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

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/β 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.

Proton RBE dependence on dose in the setting of hypofractionation

Hypofractionated radiotherapy is attractive concerning patient burden and therapy costs, but many aspects play a role when it comes to assess its safety. While exploited for conventional photon therapy and carbon ion therapy, hypofractionation with protons is only rarely applied. One reason for this is uncertainty in the described dose, mainly due to the relative biological effectiveness (RBE), which is small for protons, but not negligible. RBE is generally dose-dependent, and for higher doses as used in hypofractionation, a thorough RBE evaluation is needed. This review article focuses on the RBE variability in protons and associated issues or implications for hypofractionation.

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.

RBE and related modeling in carbon-ion therapy

Carbon ion therapy is a promising evolving modality in radiotherapy to treat tumors that are radioresistant against photon treatments. As carbon ions are more effective in normal and tumor tissue, the relative biological effectiveness (RBE) has to be calculated by bio-mathematical models and has to be considered in the dose prescription. This review (i) introduces the concept of the RBE and its most important determinants, (ii) describes the physical and biological causes of the increased RBE for carbon ions, (iii) summarizes available RBE measurements in vitro and in vivo, and (iv) describes the concepts of the clinically applied RBE models (mixed beam model, local effect model, and microdosimetric-kinetic model), and (v) the way they are introduced into clinical application as well as (vi) their status of experimental and clinical validation, and finally (vii) summarizes the current status of the use of the RBE concept in carbon ion therapy and points out clinically relevant conclusions as well as open questions. The RBE concept has proven to be a valuable concept for dose prescription in carbon ion radiotherapy, however, different centers use different RBE models and therefore care has to be taken when transferring results from one center to another. Experimental studies significantly improve the understanding of the dependencies and limitations of RBE models in clinical application. For the future, further studies investigating quantitatively the differential effects between normal tissues and tumors are needed accompanied by clinical studies on effectiveness and toxicity.

Numerical insight into the Dual Radiation Action Theory

This work studies the first and second order mechanisms for the induction of lethal lesions in DNA after irradiation with protons and α-particles. The purpose is to numerically study the mechanisms behind the Dual Radiation Action Theory (DRAT) for these heavy particles. A genetic material geometrical model with atomic resolution is used. It accounts for the explicit position of 5.47 × 10⁹ base pairs, organized up to the chromatin level. The GEANT4-DNA Monte Carlo code was employed to simulate the interaction of these ions with the genetic material model. The number of lethal lesions induced by one- and two-track mechanisms was determined as a function of dose. Values of the α/β ratio were estimated as well as corresponding relative biological effectiveness (RBE). The number of lethal lesions produced by one-track and two-track mechanisms depends on the dose and squared dose, respectively, as predicted by the DRAT. RBE values consistent with experimental results were found, at least for LET below ∼100 keV/μm. Double strand break spatial distributions are qualitatively analyzed. According to this work, the α parameter determined from cellular surviving curves depends on both the physical α and β parameters introduced here, and on the specific energy deposited by a single track into the region of interest. We found an increment of the β parameter with LET, yet at a slower rate than α so that the α/β ratio increases with LET. In addition, we observed and explained the saturation of the α parameter as the dose increases above ∼6 Gy.

Why RBE must be a variable and not a constant in proton therapy

OBJECTIVE

This article considered why the proton therapy (PT) relative biological effect (RBE) should be a variable rather than a constant.

METHODS

The reasons for a variable proton RBE are enumerated, with qualitative and quantitative arguments. The heterogeneous data sets collated by Paganetti et al (2002) and the more homogeneous data of Britten et al (2013) are further analyzed using linear regression fitting and RBE-inclusive adaptations of the linear-quadratic (LQ) radiation model.

RESULTS

The in vitro data show RBE increasing as dose per fraction is lowered. In the Paganetti et al (2002) data sets, the differences between observed and expected effects are smaller when the LQ model is used, but with such data heterogeneity, firm statistical conclusions cannot be obtained. The more homogeneous data set shows an unequivocal variation in RBE with dose per faction. The in vivo data are inappropriate for assessments of late normal tissue effects in radiotherapy. Also, if there is the same degree of uncertainty in an RBE of 1.1 or in an RBE of 2-3 for C ions, the fractional and biological effective doses can vary considerably and be greater in the proton case. So, errors in RBE assignment are important for protons, just as with C ions.

CONCLUSION

Further experimental programmes are proposed, including late normal tissue end points. Better RBE allocations might further improve PT outcomes.

