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Background: For proton therapy, a relative biological effectiveness (RBE) of 1.1 is widely applied clinically. However, due to abundant evidence of variable RBE in vitro, and as suggested in studies of patient outcomes, RBE might increase by the end of the proton tracks, as described by several proposed variable RBE models. Typically, the dose averaged linear energy transfer (LETd) has been used as a radiation quality metric (RQM) for these models. However, the optimal choice of RQM has not been fully explored. Purpose: This study aims to propose novel RQMs that effectively weight protons of different energies, and assess their predictive power for variable RBE in proton therapy. The overall objective is to identify an RQM that better describes the contribution of individual particles to the RBE of proton beams. Methods: High-throughput experimental set-ups of in vitro cell survival studies for proton RBE determination are simulated utilizing the SHIELD-HIT12A Monte Carlo particle transport code. For every data point, the proton energy spectra are simulated, allowing the calculation of novel RQMs by applying different power levels to the spectra of LET or effective Q (Qeff) values. A phenomenological linear-quadratic-based RBE model is then applied to the in vitro data, using various RQMs as input variables, and the model performance is evaluated by root-mean-square-error (RMSE) for the logarithm of cell surviving fractions of each data point. Results: Increasing the power level, that is, putting an even higher weight on higher LET particles when constructing the RQM is generally associated with an increased model performance, with dose averaged LET3 (i.e., dose averaged cubed LET, cLETd) resulting in a RMSE value 0.31, compared to 0.45 for a model based on (linearly weighted) LETd, with similar trends also observed for track averaged and Qeff-based RQMs. Conclusions: The results indicate that improved proton variable RBE models can be constructed assuming a non-lin

Linear Energy Transfer (LET) is widely used to express the radiation quality of ion beams, when characterizing the biological effectiveness. However, averaged LET may be defined in multiple ways, and the chosen definition may impact the resulting reported value. We review averaged LET definitions found in the literature, and quantify which impact using these various definitions have for different reference setups. We recorded the averaged LET definitions used in 354 publications quantifying the relative biological effectiveness (RBE) of hadronic beams, and investigated how these various definitions impact the reported averaged LET using a Monte Carlo particle transport code. We find that the kind of averaged LET being applied is, generally, poorly defined. Some definitions of averaged LET may influence the reported averaged LET values up to an order of magnitude. For publications involving protons, most applied dose averaged LET when reporting RBE. The absence of what target medium is used and what secondary particles are included further contributes to an ill-defined averaged LET. We also found evidence of inconsistent usage of averaged LET definitions when deriving LET-based RBE models. To conclude, due to commonly ill-defined averaged LET and to the inherent problems of LET-based RBE models, averaged LET may only be used as a coarse indicator of radiation quality. We propose a more rigorous way of reporting LET values, and suggest that ideally the entire particle fluence spectra should be recorded and provided for future RBE studies, from which any type of averaged LET (or other quantities) may be inferred.

Ion beams passing through lung tissue show more pronounced energy straggling than expected for solid materials of the same thickness. Energy straggling in active scanning particle therapy can enlarge the pencil beam Bragg peaks in-depth as well as displace them, deteriorating the dose coverage of a target within the lung. While this is not yet considered in any known treatment planning system, we implement a mathematical model to be used for treatment planning, using TRiP98, which relies on a deterministic pencil beam algorithm. Through a randomization process based on a continuous Poisson probability distribution, the HU values of lung voxels are replaced with a modified value in successive iterations. The beam-modulation effect of the lung can thus be taken into account in treatment planning by recalculating the dose n times for n randomized CTs using the raster scan file of a plan that was optimized on the nonmodulated CT. The evaluation follows by averaging the resulting n dose distributions and comparing to the corresponding nonmodulated dose distribution, attending at dosimetric indices and dose-volume histograms. In this work, the functionality of these routines was tested for proton and carbon ion plans for two selected lung cancer patient cases with deep-seated tumors, showing that, with existing standard tools, it is possible to calculate the beam-modulation effect of the lung in TRiP98 in a transparent way. Variable model parameters, such as modulation power, voxel size and density voxel selection range, were evaluated. Furthermore, a systematic study for spherical geometries in a lung tissue CT cube is presented to investigate general trends.

