Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

PURPOSE: The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. METHODS: The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. RESULTS: The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. CONCLUSIONS: The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

A patient-specific aperture system with an energy absorber for spot scanning proton beams: Verification for clinical application.

PURPOSE: In the authors' proton therapy system, the patient-specific aperture can be attached to the nozzle of spot scanning beams to shape an irradiation field and reduce lateral fall-off. The authors herein verified this system for clinical application. METHODS: The authors prepared four types of patient-specific aperture systems equipped with an energy absorber to irradiate shallow regions less than 4 g/cm(2). The aperture was made of 3-cm-thick brass and the maximum water equivalent penetration to be used with this system was estimated to be 15 g/cm(2). The authors measured in-air lateral profiles at the isocenter plane and integral depth doses with the energy absorber. All input data were obtained by the Monte Carlo calculation, and its parameters were tuned to reproduce measurements. The fluence of single spots in water was modeled as a triple Gaussian function and the dose distribution was calculated using a fluence dose model. The authors compared in-air and in-water lateral profiles and depth doses between calculations and measurements for various apertures of square, half, and U-shaped fields. The absolute doses and dose distributions with the aperture were then validated by patient-specific quality assurance. Measured data were obtained by various chambers and a 2D ion chamber detector array. RESULTS: The patient-specific aperture reduced the penumbra from 30% to 70%, for example, from 34.0 to 23.6 mm and 18.8 to 5.6 mm. The calculated field width for square-shaped apertures agreed with measurements within 1 mm. Regarding patient-specific aperture plans, calculated and measured doses agreed within -0.06% ± 0.63% (mean ± SD) and 97.1% points passed the 2%-dose/2 mm-distance criteria of the γ-index on average. CONCLUSIONS: The patient-specific aperture system improved dose distributions, particularly in shallow-region plans.

Biological effect of dose distortion by fiducial markers in spot-scanning proton therapy with a limited number of fields: a simulation study.

PURPOSE: In accurate proton spot-scanning therapy, continuous target tracking by fluoroscopic x ray during irradiation is beneficial not only for respiratory moving tumors of lung and liver but also for relatively stationary tumors of prostate. Implanted gold markers have been used with great effect for positioning the target volume by a fluoroscopy, especially for the cases of liver and prostate with the targets surrounded by water-equivalent tissues. However, recent studies have revealed that gold markers can cause a significant underdose in proton therapy. This paper focuses on prostate cancer and explores the possibility that multiple-field irradiation improves the underdose effect by markers on tumor-control probability (TCP). METHODS: A Monte Carlo simulation was performed to evaluate the dose distortion effect. A spherical gold marker was placed at several characteristic points in a water phantom. The markers were with two different diameters of 2 and 1.5 mm, both visible on fluoroscopy. Three beam arrangements of single-field uniform dose (SFUD) were examined: one lateral field, two opposite lateral fields, and three fields (two opposite lateral fields + anterior field). The relative biological effectiveness (RBE) was set to 1.1 and a dose of 74 Gy (RBE) was delivered to the target of a typical prostate size in 37 fractions. The ratios of TCP to that without the marker (TCP(r)) were compared with the parameters of the marker sizes, number of fields, and marker positions. To take into account the dependence of biological parameters in TCP model, α∕ß values of 1.5, 3, and 10 Gy (RBE) were considered. RESULTS: It was found that the marker of 1.5 mm diameter does not affect the TCPs with all α∕ß values when two or more fields are used. On the other hand, if the marker diameter is 2 mm, more than two irradiation fields are required to suppress the decrease in TCP from TCP(r) by less than 3%. This is especially true when multiple (two or three) markers are used for alignment of a patient. CONCLUSIONS: It is recommended that 1.5-mm markers be used to avoid the reduction of TCP as well as to spare the surrounding critical organs, as long as the markers are visible on x-ray fluoroscopy. When 2-mm markers are implanted, more than two fields should be used and the markers should not be placed close to the distal edge of any of the beams.

GPU-based fast pencil beam algorithm for proton therapy.

Performance of a treatment planning system is an essential factor in making sophisticated plans. The dose calculation is a major time-consuming process in planning operations. The standard algorithm for proton dose calculations is the pencil beam algorithm which produces relatively accurate results, but is time consuming. In order to shorten the computational time, we have developed a GPU (graphics processing unit)-based pencil beam algorithm. We have implemented this algorithm and calculated dose distributions in the case of a water phantom. The results were compared to those obtained by a traditional method with respect to the computational time and discrepancy between the two methods. The new algorithm shows 5-20 times faster performance using the NVIDIA GeForce GTX 480 card in comparison with the Intel Core-i7 920 processor. The maximum discrepancy of the dose distribution is within 0.2%. Our results show that GPUs are effective for proton dose calculations.