TY - JOUR
AU - Najafzadeh,, Milad
AB - Abstract To validate the GATE Monte Carlo simulation code and to investigate the lateral scattering of proton pencil beams in the major body tissue elements in the therapeutic energy range. In this study, GATE Monte Carlo simulation code was used to compute absorbed dose and fluence of protons in a water cubic phantom for the clinical energy range. To apply the suitable physics model for simulation, different physics lists were investigated. The present research also investigated the optimal value of the water ionization potential as a simulation parameter. Thereafter, the lateral beam profile of proton pencil beams were simulated at different energies and depths in body tissue elements. The range results obtained using the QGSP_BIC_EMY physics showed the best compatibility with the NIST database data. Moreover, it was found that the 76 eV is the optimal value for the water ionization potential. In the next step, it was shown that the beam halo can be described by adding a supplementary Gaussian function to the standard single-Gaussian model, which currently is used by treatment planning systems (TPS). INTRODUCTION Regarding the presence of the Bragg peak in the dose distribution of charged particles and their high relative biological effectiveness (RBE), a large body of literature has been devoted today to the treatment of deep-seated tumors(1). Although the Bragg peak offers an inherent advantage over the dose distribution of photons at the end of the proton range, a sharp dose drop at the end of the dose distribution profile of charged particles causes significant changes in the radiation dose with slight changes in the radiation site. The target tumor may, therefore, receive no dose at all, or a critical organ in the vicinity of the target might be mistakenly located in the Bragg peak area and completely destroyed(2). In addition to electromagnetic interactions (stopping and multiple scatterings), protons are under nuclear interactions. In therapeutic energy, about 20% of protons undergo nuclear interactions before stopping(3). Secondary particles are generated from nuclear interactions. Scattered and secondary particles produce unwanted doses outside the target volume, which may increase the risk of cancer from secondary radiation(4–6). A sharp lateral penumbra is essential to protect critical organs in the vicinity of the target volume. This is one of the most prominent features of proton beam. The lateral penumbra in the patient body depends on the design of the beam delivery system as well as the nature of interaction between protons and the patient’s body(7). Ion pencil beams carry a low-dose envelope that can be extended up to a few centimeters from the central axis of the incident beam. Depending on the energy and type of the beam, this halo mainly consists of secondary particles produced by nuclear interactions in the target or particles under multiple Coulomb scattering in the beam line components. This halo is often ignored by single-Gaussian model in the current treatment planning systems (TPS). In order to enhance the treatment planning precision, one can improve the lateral scattering model. It is also very important to keep the calculation time and the complexity of the treatment planning at a reasonable level. The treatment planning system is approved by the Monte Carlo particle transport codes, including the Geant4(8), MCNPX(9) and FLUKA(10), as one of the commonly used gold standards. Therefore, it is crucial to validate these nuclear interaction models in the clinical energy range, using these Monte Carlo codes(11). In 2005, Pedroni et al. developed a pencil beam dose model for the treatment planning system in PSI proton gantry. They proposed a summation of two Gaussian functions to describe the lateral profile of proton pencil beams(12). Schwaab et al. measured the lateral profile of proton and carbon ion pencil beams in the water and air at the Heidelberg Ion Beam Therapy Center. Accordingly, they came up with a better model to describe the beam halo, which is the double-Gaussian model(13). The results of the present study also confirmed their findings. Bellinzona et al. simulated the dose profile in the CNAO beamline with the FLUKA toolkit. They performed the best fit of the lateral dose profiles for different functions using ROOT and MINUIT. Although the best results were obtained using the triple-Gaussian function and the double-Gaussian Cauchy–Lorentz function with six parameters, the results obtained with the Gauss–Rutherford function with only four parameters were also acceptable(14). In this study, after validating the GATE Monte Carlo simulation code, the lateral dose profile of proton beams was simulated at different energies and depths in body tissue elements (which have the highest percentage of tissue component) with the GATE code. Afterwards, an appropriate description of the halo beam in the tissue elements was obtained by fitting the proposed functions to proton lateral scattering in a water medium. The advantage of the proposed model over the experimental methods and Monte Carlo simulation is its precision in obtaining the lateral scattering proton and minimum lateral scattering calculation time. MATERIAL AND METHODS In this study, we used GATE code (V8) to simulate the lateral profile of proton pencil beams. Simulation geometry In the present study, the dimensions of the world volume are assumed to be 5 × 5 × 5 m3. The standard phantom used in proton therapy studies is a cubic water phantom with dimensions of 40 × 40 × 40 cm3. Therefore, in this