Heavy particles in therapy: an application of track theory

Research Trends in the Study of the Relative Biological Effectiveness: A Bibliometric Study

The relative biological effectiveness is a mathematical quantity first defined in the 1950s. This has resulted in more than 4,000 scientific papers published to date. Yet defining the correct value of the RBE to use in clinical practice remains a challenge. A scientific analysis in the radiation research literature can provide an understanding of how this mathematical quantity has evolved. The purpose of this study is to investigate documents published since 1950 using bibliometric indicators and network visualization. This analysis seeks to provide an assessment of global research activities, key themes, and RBE research within the radiation-related field. It strives to highlight top-performing authors, organizations, and nations that have made major contributions to this research domain, as well as their interactions. The Scopus Collection was searched for articles and reviews pertaining to RBE in radiation research from 1950 through 2023. Scopus and Bibiometrix analytic tools were used to investigate the most productive countries, researchers, collaboration networks, journals, along with the citation analysis of references and keywords. A total of 4,632 documents were retrieved produced by authors originating from 71 countries. Publication trends could be separated in 20-year groupings beginning with slow accrual from 1950 to 1970, an early rise from 1970-1990, followed by a sharp increase in the years 1990s-2010s that matches the development of charged particle therapy in clinics worldwide and opened discussion on the true value of the RBE in proton beam therapy. Since the 2010s, a steady 200 papers, on average, have been published per year. The United States produced the most publications overall (N = 1,378) and Radiation Research was the most likely journal to have published articles related to the RBE (606 publications during this period). J. Debus was the most prolific author (112 contributions, with 2,900 citations). The RBE has captured the research interest of over 7,000 authors in the past decade alone. This study supports that notion that the growth of the body of evidence surrounding the RBE, which started 75 years ago, is far from reaching its end. Applications to medicine have continuously dominated the field, with physics competing with Biochemistry, Genetics and Molecular Biology for second place over the decades. Future research can be predicted to continue.

Effects of Differing Underlying Assumptions in In Silico Models on Predictions of DNA Damage and Repair

The induction and repair of DNA double-strand breaks (DSBs) are critical factors in the treatment of cancer by radiotherapy. To investigate the relationship between incident radiation and cell death through DSB induction many in silico models have been developed. These models produce and use custom formats of data, specific to the investigative aims of the researchers, and often focus on particular pairings of damage and repair models. In this work we use a standard format for reporting DNA damage to evaluate combinations of different, independently developed, models. We demonstrate the capacity of such inter-comparison to determine the sensitivity of models to both known and implicit assumptions. Specifically, we report on the impact of differences in assumptions regarding patterns of DNA damage induction on predicted initial DSB yield, and the subsequent effects this has on derived DNA repair models. The observed differences highlight the importance of considering initial DNA damage on the scale of nanometres rather than micrometres. We show that the differences in DNA damage models result in subsequent repair models assuming significantly different rates of random DSB end diffusion to compensate. This in turn leads to disagreement on the mechanisms responsible for different biological endpoints, particularly when different damage and repair models are combined, demonstrating the importance of inter-model comparisons to explore underlying model assumptions.

Extension of TOPAS for the simulation of proton radiation effects considering molecular and cellular endpoints

The aim of this work is to extend a widely used proton Monte Carlo tool, TOPAS, towards the modeling of relative biological effect (RBE) distributions in experimental arrangements as well as patients. TOPAS provides a software core which users configure by writing parameter files to, for instance, define application specific geometries and scoring conditions. Expert users may further extend TOPAS scoring capabilities by plugging in their own additional C++ code. This structure was utilized for the implementation of eight biophysical models suited to calculate proton RBE. As far as physics parameters are concerned, four of these models are based on the proton linear energy transfer, while the others are based on DNA double strand break induction and the frequency-mean specific energy, lineal energy, or delta electron generated track structure. The biological input parameters for all models are typically inferred from fits of the models to radiobiological experiments. The model structures have been implemented in a coherent way within the TOPAS architecture. Their performance was validated against measured experimental data on proton RBE in a spread-out Bragg peak using V79 Chinese Hamster cells. This work is an important step in bringing biologically optimized treatment planning for proton therapy closer to the clinical practice as it will allow researchers to refine and compare pre-defined as well as user-defined models.

