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.

Tumor Control Probability Analysis for Single-Fraction Carbon-Ion Radiation Therapy of Early-Stage Non-small Cell Lung Cancer.

PURPOSE: To investigate the suitability of the linear-quadratic (LQ) and universal survival curve (USC) models in describing the 3-year tumor control probability data of patients with stage I non-small cell lung cancer treated with carbon-ion radiation therapy. Carbon-ion radiation therapy was given at a total dose of 59.4 to 95.4 Gy (relative biological effectiveness [RBE]) in 18 fractions, at 72 Gy[RBE] in 9 fractions, at 52.8 to 60 Gy[RBE] in 4 fractions, and at 28 to 50 Gy[RBE] in a single fraction. METHODS AND MATERIALS: A meta-analysis of published clinical data from 394 patients presenting with early-stage non-small cell lung cancer was conducted. Tumor control probability modeling based on the LQ and USC models was performed by simultaneously fitting the clinical data obtained from the different fractionation schedules while considering several spread-out Bragg peak (SOBP) sizes. Radiobiological parameters were derived from the fit. On the basis of the results, a novel SOBP was created for the single-fraction regimen that was optimized with respect to the USC model and aimed at achieving a 95% local control. RESULTS: The USC model gave a better fit to the 3-year local control data than the LQ model did. The fit using various SOBP sizes yielded transition doses between 5.6 and 7.0 Gy. The results also revealed α/ß ratios between 7.4 and 9.1 Gy for the LQ model and between 7.4 and 9.4 Gy for the USC model. CONCLUSIONS: The USC model provided a better estimate of the local control rate for the single-fraction course. For the schemes with a greater number of fractions, the local control rate estimates from the LQ and USC models were comparable. A USC-based SOBP design was then created for the single-fraction schedule. The updated design resulted in a flatter RBE profile compared with the conventional SOBP design. It also gave a better clinical dose prediction to optimize the tumor control rate.

An evaluation method of clinical impact with setup, range, and radiosensitivity uncertainties in fractionated carbon-ion therapy.

In light ion therapy, the dose concentration is highly sensitive to setup and range errors. Here we propose a method for evaluating the effects of these errors by using the correlation between fractions on tumour control probability (TCP) in carbon-ion therapy. This method incorporates the concept of equivalent stochastic dose (Cranmer-Sargison and Zavgorodni 2005 Phys. Med. Biol. 50 4097-109), which was defined as a dose that gives the mean expected survival fraction (SF) for the stochastically variable dose. The mean expected SFs were calculated while considering the correlation between fractions for setup and range errors. By using this SF, equivalent stochastic clinical doses (ESCD), which are weighted by relative biological effectiveness, of lung and prostate cases with varying errors were derived. To account for spatial dose heterogeneity, equivalent uniform stochastic clinical doses (EUSCD) were obtained by using the mean expected SF in the volume of interest. TCP curves were calculated for each assumed error considering inter-patient sensitivity variation with a fractionation effect. ESCD distributions, EUSCD, and TCP curves were affected by the inter-fraction correlation and the contribution of setup and range errors. Irradiated areas that could be affected by these errors can be visualized quantitatively by using the ESCD distribution. TCP curves for the errors of various conditions converged around the TCP curve in nominal conditions by using the EUSCD. EUSCD correlated well with TCP in setup and range errors when the errors were not large and was comparatively stably insensitive to uncertain biological parameters. The proposed evaluation method with EUSCD and TCP calculations will be useful to indicate tumour doses to improve realistic dose distributions in carbon-ion therapy.

A robustness analysis method with fast estimation of dose uncertainty distributions for carbon-ion therapy treatment planning.

