Calculation of high-LET radiotherapy dose required for compensation of overall treatment time extensions

Determining RBE for development of lung fibrosis induced by fractionated irradiation with carbon ions utilizing fibrosis index and high-LET BED model

BACKGROUND AND PURPOSES

Carbon ion radiotherapy (CIRT) with raster scanning technology is a promising treatment for lung cancer and thoracic malignancies. Determining normal tissue tolerance of organs at risk is of utmost importance for the success of CIRT. Here we report the relative biological effectiveness (RBE) of CIRT as a function of dose and fractionation for development of pulmonary fibrosis using well established fibrosis index (FI) model.

MATERIALS AND METHODS

Dose series of fractionated clinical quality CIRT versus conventional photon irradiation to the whole thorax were compared in C57BL6 mice. Quantitative assessment of pulmonary fibrosis was performed by applying the FI to computed tomography (CT) data acquired 24-weeks post irradiation. RBE was calculated as the ratio of photon to CIRT dose required for the same level of FI. Further RBE predictions were performed using the derived equation from high-linear energy transfer biologically effective dose (high-LET BED) model.

RESULTS

The averaged lung fibrosis RBE of 5-fraction CIRT schedule was determined as 2.75 ± 0.55. The RBE estimate at the half maximum effective dose (RBE_ED50) was estimated at 2.82 for clinically relevant fractional sizes of 1-6 Gy. At the same dose range, an RBE value of 2.81 ± 0.40 was predicted by the high-LET BED model. The converted biologically effective dose (BED) of CIRT for induction of half maximum FI (BED_ED50) was identified to be 58.12 Gy_3.95. In accordance, an estimated RBE of 2.88 was obtained at the BED_ED50 level. The LQ model radiosensitivity parameters for 5-fraction was obtained as α_H = 0.3030 ± 0.0037 Gy^-1 and β_H = 0.0056 ± 0.0007 Gy^-2.

CONCLUSION

This is the first report of RBE estimation for CIRT with the endpoint of pulmonary fibrosis in-vivo. We proposed in present study a novel way to mathematically modeling RBE by integrating RBE_max and α/β_L based on conventional high-LET BED conception. This model well predicted RBE in the clinically relevant dose range but is sensitive to the uncertainties of α/β estimates from the reference photon irradiation (α/β_L). These findings will assist to eliminate current uncertainties in prediction of CIRT induced normal tissue complications and builds a solid foundation for development of more accurate in-vivo data driven RBE estimates.

The evolution of practical radiobiological modelling

A summary of the key aspects of radiobiological modelling is provided, based on the theoretical and practical concepts of the linear quadratic model, which gradually replaced other numerical approaches. The closely related biological effective dose concept is useful in many clinical applications. Biological effective dose formulations in conventional photon-based radiotherapy continue to be developed, and can be extended to the now increasingly used proton and ion-beam therapy, to very low or high dose ranges, the dose rate effect, hypoxia and repopulation. Such established and new research developments will be of interest to clinicians, physicists and biologists to better understand the processes underlying radiotherapy and assist their collaborative efforts to make radiotherapy safer and more effective.

Theoretical implications of incorporating relative biological effectiveness into radiobiological equivalence relationships

OBJECTIVE

Earlier radiobiological equivalence relationships as derived for low-linear energy transfer (LET) radiations are revisited in the light of newer radiobiological models that incorporate an allowance for relative biological effectiveness (RBE).

METHODS

Linear-quadratic (LQ) radiobiological equations for calculating biologically effective dose at both low- and high-LET radiations are used to derive new conditions of equivalence between a variety of radiation delivery techniques. The theoretical implications are discussed.

RESULTS

The original (pre-LQ) concept of equivalence between fractionated and continuous radiotherapy schedules, in which the same physical dose is delivered in each schedule, inherently assumed that low-LET radiation would be used in both schedules. LQ-based equivalence relationships that allow for RBE and are derived assuming equal total physical dose between schedules are shown to be valid only in limited circumstances. Removing the constraint of equality of total physical dose allows the identification of more general (and more practical) relationships.

CONCLUSION

If the respective schedules under consideration for equivalence both involve radiations of identical LET, then the original equivalence relationships remain valid. However, if the compared schedules involve radiations of differing LET, then new (and more restrictive) equivalence relationships are found to apply.

ADVANCES IN KNOWLEDGE

Theoretically derived equivalence relationships based on the LQ model provide a framework for the design and intercomparison of a wide range of clinical techniques including those involving high- and/or low-LET radiations. They also provide a means of testing for the validity of variously assumed tissue repair kinetics.

Dilemmas concerning dose distribution and the influence of relative biological effect in proton beam therapy of medulloblastoma

OBJECTIVE

To improve medulloblastoma proton therapy. Although considered ideal for proton therapy, there are potential disadvantages. Expected benefits include reduced radiation-induced cancer and circulatory complications, while avoiding small brain volumes of dose in-homogeneity when compared with conventional X-rays. Several aspects of proton therapy might contribute to reduced tumour control due to (a) the use of more homogenous dose levels which can result in under-dosage, (b) differences in relative biological effectiveness (RBE) between that prescription RBE of 1.1 and the RBE of brain and spinal cord (likely to exceed 1.1) and in medulloblastoma cells (where RBE is likely to be below 1.1). Such changes, although speculative for RBE, might result in potential underdosage of tumour cells and a higher bio-effect in brain tissue.