study, we consider this geometry. Monoenergetic proton pencil beams struck the phantom along the z-axis. Figure 1 shows the voxelized phantom and the axis of incident beam. Figure 1 Open in new tabDownload slide The geometry of the phantom. Figure 1 Open in new tabDownload slide The geometry of the phantom. Pencil beam model The present study used a PBS model with a Gaussian spatial distribution. Proton beams were with the energy of 5–250 MeV and a standard deviation of 0 MeV. The incident beam was selected along the z-axis and the lateral dimensions along the x- and y-axis. The ‘spot size’ or the standard deviation, represented by |${\sigma}_x$| and |${\sigma}_y$| in the isocenter, was 3 mm. The inherent divergence of the beam was also regarded as the negligible value of |$\sigma =3\ mrad$|⁠. Physics list selection Several physics list packages are currently available in Geant4 V10.3.3, and the user can select the proper model as required. Physical models in the reference physics lists recommended for medical applications and ion therapy were therefore used, including QGSP_BIC_EMY, FTFP_BERT, QGSP_BIC_EMZ, QGSP_BIC_AllHP and QGSP_BIC_HP_EMY. The quark–gluon string with precompound (QGSP) model was implemented to handle the collision of high-energy hadrons. Two different shower models, namely, the binary light ion cascade (BIC) and Bertini cascade (BERT), were used. These models are responsible to track low-energy regions. For medical applications of physics, the EM standard package with the Option3 (EMY) and Option4 (EMZ) are available. The inelastic hadron–nucleus processes are implemented by the FTF, Bertini and precompound models. The QGSP_BIC_AllHP is identical to QGSP_BIC except that the neutrons with the energy of 20 MeV and lower use the high-precision neutron models and cross-sections to describe elastic and inelastic scattering, capture and fission(15). Actor selection To record the dose and fluence, the desired actors were added to the phantom. The voxel size for the phantom along the incident beam direction (z) was set at 0.01 cm. The phantom was therefore divided into cubic cells with dimensions of 0.01 cm, along the beam direction and 40 × 40 cm2 perpendicular to the beam direction. Simulation parameters A range cut-off and therefore cut-off energy are defined in the Geant4 for the production of secondary particles. The initial particle is therefore tracked until reaching zero energy, while no further secondary particles are produced under this cut-off energy, which reduces the simulation time(16). This parameter was set at 0.01 mm, and a step length of 0.005 mm was selected based on a study by Jia et al.(17). To achieve high precision, the number of primary particles was set at 106 for all energies. Ionization potential The proton range basically depends on the mean ionization potential (I) of the medium. Water ionization potential is a topic of interest reported between 67.2 and 85 eV(18). The unknown ionization potential of a medium is calculated using Bragg’s additivity law. Ionization potential is 70.9 eV for water in the GEANT4 and is calculated by default based on the Bragg’s additivity law(19) for all user-defined media; however, it can be changed by the user. For validation, we investigated different values from 70 to 80 eV and compared the results with the NIST data. Lateral scattering In the next step, the phantom was voxelized in the depth and lateral directions to evaluate lateral scattering. Obviously, lateral scattering does not require to be investigated by examining both lateral directions due to the problem’s symmetry. At this stage, scattering simulations were performed for each of the major tissue elements in five different energy scenarios (50, 70, 125, 150 and 200 MeV). The major elements in body tissues are hydrogen, nitrogen, oxygen and carbon. After performing the simulations, the lateral scattering was investigated at three different depths(1): the proton entrance depth(2), Bragg peak depth and(3) the proton range. Thereafter, we examined the Gaussian and double-Gaussian models in a water medium(13,14). The relationship between these functions is as follows: Single-Gaussian model: The lateral scattering of a proton beam in the target is usually approximated with an ideal Gaussian distribution(20), by considering the direct superposition of several spreading portions. $$\begin{equation} f(y)=N\frac{1}{\sqrt{2\pi}\sigma}\mathit{\exp}\left[-\frac{y^2}{2{\sigma}^2}\right] \end{equation}$$ (1) where σ is the standard deviation and N is the normalization factor. This function has only two free parameters. Double-Gaussian model: To improve the previous Gaussian model, a second broader Gaussian function is added to describe the tails of dose distribution proposed by Fruhwirth and Regler(21). For simplicity, this discussion was limited to a combination of two Gaussian distributions with the same zero mean and with different standard deviations. $$\begin{align} f(y)=&\;N\Big\{\left(1-W\right)\frac{1}{\sqrt{2\pi }{\sigma}_1}\mathit{\exp}\Big[-\frac{y^2}{2{\sigma}_1^2}\Big]\nonumber\\ & +\,W\frac{1}{\sqrt{2\pi }{\sigma}_2}\mathit{\exp}\Big[-\frac{y^2}{2{\sigma}_2^2}\Big]\Big\} \end{align}$$ (2) In this parameterization, the core is described with a narrow Gaussian distribution of width σ1, and the tail of lateral profile is described with the large Gaussian of width σ2. According to equation (2), the double-Gaussian distribution depends on four free parameters: σ1, σ2, relative weight W and a normalizing factor N. RESULTS Physics list analysis Figure 2 shows the results of the depth dose profile of 