consistent. We aimed to evaluate the associations between low-dose radiation exposure (<0.1 Gy) and the incidence of circulatory disease in a large cohort of Korean radiation workers. We collected data from a cohort of 187,001 radiation workers monitored for personal radiation dose since 1984 and linked with the National Health Insurance Service data from 2002 to 2021. Excess relative risks (ERRs) per 100 mGy were calculated to quantify the radiation dose-response relationship. The mean duration of follow-up was 13.3 years. A total of 12,705 cases of cerebrovascular disease (CeVD) and 19,647 cases of ischemic heart disease (IHD) were diagnosed during the follow-up period (2002-2021). The average cumulative heart dose was 4.10 mGy, ranging from 0 to 992.62 mGy. The ERR per 100 mGy with 10-year lagged cumulative heart doses was estimated at -0.094 (95% CI -0.248, 0.070) for CeVD and -0.173 (95% CI -0.299, -0.041) for IHD. The ERRs were not significantly changed after adjusting for confounding factors such as smoking, income, blood pressure, body mass index, and blood glucose level. A linear quadratic model was found to provide a better fit for the ERR of CeVD and IHD than a linear model (P = 0.009 and 0.030, respectively). There were no statistically significant variations in ERR/100 mGy estimates for either CeVD or IHD in terms of sex, attained age, and duration of employment; however, heterogeneity in the ERR/100 mGy estimates for CeVD among occupations was observed (P = 0.001). Our study did not find conclusive evidence supporting the association between occupational low-dose radiation and an increased risk of circulatory diseases. The significant negative ERR estimates for IHD need further investigation with a more extended follow-up period.

Optimistic value models of saddle point equilibrium control problems for uncertain jump systems

The saddle point equilibrium control problem is of great importance in differential game theory. In this paper, we investigated the optimistic value model for the saddle point equilibrium control problem based on multi-dimensional uncertain differential equations with jumps. The equilibrium equation for the proposed model is presented. Then a linear quadratic game optimistic value model and a bang-bang game optimistic value model are discussed, respectively. Finally, some applications are analysed by the results obtained in this paper.

Analytic optimal control for multi-satellite assembly using linearized twistor-based model

This paper presents Guidance and Control (G&C) systems for multi-satellite assembly in proximity operations. The systems utilize the twistor model, which is linearized through Taylor’s series. Decentralized control laws, designed using Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC), are employed to track an energy-optimal trajectory generated using the Hamiltonian approach. Data exchange between satellites and their neighbors is represented using graph theory. The decentralized MPC framework is implemented using the CasADi package. To ensure collision avoidance between the satellites, a repulsive control law is designed, considering symmetric input saturation in the actuators. The proposed G&C systems are tested using a high-fidelity nonlinear satellite relative motion model that incorporates orbital perturbations. Numerical simulations are performed in a MATLAB® environment, and the results are visualized using STK®. Furthermore, a comparative study is conducted to evaluate tracking performance and fuel consumption between the two control methods. The results demonstrate that the use of an optimal trajectory reduces fuel consumption for both control algorithms.

The Emission of Internal Conversion Electrons Rather Than Auger Electrons Increased the Nucleus-Absorbed Dose for 161Tb Compared with 177Lu with a Higher Dose Response for [161Tb]Tb-DOTA-LM3 Than for [161Tb]Tb-DOTATATE.

