THE mono-energetic hadron beam such as heavy-ions or

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1 Verification of the Dose Distributions with GEANT4 Simulation for Proton Therapy T.Aso, A.Kimura, S.Tanaka, H.Yoshida, N.Kanematsu, T.Sasaki, T.Akagi Abstract The GEANT4 based simulation of an irradiation system for the proton therapy has been developed for the verification of dose distributions. The simulation represents a treatment room with the beam irradiation system at the Hyogo Ion Beam Medical Center (HIBMC). The beam irradiation system consists of a lateral beam-spreading system and a range modulating system, so that the dose distribution is achieved in three dimensionally. The simulation was carried out for the proton beams at the isocentric gantry nozzle for the therapeutic energy of 15, 19, and 23 MeV, respectively. The simulated dose distributions are compared with measurements, where dose distributions are obtained using a water phantom at an isocenter, which simulate practical situations of the beam irradiation to the patients. The validation of the simulation was performed for the proton ranges in important materials at beam line and lateral uniformity of the irradiation field at an isocenter, respectively. Then, the dose distribution in simulation based on GEANT4 were verified with measurements for Bragg peak and spread out Bragg peak, respectively. The result of verification shows the depth-dose distributions in simulation are in good agreement with measurements. Index Terms GEANT4, Proton therapy, Dose distribution, HIBMC I. INTRODUCTION THE mono-energetic hadron beam such as heavy-ions or protons, stops at a certain depth in a substance and deposits a large portion of energy near the end of the range. The deposited energy forms a narrow dose peak known as the Bragg peak. This physical characteristics is suitable for the radio-therapeutic treatment of tumors, because it works as the sterilization of cells in the target volume with reducing injuries of healthy tissues at the entrance part of the irradiation path. At a hadron therapy facility, it is requested to develop simulation tools for designing the beam irradiation system and for proposing the treatment planning. Those works have been employed experimentally or analytically, so far [1], [2]. Using the reliable simulation tools for the hadron therapy, it will become possible to validate treatment planning and select the most effective one. However, for the use of a simulation in This work was partly supported by Core Research for Evaluational Science and Technology (CREST) of the Japan Science and Technology Corporation (JST). T.Aso is with the Toyama College of Maritime Technology, Japan. A.Kimura are with the Core Research for Evaluational Science and Technology (CREST), Japan. S.Tanaka are with the Ritsumeikan University, Japan. H.Yoshida is with the Naruto University of Education, Japan. N.Kanematsu is with the National Institute of Radiological Sciences, Japan. T.Sasaki is with the High Energy Accelerator Research Organization, Japan. T.Akagi is with the Hyogo Ion Beam Medical Center, Japan Wobbler Magnets Scatterer Secondary Main Ridge Filter Range Shifter Flatness Multi Leaf Collimator Range Compensator X ioscentre ~33 Distance from isocenter (mm) Fig. 1. A schematic layout of the beam delivery system (gantry nozzle) of the treatment room at HIBMC facility. For the measurement referred in this report, range shifter and range compensator were removed from the beam line. the clinical application, the simulation has to reproduce the dose distributions in three-dimensions with the best accuracy for ensuring the patient safety. For the verification of the simulated dose distribution to the measurements, the GEANT4 [3] based simulation of an irradiation system for the proton therapy has been developed. The simulation represents a treatment room including a beam irradiation system, at the Hyogo Ion Beam Medical Center (HIBMC) [4]. In this report, we describe a belief description of the developed simulation, and the comparisons of simulated dose distributions with measurements as well as the validation of the beam irradiation system. II. IRRADIATION SYSTEM FOR PROTON THERAPY The HIBMC was opened in 1 as the facility to provide both proton and carbon ion beam therapy. The synchrotron at HIBMC can accelerate protons up to 23 MeV and carbon ions up to 3 MeV/u. The energy of the therapeutic beam is currently fixed at 15, 19 and 23 MeV for protons, and 25 and 3 MeV/u for carbon ions. The beam is provided to five treatment rooms. A beam irradiation system, called nozzle, is placed at the end of each beam line. The dose distributions referred in this report, are taken at the isocentric gantry nozzle which is up to 3. m in length and typically 15 cm square maximum irradiation field for proton therapy. The schematic layout of nozzle is shown in Fig.1. The nozzle comprises a lateral beam-spreading system, beam monitors, a bar ridge filter, and a multi-leaf collimator. The lateral beamspreading system consists of a pair of wobbler (dipole) magnets and a scatterer. The wobbler magnets make a proton beam draw /4/$. (C) 4 IEEE

