Response of cells to fast neutrons, stopped pions, and heavy ion beams

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.

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.

The application of amorphous track models to study cell survival in heavy ions beams

In a study of amorphous track models, in the local effect model (LEM), the Kellerer algorithm was used, which folds radial dose distributions from different ion tracks. In representative set of 10 experimental cell survival curves of normal human skin fibroblast cells irradiated with carbon ions, the method that applies the Kellerer algorithm was found to be more accurate and 10(4) times faster than the usual Monte Carlo summation method based on a regular grid.

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

The Physical and Radiobiological Basis of the Local Effect Model:A Response to the Commentary by R. Katz

The physical and biological basis of our model to calculate the biological effects of charged particles, termed the local effect model (LEM), has recently been questioned in a commentary by R. Katz. Major objections were related to the definition of the target size and the use of the term cross section. Here we show that the objections raised against our approach are unjustified and are largely based on serious misunderstandings of the conceptual basis of the local effect model. Furthermore, we show that the approach developed by Katz and coworkers itself suffers from exactly those deficiencies for which Katz criticizes our model. The essential conceptual differences between the two models are discussed by means of some illustrative examples, based on a comparison with experimental data. For these examples, the predictions of the local effect model are fully consistent with the experimental data. In contrast, e.g. for very heavy ions, there are significant discrepancies observed for the Katz approach. These discrepancies can be attributed to the inadequate definition of the target size in this model. Experimental data are thus clearly in favor of the definition of the target as used in the local effect model. Agreement with experimental data is achieved for protons within the Katz approach but at the cost of questionable approximations in combination with the violation of the fundamental physical principle of energy conservation.

The parameter-free track structure model of Scholz and Kraft for heavy-ion cross sections

The "parameter-free", "local effects" theory of Scholz and Kraft is an extension to mammalian cells of the theory of RBE for dry enzymes and viruses of Butts and Katz. Its claim for parameter freedom has been challenged elsewhere. Here we examine its conceptual base and find errors in its use of the physical concept of cross section and its neglect of the radiobiological relationship between target size and radiosensitivity in evaluating the radiation damage to "point targets".

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.

Radiobiological significance of beamline dependent proton energy distributions in a spread-out Bragg peak

Similar target doses can be achieved with different mixed radiation fields, i.e., particle energy distributions, produced by a practical proton beam and a range modulator. The dose delivered in particle therapy can be described as the integral of fluence times the total mass stopping power over the particle energy distributions. We employed Monte Carlo simulations to explore the influence on the relative biological effectiveness (RBE) of the energy and the energy spread of the proton beam incident on a range modulator system. Using different beams, the conditions of beam delivery were adjusted so that similar spread out Bragg peak (SOBP) doses were delivered to a simulated water phantom. We calculated the RBE for inactivation of three different cell lines using the track structure model. The RBE depends on the details of the dose deposition and the biological characteristics of the irradiated tissue. Our calculations show that, for differing beam conditions, the corresponding differences in the total mass stopping power distributions are reflected in differences in the RBE. However, these differences are remarkable only at the very distal edge of the SOBP, for low doses, and/or for large differences in beam setup.

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.

Heavy ion inactivation in Escherichia coli cells: experiment and theory

Cross sections for inactivation of stationary cells of E. coli strains (B(s-1) and B/r) by heavy ions (Z = 8-92) with energies <15 MeV/u were determined from survival curves and compared with track structure calculations. Whereas for low energies, inactivation cross sections for both strains are similar, and thus do not reflect their difference in X-ray sensitivity, the ratios of cross sections of the two strains approach the ratio of X-rays sensitivities for heavy ions at high energies. The essential features of the experimental data are reproduced well by the track structure calculations, which do not use fitted values for the model parameters but independently determined values for the X-ray sensitivities and the size of the target structure. Quantitatively, the calculations underestimate the cross sections for heavier ions as well as their ratios at higher energies. Some possible reasons for these discrepancies are discussed.