Proton radiobiology

In addition to the physical advantages (Bragg peak), the use of charged particles in cancer therapy can be associated with distinct biological effects compared to X-rays. While heavy ions (densely ionizing radiation) are known to have an energy- and charge-dependent increased Relative Biological Effectiveness (RBE), protons should not be very different from sparsely ionizing photons. A slightly increased biological effectiveness is taken into account in proton treatment planning by assuming a fixed RBE of 1.1 for the whole radiation field. However, data emerging from recent studies suggest that, for several end points of clinical relevance, the biological response is differentially modulated by protons compared to photons. In parallel, research in the field of medical physics highlighted how variations in RBE that are currently neglected might actually result in deposition of significant doses in healthy organs. This seems to be relevant in particular for normal tissues in the entrance region and for organs at risk close behind the tumor. All these aspects will be considered and discussed in this review, highlighting how a re-discussion of the role of a variable RBE in proton therapy might be well-timed.

Radial dose distributions from protons of therapeutic energies calculated with Geant4-DNA

Models based on the amorphous track structure approximation have been successful in predicting the biological effects of heavy charged particles. Development of such models remains an active area of research that includes applications to hadrontherapy. In such models, the radial distribution of the dose deposited by delta electrons and directly by the particle is the main characteristic of track structure. We calculated these distributions with Geant4-DNA Monte Carlo code for protons in the energy range from 10 to 100 MeV. These results were approximated by a simple formula that combines the well-known inverse square distance dependence with two factors that eliminate the divergence of the radial dose integral at both small and large distances. A clear physical interpretation is given to the asymptotic behaviour of the radial dose distribution resulting from these two factors. The proposed formula agrees with the Monte Carlo data within 10% for radial distances of up to 10 μm, which corresponds to a dose range covering over eight orders of magnitude. Differences between our results and those of previously published analytical models are discussed.

Exposure to heavy ion radiation induces persistent oxidative stress in mouse intestine

Ionizing radiation-induced oxidative stress is attributed to generation of reactive oxygen species (ROS) due to radiolysis of water molecules and is short lived. Persistent oxidative stress has also been observed after radiation exposure and is implicated in the late effects of radiation. The goal of this study was to determine if long-term oxidative stress in freshly isolated mouse intestinal epithelial cells (IEC) is dependent on radiation quality at a dose relevant to fractionated radiotherapy. Mice (C57BL/6J; 6 to 8 weeks; female) were irradiated with 2 Gy of γ-rays, a low-linear energy transfer (LET) radiation, and intestinal tissues and IEC were collected 1 year after radiation exposure. Intracellular ROS, mitochondrial function, and antioxidant activity in IEC were studied by flow cytometry and biochemical assays. Oxidative DNA damage, cell death, and mitogenic activity in IEC were assessed by immunohistochemistry. Effects of γ radiation were compared to ⁵⁶Fe radiation (iso-toxic dose: 1.6 Gy; energy: 1000 MeV/nucleon; LET: 148 keV/µm), we used as representative of high-LET radiation, since it's one of the important sources of high Z and high energy (HZE) radiation in cosmic rays. Radiation quality affected the level of persistent oxidative stress with higher elevation of intracellular ROS and mitochondrial superoxide in high-LET ⁵⁶Fe radiation compared to unirradiated controls and γ radiation. NADPH oxidase activity, mitochondrial membrane damage, and loss of mitochondrial membrane potential were greater in ⁵⁶Fe-irradiated mice. Compared to γ radiation oxidative DNA damage was higher, cell death ratio was unchanged, and mitotic activity was increased after ⁵⁶Fe radiation. Taken together our results indicate that long-term functional dysregulation of mitochondria and increased NADPH oxidase activity are major contributing factors towards heavy ion radiation-induced persistent oxidative stress in IEC with potential for neoplastic transformation.

Modelling of the oxygen enhancement ratio for ion beam radiation therapy

The poor treatment prognosis for tumours with oxygen-deficient areas is usually attributed to the increased radioresistance of hypoxic cells. It can be expressed by the oxygen enhancement ratio (OER), which decreases with increasing linear energy transfer (LET) suggesting a potential clinical advantage of high-LET radiotherapy with heavy ion beams compared to low-LET photon or proton irradiation. The aim of this work is to review the experimental cell survival data from the literature and, based on them, to develop a simple OER model to estimate the clinical impact of OER variations. For this purpose, the standard linear-quadratic model and the Alper-Howard-Flanders model are used. According to our calculations for a carbon ion spread-out Bragg peak at clinically relevant intermediate oxygen levels (0.5-20 mmHg), the advantage of carbon ions might be relatively moderate, with OER values about 1%-15% smaller than for protons. Furthermore, the variations of OER with LET are much smaller in vivo than in vitro due to different oxygen partial pressures used in cell experiments or measured inside tumours. The proposed OER model is a simple tool to quantify the oxygen effect in a practical way and provides the possibility to do hypoxia-based biological optimization in treatment planning.