ADVANCES IN KNOWLEDGE

This study provides a rigorous critique of the 1.1 RBE used for protons, from theoretical and practical standpoints. Data analysis shows that the LQ model is more appropriate than simple linear regression. Comprehensive research programmes are suggested.

Effects of Charged Particles on Human Tumor Cells

The use of charged particle therapy in cancer treatment is growing rapidly, in large part because the exquisite dose localization of charged particles allows for higher radiation doses to be given to tumor tissue while normal tissues are exposed to lower doses and decreased volumes of normal tissues are irradiated. In addition, charged particles heavier than protons have substantial potential clinical advantages because of their additional biological effects, including greater cell killing effectiveness, decreased radiation resistance of hypoxic cells in tumors, and reduced cell cycle dependence of radiation response. These biological advantages depend on many factors, such as endpoint, cell or tissue type, dose, dose rate or fractionation, charged particle type and energy, and oxygen concentration. This review summarizes the unique biological advantages of charged particle therapy and highlights recent research and areas of particular research needs, such as quantification of relative biological effectiveness (RBE) for various tumor types and radiation qualities, role of genetic background of tumor cells in determining response to charged particles, sensitivity of cancer stem-like cells to charged particles, role of charged particles in tumors with hypoxic fractions, and importance of fractionation, including use of hypofractionation, with charged particles.

A Simpler Energy Transfer Efficiency Model to Predict Relative Biological Effect for Protons and Heavier Ions

The aim of this work is to predict relative biological effectiveness (RBE) for protons and clinically relevant heavier ions, by using a simplified semi-empirical process based on rational expectations and published experimental results using different ion species. The model input parameters are: Z (effective nuclear charge) and radiosensitivity parameters α_L and β_L of the control low linear energy transfer (LET) radiation. Sequential saturation processes are assumed for: (a) the position of the turnover point (LET_U) for the LET–RBE relationship with Z, and (b) the ultimate value of α at this point (α_U) being non-linearly related to α_L. Using the same procedure for β, on the logical assumption that the changes in β with LET, although smaller than α, are symmetrical with those of α, since there is symmetry of the fall off of LET–RBE curves with increasing dose, which suggests that LET_U must be identical for α and β. Then, using iso-effective linear quadratic model equations, the estimated RBE is scaled between α_U and α_L and between β_U and β_L from for any input value of Z, α_L, β_L, and dose. The model described is fitted to the data of Barendsen (alpha particles), Weyrather et al. (carbon ions), and Todd for nine different ions (deuterons to Argon), which include variations in cell surviving fraction and dose. In principle, this new system can be used to complement the more complex methods to predict RBE with LET such as the local effect and MKM models which already have been incorporated into treatment planning systems in various countries. It would be useful to have a secondary check to such systems, especially to alert clinicians of potential risks by relatively easy estimation of relevant RBEs. In clinical practice, LET values smaller than LET_U are mostly encountered, but the model extends to higher values beyond LET_U for other purposes such as radiation, protection, and astrobiology. Considerable further research is required, perhaps in a dedicated international laboratory, using a basket of different models to determine what the best system or combination of systems will be to make proton and ion beam radiotherapy as safe as possible and to produce the best possible clinical results.

Towards Achieving the Full Clinical Potential of Proton Therapy by Inclusion of LET and RBE Models

Despite increasing use of proton therapy (PBT), several systematic literature reviews show limited gains in clinical outcomes, with publications mostly devoted to recent technical developments. The lack of randomised control studies has also hampered progress in the acceptance of PBT by many oncologists and policy makers. There remain two important uncertainties associated with PBT, namely: (1) accuracy and reproducibility of Bragg peak position (BPP); and (2) imprecise knowledge of the relative biological effect (RBE) for different tissues and tumours, and at different doses. Incorrect BPP will change dose, linear energy transfer (LET) and RBE, with risks of reduced tumour control and enhanced toxicity. These interrelationships are discussed qualitatively with respect to the ICRU target volume definitions. The internationally accepted proton RBE of 1.1 was based on assays and dose ranges unlikely to reveal the complete range of RBE in the human body. RBE values are not known for human (or animal) brain, spine, kidney, liver, intestine, etc. A simple efficiency model for estimating proton RBE values is described, based on data of Belli et al. and other authors, which allows linear increases in α and β with LET, with a gradient estimated using a saturation model from the low LET α and β radiosensitivity parameter input values, and decreasing RBE with increasing dose. To improve outcomes, 3-D dose-LET-RBE and bio-effectiveness maps are required. Validation experiments are indicated in relevant tissues. Randomised clinical studies that test the invariant 1.1 RBE allocation against higher values in late reacting tissues, and lower tumour RBE values in the case of radiosensitive tumours, are also indicated.

