Monte Carlo Study on 6MV Photon Beams of a Cyberknife Stereotactic
11111Xiaoqing DONG Wenyun LUO Kun YUE Chuanshan WANG Shiqing ZHOU Fuxing
122PAN Enmin WANG Chaozhuang WANG 1 Shanghai Applied Radiation Institute, Shanghai University, Shanghai 200444, China 2 Department of Radiation Therapy, Hua Shan Hospital Affiliated to School of Shanghai Fu Dan
China University, Shanghai 201206？
Abstract: In this paper, the different-field dosimetry for a Cyberknife system is studied with the PENELOPE Monte Carlo code. The absolute doses for circular collimator sizes of 10 to 60 mm were also calculated. The percent depth-dose curves for circular collimator sizes of 30mm, 40mm, 50mm, 60 mm were evaluated by Monte Carlo simulations. The agreement in the dose distributions in water phantom between the calculation and measurement was within 3.0% for various collimator sizes. Additionally, the influence of flattening filter on the X-ray energy has been discussed as well.
20The TPR for the Cyberknife system was 0.632, which was slightly smaller than the measured 10
one. MC simulations were effective and feasible for the Cyberknife system.
Key words: Monte Carlo, PENELOPE, Cyberknife, Beam quality, PDD
The Cyberknife stereotactic radiosurgery system was researched cooperatively by
Accuray Inc. and the college of Stanford . It utilizes a compact 6 MV photon beam
linear accelerator installed on a robotic arm, and has the following advantages: advanced image guidance technology, great flexibility in targeting and accuracy in
[2-3]tracking patient and target positions during treatment , hence highly conformal
dose to the target was provided by the Cyberknife system while sparing nearby
critical structures . The Cyberknife system employs a stable primary collimator system and twelve final circular collimators to form beams of 5-60mm nominal diameter de?ned at 80 cm source-to-surface distance (SSD) from the upstream surface of the target. It can afford single or multiple beams to treat patients and
achieve sub-mm accuracy, so it is used to treat pathological changes in complex
patient geometries such as head, lung and neck.
Monte Carlo (MC) technique is a random sampling technique. It had high accuracy and can solve complex physical and mathematical problems？particularly
those involving multiple independent variables where more conventional numerical
methods would demand formidable amounts of memory and computer time. Due to
it directly scores the absorbed energy in the unit mass, it can calculate accurate dose. Radiation transport and especially dose distributions have been extensively studied
[6-9]by application of the MC technique in radiotherapy clinic . Monte Carlo codes in
common use include MCNP , EGS4 , Geant4 , PENELOPE , etc.
In this work, MC simulations were used to investigate different-field dosimetry for the Cyberknife system. The accurate of MC model was validated by comparing the simulation results with the clinical measurement. The percent depth dose (PDD) for the 30-60mm collimators (at a source-to-surface distance of 80cm) were calculated, and compared with the values measured with a diode detector. The beam quality of Cyberknife system was also calculated and compared with the measured one. Meanwhile, the influence of flattening filter on the X-ray energy has been discussed as well.
Fig.1. Sketch map of the treatment head used in the PENELOPE simulations for the Cyberknife system. The
phase space scoring plane is taken upper second collimator.
2. Materials and method
The MC code PENELOPE-2006(F.Salvat) which is compiled with FORTRAN 77
has been adopted . The transportation of electron, positron and photon with the energy range of 100eV–1GeV in arbitrary materials can be simulated by this MC
code. A schematic of the treatment head of the Cyberknife system is shown in Fig.1.
The geometry and the materials used in the simulation are based on the speci?cations
of the linear accelerator treatment head. For this study, the electron incident energy is
6.0 MeV of monoenergetic beam. The upper surface of a water phantom is placed at 80 cm SSD from the upstream surface of the target. The phase-space plane is taken on top of the second collimators. The phase-space information included the charge, energy, position, angle and weight of particles crossing the phase-space plane. The stored phase-space files were used repeatedly as inputs to each secondary collimator. The second collimator and the water phantom were modeled to calculate PDDs.
For ionizing radiation in radiation therapy, many parameters are dependent on the
radiation energy. The beam quality is described as the transmission ability of the ionizing radiation. For the 6-MV Cyberknife, the beam quality is specified in terms of
20the TPR beam quality index (IAEA TRS-398) . 10
The TPR is defined as follows:
DQ (1) TPR;DQref
where D is the dose in a phantom at arbitrary point Qon the beam central axis and Q
D is the dose in a phantom at a reference depth z(typically 5 or 10 cm) on the Qrefref
beam central axis .
20The TPR is defined as follows: 10
TPR2020TPR; (2) 10TPR10
where TPR and TPRare the TPR at depths of 20cm and 10cm in water phantom, 2010
respectively, under the condition of the same distance from the target to the detector. TPR and TPR were simulated at SDD=80cm (the source–detector distance) from 2010
the upstream surface of the target. MC calculation was performed under identical
6conditions to those of measurement. A total of 2×10 electron histories incident on the
target were simulated about 10mm, 20mm, 30mm, 40mm, 50mm and 60mm circular collimators.
The sample program PENMAIN of 2006 PENELOPE is employed. The main program controls the evolution of the simulated tracks and keeps score of the relevant quantities. All the interaction events in a photon history are simulated in chronological succession. The simulation of electron and positron transport is
performed by means of a mixed procedure: hard interactions are simulated in detail, while soft interactions are described by means of multiple-scattering approaches. The basic idea of splitting and interaction forcing were employed in the simulation, while Russian roulette was not. This procedure ensures reliable simulation results,
while saving simulation CPU time .