A simple track structure model of ion beam radiotherapy

A simple radiotherapy ion beam calculation based on the cellular track structure model, using in vitro cell survival parameters fitted from recent experimental data, is presented. The calculation represents a single-fraction ion exposure (roughly corresponding to a 2 Gy fraction of megavolt X rays) and exploits concepts used in clinical radiotherapy, such as entrance, or 'skin' ion dose. The depth distribution of cells surviving their irradiation by a beam of 385 MeV amu(-1) carbon ions is calculated over the range of the stopping ions, as a sequence of track-segments, in the continuous slowing-down approximation. An interpretation of the 'clinical relative biological effectiveness' concept is suggested.

Cellular parameters and RBE-LET dependences for modelling heavy-ion radiotherapy

Sets of four parameters (m, E0, sigma0 and kappa) of the cellular track structure model of Katz have been fitted to recently published data concerning human melanoma (AA) and mammalian (V79) cells exposed to a variety of lighter ions and to mixed ion-Co60 and ion-ion irradiation. Using these parameters, model predictions of V79 survival were verified against experimental data. RBE-LET dependences were calculated and compared with experimental data obtained for V79 cells after exposure to 3He, 12C and 20Ne ion beams. The presented track-segment approach used in track structure calculations, while satisfactory for heavier ions, may be of limited value for predicting the RBE-LET dependence of proton and helium radiotherapy beams in regions close to the distal range of these particles. We discuss the predictive capability of this model and propose standards in reporting cellular radiobiology data for application in modelling heavy ion beam radiotherapy.

Significance and implementation of RBE variations in proton beam therapy

Key to radiation therapy is to apply a high tumor-destroying dose while protecting healthy tissue, especially near organs at risk. To optimize treatment for ion therapy not the dose but the dose multiplied by the relative biological effectiveness (RBE) is decisive. Proton therapy has been based on the use of a generic RBE, which is applied to all treatments independent of dose/fraction, position in the spread-out Bragg peak (SOBP), initial beam energy or the particular tissue. Dependencies of the RBE on various physical and biological properties are disregarded. The variability of RBE in clinical situations is believed to be within 10-20%. This is in the same range of effects that receive high attention these days, i.e., patient set-up uncertainties, organ motion effects, and dose calculation accuracy all affecting proton as well as conventional radiation therapy. Elevated RBE values can be expected near the edges of the target, thus probably near critical structures. This is because the edges show lower doses and, depending on the treatment plan, may be identical with the beam's distal edge, where dose is deposited in part by high-LET protons. We assess the rationale for the continued use of a generic RBE and whether the magnitude of RBE variation with treatment parameters is small relative to our abilities to determine RBE's. Two aspects have to be considered. Firstly, the available information from experimental studies and secondly, our ability to calculate RBE values for a given treatment plan based on parameters extracted from such experiments. We analyzed published RBE values for in vitro and in vivo endpoints. The values for cell survival in vitro indicate a substantial spread between the diverse cell lines. The average value at mid SOBP over all dose levels is approximately 1.2 in vitro and approximately 1.1 in vivo. Both in vitro and in vivo data indicate a statistically significant increase in RBE for lower doses per fraction, which is much smaller for in vivo systems. The experimental in vivo data indicate that continued employment of a generic RBE value of 1.1 is reasonable. At present, there seems to be too much uncertainty in the RBE value for any human tissue to propose RBE values specific for tissue, dose/fraction, etc. There is a clear need for prospective assessments of normal tissue reactions in proton irradiated patients and determinations of RBE values for several late responding tissues in animal systems, especially as a function of dose in the range of 1-4 Gy. However, there is a measurable increase in RBE over the terminal few mm of the SOBP, which results in an extension of the bio-effective range of the beam of a few mm. This needs to be considered in treatment planning, particularly for single field plans or for an end of range in or close to a critical structure. To assess our ability to calculate RBE values we studied two approaches, which are both based on the track structure theory of radiation action. RBE calculations are difficult since both the physical input parameters, i.e., LET distributions, and, even more so, the biological input parameters, i.e., local cellular response, have to be known with high accuracy. Track structure theory provides a basis for predicting dose-response curves for particle irradiation. However, designed for heavy ion applications the models show weaknesses in the prediction of proton radiation effects. We conclude that, at present, RBE modeling in treatment planning involves significant uncertainties. To incorporate RBE variations in treatment planning there has to be a reliable biological model to calculate RBE values based on the physical characteristics of the radiation field and based on well-known biological input parameters. In order to do detailed model calculations more experimental data, in particular for in vivo endpoints, are needed

