Simulation of distribution of radiation energy density in water balls

Vol.16 No.6NUCLEAR SCIENCE AND TECHNIQUESDecember 2005Simulation of distribution of radiation energydensity in water ballsTANG Shi-Biao'*, MA Qing-Li, YIN Ze-Jie', TANG Yu', HUANG Huan', RAO Nan-Xia', ZHU Da-Ming2( ' Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;2 Department of Physics, University of Missouri-Kansas City, Kansas City, Missouri 64110, USA)Abstract The distribution of energy deposition density in radiate region and its surrounding areas from γy-rays wassimulated and analyzed for a water-ball model with Geant4 package ( Geant4.7.0,2005 ) developed by CERN (theCenter of European Research of Nucleus). The results show that the distribution depends strongly on the collimat-ing condition of radiation beam. A well-collimated beam would reduce radiation effects on surrounding areas.Key words Water ball, Radiation energy density distribution, Energy deposition, Geant 4CLC numbers TN25, 0571.33IntroductionComputer simulationIn this work, we have carried out a numericalWe have used a Monte Carlo program, Geant 4,simulation on energy deposition from γ-rays generatedwhich is a toolkit designed initially for simulating nu-by ""Co sources under different collimating conditionsclear and high energy physics experiments, but in re-and hope to shed light on how to optimize the size of acent years has been applied in a wide range of subjectsradiation beam and its collimation.including radiation analysis, space and cosmic rayFig. 1 ilustrates a typical situation, where regionanalysis and, more recently, medical oncology analy-A (malignant tissue) represents the area that need to besis and evaluations. The toolkit is based on the ob-radiated, region B represents the immediate surround-ject oriented technology. It provides transparency forings of region A. The radiation passes through regionimplementation of various physics parameters.B before entering region A and it penetrates throughA set of models that describes the interaction ofregion B. In addition, the interaction of the radiationphotons and electrons with matters at low energies haswith atoms and molecules in region A could generatebeen implemented in the toolkit. The physical proc-secondary radiation effect in region B. In order toesses involved include photoelectric effect, Comptonminimize the radiation effect on region B, a number ofscattering, Raleigh effect, Bremsstrahlung and ioniza-factors need to be considered and adjusted.tion.2J A low energy limit for particle interaction cor-responding to the minimal energy within the validityrange of the models is denied. A higher threshold forSecondary radiation二==any specific application can be alternatively definedRadiationby user.B]Region BGeant 4 is supported under various operatingRegion Asystems. In our simulation, we used the one underLinux (Redhat8). The simulation was run on dedicatedFig.1 Effect of radiation on tssue.Pentium-IV personal computers.Supported by“Hundred people Plan Fund" of CAS* Corresponding author中国煤化工Received date: 2005-07-04MHCNMH G.NUCLEAR SCIENCE AND TECHNIQUESVol.163 Simulation methody-rays at these two different energies and at an aver-aged energy of 1.25 MeV. Our simulation shows thatThe radiation source used in the simulation isthe difference in the energy deposition for Y-rays at°0Co which emits y-rays with two dfferent energies atthese different energies is not significant. Thus in1.333 and 1.173 Mev.!4] Table 1 gives radiation char-the following we only display the results obtained foracteristics of °'Co. We do simulation by consideringγ-rays of 1.333MeV.Table 1 Radiation characteristic of 6°CoSymbolHalflife (a)Disintegration type and energy (MeV)Production method__γ60Co5.263(63)0.318(99.9%)1.173(99.86%)S9Co(n,r)1.491(0.1%).33399.98%)5Co(d,p)We assumed that the radiate region has a spheri-The first one is that the radiation source is a pointcal shape, thus the situation can be modeled as a wa-source and the radiated Y-ray is perfectly collimated,ter-ball with center region being the radiate part and(in this model we assume that the point source is athe other areas being the surrounding areas. The waterperfect point, so the Y-ray radiation from the source isball in the simulation was divided evenly into N shellsalso a perfect beeline) as shown in Fig.2(a). The sec-with each shell thickness to be (R- -RJ)IN, where R andond case is that the γ radiation source is a point source,R。are the radius of the water ball and the radiate re-but the radiated Y-ray is spread over an angle 0, andgion,respectively. In most cases, we choose N= 100.the angle θ satisfies sinθ RJL, where R。is the radiusThe energy deposition is integrated for each shell. Theof the malignant tissues, as shown in Fig.2(b).Theradius of the water ball was chosen to be 15 cm.third case is that radiated γY-ray remains to be perfectlycollimated, but the size of the source and the beam tobe a nonzero Rs as shown in Fig.2(c). A combinationr 1.33MleVof the second and the third cases allows one to resem-ble a case close to a realistic radiation source.(a)Case 1Results and discussions。。From the simulation, we got the energy deposited+HE中井(GeV) of different radial shell and the average energy↓R.density deposited (GeV/cm') in a given shell. For case1 and case 2, when calculating the density, since what(b)Case2we care is only the comparative tendency, we can ig-- FR←nore the constant 4π/3 and R'. Table 2 and Table 3display respectively the results of case 1 and case 2.From the values under the different ratio of e/80(where ε is energy density deposited in a given shelland &0 is the averaged energy density deposited in themalignant region) on the different radiate region size,↓↓↓(C) Case 3we can obtain that if the radiate region size increases,Fig.2 Various Y-ray source-water ball configurations.energy density deposited in a given shell falls offWe first focus on the r/-ray radiation from theslower and slower as the radius increases. For exam-source. We considered three simplest possible cases.ple, for case” 中国煤化工meter is 0.03cm,YHCNMHG.No.6TANG Shi-Biao et al : Simulation of distribution of radiation energy density in water balls349the value e/ &0 falls off to 1/10000 at the 0.93cm to the1/10000 at the 12cm to the center. So it means that thecenter of radiate region. But if the radiate region di-larger the radiate region size is, the more serious theameter is 0.3cm, the value c/&0 falls off to 1/100 at thedamage to the area surrounding radiate region is.1cm to the center of radiate region and reaches toTable 2 Simulation result in case 1 (R=15.0 cm)Malignant region radiusn_c/Ene/20 at 15cm1/10 .1/1001/10001/100000.015 cm10000.035 cm .0.1 cm0.3 cm0.93 cm~1/19160000.025 cm6000.062 cm0.152 cm0.47 cm .1.59 cm~1/7130000.03 cm5000.074 cm0.19 cm .0.58 cm1, 98 cm~1/4704000.0375 cm4000.091 cm .0.244 cm0.73 cm2.5 cm~1/2930000.05 cm3000.12 cm0.32 cm1.0 cm3.6 cm~1/1653400.075 cm2000.18 cm0.48 cm1.54 cm5.66 cm~ 1/689000.15 cm .0.35 cm0.95 cm12.15 cm~1/16600Table 3 Simulation result in case 2 (R=15.0 cm, source rays spread over an angle日)Malignant region radius 1_ε/soe/60 at 15cm1/101.0cm002.3 cm8.6 cm~ 1/300~1/3660.9 cm1002.16 cm7.75 cm~1/3790.8 cm1.87 cm6.7 cm~1/4870.7 cm1.65 cm5.85 cm~1/6170.6 cm1.43 cm4.9 cm~1/8190.5 cm1.18 cm4.03 cm~1/12001000 .1.1 cm3.9 cm .14.2 cm~1/14400.4 cm3.1 cm11.35 cm~1/18250.74 cm8.3 cm~1/33000.2 cm0.49 cm1.5 cm5.2 cm .