Preclinical data have shown that 161Tb-labeled peptides targeting the somatostatin receptor are therapeutically more effective for peptide receptor radionuclide therapy than are their 177Lu-labeled counterparts. To further substantiate this enhanced therapeutic effect, we performed cellular dosimetry to quantify the absorbed dose to the cell nucleus and compared dose-response curves to evaluate differences in relative biological effectiveness invitro. Methods: CA20948 cell survival was assessed after treatment with [161Tb]Tb- and [177Lu]Lu-DOTATATE (agonist) and with [161Tb]Tb- and [177Lu]Lu-DOTA-LM3 (antagonist) via a clonogenic assay. Cell binding, internalization, and dissociation assays were performed up to 7 d to acquire time-integrated activity coefficients. Separate S values for each type of particle emission (Auger/internal conversion [IC] electrons and β- particles) were computed via Monte Carlo simulations, while considering spheric cells. Once the absorbed dose to the cell nucleus was calculated, survival curves were fitted to the appropriate linear or linear-quadratic model and corresponding relative biological effectiveness was evaluated. Results: Although the radiopeptide uptake was independent of the radionuclide, [161Tb]Tb-DOTATATE and [161Tb]Tb-DOTA-LM3 delivered a 3.6 and 3.8 times higher dose to the nucleus, respectively, than their 177Lu-labeled counterparts on saturated receptor binding. This increased nucleus-absorbed dose was mainly due to the additional emission of IC and not Auger electrons by 161Tb. When activity concentrations were considered, both [161Tb]Tb-DOTATATE and [161Tb]Tb-DOTA-LM3 showed a lower survival fraction than did labeling with 177Lu. When the absorbed dose to the nucleus was considered, no significant difference could be observed between the dose-response curves for [161Tb]Tb- and [177Lu]Lu-DOTATATE. [161Tb]Tb-DOTA-LM3 showed a linear-quadratic dose response, whereas [161Tb]Tb-DOTATATE showed only a linear dose response within the observed dose range, suggesting additional cell membrane damage by Auger electrons. Conclusion: The IC, rather than Auger, electrons emitted by 161Tb resulted in a higher absorbed dose to the cell nucleus and lower clonogenic survival for [161Tb]Tb-DOTATATE and [161Tb]Tb-DOTA-LM3 than for the 177Lu-labeled analogs. In contrast, [161Tb]Tb-DOTATATE showed no higher dose response than [177Lu]Lu-DOTATATE, whereas for [161Tb]Tb-DOTA-LM3 an additional quadratic response was observed. Because of this quadratic response, potentially caused by cell membrane damage, [161Tb]Tb-DOTA-LM3 is a more effective radiopeptide than [161Tb]Tb-DOTATATE for labeling with 161Tb.

Dimension reduction for Quasi-Monte Carlo methods via quadratic regression

Quasi-Monte Carlo (QMC) methods have been gaining popularity in computational finance as they are competitive alternatives to Monte Carlo methods that can accelerate numerical accuracy. This paper develops a new approach for reducing the effective dimension combined with a randomized QMC method. A distinctive feature of the proposed approach is its sample-based transformation that enables us to choose a flexible manipulation via regression. In the proposed approach, the first step is to perform a regression using the samples to estimate the parameters of the regression model. An optimal transformation is proposed based on the regression result to minimize the effective dimension. An advantage of this approach is that adopting a statistical approach allows greater flexibility in selecting the regression model. In addition to a linear model, this paper proposes a dimension reduction method based on a linear-quadratic model for regression. In numerical experiments, we focus on pricing different types of exotic options to test the effectiveness of the proposed approach. The numerical results show that different regression models are chosen depending on the underlying risk process and the type of derivative securities. In particular, we show several examples where the proposed method works while existing dimension reductions are ineffective.

Linear-quadratic Tobit regression model with a change point due to a covariate threshold

This paper considers a linear-quadratic Tobit regression model, which is developed for modelling the mixture structure with a line segment and a quadratic segment intersecting at an unknown change point. Due to the smoothness of such model structure, the regression coefficients and the change point can be obtained by directly maximising the likelihood function. The proposed estimator has rapid convergence rate and high estimation accuracy, without other computation burden. The asymptotic properties for the proposed estimator are derived by using empirical process theory. A sup-likelihood ratio test procedure is developed for testing the existence of a change point, and its limiting distributions are derived. The good finite sample performances of the proposed estimator are illustrated by numerical studies and empirical applications to the MGUS and GDP data.

Human-in-the-Loop Behavior Modeling via an Integral Concurrent Adaptive Inverse Reinforcement Learning.

One goal of artificial intelligence (AI) research is to teach machines how to learn from humans, such that they can perform a certain task in a natural human-like way. In this article, an online adaptive inverse reinforcement learning (IRL) approach to human behavior modeling is proposed to enhance machine intelligence for a class of linear human-in-the-loop (HiTL) systems using the state data only, where the human behavior is described by a linear quadratic optimal control model with an unknown weighting matrix for the quadratic cost function. First, an integral concurrent adaptive law is developed to learn the human feedback gain matrix online using the demonstrated state data only, which removes the persistent excitation (PE) conditions required by traditional adaptive estimation approaches and thus is more in line with real applications. Then, with the learned feedback gain matrix, the IRL problem is formulated as a linear matrix inequality (LMI) optimization problem, which can be efficiently solved to retrieve the weighting matrix of the human cost function. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.

Prediction of Cell Survival Rate Based on Physical Characteristics of Heavy Ion Radiation.