Purpose: Conventional X-ray radiotherapy induces a pro-inflammatory response mediated by altered expression of inflammation-regulating cytokines. Proton scanning and X-ray irradiation produce distinct changes to cytokine gene expression in vitro suggesting that proton beam therapy may induce an inflammatory response dissimilar to that of X-ray radiation. The purpose of the present study was to determine whether proton scanning beam radiation and conventional X-ray photon radiation would induce differential regulation of circulating cytokines in vivo. Materials and methods: Female CDF1 mice were irradiated locally at the right hind leg using proton pencil beam scanning or X-ray photons. Blood samples were obtained from two separate mice groups. Samples from one group were drawn by retro-orbital puncture 16 months post irradiation, while samples from the other group were drawn 5 and 30 days post irradiation. Concentration of the cytokines IL-6, IL-1 beta, IL-10, IL-17A, IFN-gamma, and TNF alpha was measured in plasma using bead-based immunoassays. Results: The cytokines IL-6, IL-1 beta, IL-10, IFN-gamma, and TNF alpha were expressed at lower levels in plasma samples from proton-irradiated mice compared with X-ray-irradiated mice 16 months post irradiation. The same cytokines were downregulated in proton-irradiated mice 5 days post irradiation when compared to controls, while at day 30 expression had increased to the same level or higher. X-ray radiation did not markedly change expression levels at days 5 and 30. Conclusions: The inflammatory response to proton and X-ray irradiation seem to be distinct as the principal pro-inflammatory cytokines are differentially regulated short- and long-term following irradiation. Both the development of normal tissue damage and efficacy of immunotherapy could be influenced by an altered inflammatory response to irradiation.

Purpose: The dose response of Gafchromic EBT3 films exposed to proton beams depends on the dose, and additionally on the beam quality, which is often quantified with the linear energy transfer (LET) and, hence, also referred to as LET quenching. Fundamentally different methods to determine correction factors for this LET quenching effect have been reported in literature and a new method using the local proton fluence distribution differential in LET is presented. This method was exploited to investigate whether a more practical correction based on the dose- or fluence-averaged LET is feasible in a variety of clinically possible beam arrangements. Methods: The relative effectiveness (RE) was characterized within a high LET spread-out Bragg peak (SOBP) in water made up by the six lowest available energies (62.4-67.5 MeV, configuration b(1)) resulting in one of the highest clinically feasible dose-averaged LET distributions. Additionally, two beams were measured where a low LET proton beam (252.7 MeV) was superimposed on b1, which contributed either 50% of the initial particle fluence or 50% of the dose in the SOBP, referred to as configuration b(2) and b(3), respectively. The proton LET spectrum was simulated with GATE/Geant4 at all measurement positions. The net optical density change differential in LET was integrated over the local proton spectrum to calculate the net optical density and therefrom the beam quality correction factor. The LET dependence of the film response was accounted for by an LET dependence of one of the three parameters in the calibration function and was determined from inverse optimization using measurement b(1). This method was then validated on the measurements of b(2) and b(3) and subsequently used to calculate the RE at 900 positions in nine clinically relevant beams. The extrapolated RE set was used to derive a simple linear correction function based on dose-averaged LET (L-d) and verify the validity in all points of the comprehensive RE

The ion recombination is examined in parallel-plate ionization chambers in scanning proton beams at the Danish Centre for Particle Therapy and the Skandion Clinic. The recombination correction factor k(s) is investigated for clinically relevant energies between 70 MeV and 244 MeV for dose rates below 400 Gy min(-1) in air. The Boutillon formalism is used to separate the initial and general recombination. The general recombination is compared to predictions from the numerical recombination code IonTracks and the initial recombination to the Jaffe theory. k(s) is furthermore calculated with the two-voltage method (TVM) and extrapolation approaches, in particular the recently proposed three-voltage (3VL) method. The TVM is in agreement with the Boutillon method and IonTracks for dose rates above 100 Gy min(-1). However, the TVM calculated k(s) is closer related to the Jaffe theory for initial recombination for lower dose rate, indicating a limited application in scanning light ion beams. The 3VL is in turn found to generally be in agreement with Boutillon's method. The recombination is mapped as a function of the dose rate and proton energy at the two centres using the Boutillon formalism: the initial recombination parameter was found to be A = (0.10 +/- 0.01) V at DCPT and A = (0.22 +/- 0.13) V at Skandion, which is in better agreement with the Jaffe theory for initial recombination than previously reported values. The general recombination parameter was estimated to m2=(4.7 +/- 0.1).103V2nA-1cm-1m2=(7.2 +/- 0.1).103V2nA-1cm-1

