Introduction Significant advances in systemic therapy have improved survival for patients with advanced-stage non-small cell lung cancer (NSCLC). However, the present treatment strategies and dose-fractionation for high-dose palliative radiotherapy (RT) are based on trials from the 1990s, when RT planning was simple with less precise delivery. Contemporary lung RT uses 4D-CT, volumetric modulated arc radiotherapy, aided by online verification using cone beam CT, which enables greater accuracy and better target volume coverage, while reducing doses to normal organs at risk. The Shortened High-dose Palliative Radiotherapy for Lung Cancer study aims to evaluate the safety and feasibility of reducing the number of RT fractions and RT duration, using contemporary planning, verification and delivery techniques.Methods and analysis This single-arm, multicentre, phase-II study will test the shortened hypofractionated accelerated palliative RT regimen of 30 Gy in 6 alternate-day fractions, with strict normal tissue dose constraints. We aim to recruit 37 patients across 4 sites within the West Midlands. Quality assurance for the RT is supported by the Radiotherapy Trials Quality Assurance Group (RTTQA). Patients with locally advanced or metastatic NSCLC, who are candidates for high-dose palliative RT, before or after first-line systemic therapy, are eligible for recruitment. The primary objective of this study is to assess the safety of the proposed dose-fractionation. Secondary objectives include evaluating toxicity profiles, patient-reported outcome measures, time to progression, feasibility and the National Health Service cost-saving.Ethics and dissemination This study is conducted in accordance with the International Council for Harmonisation Good Clinical Practice (ICH GCP) guidelines and all applicable regulatory frameworks, including, but not limited to, the UK policy framework for health and social care research, as well as the Health Research Authority and Health and Care Research Wales regulations. Approval for the study was granted on 18 April 2024 (IRAS project ID: 332998; REC reference: 24/WM/0032). The chief investigator is responsible for obtaining informed consent from participants. Any individual delegated this responsibility is thoroughly authorised, trained and competent to conduct the informed consent process. On completion of the trial, the results will be shared with participants in a plain language summary and will be submitted for publication in a peer-reviewed journal. If successful, this study will inform a phase III randomised controlled trial to assess efficacy. For updates on the study, visit the study web page (https://research.mededcoventry.org/About-Us/Meet-The-Team/TMU/Ship-Rt).Trial registration number NCT06483308.

Aim of studyFast neutron data from Hammersmith (UK) showed that the inverse relationship between dose and RBE (Relative Biological Effectiveness) is not maintained in many in vivo situations, originally attributed to hypoxic effects. The present study aims to simulate these RBE patterns in two cancers and one normal tissue for neutrons as well as protons.MethodsA new model uses LQ formulism with radiosensitivity changes increasing with LET and with LET-related reductions in hypoxia. Inequalities are defined for the parameter ratios used to estimate RBEs in oxic and hypoxic compartments, with the overall RBE being also determined by the initial hypoxic fraction and the compartmental surviving fractions with increasing dose. Extrapolation from neutrons to protons is assumed by using a 90% RBE reduction for the excess of RBE beyond unity. Also, the separate influence of the dose rate effect on RBE at higher doses is investigated.ResultsFor normal skin, the C3H mouse mammary carcinoma and the Ehrlich ascites cancer, three quite different RBE responses are fitted by the model within practical statistical bounds. The overall RBE initially follows the oxic curve but shifts with increasing dose to the higher hypoxic RBE curve, the response depending mostly on the pretreatment hypoxic fraction and other hypoxia parameters. Such patterns of RBE changes are also obtained for protons, but cannot be obtained from the dose rate effect at higher dose, although the DNA repair rate will increase RBE with dose.ConclusionsThis tentative but complex radiobiological modelling study shows that the Hammersmith neutron RBE results can be simulated by the presence of two physiological compartments and that similar RBE changes may occur for protons. Further experimental research is suggested for determining if protons do show effects at similar dose ranges, which could be relevant for hypo-fractionated or single fraction schedules.

Purpose: The purpose of this study is to analyze the relationship between nuclear charge (Z), atomic mass (A), LET (linear energy transfer for maximal relative biological effectiveness (RBE)) for accelerated ions based on the hypothesis that for each ion, LETU is related to their nuclear radius. Methods: Published LETU data for proton, helium, carbon, neon, silicon, argon, and iron ions and their Z and A numbers are fitted by a power law function (PLF) and compared with PLF based on atomic cross-sections and nuclear dimensions for spherical or spheroidal atomic nuclei. The PLF allows for isoeffective RBE estimations for different ions at any value of LET based on the LETU estimations. For any two ions, A and B, and a specified bioeffect obtained at LETA, the equivalent isoeffective LETB, is estimated using LETB=LETA.LETU[B]LETU[A]. Results: The data-fitting program provided the following results: LETU=78.1.A0.26, and LETU=86.6.Z0.29, where 78.1 and 86.6 keV.μm−1 are the proton LETU values (i.e., without proton cellular range limit considerations). Goodness-of-fit tests are similar for each model, but the proton estimations differ. These exponents are lower than 0.66 and 0.33 (those for nuclear cross-sections and spherical nuclear radii, respectively), but suggest prolate nuclear shapes in most of the ions studied. Worked examples of estimating isoeffective LET values for two different ions are provided. Conclusions: The fitted power law relationships between LETU and Z or A are broadly equivalent and compatible with prolate nuclear shapes. These models may offer a more rational basis for future ion-beam radiobiology research.

