Monte Carlo calculation of beam quality correction factors in proton beams using PENH

ESTRO-EPTN radiation dosimetry guidelines for the acquisition of proton pencil beam modelling data

Proton therapy (PT) is an advancing radiotherapy modality increasingly integrated into clinical settings, transitioning from research facilities to hospital environments. A critical aspect of the commissioning of a proton pencil beam scanning delivery system is the acquisition of experimental beam data for accurate beam modelling within the treatment planning system (TPS). These guidelines describe in detail the acquisition of proton pencil beam modelling data. First, it outlines the intrinsic characteristics of a proton pencil beam-energy distribution, angular-spatial distribution and particle number. Then, it lists the input data typically requested by TPSs. Finally, it describes in detail the set of experimental measurements recommended for the acquisition of proton pencil beam modelling data-integrated depth-dose curves, spot maps in air, and reference dosimetry. The rigorous characterization of these beam parameters is essential for ensuring the safe and precise delivery of proton therapy treatments.

Experimental comparison of cylindrical and plane parallel ionization chambers for reference dosimetry in continuous and pulsed scanned proton beams

Objective. In this experimental work we compared the determination of absorbed dose to water using four ionization chambers (ICs), a PTW-34045 Advanced Markus, a PTW-34001 Roos, an IBA-PPC05 and a PTW-30012 Farmer, irradiated under the same conditions in one continuous- and in two pulsed-scanned proton beams.Approach. The ICs were positioned at 2 cm depth in a water phantom in four square-field single-energy scanned-proton beams with nominal energies between 80 and 220 MeV and in the middle of 10 × 10 × 10 cm3dose cubes centered at 10 cm or 12.5 cm depth in water. The water-equivalent thickness (WET) of the entrance window and the effective point of measurement was considered when positioning the plane parallel (PP) ICs and the cylindrical ICs, respectively. To reduce uncertainties, all ICs were calibrated at the same primary standards laboratory. We used the beam quality (kQ) correction factors for the ICs under investigation from IAEA TRS-398, the newly calculated Monte Carlo (MC) values and the anticipated IAEA TRS-398 updated recommendations.Main results. Dose differences among the four ICs ranged between 1.5% and 3.7% using both the TRS-398 and the newly recommendedkQvalues. The spread among the chambers is reduced with the newlykQvalues. The largest differences were observed between the rest of the ICs and the IBA-PPC05 IC, obtaining lower dose with the IBA-PPC05.Significance. We provide experimental data comparing different types of chambers in different proton beam qualities. The observed dose differences between the ICs appear to be related to inconsistencies in the determination of thekQvalues. For PP ICs, MC studies account for the physical thickness of the entrance window rather than the WET. The additional energy loss that the wall material invokes is not negligible for the IBA-PPC05 and might partially explain the lowkQvalues determined for this IC. To resolve this inconsistency and to benchmark MC values,kQvalues measured using calorimetry are needed.

Fano cavity test and investigation of the response of the Roos chamber irradiated by proton beams in perpendicular magnetic fields up to 1 T

Objective. The aim of this work is to investigate the response of the Roos chamber (type 34001) irradiated by clinical proton beams in magnetic fields.Approach. At first, a Fano test was implemented in Monte Carlo software package GATE version 9.2 (based on Geant4 version 11.0.2) using a cylindrical slab geometry in a magnetic field up to 1 T. In accordance to an experimental setup (Fuchset al2021), the magnetic field correction factorskQB⃗of the Roos chamber were determined at different energies up to 252 MeV and magnetic field strengths up to 1 T, by separately simulating the ratios of chamber signalsMQ/MQB⃗,without and with magnetic field, and the dose-conversion factorsDw,QB⃗/Dw,Qin a small cylinder of water, with and without magnetic field. Additionally, detailed simulations were carried out to understand the observed magnetic field dependence.Main results. The Fano test was passed with deviations smaller than 0.25% between 0 and 1 T. The ratios of the chamber signals show both energy and magnetic field dependence. The maximum deviation of the dose-conversion factors from unity of 0.22% was observed at the lowest investigated proton energy of 97.4 MeV andB⃗= 1 T. The resultingkQB⃗factors increase initially with the applied magnetic field and decrease again after reaching a maximum at around 0.5 T; except for the lowest 97.4 MeV beam that show no observable magnetic field dependence. The deviation from unity of the factors is also larger for higher proton energies, where the maximum lies at 1.0035(5), 1.0054(7) and 1.0069(7) for initial energies ofE0= 152, 223.4 and 252 MeV, respectively.Significance. Detailed Monte Carlo studies showed that the observed effect can be mainly attributed to the differences in the transport of electrons produced both outside and inside of the air cavity in the presence of a magnetic field.