The ion recombination is examined in parallel-plate ionization chambers in scanning proton beams at the Danish Centre for Particle Therapy and the Skandion Clinic. The recombination correction factorksis investigated for clinically relevant energies between 70 MeV and 224 MeV for dose rates below 400 Gy/min in air. The Boutillon formalism is used to separate the initial and general recombination. The general recombination is compared to predictions from the numerical recombination code IonTracks and the initial recombination to the Jaffé theory.ksis furthermore calculated with the two-voltage method (TVM) and extrapolation approaches, in particular the recently proposed three-voltage (3VL) method.. The TVM is in agreement with the Boutillon method and IonTracks for dose rates above 100 Gy/min. However, the TVM calculatedksis closer related to the Jaffé theory for initial recombination for lower dose rate, indicating a limited application in scanning light ion beams. The 3VL is in turn found to generally be in agreement with Boutillon's method. The recombination is mapped as a function of the dose rate and proton energy at the two centres using the Boutillon formalism: the initial recombination parameter was found to beA=(0.10±0.01) V at DCPT andA=(0.22±0.13) V at Skandion, which is in better agreement with the Jaffé theory for initial recombination than previously reported values. The general recombination parameter was estimated tom2= (4.7±0.1)×103V2nA-1cm-1andm2= (7.2±0.1)×103V2nA-1cm-1. Furthermore, the numerical algorithm IonTracks is demonstrated to correctly predict the initial recombination at low dose rates and general recombination at high dose rates.

Ionization quenching in ion beam dosimetry is often related to the fluence- or dose-averaged linear energy transfer (LET). Both quantities are however averaged over a wide LET range and a mixed field of primary and secondary ions. We propose a novel method to correct the quenched luminescence in scintillators exposed to ion beams. The method uses the energy spectrum of the primaries and accounts for the varying quenched luminescence in heavy, secondary ion tracks through amorphous track structure theory. The new method is assessed against more traditional approaches by correcting the quenched luminescence response from the BCF-12, BCF-60, and 81-0084 plastic scintillators exposed to a 100 MeV pristine proton beam in order to compare the effects of the averaged LET quantities and the secondary ions. Calculations and measurements show that primary protons constitute more than 92% of the energy deposition but account for more than 95% of the luminescence signal in the scintillators. The quenching corrected luminescence signal is in better agreement with the dose measurement when the secondary particles are taken into account. The Birks model provided the overall best quenching corrections, when the quenching corrected signal is adjusted for the number of free model parameters. The quenching parameter kB for the BCF-12 and BCF-60 scintillators is in agreement with literature values and was found to be kB = (10.6 +/- 0.1) x 10(-2) mu m keV(-1) for the 81-0084 scintillator. Finally, a fluence threshold for the 100 MeV proton beam was calculated to be of the order of 10(10) cm(-2), corresponding to 110 Gy, above which the quenching increases non-linearly and the Birks model no longer is applicable.