METHODS

Dose distributions for X-ray and proton treatment are compared, with allocation of likely RBE values for fast growing medullolastoma cells and stable central nervous system tissue.

RESULTS

These physical and radiobiological factors are shown to combine to give a higher risk of tumour recurrence with further risks on tumour control when dose reduction schedules used for X-ray therapy are replicated for proton therapy for "low-risk" patients.

CONCLUSION

The dose distributions and prescribed doses of proton therapy, taking into account RBE, in children and adults with medulloblastoma, need to be reconsidered.

The potential impact of relative biological effectiveness uncertainty on charged particle treatment prescriptions

There continues to be uncertainty regarding the relative biological effectiveness (RBE) values that should be used in charged particle radiotherapy (CPT) prescriptions using protons and heavier ions. This uncertainty could potentially offset the physical dose advantage gained by exploiting the Bragg peak effect and it needs to be clearly understood by clinicians and physicists. This paper introduces a combined radiobiological and physical sparing factor (S). This factor includes the ratio of the most relevant physical doses in tumour and normal tissues in combination with their respective RBE values and can be extended to contain the uncertainties in RBE. S factors can be used to study, in a simplified way for tentative modelling, those clinical situations in which high-linear energy transfer (LET) irradiations are likely to prove preferable over their low-LET counterparts for a matched tumour iso-effect. In cases where CPT achieves an excellent degree of normal tissue sparing, the radiobiological factors become less important and any uncertainties in the tumour and healthy tissue RBE values are correspondingly less problematic. When less normal tissue sparing can be achieved, however, the RBE uncertainties assume greater relevance and will affect the reliability of the dose-prescription methodology. More research is required to provide accurate RBE estimation, focusing attention on the associated statistical uncertainties and potential differences in RBE between different tissue types.

Fast neutron relative biological effects and implications for charged particle therapy

In two fast neutron data sets, comprising in vitro and in vivo experiments, an inverse relationship is found between the low-linear energy transfer (LET) α/β ratio and the maximum value of relative biological effect (RBE(max)), while the minimum relative biological effect (RBE(min)) is linearly related to the square root of the low-LET α/β ratio. RBE(max) is the RBE at near zero dose and can be represented by the ratio of the α parameters at high- and low-LET radiation exposures. RBE(min) is the RBE at very high dose and can be represented by the ratio of the square roots of the β parameters at high- and low-LET radiation exposures. In principle, it may be possible to use the low-LET α/β ratio to predict RBE(max) and RBE(min, )providing that other LET-related parameters, which reflect intercept and slopes of these relationships, are used. These two limits of RBE determine the intermediate values of RBE at any dose per fraction; therefore, it is possible to find the RBE at any dose per fraction. Although these results are obtained from fast neutron experiments, there are implications for charged particle therapy using protons (when RBE is scaled downwards) and for heavier ion beams (where the magnitude of RBE is similar to that for fast neutrons). In the case of fast neutrons, late reacting normal tissue systems and very slow growing tumours, which have the smallest values of the low-LET α/β ratio, are predicted to have the highest RBE values at low fractional doses, but the lowest values of RBE at higher doses when they are compared with early reacting tissues and fast growing tumour systems that have the largest low-LET α/β ratios.

21 years of biologically effective dose

In 1989 the British Journal of Radiology published a review proposing the term biologically effective dose (BED), based on linear quadratic cell survival in radiobiology. It aimed to indicate quantitatively the biological effect of any radiotherapy treatment, taking account of changes in dose-per-fraction or dose rate, total dose and (the new factor) overall time. How has it done so far? Acceptable clinical results have been generally reported using BED, and it is in increasing use, although sometimes mistaken for "biologically equivalent dose", from which it differs by large factors, as explained here. The continuously bending nature of the linear quadratic curve has been questioned but BED has worked well for comparing treatments in many modalities, including some with large fractions. Two important improvements occurred in the BED formula. First, in 1999, high linear energy transfer (LET) radiation was included; second, in 2003, when time parameters for acute mucosal tolerance were proposed, optimum overall times could then be "triangulated" to optimise tumour BED and cell kill. This occurs only when both early and late BEDs meet their full constraints simultaneously. New methods of dose delivery (intensity modulated radiation therapy, stereotactic body radiation therapy, protons, tomotherapy, rapid arc and cyberknife) use a few large fractions and obviously oppose well-known fractionation schedules. Careful biological modelling is required to balance the differing trends of fraction size and local dose gradient, as explained in the discussion "How Fractionation Really Works". BED is now used for dose escalation studies, radiochemotherapy, brachytherapy, high-LET particle beams, radionuclide-targeted therapy, and for quantifying any treatments using ionising radiation.