Investigation of ionization chamber perturbation factors using proton beam and Fano cavity test for the Monte Carlo simulation code PHITS

The reference dose for clinical proton beam therapy is based on ionization chamber dosimetry. However, data on uncertainties in proton dosimetry are lacking, and multifaceted studies are required. Monte Carlo simulations are useful tools for calculating ionization chamber dosimetry in radiation fields and are sensitive to the transport algorithm parameters when particles are transported in a heterogeneous region. We aimed to evaluate the proton transport algorithm of the Particle and Heavy Ion Transport Code System (PHITS) using the Fano test. The response of the ionization chamber f Q and beam quality correction factors k Q were calculated using the same parameters as those in the Fano test and compared with those of other Monte Carlo codes for verification. The geometry of the Fano test consisted of a cylindrical gas-filled cavity sandwiched between two cylindrical walls. f Q was calculated as the ratio of the absorbed dose in water to the dose in the cavity in the chamber. We compared the f Q calculated using PHITS with that of a previous study, which was calculated using other Monte Carlo codes (Geant4, FULKA, and PENH) under similar conditions. The flight mesh, a parameter for charged particle transport, passed the Fano test within 0.15%. This was shown to be sufficiently accurate compared with that observed in previous studies. The f Q calculated using PHITS were 1.116 ± 0.002 and 1.124 ± 0.003 for NACP-02 and PTW-30013, respectively, and the k Q were 0.981 ± 0.008 and 1.027 ± 0.008, respectively, at 150 MeV. Our results indicate that PHITS can calculate the f Q and k Q with high precision.

The influence of different versions of FLUKA and GEANT4 on the calculation of response functions of ionization chambers in clinical proton beams

Objective.To investigate the influence of different versions of the Monte Carlo codesgeant4 andflukaon the calculation of overall response functionsfQof air-filled ionization chambers in clinical proton beams.Approach. fQfactors were calculated for six plane-parallel and four cylindrical ionization chambers withgeant4 andfluka. These factors were compared to already published values that were derived using older versions of these codes.Main results.Differences infQfactors calculated with different versions of the same Monte Carlo code can be up to ∼1%. Especially forgeant4, the updated version leads to a more pronounced dependence offQon proton energy and to smallerfQfactors for high energies.Significance.Different versions of the same Monte Carlo code can lead to differences in the calculation offQfactors of up to ∼1% without changing the simulation setup, transport parameters, ionization chamber geometry modeling, or employed physics lists. These findings support the statement that the dominant contributor to the overall uncertainty of Monte Carlo calculatedfQfactors are type-B uncertainties.

Monte Carlo-calculated beam quality and perturbation correction factors validated against experiments for Farmer and Markus type ionization chambers in therapeutic carbon-ion beams

Objective. In current dosimetry protocols, the estimated uncertainty of the measured absorbed dose to waterDwin carbon-ion beams is approximately 3%. This large uncertainty is mainly contributed by the standard uncertainty of the beam quality correction factorkQ. In this study, thekQvalues in four cylindrical chambers and two plane-parallel chambers were calculated using Monte Carlo (MC) simulations in the plateau region. The chamber-specific perturbation correction factorPof each chamber was also determined through MC simulations.Approach.kQfor each chamber was calculated using MC code Geant4. The simulatedkQratios in subjected chambers and reference chambers were validated through comparisons against our measured values. In the measurements in Heavy-Ion Medical Accelerator in Chiba,kQratios were obtained fromDwvalues of60Co, 290- and 400 MeV u-1carbon-ion beams that were measured with the subjected ionization chamber and the reference chamber. In the simulations,fQ(the product of the water-to-air stopping power ratio andP) was acquired fromDwand the absorbed dose to air calculated in the sensitive volume of each chamber.kQvalues were then calculated from the simulatedfQand the literature-extractedWairand compared with previous publications.Main results. The calculatedkQratios in the subjected chambers to the reference chamber agreed well with the measuredkQratios. ThekQuncertainty was reduced from the current recommendation of approximately 3% to 1.7%. ThePvalues were close to unity in the cylindrical chambers and nearly 1% above unity in the plane-parallel chambers.Significance. ThekQvalues of carbon-ion beams were accurately calculated in MC simulations and thekQratios were validated through ionization chamber measurements. The results indicate a need for updating the current recommendations, which assume a constantPof unity in carbon-ion beams, to recommendations that consider chamber-induced differences.