Purpose: To identify differential cellular responses after proton and photon irradiation by comparing transcriptomes of primary fibroblasts irradiated with either radiation type. Methods and Materials: A panel of primary dermal fibroblast cultures was irradiated with low and higher linear energy transfer (LET) proton beams. Cobalt-60 photon irradiation was used as reference. Dose was delivered in 3 fractions of 3.5 Gy (relative biological effectiveness) using a relative biological effectiveness of 1.1 for proton doses. Cells were harvested 2 hours after the final fraction was delivered, and RNA was purified. RNA sequencing was performed using Illumina NextSeq 500 with high-output kit. The edgeR package in R was used for differential gene expression analysis. Results: Pairwise comparisons of the transcriptomes in the 3 treatment groups showed that there were 84 and 56 differentially expressed genes in the low LET group compared with the Cobalt-60 group and the higher LET group, respectively. The higher LET proton group and the Cobalt-60 group had the most distinct transcriptome profiles, with 725 differentially regulated genes. Differentially regulated canonical pathways and various regulatory factors involved in regulation of biological mechanisms such as inflammation, carcinogenesis, and cell cycle control were identified. Conclusions: Inflammatory regulators associated with the development of normal tissue complications and malignant transformation factors seem to be differentially regulated by higher LET proton and Cobalt-60 photon irradiation. The reported transcriptome differences could therefore influence the progression of adverse effects and the risk of developing secondary cancers.

Radiotherapy beams of protons or heavier ions generate secondary particles through nuclear interactions over different patient tissues. The resulting particle spectra depend on the tissue composition and on charge and energy of the primary beam ions. In proton radiotherapy, predictive radiobiological models usually apply dose-averaged linear energy transfer (LET). Microdosimetry-based models for proton or heavier ion primary beams also rely on dose-averaged quantities, the values of which depend on whether the produced secondaries are included or excluded in the calculation. In turn, this will affect the results of calculations of the relative biological effectiveness (RBE) of these beams. In this brief note, we study quantitatively the influence of the secondary radiation spectra on the averaged expectation values of LET and their impact on predictions of RBE. It is noted that for microdosimetry-based quantities and for corresponding LET-based parameters the trends are similar and that fluence-averaged quantities should be studied more closely.

Purpose: Radiotherapy using grids containing cm-wide beam elements has been carried out sporadically for more than a century. During the past two decades, preclinical research on radiotherapy with grids containing small beam elements, 25 m-0.7 mm wide, has been performed. Grid therapy with larger beam elements is technically easier to implement, but the normal tissue tolerance to the treatment is decreasing. In this work, a new approach in grid therapy, based on irradiations with grids containing narrow carbon-ion beam elements was evaluated dosimetrically. The aim formulated for the suggested treatment was to obtain a uniform target dose combined with well-defined grids in the irradiated normal tissue. The gain, obtained by crossfiring the carbon-ion beam grids over a simulated target volume, was quantitatively evaluated. Methods: The dose distributions produced by narrow rectangular carbon-ion beams in a water phantom were simulated with the PHITS Monte Carlo code. The beam-element height was set to 2.0 cm in the simulations, while the widths varied from 0.5 to 10.0 mm. A spread-out Bragg peak (SOBP) was then created for each beam element in the grid, to cover the target volume with dose in the depth direction. The dose distributions produced by the beam-grid irradiations were thereafter constructed by adding the dose profiles simulated for single beam elements. The variation of the valley-to-peak dose ratio (VPDR) with depth in water was thereafter evaluated. The separation of the beam elements inside the grids were determined for different irradiation geometries with a selection criterion. Results: The simulated carbon-ion beams remained narrow down to the depths of the Bragg peaks. With the formulated selection criterion, a beam-element separation which was close to the beam-element width was found optimal for grids containing 3.0-mm-wide beam elements, while a separation which was considerably larger than the beam-element width was found advantageous for grids

In this chapter, we describe two different methods, analytical (pencil beam) algorithms and Monte Carlo simulations, used to obtain the intended dose distributions in patients and evaluate their strengths and shortcomings. We discuss the difference between the prescribed physical dose and the biologically effective dose, the relative biological effectiveness (RBE) between ions and photons and the dependence of RBE on the linear energy transfer (LET). Lastly, we show how LET- or RBE-based optimization can be used to improve treatment plans and explore how the availability of multimodality ion beam facilities can be used to design a tumor-specific optimal treatment.

Gafchromic EBT3 films are applied in proton radiotherapy for 2D dose mapping because they demonstrate spatial resolution well below 1mm. However, the film response must be corrected in order to reach the accuracy of dose measurements required for the clinical use. The in-house developed AnalyseGafchromic software allows to analyze and correct the measured response using triple channel dose calibration, statistical scan-to-scan fluctuations as well as experimentally determined dose and LET dependence. Finally, the optimized protocol for evaluation of response of Gafchromic EBT3 films was applied to determine 30 x 40 cm(2) dose profiles of the scanning therapy unit at the Cyclotron Centre Bronowice, CCB in Krakow, Poland.

