Simplified Monte Carlo Method Research Articles

Development of a new ridge filter with honeycomb geometry for a pencil beam scanning system in particle radiotherapy

A ridge filter (RGF), a beam energy modulation device, is usually used for particle radiotherapy with a pencil beam scanning system. The conventional RGF has a one-dimensional (1D) periodic laterally stepped structure in orthogonal plane with a central beam direction. The energy of a beam passing through the different thicknesses of the stepped RGF is modulated. Although the lateral pencil beam size is required to cover the several stepped RGF units to modulate its energy as designed, the current trend is to decrease lateral beam size to improve the scanning system. As a result, the beam size becomes smaller than the size of the individual RGF unit. The aim of this study was to develop a new RGF with two-dimensional (2D) honeycomb geometry to simultaneously achieve both a decrease in lateral beam size and the desired energy modulation.The conventional 1D-RGF and the 2D-RGF with honeycomb geometry were both designed so that the Bragg peak size of a 79MeV/u carbon ion pencil beam in water was 1mm RMS in the beam direction. To validate the design of the 2D-RGF, we calculated depth dose distributions in water using a simplified Monte Carlo method. In the calculations, we decreased the lateral pencil beam size at the entrance of the RGF and investigated the threshold of lateral beam size with which the pencil beam can reproduce the desired Bragg peak size for each type of RGF. In addition, we calculated lateral dose distributions in air downstream from the RGF and evaluated the inhomogeneity of the lateral dose distributions.Using the 2D-RGF, the threshold of lateral beam size with which the pencil beam can reproduce the desired Bragg peak size was smaller than that using the 1D-RGF. Moreover, the distance from the RGF at which the lateral dose distribution becomes uniform was shorter using the 2D-RGF than that using the 1D-RGF. These results indicate that when the periodic length of both RGFs is the same, the 2D-RGF allows use of a pencil beam with smaller lateral beam size and a shorter distance from the RGF to the target, resulting in improvement in the conformity of dose distribution in a tumor.

Application of dose kernel calculation using a simplified Monte Carlo method to treatment plan for scanned proton beams.

Full Monte Carlo (FMC) calculation of dose distribution has been recognized to have superior accuracy, compared with the pencil beam algorithm (PBA). However, since the FMC methods require long calculation time, it is difficult to apply them to routine treatment planning at present. In order to improve the situation, a simplified Monte Carlo (SMC) method has been introduced to the dose kernel calculation applicable to dose optimization procedure for the proton pencil beam scanning. We have evaluated accuracy of the SMC calculation by comparing a result of the dose kernel calculation using the SMC method with that using the FMC method in an inhomogeneous phantom. The dose distribution obtained by the SMC method was in good agreement with that obtained by the FMC method. To assess the usefulness of SMC calculation in clinical situations, we have compared results of the dose calculation using the SMC with those using the PBA method for three clinical cases of tumor treatment. The dose distributions calculated with the PBA dose kernels appear to be homogeneous in the planning target volumes (PTVs). In practice, the dose distributions calculated with the SMC dose kernels with the spot weights optimized with the PBA method show largely inhomogeneous dose distributions in the PTVs, while those with the spot weights optimized with the SMC method have moderately homogeneous distributions in the PTVs. Calculation using the SMC method is faster than that using the GEANT4 by three orders of magnitude. In addition, the graphic processing unit (GPU) boosts the calculation speed by 13 times for the treatment planning using the SMC method. Thence, the SMC method will be applicable to routine clinical treatment planning for reproduction of the complex dose distribution more accurately than the PBA method in a reasonably short time by use of the GPU‐based calculation engine.PACS number(s): 87.55.Gh

<i>In Vivo</i> Dosimetry of an Anthropomorphic Phantom Using the RADPOS for Proton Beam Therapy