Nuclear interactions in proton therapy: dose and relative biological effect distributions originating from primary and secondary particles

The dose distribution delivered in charged particle therapy is due to both primary and secondary particles. The secondaries, originating from non-elastic nuclear interactions, are of interest for three reasons. First, if fast Monte Carlo treatment planning is envisaged, the question arises whether all nuclear interaction products deliver a significant contribution to the total dose and, hence, need to be tracked. Second, there could be an enhanced relative biological effectiveness (RBE) due to low energy and/or heavy secondaries. Third, neutrons originating from nuclear interactions may deliver dose outside the target volume. The particle yield from different nuclear interaction channels as a function of proton penetration depth was studied theoretically for different proton beam energies. Three-dimensional dose distributions from primary and secondary particles were simulated for an unmodulated 160 MeV proton beam with and without including a slice of bone material and for a spread-out Bragg peak (SOBP) of 3 x 3 x 3 cm3 in water. Secondary protons deliver up to 10% of the total dose proximal to the Bragg peak of an unmodulated proton beam and they affect the flatness of the SOBP. Furthermore, they cause a dose build-up due to forward emission of secondary particles from nuclear interactions. The dose deposited by d, t, 3He and alpha-particles was found to contribute less than 0.1% of the total dose. The dose distal to the target volume caused by liberated neutrons was studied for four proton beam energies in the range of 160-250 MeV and found to be below 0.05% (2 cm distal to SOBP) of the prescribed target dose for a 3 x 3 x 3 cm3 target. RBE values relative to 60Co were calculated proximal to and within the SOBP. The RBE proximal to the Bragg peak (100% dose) is influenced by secondary particles (mainly protons and a-particles) with a strong dose dependency resulting in RBE values up to 1.2 (2 Gy; inactivation of V79). Depending on the endpoint considered, secondary particles cause a shift in RBE by up to 8% at 2 Gy. In contrast, the RBE in the Bragg peak is almost entirely determined by primary protons due to a decreasing secondary particle fluence with depth. RBE values up to 1.3 (2 Gy; inactivation of V79) at 1 cm distal to the Bragg peak maximum were found. The inactivations of human skin fibroblasts and mouse lymphoma cells were also analysed and reveal a substantial tissue dependency of the total RBE. The outcome of this study shows that elevated RBE values occur not only at the distal edge of the SOBP. Although the variations are modest, and in most cases might have no observable clinical effect, they might have to be considered in certain treatment situations. The biological effect downstream of the target caused by neutrons was analysed using a radiation quality factor of 10. The biological dose was found to be below 0.5% of the prescribed target dose (for a 3 x 3 x 3 cm3 SOBP) but depends on the size of the SOBP. This dose should not be significant with respect to late effects, e.g. cancer induction.

Calculation of the spatial variation of relative biological effectiveness in a therapeutic proton field for eye treatment

The relative biological effectiveness (RBE) of protons under conditions suitable for eye treatment has been studied. A complete three-dimensional modelling of the beam delivery system has been performed. Proton Monte Carlo transport calculations have been performed to obtain the proton energy distributions at different positions in a water phantom including the influence of range shifter, modulator wheel, scattering foils and collimators. A beam with a kinetic energy of 68 MeV +/- 250 keV has been simulated with respect to the HMI-Berlin eye treatment facility. The dependence of the RBE on absorbed dose and position within a spread-out Bragg peak (SOBP) has been investigated with the track structure model. Due to a decreasing proton energy with depth, the energy transfer per pathlength within the SOBP increases, affecting the RBE. An RBE increasing with depth as well as with decreasing absorbed dose has been found for the endpoint inactivation of V79 and CH2B2 hamster cells. RBE values at the distal end of the SOBP up to 1.3 and 1.5 have been found at a dose of 14 Gy and 2 Gy respectively. Within the SOBP plateau, no lateral variation of RBE has been found for a given depth. The model used offers the possibility of introducing a variable RBE in treatment planning.