250-MeV proton pencil beams for all studied physics lists. For a better comparison, Figure 3 shows the graph of delta range in terms of incident energy in which delta range is the difference between the simulation results with the NIST data. Table 1 shows the entire energy range for each physics lists and NIST data. Figure 2 Open in new tabDownload slide Pristine depth dose profiles in the water phantom for a 250-MeV proton pencil beam with different physics lists. Figure 2 Open in new tabDownload slide Pristine depth dose profiles in the water phantom for a 250-MeV proton pencil beam with different physics lists. Figure 3 Open in new tabDownload slide Deviations of the beam range obtained by different physics lists as a function of energy. (Delta range is the difference between the simulation results with the NIST data.) Figure 3 Open in new tabDownload slide Deviations of the beam range obtained by different physics lists as a function of energy. (Delta range is the difference between the simulation results with the NIST data.) Table 1 The range of protons in the therapeutic energy with different physics lists. Energy (MeV) . R80 (mm) QGSP_BIC_EMY . R80 (mm) FTFP_BERT . R80 (mm) QGSP_BIC_EMZ . R80 (mm) QGSP_BIC_AllHP . R80 (mm) QGSP_BIC_HP_EMY . NIST (mm) . 5 0.370 0.370 0.370 0.370 0.370 0.362 10 1.186 1.188 1.185 1.188 1.186 1.230 15 2.493 2.497 2.492 2.497 2.493 2.539 20 4.218 4.223 4.215 4.223 4.218 4.260 25 6.329 6.334 6.325 6.334 6.329 6.370 30 8.817 8.818 8.811 8.818 8.816 8.853 40 14.838 14.838 14.830 14.839 14.838 14.890 50 22.210 22.209 22.200 22.209 22.209 22.270 60 30.861 30.857 30.850 30.860 30.861 30.930 70 40.720 40.714 40.701 40.714 40.717 40.800 80 51.738 51.728 51.713 51.724 51.739 51.840 90 63.856 63.853 63.831 63.848 63.859 63.980 100 77.044 77.026 77.007 77.027 77.043 77.180 110 91.245 91.227 91.199 91.228 91.250 91.400 120 106.416 106.406 106.384 106.407 106.425 106.600 130 122.547 122.528 122.501 122.530 122.551 122.800 140 139.582 139.565 139.525 139.552 139.581 139.800 150 157.498 157.460 157.421 157.449 157.488 157.700 160 176.251 176.205 176.169 176.215 176.231 176.500 170 195.814 195.791 195.738 195.779 195.825 196.100 180 216.180 216.147 216.092 216.132 216.178 216.500 190 237.314 237.260 237.223 237.258 237.301 237.700 200 259.172 259.086 259.055 259.114 259.173 259.600 210 281.746 281.659 281.618 281.665 281.735 282.200 220 305.033 304.954 304.881 304.940 305.002 305.500 230 328.974 328.868 328.799 328.886 328.971 329.500 240 353.549 353.452 353.387 353.459 353.579 354.100 250 378.772 378.672 378.581 378.662 378.785 379.400 Energy (MeV) . R80 (mm) QGSP_BIC_EMY . R80 (mm) FTFP_BERT . R80 (mm) QGSP_BIC_EMZ . R80 (mm) QGSP_BIC_AllHP . R80 (mm) QGSP_BIC_HP_EMY . NIST (mm) . 5 0.370 0.370 0.370 0.370 0.370 0.362 10 1.186 1.188 1.185 1.188 1.186 1.230 15 2.493 2.497 2.492 2.497 2.493 2.539 20 4.218 4.223 4.215 4.223 4.218 4.260 25 6.329 6.334 6.325 6.334 6.329 6.370 30 8.817 8.818 8.811 8.818 8.816 8.853 40 14.838 14.838 14.830 14.839 14.838 14.890 50 22.210 22.209 22.200 22.209 22.209 22.270 60 30.861 30.857 30.850 30.860 30.861 30.930 70 40.720 40.714 40.701 40.714 40.717 40.800 80 51.738 51.728 51.713 51.724 51.739 51.840 90 63.856 63.853 63.831 63.848 63.859 63.980 100 77.044 77.026 77.007 77.027 77.043 77.180 110 91.245 91.227 91.199 91.228 91.250 91.400 120 106.416 106.406 106.384 106.407 106.425 106.600 130 122.547 122.528 122.501 122.530 122.551 122.800 140 139.582 139.565 139.525 139.552 139.581 139.800 150 157.498 157.460 157.421 157.449 157.488 157.700 160 176.251 176.205 176.169 176.215 176.231 176.500 170 195.814 195.791 195.738 195.779 195.825 196.100 180 216.180 216.147 216.092 216.132 216.178 216.500 190 237.314 237.260 237.223 237.258 237.301 237.700 200 259.172 259.086 259.055 259.114 259.173 259.600 210 281.746 281.659 281.618 281.665 281.735 282.200 220 305.033 304.954 304.881 304.940 305.002 305.500 230 328.974 328.868 328.799 328.886 328.971 329.500 240 353.549 353.452 353.387 353.459 353.579 354.100 250 378.772 378.672 378.581 378.662 378.785 379.400 Open in new tab Table 1 The range of protons in the therapeutic energy with different physics lists. Energy (MeV) . R80 (mm) QGSP_BIC_EMY . R80 (mm) FTFP_BERT . R80 (mm) QGSP_BIC_EMZ . R80 (mm) QGSP_BIC_AllHP . R80 (mm) QGSP_BIC_HP_EMY . NIST (mm) . 5 0.370 0.370 0.370 0.370 0.370 0.362 10 1.186 1.188 1.185 1.188 1.186 1.230 15 2.493 2.497 2.492 2.497 2.493 2.539 20 4.218 4.223 4.215 4.223 4.218 4.260 25 6.329 6.334 6.325 6.334 6.329 6.370 30 8.817 8.818 8.811 8.818 8.816 8.853 40 14.838 14.838 14.830 14.839 14.838 14.890 50 22.210 22.209 22.200 22.209 22.209 22.270 60 30.861 30.857 30.850 30.860 30.861 30.930 70 40.720 40.714 40.701 40.714 40.717 40.800 80 51.738 51.728 51.713 51.724 51.739 51.840 90 63.856 63.853 63.831 63.848 63.859 63.980 100 77.044 77.026 77.007 77.027 77.043 77.180 110 91.245 91.227 91.199 91.228 91.250 91.400 120 106.416 106.406 106.384 106.407 106.425 106.600 130 122.547 122.528 122.501 122.530 122.551 122.800 140 139.582 139.565 139.525 139.552 139.581 139.800 150 157.498 157.460 157.421 157.449 157.488 157.700 160 176.251 176.205 176.169 176.215 176.231 176.500 170 195.814 195.791 195.738 195.779 195.825 196.100 180 216.180 216.147 216.092 216.132 216.178 216.500 190 237.314 237.260 237.223 237.258 237.301 237.700 200 259.172 259.086 259.055 259.114 259.173 259.600 210 281.746 281.659 281.618 281.665 281.735 282.200 220 305.033 304.954 304.881 304.940 305.002 305.500 230 328.974 328.868 328.799 328.886 328.971 329.500 240 353.549 353.452 353.387 353.459 353.579 354.100 250 378.772 378.672 378.581 378.662 378.785 379.400 Energy (MeV) . R80 (mm) QGSP_BIC_EMY . R80 (mm) FTFP_BERT . R80 (mm) QGSP_BIC_EMZ . R80 (mm) QGSP_BIC_AllHP . R80 (mm) QGSP_BIC_HP_EMY . NIST (mm) . 