Monte Carlo calculated ionization chamber correction factors in clinical proton beams - deriving uncertainties from published data

For the update of the IAEA TRS-398 Code of Practice (CoP), global ionization chamber factors (fQ) and beam quality correction factors (kQ) for air-filled ionization chambers in clinical proton beams have been calculated with different Monte Carlo codes. In this study, average Monte Carlo calculated fQ and kQ factors are provided and the uncertainty of these factors is estimated. Average fQ factors in monoenergetic proton beams with energies between 60 MeV and 250 MeV were derived from Monte Carlo calculated fQ factors published in the literature. Altogether, 195 fQ factors for six plane-parallel and three cylindrical ionization chambers calculated with penh, fluka and geant4 were incorporated. Additionally, a weighted standard deviation of fQ factors was calculated, where the same weight was assigned to each Monte Carlo code. From average fQ factors, kQ factors were derived and compared to the values from the IAEA TRS-398 CoP published in 2000 as well as to the values of the upcoming version. Average Monte Carlo calculated fQ factors are constant within 0.6% over the energy range investigated. In general, the different Monte Carlo codes agree within 1% for low energies and show larger differences up to 2% for high energies. As a result, the standard deviation of fQ factors increases with energy and is ∼0.3% for low energies and ∼0.8% for high energies. kQ factors derived from average Monte Carlo calculated fQ factors differ from the values presented in the IAEA TRS-398 CoP by up to 2.4%. The overall estimated uncertainty of Monte Carlo calculated kQ factors is ∼0.5%-1% smaller than the uncertainties estimated in IAEA TRS-398 CoP since the individual ionization chamber characteristics (e.g. fluence perturbations) are considered in detail in Monte Carlo calculations. The agreement between Monte Carlo calculated kQ factors and the values of the upcoming version of IAEA TRS-398 CoP is better with deviations smaller than 1%.

Ion recombination correction factors and detector comparison in a very-high dose rate proton scanning beam

PURPOSE

Accurate dosimetry is paramount to study the FLASH biological effect since dose and dose rate are critical dosimetric parameters governing its underlying mechanisms. With the goal of assessing the suitability of standard clinical dosimeters in a very-high dose rate (VHDR) experimental setup, we evaluated the ion collection efficiency of several commercially available air-vented ionization chambers (IC) in conventional and VHDR proton irradiation conditions.

METHODS

A cyclotron at the Orsay Proton Therapy Center was used to deliver VHDR pencil beam scanning irradiation. Ion recombination correction factors (k_s) were determined for several detectors (Advanced Markus, PPC05, Nano Razor, CC01) at the entrance of the plateau and at the Bragg peak, using the Niatel model, the Two-voltage method and Boag's analytical formula for continuous beams.

RESULTS

Mean dose rates ranged from 4 Gy/s to 385 Gy/s, and instantaneous dose rates up to 1000 Gy/s were obtained with the experimental set-up. Recombination correction factors below 2 % were obtained for all chambers, except for the Nano Razor, at VHDRs with variations among detectors, while k_s values were significantly smaller (0.8 %) for conventional dose rates.

CONCLUSIONS

While the collection efficiency of the probed ICs in scanned VHDR proton therapy is comparable to those in the conventional regime with recombination coefficiens smaller than 1 % for mean dose rates up to 177 Gy/s, the reduction in collection efficiency for higher dose rates cannot be ignored when measuring the absorbed dose in pre-clinical proton scanned FLASH experiments and clinical trials.

