Extending the linear–quadratic model for large fraction doses pertinent to stereotactic radiotherapy

Radiobiological Meta-Analysis of the Response of Prostate Cancer to High-Dose-Rate Brachytherapy: Investigation of the Reduction in Control for Extreme Hypofractionation

BACKGROUND/OBJECTIVES

Clinical studies have shown a marked reduction in tumor control in prostate cancer treated with radically hypofractionated high-dose-rate brachytherapy (HDR-BT). The purpose of this study was to analyze the dose-response of prostate cancer treated with HDR-BT, specifically aiming at investigating the potential failure of the linear-quadratic (LQ) model to describe the response at large doses-per-fraction.

METHODS

We collated a dataset of dose-response to HDR-BT (3239 patients). The analysis was conducted separately for low and intermediate risk, resulting in 21 schedules (1633 patients) and 23 schedules (1606 patients), respectively. Data were fitted to tumor control probability models based on the LQ model, the linear-quadratic-linear (LQL), and a modification of the LQ model to include the effect of reoxygenation during treatment.

RESULTS

The LQ cannot fit the data unless the α/β is allowed to be high (∼[20, >100] Gy, 95% confidence interval). If the α/β is constrained to be low (≤8 Gy), the LQ model cannot reproduce the clinical results, and the LQL model, which includes a moderation of radiation damage with increasing dose, significantly improves the fitting. On the other hand, the reoxygenation model does not match the results obtained with the LQL. The clinically observed reduction in tumor control in prostate cancer treated with radical HDR-BT is better described by the LQL model. Using the best-fitting parameters, the BED for a 20 Gy × 1 treatment (128 Gyα/β) is far less than that of a conventional 2 Gy × 37 fractionation (196 Gyα/β).

CONCLUSIONS

Our analysis showed that the substantial loss of tumor control observed in extremely hypofractionated HDR-BT trials can only be explained by the LQ model if the α/β is very large (≥100 Gy), in clear disagreement with the limits set in the analysis of external radiotherapy data. It seems more reasonable that there is a moderation of the LQ-predicted effect with increasing dose per fraction. These results may assist in the design of radical HDR-BT treatments.

Reirradiation for Locally Recurrent Head and Neck Cancer: State-of-the-Art and Future Directions

Reirradiation of the head and neck presents one of the most complex and challenging scenarios faced by (for) clinicians due to the narrow therapeutic window. Its use is increasing in clinical practice, often guided by empirical and pragmatic approaches due to the limited availability of high-level evidence from randomized clinical trials. Successful reirradiation requires a precise balance between tumor control probability (TCP) and normal tissue complication probability (NTCP). Advances in radiation technologies, including intensity-modulated radiation therapy (IMRT), proton beam therapy (PBT), and stereotactic body radiation therapy (SBRT), have enabled more precise high-dose delivery, potentially improving dose distribution and reducing severe toxicity. This review explores current state-of-the-art approaches to reirradiating recurrent head and neck cancer, focusing on modern reirradiation techniques and critically assessing the literature on their clinical application, integration with systemic therapy, and future directions. It also addresses key practical challenges related to patient selection and toxicity/risk management, offering a comprehensive overview of the evolving treatment landscape and highlighting some of the most complex issues clinicians face in reirradiation.

Replacing 2 Gy Per Fraction Equivalent Dose with Fractionation-Specific Biological Equivalent Dose for Normal Tissues

The 2 Gy per fraction equivalent dose (EQD2) is an important quantity used in determining equivalent prescription doses for different fractionation regimens and evaluating different fractionation regimens, but it does not match its definition when it is used for normal tissues. We propose to use the fractionation-specific biological equivalent dose to determine normal tissue dose constraints for different fractionation regimens. The concept of the biological equivalent dose is defined based on the linear-quadratic equation. The EQD2 is derived based on the biological effective dose (BED), mimicking the prescription dose of a standard fractionation regimen with a fractional dose of 2 Gy and a fixed number of fractions. The FEQD(n) is also defined based on the BED as a function of the number of fractions, n, which is determined by the dose prescription. The FEQD(n) mimics any fractionation regimens with any fractional doses and numbers of fractionations. A given dose constraint can have different BED values and EQD2 values for different fractionation regimens. The number of fractions for a given 2 Gy per fraction regimen derived from the EQD2 for the target dose is different from that for the normal tissues. The value of the EQD2 derived for the target represents the total dose for the target for the 2 Gy fractional dose regimen, but the EQD2 value derived for the normal tissues does not represent the total dose for the normal tissue for the same fractionation regimen. The fractionation-specific biological equivalent dose (FEQD(n)) for both target and normal tissues has the same number of fractions for any fractionation regimen, and represents the total dose for either the target or the normal tissue. Based on the clinical outcomes, the FEQD(n) curves for the brainstem, spinal cord, rectum, and lung were derived and can be directly used as dose constraints for various fractionation regimens in clinical practice. The EQD2 does not match its definition and is not realistic when describing the biological equivalent dose for normal tissues. It is also not practical when used in determining tolerance doses or dose constraints. Instead, the FEQD(n) can be used to determine or convert the normal tissue dose constraints for any fractionation regimens in a realistic and practical manner. Using the FEQD(n), the dose constraints as a function of the number of fractions for the brainstem, spinal cord, rectum, and lung, which correspond to the given toxicity rates, were derived and can be directly used in clinical practice.

A Population-Based Tumor-Volume Model for Head and Neck Cancer During Radiation Therapy With a Dynamic Oxygenated Compartment

PURPOSE

With the coming era of digital medicine and healthcare technology, mathematical modeling of tumors has become a key step to optimize and realize precision radiation therapy. The purpose of this study was to develop a mathematical model for simulating the change of head and neck (HN) tumor volume during radiation therapy.

METHODS AND MATERIALS

A formula was developed to describe the dynamic change of oxygenated compartment within a tumor, which was combined with the lethal lesions model to describe various cell processes during radiation therapy, including potentially lethal lesion repair and misrepair, cell proliferation/loss, and tumor reoxygenation. Parameter sensitivity analysis was performed to evaluate the impacts of lesion- and repair-related biological factors on radiation therapy outcomes.

RESULTS

We tested our model on 14 available patients with HN cancer and compared the performance with 3 other models. The mean error of our model for the 12 good fit cases was 12.2%, which is considerably smaller than that of the linear quadratic model (19.7%), the generalized linear quadratic model (19.1%), and a 4-level cell population model (16.6%). Correlation analysis results revealed that for small tumors, there was a positive correlation (correlation coefficient r=0.9416) between hypoxic fraction (hf) and tumor volume, whereas the correlation became negative and not significant (r=-0.4365) for large tumors. It is demonstrated from sensitivity analysis that the production rate of lethal lesions (ηl) has a far greater impact on tumor volume than other parameters. The hf had an insignificant impact on tumor volume but had a notable influence on the volume of surviving cells. The final volume of surviving cells athf=0.5 was almost 8 ×102 times that of hf=0.01. The potentially lethal lesion-related parameters (the production rate of potentially lethal lessions per unit dose ηpl, the rate of correct repair per unit time εpl, and the rate of binary misrepair per unit time ε2pl) had rather small impacts (<1%) on both tumor volume and the volume of surviving cells, which indicates that the repaired and misrepaired sublethal cells only take up a small portion of the total cancer cell population.

CONCLUSIONS

A population-based tumor-volume model for HN cancer during radiation therapy with a dynamic oxygenated compartment was developed in this study. Comprehensively considering the damage process of tumor cells caused by radiation therapy, the accurate prediction of the volume change of HN tumors during treatment was revealed. Meanwhile, various cell activities and their principles in the process of antitumor treatment were reflected, which has positive clinical reference significance for radiobiology.

Brachial plexopathy following stereotactic body radiation therapy in apical lung malignancies: A dosimetric pooled analysis of individual patient data

BACKGROUND AND OBJECTIVES

The aim of this study is to establish dosimetric constraints for the brachial plexus at risk of developing grade ≥ 2 brachial plexopathy in the context of stereotactic body radiation therapy (SBRT).

PATIENTS AND METHODS

Individual patient data from 349 patients with 356 apical lung malignancies who underwent SBRT were extracted from 5 articles. The anatomical brachial plexus was delineated following the guidelines provided in the atlases developed by Hall, et al. and Kong, et al.. Patient characteristics, pertinent SBRT dosimetric parameters, and brachial plexopathy grades (according to CTCAE 4.0 or 5.0) were obtained. Normal tissue complication probability (NTCP) models were used to estimate the risk of developing grade ≥ 2 brachial plexopathy through maximum likelihood parameter fitting.