The radiation positioning system (RADPOS) combines an electromagnetic positioning sensor with metal oxide semiconductor field-effect transistor (MOSFET) dosimetry, enabling simultaneous online measurement of dose and spatial position. Evaluation points can be determined with the RADPOS. The accuracy of in-vivo proton dosimetry was evaluated using the RADPOS and an anthropomorphic head and neck phantom. MOSFET doses measured at 3D positions obtained with the RADPOS were compared with treatment plan values calculated using a simplified Monte Carlo (SMC) method. MOSFET responses, which depend strongly on the linear energy transfer of the proton beam, were corrected using the SMC method. The SMC method was used to calculate only dose deposition determined by the experimental depth-dose distribution and lateral displacement of protons due to the multiple scattering effect in materials and incident angle. This method thus enabled rapid calculation of accurate doses in even heterogeneities. In vivo dosimetry using the RADPOS, as well as MOSFET doses, agreed with SMC calculations in the range of ?3.0% to 8.3%. Most measurement errors occurred because of uncertainties in dose calculations due to the 1-mm position error. The results indicate that uncertainties in measurement position can be controlled successfully within 1 mm when using the RADPOS with in-vivo proton dosimetry.

SU‐E‐T‐805: Verification of the Simplified Monte Carlo Method for Simulation in An Inhomogeneous Phantom

Purpose:A simplified Monte Carlo (SMC) method has been developed to obtain fast and accurate dose calculation in heterogeneous tissues to improve the accuracy of dose calculation. We have applied the SMC method to calculation of dose kernels for the pencil beam scanning. While the SMC method tracks individual primary protons in medium, it simplifies the dose calculation by using a measured depth‐dose distribution instead of considering nuclear reactions and tracking secondary particles. To verify the accuracy of SMC calculation, we compared a dose‐calculation Result using the SMC method with that using the Full Monte Carlo (FMC) method in an inhomogeneous phantom.Methods:As a model of the inhomogeneous media, we considered a phantom complied of a rectangular acrylic block of size 150*300*200 mm 3 immersed in water within a virtual container with a size of 300*300*400 mm3.Results:We found excellent agreement of overall dose distributions between the SMC and FMC methods. As for the laterally integrated depth‐dose distributions, slight difference was found in front of the second Bragg‐Peak between the two algorithms. While it took 25717.0 s on 2.7 GHz Intel Core i7 for the FMC method to complete the calculation, it took 15.4 s for the SMC method to complete it. The SMC method can calculate the dose distribution approximately 1675 times faster than the FMC method.Conclusion:The dose distribution obtained by SMC method agreed well that obtained by the FMC method in a simple inhomogeneous phantom. In contrast, calculation time by the SMC method has been reduced by three orders in magnitude compared with the FMC method.

SU-E-T-263: Development of Dose Monitor Unit Calculation Using Clarkson Integration for Proton Beam Therapy Using Beam-Wobbling System

Purpose: The purpose of the present study is to develop a calculation method of dose-calibration-factor using Clarkson integration for proton therapy employing the wobbling system and to evaluate accuracy of the calculation by comparison between calculations and measurements. Methods: CF and CALF stand for a dose-calibration-factor and a dose per monitor unit (MU), respectively. A measured dose-calibration-factor CFmeas is defined as a ratio of the measured dose per monitor unit in a patient-specific condition CALFpat to the measured dose per MU in a reference beam condition CALFref. The CFcalc is a product of three factors: CF1, CF2 and CF3. The CF1 and CF2 are a factor reflecting the effect of common beam delivery devices and that of patient specific devices and parameter (an aperture collimator, a range compensator and an air gap), respectively. The CF1 was obtained by interpolation using measured data. The CF2 was calculated using the Simplified Monte Carlo (SMC) method. The SMC method calculates a dose distribution by tracing individual protons and by using a measured Bragg curve in water. The CF3 representing the correction factor of field size effect was obtained by using the Clarkson integration. We compared the calculated and measured CF values for 20 prostate cases. Results: Field size correction was found to be important. The calculations reproduce the measurement results within an error of ±2.0%, except for a few cases. The error was about –3.1% for the small field area of less than19 square centimeters. Conclusion: We have developed a calculation method of dose-calibration-factor. Calculations agreed with measurements within ±2.0% for 90% of 20 prostate cases. Except for a small field size cases, the calculation method can be applied to determine the dose-calibration–factor for majority cases of prostate cancer.

