A generalised method for calculating repopulation-corrected tumour EQD2 values in a wide range of clinical situations, including interrupted treatments.

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 × 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.

Feasibility and safety of shortened hypofractionated high-dose palliative lung radiotherapy - A retrospective planning study.

OBJECTIVE: Assess the safety and feasibility of shortened hypofractionated high-dose palliative lung radiotherapy in a retrospective planning study. METHODS: Fifteen late stage (III or IV) NSCLC lung radiotherapy patients previously treated with the standard palliative 36 Gy in 12 fractions (12F) schedule were non-randomly selected to achieve a representative distribution of tumour sizes, volumes, and location. Plans were produced using 30 Gy in 5 fractions (5F) and 6 fractions (6F) using a 6MV FFF co-planar VMAT technique. Plans were optimised to meet dose-constraints for planning target volumes (PTVs) and organs at risk (OARs) with established OAR constraints expressed as biological equivalent doses (BEDs). The potential safety was assessed using these BEDs and also with reductions of 10% (BED-10%) and 20% (BED-20%) to account for a reduction in tolerance doses from the effects of chemotherapy or surgery. RESULTS: Mandatory BED constraints were met for all fifteen 5F and 6F plans; BED-10% constraints were met by all 6F plans and six 5F plans. BED-20% constraints were met by six 6F and three 5F respectively. CONCLUSION: It is potentially safe and feasible to deliver high-dose palliative radiotherapy for late stage NSCLC using the 5F or 6F regimes described, when planned to comparable OAR BEDs as standard radical techniques. It appears toxicity from these regimes should be within acceptable limits provided the dose-constraints described are met. A Phase II study is required to fully assess safety and feasibility, the outcomes of which could reduce the number of patient hospital visits for radiotherapy, thereby benefiting patients and optimising resource utilisation.

Improving the Accuracy of Biologically Effective Dose Estimates, from a Previously Published Study, After Radiosurgery for Acoustic Neuromas.

OBJECTIVE: To recalculate biological effective dose values (BED) for radio-surgical treatments of acoustic neuroma from a previous study. BEDs values were previously overestimated by only using beam-on times in calculations, so excluding the important beam-off-times (when deoxyribonucleic acid repair continues) which contribute to the overall treatment time. Simple BED estimations 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 parameters, 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 includes fast and slow components of DNA damage repair over a wider time range. RESULTS: The revised BED estimates differed significantly from previously published values. The overestimates of BED, obtained using beam-on-time only, varied from 0%-40.3%. 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.

The influence of hypoxia on LET and RBE relationships with implications for ultra-high dose rates and FLASH modelling.

Objective. To investigate relationships between linear energy transfer (LET), fluence rates, changes in radiosensitivity and the oxygen enhancement ratio (OER) in different ion beams and extend these concepts to ultra-high dose rate (UHDR) or FLASH effects.Approach.LET values providing maximum relative biological effect (RBE), designated as LETU, are found for neon, carbon and helium beams. Proton experiments show reduced RBEs with depth in scattered (divergent) beams, but not with scanned beams, suggesting that instantaneous fluence rates (related to track separation distances) can modify RBE, all other RBE-determining factors being equal. Micro-volumetric energy transfer perµm3(mVET) is defined by LET × fluence. High fluence rates will increase mVET rates, with proportional shifts of LETUto lower values due to more rapid energy transfer. From the relationship between LETUand OER at conventional dose rates, OER reductions in UHDR/FLASH exposures can be estimated and biological effective dose analysis of experimental lung and skin reactions becomes feasible.Main results.The Furusawaet aldata show that hypoxic LETUvalues exceed their oxic counterparts. OER reduces from around 3-1.25 at LETU, although the relative radiosensitivities of the oxic and hypoxicαparameters (the OER(α)) exceed those of the standard OER values. Increased fluence rates are predicted to reduce LETUand OER. Large FLASH single doses will minimise RBE increments due to theßparameter reducing by a factor of 0.5-0.25 consistent with oxygen depletion, causing radioresistance. Similar results will occur for photons. Tissueα/ßratios increase by around 10 in FLASH conditions, agreeing with derived ion-beam dose rate equations.Significance.Increasing dose rates enhance local energy deposition rate per unit volume, probably causing oxygen depletion and radioresistance in pre-existing hypoxic sites during UHDR/FLASH exposures. The modelled equations provide testable hypotheses for further dose rate investigations in photon, proton and ion beams.

Further development of spinal cord retreatment dose estimation: including radiotherapy with protons and light ions.