RESULTS

The prescription dose/fractionation schedules for SBRT ranged from 27 to 60 Gy in 1 to 8 fractions. During a follow-up period spanning from 6 to 113 months, 22 patients (6.3 %) developed grade ≥2 brachial plexopathy (4.3 % grade 2, 2.0 % grade 3); the median time to symptoms onset after SBRT was 8 months (ranged, 3-54 months). NTCP models estimated a 10 % risk of grade ≥2 brachial plexopathy with an anatomic brachial plexus maximum dose (Dmax) of 20.7 Gy, 34.2 Gy, and 42.7 Gy in one, three, and five fractions, respectively. Similarly, the NTCP model estimates the risks of grade ≥2 brachial plexopathy as 10 % for BED Dmax at 192.3 Gy and EQD2 Dmax at 115.4 Gy with an α/β ratio of 3, respectively. Symptom persisted after treatment in nearly half of patients diagnosed with grade ≥2 brachial plexopathy (11/22, 50 %).

CONCLUSIONS

This study establishes dosimetric constraints ranging from 20.7 to 42.7 Gy across 1-5 fractions, aimed at mitigating the risk of developing grade ≥2 brachial plexopathy following SBRT. These findings provide valuable guidance for future ablative SBRT in apical lung malignancies.

A multi-centre retrospective study of long-term outcomes of spinal re-irradiation with SABR

INTRODUCTION

Stereotactic ablative body radiotherapy (SABR) is a highly conformal technique utilising a high dose per fraction commonly employed in the re-treatment of spinal metastases. This study sought to determine the safety and efficacy of re-irradiation with SABR to previously treated spinal metastases.

METHODS

This was a retrospective analysis of patients at three Australian centres who have undergone spinal SABR after previous spinal radiotherapy to the same or immediately adjacent vertebral level. Efficacy was determined in terms of rates of local control, while safety was characterised by rates of serious complications.

RESULTS

Thirty-three spinal segments were evaluated from 32 patients. Median follow-up for all patients was 2.6 years, and median overall survival was 4.3 years. Eleven of 33 (33.3%) treated spinal segments had local progression, with a local control rate at 12 months of 71.4% (95% C.I. 55.2%-92.4%). Four patients (16.7%) went on to develop cauda equina or spinal cord compression. Thirteen out of 32 patients (40.6%) experienced acute toxicity, of which 12 were grade 2 or less. Five out of 30 spinal (16.7%) segments with follow-up imaging had a radiation-induced vertebral compression fracture. There was one case of radiation myelitis which occurred in a patient who had mediastinal radiotherapy with a treatment field which overlapped their prior spinal radiation.

CONCLUSION

The patients in this study experienced long median survival, durable tumour control and high rates of freedom from long-term sequelae of treatment. These results support the use of SABR in patients who progress in the spine despite previous radiotherapy.

Modelling Cellular Response to Ionizing Radiation: Mechanistic, Semi-Mechanistic, and Phenomenological Approaches - A Historical Perspective

Radiation research is a multidisciplinary field, and among its many branches, mathematical and computational modelers have played a significant role in advancing boundaries of knowledge. A fundamental contribution is modelling cellular response to ionizing radiation as that is the key to not only understanding how radiation can kill cancer cells, but also cause cancer and other health issues. The invention of microdosimetry in the 1950s by Harold Rossi paved the way for brilliant scientists to study the mechanism of radiation at cellular and sub-cellular scales. This paper reviews some snippets of ingenious mathematical and computational models published in microdosimetry symposium proceedings and publications of the radiation research community. Among these are simulations of radiation tracks at atomic and molecular levels using Monte Carlo methods, models of cell survival, quantification of the amount of energy required to create a single strand break, and models of DNA-damage-repair. These models can broadly be categorized into mechanistic, semi-mechanistic, and phenomenological approaches, and this review seeks to provide historical context of their development. We salute pioneers of the field and great teachers who supported and educated the younger members of the community and showed them how to build upon their work.

Association of increasing gross tumor volume dose with tumor volume reduction and local control in fractionated stereotactic radiosurgery for unresected brain metastases

BACKGROUND

Fractionated stereotactic radiosurgery (fSRS) is an important treatment strategy for unresected brain metastases. We previously reported that a good volumetric response 6 months after fSRS can be the first step for local control. Few studies have reported the association between gross tumor volume (GTV) dose, volumetric response, and local control in patients treated with the same number of fractions. Therefore, in this study, we aimed to investigate the GTV dose and volumetric response 6 months after fSRS in five daily fractions and identify the predictive GTV dose for local failure (LF) for unresected brain metastasis.

METHODS

This retrospective study included 115 patients with 241 unresected brain metastases treated using fSRS in five daily fractions at our hospital between January 2013 and April 2022. The median prescription dose was 35 Gy (range, 30-35 Gy) in five fractions. The median follow-up time after fSRS was 16 months (range, 7-66 months).

RESULTS

GTV D80 > 42 Gy and GTV D98 > 39 Gy were prognostic factors for over 65% volume reduction (odds ratio, 3.68, p < 0.01; odds ratio, 4.68, p < 0.01, respectively). GTV D80 > 42 Gy was also a prognostic factor for LF (hazard ratio, 0.37; p = 0.01).

CONCLUSIONS

GTV D80 > 42 Gy in five fractions led to better volume reduction and local control. The goal of planning an inhomogeneous dose distribution for fSRS in brain metastases may be to increase the GTV D80 and GTV D98. Further studies on inhomogeneous dose distributions are required.

The Use of Survival Dose-Rate Dependencies as Theoretical Discrimination Criteria for In-Silico Dynamic Radiobiological Models

Introduction

Cell repair dynamics are crucial in optimizing anti-cancer therapies. Various assays (eg, comet assay and γ-H2AX) assess post-radiation repair kinetics, but interpreting such data is challenging and model-based data analyses are required. However, ambiguities in parameter calibration remain an unsolved challenge. To address this, we propose combining survival dose-rate effects with computer simulations to gain knowledge about repair kinetics.

Methods

After a literature review, theoretical discriminators based on common fractionation/dose-rate-related effects were defined to discard unrealistic model dynamics. The Multi-Hit Repair (MHR) model was calibrated with canine osteosarcoma Abrams cell line data to study the discriminators' efficacy in scenarios with limited survival data. Additionally, survival dose-rate-dependent data from the human SiHa cervical cancer cell line were used to illustrate the survival behavior at diverse dose-rates and the capability of the MHR to model these data.

Results

SiHa data confirmed the validity of the proposed discriminators. The discriminators filtered 99% of parameter sets, improving the calibration of Abrams cells data. Furthermore, results from both cell lines may hint universal aspects of cellular repair.

Conclusions

Dose-rate theoretical discrimination criteria are an effective method to understand repair kinetics and improve radiobiological model calibration. Moreover, this methodology may be used to analyze diverse biological data using dynamic models in-silico.

Overview and Recommendations for Prospective Multi-institutional Spatially Fractionated Radiation Therapy Clinical Trials

PURPOSE

The highly heterogeneous dose delivery of spatially fractionated radiation therapy (SFRT) is a profound departure from standard radiation planning and reporting approaches. Early SFRT studies have shown excellent clinical outcomes. However, prospective multi-institutional clinical trials of SFRT are still lacking. This NRG Oncology/American Association of Physicists in Medicine working group consensus aimed to develop recommendations on dosimetric planning, delivery, and SFRT dose reporting to address this current obstacle toward the design of SFRT clinical trials.

METHODS AND MATERIALS

Working groups consisting of radiation oncologists, radiobiologists, and medical physicists with expertise in SFRT were formed in NRG Oncology and the American Association of Physicists in Medicine to investigate the needs and barriers in SFRT clinical trials.

RESULTS

Upon reviewing the SFRT technologies and methods, this group identified challenges in several areas, including the availability of SFRT, the lack of treatment planning system support for SFRT, the lack of guidance in the physics and dosimetry of SFRT, the approximated radiobiological modeling of SFRT, and the prescription and combination of SFRT with conventional radiation therapy.

CONCLUSIONS

Recognizing these challenges, the group further recommended several areas of improvement for the application of SFRT in cancer treatment, including the creation of clinical practice guidance documents, the improvement of treatment planning system support, the generation of treatment planning and dosimetric index reporting templates, and the development of better radiobiological models through preclinical studies and through conducting multi-institution clinical trials.

