Perturbation factors for cylindrical ionization chambers in proton beams. Part I: corrections for gradients

Current best estimates of beam quality correction factors for reference dosimetry of clinical proton beams

Objective. To review the currently available data on beam quality correction factors, k Q , for ionization chambers in clinical proton beams and derive their current best estimates for the updated recommendations of the IAEA TRS-398 Code of Practice. Approach. The reviewed data come from 20 publications from which k Q values can be derived either directly from calorimeter measurements, indirectly from comparison with other chambers or from Monte Carlo calculated overall chamber factors, f Q . For cylindrical ionization chambers, a distinction is made between data obtained in the centre of a spread-out Bragg peak and those obtained in the plateau region of single-energy fields. For the latter, the effect of depth dose gradients has to be considered. To this end an empirical model for previously published displacement correction factors for single-layer scanned beams was established, while for unmodulated scattered beams experimental data were used. From all the data, chamber factors, f Q , and chamber perturbation correction factors, p Q , were then derived and analysed. Main results. The analysis showed that except for the beam quality dependence of the water-to-air mass stopping power ratio and, for cylindrical ionization chambers in unmodulated beams, of the displacement correction factor, there is no remaining beam quality dependence of the chamber perturbation correction factors p Q . Based on this approach, average values of the beam quality independent part of the perturbation factors were derived to calculate k Q values consistent with the data in the literature. Significance. The resulting data from this analysis are current best estimates of k Q values for modulated scattered beams and single-layer scanned beams used in proton therapy. Based on this, a single set of harmonized values is derived to be recommended in the update of IAEA TRS-398.

Experimental determination of the effective point of measurement of the PTW-31010 ionization chamber in proton and carbon ion beams

PURPOSE

The accurate knowledge of the effective point of measurement (P_eff ) is particularly important for measurements in proximity to high dose gradients such as in the distal fall-off of particle beams. For plane-parallel ionization chambers (ICs), P_eff is well known and located at the center of the inner surface of the entrance window. For cylindrical ICs, P_eff is shifted from the chamber's center toward the beam source. According to IAEA TRS-398, this shift can be calculated as 0.75·r_cyl for light ions with r_cyl being the radius of the cavity. For proton beams and in absence of a dose gradient, no shift is recommended. We have experimentally determined P_eff for the 0.125 cc Semiflex IC in both proton and carbon ion beams.

METHODS

The first method consisted of simultaneous irradiation of a plane-parallel IC and the Semiflex in a 4-cm wide spread-out Bragg peak. In the second method, a single-energy beam was used, and both ICs were positioned successively at the same measurement depths. For both approaches, the shift of the distal edge of the depth ionization distributions recorded by the two chambers at different reference points was used to calculate P_eff of the Semiflex. Both methods were applied in carbon ion beams, and only the latter was applied in proton beams.

RESULTS

Both methods yielded a similar P_eff for carbon ions, 0.88·r_cyl , and 0.84·r_cyl , which results in a difference of only 0.1 mm. The difference to the recommended value of 0.75·r_cyl is 0.4 and 0.3 mm, respectively, which is larger than the positioning uncertainty. In the proton beam, a P_eff of 0.92·r_cyl was obtained.

CONCLUSIONS

The P_eff for the 0.125 cc Semiflex IC is shifted further from the cavity center as recommended by IAEA TRS-398 for light ions, with the shift for proton beams being even larger than for carbon ion beams.

Monte Carlo calculation of perturbation correction factors for air-filled ionization chambers in clinical proton beams using TOPAS/GEANT

INTRODUCTION

Current dosimetry protocols for clinical protons using air-filled ionization chambers assume that the perturbation correction factor is equal to unity for all ionization chambers and proton energies. Since previous Monte Carlo based studies suggest that perturbation correction factors might be significantly different from unity this study aims to determine perturbation correction factors for six plane-parallel and four cylindrical ionization chambers in proton beams at clinical energies.