PURPOSE: A graphical user interface (GUI) was developed to aid in the assessment of changes in the radiation tolerance of spinal cord/similar central nervous system tissues with time between two individual treatment courses. METHODS: The GUI allows any combination of photons, protons (or ions) to be used as the initial, or retreatment, radiotherapy courses. Allowances for clinical circumstances, of reduced tolerance, can also be made. The radiobiological model was published previously and has been incorporated with additional checks and safety features, to be as safe to use as possible. The proton option includes use of a fixed RBE of 1.1 (set as the default), or a variable RBE, the latter depending on the proton linear energy transfer (LET) for organs at risk. This second LET-based approach can also be used for ions, by changing the LET parameters. RESULTS: GUI screenshots are used to show the input and output parameters for different clinical situations used in worked examples. The results from the GUI are in agreement with manual calculations, but the results are now rapidly available without tedious and error-prone manual computations. The software outputs provide a maximum dose limit boundary, which should not be exceeded. Clinicians may also choose to further lower the number of treatment fractions, whilst using the same dose per fraction (or conversely a lower dose per fraction but with the same number of fractions) in order to achieve the intended clinical benefit as safely as possible. CONCLUSIONS: The new GUI will allow scientific-based estimations of time related radiation tolerance changes in the spinal cord and similar central nervous tissues (optic chiasm, brainstem), which can be used to guide the choice of retreatment dose fractionation schedules, with either photons, protons or ions.

Low radiation dose to treat pneumonia and other inflammations.

Infection, the invasion of pathogenic microorganisms and viruses, causes reactive inflammation mediated by endogenous signals, with influx of leucocytes with distinct properties and capable of mounting a cellular or antibody response. Different forms of inflammation may also occur in response to tumours, in allergy and autoimmune disorders. Pneumonia, respiratory tract infection and septic shock for instance can arise as serious complications of the Covid-19 virus. While radiotherapy has been most widely used to control malignant tumours, it has also been used for treatment of non-malignant diseases, including acute and chronic inflammation in situations where anti-inflammatory drugs may be ineffective or contraindicated. The present review examines the history and prospects for low-dose anti-inflammatory radiation treatments, the present interest largely being motivated by the increased incidence of pulmonary disease associated Covid-19 infections. Evidence in support of the suggested efficacy are covered, together with an appraisal of one of the number of potential convenient sources that could complement external beam arrangements.

Fast neutron energy based modelling of biological effectiveness with implications for proton and ion beams.

A practical neutron energy dependent RBE model has been developed, based on the relationship between a mono-energetic neutron energy and its likely recoil proton energy. Essentially, the linear energy transfer (LET) values of the most appropriate recoil proton energies are then used to modify the linear quadratic model radiosensitivities (α and ß) from their reference LET radiation values to provide the RBE estimates. Experimental neutron studies published by Hall (including some mono-energetic beams ranging from 0.2 to 15 MeV), Broerse, Berry, and data from the Clatterbridge and Detroit clinical neutron beams, which all contain some data from a spectrum of neutron energies, are used to derive single effective neutron energies (NEeff) for each spectral beam. These energies yield a recoil proton spectrum, but with an effective mean proton energy (being around 50% of NEeff). The fractional increase in LET is given by the recoil proton LET divided by the proton (LETU) value which provides the highest RBE. This ratio is then used to determine the change in the linear-quadratic model α and ß parameters, from those of the reference radiation, to estimate the RBE. The predicted proton recoil RBE is then reasonably close to the experimental neutron RBE values found when taking into account the variation inherent in biological experiments. The work has some important consequences. The data of Hall et al (1975 Radiat. Res. 64 245-55) shows that the highest RBE values are found with neutron energies around 0.3-0.4 MeV, but this energy cannot possibly generate recoil proton energies which are higher, as necessary for a 0.68 MeV proton with a 30.5 keV µm-1 LETU (the LET value which provides the maximum obtainable RBE for a specified ion). For 0.4 MeV neutrons with proton recoil energies of around 0.2 MeV, the latter have a LET of around 62.88 keV µm-1. This could have an impact on proton beam RBE modelling. However, this is compensated by finding that the maximum radiosensitivity for mono-energetic neutrons was around 1.7 times larger than previously suggested from experimental ion beam studies, probably due to the necessary spreading out of Bragg peaks for ion beam experimental purposes, sampling errors and particle range considerations. This semi-empirical model can be used with minimal computer support and could have applications in ionic beams and in radioprotection.

Clinical Radiobiology of Fast Neutron Therapy: What Was Learnt?