AAPM Task Group Report 267: A joint AAPM GEC-ESTRO report on biophysical models and tools for the planning and evaluation of brachytherapy

Brachytherapy utilizes a multitude of radioactive sources and treatment techniques that often exhibit widely different spatial and temporal dose delivery patterns. Biophysical models, capable of modeling the key interacting effects of dose delivery patterns with the underlying cellular processes of the irradiated tissues, can be a potentially useful tool for elucidating the radiobiological effects of complex brachytherapy dose delivery patterns and for comparing their relative clinical effectiveness. While the biophysical models have been used largely in research settings by experts, it has also been used increasingly by clinical medical physicists over the last two decades. A good understanding of the potentials and limitations of the biophysical models and their intended use is critically important in the widespread use of these models. To facilitate meaningful and consistent use of biophysical models in brachytherapy, Task Group 267 (TG-267) was formed jointly with the American Association of Physics in Medicine (AAPM) and The Groupe Européen de Curiethérapie and the European Society for Radiotherapy & Oncology (GEC-ESTRO) to review the existing biophysical models, model parameters, and their use in selected brachytherapy modalities and to develop practice guidelines for clinical medical physicists regarding the selection, use, and interpretation of biophysical models. The report provides an overview of the clinical background and the rationale for the development of biophysical models in radiation oncology and, particularly, in brachytherapy; a summary of the results of literature review of the existing biophysical models that have been used in brachytherapy; a focused discussion of the applications of relevant biophysical models for five selected brachytherapy modalities; and the task group recommendations on the use, reporting, and implementation of biophysical models for brachytherapy treatment planning and evaluation. The report concludes with discussions on the challenges and opportunities in using biophysical models for brachytherapy and with an outlook for future developments.

Primary study of the relative and compound biological effectiveness model for boron neutron capture therapy based on nanodosimetry

BACKGROUND

The current radiobiological model employed for boron neutron capture therapy (BNCT) treatment planning, which relies on microdosimetry, fails to provide an accurate representation the biological effects of BNCT. The precision in calculating the relative biological effectiveness (RBE) and compound biological effectiveness (CBE) plays a pivotal role in determining the therapeutic efficacy of BNCT. Therefore, this study focuses on how to improve the accuracy of the biological effects of BNCT.

PURPOSE

The purpose of this study is to propose new radiation biology models based on nanodosimetry to accurately assess RBE and CBE for BNCT.

METHODS

Nanodosimetry, rooted in ionization cluster size distributions (ICSD), introduces a novel approach to characterize radiation quality by effectively delineating RBE through the ion track structure at the nanoscale. In the context of prior research, this study presents a computational model for the nanoscale assessment of RBE and CBE. We establish a simplified model of DNA chromatin fiber using the Monte Carlo code TOPAS-nBio to evaluate the applicability of ICSD to BNCT and compute nanodosimetric parameters.

RESULTS

Our investigation reveals that both homogeneous and heterogeneous nanodosimetric parameters, as well as the corresponding biological model coefficients α and β, along with RBE values, exhibit variations in response to varying intracellular 10B concentrations. Notably, the nanodosimetric parameterM 1 C 2 $M_1^{{{\mathrm{C}}}_2}$ effectively captures the fluctuations in model coefficients α and RBE.

CONCLUSION

Our model facilitates a nanoscale analysis of BNCT, enabling predictions of nanodosimetric quantities for secondary ions as well as RBE, CBE, and other essential biological metrics related to the distribution of boron. This contribution significantly enhances the precision of RBE calculations and holds substantial promise for future applications in treatment planning.

Historical Progress of Stereotactic Radiation Surgery

Radiosurgery and stereotactic radiotherapy have established themselves as precise and accurate areas of radiation oncology for the treatment of brain and extracranial lesions. Along with the evolution of other methods of radiotherapy, this type of treatment has been associated with significant advances in terms of a variety of modalities and techniques to improve the accuracy and efficacy of treatment. This paper provides a comprehensive overview of the progress in stereotactic radiosurgery (SRS) over several decades, and includes a review of various articles and research papers, commencing with the emergence of stereotactic techniques in radiotherapy. Key clinical aspects of SRS, such as fixation methods, radiobiology considerations, quality assurance practices, and treatment planning strategies, are presented. In addition, the review highlights the technological advancements in treatment modalities, encompassing the transition from cobalt-based systems to linear accelerator-based modalities. By addressing these topics, this study aims to offer insights into the advancements that have shaped the field of SRS, that have ultimately enhanced the accuracy and effectiveness of treatment.

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

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

Brain Re-Irradiation Robustly Accounting for Previously Delivered Dose

(1) Background: The STRIDeR (Support Tool for Re-Irradiation Decisions guided by Radiobiology) planning pathway aims to facilitate anatomically appropriate and radiobiologically meaningful re-irradiation (reRT). This work evaluated the STRIDeR pathway for robustness compared to a more conservative manual pathway. (2) Methods: For ten high-grade glioma reRT patient cases, uncertainties were applied and cumulative doses re-summed. Geometric uncertainties of 3, 6 and 9 mm were applied to the background dose, and LQ model robustness was tested using α/β variations (values 1, 2 and 5 Gy) and the linear quadratic linear (LQL) model δ variations (values 0.1 and 0.2). STRIDeR robust optimised plans, incorporating the geometric and α/β uncertainties during optimisation, were also generated. (3) Results: The STRIDeR and manual pathways both achieved clinically acceptable plans in 8/10 cases but with statistically significant improvements in the PTV D98% (p < 0.01) for STRIDeR. Geometric and LQ robustness tests showed comparable robustness within both pathways. STRIDeR plans generated to incorporate uncertainties during optimisation resulted in a superior plan robustness with a minimal impact on PTV dose benefits. (4) Conclusions: Our results indicate that STRIDeR pathway plans achieved a similar robustness to manual pathways with improved PTV doses. Geometric and LQ model uncertainties can be incorporated into the STRIDeR pathway to facilitate robust optimisation.

Radiobiological Meta-Analysis of the Response of Prostate Cancer to Different Fractionations: Evaluation of the Linear-Quadratic Response at Large Doses and the Effect of Risk and ADT

The purpose of this work was to investigate the response of prostate cancer to different radiotherapy schedules, including hypofractionation, to evaluate potential departures from the linear-quadratic (LQ) response, to obtain the best-fitting parameters for low-(LR), intermediate-(IR), and high-risk (HR) prostate cancer and to investigate the effect of ADT on the radiobiological response. We constructed a dataset of the dose-response containing 87 entries/16,536 patients (35/5181 LR, 32/8146 IR, 20/3209 HR), with doses per fraction ranging from 1.8 to 10 Gy. These data were fit to tumour control probability models based on the LQ model, linear-quadratic-linear (LQL) model, and a modification of the LQ (LQmod) model accounting for increasing radiosensitivity at large doses. Fits were performed with the maximum likelihood expectation methodology, and the Akaike information criterion (AIC) was used to compare the models. The AIC showed that the LQ model was superior to the LQL and LQmod models for all risks, except for IR, where the LQL model outperformed the other models. The analysis showed a low α/β for all risks: 2.0 Gy for LR (95% confidence interval: 1.7-2.3), 3.4 Gy for IR (3.0-4.0), and 2.8 Gy for HR (1.4-4.2). The best fits did not show proliferation for LR and showed moderate proliferation for IR/HR. The addition of ADT was consistent with a suppression of proliferation. In conclusion, the LQ model described the response of prostate cancer better than the alternative models. Only for IR, the LQL model outperformed the LQ model, pointing out a possible saturation of radiation damage with increasing dose. This study confirmed a low α/β for all risks.

Re-irradiation for recurrent/progressive pediatric brain tumors: from radiobiology to clinical outcomes

INTRODUCTION

Brain tumors are the most common solid tumors in children. Neurosurgical excision, radiotherapy, and/or chemotherapy represent the standard of care in most histopathological types of pediatric central nervous system (CNS) tumors. Even though the successful cure rate is reasonable, some patients may develop recurrence locally or within the neuroaxis.

AREA COVERED

The management of these recurrences is not easy; however, significant advances in neurosurgery, radiation techniques, radiobiology, and the introduction of newer biological therapies, have improved the results of their salvage treatment. In many cases, salvage re-irradiation is feasible and has achieved encouraging results. The results of re-irradiation depend upon several factors. These factors include tumor type, extent of the second surgery, tumor volume, location of the recurrence, time that elapses between the initial treatment, the combination with other treatment agents, relapse, and the initial response to radiotherapy.

EXPERT OPINION

Reviewing the radiobiological basis and clinical outcome of pediatric brain re-irradiation revealed that re-irradiation is safe, feasible, and indicated for recurrent/progressive different tumor types such as; ependymoma, medulloblastoma, diffuse intrinsic pontine glioma (DIPG) and glioblastoma. It is now considered part of the treatment armamentarium for these patients. The challenges and clinical results in treating recurrent pediatric brain tumors were highly documented.

A Biomathematical Model of Tumor Response to Radioimmunotherapy With αPDL1 and αCTLA4

There is evidence of synergy between radiotherapy and immunotherapy. Radiotherapy can increase liberation of tumor antigens, causing activation of antitumor T-cells. This effect can be boosted with immunotherapy. Radioimmunotherapy has potential to increase tumor control rates. Biomathematical models of response to radioimmunotherapy may help on understanding of the mechanisms affecting response, and assist clinicians on the design of optimal treatment strategies. In this work we present a biomathematical model of tumor response to radioimmunotherapy. The model uses the linear-quadratic response of tumor cells to radiation (or variation of it), and builds on previous developments to include the radiation-induced immune effect. We have focused this study on the combined effect of radiotherapy and αPDL1/ αCTLA4 therapies. The model can fit preclinical data of volume dynamics and control obtained with different dose fractionations and αPDL1/ αCTLA4. A biomathematical study of optimal combination strategies suggests that a good understanding of the involved biological delays, the biokinetics of the immunotherapy drug, and the interplay between them, may be of paramount importance to design optimal radioimmunotherapy schedules. Biomathematical models like the one we present can help to interpret experimental data on the synergy between radiotherapy and immunotherapy, and to assist in the design of more effective treatments.