5 0.370 0.370 0.370 0.370 0.370 0.362 10 1.186 1.188 1.185 1.188 1.186 1.230 15 2.493 2.497 2.492 2.497 2.493 2.539 20 4.218 4.223 4.215 4.223 4.218 4.260 25 6.329 6.334 6.325 6.334 6.329 6.370 30 8.817 8.818 8.811 8.818 8.816 8.853 40 14.838 14.838 14.830 14.839 14.838 14.890 50 22.210 22.209 22.200 22.209 22.209 22.270 60 30.861 30.857 30.850 30.860 30.861 30.930 70 40.720 40.714 40.701 40.714 40.717 40.800 80 51.738 51.728 51.713 51.724 51.739 51.840 90 63.856 63.853 63.831 63.848 63.859 63.980 100 77.044 77.026 77.007 77.027 77.043 77.180 110 91.245 91.227 91.199 91.228 91.250 91.400 120 106.416 106.406 106.384 106.407 106.425 106.600 130 122.547 122.528 122.501 122.530 122.551 122.800 140 139.582 139.565 139.525 139.552 139.581 139.800 150 157.498 157.460 157.421 157.449 157.488 157.700 160 176.251 176.205 176.169 176.215 176.231 176.500 170 195.814 195.791 195.738 195.779 195.825 196.100 180 216.180 216.147 216.092 216.132 216.178 216.500 190 237.314 237.260 237.223 237.258 237.301 237.700 200 259.172 259.086 259.055 259.114 259.173 259.600 210 281.746 281.659 281.618 281.665 281.735 282.200 220 305.033 304.954 304.881 304.940 305.002 305.500 230 328.974 328.868 328.799 328.886 328.971 329.500 240 353.549 353.452 353.387 353.459 353.579 354.100 250 378.772 378.672 378.581 378.662 378.785 379.400 Open in new tab In this study, the statistical test was used to compare the results of each physics with NIST data. The p-value was obtained 0.831 with the Mann–Whitney test, indicating that there is no significant difference between the range obtained from each physics list and NIST data. In addition, no significant difference was observed between QGSP_BIC_EMY and QGSP_BIC_HP_EMY in this study after examining the statistical uncertainty and difference between the ranges of each physics in all energies. The relative statistical uncertainty for all voxels prior to the Bragg peaks at all energies is below 0.01%. Table 2 also shows the difference between proton ranges and NIST data. The purpose of this comparison is to establish whether this difference is greater than the uncertainty. In other words, it is tried to establish whether this difference is significant. The R80 calculation error is obtained from the corresponding statistical uncertainty in the dose calculation. To this end, we calculated the uncertainty in measuring the depth at 80% of the maximum dose by adding and subtracting the uncertainty value in measuring the voxel dose, corresponding to the depth at 80% of the maximum dose, to the absolute value of the dose in the voxel. Table 2 The comparison between the differences obtained for the proton range with simulation and NIST data. Energy (MeV) . Delta range (mm) QGSP_BIC_EMY . Delta range (mm) FTFP_BERT . Delta range (mm) QGSP_BIC_EMZ . Delta range (mm) QGSP_BIC_AllHP . Delta range (mm) QGSP_BIC_HP_EMY . 5 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 10 4.40E-02 4.20E-02 4.50E-02 4.20E-02 4.40E-02 15 4.60E-02 4.20E-02 4.70E-02 4.20E-02 4.60E-02 20 4.20E-02 3.70E-02 4.50E-02 3.70E-02 4.20E-02 25 4.10E-02 3.60E-02 4.50E-02 3.60E-02 4.10E-02 30 3.60E-02 3.50E-02 4.20E-02 3.50E-02 3.70E-02 40 5.20E-02 5.20E-02 6.00E-02 5.10E-02 5.20E-02 50 6.00E-02 6.10E-02 7.00E-02 6.10E-02 6.10E-02 60 6.90E-02 7.30E-02 8.00E-02 7.00E-02 6.90E-02 70 8.00E-02 8.60E-02 9.90E-02 8.60E-02 8.30E-02 80 1.02E-01 1.12E-01 1.27E-01 1.16E-01 1.01E-01 90 1.24E-01 1.27E-01 1.49E-01 1.32E-01 1.21E-01 100 1.36E-01 1.54E-01 1.73E-01 1.53E-01 1.37E-01 110 1.55E-01 1.73E-01 2.01E-01 1.72E-01 1.50E-01 120 1.84E-01 1.94E-01 2.16E-01 1.93E-01 1.75E-01 130 2.53E-01 2.72E-01 2.99E-01 2.70E-01 2.49E-01 140 2.18E-01 2.35E-01 2.75E-01 2.48E-01 2.19E-01 150 2.02E-01 2.40E-01 2.79E-01 2.51E-01 2.12E-01 160 2.49E-01 2.95E-01 3.31E-01 2.85E-01 2.69E-01 170 2.86E-01 3.09E-01 3.62E-01 3.21E-01 2.75E-01 180 3.20E-01 3.53E-01 4.08E-01 3.68E-01 3.22E-01 190 3.86E-01 4.40E-01 4.77E-01 4.42E-01 3.99E-01 200 4.28E-01 5.14E-01 5.45E-01 4.86E-01 4.27E-01 210 4.54E-01 5.41E-01 5.82E-01 5.35E-01 4.65E-01 220 4.67E-01 5.46E-01 6.19E-01 5.60E-01 4.98E-01 230 5.26E-01 6.32E-01 7.01E-01 6.14E-01 5.29E-01 240 5.51E-01 6.48E-01 7.13E-01 6.41E-01 5.21E-01 250 6.28E-01 7.28E-01 8.19E-01 7.38E-01 6.15E-01 Energy (MeV) . Delta range (mm) QGSP_BIC_EMY . Delta range (mm) FTFP_BERT . Delta range (mm) QGSP_BIC_EMZ . Delta range (mm) QGSP_BIC_AllHP . Delta range (mm) QGSP_BIC_HP_EMY . 5 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 10 4.40E-02 4.20E-02 4.50E-02 4.20E-02 4.40E-02 15 4.60E-02 4.20E-02 4.70E-02 4.20E-02 4.60E-02 20 4.20E-02 3.70E-02 4.50E-02 3.70E-02 4.20E-02 25 4.10E-02 3.60E-02 4.50E-02 3.60E-02 4.10E-02 30 3.60E-02 3.50E-02 4.20E-02 3.50E-02 3.70E-02 40 5.20E-02 5.20E-02 6.00E-02 5.10E-02 5.20E-02 50 6.00E-02 6.10E-02 7.00E-02 6.10E-02 6.10E-02 60 6.90E-02 7.30E-02 8.00E-02 7.00E-02 6.90E-02 70 8.00E-02 8.60E-02 9.90E-02 8.60E-02 8.30E-02 80 1.02E-01 1.12E-01 1.27E-01 1.16E-01 1.01E-01 90 1.24E-01 1.27E-01 1.49E-01 1.32E-01 1.21E-01 100 1.36E-01 1.54E-01 1.73E-01 1.53E-01 1.37E-01 110 1.55E-01 1.73E-01 2.01E-01 1.72E-01 1.50E-01 120 1.84E-01 1.94E-01 2.16E-01 1.93E-01 1.75E-01 130 2.53E-01 2.72E-01 2.99E-01 2.70E-01 2.49E-01 140 2.18E-01 2.35E-01 2.75E-01 2.48E-01 2.19E-01 150 2.02E-01 2.40E-01 2.79E-01 2.51E-01 2.12E-01 160 2.49E-01 2.95E-01 3.31E-01 2.85E-01 2.69E-01 170 2.86E-01 3.09E-01 3.62E-01 3.21E-01 2.75E-01 180 3.20E-01 3.53E-01 4.08E-01 3.68E-01 3.22E-01 190 3.86E-01 4.40E-01 4.77E-01 4.42E-01 3.99E-01 200 4.28E-01 5.14E-01 5.45E-01 4.86E-01 4.27E-01 210 4.54E-01 5.41E-01 5.82E-01 5.35E-01 4.65E-01 220 4.67E-01 5.46E-01 6.19E-01 5.60E-01 4.98E-01 230 5.26E-01 6.32E-01 7.01E-01 6.14E-01 5.29E-01 240 5.51E-01 6.48E-01 7.13E-01 6.41E-01 5.21E-01 250 6.28E-01 7.28E-01 8.19E-01 7.38E-01 6.15E-01 Open in new tab Table 2 The comparison between the differences obtained for the proton range with simulation and NIST data. Energy (MeV) . Delta range (mm) QGSP_BIC_EMY . Delta range (mm) FTFP_BERT . Delta range (mm) QGSP_BIC_EMZ . Delta range (mm) QGSP_BIC_AllHP . Delta range (mm) QGSP_BIC_HP_EMY . 