Stereotactic ablative body radiotherapy (SABR) is routinely used for the management of oligometastatic disease. Increasingly, there is overlap of targets or organs at risk with previous radiotherapy fields. As substantial variation in delivery of clinical practice exists, the UK SABR Consortium worked with a collaborative national group to develop pelvic SABR re-irradiation consensus guidelines. The scope of the guidance includes patient selection criteria, pre-treatment considerations, delineation guidelines, dose prescription, calculations of cumulative dose constraints, and optimal planning technique. This guidance is part of an ongoing national prospective audit in collaboration with the Royal College of Radiologists and EORTC ReCare.

PURPOSE:To model relative biological effectiveness (RBE) differences found in two studies which used spread-out Bragg-peaks (SOBP) placed at (a) superficial depth and (b) at the maximum range depth. For pencil beam scanning (PBS), RBE at similar points within the SOBP did not change between the two extreme SOBP placement depths; in passively scattered beams (PSB), high RBE values (typically 1.2-1.3) were found within superficially- placed SOBP but reduced to lower values (1-1.07) at similar points within the extreme-depth positioned SOBP. The dose, LET (linear energy transfer) distributions along each SOBP were closely comparable regardless of placement depth, but significant changes in dose rate occurred with depth in the PSB beam. METHODS:The equations used allow α and β changes with falling dose rate (the converse to FLASH studies) in PSB, resulting in reduced α/β ratios, compatible with a reduction in micro-volumetric energy transfer (the product of Fluence and LET), with commensurate reductions in RBE. The experimental depth-distances, positions within SOBP, observed dose-rates and radiosensitivity ratios were used to estimate the changes in RBE. RESULTS:RBE values within a 5 % tolerance limit of the experimental results for PSB were found at the deepest SOBP placement. No RBE changes were predicted for PBS beams, as in the published results. CONCLUSIONS:Enhanced proton therapy toxicity might occur with PBS when compared with PSB for deeply positioned SOBP due to the maintenance of higher RBE. Scanned pencil beam users need to be vigilant about RBE and further research is indicated.

Any radiotherapy schedule can be characterised by its 2 Gy per fraction equivalent dose (EQD2). EQD2s are easily calculated for late-responding normal tissues but for tumours significant errors may arise if no allowance is made for any repopulation which occurs in the reference and/or the derived EQD2 schedule. This article presents a systematic approach to calculating tumour EQD2 values utilising the concept of biologically effective dose (BED) with inclusion of repopulation effects. A factor (f) is introduced which allows the inter-dependence between EQD2 and its delivery time (and, hence, the amount of repopulation involved) to be embedded within the formulation without any additional assumptions. There exists a transitional BED below which simple methods of calculating tumour EQD2 remain valid. In cases where simpler approaches are inadequate, the correct EQD2 may be determined from the reference schedule BED (BEDref) by the relationship: EQD2 = A x BEDref - B, where A and B are constants which involve the same radiobiological parameters as are conventionally used in deriving tumour BED values. Some Worked Examples illustrate application of the method to fractionated radiotherapy and indicate that there can be substantial differences with results obtained from using over-simplified approaches. Since reference BEDs are calculable for other types of radiotherapy (brachytherapy, permanent implants, high-LET applications, etc) the methodology allows estimation of tumour EQD2 values in a wide range of clinical circumstances, including cases which involve interrupted treatments.

-OBJECTIVE: To recalculate biological effective dose values (BED) for radio-surgical treatments of acoustic neuroma from a previous study. BEDs values were previ-ously overestimated by only using beam-on times in cal-culations, so excluding the important beam-off-times (when deoxyribonucleic acid repair continues) which contribute to the overall treatment time. Simple BED esti-mations using a mono-exponential approximation may not always be appropriate but if used should include overall treatment time.-METHODS: Time intervals between isocenters were estimated. These were especially important for the Gamma Knife Model 4C cases since manual changes significantly increase overall treatment times. Individual treatment pa-rameters, such as iso-center number, beam-on-time, and beam-off-time, were then used to calculate BED values using a more appropriate bi-exponential model that in-cludes fast and slow components of DNA damage repair over a wider time range.-RESULTS: The revised BED estimates differed signifi-cantly from previously published values. The overestimates of BED, obtained using beam-on-time only, varied from 0%e40.3%. BED subclasses, each with a BED range of 5 Gy2.47, indicated that revised values were consistently reduced when compared with originally quoted values, especially for 4C compared with Perfexion cases. Furthermore, subdivision of 4C cases by collimator number further emphasized the impact of scheduled gap times on BED. Further analysis demonstrated important limitations of the mono-exponential model. Target volume was a major confounding factor in the interpretation of the results of this study.-CONCLUSIONS: BED values should be estimated by including beam-on and beam-off times. Suggestions are provided for more accurate BED estimations in future studies.