Accumulation of sublethal radiation damage and its effect on cell survival

Objective.Determine the extent of sublethal radiation damage (SRD) in a cell population that received a given dose of radiation and the impact of this damage on cell survival.Approach.We developed a novel formalism to account for accumulation of SRD with increasing dose. It is based on a very general formula for cell survival that correctly predicts the basic properties of cell survival curves, such as the transition from the linear-quadratic to a linear dependence at high doses. Using this formalism we analyzed extensive experimental data for photons, protons and heavy ions to evaluate model parameters, quantify the extent of SRD and its impact on cell survival.Main results.Significant accumulation of SRD begins at doses below 1 Gy. As dose increases, so does the number of damaged cells and the amount of SRD in individual cells. SRD buildup in a cell increases the likelihood of complex irrepairable damage. For this reason, during a dose fraction delivery, each dose increment makes cells more radiosensitive. This gradual radosensitization is evidenced by the increasing slope of survival curves observed experimentally. It continues until the fraction is delivered, unless radiosensitivity reaches its maximum first. The maximum radiosensitivity is achieved when SRD accumulated in most cells is the maximum damage they can repair. After this maximum is reached, the slope of a survival curve, logarithm of survival versus dose, becomes constant, dose independent. The survival curve becomes a straight line, as experimental data at high doses show. These processes are random. They cause large cell-to-cell variability in the extent of damage and radiosensitivity of individual cells.Significance.SRD is in effect a radiosensitizer and its accumulation is a significant factor affecting cell survival, especially at high doses. We developed a novel formalism to study this phenomena and reported pertinent data for several particle types.

Endorectal contact radiation boosting: Making the case for dose AND volume reporting

INTRODUCTION

The various rectal endoluminal radiation techniques all have steep, but different, dose gradients. In rectal contact brachytherapy (CXB) doses are typically prescribed and reported to the applicator surface and not to the gross tumor volume (GTV), clinical target volume (CTV) or organs at risk (OAR), which is crucial to understand tumor response and toxicity rates. To quantify the above-described problem, we performed a dose modeling study using a fixed prescription dose at the surface of the applicator and varied tumor response scenarios.

METHODS

Endorectal ultrasound-based 3D-volume-models of rectal tumors and the rectal wall were used to simulate the delivered dose to GTV, CTV and the rectal wall layers, assuming treatment with Maastro HDR contact applicator for rectal cancer with a fixed prescription dose to the applicator surface (equivalent to 3 × 30 Gy CXB) and various response scenarios.

RESULTS

An identical prescribed dose to the surface of the applicator resulted in a broad range of doses delivered to the GTV, CTV and the uninvolved intestinal wall. For example, the equieffective dose in 2 Gy per fraction (EQD2) D90% of the GTV varied between 63 and 231 Gy, whereas the EQD2 D2cc of the rectal wall varied between 97 and 165 Gy.

CONCLUSION

Doses prescribed at the surface are not representative of the dose received by the tumor and the bowel wall. This stresses the relevance of dose reporting and prescription to GTV and CTV volumes and OAR in order to gain insight between delivered dose, local control and toxicity and to optimize treatment protocols.

Bone-only oligometastatic renal cell carcinoma patients treated with stereotactic body radiotherapy: a multi-institutional study

PURPOSE

This study aimed to analyze the prognostic factors associated with overall survival (OS) and progression-free survival (PFS) in patients with bone-only metastatic renal cell carcinoma (RCC) who have five or fewer lesions treated with stereotactic body radiotherapy (SBRT).

METHODS

The clinical data of 54 patients with 70 bone metastases undergoing SBRT treated between 2013 and 2020 with a dose of at least 5 Gy per fraction and a biologically effective dose (BED) of at least 90 Gy were retrospectively evaluated.

RESULTS

The majority of lesions were located in the spine (57.4%) and had only one metastasis (64.8%). After a median follow-up of 22.4 months, the 1‑ and 2‑year OS rates were 84.6% and 67.3%, respectively, and median OS was 43.1 months. The 1‑ and 2‑year PFS rates and median PFS were 63.0%, 38.9%, and 15.3 months, respectively. In SBRT-treated lesions, the 1‑year local control (LC) rate was 94.9%. Age, metastasis localization, and number of fractions of SBRT were significant prognostic factors for OS in univariate analysis. In multivariate analysis, patients with spinal metastasis had better OS compared to their counterparts, and patients who received single-fraction SBRT had better PFS than those who did not. No patient experienced acute or late toxicities of grade 3 or greater.

CONCLUSION

Despite excellent LC at the oligometastatic site treated with SBRT, disease progression was observed in nearly half of patients 13 months after metastasis-directed local therapy, particularly as distant disease progression other than the treated lesion, necessitating an effective systemic treatment to improve treatment outcomes.

Evaluation of Biological Effective Dose in Gamma Knife Staged Stereotactic Radiosurgery for Large Brain Metastases

Objective

Gamma knife (GK) staged stereotactic radiosurgery (Staged-SRS) has become an effective treatment option for large brain metastases (BMs); however, it has been challenging to evaluate the total dose because of tumor shrinkage between two staged sessions. This study aims to evaluate total biological effective dose (BED) in Staged-SRS, and to compare the BED with those in single-fraction SRS (SF-SRS) and hypo-fractionated SRS (HF-SRS).

Methods

Patients treated with GK Staged-SRS at a single institution were retrospectively included. The dose delivered in two sessions of Staged-SRS was summed using the deformable image registration. Each patient was replanned for SF-SRS and HF-SRS. The total BEDs were computed using the linear-quadratic model. Tumor BED_98% and brain V_84Gy2, equivalent to V_12Gy in SF-SRS, were compared between SF-SRS, HF-SRS, and Staged-SRS plans with the Wilcoxon test.

Results

Twelve patients with 24 BMs treated with GK Staged-SRS were identified. We observed significant differences (p < 0.05) in tumor BED_98% but comparable brain V_84Gy2 (p = 0.677) between the Staged-SRS and SF-SRS plans. No dosimetric advantages of Staged-SRS over HF-SRS were observed. Tumor BED_98% in the HF-SRS plans were significantly higher than those in the Staged-SRS plans (p < 0.05). Despite the larger PTVs, brain V_84Gy2 in the HF-SRS plans remained lower (p < 0.05).

Conclusion

We presented an approach to calculate the composite BEDs delivered to both tumor and normal brain tissue in Staged-SRS. Compared to SF-SRS, Staged-SRS delivers a higher dose to tumor but maintains a comparable dose to normal brain tissue. Our results did not show any dosimetric advantages of Staged-SRS over HF-SRS.

Applying Artificial Neural Networks to Develop a Decision Support Tool for Tis-4N0M0 Non-Small-Cell Lung Cancer Treated With Stereotactic Body Radiotherapy

PURPOSE

Clear evidence indicating whether surgery or stereotactic body radiation therapy (SBRT) is best for non-small-cell lung cancer (NSCLC) is lacking. SBRT has many advantages. We used artificial neural networks (NNs) to predict treatment outcomes for patients with NSCLC receiving SBRT, aiming to aid in decision making.

PATIENTS AND METHODS

Among consecutive patients receiving SBRT between 2005 and 2019 in our institution, we retrospectively identified those with Tis-T4N0M0 NSCLC. We constructed two NNs for prediction of overall survival (OS) and cancer progression in the first 5 years after SBRT, which were tested using an internal and an external test data set. We performed risk group stratification, wherein 5-year OS and cancer progression were stratified into three groups.

RESULTS

In total, 692 patients in our institution and 100 patients randomly chosen in the external institution were enrolled. The NNs resulted in concordance indexes for OS of 0.76 (95% CI, 0.73 to 0.79), 0.68 (95% CI, 0.60 to 0.75), and 0.69 (95% CI, 0.61 to 0.76) and area under the curve for cancer progression of 0.80 (95% CI, 0.75 to 0.84), 0.72 (95% CI, 0.60 to 0.83), and 0.70 (95% CI, 0.57 to 0.81) in the training, internal test, and external test data sets, respectively. The survival and cumulative incidence curves were significantly stratified. NNs selected low-risk cancer progression groups of 5.6%, 6.9%, and 7.0% in the training, internal test, and external test data sets, respectively, suggesting that 48% of patients with peripheral Tis-4N0M0 NSCLC can be at low-risk for cancer progression.