The apparent increase in the {beta}-parameter of the linear quadratic model with increased linear energy transfer during fast neutron irradiation

The issue of whether the beta-parameter of the linear quadratic model changes with linear energy transfer (LET) remains controversial. Retrospective analysis of UK fast neutron experimental data using human cell lines at Clatterbridge shows that the beta-parameter of the linear quadratic model probably does increase with LET during neutron irradiation. For cells without a deficiency in DNA damage repair and for experiments in which beta-parameter estimates were considered to be unreliably low, a provisional relationship of beta(H) = 1.82 beta(L) was found (where the suffixes refer to high and low LET exposures, respectively). This implies that radicalbeta increases by around 1.35 in the specific case of 62.5 MeV neutrons relative to 4 MeV X-rays. Increments in the beta-parameter with LET influence the relative biological effect (RBE), especially at high doses per fraction. Large fractions are being used in experimental carbon ion therapy, in which broadly similar RBE values to fast neutrons are found. These interesting findings after fast neutron exposure need to be studied further for applications in charged particle beam therapy using light ions, which is presently undergoing a worldwide expansion.

Modelling carcinogenesis after radiotherapy using Poisson statistics: implications for IMRT, protons and ions

Current technical radiotherapy advances aim to (a) better conform the dose contours to cancers and (b) reduce the integral dose exposure and thereby minimise unnecessary dose exposure to normal tissues unaffected by the cancer. Various types of conformal and intensity modulated radiotherapy (IMRT) using x-rays can achieve (a) while charged particle therapy (CPT)-using proton and ion beams-can achieve both (a) and (b), but at greater financial cost. Not only is the long term risk of radiation related normal tissue complications important, but so is the risk of carcinogenesis. Physical dose distribution plans can be generated to show the differences between the above techniques. IMRT is associated with a dose bath of low to medium dose due to fluence transfer: dose is effectively transferred from designated organs at risk to other areas; thus dose and risk are transferred. Many clinicians are concerned that there may be additional carcinogenesis many years after IMRT. CPT reduces the total energy deposition in the body and offers many potential advantages in terms of the prospects for better quality of life along with cancer cure. With C ions there is a tail of dose beyond the Bragg peaks, due to nuclear fragmentation; this is not found with protons. CPT generally uses higher linear energy transfer (which varies with particle and energy), which carries a higher relative risk of malignant induction, but also of cell death quantified by the relative biological effect concept, so at higher dose levels the frank development of malignancy should be reduced. Standard linear radioprotection models have been used to show a reduction in carcinogenesis risk of between two- and 15-fold depending on the CPT location. But the standard risk models make no allowance for fractionation and some have a dose limit at 4 Gy. Alternatively, tentative application of the linear quadratic model and Poissonian statistics to chromosome breakage and cell kill simultaneously allows estimation of relative changes in carcinogenesis that incorporate fractionation and relative biological effects (RBE). This alternative modelling approach allows absolute and relative risk estimations per cell and can be extended to tissues. The classical turnover point in carcinogenesis occurring after a single exposure is a feature of the model; also, the dose-response relationship becomes pseudo-linear with extended fractionation and when heterogeneity of the radiosensitivity parameters is introduced; there is also an inverse relationship between dose per fraction and cancer induction. In principle, this new approach might influence the conduct of proton and ion beam therapy, particularly beam placements and fractionation policies. The theoretical implications for future radiotherapy are considerable, but these predictions should be subjected to cellular and tissue experiments that simulate these forms of treatment, including any secondary neutron production in some cases depending on the beam delivery technique, e.g. in tissue equivalent humanoid phantoms using cell transformation techniques. Since the UK has no working high energy particle beam facility over 100 MeV, British scientists would require use of particle beam facilities in Europe, USA or Japan to perform experiments.

Why more needs to be known about RBE effects in modern radiotherapy

Radiation therapy remains a very effective tool in the clinical management and cure of cancer and new techniques of radiation delivery continue to be developed. Of particular note is the growing world-wide interest in particle beam therapy (PBT) using protons or light ions. Such beams (particularly light ions) are associated with an increased relative biological effectiveness (RBE) which, when viewed alongside the more favourable physical distributions of radiation dose available with all forms of particle beams, makes them especially attractive for treating tumours which are associated with disappointing outcomes following conventional X-ray therapy. Although the large body of clinical experience already gained with conventional X-ray therapy will be of paramount importance in guiding the development of treatment programmes using particle beams, understanding and quantification of the RBE effects which are unique to the latter will also be essential. This is because the magnitude of RBE effect is not fixed for any one radiation/tissue combination but is subject to a number of other radiobiological influences. Such relationships may be quantified within the linear-quadratic radiobiological model, within which the associated concept of biologically effective dose (BED) provides a way of inter-comparing the overall biological impact of existing and projected treatments. This paper summarises the main features of RBE and BED, discusses the main quantitative implications for PBT and highlights why clear understanding of RBE effects will be essential to make best use of PBT. It also summarises other clinical applications where knowledge of and allowance for RBE effects is important and suggests that more needs to be done to allow safer practical applications.