Emission of dimers from a free surface of heated water

The emission rate of water dimers from a free surface and a wetted solid surface in various cases was calculated by a simplified Monte Carlo method with the use of the binding energy of water molecules. The binding energy of water molecules obtained numerically assuming equilibrium between the free surface of water and vapor in the temperature range of 298–438 K corresponds to the coordination number for liquid water equal to 4.956 and is close to the reference value. The calculation results show that as the water temperature increases, the free surface of water and the wetted solid surface become sources of free water dimers. At a temperature of 438 K, the proportion of dimers in the total flow of water molecules on its surface reaches 1%. It is found that in the film boiling mode, the emission rate of dimers decreases with decreasing saturation vapor. Two mechanisms of the emission are described.

A method of neutron-energy evaluation based on the position distribution of recoil protons

A method of neutron-energy evaluation, which was recently proposed by the author’s group, has been applied to the investigation of an Am-Be source in order to confirm the validity of this novel approach; the method is based on the position distribution measurement of recoil protons by an imaging plate (IP) combined with a cone-like converter. The observed position distribution of recoil protons apparently involved neutron-energy information. An unfolding of the position distribution was plainly attempted with the response functions calculated by a simplified Monte Carlo method; the evaluated neutron spectra indicated the energy characteristics of an Am-Be source. When a full Monte Carlo Code, PHITS, was used to calculate the position distributions of recoil protons in order to obtain more correct response functions, the result of neutron-spectra evaluation has been much improved. The evaluation of neutron-energy spectrum by the present method will be further improved by the more accurate calculation of response functions with taking account of the complicated response of IP to low energy protons carefully, as well as by the application of more reliable unfolding algorithms and more appropriate position sensitive detectors.

Experimental verification of dose calculation using the simplified Monte Carlo method with an improved initial beam model for a beam-wobbling system

A beam delivery system using a single-radius-beam-wobbling method has been used to form a conformal irradiation field for proton radiotherapy in Japan. A proton beam broadened by the beam-wobbling system provides a non-Gaussian distribution of projection angle different in two mutually orthogonal planes with a common beam central axis, at a certain position. However, the conventional initial beam model for dose calculations has been using an approximation of symmetric Gaussian angular distribution with the same variance in both planes (called here a Gaussian model with symmetric variance (GMSV)), instead of the accurate one. We have developed a more accurate initial beam model defined as a non-Gaussian model with asymmetric variance (NonGMAV), and applied it to dose calculations using the simplified Monte Carlo (SMC) method. The initial beam model takes into account the different distances of two beam-wobbling magnets from the iso-center and also the different amplitudes of kick angle given by each magnet. We have confirmed that the calculation using the SMC with NonGMAV reproduced the measured dose distribution formed in air by a mono-energetic proton beam passing through a square aperture collimator better than with the GMSV and with a Gaussian model with asymmetric variance (GMAV) in which different variances of angular distributions are used in the two mutually orthogonal planes. Measured dose distributions in a homogeneous phantom formed by a modulated proton beam passing through a range shifter and an L-shaped range compensator, were consistent with calculations using the SMC with GMAV and NonGMAV, but in disagreement with calculations using the SMC with GMSV. Measured lateral penumbrae in a lateral direction were reproduced better by calculations using the SMC with NonGMAV than by those with GMAV, when an aperture collimator with a smaller opening was used. We found that such a difference can be attributed to the non-Gaussian angular distribution of the initial beam at a lateral position for the beam-wobbling system. Calculations using the SMC with NonGMAV are effective to reproduce dose distributions formed by a beam-wobbling system more accurately than that with GMSV or that with GMAV.