CONCLUSION

Predictions of SBRT outcomes using NNs were useful for Tis-4N0M0 NSCLC. Our results are anticipated to open new avenues for NN predictions and provide decision-making guidance for patients and physicians.

Volumetric reduction of brain metastases after stereotactic radiotherapy: Prognostic factors and effect on local control

BACKGROUND AND PURPOSE

Few reports include volumetric measurements as endpoints after stereotactic radiotherapy (SRT) despite the importance of such measurements. This study aimed to (1) investigate the impact of the volumetric response (specifically, an over 65% and over 90% volume reduction in brain metastases) at 6 months post-SRT on local control and (2) identify the predictive factors for a volumetric response of over 65% and over 90%.

MATERIALS AND METHODS

This study included 250 unresected brain metastases (>0.3 cc) treated with SRT. Doses were stratified according to the biological effective dose (BED). The BED was calculated using four models: linear-quadratic (LQ): α/β = 10; LQ: α/β = 20; LQ cubic: α/β = 12; and LQ linear: α/β = 10. The median prescription dose was 30 Gy/3 fractions (BED20, 45). The median follow-up time after SRT was 18.6 months (range, 6.4-81.8 months).

RESULTS

In the multivariate analysis, over 65% volume reduction and over 90% volume reduction were prognostic factors for local control (hazard ratio: 2.370, p = 0.011 and hazard ratio: 3.161, p = 0.014, respectively). A dose of 80% of the gross tumor volume (GTV) D80 > BED20 58 was a predictive factor for over 65% and over 90% volume reductions (odds ratio: 1.975, p = 0.023; odds ratio: 3.204, p < 0.001, respectively).

CONCLUSION

Robust volume reduction of brain metastases at 6 months post-SRT can predict local control. GTV D80 in the LQ model: α/β = 20 may be warranted for good volume reduction.

Radiobiological and Treatment-Related Aspects of Spatially Fractionated Radiotherapy

The continuously evolving field of radiotherapy aims to devise and implement techniques that allow for greater tumour control and better sparing of critical organs. Investigations into the complexity of tumour radiobiology confirmed the high heterogeneity of tumours as being responsible for the often poor treatment outcome. Hypoxic subvolumes, a subpopulation of cancer stem cells, as well as the inherent or acquired radioresistance define tumour aggressiveness and metastatic potential, which remain a therapeutic challenge. Non-conventional irradiation techniques, such as spatially fractionated radiotherapy, have been developed to tackle some of these challenges and to offer a high therapeutic index when treating radioresistant tumours. The goal of this article was to highlight the current knowledge on the molecular and radiobiological mechanisms behind spatially fractionated radiotherapy and to present the up-to-date preclinical and clinical evidence towards the therapeutic potential of this technique involving both photon and proton beams.

Variability of α/β ratios for prostate cancer with the fractionation schedule: caution against using the linear-quadratic model for hypofractionated radiotherapy

BACKGROUND

Prostate cancer (PCa) is known to be suitable for hypofractionated radiotherapy due to the very low α/β ratio (about 1.5-3 Gy). However, several randomized controlled trials have not shown the superiority of hypofractionated radiotherapy over conventionally fractionated radiotherapy. Besides, in vivo and in vitro experimental results show that the linear-quadratic (LQ) model may not be appropriate for hypofractionated radiotherapy, and we guess it may be due to the influence of fractionation schedules on the α/β ratio. Therefore, this study attempted to estimate the α/β ratio in different fractionation schedules and evaluate the applicability of the LQ model in hypofractionated radiotherapy.

METHODS

The maximum likelihood principle in mathematical statistics was used to fit the parameters: α and β values in the tumor control probability (TCP) formula derived from the LQ model. In addition, the fitting results were substituted into the original TCP formula to calculate 5-year biochemical relapse-free survival for further verification.

RESULTS

Information necessary for fitting could be extracted from a total of 23,281 PCa patients. A total of 16,442 PCa patients were grouped according to fractionation schedules. We found that, for patients who received conventionally fractionated radiotherapy, moderately hypofractionated radiotherapy, and stereotactic body radiotherapy, the average α/β ratios were 1.78 Gy (95% CI 1.59-1.98), 3.46 Gy (95% CI 3.27-3.65), and 4.24 Gy (95% CI 4.10-4.39), respectively. Hence, the calculated α/β ratios for PCa tended to become higher when the dose per fraction increased. Among all PCa patients, 14,641 could be grouped according to the risks of PCa in patients receiving radiotherapy with different fractionation schedules. The results showed that as the risk increased, the k (natural logarithm of an effective target cell number) and α values decreased, indicating that the number of effective target cells decreased and the radioresistance increased.

CONCLUSIONS

The LQ model appeared to be inappropriate for high doses per fraction owing to α/β ratios tending to become higher when the dose per fraction increased. Therefore, to convert the conventionally fractionated radiation doses to equivalent high doses per fraction using the standard LQ model, a higher α/β ratio should be used for calculation.

Comprehensive comparison of local effect model IV predictions with the particle irradiation data ensemble

PURPOSE

The increased relative biological effectiveness (RBE) of ions is one of the key benefits of ion radiotherapy compared to conventional radiotherapy with photons. To account for the increased RBE of ions during the process of ion radiotherapy treatment planning, a robust model for RBE predictions is indispensable. Currently, at several ion therapy centers the local effect model I (LEM I) is applied to predict the RBE, which varies with biological and physical impacting factors. After the introduction of LEM I, several model improvements were implemented, leading to the current version, LEM IV, which is systematically tested in this study.

METHODS

As a comprehensive RBE model should give consistent results for a large variety of ion species and energies, the particle irradiation data ensemble (PIDE) is used to systematically validate the LEM IV. The database covers over 1100 photon and ion survival experiments in form of their linear-quadratic parameters for a wide range of ion types and energies. This makes the database an optimal tool to challenge the systematic dependencies of the RBE model. After appropriate filtering of the database, 571 experiments were identified and used as test data.

RESULTS

The study confirms that the LEM IV reflects the RBE systematics observed in measurements well. It is able to reproduce the dependence of RBE on the linear energy transfer (LET) as well as on the α_γ /β_γ ratio for several ion species in a wide energy range. Additionally, the systematic quantitative analysis revealed precision capabilities and limits of the model. At lower LET values, the LEM IV tends to underestimate the RBE with an increasing underestimation with increasing atomic number of the ion. At higher LET values, the LEM IV overestimates the RBE for protons or helium ions, whereas the predictions for heavier ions match experimental data well.

CONCLUSIONS

The LEM IV is able to predict general RBE characteristics for several ion species in a broad energy range. The accuracy of the predictions is reasonable considering the small number of input parameters needed by the model. The detailed quantification of possible systematic deviations, however, enables to identify not only strengths but also limitations of the model. The gained knowledge can be used to develop model adjustments to further improve the model accuracy, which is on the way.

Theoretical derivation and clinical dose-response quantification of a unified multi-activation (UMA) model of cell survival from a logistic equation

OBJECTIVE

To theoretically derive a unified multiactivation (UMA) model of cell survival after ionising radiation that can accurately assess doses and responses in radiotherapy and X-ray imaging.

METHODS

A unified formula with only two parameters in fitting of a cell survival curve (CSC) is first derived from an assumption that radiation-activated cell death pathways compose the first- and second-order reaction kinetics. A logit linear regression of CSC data is used for precise determination of the two model parameters. Intrinsic radiosensitivity, biologically effective dose (BED), equivalent dose to the traditional 2 Gy fractions (EQD2), tumour control probability, normal-tissue complication probability, BED₅₀ and steepness (Γ50) at 50% of tumour control probability (or normal-tissue complication probability) are analytical functions of the model and treatment (or imaging) parameters.

RESULTS

The UMA model has almost perfectly fit typical CSCs over the entire dose range with R²≥0.99. Estimated quantities for stereotactic body radiotherapy of early stage lung cancer and the skin reactions from X-ray imaging agree with clinical results.

CONCLUSION

The proposed UMA model has theoretically resolved the catastrophes of the zero slope at zero dose for multiple target model and the bending curve at high dose for the linear quadratic model. More importantly, it analytically predicts dose-responses to various dose-fraction schemes in radiotherapy and to low dose X-ray imaging based on these preclinical CSCs.

ADVANCES IN KNOWLEDGE

The discovery of a unified formula of CSC over the entire dose range may reveal a common mechanism of the first- and second-order reaction kinetics among multiple CD pathways activated by ionising radiation at various dose levels.