Purpose Equivalent dose in 2 Gy fractions (EQD2), based on the original biological effective dose (BED) equation, is frequently used to guide treatment in the clinic. This work addresses the limitations of EQD2 in the context of voxelized dosimetry, clarifies potential sources of confusion, and provides an alternative formulation for improved precision. Methods and Materials The EQD2 formula was evaluated by a simple insertion of the EQD2 dose into the BED equation. The mathematically exact form of EQD2, referred to here as equivalent physical dose (EPD), was provided by solving the linear-quadratic model BED equation for dose using the quadratic formula. The EPD derivation was compared in terms of absolute error to the EQD2 derivation, which separates the Relative Effect term from the BED equation. Results The EQD2 expression implicitly assumed a homogenous dose, demonstrating that its use in voxelized dosimetry can mislead. As an alternative formulation, EPD was shown to adhere more closely to the first principles of radiobiological modeling. An error analysis identified absolute errors from EQD2 sometimes in excess of 10%. Conclusions Assumptions in the standard EQD2 equation are inappropriate in the context of voxelized dosimetry, where voxels within a structure, such as a target volume, may receive a dose that differs from the prescribed dose. Using EPD (or BED) instead of EQD2 would address these areas of confusion. Optimizing therapy according to biological properties in this way could provide enhanced and more reliable radiobiological input to radiotherapy treatment planning. ### Competing Interest Statement Elliot Abbott has a patent pending PCT/US2022/049727. Bleddyn Jones is occasionally asked to provide competency and causation evidence to UK courts regarding radiation oncology errors and/or treatment delays, where there is some difficulty requiring specialist clinical radiobiological knowledge and where radiobiological modeling is indicated in the analysis of individual patient adverse events (paid on a retrospective basis); has participated on a board for ESTRO proton therapy network. Adam Turner has stock in GT Medical Technologies, Inc. Katherine Vallis has provided grant funding to CRUK Oxford Radnet Centre since the initial planning of the work; has received grant funding from Prostate Cancer UK, BBSRC, Theradnet (EU MC-ITN); has received consulting fees for Guidepoint Global; has received keynote speaker honorarium for Allied Health Sciences Conference at West China Hospital; has received travel and accommodation support as a speaker for GRC Conference Metals in Medicine 2022, PEGs Boston Conference 2023, Allied Health Sciences Conferences at West China Hospital, and visiting Professorship at Tri Service Hospital, Taipei; has patent pending WOPCT/GB2022/052093; is a member of the External Advisory Board (without payment) at Princess Margaret Comprehensive Cancer Centre Radiation Medicine Program, Toronto and at MITHRaS (Molecular Imaging and Therapy with Radionuclides) Program, Kings College London; is the Deputy Chair of the Grant Review Panel (without payment) for Breast Cancer Now; is a member of the Grant Review Panel (without payment) for Prostate Cancer UK; is a member of the User Selection Group (without payment) for PRISMAP (European Network for Medical Radionuclides); is Chair for the Review Panel for Selection of Integrated Cancer Research Sites, 2022 (Honorarium) at the French National Cancer Institute. ### Funding Statement KV acknowledges grant support from CRUK (C6078/A28736). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present work are contained in the manuscript

This article considers quantitative comparisons of radiation effectiveness across a large range of dose rates, including low (LDR), medium, conventional or high (HDR) and ultra-high (or FLASH) dose rates. For comparisons of different continuous radiotherapy prescriptions, the linear quadratic model was used to derive 'biological effective dose' (BED) equations which included time-dependent enzymatic DNA repair in the low to high dose rate range for monophasic or biphasic repair kinetics. In a recent publication, much higher dose rates, associated with increasing overall radioresistance, was thought to be governed by a cube root (or similar) function of dose rate (which expresses the intensification of micro-volumetric linear energy transfer per unit volume and correlates with average inter-track distances) with resultant increases in the apparent alpha/beta ratios. Explicit equations for assessments of BED* (defined as the excess BED beyond the threshold BED) are presented for dose rates ranging from around 0.1-5 x 106 Gy per hr. The method can also be adapted for tumour control comparisons. Graphical presentations are used to determine iso-effective doses of similar BED* values at different dose rates, for specified radiation doses. The threshold BEDs for radio-tolerance reduce in proportion to the change in the alpha radiosensitivity parameter. For dose rates above the HDR range, the intrinsic alpha/beta ratio, which is independent of dose rate, continues to influence the magnitude of the changes in BED and dose required for a specified bio-effect, but in a modified form. For further research purposes, these tentative methods can provide isoeffective dose estimates to guide ra-diation use at different dose rates, but require further specific experimental validation. The methods may seem complex and contain many pitfalls. Further research is also required to identify residual enigmas, such as the exact dose rate and dose at which biological FLASH effects begin to operate and to validate these isoeffective dose predictions.