The simulation parameters are showed by Table1.
Table1 Simulation parameters of Penelope
parameter For all material
3 1.0eE(γ)(eV) abs4-+ 1.0eE( e/e)(eV) abs
4 1eW(eV) cc3 1eW(eV) cr
A 6 MV photon beam from a Cyberknife system was provided by the department of Radiation Oncology of HUA SHAN Hospital Affiliated to FU DAN University in this study. All measurements for the Cyberknife system were performed in a motorized water phantom (MP3, PTW, Freiburg, Germany) for the whole set of system collimators for depths ranging from 0cm up to 30cm at isocentric setup. The
2PDD-curves were measured with a PTW T60008 shielded diode detector (1 mm
cross section and 2.5 µm thickness of active layer) for 30mm, 40mm, 50mm and 60mm circular collimators. The detector was positioned at isocentric setup along
203vertical direction, i.e. SSD = 80 cm. TPR was measured with a waterproof 0.6cm 10
Farmer ionization chamber (TW30013, PTW, Freiburg, Germany) placed at d1=10cm and d2=20cm in water, SDD= 80cm, for the largest, 60mm collimator. 3. RESULTS AND DISCUSSION
0.8 60mm 50mm0.7 40mm0.6 30mm 20mm0.5 10mm
Fig.2 Monte Carlo calculated absolute dose in water phantom for 10, 20, 30, 40, 50 and 60 mm circular
collimators of a 6 MV photon beam from a Cyberknife system.
Fig.2 shows the MC calculated absolute dose for 10, 20, 30, 40, 50 and 60mm circular collimators of a 6MV photon beam in a Cyberknife system (SSD=80 cm). The result showed that the dose in water phantom decreases with the size of field. According to the size of tumor, medical physicists can choice different size of filed in clinic.
The flattening filter was adopted to improve the X-ray energy. The flattening filter can strain more low energy than high energy. The mean energy of X-ray after the
flattening filter was higher than before . Therefore, the skin can be prevented from
the extravagant dose caused by the transmitted low-energy X-ray. The energy distribution of transmitted photons is shown in Fig.3. The mean energy of X-ray from Cyberknife is 1.46MeV. Compared with the mean energy (1.55MeV) of X-ray that
 Yamamoto et al calculated for their Cyberknife machine, the result was slightly lower. The discrepancy is primarily due to the fact that the size of aluminum filter in our simulations was thinner than that in Yamamoto’s simulation. Compared with the
 mean energy (1.72MeV) of X-ray that Jun Deng et al calculated for their
Cyberknife machine, the result was slightly lower. The discrepancy is primarily due to the fact that the material used in this research (aluminum) was different from that in Jun Deng’s simulation (lead). In conclusion, thickness and materials of the flattening filter affect the X-ray energy spectrum. So it is significant to take the size and materials of flattening filter under consideration during the design of accelerator.
-35.0x10 probability density
probability density (1/Mev)-31.0x10
Fig.3 The energy distribution of 6 MV X-ray from Cyberknife.
In clinic, what the oncologist considered is target dose rather than the energy. The quality assurance of treatment can be influenced by the beam quality. The
20radiation energy is expressed as the beam quality which is represented by TPR 10
mentioned above. The beam quality of Cyberknife is 0.632-0.644. Compared with
20the measured TPR(0.640), the calculated one (0.632) was slightly lower. The 10
accuracy of the simulated beam quality was validated by the agreement within 1.2% between the MC calculated and measured. Due to the X-ray energy has influence on therapeutic effect, it is important to verify the energy of the accelerator frequently.
Fig.4 presents the comparisons between measured and MC calculated percent depth-dose curves for 30, 40, 50 and 60 mm circular collimators from the Cyberknife system. Each measurement of depth-dose curve was taken at a depth of 1.5cm on the beam central axis. The errors between calculated PDD-curves and the measurements were under 3% in all collimators. The calculated depth of maximum dose (d=1.4cm) was slightly smaller than the measured one (d=1.5cm). This result maxmax
accorded with the fact that the discrepancy of beam penetrability between experimental data and the value stipulated by national standard should not exceed
3mm . The main cause of the result was due to the low mean energy of X-ray. Fig.2 shows that the surface absorbed doses were less than 47 percent for all of field in the center of axis in the buildup region. This result can meet the requirement of the national standard, which the surface absorbed dose in the center of axis should be less than 60 percent of the maximum absorbed dose .
110110100100909060mm circular collimator,SSD=80cm50mm circular collimator,SSD=80cm80807070 measure60 measure60 MC MC5050PDD (%)PDD (%)404030302020101000051015202530051015202530Depth (cm)Depth (cm)
110110100100909040mm circular collimator,SSD=80cm30mm circular collimator,SSD=80cm80807070 measure measure60 MC60 MC5050PDD (%)PDD (%)404030302020101000051015202530051015202530Depth (cm)Depth (cm)
Fig.4 Comparison of measured and Monte Carlo calculated percent depth-dose curves for 30, 40, 50 and 60 mm circular collimators for the Cyberknife system.
The geometrical dummy of Cyberknife treatment head can simulate dose distribution factually. It has been shown that the agreement in the dose distributions in water phantom between the calculation and measurement was within 3.0% for various collimator sizes, which satisfied an accuracy of about 5% in dose delivery by
20[20, 21]radiotherapy . The calculated TPR was slightly lower. These results 10
demonstrated the efficiency and feasibility of our simulations. MC simulation is an extremely powerful tool in modern radiotherapy.
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