5 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 10 4.40E-02 4.20E-02 4.50E-02 4.20E-02 4.40E-02 15 4.60E-02 4.20E-02 4.70E-02 4.20E-02 4.60E-02 20 4.20E-02 3.70E-02 4.50E-02 3.70E-02 4.20E-02 25 4.10E-02 3.60E-02 4.50E-02 3.60E-02 4.10E-02 30 3.60E-02 3.50E-02 4.20E-02 3.50E-02 3.70E-02 40 5.20E-02 5.20E-02 6.00E-02 5.10E-02 5.20E-02 50 6.00E-02 6.10E-02 7.00E-02 6.10E-02 6.10E-02 60 6.90E-02 7.30E-02 8.00E-02 7.00E-02 6.90E-02 70 8.00E-02 8.60E-02 9.90E-02 8.60E-02 8.30E-02 80 1.02E-01 1.12E-01 1.27E-01 1.16E-01 1.01E-01 90 1.24E-01 1.27E-01 1.49E-01 1.32E-01 1.21E-01 100 1.36E-01 1.54E-01 1.73E-01 1.53E-01 1.37E-01 110 1.55E-01 1.73E-01 2.01E-01 1.72E-01 1.50E-01 120 1.84E-01 1.94E-01 2.16E-01 1.93E-01 1.75E-01 130 2.53E-01 2.72E-01 2.99E-01 2.70E-01 2.49E-01 140 2.18E-01 2.35E-01 2.75E-01 2.48E-01 2.19E-01 150 2.02E-01 2.40E-01 2.79E-01 2.51E-01 2.12E-01 160 2.49E-01 2.95E-01 3.31E-01 2.85E-01 2.69E-01 170 2.86E-01 3.09E-01 3.62E-01 3.21E-01 2.75E-01 180 3.20E-01 3.53E-01 4.08E-01 3.68E-01 3.22E-01 190 3.86E-01 4.40E-01 4.77E-01 4.42E-01 3.99E-01 200 4.28E-01 5.14E-01 5.45E-01 4.86E-01 4.27E-01 210 4.54E-01 5.41E-01 5.82E-01 5.35E-01 4.65E-01 220 4.67E-01 5.46E-01 6.19E-01 5.60E-01 4.98E-01 230 5.26E-01 6.32E-01 7.01E-01 6.14E-01 5.29E-01 240 5.51E-01 6.48E-01 7.13E-01 6.41E-01 5.21E-01 250 6.28E-01 7.28E-01 8.19E-01 7.38E-01 6.15E-01 Energy (MeV) . Delta range (mm) QGSP_BIC_EMY . Delta range (mm) FTFP_BERT . Delta range (mm) QGSP_BIC_EMZ . Delta range (mm) QGSP_BIC_AllHP . Delta range (mm) QGSP_BIC_HP_EMY . 5 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 −7.70E-03 10 4.40E-02 4.20E-02 4.50E-02 4.20E-02 4.40E-02 15 4.60E-02 4.20E-02 4.70E-02 4.20E-02 4.60E-02 20 4.20E-02 3.70E-02 4.50E-02 3.70E-02 4.20E-02 25 4.10E-02 3.60E-02 4.50E-02 3.60E-02 4.10E-02 30 3.60E-02 3.50E-02 4.20E-02 3.50E-02 3.70E-02 40 5.20E-02 5.20E-02 6.00E-02 5.10E-02 5.20E-02 50 6.00E-02 6.10E-02 7.00E-02 6.10E-02 6.10E-02 60 6.90E-02 7.30E-02 8.00E-02 7.00E-02 6.90E-02 70 8.00E-02 8.60E-02 9.90E-02 8.60E-02 8.30E-02 80 1.02E-01 1.12E-01 1.27E-01 1.16E-01 1.01E-01 90 1.24E-01 1.27E-01 1.49E-01 1.32E-01 1.21E-01 100 1.36E-01 1.54E-01 1.73E-01 1.53E-01 1.37E-01 110 1.55E-01 1.73E-01 2.01E-01 1.72E-01 1.50E-01 120 1.84E-01 1.94E-01 2.16E-01 1.93E-01 1.75E-01 130 2.53E-01 2.72E-01 2.99E-01 2.70E-01 2.49E-01 140 2.18E-01 2.35E-01 2.75E-01 2.48E-01 2.19E-01 150 2.02E-01 2.40E-01 2.79E-01 2.51E-01 2.12E-01 160 2.49E-01 2.95E-01 3.31E-01 2.85E-01 2.69E-01 170 2.86E-01 3.09E-01 3.62E-01 3.21E-01 2.75E-01 180 3.20E-01 3.53E-01 4.08E-01 3.68E-01 3.22E-01 190 3.86E-01 4.40E-01 4.77E-01 4.42E-01 3.99E-01 200 4.28E-01 5.14E-01 5.45E-01 4.86E-01 4.27E-01 210 4.54E-01 5.41E-01 5.82E-01 5.35E-01 4.65E-01 220 4.67E-01 5.46E-01 6.19E-01 5.60E-01 4.98E-01 230 5.26E-01 6.32E-01 7.01E-01 6.14E-01 5.29E-01 240 5.51E-01 6.48E-01 7.13E-01 6.41E-01 5.21E-01 250 6.28E-01 7.28E-01 8.19E-01 7.38E-01 6.15E-01 Open in new tab It was observed that at all energies, the difference between proton range and NIST data is smaller than the statistical uncertainty. For a better comparison, the least squares method was used. Table 3 presents the results from the least squares method for all physics lists. It is seen that this value is the minimum for QGSP_BIC_EMY, and therefore we proposed QGSP_BIC_EMY as a physics list for proton therapy applications. Table 3 The results of the least square method. Name of physics . Least squares . QGSP_BIC_EMY 2.258 QGSP_BERT_HP_EMY 2.565 QBBC 3.848 FTFP_BERT 3.038 QGSP_BIC_EMZ 3.757 QGSP_BIC_AllHP 3.028 QGSP_BIC_HP_EMY 2.266 Name of physics . Least squares . QGSP_BIC_EMY 2.258 QGSP_BERT_HP_EMY 2.565 QBBC 3.848 FTFP_BERT 3.038 QGSP_BIC_EMZ 3.757 QGSP_BIC_AllHP 3.028 QGSP_BIC_HP_EMY 2.266 Open in new tab Table 3 The results of the least square method. Name of physics . Least squares . QGSP_BIC_EMY 2.258 QGSP_BERT_HP_EMY 2.565 QBBC 3.848 FTFP_BERT 3.038 QGSP_BIC_EMZ 3.757 QGSP_BIC_AllHP 3.028 QGSP_BIC_HP_EMY 2.266 Name of physics . Least squares . QGSP_BIC_EMY 2.258 QGSP_BERT_HP_EMY 2.565 QBBC 3.848 FTFP_BERT 3.038 QGSP_BIC_EMZ 3.757 QGSP_BIC_AllHP 3.028 QGSP_BIC_HP_EMY 2.266 Open in new tab Ionization potential Table 4 shows the range for a 100-MeV proton pencil beam obtained by changing water ionization potential in comparison with data available in the NIST library. The range of proton beams is 77.18 mm in the energy of 100 MeV in the NIST. Table 4 Different values of the range obtained by changing the ionization potential of the environment. I (eV) . 70 . 71 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 80 . R80 (mm) 76.374 76.512 76.645 76.774 76.911 77.046 77.172 77.297 77.433 77.555 77.681 I (eV) . 70 . 71 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 80 . R80 (mm) 76.374 76.512 76.645 76.774 76.911 77.046 77.172 77.297 77.433 77.555 77.681 Open in new tab Table 4 Different values of the range obtained by changing the ionization potential of the environment. I (eV) . 70 . 