Effect of heterogeneous target dose and radiosensitivity on BED and TCP for different treatment regimens

Purpose.To evaluate how heterogeneity of the target dose and heterogeneity of intra-tumor radiosensitivity affect biologically effective dose (BED) and tumor control probability (TCP) depending on the number of fractions (Nf).Methods.The dependences of TCP and BED in the planning target volume onNfare studied using the linear-quadratic model. In the considered case, the nominal biologically effective dose(BEDnom)is fixed and the variances of the target dose (σD) and radiosensitivity (σα) are assumed to be small.Results.By using series expansion of the survival probability of malignant cells, it is analytically shown that for smallσDandσαboth BED and TCP increase with increasingNfunder the conditionBEDnom=const.In addition, the dependences of BED and TCP onNffor different values ofσDandσαare studied by using an analytical expression for BED in the case of Gaussian distributions of both target dose and radiosensitivity.Conclusions.Small variations in the absorbed dose and intratumor radiosensitivity can significantly reduce BED and TCP. The decreases in these quantities can be reduced by increasing the number of fractions. The findings of this study indicate that hypofractionated regimens withNf=20and dose per fractiond≤5Gy can lead to higher BED and TCP compared to treatment regimens withNf≤5andd≥10Gy commonly used for stereotactic body radiation therapy (SBRT) and stereotactic radiosurgery (SRS).

Classification of tolerable/intolerable mucosal toxicity of head-and-neck radiotherapy schedules with a biomathematical model of cell dynamics

Purpose

The purpose of this study is to present a biomathematical model based on the dynamics of cell populations to predict the tolerability/intolerability of mucosal toxicity in head‐and‐neck radiotherapy.

Methods and Materials

Our model is based on the dynamics of proliferative and functional cell populations in irradiated mucosa, and incorporates the three As: Accelerated proliferation, loss of Asymmetric proliferation, and Abortive divisions. The model consists of a set of delay differential equations, and tolerability is based on the depletion of functional cells during treatment. We calculate the sensitivity (sen) and specificity (spe) of the model in a dataset of 108 radiotherapy schedules, and compare the results with those obtained with three phenomenological classification models, two based on a biologically effective dose (BED) function describing the tolerability boundary (Fowler and Fenwick) and one based on an equivalent dose in 2 Gy fractions (EQD₂) boundary (Strigari). We also perform a machine learning‐like cross‐validation of all the models, splitting the database in two, one for training and one for validation.

Results

When fitting our model to the whole dataset, we obtain predictive values (sen + spe) up to 1.824. The predictive value of our model is very similar to that of the phenomenological models of Fowler (1.785), Fenwick (1.806), and Strigari (1.774). When performing a k = 2 cross‐validation, the specificity and sensitivity in the validation dataset decrease for all models, from ˜1.82 to ˜1.55–1.63. For Fowler, the worsening is higher, down to 1.49.

Conclusions

Our model has proved useful to predict the tolerability/intolerability of a dataset of 108 schedules. As the model is more mechanistic than other available models, it could prove helpful when designing unconventional dose fractionations, schedules not covered by datasets to which phenomenological models of toxicity have been fitted.

Revisiting the formalism of equivalent uniform dose based on the linear-quadratic and universal survival curve models in high-dose stereotactic body radiotherapy

PURPOSE

To examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT).

MATERIALS AND METHODS

For nine non-small-cell carcinoma cell (NSCLC) lines, the linear-quadratic (LQ) and USC models were used to calculate the EUD of a set of hypothetical two-compartment tumor dose-volume histogram (DVH) models. The dose was varied by ±5%, ±10%, and ±20% about the prescription dose (60 Gy/3 fractions) to the first compartment, with fraction volume varying from 1% and 5% to 30%. Clinical DVHs of 21 SBRT treatments of NSCLC prescribed to the 70-83% isodose lines were also considered. The EUD of non-standard SBRT dose fractionation (EUDSBRT) was further converted to standard fractionation of 2 Gy (EUDCFRT) using the LQ and USC models to facilitate comparisons between different SBRT dose fractionations. Tumor control probability (TCP) was then estimated from the LQ- and USC-EUDCFRT.

RESULTS

For non-standard SBRT fractionation, the deviation of the USC- from the LQ-EUDSBRT is largely limited to 5% in the presence of dose variation up to ±20% to fractional tumor volume up to 30% in all NSCLC cell lines. Linear regression with zero constant yielded USC-EUDSBRT = 0.96 × LQ-EUDSBRT (r2 = 0.99) for the clinical DVHs. Converting EUDSBRT into standard 2‑Gy fractions by the LQ formalism produced significantly larger EUDCFRT than the USC formalism, particularly for low [Formula: see text] ratios and large fraction dose. Simplified two-compartment DVH models illustrated that both the LQ- and USC-EUDCFRT values were sensitive to cold spot below the prescription dose with little volume dependence. Their deviations were almost constant for up to 30% dose increase above the prescription. Linear regression with zero constant yielded USC-EUDCFRT = 1.56 × LQ-EUDCFRT (r2 = 0.99) for the clinical DVHs. The clinical LQ-EUDCFRT resulted in median TCP of almost 100% vs. 93.8% with USC-EUDCFRT.

CONCLUSION

A uniform formalism of EUD should be defined among the SBRT community in order to apply it as a single metric for dose reporting and dose-response modeling in high-dose-gradient SBRT because its value depends on the underlying cell survival model and the model parameters. Further investigations of the optimal formalism to derive the EUD through clinical correlations are warranted.

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

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

The role of the spatially fractionated radiation therapy in the management of advanced bulky tumors

Spatially fractionated radiation therapy (SFRT) refers to the delivery of a single large dose of radiation within the target volume in a heterogeneous pattern using either a custom GRID block, multileaf collimators, and virtual methods such as helical tomotherapy or synchrotron-based microbeams. The potential impact of this technique on the regression of bulky deep-seated tumors that do not respond well to conventional radiotherapy has been remarkable. To date, a large number of patients have been treated using the SFRT techniques. However, there are yet many technical and medical challenges that have limited their routine use to a handful of clinics, most commonly for palliative intent. There is also a poor understanding of the biological mechanisms underlying the clinical efficacy of this approach. In this article, the methods of SFRT delivery together with its potential biological mechanisms are presented. Furthermore, technical challenges and clinical achievements along with the radiobiological models used to evaluate the efficacy and safety of SFRT are highlighted.

Evaluation of indirect damage and damage saturation effects in dose-response curves of hypofractionated radiotherapy of early-stage NSCLC and brain metastases

BACKGROUND AND PURPOSE

To investigate the possible contribution of indirect damage and damage saturation to tumour control obtained with SBRT/SRS treatments for early-stage NSCLC and brain metastases.

METHODS AND MATERIALS

We have constructed a dataset of early-stage NSCLC and brain metastases dose-response. These data were fitted to models based on the linear-quadratic (LQ), the linear-quadratic-linear (LQL), and phenomenological modifications of the LQ-model to account for indirect cell damage. We use the Akaike-Information-Criterion formalism to compare performance, and studied the stability of the results with changes in fitting parameters and perturbations on dose/TCP values.

RESULTS

In NSCLC, a modified LQ-model with a beta-term increasing with dose yields the best-fits for α/β = 10 Gy. Only the inclusion of very fast accelerated proliferation or low α/β values can eliminate such superiority. In brain, the LQL model yields the best-fits, and the ranking is not affected by variations of fitting parameters or dose/TCP perturbations.

CONCLUSIONS

For α/β = 10 Gy, a modified LQ-model with a beta-term increasing with dose provides better fits to NSCLC dose-response curves. For brain metastases, the LQL provides the best fit. This might be interpreted as a hint of indirect damage in NSCLC, and damage saturation in brain metastases. The results for NSCLC are strongly dependent on the value of α/β and may require further investigation, while those for brain seem to be clearly significant. Our results can assist in the design of improved radiotherapy for NSCLC and brain metastases, aiming at avoiding over/under-treatment.

Stereotactic Body Radiation Therapy With a High Maximum Dose Improves Local Control, Cancer-Specific Death, and Overall Survival in Peripheral Early-Stage Non-Small Cell Lung Cancer

PURPOSE

We investigated whether delivery of a high biologically effective dose (BED) to primary tumors affects systemic outcomes of cancer-specific death (CSD) and overall survival (OS) rates after stereotactic body radiation therapy (SBRT) in patients with early-stage non-small cell lung cancer (ES-NSCLC).

METHODS AND MATERIALS

Among consecutive ES-NSCLC patients treated with SBRT between 2005 and 2019, we retrospectively identified patients who received a prescription of 50 to 60 Gy in 5 fractions with maximum doses of 62.5 to 100 Gy. Patients were categorized by maximum BED within the planning target volume with a threshold dose of 200 Gy. Outcomes were analyzed in all and matched patients.