A simple and efficient approach is needed for robustness evaluation and optimization of treatment planning in routine clinical particle therapy. Here we propose a robustness analysis method using dose standard deviation (SD) in possible scenarios such as the robustness indicator and a fast dose warping method, i.e. deformation of dose distributions, taking into account the setup and range errors in carbon-ion therapy. The dose warping method is based on the nominal dose distribution and the water-equivalent path length obtained from planning computed tomography data with a clinically commissioned treatment planning system (TPS). We compared, in a limited number of scenarios at the extreme boundaries of the assumed error, the dose SD distributions obtained by the warping method with those obtained using the TPS dose recalculations. The accuracy of the warping method was examined by the standard-deviation-volume histograms (SDVHs) for varying degrees of setup and range errors for three different tumor sites. Furthermore, the influence of dose fractionation on the combined dose uncertainty, taking into consideration the correlation of setup and range errors between fractions, was evaluated with simple equations using the SDVHs and the mean value of SDs in the defined volume of interest. The results of the proposed method agreed well with those obtained with the dose recalculations in these comparisons, and the effectiveness of dose SD evaluations at the extreme boundaries of given errors was confirmed from the responsivity and DVH analysis of relative SD values for each error. The combined dose uncertainties depended heavily on the number of fractions, assumed errors and tumor sites. The typical computation time of the warping method is approximately 60 times less than that of the full dose calculation method using the TPS. The dose SD distributions and SDVHs with the fractionation effect will be useful indicators for robustness analysis in treatment planning, and the results of our comparative study show that the proposed analysis method would be beneficial in routine clinical use.

Semi-analytical model for output factor calculations in proton beam therapy with consideration for the collimator aperture edge.

In the development of an external radiotherapy treatment planning system, the output factor (OPF) is an important value for the monitor unit calculations. We developed a proton OPF calculation model with consideration for the collimator aperture edge to account for the dependence of the OPF on the collimator aperture and distance in proton beam therapy. Five parameters in the model were obtained by fitting with OPFs measured by a pinpoint chamber with the circular radiation fields of various field radii and collimator distances. The OPF model calculation using the fitted model parameters could explain the measurement results to within 1.6% error in typical proton treatment beams with 6- and 12 cm SOBP widths through a range shifter and a circular aperture more than 10.6 mm in radius. The calibration depth dependences of the model parameters were approximated by linear or quadratic functions. The semi-analytical OPF model calculation was tested with various MLC aperture shapes that included circles of various sizes as well as a rectangle, parallelogram, and L-shape for an intermediate proton treatment beam condition. The pre-calculated OPFs agreed well with the measured values, to within 2.7% error up to 620 mm in the collimator distance, though the maximum difference was 5.1% in the case of the largest collimator distance of 740 mm. The OPF calculation model would allow more accurate monitor unit calculations for therapeutic proton beams within the expected range of collimator conditions in clinical use.

A model-based analysis of a simplified beam-specific dose output in proton therapy with a single-ring wobbling system.

In radiation therapy, it is necessary to preset a monitor unit in an irradiation control system to deliver a prescribed absolute dose to a reference point in the planning target volume. The purpose of this study was to develop a model-based monitor unit calculation method for proton-beam therapy with a single-ring wobbling system. The absorbed dose at a calibration point per monitor unit had been measured for each beam-specific measurement condition without a patient-specific collimator or range compensator before proton therapeutic irradiation at Shizuoka Cancer Center. In this paper, we propose a simplified dose output model to obtain the output ratio between a beam-specific dose and a reference field dose, from which a monitor unit for the proton treatment could be derived without beam-specific measurements. The model parameters were determined to fit some typical data measured in a proton treatment room, called a Gantry 1 course. Then, the model calculation was compared with 5456 dose output ratios that had been measured for 150-, 190- and 220 MeV therapeutic proton beams in two treatment rooms over the past decade. The mean value and standard deviation of the difference between the measurement and the model calculation were respectively 0.00% and 0.27% for the Gantry 1 course, and -0.25% and 0.35% for the Gantry 2 course. The model calculation was in good agreement with the measured beam-specific doses, within 1%, except for conditions less frequently used for treatment. The small variation for the various beam conditions shows the high long-term reproducibility of the measurement and high degree of compatibility of the two treatment rooms. Therefore, the model was expected to assure the setting value of the dose monitor for treatment, to save the effort required for beam-specific measurement, and to predict the dose output for new beam conditions in the future.