MATERIALS AND METHODS

The dose deposited in the air cavity of the ionization chambers was calculated with the help of the Monte Carlo code TOPAS/Geant4 while specific constructive details of the chambers were removed step by step. By comparing these dose values the individual perturbation correction factors p_cel, p_stem, p_sleeve, p_wall, p_cav⋅p_dis as well as the total perturbation correction factor p_Q were derived for typical clinical proton energies between 80 and 250MeV.

RESULTS

The total perturbation correction factor p_Q was smaller than unity for almost every ionization chamber and proton energy and in some cases significantly different from unity (deviation larger than 1%). The maximum deviation from unity was 2.0% for cylindrical and 1.5% for plane-parallel ionization chambers. Especially the factor p_wall was found to differ significantly from unity. It was shown that this is due to the fact that secondary particles, especially alpha particles and fragments, are scattered from the chamber wall into the air cavity resulting in an overresponse of the chamber.

CONCLUSION

Perturbation correction factors for ionization chambers in proton beams were calculated using Monte Carlo simulations. In contrast to the assumption of current dosimetry protocols the total perturbation correction factor p_Q can be significantly different from unity. Hence, beam quality correction factors [Formula: see text] that are calculated with the help of perturbation correction factors that are assumed to be unity come with a corresponding additional uncertainty.

Gradient corrections for reference dosimetry using Farmer-type ionization chambers in single-layer scanned proton fields

PURPOSE

The local depth dose gradient and the displacement correction factor for Farmer-type ionization chambers are quantified for reference dosimetry at shallow depth in single-layer scanned proton fields.

METHOD

Integrated radial profiles as a function of depth (IRPDs) measured at three proton therapy centers were smoothed by polynomial fits. The local relative depth dose gradient at measurement depths from 1 to 5 cm were derived from the derivatives of those fits. To calculate displacement correction factors, the best estimate of the effective point of measurement was derived from reviewing experimental and theoretical determinations reported in the literature. Displacement correction factors for the use of Farmer-type ionization chambers with their reference point (at the center of the cavity volume) positioned at the measurement depth were derived as a ratio of IRPD values at the measurement depth and at the effective point of measurement.

RESULTS

Depth dose gradients are as low as 0.1-0.4% per mm at measurement depths from 1 to 5 cm in the highest clinical proton energies (with residual ranges higher than 15 cm) and increase to 1% per mm at a residual range of 4 cm and become larger than 3% per mm for residual ranges lower than 2 cm. The literature review shows that the effective point of measurement of Farmer-type ionization chambers is, similarly as for carbon ion beams, located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. If a maximum displacement correction of 2% is deemed acceptable to be included in calculated beam quality correction factors, Farmer-type ICs can be used at measurements depths from 1 to 5 cm for which the residual range is 4 cm or larger. If one wants to use the same beam quality correction factors as applicable to the conventional measurement point for scattered beams, located at the center of the SOBP, the relative standard uncertainty on the assumption that the displacement correction factor is unity can be kept below 0.5% for measurement depths of at least 2 cm and for residual ranges of 15 cm or higher.

CONCLUSION

The literature review confirmed that for proton beams the effective point of measurement of Farmer-type ionization chambers is located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. Based on the findings in this work, three options can be recommended for reference dosimetry of scanned proton beams using Farmer-type ionization chambers: (a) positioning the effective point of measurement at the measurement depth, (b) positioning the reference point at the measurement depth and applying a displacement correction factor, and (c) positioning the reference point at the measurement depth without applying a displacement correction factor. Based on limiting the acceptable uncertainty on the gradient correction factor to 0.5% and the maximum deviation of the displacement perturbation correction factor from unity to 2%, the first two options can be allowed for residual ranges of at least 4 cm while the third option only for residual ranges of at least 15 cm.

Beam monitor calibration of a synchrotron-based scanned light-ion beam delivery system

PURPOSE

This paper presents the implementation and comparison of two independent methods of beam monitor calibration in terms of number of particles for scanned proton and carbon ion beams.