RESULTS

Overall, 433 patients were eligible, and 262 and 171 patients were categorized into HighBED and LowBED groups, respectively. After propensity score matching, pairs of 154 patients were selected. Median follow-up times for the HighBED and LowBED groups were 52.3 months (range, 0.8-107.2 months) and 121.6 months (range, 3.0-162.8 months), respectively. The local recurrence rate in the HighBED group was significantly lower than that in the LowBED group (5-year rate, 1.3% and 7.2%; hazard ratio [HR], 0.15; 95% confidence interval [CI], 0.03-0.65; P = .011). Rates of any recurrence and CSD in the HighBED group were significantly lower (5-year any recurrence: 18.1% and 32.1%; HR, 0.52; 95% CI, 0.33-0.83; P = .0058; 5-year CSD: 9.5% and 21.8%; HR, 0.38; 95% CI, 0.20-0.70; P = .002), and OS in the HighBED group was significantly better compared with the LowBED group (5-year rate: 61.7% and 51.8%; HR, 0.71; 95% CI, 0.50-1.00; P = .047).

CONCLUSION

In patients with peripheral ES-NSCLC, SBRT with a high maximum dose may improve not only local control, but also any recurrence, CSD, and OS rates without increased toxicity. Further trials designed to evaluate whether higher intensity SBRT increases local control rates and contributes to improved CSD and OS outcomes are anticipated.

A unified multi-activation (UMA) model of cell survival curves over the entire dose range for calculating equivalent doses in stereotactic body radiation therapy (SBRT), high dose rate brachytherapy (HDRB), and stereotactic radiosurgery (SRS)

PURPOSE

Application of linear-quadratic (LQ) model to large fractional dose treatments is inconsistent with observed cell survival curves having a straight portion at high doses. We have proposed a unified multi-activation (UMA) model to fit cell survival curves over the entire dose range that allows us to calculate EQD2 for hypofractionated SBRT, SRT, SRS, and HDRB.

METHODS

A unified formula of cell survival S = n / e D D o + n - 1 using only the extrapolation number of n and the dose slope of D_o was derived. Coefficient of determination, R² , relative residuals, r, and relative experimental errors, e, normalized to survival fraction at each dose point, were calculated to quantify the goodness in modeling of a survival curve. Analytical solutions for α and β, the coefficients respectively describe the linear and quadratic parts of the survival curve, as well as the α/β ratio for the LQ model and EQD2 at any fractional doses were derived for tumor cells undertaking any fractionated radiation therapy.

RESULTS

Our proposed model fits survival curves of in-vivo and in-vitro tumor cells with R²  > 0.97 and r < e. The predicted α, β, and α/β ratio are significantly different from their values in the LQ model. Average EQD2 of 20-Gy SRS of glioblastomas and melanomas metastatic to the brain, 10-Gy × 5 SBRT of the lung cancer, and 7-Gy × 5 HDRB of endometrial and cervical carcinomas are 36.7 (24.3-48.5), 114.1 (86.6-173.1),, and 45.5 (35-52.6) Gy, different from the LQ model estimates of 50.0, 90.0, and 49.6 Gy, respectively.

CONCLUSION

Our UMA model validated through many tumor cell lines can fit cell survival curves over the entire dose range within their experimental errors. The unified formula theoretically indicates a common mechanism of cell inactivation and can estimate EQD2 at all dose levels.

Impact of target dose inhomogeneity on BED and EUD in lung SBRT

PURPOSE

To evaluate the effect of dose heterogeneity in the treatment target on biologically effective dose (BED) for frequently used hypofractionation regimens in stereotactic body radiation therapy (SBRT).

METHODS

In the case of non-uniform target dose, BED in the planning target volume (PTV) is determined by using the linear-quadratic model. An expression for BED is obtained for an arbitrary dose distribution in the PTV in the case of small variance of the target dose. Another analytical expression for BED is obtained by assuming a Gaussian dose distribution in the target.

RESULTS

Analytical expressions for BED as a function of the variance of the target dose have been derived. It is shown that a relatively small dose inhomogeneity (<5%-6%) can cause a significant reduction (i.e. >10%) in the corresponding BED and equivalent uniform dose (EUD) compared to the case of uniform target dose.

CONCLUSIONS

Small variations in the absorbed dose can significantly reduce BED and EUD in the PTV. The effect of dose non-uniformity on BED increases with increasing dose per fraction. The observed reduction in BED compared to that for uniform target dose can be several times greater for SBRT than for standard fractionation with dose per fraction varying between 1.8 and 2 Gy.

[Repeated irradiation of brain metastases under stereotactic conditions: A review of the literature]

Stereotactic radiotherapy has become a standard in the management of patients with brain metastases; its main interest is to differ whole brain radiotherapy, provider of neurocognitive toxicity and to increase the rate of local control. The repetition of radiotherapy sessions under stereotactic conditions is not codified, neither on the number of technically and clinically possible sessions, nor on the maximum total number or volume of metastases to be treated. The purpose of this review is to analyse the data in the literature concerning repeated irradiations under stereotactic conditions. The second reirradiation in stereotactic condition shows satisfactory results in terms of overall survival, local control, and toxicity. However, we lack data for patients receiving more than two sessions of SRS as well as to define dose constraints to reirradiated healthy tissues. Prospective trials are still needed to validate the management of recurrent brain metastases after initial SRS.

Formulation of objective indices to quantify machine failure risk analysis for interruptions in radiotherapy

Objectives

To evaluate the effect of interruption in radiotherapy due to machine failure in patients and medical institutions using machine failure risk analysis (MFRA).

Material and methods

The risk of machine failure during treatment is assigned to three scores (biological effect, B; occurrence, O; and cost of labor and repair parts, C) for each type of machine failure. The biological patient risk (BPR) and the economic institution risk (EIR) are calculated as the product of B and O (B×O) and C and O (C×O), respectively. The MFRA is performed in two linear accelerators (linacs).

Result

The multileaf collimator (MLC) fault has the highest BPR and second highest EIR. In particular, TrueBeam has a higher BPR and EIR for MLC failures. The total EIR in TrueBeam was significantly higher than that in Clinac iX. The minor interlock had the second highest BPR, whereas a smaller EIR. Meanwhile, the EIR for the LaserGuard fault was the highest, and that for the monitor chamber fault was the second highest. These machine failures occurred in TrueBeam. The BPR and EIR should be evaluated for each linac. Further, the sensitivity of the BPR, it decreased with higher T1/2 and α/β values. No relative difference is observed in the BPR for each machine failure when T1/2 and α/β were varied.

Conclusion

The risk faced by patients and institutions in machine failure may be reduced using MFRA.

Advances in knowledge

For clinical radiotherapy, interruption can occur from unscheduled downtime with machine failures. Interruption causes sublethal damage repair. The current study evaluated the effect of interruption in radiotherapy owing to machine failure on patients and medical institutions using a new method, that is, machine failure risk analysis.

A kinetic model of continuous radiation damage to populations of cells: comparison to the LQ model and application to molecular radiotherapy

The linear-quadratic (LQ) model to describe the survival of irradiated cells may be the most frequently used biomathematical model in radiotherapy. There has been an intense debate on the mechanistic origin of the LQ model. An interesting approach is that of obtaining LQ-like behavior from kinetic models, systems of differential equations that model the induction and repair of damage. Development of such kinetic models is particularly interesting for application to continuous dose rate therapies, such as molecular radiotherapy or brachytherapy. In this work, we present a simple kinetic model that describes the kinetics of populations of tumor cells, rather than lethal/sub-lethal lesions, which may be especially useful for application to continuous dose rate therapies, as in molecular radiotherapy. The multi-compartment model consists of a set of three differential equations. The model incorporates in an easy way different cross-interacting compartments of cells forming a tumor, and may be of especial interest for studying dynamics of treated tumors. In the fast dose delivery limit, the model can be analytically solved, obtaining a simple closed-form expression. Fitting of several surviving curves with both this solution and the LQ model shows that they produce similar fits, despite being functionally different. We have also investigated the operation of the model in the continuous dose rate scenario, firstly by fitting pre-clinical data of tumor response to ¹³¹I-CLR1404 therapy, and secondly by showing how damage repair and proliferation rates can cause a treatment to achieve control or not. Kinetic models like the one presented in this work may be of special interest when modeling response to molecular radiotherapy.