Calculation of relative biological effectiveness for proton beams using biological weighting functions

PURPOSE

The microdosimetric weighting function approach is used widely for beam comparison studies. The suitability of this model to predict the relative biological effectiveness (RBE) of therapeutic proton beams was studied. The RBE(alpha) (i.e., linear approximation) dependence on the type of biological end point, initial proton energy, energy spread of the input proton beam, and depth of beam penetration was investigated.

METHODS AND MATERIALS

Proton transport calculations for a proton energy range from 70 to 250 MeV were performed to obtain proton energy spectra at a given depth. The corresponding microdosimetric distributions of lineal energy were calculated. To these distributions the biological response function approach was applied to calculate RBE(alpha) the biological effectiveness based on a linear dose-response relationship. The early intestinal tolerance assessed by crypt regeneration in mice and the inactivation of V79 cells were taken as biological end points.

RESULTS

The RBE(alpha) values approach about 1 in the plateau region and gradually increase with the proton penetration depth. In the center of the Bragg peak, at the maximum dose delivery, the values of RBE(alpha) range from 1.1 (250-MeV beam, early intestinal tolerance in mice) to 1.9 (70-MeV beam, Chinese hamster V79 cells in G1/S phase). Distal to the Bragg peak, where only a small fraction of dose is delivered, the RBE(alpha) was found to be even higher. For modulated proton beams we found an increasing RBE(alpha) with depth in the spread-out Bragg peak (SOBP). Values up to 1.37 at the distal end of the SOBP plateau (155-MeV beam, SOBP between 5.3 and 13.2 cm) were obtained.

CONCLUSION

More experimental work on the determination of microdosimetric weighting functions is needed. The results of the presented calculations indicate that for therapy planning it may be necessary to account for a depth dependence on proton RBE, especially for lower energy.

The influence of the beam modulation technique on dose and RBE in proton radiation therapy

Because a dose can be described as fluence times LET, it is evident that, in a mixed radiation field, similar doses can be achieved with different particle energy distributions. Isodose contours are iso-effect contours only if the energy spectra of the accompanying particles remain constant. Under this condition, the beam delivery technique used to build a spread-out Bragg peak (SOBP) can influence the relative biological effectiveness (RBE). We investigated the influence of the beam modulation method on the dose distribution and, taking into account the respective RBEs, on the biological dose distribution. For this, we first performed proton transport calculations in order to obtain the dose and the proton energy spectra at a given depth. Secondly, RBE values were calculated using the microdosimetric response function and the track structure model for two biological end points. We found an increasing RBE with depth within the SOBP. The higher the energy used for modulation the lower the average LET and the RBE and the higher the proton fluence. The RBE for an active beam modulation system behaves like the respective RBE of a passive system with similar initial beam energy.

Mammalian cell survival and radiation quality: analysis with allowance for delta tracks

The RBE for mammalian cell survival is analysed in relation to the distribution of LET. Complex target theory is described, together with a procedure for applying LET distributions to experimental findings in order to estimate the modes of cellular inactivation. Track segment theory is shown to have previously unrecognised limitations. The stepwise method is adopted to calculate the LET distributions for the radiations (alpha-particles, deuterons and x-rays) used by Barendsen et al (1966) in their study of the survival of T1 cells of human origin. Satisfactory fits of theory to experiment are obtained. Three distinctive modes of cellular inactivation, with independent energy transfers (direct and indirect) to complex targets comprising 2, 4 adn 6 elements respectively, appear to be involved overall. At 'low dose', no contribution from the 2-transfer-mode can be discerned; only this mode is reparable. Saturation cross-sections (at high LET) for the 2- and 4-transfer-, but not the 6-transfer-mode, are oxygen-dependent. All three modes of inactivation might entail unrepaired double strand breaks and/or some form of mutation in DNA, at 1, 2 and 3 vulnerable sections, respectively.

RBE-dose relations for neutrons and pions

From cellular radiosensitivity parameters and theoretical particle-energy spectra in tissue, of the secondary particles from neutron and negative pion irradiations, RBE-Dose relations have been calculated. The theoretical results are compared with clinical and radiobiological data for normal tissue, tumours and cells in culture. Formulae for calculation, cellular parameters and the needed properties of equivalent 'track-segment bombardments' are given, for several mammalian cells irradiated with pions and with neutrons of several energies.