METHODS

In the first method, called the single-layer method, dose-area-product to water (DAP_w) is derived from the absorbed dose to water determined using a Roos-type plane-parallel ionization chamber in single-energy scanned beams. This is considered the reference method for the beam monitor calibration in the clinically relevant proton and carbon energy ranges. In the second method, called the single-spot method, DAP_w of a single central spot is determined using a Bragg-peak (BP) type large-area plane-parallel ionization chamber. Emphasis is given to the detailed characterization of the ionization chambers used for the beam monitor calibration. For both methods a detailed uncertainty budget on the DAP_w determination is provided as well as on the derivation of the number of particles.

RESULTS

Both calibration methods agreed on average within 1.1% for protons and within 2.6% for carbon ions. The uncertainty on DAP_w using single-layer beams is 2.1% for protons and 3.1% for carbon ions with major contributions from the available values of k_Q and the average spot spacing in both lateral directions. The uncertainty using the single-spot method is 2.2% for protons and 3.2% for carbon ions with major contributions from the available values of k_Q and the non-uniformity of the BP chamber response, which can lead to a correction of up-to 3.2%. For the number of particles, an additional dominant uncertainty component for the mean stopping power per incident proton (or the CEMA) needs to be added.

CONCLUSION

The agreement between both methods enhances confidence in the beam monitor calibration and the estimated uncertainty. The single-layer method can be used as a reference and the single-spot method is an alternative that, when more accumulated knowledge and data on the method becomes available, can be used as a redundant dose monitor calibration method. This work, together with the overview of information from the literature provided here, is a first step towards comprehensive information on the single-spot method.

Time-resolved dosimetry for validation of 4D dose calculation in PBS proton therapy

Four-dimensional dose calculation (4D-DC) is crucial for predicting the dosimetric outcome in the presence of intra-fractional organ motion. Time-resolved dosimetry can provide significant insights into 4D pencil beam scanning dose accumulation and is therefore irreplaceable for benchmarking 4D-DC. In this study a novel approach of time-resolved dosimetry using five PinPoint ionization chambers (ICs) embedded in an anthropomorphic dynamic phantom was employed and validated against beam delivery details. Beam intensity variations as well as the beam delivery time structure were well reflected with an accuracy comparable to the temporal resolution of the IC measurements. The 4D dosimetry approach was further applied for benchmarking the 4D-DC implemented in the RayStation 6.99 treatment planning system. Agreement between computed values and measurements was investigated for (i) partial doses based on individual breathing phases, and (ii) temporally distributed cumulative doses. For varied beam delivery and patient-related parameters the average unsigned dose difference for (i) was 0.04 ± 0.03 Gy over all considered IC measurement values, while the prescribed physical dose was 2 Gy. By implementing (ii), a strong effect of the dose gradient on measurement accuracy was observed. The gradient originated from scanned beam energy modulation and target motion transversal to the beam. Excluding measurements in the high gradient the relative dose difference between measurements and 4D-DCs for a given treatment plan at the end of delivery was 3.5% on average and 6.6% at maximum over measurement points inside the target. Overall, the agreement between 4D dose measurements in the moving phantom and retrospective 4D-DC was found to be comparable to the static dose differences for all delivery scenarios. The presented 4D-DC has been proven to be suitable for simulating treatment deliveries with various beam- as well as patient-specific parameters and can therefore be employed for dosimetric validation of different motion mitigation techniques.