A simple dosimetric approach to spatially fractionated GRID radiation therapy using the multileaf collimator for treatment of breast cancers in the prone position

The purpose of this study was to explore the treatment planning methods of spatially fractionated radiation therapy (SFRT), commonly referred to as GRID therapy, in the treatment of breast cancer patients using multileaf collimator (MLC) in the prone position. A total of 12 patients with either left or right breast cancer were retrospectively chosen. The computed tomography (CT) images taken for the whole breast external beam radiation therapy (WB‐EBRT) were used for GRID therapy planning. Each GRID plan was made by using two portals and each portal had two fields with 1‐cm aperture size. The dose prescription point was placed at the center of the target volume, and a dose of 20 Gy with 6‐MV beams was prescribed. Dose‐volume histogram (DVH) curves were generated to evaluate dosimetric properties. A modified linear‐quadratic (MLQ) radiobiological response model was used to assess the equivalent uniform doses (EUD) and therapeutic ratios (TRs) of all GRID plans. The DVH curves indicated that these MLC‐based GRID therapy plans can deliver heterogeneous dose distribution in the target volume as seen with the conventional cerrobend GRID block. The plans generated by the MLC technique also demonstrated the advantage for accommodating different target shapes, sparing normal structures, and reporting dose metrics to the targets and the organs at risks. All GRID plans showed to have similar dosimetric parameters, implying the plans can be made in a consistent quality regardless of the shape of the target and the size of volume. The mean dose of lung and heart were respectively below 0.6 and 0.7 Gy. When the size of aperture is increased from 1 to 2 cm, the EUD and TR became smaller, but the peak/valley dose ratio (PVDR) became greater. The dosimetric approach of this study was proven to be simple, practical and easy to be implemented in clinic.

Radial basis function-generated finite difference scheme for simulating the brain cancer growth model under radiotherapy in various types of computational domains

BACKGROUND AND OBJECTIVES

We extend the original mathematical model, i.e., Swanson's reaction-diffusion equation to the surfaces with no boundary, and we find a new numerical method based on a meshless approach for solving numerically Swanson's reaction-diffusion model in the square and on the sphere.

METHODS

To solve numerically the Swanson's reaction-diffusion model and its extension version, a collocation meshless technique, namely radial basis function-generated finite difference (RBF-FD) scheme is employed for approximating the spatial variables in the square domain and on the sphere, respectively. Also, to approximate the time variable of the studied models, a first-order semi-implicit backward Euler scheme is used. The resulting fully discrete scheme is a linear system of algebraic equations per time step that is solved via the biconjugate gradient stabilized (BiCGSTAB) iterative algorithm with a zero-fill incomplete lower-upper (ILU) preconditioner.

RESULTS

The numerical simulations show the growth of untreated and treated brain tumors with radiotherapy using estimated and clinical data (given from magnetic resonance imaging (MRI) scans of patients). Moreover, the results reported here can be used for improving the treatment strategies of the invasive brain tumor.

CONCLUSIONS

Using the developed numerical scheme in this paper, we can simulate the behavior of the invasive form of brain tumor response to radiotherapy. Also, we can see the effects of radiation response on the brain tumor cell concentration of individual patients. The proposed meshless technique, which is applied for solving numerically the studied model, does not depend on any background mesh or triangulation for approximation in comparison with mesh-dependent methods. Moreover, we apply this technique to the sphere via any set of distributed points easily.

Advances in Radiobiology of Stereotactic Ablative Radiotherapy

Radiotherapy (RT) has been developed with remarkable technological advances in recent years. The accuracy of RT is dramatically improved and accordingly high dose radiation of the tumors could be precisely projected. Stereotactic radiosurgery (SRS) and stereotactic body radiotherapy (SBRT), also known as stereotactic ablative radiotherapy (SABR), are rapidly becoming the accepted practice in treating solid small sized tumors. Compared with the conventional fractionation external beam radiotherapy (EBRT), SABR with very high dose per fraction and hypo-fractionated irradiation yields convincing and satisfied therapeutic effects with low toxicity, since tumor cells could be directly ablated like radiofrequency ablation (RFA). The impressive clinical efficacy of SABR is greater than expected by the linear quadratic model and the conventional radiobiological principles, i.e., 4 Rs of radiobiology (reoxygenation, repair, redistribution, and repopulation), which may no longer be suitable for the explanation of SABR's ablation effects. Based on 4 Rs of radiobiology, 5 Rs of radiobiology emphasizes the intrinsic radiosensitivity of tumor cells, which may correlate with the responsiveness of SABR. Meanwhile, SABR induced the radiobiological alteration including vascular endothelial injury and the immune activation, which has been indicated by literature reported to play a crucial role in tumor control. However, a comprehensive review involving these advances in SABR is lacking. In this review, advances in radiobiology of SABR including the role of the 4 Rs of radiobiology and potential radiobiological factors for SABR will be comprehensively reviewed and discussed.

A mathematical model of dynamics of cell populations in squamous epithelium after irradiation

PURPOSE

To develop multi-compartment mechanistic models of dynamics of stem and functional cell populations in epithelium after irradiation. Methods and materials: We present two models, with three (3C) and four (4C) compartments respectively. We use delay differential equations, and include accelerated proliferation, loss of division asymmetry, progressive death of abortive stem cells, and turnover of functional cells. The models are used to fit experimental data on the variations of the number of cells in mice mucosa after irradiation with 13 Gy and 20 Gy. Akaike information criteria (AIC) was used to evaluate the performance of each model.

RESULTS

Both 3C and 4C models provide good fits to experimental data for 13 Gy. Fits for 20 Gy are slightly poorer and may be affected by larger uncertainties and fluctuations of experimental data. Best fits are obtained by imposing constraints on the fitting parameters, so to have values that are within experimental ranges. There is some degeneration in the fits, as different sets of parameters provide similarly good fits.

CONCLUSIONS

The models provide good fits to experimental data. Mechanistic approaches like this can facilitate the development of mucositis response models to nonstandard schedules/treatment combinations not covered by datasets to which phenomenological models have been fitted. Studying the dynamics of cell populations in multifraction treatments, and finding links with induced toxicity, is the next step of this work.

Holistic View on Cell Survival and DNA Damage: How Model-Based Data Analysis Supports Exploration of Dynamics in Biological Systems

In this work, a method is established to calibrate a model that describes the basic dynamics of DNA damage and repair. The model can be used to extend planning for radiotherapy and hyperthermia in order to include the biological effects. In contrast to “syntactic” models (e.g., describing molecular kinetics), the model used here describes radiobiological semantics, resulting in a more powerful model but also in a far more challenging calibration. Model calibration is attempted from clonogenic assay data (doses of 0–6 Gy) and from time-resolved comet assay data obtained within 6 h after irradiation with 6 Gy. It is demonstrated that either of those two sources of information alone is insufficient for successful model calibration, and that both sources of information combined in a holistic approach are necessary to find viable model parameters. Approximate Bayesian computation (ABC) with simulated annealing is used for parameter search, revealing two aspects that are beneficial to resolving the calibration problem: (1) assessing posterior parameter distributions instead of point-estimates and (2) combining calibration runs from different assays by joining posterior distributions instead of running a single calibration run with a combined, computationally very expensive objective function.

Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy

The present work of review collects and evidences the main results of our previous papers on the optimization of fractionated radiotherapy protocols. The problem under investigation is presented here in a unitary framework as a nonlinear programming application that aims to determine the optimal schemes of dose fractionation commonly used in external beam radiotherapy. The radiation responses of tumor and normal tissues are described by means of the linear quadratic model. We formulate a nonlinear, non-convex optimization problem including two quadratic constraints to limit the collateral normal tissue damages and linear box constraints on the fractional dose sizes. The general problem is decomposed into two subproblems: (1) analytical determination of the optimal fraction dose sizes as a function of the model parameters for arbitrarily fixed treatment lengths; and (2) numerical determination of the optimal fraction number, and of the optimal treatment time, in different parameter settings. After establishing the boundedness of the optimal number of fractions, we investigate by numerical simulation the optimal solution behavior for experimentally meaningful parameter ranges, recognizing the crucial role of some parameters, such as the radiosensitivity ratio, in determining the optimality of hypo- or equi-fractionated treatments. Our results agree with findings of the theoretical and clinical literature.

A radiobiological study of the schemes with a low number of fractions in high-dose-rate brachytherapy as monotherapy for prostate cancer

Purpose

Schemes with high doses per fraction and small number of fractions are commonly used in high-dose-rate brachytherapy (HDR-BT) for prostate cancer. Our aim was to analyze the differences between published clinical results and the predictions of radiobiological models for absorbed dose required in a single fraction monotherapy HDR-BT.

Material and methods

Published HDR-BT clinical results for low- and intermediate-risk patients with prostate cancer were revised. For 13 clinical studies with 16 fractionation schedules between 1 and 9 fractions, a dose-response relation in terms of the biochemical control probability (BC) was established using Monte Carlo-based statistical methods.

Results

We obtained a value of α/β = 22.8 Gy (15.1-60.2 Gy) (95% CI) much larger than the values in the range 1.5-3.0 Gy that are usually considered to compare the results of different fractionation schemes in prostate cancer radiotherapy using doses per fraction below 6 Gy. The doses in a single fraction producing BC = 90% and 95% were 22.3 Gy (21.5-24.2 Gy) and 24.3 Gy (23.0-27.9 Gy), respectively.

Conclusions

The α/β obtained in our analysis of 22.8 Gy for a range of dose per fraction between 6 and 20.5 Gy was much greater than the one currently estimated for prostate cancer using low doses per fraction. This high value of α/β explains reasonably well the data available in the region of high doses per fraction considered.