SU-E-T-488: Dose Calculation Model Using the Simplified Monte Carlo Method with an Initial Beam Model Adapted to a Beam-Wobbling System

We have developed an accurate dose calculation model based on a simplified Monte Carlo (SMC) method adapted to a beam-wobbling delivery system at National Cancer Center Hospital East (NCCHE). We used an initial beam model specific to the beam-wobbling system to reproduce accurately different dose distributions in two lateral directions (x- and y-directions) perpendicular to each other. The SMC calculates a dose distribution by tracking individual protons. The SMC starts tracking protons at an entrance of a range compensator. Protons are generated in an initial phase space adapted to the wobbler system. Since two wobbling-magnets are located at separate places with different distances from the iso-center, different dose distributions are formed in x- and y-directions. We derived an initial phase space distribution for the beam-wobbling system using an analytical method. We used the SMC method with the initial beam model to calculate dose distributions accurately. To verify accuracy of the calculation method, we measured the dose distribution in a homogeneous phantom formed by 235 MeV protons passing through a L-shaped range compensator. We used a 2D-array of parallel-plate ionization chambers (2D Array seven29®) to measure dose distributions with a sampling period of 5 mm. The measured dose distribution in the x-direction was different from that in the y-direction. Our calculation model reproduces the measurement results well in both lateral directions. In addition, the calculation reproduced the dose increments in edge regions contributed by edge-scattered protons in collimator. It indicates the advantage of the SMC. A dose calculation model has been developed based on the simplified Monte Carlo method applied to a beam-wobbling system. By adapting the initial beam model to the wobbling system, the SMC method is found to reproduce observed different dose distributions in x- and y-directions well.

Clinical implementation of a GPU-based simplified Monte Carlo method for a treatment planning system of proton beam therapy

We implemented the simplified Monte Carlo (SMC) method on graphics processing unit (GPU) architecture under the computer-unified device architecture platform developed by NVIDIA. The GPU-based SMC was clinically applied for four patients with head and neck, lung, or prostate cancer. The results were compared to those obtained by a traditional CPU-based SMC with respect to the computation time and discrepancy. In the CPU- and GPU-based SMC calculations, the estimated mean statistical errors of the calculated doses in the planning target volume region were within 0.5% rms. The dose distributions calculated by the GPU- and CPU-based SMCs were similar, within statistical errors. The GPU-based SMC showed 12.30–16.00 times faster performance than the CPU-based SMC. The computation time per beam arrangement using the GPU-based SMC for the clinical cases ranged 9–67 s. The results demonstrate the successful application of the GPU-based SMC to a clinical proton treatment planning.

SU-E-T-352: Comparison of Dose Distributions Between Two Arrangements of a Range Compensator and of An Aperture Collimator in a Passive Scattering Method for Proton Therapy

Purpose: Two arrangements of a range compensator (RC) and an aperture collimator (AC), RC placed in front of AC (ARGT‐1) or AC placed in front of RC (ARGT‐2), are currently used in proton therapy. We studied difference of the dose distributions for two arrangements.Methods: We calculated dose distributions in water formed by a 190‐MeV modulated proton beam (SOBP width 80 mm) passing through two arrangements of a simple geometrical RC and an AC using a Simplified Monte Carlo method. The air gap between the downstream device and water surface was set at 195 mm. Results: Calculated dose distributions were normalized in the same uniform‐dose region. We compared sharpness of the 80%–20% dose falloffs at a depth of 150 mm where protons passing through the thinnest part of RC mainly contribute the dose. The value for the ARGT‐1 is written first and that for the ARGT‐2 next. Dose falloffs were 8.5±0.2 mm / 7.9±0.2 mm near an inner RC edge. Dose falloffs were 7. 1±0.2 mm / 8.0±0.2 near the AC edge region. In addition, dose contributions of edge‐scattered protonsscattered in the AC at water surface were 19% / 10% Conclusions: We verified that ARGT‐1 is superior to the other in dose conformation near the lateral target boundary and that ARGT‐2 is superior to the other in that near the distal target boundary. We also noticed that the RC serves to absorb a part of scatteredprotons in the AC for ARGT‐2.