Radiation effects in space

The radiation protection guidelines of the National Aeronautics and Space Administration (NASA) are under review by Scientific Committee 75 of the National Council Protection and Measurements. The re-evaluation of the current guidelines is necessary, first, because of the increase in information about radiation risks since 1970 when the original recommendations were made and second, the population at risk has changed. For example, women have joined the ranks of the astronauts. Two types of radiation, protons and heavy ions, are of particular concern in space. Unfortunately, there is less information about the effects on tissues and cancer by these radiations than by other radiations. The choice of Quality Factors (Q) for obtaining dose equivalents for these radiations, is an important aspect of the risk estimate for space travel. There are not sufficient data for the induction of late effects by either protons or by heavy ions. The current information suggests a RBE for the relative protons of about 1, whereas, a RBE of 20 for tumor induction by heavy ions, such as iron-56, appears appropriate. The recommendations for the dose equivalent career limits for skin and the lens of the eye have been reduced but the 30-day and annual limits have been raised.

HZE effects on mammalian cells

In track segment experiments cell survival and chromosome aberrations of mammalian cells have been measured for various heavy ion beams between helium and uranium in the energy range between 0.5 and 960 MeV/u, corresponding to a velocity range of 0.03 to 0.87 C, and an LET spectrum from 10 to 15 000 keV/micrometers. At low LET, the cross section (sigma) for cell killing increases with increasing LET and shows a common curve for all ions regardless of the atomic number. This indicates that in this region the track structure of the different ions is of only a minor influence, and it is rather the total energy transfer, which is important for cell killing. At higher LET values, deviations from a common sigma-LET curve can be observed which indicate a saturation effect. The saturation of the lighter ions occurs at lower LET values than for the heavier ions. These findings are also confirmed by the chromosome data, where the efficiency for the induction of chromosomal aberrations for high LET particles depends on the track structure and is nearly independent of LET. In the heavier beams (Z > or = 10) individual particles cause multiple chromosome breaks in mitotic cells.

Inactivation probability of heavy ion-irradiated Bacillus subtilis spores as a function of the radial distance to the particle's [correction of paricle's] trajectory

The understanding of the radiobiological action of heavy ions requires the knowledge of the dependence of the inactivation probability on the distance between the particle's trajectory and the biological test organism (the impact parameter). Spores of Bacillus subtilis with a cytoplasmic core of about 0.22 micrometer cross section are suitable test objects for the study of this radial inactivation probability in its microscopic details. The spores are irradiated at low fluences of some 10(6) ions/cm2 with very heavy ions at different specific energies up to 10 MeV per atomic mass unit u while in fixed contact with visual nuclear track detectors. The methods are described by which the biological response of individual cells can be evaluated and the impact parameter be determined with an accuracy typically better than 0.2 micrometer. The results demonstrate that the common characteristics of inactivation, e.g., an effective range of inactivation extending to at least 3 micrometers, a nonmonotonic dependence of the inactivation probabilities on the radial distance, and the fact that the inactivation probability even for direct central hits on the cytoplasmic core is substantially below one, are nearly independent of the particle energy and type. The results are incompatible with the assumption that the radiobiological effectiveness can be attributed to the dose of secondary electrons as currently understood. They also demonstrate that the widely held notion of an "overkill" at low impact parameters does not apply for the spores even with the most densely ionizing ions.

Calculated responses to a thermal neutron beam for hamster and HeLa cells containing boron-10 at different concentrations

Hamster and HeLa cells containing boron-10 at different concentrations were irradiated by a thermal neutron beam from a reactor. The survival curves were calculated according to the Katz and Sharma theory of track structure for heavy charged particles. The thickness of cell specimens irradiated was taken to be 0.02 cm to enable the first collision dose to be used. The boron-10 concentrations were 0, 2,5, 10, 20, 40 and 60 microgram per g of tissue. For comparison with the experiments of Davis et al. the effect of fast neutorns was taken into account. Values for relative biological effectiveness (RBE) are given for different boron-10 concentrations and various surviving fractions. Isosurvival dose curves are defined and drawn which show the relation between neutron fluences and absorbed dose for different boron-10 concentrations. The RBE values increase with decreasing dose and change only slightly with increasing boron-10 concentration for an equal surviving fraction. Some differences were found between the calculated results for HeLa cells in the thin layer and the experimental data for the cells in a monolayer. The results of the calculations are discussed.

Systematic evaluation of cellular radiosensitivity parameters

Cellular radiosensitivity parameters of the track structure theory of Katz and co-workers are evaluated from a sum of squares minimizing computer program for nonlinear models. Based on these observations, suggestions are presented for efficient experiment design for the determination of these parameters from track-segment bombardments of high LET radiations.

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.