2 a circular trace, then the wobbled beam is scattered by passing a lead plate scatterer to produce a uniform irradiation field. The bar ridge filter is a range modulator and is used to spread out the Bragg peak (SOBP) in the depth-dose distribution. Therefore, the uniform physical dose area is obtained in the SOBP region three-dimensionally. The bar ridge filter made of aluminum and consists of 24 bars of which base distance is taken as 5 mm for the gantry nozzle. The height of ridges is about 4 cm and 6 cm for 9 cm width SOBP and 12 cm width SOBPs, respectively. The bar ridge filters were designed in the maximum radiation field for 15 MeV and 19 MeV proton beams. The dosimetry system consists of a water phantom and a ionization chamber. The phantom is placed so as the Bragg peak coincides with the isocenter for every therapeutic energy, so that the source-surface distance is fixed. Depth-dose profiles were measured by scanning the chamber in the phantom. III. SIMULATION SOFTWARE The simulation is developed based on the GEANT4 simulation toolkit. GEANT4 provides a comprehensive set of physics processes to model the behavior of particles and materials. It is designed to utilize those physics process models and to handle complex geometries. The final purpose of the simulation is not only to validate the treatment planning, but also to design a beam irradiation system according to the treatment planning. Therefore, each element of the beam irradiation system has to be modified easily in geometries and materials. Our simulation is designed to read basic configuration parameters from ASCII files, so that the configuration is easily changed by describing the elements in the files without recompiling. The complete components of the gantry nozzle with a water phantom have been implemented in the simulation. The water phantom was defined as a box of cm cm 5 cm and placed in the same way as measurements. However, only the dose in the centric area of 8 mm 8 mm perpendicular to the beam axis was encountered for the depth-dose distribution, where the equivalent area was covered by the ionization chamber in measurements. The depthdose distributions are then obtained for every 8 mm 8mm.5 mm volumes with respect to the beam axis. The materials on the beam line increase beam divergence, so that the material properties have to be defined precisely. The material properties are taken from the values in [5]. The density and mean excitation energy of water are assumed to be 1 g/cm 3 and 75 ev [5], [6], respectively. The hadron ionization process with low energy extension in GEANT4 is adopted for a proton, where the ionization energy loss is calculated by the Bethe-Bloch formula or electronic stopping power parameterization with the energy loss fluctuation model, according to the kinetic energy of a proton. Here, the kinetic energy which switches the calculation of energy loss is 2 MeV by default. The low energy extension provides alternative models extended down to lower energies than the standard ionization process in GEANT4. We chose a SRIM [8] parameterization up to the proton kinetic energy of 1 MeV, Energy Water Lead Aluminum (MeV) (mm) (mm) (mm) NIST GEANT4 NIST GEANT4 NIST GEANT TABLE I COMPARISON OF RANGE IN WATER, LEAD AND ALUMINUM. because the smooth conjunction to the Bethe-Bloch formula is obtained. For example, the discrepancy of the Bethe-Bloch formula and SRIM in water is less than.3% at 1 MeV, while about 2.6 % at 2 MeV. In the case of ICRU49, the discrepancy is about 13 % at 2 MeV. For electromagnetic processes, it is important to have a production threshold to suppress the generation of large numbers of soft electrons and gammas. In GEANT4, charged particles are tracked to the end of their ranges, so that the range is used to suppress the particle production. This is so-called the range cut. Since the energy of non-produced particles is transfered from the discrete process to the continuous process, the