Improved dose-calculation accuracy in proton treatment planning using a simplified Monte Carlo method verified with three-dimensional measurements in an anthropomorphic phantom

Treatment planning for proton tumor therapy requires a fast and accurate dose-calculation method. We have implemented a simplified Monte Carlo (SMC) method in the treatment planning system of the National Cancer Center Hospital East for the double-scattering beam delivery scheme. The SMC method takes into account the scattering effect in materials more accurately than the pencil beam algorithm by tracking individual proton paths. We confirmed that the SMC method reproduced measured dose distributions in a heterogeneous slab phantom better than the pencil beam method. When applied to a complex anthropomorphic phantom, the SMC method reproduced the measured dose distribution well, satisfying an accuracy tolerance of 3 mm and 3% in the gamma index analysis. The SMC method required approximately 30 min to complete the calculation over a target volume of 500 cc, much less than the time required for the full Monte Carlo calculation. The SMC method is a candidate for a practical calculation technique with sufficient accuracy for clinical application.

A Monte Carlo method for thermal building simulation

A simplified Monte Carlo method for finding an approximation of the building inside temperature distribution is given. Present simulation techniques are either over-simplified and use only a deterministic method, or are highly complex stochastic models. The new method consists of a Monte Carlo approach to find typical input distributions, used in conjunction with a more traditional deterministic building thermal simulation model. The output distribution is obtained by estimating the output distribution from a carefully selected sample of input distributions. Radiation and temperature input data are simulated separately, and then the combined effect is found with a numerical convolution integral. Because the convolution integral is only strictly valid for independent variables, a verification study is also presented, using four different buildings and five different ventilation rates. Complete experimental verification of the method requires measuring the inside temperature distribution for 5 years, with five different ventilation rates for the same four buildings. This was out of the timeframe of this study. Therefore, the method was verified by comparison of results obtained with the new technique and comprehensive results obtained by simulating every day for the same period with historical weather data. The results show that the average predicted temperature error is 0.68 °C, with a standard deviation of 1.37 °C. The verification thus shows that by using the new Monte Carlo method a good approximation can be found for the inside temperature distribution by using only 4% of the days from the 5-year period.

Experimental evaluation of validity of simplified Monte Carlo method in proton dose calculations

It is important for proton therapy to calculate dose distributions accurately in treatment planning. Dose calculations in the body for treatment planning are converted to dose distributions in water, and the converted calculations are then generally evaluated by the dose measurements in water. In this paper, proton dose calculations were realized for a phantom simulating a clinical heterogeneity. Both dose calculations in the phantom calculated by two dose calculation methods, the range-modulated pencil beam algorithm (RMPBA) and the simplified Monte Carlo (SMC) method, and dose calculations converted to dose distributions in water by the same two methods were verified experimentally through comparison with measured distributions, respectively. For the RMPBA, though the converted calculations in water agreed moderately well with the measured ones, the calculated results in the actual phantom produced large errors. This meant that dose calculations in treatment planning should be evaluated by the dose measurements not in water but in the body with heterogeneity. On the other hand, the results calculated in the phantom, even by the less rigorous SMC method, reproduced the experimental ones well. This finding showed that actual dose distributions in the body should be predicted by the SMC method.

Universal correction procedure for electron-probe microanalysis. I. Measurement of X-ray depth distributions in solids

X-ray distributions in aluminium, gold and carbon have been measured using the tracer technique. The results have been compared with calculations using the simplified Monte Carlo method of Love et al. (1977). It is concluded that the Monte Carlo model predicts too high a peak to the X-ray distribution and that the discrepancy is worse at lower overvoltage ratios. Calculated surface ionisation functions Phi (0) are, however, closer to experimental values and the general shape of the Phi ( rho z) curve is considered satisfactory. The more rigorous model of Myklebust et al. (1976) also overestimates the height of the peak in the Phi ( rho z) curve and, whilst it performs rather better than the simplified model for gold, it gives even more unrealistic data on carbon.