Neutron therapy was developed from neutron radiobiology experiments, and had identified a higher cell kill per unit dose and an accompanying reduction in oxygen dependency. But experts such as Hal Gray were sceptical about clinical applications, for good reasons. Gray knew that the increase in relative biological effectiveness (RBE) with dose fall-off could produce marked clinical limitations. After many years of research, this treatment did not produce the expected gains in tumour control relative to normal tissue toxicity, as predicted by Gray. More detailed reasons for this are discussed in this paper. Neutrons do not have Bragg peaks and so did not selectively spare many tissues from radiation exposure; the constant neutron RBE tumour prescription values did not represent the probable higher RBE values in late-reacting tissues with low α/ß values; the inevitable increase in RBE as dose falls along a beam would also contribute to greater toxicity than in a similar megavoltage photon beam. Some tissues such as the central nervous system white matter had the highest RBEs partly because of the higher percentage hydrogen content in lipid-containing molecules. All the above factors contributed to disappointing clinical results found in a series of randomised controlled studies at many treatment centres, although at the time they were performed, neutron therapy was in a catch-up phase with photon-based treatments. Their findings are summarised along with their technical aspects and fractionation choices. Better understanding of fast neutron experiments and therapy has been gained through relatively simple mathematical models-using the biological effective dose concept and incorporating the RBEmax and RBEmin parameters (the limits of RBE at low and high dose, respectively-as shown in the Appendix). The RBE itself can then vary between these limits according to the dose per fraction used. These approaches provide useful insights into the problems that can occur in proton and ion beam therapy and how they may be optimised. This is because neutron ionisations in living tissues are mainly caused by recoil protons of energy proportional to the neutron energy: these are close to the proton energies that occur close to the Bragg peak region. To some extent, neutron RBE studies contain the highest RBE ranges found within proton and ion beams near Bragg peaks. In retrospect, neutrons were a useful radiobiological tool that has continued to inform the scientific and clinical community about the essential radiobiological principles of all forms of high linear energy transfer therapy. Neutron radiobiology and its implications should be taught on training courses and studied closely by clinicians, physicists, and biologists engaged in particle beam therapies.

The influence of the α/ß ratio on treatment time iso-effect relationships in the central nervous system.

Purpose: To investigate the influence of changes in α/ß ratio (range 1.5-3 Gy) on iso-effective doses, with varying treatment time, in spinal cord and central nervous system tissues with comparable radio-sensitivity. It is important to establish if an α/ß ratio of 2 Gy, the accepted norm for neuro-oncology iso-effect estimations, can be used.Methods: The rat spinal cord irradiation data of Pop et al. provided ED50 values for radiation myelopathy for treatment times that varied from minutes to ∼6 days. Analysis using biphasic repair kinetics, allowing for variable dose-rates, provided the best fit with repair half-times of 0.19 and 2.16 hr, each providing ∼50% of overall repair; with an α/ß ratio 2.47 Gy (CI 1.5-3.95 Gy). Using the above data set, graphical methods were used to investigate changes in the repair parameters for differing fixed α/ß ratios between 1.5 and 3.0 Gy. Two different intermittent dose delivery equations were used to evaluate the implications in a radiosurgery setting.Results: Changes in the α/ß ratio (1.5-3.0 Gy) have a minor effect on equivalent doses for radiation myelopathy for treatment durations of a few hours. Changing the α/ß value from 2 Gy to 2.47 Gy, modified equivalent single doses by < 1% when overall treatment times ranged from 0.1 to 5.0 hr. Significant changes were only found for treatment times longer than 5-10 hr. These two α/ß ratios were also compared in a practical radiosurgery situation, using two different models for estimating BED, again there was no significant loss of accuracy.Conclusions: It is reasonable to use an α/ß ratio of 2 Gy for CNS tissue, with the same repair half-times as published in the original publication by Pop et al., in situations where the assessment of the BED in radiosurgery is used with other form of radiotherapy. In radiosurgery, the variation in BED with treatment duration (for a fixed physical dose) is very similar, but absolute BED values depend on the α/ß value. In radiosurgery, clinical recommendations obtained using BED calculations using the originally proposed α/ß ratio of 2.47 Gy are still appropriate. For calculations involving a combination of radiosurgery and other modalities, such as fractionated radiotherapy, it would be appropriate in all cases to apply a value of 2 Gy, the accepted norm in neuro-oncology, without significant loss of accuracy in the radio-surgical component. This may have important applications in retreatment situations.

Clinical and practical considerations in the design of appropriate compensation schedules following treatment interruptions.