dose distribution depends on the range cut. The range cut is defined as 1 mm by default, but we set it as 15 µm. Since the doses are calculated for every.5 mm length in our simulation, the value of range cut represents about 3 % of our unit length in the dose calculation. For the hadronic interactions, LHEP PRECO HP is used for simulation, which includes a pre-equilibrium decay model for modeling the inelastic interactions nucleons, and available as one of Educated Guess Physics Lists [9]. IV. VALIDATION OF IRRADIATION SYSTEM A. Proton Range As the validation of the materials in the irradiation system, the ranges of proton are evaluated for the important materials in the irradiation system. In the simulation, range is obtained by switching off all the physics processes except for ionization process, and defined as average value of the depth to which a proton penetrates in the course of slowing down to rest. Here, the depth is defined along the initial direction of the primary proton. The range has been compared with the calculated value by the PSTAR program [7] using continuous-slowingdown approximation available from the National Institute of Standards and Technology (NIST). Table I shows the ranges in the simulation with the value of PSTAR for three important materials. The ranges in the simulation at every therapeutic beam energy agree well with PSTAR program within an accuracy of better than.1 % in water,.3 % in lead and.2 % in aluminum, respectively. B. Irradiation Field The irradiation system has been validated in the uniformity of the irradiation field at an isocenter by passing protons from /4/$. (C) 4 IEEE

3 Beam dispersion (mm) HIBMC 15MeV Geant4 15MeV HIBMC 19MeV Geant4 19MeV HIBMC 23MeV Geant4 23MeV Lead thickness (mm) Fig. 2. Standard deviation of the beam dispersion at an isocenter as a function of thickness of lead scatterer. just outside of a nozzle to the isocenter. The uniform irradiation field is achieved by using a lateral beam-spreading system which consists of a pair of wobbler magnets and scatterer. The beam spot size from the accelerator is derived from comparing the measurement with the simulation at an isocenter without beam-spreading system, where the parallel beam and Gaussian intensity distribution were assumed at the entrance of nozzle in the simulation. The beam spot sizes in standard deviation at the nozzle entrance are estimated as 11.4 mm, 11.1 mm, and 1.2 mm, for 15 MeV, 19 MeV, and 23 MeV beam energies, respectively, and used in the simulation. The beam dispersion from the accelerator is then enlarged by the lead scatterer. Fig.2 shows a beam dispersion at an isocenter as a function of the scatter thickness. The simulation reproduces the measured beam dispersions. An appropriate wobbling radius for the beam gives us a uniform dose distribution around the beam axis. The magnetic field of a pair of wobbler magnets is adjusted to fit a radius of circular trace at an isocenter in the measurement. A set of corresponding magnetic fields is randomly changed for each one of primary protons in the simulation. Fig.3 shows the uniformity of the lateral irradiation at an isocenter as a representative example. The combination of 2.5 mm thickness lead scatterer and wobbling magnets which gives 99 mm wobbling radius for 19 MeV proton beam realize 15 cm diameter field with ±2% uniformity in the simulation, which is equivalent to the requirement in the treatments. V. RESULTS ON DOSE DISTRIBUTION A. Bragg Peak Distribution The dose distributions of a proton beam in the water phantom are compared with measurements, using validated irradiation system without range modulating system. The comparison of simulated and measured distributions are done by normalizing both distributions at the peak, then the measured depth-dose profile is adjusted to fit the simulated profile in the measured region. The fitting function is defined by f mes (z) =bd mes (z+a) with a simple linear interpolation of measured data points. Here ) 2 Relative proton flux (/cm ) 2 Relative proton flux (/cm (a) Horizontal position (mm) (b) Vertical position (mm) Fig. 3. Relative proton flux at an isocenter for the beam energy of 19 MeV, as a function of horizontal position (a) and vertical position (b), where wobbling radius and thickness of lead scatterer are chosen as 99 mm and 2.5 mm, respectively. D mes (z) represents a measured dose at a depth z, and fitting parameters a and b represent displacement and normalization factors, respectively. The depth-dose distributions of a proton beam are shown in Fig.4 for the