71 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 80 . R80 (mm) 76.374 76.512 76.645 76.774 76.911 77.046 77.172 77.297 77.433 77.555 77.681 I (eV) . 70 . 71 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 80 . R80 (mm) 76.374 76.512 76.645 76.774 76.911 77.046 77.172 77.297 77.433 77.555 77.681 Open in new tab Figure 4 presents the changes in the obtained difference in range compared to the NIST library data by increasing water ionization potential. As observed in this figure, the proton range is heavily influenced by the ionization potential of the medium and significantly increases by increasing I from 70 to 80 eV. The red line in this diagram indicates that there is not any difference between the obtained results and the NIST data, suggesting a minimum difference in the ionization potential of 76 eV. The ionization potential of water was therefore determined 76 eV based on these results. Figure 4 Open in new tabDownload slide Delta range in terms of ionization potential of the medium. (Delta range is the difference between the simulation results with the NIST data.) Figure 4 Open in new tabDownload slide Delta range in terms of ionization potential of the medium. (Delta range is the difference between the simulation results with the NIST data.) Lateral dose profiles The lateral profile for the proton pencil beam at the depth corresponding to the entrance depth, Bragg peak depth, the proton range(16,22) and energies of 50, 70, 125, 150 and 200 MeV are shown in Figure 5a–c. Here, we present the results for the carbon element selectively with sample atomic number important in biology and dosimetry. It can be seen that the lateral scattering increases with increasing penetration depth. The slight changes in each of these graphs are due to changes in the medium and incident energy. Figure 5 Open in new tabDownload slide Lateral profile of deposited dose for a) 50-, b) 150- and c) 200-MeV proton pencil beams in three different depths of carbon. Figure 5 Open in new tabDownload slide Lateral profile of deposited dose for a) 50-, b) 150- and c) 200-MeV proton pencil beams in three different depths of carbon. Parametrizations Figure 6a–c shows the lateral dose profile for proton pencil beams at the intended depths and energies with fitted functions. The fitted functions are the Gaussian and the double-Gaussian function represented by Formulas (1) and (2). Figure 6 Open in new tabDownload slide Lateral half-profile of deposited dose for a) 50-, b) 150- and c) 200-MeV proton pencil beam in Bragg peak depth of carbon with fitted functions. Figure 6 Open in new tabDownload slide Lateral half-profile of deposited dose for a) 50-, b) 150- and c) 200-MeV proton pencil beam in Bragg peak depth of carbon with fitted functions. It is clear that changing each of the three parameters, namely, the medium, energy and depth, affects the lateral scattering. According to these diagrams, the double-Gaussian model has the highest approximation with our simulation data. In conclusion, this model can be used to describe the scattering of proton pencil beams in body tissue elements. FWHM and lateral penumbra analysis Figure 7 shows selectively the lateral profiles in the oxygen medium at the depths corresponding to Bragg peak positions for each energy. As shown in these diagrams, the lateral scattering increases at the depth corresponding to the Bragg peak position with increasing the energy. Figure 7 Open in new tabDownload slide The lateral dose profiles for the proton pencil beams at depths corresponding to Bragg peak positions at different energies. Figure 7 Open in new tabDownload slide The lateral dose profiles for the proton pencil beams at depths corresponding to Bragg peak positions at different energies. The amount of absorbed dose in the organs around the normal tissue increases with increasing the lateral scattering. From these curves, the values of FWHM and lateral penumbra (80–20%) are investigated at the depths corresponding to the Bragg peak positions for each beam energy. The results are shown in Figure 8a and b. According to the lateral dose curves, the values of FWHM and lateral penumbra (80–20%) were obtained at the depth corresponding to the Bragg peak position in each energy for all elements (Tables 5 and 6). Figure 8 Open in new tabDownload slide a) The FWHM values and b) The Penumbra (80–20%) of the lateral dose profiles as a function of energy for proton pencil beams at depths corresponding to Bragg peak positions. Figure 8 Open in new tabDownload slide a) The FWHM values and b) The Penumbra (80–20%) of the lateral dose profiles as a function of energy for proton pencil beams at depths corresponding to Bragg peak positions. DISCUSSION The present study was conducted in the first step to validate the GATE simulation code, investigate the range of proton beams and examine the role of different physics lists in improving the depth of the Bragg peak. At this stage, simulations were performed in a water phantom with clinically used energy of 5–250 MeV. In the next step, we examined the lateral dose profile by changing each of the three parameters, namely, the type of medium, incident energy and depth. Moreover, this study analyzed various parameters currently used to describe the lateral dose profile in proton therapy. The lateral dose profile resulted from the GATE simulation was fitted with two different models used to describe the lateral dose profile in the water phantom. It was shown that the simulation results were more consistent with the double-Gaussian model. As was mentioned earlier, the lateral scattering is often estimated by a single-Gaussian model in the current