Microdosimetric approach to NIRS-defined biological dose measurement for carbon-ion treatment beam.

The RBE-weighted absorbed dose, called "biological dose," has been routinely used for carbon-ion treatment planning in Japan to formulate dose prescriptions for treatment protocols. This paper presents a microdosimetric approach to measuring the biological dose, which was redefined to be derived from microdosimetric quantities measured by a tissue-equivalent proportional counter (TEPC). The TEPC was calibrated in (60)Co gamma rays to assure a traceability of the TEPC measurement to Japanese standards and to eliminate the discrepancies among matching counters. The absorbed doses measured by the TEPC were reasonably coincident with those measured by a reference ionization chamber. The RBE value was calculated from the microdosimetric spectrum on the basis of the microdosimetric kinetic model. The biological doses obtained by the TEPC were compared with those prescribed in the carbon-ion treatment planning system. We found that it was reasonable for the measured biological doses to decrease with depth around the rear SOBP region because of beam divergence, scattering effect, and fragmentation reaction. These results demonstrate that the TEPC can be an effective tool to assure the radiation quality in carbon-ion radiotherapy.

Evaluation of w values for carbon beams in air, using a graphite calorimeter.

Despite recent progress in carbon therapy, accurate values for physical data such as the w value in air or stopping power ratios for ionization chamber dosimetry have not been obtained. The absorbed dose to graphite obtained with the graphite calorimeter was compared with that obtained using the ionization chambers following the IAEA protocol in order to evaluate the w values in air for mono-energetic carbon beams of 135, 290, 400 and 430 MeV/n. Two cylindrical chambers (PTW type 30001 and PTW type 30011, Farmer) and two plane-parallel chambers (PTW type 23343, Markus and PTW type 34001, Roos) calibrated by the absorbed dose to graphite and exposure to the (60)Co photon beam were used. The comparisons to our calorimeter measurements revealed that, using the ionization chambers, the absorbed dose to graphite comes out low by 2-6% in this experimental energy range and with these chamber types and calibration methods. In the therapeutic energy range, the w values in air for carbon beams indicated a slight energy dependence; we, however, assumed these values to be constant for practical use because of the large uncertainty and unknown perturbation factors of the ionization chambers. The w values in air of the carbon beams were evaluated to be 35.72 J C(-1) +/- 1.5% in the energy range used in this study. This value is 3.5% larger than that recommended by the IAEA TRS 398 for heavy-ion beams. Using this evaluated result, the absorbed dose to water in the carbon beams would be increased by the same amount.

[Field-size Dependence of the Glass Dosimeter in 6 MV Photon Beams].

The postal dose audit using radio-photoluminescence glass dosimeters was begun in November 2007 in order to improve the quality of radiotherapy in Japan. However, the irradiation conditions are now limited to the reference conditions which are 10×10 cm(2) field and 10 cm depth. The application of the glass dosimeters to non-reference conditions is strongly desired. This study dealt with the field-size dependence of the glass dosimeter outputs in the 6 MV photon beams of a medical linear accelerator (Varian Clinac21EX). We irradiated glass dosimeters with square field sizes of 5, 7, 10, 13, 16, 20, 23 and 25 cm side lengths at the 10 cm depth of the water equivalent phantom (SSD=90 cm). The outputs were compared with ionization chamber outputs. The ratio of the glass dosimeter outputs to the absorbed dose to water obtained with the ionization chamber increased approximately 1.5% between 5×5 cm(2) and 25×25 cm(2). We have to consider this field-size dependence when we apply the glass dosimeters to non-reference conditions.

Development of a portable graphite calorimeter for radiation dosimetry.