The linear energy transfer (LET) is commonly used as a parameter which describes the quality of the radiation applied in radiation therapy with fast ions. In particular in proton therapy, most models which predict the radiobiological properties of the applied beam, are fitted to the dose-averaged LET, LETd. The related parameter called the fluence-or track-averaged LET, LETt, is less frequently used. Both LETt and in particular LETd depends profoundly on the encountered secondary particle spectrum. For proton beams including all secondary particles, LETd may reach more than 3 keV/um in the entry channel of the proton field. However, typically the charged particle spectrum is only averaged over the primary and secondary protons, which is in the order of 0.5 keV/um for the same region. This is equal to assuming that the secondary particle spectrum from heavier ions is irrelevant for the resulting radiobiology, which is an assertion in the need of closer investigation. Models which rely on LETd should also be clear on what type of LETd is used, which is not always the case. Within this work, we have extended the Monte Carlo particle transport code SHIELD-HIT12A to provide dose-and track-average LET-maps for ion radiation therapy treatment plans.

A ripple filter (RiFi) is a passive energy modulator used in scanned particle therapy to broaden the Bragg peak, thus lowering the number of accelerator energies required for homogeneous target coverage, which significantly reduces the irradiation time. As we have previously shown, a new 6 mm thick RiFi with 2D groove shapes produced with 3D printing can be used in carbon ion treatments with a similar target coverage and only a marginally worse planning conformity compared to treatments with in-use 3 mm thick RiFis of an older 1D design. Where RiFis are normally not used with protons due to larger scattering and straggling effects, this new design would be beneficial in proton therapy too. Measurements of proton Bragg curves and lateral beam profiles were carried out for different RiFi designs and thicknesses as well as for no RiFi at the Heidelberg lonenstrahl-Therapiezentrum. Base data for proton treatment planning were generated with the Monte Carlo code SHIELD-HIT12A with and without the 2D 6 mm RiFi. Plans on spherical targets in water were calculated with TRiP98 for a systematic RiFi performance analysis and for comparisons with carbon ion plans for the same respective energy depth step sizes. Plans for 9 stage I static non small cell lung cancer patients were calculated with Eclipse 13.7.15. Dose-volume-histograms, spatial dose distributions and dosimetric indexes were used for plan evaluation. Measurements confirm the functionality of the new 2D RiFi design, which reduces the beam spot size compared to 1D RiFis of the same thickness. Planning studies show that a 6 mm thick 2D RiFi could be used in proton therapy to lower the irradiation time. Although slightly worse planning conformity and dose homogeneity were found for plans with the RiFi compared to plans without, satisfactory results within the planning objective were obtained for all cases.

Background: Grid therapy has in the past normally been performed with single field photon-beamgrids. In this work, we evaluated a method to deliver grid therapy based on interlacing and crossfiringgrids of mm-wide proton beamlets over a target volume, by Monte Carlo simulations. Material and methods: Dose profiles for single mm-wide proton beamlets (1, 2 and 3 mm FWHM) inwater were simulated with the Monte Carlo code TOPAS. Thereafter, grids of proton beamlets weredirected toward a cubic target volume, located at the center of a water tank. The aim was to deliver anearly homogeneous dose to the target, while creating high dose heterogeneity in the normal tissue,i.e., high gradients between valley and peak doses in the grids, down to the close vicinity of thetarget. Results: The relative increase of the beam width with depth was largest for the smallest beams(þ6.9mm for 1 mm wide and 150MeV proton beamlets). Satisfying dose coverage of the cubic targetvolume (r< ±5%) was obtained with the interlaced-crossfiring setup, while keeping the grid pattern ofthe dose distribution down to the target (valley-to-peak dose ratio<0.5 less than 1 cm before the tar-get). Center-to-center distances around 7–8 mm between the beams were found to give the best com-promise between target dose homogeneity and low peak doses outside of the target. Conclusions: A nearly homogeneous dose distribution can be obtained in a target volume by crossfir-ing grids of mm-wide proton-beamlets, while maintaining the grid pattern of the dose distribution atlarge depths in the normal tissue, close to the target volume. We expect that the use of this methodwill increase the tumor control probability and improve the normal tissue sparing in grid therapy.