The effect of ionizing radiation on cells is a complex process dependent on several parameters. Cancer treatment commonly involves the use of radiotherapy. In addition to the effective killing of cancer cells, another key aspect of radiotherapy is the protection of healthy cells. An interesting position is occupied by heavy ion radiation in the field of radiotherapy due to its high relative biological effectiveness, making it an effective method of treatment. The high biological efficiency of heavy ion radiation can also pose a danger to healthy cells. The extent of cell death induced by heavy ion radiation in cells was investigated using statistical learning methods in this study. The objective was to predict the healthy cell survival rate based on the physical parameters of the available ionizing radiation. This paper is based on secondary research utilizing the PIDE database. Throughout this study, a local regression and a random forest model were generated. Their predictions were compared to the results of a linear-quadratic model commonly utilized in the field of ionizing radiation using various metrics. The relationship between dose and cell survival rate was examined using the linear-quadratic (LQM) model and local regression (LocReg). An R2 value of 88.43% was achieved for LQM and 89.86% for LocReg. Upon incorporating linear energy transfer, the random forest model attained an R2 value of 96.85%. In terms of RMSE, the linear-quadratic model yielded 9.5910-2, the local regression 9.2110-2, and the random forest 1.96 × 10-2 (lower values indicate better performance). All of these methods were also applied to a log-transformed dataset to decrease the right skewedness of the distribution of the datapoints. This significantly reduced the estimates made with LQM and LocReg (28% decrease in the case of R2), while the random forest retained nearly the same level of estimation as the untransformed data. In conclusion, it can be inferred that dose alone provides a somewhat satisfactory explanatory power for cell survival rate, but the inclusion of linear energy transfer can significantly enhance prediction accuracy in terms of variance and explanatory power.

Exploration Noise for Learning Linear-Quadratic Mean Field Games

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called fictitious play, and this without any further potential or monotone structure. Several numerical examples are provided to support our theoretical analysis. Funding: F. Delarue acknowledges the financial support of the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme [AdG ELISA project, Grant 101054746]. A. Vasileiadis acknowledge the financial support of French ANR project ANR-19-P3IA-0002-3IA Côte d'Azur-Nice-Interdisciplinary Institute for Artificial Intelligence.

Re-irradiation practice and ESTRO/EORTC consensus recommendations: 2023 ASTRO education panel.

Indications for re-irradiation are increasing both for palliation and potentially curative attempts to achieve durable local control. This has been in part driven by the technological advances in the last decade including image-guided brachytherapy, volumetric-modulated arc therapy and stereotactic body radiotherapy. These enable high dose focal irradiation to be delivered to a limited target volume with minimal normal tissue re-irradiation. The European Society for Radiotherapy and Oncology (ESTRO) and the European Organisation for Research and Treatment of Cancer (EORTC) have collaboratively developed a comprehensive consensus on re-irradiation practices, aiming to standardise definitions, reporting, and clinical decision-making processes. The document introduces a universally applicable definition for re-irradiation, categorised into two primary types based on the presence of geometric overlap of irradiated volumes and concerns for cumulative dose toxicity. It also identifies "repeat organ irradiation" and "repeat irradiation" for cases without such overlap, emphasising the need to consider toxicity risks associated with cumulative doses. Additionally, the document presents detailed reporting guidelines for re-irradiation studies, specifying essential patient and tumour characteristics, treatment planning and delivery details, and follow-up protocols. These guidelines are designed to improve the quality and reproducibility of clinical research, thus fostering a more robust evidence base for future re-irradiation practices. The consensus underscores the necessity of interdisciplinary collaboration and shared decision-making, highlighting performance status, patient survival estimates, and response to initial radiotherapy as critical factors in determining eligibility for re-irradiation. It advocates for a patient-centric approach, with transparent communication about treatment intent and potential risks. Radiobiological considerations, including the application of the linear-quadratic model, are recommended for assessing cumulative doses and guiding re-irradiation strategies. By providing these comprehensive recommendations, the ESTRO-EORTC consensus aims to enhance the safety, efficacy, and quality of life for patients undergoing re-irradiation, while paving the way for future research and refinement of treatment protocols in the field of oncology.

Lymphocyte radiosensitivity: An extension to the linear-quadratic model?