treatment planning systems. It is worth noting that deposited doses are stored in cubic cells. Regarding that the present study used 4000 voxels with a dimension of 0.1 mm to record the dose, the depth calculation accuracy was 0.1 mm at 80% of the maximum dose. According to Table 2, the obtained differences in the range compared to the NIST data are smaller than the statistical uncertainty in all energies. Moreover, according to Figure 3, the difference in the results of physics at higher energies is higher, as with changing the physics only the nuclear part changes and nuclear interactions have a higher cross-section or probability of occurrence at higher energies. The present study used statistical tests to compare the observed differences between the results obtained from every physics list and the NIST library data. The Mann–Whitney test suggested no significant differences in the ranges obtained from every physics list and the NIST library data (p = 0.831). Further analytical methods were also used to evaluate the obtained ranges with high accuracy. The least squares method used for the sake of a higher accuracy showed that QGSP_BIC_EMY physics presents the smallest difference compared to the NIST data. The QGSP_BIC_EMY was therefore proposed. A noteworthy point is how the maximum dose changes by increasing the penetration depth in the lateral dose profiles. The altitude in the lateral dose profile initially decreases with increasing depth, and this reduction slows down with further increases in depth until the trend reverses at a certain depth by starting to increase, reaching a maximum at a depth corresponding to the Bragg peak in the depth dose profile. This trend is more evident for smaller lateral cells used to calculate the lateral dose profile and for a higher beam energy. This behavior can be explained by the fact that the number of particles passing through the central cells decreases with increasing penetration depth due to multiple scattering and consequently lateral scattering, which reduces the absorbed energy. Moreover, increasing depth increases the stopping power, which rather compensates for the reduction in the absorbed energy caused by flux reductions. The energy reduction caused by the lateral scattering surpasses the increase in the stopping power up to a certain depth, and the total absorbed energy reduces. Afterwards, the increasing effect of the stopping power overcomes the lateral scattering and increases the absorbed energy. The relative absorbed energy can therefore be larger at the beginning of the particle path compared to the end regions depending on the size of the cells, when only the cells on the trajectory of the input beam are considered. The diagram of the depth dose profile, in which the lateral dimension of the cells is large enough, cannot therefore fully describe the relative absorbed energy and relative dose, and examining and evaluating the lateral scattering of the incident beam with the penetration depth is essential. A pencil beam algorithm is a common approach in clinical applications, which usually results in a satisfactory outcome in treatment planning. However, in sensitive situations (for example, small fields or large depths), a relatively broad component of the pencil beam dose can lead to an inaccurate estimate of the dose. Therefore, in situations where the simple single-Gaussian approximation is not enough, a more precise description of the lateral beam profile can improve the accuracy of the irradiation to the tumor. This idea is based on Pedroni et al., who proposed a summation of two Gaussian functions for describing the proton lateral beam profile(12). Mainly this halo beam is due to the secondary particles produced by nuclear interactions in a water phantom (for energetic protons) or from particles that are scattered in a large angle in the beamline components (for low-energy protons)(23). Table 5 FWHM values for each element in different energies. Energy (MeV) . FWHM for C (cm) . FWHM for H (cm) . FWHM for N (cm) . FWHM for O (cm) . 50 0.7402 0.7352 0.7388 0.7468 70 0.743 0.7261 0.754 0.763 125 0.8828 0.71 0.9063 0.9704 150 0.9957 0.702 1.0661 1.1397 200 1.3654 0.6915 1.4486 1.6216 Energy (MeV) . FWHM for C (cm) . FWHM for H (cm) . FWHM for N (cm) . FWHM for O (cm) . 50 0.7402 0.7352 0.7388 0.7468 70 0.743 0.7261 0.754 0.763 125 0.8828 0.71 0.9063 0.9704 150 0.9957 0.702 1.0661 1.1397 200 1.3654 0.6915 1.4486 1.6216 Open in new tab Table 5 FWHM values for each element in different energies. Energy (MeV) . FWHM for C (cm) . FWHM for H (cm) . FWHM for N (cm) . FWHM for O (cm) . 50 0.7402 0.7352 0.7388 0.7468 70 0.743 0.7261 0.754 0.763 125 0.8828 0.71 0.9063 0.9704 150 0.9957 0.702 1.0661 1.1397 200 1.3654 0.6915 1.4486 1.6216 Energy (MeV) . FWHM for C (cm) . FWHM for H (cm) . FWHM for N (cm) . FWHM for O (cm) . 50 0.7402 0.7352 0.7388 0.7468 70 0.743 0.7261 0.754 0.763 125 0.8828 0.71 0.9063 0.9704 150 0.9957 0.702 1.0661 1.1397 200 1.3654 0.6915 1.4486 1.6216 Open in new tab Table 6 Penumbra (80–20%) for each element in different energies. Energy (MeV) . Penumbra for C (cm) . Penumbra for H (cm) . Penumbra for N (cm) . Penumbra for O (cm) . 50 0.3398 0.3305 0.3342 0.3379 70 0.3350 0.3315 0.3420 0.3460 125 0.4162 0.3251 0.4382 0.4583 150 0.4749 0.3224 0.5040 0.5503 200 0.6620 0.3109 0.7104 0.8031 Energy (MeV) . Penumbra for C (cm) . Penumbra for H (cm) . Penumbra for N (cm) . Penumbra for O (cm) . 