Phantom design and dosimetric characterization for multiple simultaneous cell irradiations with active pencil beam scanning

A new phantom was designed for in vitro studies on cell lines in horizontal particle beams. The phantom enables simultaneous irradiation at multiple positions along the beam path. The main purpose of this study was the detailed dosimetric characterization of the phantom which consists of various heterogeneous structures. The dosimetric measurements described here were performed under non-reference conditions. The experiment involved a CT scan of the phantom, dose calculations performed with the treatment planning system (TPS) RayStation employing both the Pencil Beam (PB) and Monte Carlo (MC) algorithms, and proton beam delivery. Two treatment plans reflecting the typical target location for head and neck cancer and prostate cancer treatment were created. Absorbed dose to water and dose homogeneity were experimentally assessed within the phantom along the Bragg curve with ionization chambers (ICs) and EBT3 films. LET_d distributions were obtained from the TPS. Measured depth dose distributions were in good agreement with the Monte Carlo-based TPS data. Absorbed dose calculated with the PB algorithm was 4% higher than the absorbed dose measured with ICs at the deepest measurement point along the spread-out Bragg peak. Results of experiments using melanoma (SKMel) cell line are also presented. The study suggested a pronounced correlation between the relative biological effectiveness (RBE) and LET_d, where higher LET_d leads to elevated cell death and cell inactivation. Obtained RBE values ranged from 1.4 to 1.8 at the survival level of 10% (RBE₁₀). It is concluded that dosimetric characterization of a phantom before its use for RBE experiments is essential, since a high dosimetric accuracy contributes to reliable RBE data and allows for a clearer differentiation between physical and biological uncertainties.

Evaluation of electromagnetic and nuclear scattering models in GATE/Geant4 for proton therapy

Purpose

The dose core of a proton pencil beam (PB) is enveloped by a low dose area reaching several centimeters off the central axis and containing a considerable amount of the dose. Adequate modeling of the different components of the PB profile is, therefore, required for accurate dose calculation. In this study, we experimentally validated one electromagnetic and two nuclear scattering models in GATE/Geant4 for dose calculation of proton beams in the therapeutic energy window (62–252 MeV) with and without range shifter (RaShi).

Methods

The multiple Coulomb scattering (MCS) model was validated by lateral dose core profiles measured for five energies at up to four depths from beam plateau to Bragg peak region. Nuclear halo profiles of single PBs were evaluated for three (62.4, 148.2, and 252.7 MeV) and two (97.4 and 124.7 MeV) energies, without and with RaShi, respectively. The influence of the dose core and nuclear halo on field sizes varying from 2–20 cm was evaluated by means of output factors (OFs), namely frame factors (FFs) and field size factors (FSFs), to quantify the relative increase of dose when increasing the field size.

Results

The relative increase in the dose core width in the simulations deviated negligibly from measurements for depths until 80% of the beam range, but was overestimated by up to 0.2 mm in σ toward the end of range for all energies. The dose halo region of the lateral dose profile agreed well with measurements in the open beam configuration, but was notably overestimated in the deepest measurement plane of the highest energy or when the beam passed through the RaShi. The root‐mean‐square deviations (RMSDs) between the simulated and the measured FSFs were less than 1% at all depths, but were higher in the second half of the beam range as compared to the first half or when traversing the RaShi. The deviations in one of the two tested hadron physics lists originated mostly in elastic scattering. The RMSDs could be reduced by approximately a factor of two by exchanging the default elastic scattering cross sections for protons.

Conclusions

GATE/Geant4 agreed satisfyingly with most measured quantities. MCS was systematically overestimated toward the end of the beam range. Contributions from nuclear scattering were overestimated when the beam traversed the RaShi or at the depths close to the end of the beam range without RaShi. Both, field size effects and calculation uncertainties, increased when the beam traversed the RaShi. Measured field size effects were almost negligible for beams up to medium energy and were highest for the highest energy beam without RaShi, but vice versa when traversing the RaShi.