Compensatory dose calculations to mitigate the deleterious effect of unscheduled treatment interruptions remain important. They may be increasingly required during and after epidemics, as with the present Covid-19 virus. The information presented to those involved in the actual dose estimations is often limited, thereby increasing the likelihood of confusion, further time delays and possibly incorrect decisions. This article sets out what aspects need to be considered by the Clinical Oncologist (or Radiation Oncologist), and the reasons why, in order to provide greater clarity. The key issues are: (a) the biological nature of the tumour (and hence its repopulation potential), (b) patient age and pre-existing medical risk factors that influence radiation tolerance, the use of chemotherapy, surgery etc, (c) the acceptable dose limits of the relevant normal tissues at risk and (d) consideration of the possibility of further field size adjustments, a change in treatment plan or acceptance of a greater role for alternative forms of radiation treatment (e.g. brachytherapy, electron boosts, etc.) or reliance on radical surgery. Only then can a compensatory schedule be more safely estimated.

The physical separation between the LET associated with the ultimate relative biological effect (RBE) and the maximum LET in a proton or ion beam.

PURPOSE: To identify the relative positions of the ultimate RBE, at a LET value of LETU (where the LET-RBE turnover point occurs independently of dose), and of the maximum LET (LETM) for a range of ions from protons to Iron ions. METHODS: For a range of relativistic velocities (ß), the kinetic energies, LET values and ranges for each ion are obtained using SRIM software. For protons and helium ions, the LET changes with ß are plotted and LETM is compared with LETU. For all the ions studied the residual ranges of particles at LETU and LETM are subtracted to provide the physical separation (S) between LETU and LETM. RESULTS: Graphical methods are used to show the above parameters for protons and helium ions. For all the ions studied, LETU occurs at kinetic energies which are higher than those at LETM, so the ultimate maximal RBE occurs proximal to the Bragg peak for individual particles and not beyond it, as is commonly supposed. The distance S, between LETU and LETM, appears to increase linearly with the atomic charge value Z. CONCLUSIONS: For the lighter elements, from protons to carbon ions, S is sufficiently small (less than the tolerance/accuracy of radiation treatments) and so will probably not influence therapeutic decisions or outcomes. For higher Z numbers such as Argon and Iron, larger S values of several centimetres occur, which may have implications not only in any proposed therapeutic beams but also at very low doses encountered in radiation protection where the few cells that are irradiated will typically be traversed by a single particle.

Establishment of a Therapeutic Ratio for Gamma Knife Radiosurgery of Trigeminal Neuralgia: The Critical Importance of Biologically Effective Dose Versus Physical Dose.

OBJECTIVE: How variations of treatment time affect the safety and efficacy of Gamma Knife (GK) radiosurgery is a matter of considerable debate. With the relative simplicity of treatment planning for trigeminal neuralgia (TN), this question has been addressed in a group of these patients. Using the concept of the biologically effective dose (BED), the effect of the two key variables, dose and treatment time, were considered. METHODS: A retrospective analysis was performed of 408 TN cases treated from 1997 to 2010. Treatment involved the use of a single 4 mm isocenter. If conditions allowed, the isocenter was placed at a median distance of 7.5 mm from the emergence of the trigeminal nerve from the brain stem. The effects were assessed in terms of the incidence of the complication, hypoesthesia, and in terms of efficacy using the incidence of pain free after 30 days and 1 and 2 years. These responses were evaluated with respect to both the physical dose and the BED, the latter using a bi-exponential repair model. RESULTS: RE-evaluation showed that the prescription doses, at the 100% isodose, varied from 75 to 97.9 Gy, delivered in 25-135 minutes. The relationship between the physical dose and the incidence of hypoesthesia was not significant; the overall incidence was ∼20%. However, a clear relationship was found between the BED and the incidence of hypoesthesia, with the incidence increasing from <5% after a BED of ∼1800 Gy2.47 to 42% after ∼2600 Gy2.47. Efficacy, in terms of freedom from pain, was ∼90%, irrespective of the BED (1550-2600 Gy2.47) at 1 and 2 years. The data suggested that "pain free" status developed more slowly at lower BED values. CONCLUSIONS: These results strongly suggest that safety and efficacy might be better achieved by prescribing a specific BED instead of a physical dose. A dose and time to BED conversion table has been prepared to enable iso-BED prescriptions. This finding could dramatically change dose-planning strategies in the future. However, this concept requires validation for other indications for which more complex dose planning is required.

Use of radiobiology in medical jurisprudence, with particular reference to delays in diagnosis and therapeutic onset.