We developed and performance-tested a portable graphite calorimeter designed to measure the absolute dosimetry of various beams including heavy-ion beams, based on a flexible and convenient means of measurement. This measurement system is fully remote-controlled by the GPIB system. This system uses a digital PID (Proportional, Integral, Derivative) control method based on the LabVIEW software. It was possible to attain stable conditions in a shorter time by this system. The standard deviation of the measurements using the calorimeter was 0.79% at a dose rate of 0.8 Gy/min in 17 calorimeter runs for a (60)Co photon beam. The overall uncertainties for the absorbed dose to graphite and water of the (60)Co photon beam using the developed calorimeter were 0.89% and 1.35%, respectively. Estimations of the correction factors due to vacuum gaps, impurities in the core, the dose gradient and the radiation profile were included in the uncertainties. The absorbed doses to graphite and water irradiated by the (60)Co photon beam were compared with dosimetry measurements obtained using three ionization chambers. The absorbed doses to graphite and water estimated by the two dosimetry methods agreed within 0.1% and 0.3%, respectively.

Microdosimetric measurements and estimation of human cell survival for heavy-ion beams.

The microdosimetric spectra for high-energy beams of photons and proton, helium, carbon, neon, silicon and iron ions (LET = 0.5-880 keV/microm) were measured with a spherical-walled tissue-equivalent proportional counter at various depths in a plastic phantom. Survival curves for human tumor cells were also obtained under the same conditions. Then the survival curves were compared with those estimated by a microdosimetric model based on the spectra and the biological parameters for each cell line. The estimated alpha terms of the liner-quadratic model with a fixed beta value reproduced the experimental results for cell irradiation for ion beams with LETs of less than 450 keV/microm, except in the region near the distal peak.

Experimental evaluation of conversion factors, N(D,w)/N(X), for Roos-type and Advanced-Markus-type plane-parallel ionization chambers.

A Japanese code of practice for clinical dosimetry, titled "Standard Dosimetry of Absorbed Dose in External Beam Radiotherapy" was published by the Japan Society of Medical Physics (JSMP) in 2002. It mostly followed IAEA Technical Reports Series No. 398, which was based on N(D,w), i.e., the calibration factor in terms of absorbed dose to water for a dosimeter. The Japanese primary standard dosimetry laboratory, however, has not supplied N(D,w) but N(X), as the calibration factor in terms of exposure. The unique feature of the Japanese code was provision of a data table of calculated conversion factors, N(D,w) / N(X) values, for many types of ionization chambers, excluding new plane-parallel ionization chambers. This paper describes the experimental evaluation of the conversion factors for the new plane-parallel ionization chambers, such as the Roos-type and Advanced Markus chambers. The obtained N(D,w) / N(X) values for PTW 34001, Wellhöfer PPC 40 and PTW 34045 were 37.96 +/- 0.19, 37.85 +/- 0.36 and 37.90 +/- 0.26 (Gy/C kg(-1)), respectively. They agreed with estimations based on Monte Carlo calculations.

Responses of a diamond detector to high-LET charged particles.

The responses of a commercial diamond detector (type 60003, PTW-Freiburg) to several heavy ions were examined. The responses to heavy-ion beams reached stable levels with relatively small pre-irradiation doses compared to photon-beam irradiations. The responses also reached stable levels with a smaller pre-irradiation dose when the dose rate of the He beams was increased. A total accumulated dose of about 5 Gy was required for the pre-irradiation dose of heavy-ion beams. No angular dependence of the detector responses was observed within a deviation of 5%. The dose-rate dependence of the detector responses to heavy-ion beams was far smaller than that to gamma rays. The decrease in the response was within 0.9%, with a variation from 0.88 to 18.2 Gy min(-1) in the carbon beam. We examined the LET dependence of the diamond detector responses using various kinds of heavy-ion beams. The responses had particle dependence in addition to LET dependence. The responses decreased more with higher LET particles and decreased less with large-Z particles. We proposed a gradual-saturation model based on the track structure under several simple assumptions to explain the LET and particle dependences of the response.