Background and purposeThe linear-quadratic (LQ) model has been pivotal for evaluating the effects of radiation on cells, but it is primarily characterized by linear responses, which has exhibited limitations when applied to lymphocyte data. The present research aims to address these limitations and to explore an alternative model extended from the conventional LQ model. Materials and methodsLiterature providing lymphocyte counts from assays investigating apoptosis and survival after in vitro irradiation was selected. To address the nonlinearity in lymphocyte responses to radiation, we developed a saturation model characterized by a negative exponential relationship between radiation dose and cellular response. We compared the performance of this saturation model against that of conventional models, including the LQ model and its variants (linear model LM and linear-quadratic-cubic model LQC), as well as the repair-misrepair (RMR) model. The models were evaluated based on prediction-residual plots, residual standard errors, and the Akaike information criterion (AIC). We applied the saturation model to two additional datasets: (1) a dataset from the existing literature that assessed stimulated and unstimulated human lymphocytes exposed to gamma irradiation in vitro and (2) a novel dataset involving T lymphocytes from rodent spleens after exposure to various radiation types (X-rays and protons). ResultsThe literature (n = 15 out of 2342) showed that lymphocyte apoptosis varies with dose, time and experimental conditions. The saturation model had a lower AIC of 718 compared to the LM, LQ, LQC and RMR models (AIC of 728, 720, 720 and 734, respectively). The saturation model had a lower residual error and more consistent error distribution. Integrating time as a covariate, the saturation model also had a better AIC for demonstrating time-dependent variations in lymphocyte responses after irradiation. For datasets involving unstimulated lymphocytes before irradiation, the saturation model provided a more accurate fit than did the LM, LQ, and RMR models. In these cases, the fit of the saturation model was comparable to that of the LQC model but offered an advantage when extrapolating to higher doses, where the LQC model might underestimate survival. For stimulated lymphocytes, which are radioresistant, all the models approximated the LM. Both the LQ and saturation models indicated greater radiosensitivity to protons in vitro. ConclusionThe new “saturation model” performed better than the LQ model in quantifying lymphocyte apoptosis and survival, estimating time dependency and assessing the role of radiation modalities or lymphocyte stimulation. Further experiments are warranted to experimentally explore the validity of the saturation model as a promising alternative in the clinical setting.

An updated variable RBE model for proton therapy

Objective. While a constant relative biological effectiveness (RBE) of 1.1 forms the basis for clinical proton therapy, variable RBE models are increasingly being used in plan evaluation. However, there is substantial variation across RBE models, and several new in vitro datasets have not yet been included in the existing models. In this study, an updated in vitro proton RBE database was collected and used to examine current RBE model assumptions, and to propose an up-to-date RBE model as a tool for evaluating RBE effects in clinical settings. Approach. A proton database (471 data points) was collected from the literature, almost twice the size of the previously largest model database. Each data point included linear-quadratic model parameters and linear energy transfer (LET). Statistical analyses were performed to test the validity of commonly applied assumptions of phenomenological RBE models, and new model functions were proposed for RBEmax and RBEmin (RBE at the lower and upper dose limits). Previously published models were refitted to the database and compared to the new model in terms of model performance and RBE estimates. Main results. The statistical analysis indicated that the intercept of the RBEmax function should be a free fitting parameter and RBE estimates were clearly higher for models with free intercept. RBEmin increased with increasing LET, while a dependency of RBEmin on the reference radiation fractionation sensitivity ( α/βx ) did not significantly improve model performance. Evaluating the models, the new model gave overall lowest RMSE and highest R2 score. RBE estimates in the distal part of a spread-out-Bragg-peak in water ( α/βx = 2.1 Gy) were 1.24–1.51 for original models, 1.25–1.49 for refits and 1.42 for the new model. Significance. An updated RBE model based on the currently largest database among published phenomenological models was proposed. Overall, the new model showed better performance compared to refitted published RBE models.

The potential of integrating stereotactic ablative radiotherapy techniques with hyperfractionation for lung cancer.

Limited literature exists on the feasibility and effectiveness of integrating stereotactic ablative radiotherapy (SABR) techniques with hyperfractionated regimens for patients with lung cancer. This study aims to assess whether the SABR technique with hyperfractionation can potentially reduce lung toxicity. We utilized the linear-quadratic model to find the optimal fraction to maximize the tumor biological equivalent dose (BED) to normal-tissue BED ratio. Validation was performed by comparing the SABR plans with 50 Gy/5 fractions and hyperfractionationed plans with 88.8 Gy/74 fractions with the same tumor BED and planning criteria for 10 patients with early-stage lung cancer. Mean lung BED, Lyman-Kutcher-Burman (LKB) normal tissue complication probability (NTCP), critical volume (CV) criteria (volume below BED of 22.92 and 25.65 Gy, and mean BED for lowest 1000 and 1500 cc) and the percentage of the lung receiving 20Gy or more (V20) were compared using the Wilcoxon signed-rank test. The transition point occurs when the tumor-to-normal tissue ratio (TNR) of the physical dose equals the TNR of α/β in the BED dose-volume histogram of the lung. Compared with the hypofractionated regimen, the hyperfractionated regimen is superior in the dose range above but inferior below the transition point. The hyperfractionated regimen showed a lower mean lung BED (6.40 Gy vs. 7.73 Gy) and NTCP (3.50% vs. 4.21%), with inferior results concerning CV criteria and higher V20 (7.37% vs. 7.03%) in comparison with the hypofractionated regimen (p < 0.01 for all). The hyperfractionated regimen has an advantage in the high-dose region of the lung but a disadvantage in the low-dose region. Further research is needed to determine the superiority between hypo- and hyperfractionation.