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 ofkQfactors for two types of ionization chambers in scanned proton beams

Objective.Experimental determination of beam qualityk_Qfactors for two types of Farmer ionization chambers, NE2571 and IBA FC65-G, in a scanned proton beam for three nominal energies (140 MeV, 180 MeV and 220 MeV) based on water calorimetry.Approach.Beam quality correction factors were determined comparing the results obtained with water calorimetry and ionometry. Water calorimetry was performed to determine the absorbed dose at a depth of measurement in water of 5 g cm^-2, limited by the extension of the calorimeter glass vessel used. For the ionometry, two chambers of each type were included in the study. The ionization chambers were calibrated in terms of absorbed dose to water in⁶⁰Co at the Swedish Secondary Standard Dosimetry Laboratory, directly traceable to the BIPM, and were used according to the IAEA TRS-398 Code of Practice.Main results. Thek_Qvalues determined in the present work have been compared with the values tabulated in TRS-398 and its forthcoming update and also with those obtained in previous water calorimetric measurements and Monte Carlo calculations. All results were found to agree within the combined uncertainties of the different data.Significance. It is expected that the present work will serve as an experimental contribution tok_Q-factors for the two chamber types and three scanned proton beam qualities used.

Monte Carlo calculation of beam quality correction factors in proton beams using FLUKA

Purpose.To provide Monte Carlo calculated beam quality correction factors (k_Q) for monoenergetic proton beams using the Monte Carlo codefluka.Materials and methods.The Monte Carlo codeflukawas used to calculate the dose absorbed in a water-filled reference volume and the air-filled cavities of six plane-parallel and four cylindrical ionization chambers. The chambers were positioned at the entrance region of monoenergetic proton beams with energies between 60 and 250 MeV. Based on these dose values,f_Qas well ask_Qfactors were calculated whilefQ0factors were taken from Andreoet al(2020Phys. Med. Biol.65095011).Results. k_Qfactors calculated in this work were found to agree with experimentally determinedk_Qfactors on the 1%-level, with only two exceptions with deviations of 1.4% and 1.9%. The comparison off_Qfactors calculated usingflukawithf_Qfactors calculated using the Monte Carlo codesgeant4 andpenhshowed a general good agreement for low energies, while differences for higher energies were pronounced. For high energies, in most cases the Monte Carlo codesflukaandgeant4 lead to comparable results while thef_Qfactors calculated withpenhare larger.Conclusion.flukacan be used to calculatek_Qfactors in clinical proton beams. The divergence of Monte Carlo calculatedk_Qfactors for high energies suggests that the role of nuclear interaction models implemented in the different Monte Carlo codes needs to be investigated in more detail.

Comment on 'Lateral response heterogeneity of Bragg peak ionization chambers for narrow-beam photon and proton dosimetry'

Kuesset al(2017Phys. Med. Biol.62206-27) irradiated several PTW 34070 ionization chambers with a narrow x-ray beam impinging at different positions of the detector entrance window and they observed that the reading of the ionization chambers decreased as the impact point of the beam approached the edge of the sensitive volume. They concluded that the radial response of the detector decreased with increasing radius and they proposed a correction factor to correct for that effect. This work shows, by means of a simple Monte Carlo simulation, that the conclusions of Kuess and co-workers do not seem to be supported by their experimental findings-quite the opposite, their experimental results seem to be compatible with a rather homogeneous radial response of the PTW 34070. It is shown that the radial decrease in the ionization chamber reading (as the impact point of the beam approaches the edge of the sensitive volume) is not due to a radial decrease of the response, but to the fact that part of the energy transferred to the secondary electrons is carried away and deposited outside the sensitive volume of the ionization chamber. As a consequence, it is believed that the method and correction factors proposed by Kuess and colleagues are not suitable to assess the response uniformity of large-area ionization chambers. Furthermore, the results of the publications that have used them thus far should be thoroughly revised.

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.

Results of an independent dosimetry audit for scanned proton beam therapy facilities

PURPOSE

An independent dosimetry audit based on end-to-end testing of the entire chain of radiation therapy delivery is highly recommended to ensure consistent treatments among proton therapy centers. This study presents an auditing methodology developed by the MedAustron Ion Beam Therapy Center (Austria) in collaboration with the National Physical Laboratory (UK) and audit results for five scanned proton beam therapy facilities in Europe.

METHODS

The audit procedure used a homogeneous and an anthropomorphic head phantom. The phantoms were loaded either with an ionization chamber or with alanine pellets and radiochromic films. Homogeneously planned doses of 10Gy were delivered to a box-like target volume in the homogeneous phantom and to two clinical scenarios with increasing complexity in the head phantom.

RESULTS

For all tests the mean of the local differences of the absolute dose to water determined with the alanine pellets compared to the predicted dose from the treatment planning system installed at the audited institution was determined. The mean value taken over all tests performed was -0.1±1.0%. The measurements carried out with the ionization chamber were consistent with the dose determined by the alanine pellets with a mean deviation of -0.5±0.6%.