Proton beam monitor chamber calibration

The first goal of this paper is to clarify the reference conditions for the reference dosimetry of clinical proton beams. A clear distinction is made between proton beam delivery systems which should be calibrated with a spread-out Bragg peak field and those that should be calibrated with a (pseudo-)monoenergetic proton beam. For the latter, this paper also compares two independent dosimetry techniques to calibrate the beam monitor chambers: absolute dosimetry (of the number of protons exiting the nozzle) with a Faraday cup and reference dosimetry (i.e. determination of the absorbed dose to water under IAEA TRS-398 reference conditions) with an ionization chamber. To compare the two techniques, Monte Carlo simulations were performed to convert dose-to-water to proton fluence. A good agreement was found between the Faraday cup technique and the reference dosimetry with a plane-parallel ionization chamber. The differences-of the order of 3%-were found to be within the uncertainty of the comparison. For cylindrical ionization chambers, however, the agreement was only possible when positioning the effective point of measurement of the chamber at the reference measurement depth-i.e. not complying with IAEA TRS-398 recommendations. In conclusion, for cylindrical ionization chambers, IAEA TRS-398 reference conditions for monoenergetic proton beams led to a systematic error in the determination of the absorbed dose to water, especially relevant for low-energy proton beams. To overcome this problem, the effective point of measurement of cylindrical ionization chambers should be taken into account when positioning the reference point of the chamber. Within the current IAEA TRS-398 recommendations, it seems advisable to use plane-parallel ionization chambers-rather than cylindrical chambers-for the reference dosimetry of pseudo-monoenergetic proton beams.

The effective depth of cylindrical ionization chambers in water for clinical proton beams

In this study, we have developed an explicit analytical model to compute the effective depth of cylindrical ionization chambers in water for clinical proton beams.We have compared our explicit analytical model with an existing series expansion model. We have calculated the shift of water equivalent depth for different cylindrical ionization chambers and have compared our results with the IAEA recommendations and series expansion model. We have developed a method to compute the elliptic integral in an explicit analytical form. Using this integral form, the shift of the water equivalent depth has been computed by accounting for individual contributions of the ionization chamber cavity, wall, central electrode and sleeve for proton energies ranging from 1.0 keV to 1.0 GeV for 34 commercially available ionization chambers. The comparison of an explicit analytical expression with a series expansion reveals that integrations calculated by the series expansion fail to converge to a precise value when the ratio of radii of cylindrical ionization chambers is greater than 0.5. For all the ion chambers selected in this study, our results vary at a maximum of 0.5 mm from the IAEA recommendations, whereas the maximum variation for the series expansion model is 1.5 mm. The findings of this study suggest that the developed analytical model is reliable for the calculation of the effective depth in water. Furthermore, the verification of these results with Monte Carlo calculation may suggest the need for a review of the standards for all commercial ionization chambers.

Dosimetry for ion beam radiotherapy

Recently, ion beam radiotherapy (including protons as well as heavier ions) gained considerable interest. Although ion beam radiotherapy requires dose prescription in terms of iso-effective dose (referring to an iso-effective photon dose), absorbed dose is still required as an operative quantity to control beam delivery, to characterize the beam dosimetrically and to verify dose delivery. This paper reviews current methods and standards to determine absorbed dose to water in ion beam radiotherapy, including (i) the detectors used to measure absorbed dose, (ii) dosimetry under reference conditions and (iii) dosimetry under non-reference conditions. Due to the LET dependence of the response of films and solid-state detectors, dosimetric measurements are mostly based on ion chambers. While a primary standard for ion beam radiotherapy still remains to be established, ion chamber dosimetry under reference conditions is based on similar protocols as for photons and electrons although the involved uncertainty is larger than for photon beams. For non-reference conditions, dose measurements in tissue-equivalent materials may also be necessary. Regarding the atomic numbers of the composites of tissue-equivalent phantoms, special requirements have to be fulfilled for ion beams. Methods for calibrating the beam monitor depend on whether passive or active beam delivery techniques are used. QA measurements are comparable to conventional radiotherapy; however, dose verification is usually single field rather than treatment plan based. Dose verification for active beam delivery techniques requires the use of multi-channel dosimetry systems to check the compliance of measured and calculated dose for a representative sample of measurement points. Although methods for ion beam dosimetry have been established, there is still room for developments. This includes improvement of the dosimetric accuracy as well as development of more efficient measurement techniques.