OBJECTIVE: This paper considers aspects of radiobiology and cell and tissue kinetics applicable to legal disputations concerned with diagnostic and treatment onset delays. METHODS: Various models for tumour volume changes with time are reviewed for estimating volume ranges at earlier times, using ranges of kinetic parameters. Statistical cure probability methods, using Poisson statistics with allowances for parameter heterogeneity, are also described to estimate the significance of treatment delays, as well as biological effective dose (BED) estimations of radiation effectiveness. RESULTS: The use of growth curves, based on parameters in the literature but with extended ranges, can identify a window of earlier times when such tumour volumes would be amenable to a cure based on the literature for curability with stage (and dimensions). Also, where tumour dimensions are not available in a post-operative setting, higher cure probabilities can be achieved if treatment had been given at earlier times. CONCLUSION: The use of radiobiological modelling can provide useful insights, with quantitative assessments of probable prior conditions and future outcomes, and thus be of assistance to a Court in deciding the most correct judgement. ADVANCES IN KNOWLEDGE: This study collates prior knowledge about aspects of radiobiology that can be useful in the accumulation of sufficient proof within medicolegal claims involving diagnostic and treatment days.

Physical characteristics at the turnover-points of relative biological effect (RBE) with linear energy transfer (LET).

This paper considers the kinematic physical characteristics of ionic beams for maximum relative bio-effectiveness (RBE). RBE studies, based on heterogenous cell survival studies at different laboratories and linear energy transfer (LET) conditions for proton, helium, carbon, neon and argon ions, have been further analysed to determine the LETU values where RBE is maximal and the LET-RBE relationship has a turnover point. The SRIM stopping power software and other classical equations are used to determine the particle velocities, kinetic energies and their effective ionic charges at LETU. The estimated mean LETU values increase with atomic number (Z). Each LETU has a unique relativistic velocity, ß = v/c, the velocity v expressed as a fraction of the speed of light, (c), and which is non-linearly proportional to Z. For ions helium and heavier ions, these velocities indicate that the effective charge Z * is around 0.99 of the full Z value at each LETU, with remarkably stable velocities of 3-4 nm · fs-1 per nucleon, or around 6-8 nm · fs-1 per unit Z. For Z = 1, (protons and deuterium) some values fall outside these ranges but the result depends on the mix of proton and deuterium used in experiments. An alternative index of ßA/Z 2 (A is the atomic mass number), suggests an average velocity of around 15 nm · fs-1 for each particle at LETU. These distances, traversed in the time of the radiochemical process initiation, are all within the dimensions of the nucleosome. Curve fitting of the data set provides a predictive equation for LETU for any ion, as LETU = 30.4 + [Formula: see text] (1 - Exp[-0.61 √ (Z - 1)]) when normalised to protons. These data can be extended to heavier ions such as silicon and iron and give values that are consistent with experimental data. Each ion probably has a unique LETU value. Kinematic studies show maximum bio-effectiveness occurs at particle velocities where electron stripping remains at around 99% and where the velocity per nucleon is around 3-4 nm · fs-1. This study enhances the limited prior knowledge about the physical conditions of particle beams that provide maximum bio-effectiveness, with applications in particle radiotherapy, radiation protection and space travel.

Effects of variations in overall treatment time on the clonogenic survival of V79-4 cells: Implications for radiosurgery.

The importance of effects related to the repair of sublethal radiation damage as treatment duration varies, partly a function of dose-rate, is a current controversy in clinical radiosurgery. Cell survival studies have been performed to verify the importance of this effect in relation to established models. Mammalian V79-4 cells were irradiated in vitro with γ-rays, either as an acute exposure in a few minutes, where the effects of sublethal irradiation damage repair over the period of exposure can be ignored, or as protracted exposures delivered over 15-120 min. Protraction was achieved either by introducing a variable time gap between two doses of 7 Gy, or as a continuous exposure at lower dose rates so that a range of doses were delivered in fixed times of 30, 60 or 120 min. For all doses there was a progressive reduction in efficacy with increasing overall treatment time. This was illustrated by the progressive increase in clonogenic cell survival with a resulting right shift of the survival curves. Cell survival curves for irradiations given either as an acute exposure (6.1 Gy/min), over fixed times (30, 60 and 120 min) or for a fixed low dose-rate (0.2 Gy/min) were well fitted by the Linear Quadratic (LQ) model giving an α/ß ratio of 4.0 Gy and a single repair half-time of 31.5 min. The present results are consistent with published data with respect to the response of solid tumors and normal tissues, whose response to both continuous and fractionated irradiation is also well described by the LQ model. This suggests the need for dose compensation in radiosurgical treatments, and other forms of radiotherapy, where dose is delivered over a similar range of protracted overall treatment times, perhaps as a prerequisite to full biological effective dose treatment planning.