Most solid-state detectors, including 3D dosimeters, show lower signal in the Bragg peak than expected, a process termed quenching. The purpose of this study was to investigate how variation in chemical composition of a recently developed radiochromic, silicone-based 3D dosimeter influences the observed quenching in proton beams. The dependency of dose response on linear energy transfer, as calculated through Monte Carlo simulations of the dosimeter, was investigated in 60 MeV proton beams. We found that the amount of quenching varied with the chemical composition: peak-to-plateau ratios (1 cm into the plateau) ranged from 2.2 to 3.4, compared to 4.3 using an ionization chamber. The dose response, and thereby the quenching, was predominantly influenced by the curing agent concentration, which determined the dosimeter's deformation properties. The dose response was found to be linear at all depths. All chemical compositions of the dosimeter showed dose-rate dependency; however this was not dependent on the linear energy transfer. Track-structure theory was used to explain the observed quenching effects. In conclusion, this study shows that the silicone-based dosimeter has potential for use in measuring 3D-dose-distributions from proton beams.

Introduction: Proton beam therapy delivers a more conformal dose distribution than conventional radiotherapy, thus improving normal tissue sparring. Increasing linear energy transfer (LET) along the proton track increases the relative biological effectiveness (RBE) near the distal edge of the Spread-out Bragg peak (SOBP). The severity of normal tissue side effects following photon beam radiotherapy vary considerably between patients. Aim: The dual study aim was to identify gene expression patterns specific to radiation type and proton beam position, and to assess whether individual radiation sensitivity influences gene expression levels in fibroblast cultures irradiated in vitro. Methods: The study includes 30 primary fibroblast cell cultures from patients previously classified as either radiosensitive or radioresistant. Cells were irradiated at three different positions in the proton beam profile: entrance, mid-SOBP and at the SOBP distal edge. Dose was delivered in three fractions × 3.5 Gy(RBE) (RBE 1.1). Cobalt-60 (Co-60) irradiation was used as reference. Real-time qPCR was performed to determine gene expression levels for 17 genes associated with inflammation response, fibrosis and angiogenesis. Results: Differences in median gene expression levels were observed for multiple genes such as IL6, IL8 and CXCL12. Median IL6 expression was 30%, 24% and 47% lower in entrance, mid-SOBP and SOBP distal edge groups than in Co-60 irradiated cells. No genes were found to be oppositely regulated by different radiation qualities. Radiosensitive patient samples had the strongest regulation of gene expression; irrespective of radiation type. Conclusions: Our findings indicate that the increased LET at the SOBP distal edge position did not generally lead to increased transcriptive response in primary fibroblast cultures. Inflammatory factors were generally less extensively upregulated by proton irradiation compared with Co-60 photon irradiation. These effects may possibly infl

The effect of carbon ion radiotherapy on hypoxic tumors has recently been questioned because of low linear energy transfer (LET) values in the spread-out Bragg peak (SOBP). The aim of this study was to investigate the role of hypoxia and local oxygenation changes (LOCs) in fractionated carbon ion radiotherapy. Three-dimensional tumors with hypoxic subvolumes were simulated assuming interfraction LOCs. Different fractionations were applied using a clinically relevant treatment plan with a known LET distribution. The surviving fraction was calculated, taking oxygen tension, dose and LET into account, using the repairable–conditionally repairable (RCR) damage model with parameters for human salivary gland tumor cells. The clinical oxygen enhancement ratio (OER) was defined as the ratio of doses required for a tumor control probability of 50% for hypoxic and well-oxygenated tumors. The resulting OER was well above unity for all fractionations. For the hypoxic tumor, the tumor control probability was considerably higher if LOCs were assumed, rather than static oxygenation. The beneficial effect of LOCs increased with the number of fractions. However, for very low fraction doses, the improvement related to LOCs did not compensate for the increase in total dose required for tumor control. In conclusion, our results suggest that hypoxia can influence the outcome of carbon ion radiotherapy because of the non-negligible oxygen effect at the low LETs in the SOBP. However, if LOCs occur, a relatively high level of tumor control probability is achievable with a large range of fractionation schedules for tumors with hypoxic subvolumes, but both hyperfractionation and hypofractionation should be pursued with caution.