CONCLUSION

The developed dosimetry audit method was successfully applied at five proton centers including various "turn-key" Cyclotron solutions by IBA, Varian and Mevion. This independent audit with extension to other tumour sites and use of the correspondent anthropomorphic phantoms may be proposed as part of a credentialing procedure for future clinical trials in proton beam therapy.

Monte Carlo calculation of quality correction factors based on air kerma and absorbed dose to water in medium energy x-ray beams

Clinical dosimetry is typically performed using ion chambers calibrated in terms of absorbed dose to water. As primary measurement standards for this quantity for low and medium energy x-rays are available only since a few years, most dosimetry protocols for this photon energy range are still based on air kerma calibration. For that reason, data for beam quality correction factors [Formula: see text], necessary for the application of dose to water based protocols, are scarce in literature. Currently the international IAEA TRS-398 Code of Practice is under revision and new [Formula: see text] factors for a large number of ion chambers will be introduced in the update of this protocol. Several international groups provided the IAEA with experimental and Monte Carlo based data for this revision. Within the European Community the EURAMET 16NRM03 RTNORM project was initiated for that purpose. In the present study, Monte Carlo based results for the beam quality correction factors in medium energy x-ray beams for six ion chambers applying different Monte Carlo codes are presented. Additionally, the perturbation factor p _Q , necessary for the calculation of dose to water from an air kerma calibration coefficient, was determined. The beam quality correction factor [Formula: see text] for the chambers varied in the investigated energy range by about 4%-5%, and for five out of six chambers the data could be fitted by a simple logarithmic function, if the half-value-layer was used as the beam quality specifier. Corresponding data using different Monte Carlo codes for the same ion chamber agreed within 0.5%. For the perturbation factor p _Q , the data did not obey a comparable simple relationship with the beam quality specifier. The variation of p _Q for all ion chambers was in the range of 3%-4%. Compared to recently published data, our p _Q data is around 1% larger, although the same Monte Carlo code has been used. Compared to the latest experimental data, there are even deviations in the range of 2%.

Single pencil beam benchmark of a module for Monte Carlo simulation of proton transport in the PENELOPE code

BACKGROUND AND PURPOSE

PENH is a recently coded module for simulation of proton transport in conjunction with the Monte Carlo code PENELOPE. PENELOPE applies class II simulation to all type of interactions, in particular, to elastic collisions. PENH uses calculated differential cross sections for proton elastic collisions that include electron screening effects as well as nuclear structure effects. Proton-induced nuclear reactions are simulated from information in the ENDF-6 database or from alternative nuclear databases in ENDF format. The purpose of this work is to benchmark this module by simulating absorbed dose distributions from a single finite spot size proton pencil beam in water.

MATERIALS AND METHODS

Monte Carlo simulations with PENH are compared with simulation results from TOPAS Monte Carlo (v3.1p2) and RayStation Monte Carlo (v6). Different beam models are examined in terms of mean energy and energy spread to match the measured profiles. The phase-space file is derived from experimental measurements. Simulated absorbed dose distributions are compared to experimental data obtained with the ionization chamber array MatriXX 2D detector (IBA Dosimetry) in a water tank. The experiments were conducted with a clinical IBA pencil beam scanning dedicated nozzle. In all simulations a Fermi-Eyges phase-space representation of a single finite spot size proton pencil beam is used.

RESULTS

In general, there is a good agreement between simulated results and experimental data up to a distance of 3 cm from the central axis. In the core region (region where the dose is more than 10% of the maximum dose) PENH shows, overall, the smallest deviations from experimental data, with the largest radial rms (root mean square) smaller than 0.2. The results achieved by TOPAS and RayStation in that region are very close to those of PENH. For the halo region, that is the area of the dose distribution outside the core region reaching down to 0.01% of the maximum intensity, the largest rms achieved by TOPAS is always smaller than 0.5, yielding better results than the rest of the codes.

CONCLUSION

The physics modeling of the PENELOPE/PENH code yields results consistent with measurements in the dose range relevant for proton therapy. The discrepancies between PENH appearing at distances larger than 3 cm from the central-beam axis are accountable to the lack of neutron simulation in this code. In contradistinction, TOPAS has a better agreement with experimental data at large distances from the central-beam axis because of the simulation of neutrons.

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.