Systematic analysis of RBE and related quantities using a database of cell survival experiments with ion beam irradiation

For tumor therapy with light ions and for experimental aspects in particle radiobiology the relative biological effectiveness (RBE) is an important quantity to describe the increased effectiveness of particle radiation. By establishing and analysing a database of ion and photon cell survival data, some remarkable properties of RBE-related quantities were observed. The database consists of 855 in vitro cell survival experiments after ion and photon irradiation. The experiments comprise curves obtained in different labs, using different ion species, different irradiation modalities, the whole range of accessible energies and linear energy transfers (LETs) and various cell types. Each survival curve has been parameterized using the linear-quadratic (LQ) model. The photon parameters, α and β, appear to be slightly anti-correlated, which might point toward an underlying biological mechanism. The RBE values derived from the survival curves support the known dependence of RBE on LET, on particle species and dose. A positive correlation of RBE with the ratio α/β of the photon LQ parameters is found at low doses, which unexpectedly changes to a negative correlation at high doses. Furthermore, we investigated the course of the β coefficient of the LQ model with increasing LET, finding typically a slight initial increase and a final falloff to zero. The observed fluctuations in RBE values of comparable experiments resemble overall RBE uncertainties, which is of relevance for treatment planning. The database can also be used for extensive testing of RBE models. We thus compare simulations with the local effect model to achieve this goal.

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.

Relative Biologic Effectiveness (RBE) of 50 kV X-rays measured in a phantom for intraoperative tumor-bed irradiation

PURPOSE

Intraoperative radiation therapy (IORT) with low-energy x-rays is used to treat the tumor bed during breast-conserving surgery. The purpose was to determine the relative biologic effectiveness (RBE) of 50-kV x-rays for inactivation of cells irradiated in a tumor-bed phantom.

METHODS AND MATERIALS

The RBE was determined for clonogenic inactivation of human tumor and normal cells (MCF7, human umbilical vein endothelial cells, normal skin fibroblasts), and hamster V79 cells. The 50-kV x-rays from the Intrabeam machine (Carl Zeiss Surgical) with a spherical 4-cm applicator were used. Cells were irradiated in a water-equivalent phantom at defined distances (8.1-22.9 mm) from the applicator surface. The 50-kV x-rays from a surface therapy machine (Dermopan, Siemens) were included for comparison; 6-MV x-rays were used as reference radiation.

RESULTS

At 8.1-mm depth in the phantom (dose rate 15.1 Gy/h), mean RBE values of 50-kV x-rays from Intrabeam were 1.26 to 1.42 for the 4 cell types at doses yielding surviving fractions in the range of 0.01 to 0.5. Confidence intervals were in the range of 1.2 and 1.5. Similar RBE values were found for 50-kV x-rays from Dermopan for V79 (1.30, CI 1.25-1.36, P=.74) and GS4 (1.42, CI 1.30-1.54, P=.67). No significant dependence of RBE on dose was found for Intrabeam, but RBE decreased at a larger distance (12.7 mm; 9.8 Gy/h).

CONCLUSIONS

An increased clinically relevant RBE was found for cell irradiation with Intrabeam at depths in the tumor bed targeted by IORT. The reduced RBE values at larger distances may be related to increased repair of sublethal damage during protracted irradiation or to hardening of the photon beam energy.

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.

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.

Calculation of the biological effects of ion beams based on the microscopic spatial damage distribution pattern

PURPOSE

To present details of the recent version of the 'Local Effect Model' (LEM), that has been developed and implemented in treatment planning for the ion beam therapy pilot project performed at GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany.

MATERIALS AND METHODS

The new version of the model is based on a detailed consideration of the spatial distribution of the initial damages, i.e., double-strand breaks (DSB). This spatial distribution of DSB is obtained from the radial dose profile of the ion track using Monte Carlo methods. These distributions are then analyzed with regard to the proximity of DSB. This version of the model also facilitates the calculation of full dose response curves up to arbitrary high doses, thus allowing to thoroughly check the approximations previously used to estimate the quadratic term (β-term) for the linear-quadratic description of dose response curves.

RESULTS

The accuracy of the model predictions is demonstrated by good agreement of the relative biological effectiveness (RBE) as a function of the linear energy transfer (LET) with experimental data obtained for V79 cells after carbon irradiation. The β-values predicted by the full simulation tend to be larger as compared to the approximation in the intermediate LET range.

CONCLUSION

The new version of the model allows a more mechanistic description of the biological effects of ion radiation. The full simulation is a prerequisite for tests of the validity of the approach at high doses, which are of particular interest for application in hypofractionation studies.