incident energy of 15 MeV, 19 MeV, and 23 MeV, respectively. The obtained displacement and normalization factors are about 1-2 mm short and 3-4 % low, respectively. The current simulation uses only theoretically calculated beam energies and estimated beam spot size with parallel beam approximation at the nozzle entrance. The result of simulation will be possibly improved by using more precise beam parameters characterized by energy, energy spread, spot size, intensity profile, angular spread, and so on. It is strongly desirable to include beam parameters which are directly measured by experiments. The shape of depth-dose distribution are similar to the measurements. At 23 MeV beam, the lower dose region is observed around 15 mm depth, but the difference to the measurement is about 2-3 %. The depth-dose distributions agree well with the measurements within 4 % accuracy. B. Spread Out Bragg Peak Distribution The ridge filters to produce 9 cm and 12 cm width SOBP for 15 MeV and 19 MeV beams were used for the comparison. Depth-dose distributions of SOBP are shown in Fig.5. The same normalization procedure for Bragg peak distribution is applied. The distribution is similar to the measurements. Especially for 12 cm width SOBP distribution, the small bump is observed around the raising edge of SOBP region in the measurements. The possible reason of the bump is thought to be a fan beam effect due to the imping angle of the beam on the bar ridge filter which originates from the sweep angle of wobbling magnets and the relative height of ridges. This small bump was /4/$. (C) 4 IEEE

4 not predictable at the analytical calculation with the parallel beam approximation in [4]. On the other hand, simulation can reproduce the bump successively. The shapes of SOBP are similar to the measurements. The difference is about 4 % at maximum. VI. CONCLUSION The GEANT4 based simulation for proton therapy at HIBMC has been developed. The validation of beam irradiation system has been confirmed by using the simulator. The dose distributions of the simulation agreed very well with the measured dose distributions for both of Bragg peak and SOBP. The results of simulation were obtained from minimum information of beam profile, so that any additional information will make simulation improved from the hadron therapy facility. From these verification studies, the ability of simulation for the proton therapy has been ensured. REFERENCES [1] Koehlar A M et al., Range modulators for protons and heavy ions, Nucl. Instr. and Meth., 131,1975, pp [2] Petti P L et al., Design of beam-modulating devices for charged-particle therapy, Med. Phys., 18,1991,pp [3] S.Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P.Arce et al., GEANT4-a simulation toolkit, Nucl. Instr. and Meth., A56,3,pp [4] T. Akagi, A. Higashi, H. Tsuggami, H. Sakamoto, Y. Masuda, and Y. Hishikawa, Ridge filter design for proton therapy at Hyogo Ion Beam Medical Center, Phys. Med. Biol., 48,3,N31-N312. [5] Particle Data Group, Review of particle physics, Eur.Phys.J.C 3, 1794,1998. [6] International Commissions on Radiation Units and Measurements, Stopping powers and ranges for protons and alpha particles, ICRU Report 49,1993. [7] M.J. Berger, J.S.Coursey, and M.A. Zucker ( Apr.). Stopping- Power and Range Tables for Protons. PSTAR. [Online]. Available [8] J.F. Ziegler, J.P. Biersack, and U. Littmark, The stopping and range of ions in solid, Pargamon Press, New York, 1985 ( new edition in 3). [9] GEANT4 hadronic physics working group(hpw) (4 Sep.). Educated Guess Physics Lists for GEANT4 Hadronic Physics. LHEP PRECO HP. [Online]. Available hpw/ghad/homepage/index.html 1 1 (a) 15 MeV (b) 19 MeV (c) 23 MeV Fig. 4. Depth-dose distributions of proton beam for measurements (points) and simulations (histograms), where a horizontal and vertical axis shows the depth in water and the relative dose, respectively. The fitting parameters a and b are 1.2 ±.8 and.96 ±.1 for 15 MeV, 1.22 ±.1 and.97 ±.1 for 19 MeV, 1.86 ±.12 and.97 ±.1 for 23 MeV, respectively /4/$. (C) 4 IEEE

5 1 1 8 (a) 15 MeV SOBP (b) 19 MeV SOBP (a) 15 MeV SOBP (b) 19 MeV SOBP Fig. 5. Depth-dose distributions of 9 cm width and 12 cm width SOBP for measurements (points) and simulations (histograms), where a horizontal and vertical axis shows the depth in water and the relative dose, respectively. The fitting parameters a and b are.5 ±.36 and 1. ±.2 for 15 MeV, 1.15±.5 and.99±.2 for 19 MeV at 9 cm width SOBP,.7±.35 and.99 ±.2 for 15 MeV, 1.3 ±.51 and.99 ±.2 for 19 MeV at 12 cm width SOBP, respectively /4/$. (C) 4 IEEE