50 0.3398 0.3305 0.3342 0.3379 70 0.3350 0.3315 0.3420 0.3460 125 0.4162 0.3251 0.4382 0.4583 150 0.4749 0.3224 0.5040 0.5503 200 0.6620 0.3109 0.7104 0.8031 Open in new tab Table 6 Penumbra (80–20%) for each element in different energies. Energy (MeV) . Penumbra for C (cm) . Penumbra for H (cm) . Penumbra for N (cm) . Penumbra for O (cm) . 50 0.3398 0.3305 0.3342 0.3379 70 0.3350 0.3315 0.3420 0.3460 125 0.4162 0.3251 0.4382 0.4583 150 0.4749 0.3224 0.5040 0.5503 200 0.6620 0.3109 0.7104 0.8031 Energy (MeV) . Penumbra for C (cm) . Penumbra for H (cm) . Penumbra for N (cm) . Penumbra for O (cm) . 50 0.3398 0.3305 0.3342 0.3379 70 0.3350 0.3315 0.3420 0.3460 125 0.4162 0.3251 0.4382 0.4583 150 0.4749 0.3224 0.5040 0.5503 200 0.6620 0.3109 0.7104 0.8031 Open in new tab In a similar study by Schwaab et al.(13), they described the beam halos by adding a Gaussian function to a single-Gaussian model. In fact, their goal was validating the profile of proton and carbon ion beams with a double-Gaussian distribution. In the process of fitting, they introduced a simple single-Gaussian model (G1) with a greater and narrower height, which describes the primary particles, and a double-Gaussian model (G2) that is flatter and broader to describe the halo beam, which is caused by large-angle scattered particles or products of the nuclear interaction. Their measured profiles are modeled with the following function: $$\begin{align} d\left(E.x.{z}_{eq}\right)=&\;n\times \big[\left(1-W\right)\times{G}_1\left(x.{\sigma}_1\left({z}_{eq}.E\right)\right)\nonumber\\ &+\,W\times{G}_2\left(x.{\sigma}_2\left({z}_{eq}.E\right)\right)\big] \end{align}$$ (3) Their empirical studies showed that the ion beam lateral profile can be parametrized by summation of two Gaussian distributions. This model was proposed to describe the halo dose in the large penetration depth in the water due to the products of nuclear interactions and also to describe the initial profile of the beam in the air, which is the effect of large angular scattering in beam monitoring systems(12). The results of the present study confirmed their findings regarding the body tissue elements. Their study was conducted in a water medium. Therefore, the findings of this study can be generalized to the parameterization of the proton beams as a sum of two Gaussian distributions in the water medium to the body tissue elements. A similar study was conducted by Bellinzona et al. They simulated the dose profile of the CNAO beam with the FLUKA code and validated it with the data obtained in the CNAO, taking into account the different energies and depths. Thereafter, the best fit was obtained using various functions. Although, the best results were obtained using triple-Gaussian and double-Gaussian Lorentz–Cauchy functions with six parameters, the Gauss–Rutherford function, with only four parameters, also produced good results(14). These models were also used in this study, and their results on the Gaussian function were consistent with the findings of the present study. This study examined the previously published models, particularly a new parameterization, called double Gaussian. More Gaussian functions can be added and analyzed, which may increase the number of parameters and thus cause a significant increase in calculation time. However, according to studies, this approach generates good results in carbon therapy too(13). This function can be further investigated in future studies. If this model is confirmed with conditions very close to the real conditions, this model can be used in future treatment planning. Figure 7 illustrates the lateral dose profile of various incident energies for the proton pencil beam at the depth corresponding to the Bragg peak position. As it is clear in these diagrams, the lateral scattering at the depth corresponding to the maximum dose position increases with increasing energy. The importance of the amount of lateral scattering is due to the fact that the transverse compatibility of the incident beam with the geometry of the tumor affects it. The dose received by adjacent healthy tissues increases with increasing the lateral scattering. Using lateral dose curves, the FWHM and lateral penumbra values were obtained at the depth corresponding to the Bragg peak position (maximum dose), and the results are shown in Figure 8a and b. According to the diagrams, FWHM and lateral penumbra increase almost like a quadratic function with constants presented in these diagrams with increasing the energy of the proton beams in each element, except for hydrogen. For example, the FWHM value of 7.5 mm in 50 MeV increased to about 13.5 mm in 200 MeV. In the case of hydrogen, no particular trend was observed, which can be due to a very low hydrogen density. In 2014, Jia et al. performed these calculations on the brain tissue and achieved similar results. They calculated the FWHM and the lateral penumbra values at the depth corresponding to the Bragg peak position in a slab head phantom irradiated with proton beams at energy ranges of 50–135 MeV. Their results of FWHM and lateral penumbra also showed the behavior of a quadratic function with increasing energy. They also concluded that the FWHM in this energy range increased by six times(17). CONCLUSION The present study was first conducted to validate the GATE Monte Carlo simulation code and examined the depth dose profile of an ideal proton beam for therapeutic energies. 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TI - GATE MODELING OF LATERAL SCATTERING OF PROTON PENCIL BEAMS
JF - Radiation Protection Dosimetry
DO - 10.1093/rpd/ncaa015
DA - 2020-07-07
UR - https://www.deepdyve.com/lp/oxford-university-press/gate-modeling-of-lateral-scattering-of-proton-pencil-beams-QyZWKXOVx3
DP - DeepDyve
ER -