Introduction. Modern particle therapy facilities enable sub-millimeter precision in dose deposition. Here, also ionization chambers (ICs) are used, which requires knowledge of the recombination effects. Up to now, recombination is corrected using phenomenological approaches for practical reasons. In this study the effect of the underlying dose distribution on columnar recombination, a quantitative model for initial recombination, is investigated. Material and methods. Jaffé's theory, formulated in 1913 quantifies initial recombination by elemental processes, providing an analytical (closed) solution. Here, we investigate the effect of the underlying charged carrier distribution around a carbon ion track. The fundamental partial differential equation, formulated by Jaffé, is solved numerically taking into account more realistic charge carrier distributions by the use of a computer program (Gascoigne 3D). The investigated charge carrier distributions are based on track structure models, which follow a 1∕r(2) behavior at larger radii and show a constant value at small radii. The results of the calculations are compared to the initial formulation and to data obtained in experiments using carbon ion beams. Results. The comparison between the experimental data and the calculations shows that the initial approach made by Jaffé is able to reproduce the effects of initial recombination. The amorphous track structure based charge carrier distribution does not reproduce the experimental data well. A small additional correction in the assessment of the saturation current or charge is suggested by the data. Conclusion. The established model of columnar recombination reproduces the experimental data well, whereas the extensions using track structure models do not show such an agreement. Additionally, the effect of initial recombination on the saturation curve (i.e. Jaffé plot) does not follow a linear behavior as suggested by current dosimetry protocols, therefore higher order co

Modern radiotherapy facilities for cancer treatment such as the Heavy Ion Therapy Centre (HIT) in Heidelberg (Germany) enable sub millimetre precision in dose deposition. For the measurement of such dose distributions and characterization of teh particle beams, detectors with high spatial resolution and high sensitivity are necessary. For exact dosimetry which is done using ionization chambers (ICs), the recombination taking place in the IC has to be known. Up to now, recombination is corrected phenomenologically and more practical approaches are currently used. Nevertheless, Jaffés theory of columnar recombination was designed to model the detector efficiency of an ionization chamber. Here, we have shown that despite the approximations and simplification made, the theory is correct for the LETs typically found in clinical radiotherapy employing particles from protons to carbon ions. As no exact closed solution is available, a numerical solver was programmed.

Purpose: Radiotherapy of cancer carries a perceived risk of inducing secondary cancer and other damage due to dose delivered to normal tissue. While expectedly small, this risk must be carefully analysed for all modalities. Especially in the use of exotic particles like pions and antiprotons, which annihilate and produce a mixed radiation field when interacting with normal matter nuclei, the biological effective dose far out of field needs to be considered in evaluating this approach. We describe first biological measurements to address the concern that medium and long range annihilation products may produce a significant background dose and reverse any benefits of higher biological dose in the target area. Materials and methods: Using the Antiproton Decelerator (AD) at CERN (Conseil Europeen pour la Recherche Nucleaire) we irradiated V-79 Chinese Hamster cells embedded in gelatine using an antiproton beam with fluence ranging from 4.5 x 10(8) to 4.5 x 10(9) particles, and evaluated the biological effect on cells located distal to the Bragg peak using clonogenic survival and the COMET assay. Results: Both methods show a substantial biological effect on the cells in the entrance channel and the Bragg Peak area, but any damage is reduced to levels well below the effect in the entrance channel 15 mm distal to the Bragg peak for even the highest particle fluence used. Conclusions: The annihilation radiation generated by antiprotons stopping in biological targets causes an increase of the penumbra of the beam but the effect rapidly decreases with distance from the target volume. No major increase in the biological effect is found in the far field outside of the primary beam.