~1/75000.26 cm0.75 cm2.4 cm8.9 cm~ 1/300003.95 cm<1/100000Fig.3 and Fig.4 display the radial distance of theferent curves correspond to different values of ratiogiven shell to the center of the ball(R) (it means rela-e/80. From the two figures, R goes up as R。increasestive energy density deposited) versus the radius of theand the relationship between the two variables is lin-radiate region (R) in the case 1 and case 2. The dif-ear.1412 E1/1000 ,1210 E10000宣110060.02 0.04 0.06 0.08 0.10 0.12 0.14 0.160.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Re (cm)Fig.3 Relationship between relative energy densityFig.4 Relationship between relative energy densitydeposited and radius of the malignant region in case 1.deposited中国煤化工on in case 2.TYHCNMH G ..350NUCLEAR SCIENCE AND TECHNIQUESVol.16In case 3, we must consider the source size (Rs).tween R and Rs. It shows that the effect of Rs on theTable 4 shows the simulation results if keeping R、energy density deposited is very small. From the fig-constant. Fig.5 displays the relationship between kure, we can see that if Rs increases ten times when theand Rc. Its shape is the same as the cases 1 and 2. Ta-value of ε/Eo is a constant, the variation of R is noble 5 shows the results if keeping Rc constant. Themore than 15%.!5]corresponding Fig.6 illustrates the relationship be-15.01413.51/100012.010.5e 9.18C7.5E100。.0 E10---.0 F.5 上0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50R。(Cm)Fig.5 Relationship between relative energy densityFig.6 Relationship between relative energy densitydeposited and radius of the malignant region in case 3.deposited and radius of the source size in case 3.Table 4 Simulation result in case 3 (R。is malignant region radius, R。is radiated source radius)RR。N_ε/&qe/&0 at 15cm1/101/1001/1000 .1/100001.0 cm0.01 cm1002.07 cm7.55 cm~1/3900.9 cm1.88 cm6.74 cm .~1/4800.8 cm001.65 cm5.85 cm .~ 1/6000.7 cm1.45 cm5.13 cm~1/7900.6 cm1.23 cm4.23 cm14.8 cm~1/10800.5 cm1.04 cm3.54 cm12.6 cm~1/14900.4 cm0.82 cm2.71 cm9.9 cm~1/23300.3 cm0.65 cm2.03 cm7.3 cm~1/41400.2 cm0.46 cm1.33 cm4.6 cm~1/94000.1 cm0.27 cm0.69 cm2.2 cm7.8 cm~1/39200Table 5 Simulation result in case 3 (considering the efect of R)ε/q)_0.50 cm1.19 cm4.04 cm14.2 cm .~1/11900.5 cm .0.45 cm1.14 cm3.84 cm13.6 cm~1/12700.40 cm1.12 cm3.79 cm .13.5 cm~1/13100.35 cm1.08 cm3.64 cm13.0 cm~1/13900.30 cm3.61 cm12.9 cm~1/14100.25 cm1.06 cm12.8 cm~1/14600.20 cm1.05 cm3.57 cm~1/15000.15 cm3.52 cm0.10 cm3.54 cm .12.7 cm0.05 cm3.53 cm12.5 cm二_1/1490中国煤化工THCNMHG.No.6TANG Shi-Biao et al : Simulation of distribution of radiation energy density in water balls351Conclusionsrealistic situation such as radiation protection and ra-diation therapy.The results presented in this paper show that en-Referencesergy deposition in unit volume, caused by a radiatedy-ray, decreases with the increase of distance of theAgostieli A, Allison J, Amako K, et al. Nucl Instr Meth,position to the center of radiate region. The larger the2003, A 506: 250radiate region is, the stronger the effects on the sur-Physics Reference Manual at the Geant 4. Availablerounding regions are. However, the effects will befrom: smaller when a well-collimated beam is used compar-Geant 4 User Guide, CERNing to a dispersed beam.American Institute of Physics, Particle physics booklet.Although the situation in which the numerical1994: 225simulation was conducted may be over-simplified,PAW-- -Physics Analysis Workstation The Completethese results probably provide a base for carrying outReference, Version 1.07, CERNelaborated simulations which are much more close to中国煤化工MHCNMH G.