Photon Beam Fluence and Energy at the Phantom Surface as a ...

Bulg. J. Phys. 45 (2018) 54–66

Photon Beam Fluence and Energy at the Phantom Surface as a Function of Primary Electron Energy: Monte Carlo Study Using BEAMnrc Code, DOSXYZnrc and BEAMDP Code M. Bencheikh, A. Maghnouj, J. Tajmouati LISTA Laboratory, Physics Department, Faculty of Sciences Dhar El-Mahraz, University of Sidi Mohamed Ben Abdellah, Fez, Morocco Received 18 September 2017 Abstract. The purpose of this study is to provide detailed characteristics of incident photon beams for different primary electron energy for the field size of 10 × 10 cm2 in terms of the photon fluence profile, energy photon fluence profile, and energy photon distribution, The method used in this study was the Monte Carlo calculation method, it is considered to be the most accurate method for dose calculation in radiotherapy. The Monte Carlo codes used were the BEAMnrc code to simulate the 6 MV photon beam produced by Varian Clinac 2100 and photon transport, DOSXYZnrc code to simulate the absorbed dose in a water phantom, and the BEAMDP for the photon beam characteristics at the surface water phantom. We have calculated the percentage depth dose (PDDs) for the 10 × 10 cm2 field size and the calculated PDDs was compared to the measured PDD, and the gamma index was determined as a function of depth in the phantom, the gamma index criterions used was 3% for dose difference and 3 mm for distance to agreement. The acceptance criterion was more than 95% and the statistical uncertainty was 1%. The photon beam characteristic maximum increased in a linear manner as a function of the primary electron energy. The percentage of the beam characteristic maximum was determined relative to the primary electron energy of 6.1 MeV. For example, for a primary electron energy of 6.7 MeV, the percentage of the photon fluence maximum was 23.22% of the photon fluence maximum at 6.1 MeV, the percentage of the photon energy fluence maximum was 32.69% of the photon energy fluence maximum at 6.1 MeV, and the percentage of the photon energy distribution maximum was 19.39% of the photon energy distribution maximum at 6.1 MeV. Our study can be useful to improve photon beam dosimetry and radiotherapy quality. PACS codes: 87.50.cm, 87.10.Rt, 87.50.st

54

c 2018 Heron Press Ltd. 1310–0157

Photon Beam Fluence and Energy at the Phantom Surface as a Function of... 1

Introduction

Medical linear accelerators (Linac) are widely used in modern radiotherapy, due to their flexibility and their high therapeutic reliability. The photon beam is produced by energetic electrons striking a target generally constructed of tungsten due to its high atomic number to facilitate the production of photons by bremsstrahlung [1-3]. In this study, the calculation method was the Monte Carlo method; the Monte Carlo methods have been used extensively in medical physics for modeling linear accelerators and for radiation therapy calculations. The Monte Carlo methods used are considered the most accurate method for predicting dose distributions for treatment-planning purposes [8-31]. Several possible approaches are described and discussed in detail in previous publications. One approach of a source model is to characterize the beam analytically, as described by Jiang et al. [45], Another approach is to perform complete Monte Carlo simulations of the radiation transport through the accelerator head [38-44]. In this study, the Monte Carlo codes used were the BEAMnrc to simulate the linac head; this code provides the phase space (PS) files [33]; the BEAMDP was used to analyze the phase space files (PSF) for determining the photon beam characterization at the water phantom surface. The DOSXYZnrc was used to simulate the photon beam transport in the water phantom and to calculate the dose within the water phantom [34]. The STATEDOSE code to read and to analyze .3ddose files output of DOSXYZnrc and to make the necessary operations on dose calculation distribution in the phantom including the dose normalization to maximum dose [47]. The geometry Monte Carlo of 6 MV photon beam produced by Varian Clinac 2100 was built with BEAMnrc based on manufacturer-provided information (Varian Medical System); the field size was 10 × 10 cm2 and the distance source surface (SSD) was 100 cm. The physical process was modelled according to EGSnrc code, wherein we have simulated the transport of radiation as realistically as possible [35]. The PSF was generated by the BEAMnrc code that contains the necessary data (position, momentum, energy, and charge) for all particles traversing the phase space scoring plane. The PSF were used in BEAMDP code, in order to analyze the PSF data in terms of photon fluence profile, photon energy fluence profile, and photon energy fluence distribution. The PS plane was at the water phantom surface (on Z axis z = 100 cm). Based on the PSF, the photon beam characterization was analyzed, the primary electron energy varied from 6.1 to 6.7 MeV with 0.2 MeV step. This study represents an investigation of the photon beam characteristic sensitivity to primary electron energy for a purpose to contribute in the linac dosimetry improvement and in the electron source above the target refinement. The measured percentage depth dose (PDD) was performed for Varian Clinac 2100 linear accelerator, the beam energy is 6 MV for the open field size of

55

M. Bencheikh, A. Maghnouj, J. Tajmouati 10 × 10 cm2 , and the SSD is 100 cm. All the reference PDD measurements were performed using a motorized scanning system in a PTW. The simulation validation of Varian Clinac 2100 was performed using the gamma index method as a technique for the quantitative evaluation of dose distribution comparison as Low et al. [20,46]. The gamma index criterions were choose as used in the work of Palta et al. [4] and they set to allow the dose difference (DD) and distance to agreement (DTA) of 3% and 3 mm respectively. The gamma index acceptance rate was almost 99% for percentage depth dose (PDD), and almost 98% for beam dose profiles, thus, the Varian Clinac 2100 Monte Carlo geometry was validated according the tolerance limit recommended by TRS430 [5] and in IAEA-TECDOC-1583 [6]. 2

Materials and Methods

agreement (DTA) of 3% and 3mm respectively. The gamma index acceptance rate was almost 99% for percentage depth dose (PDD), and almost 98% for beam dose profiles, thus, the 2.1 Monte CarloMonte simulation validation Varian Clinac 2100 Carlo geometry was validated according the tolerance limit recommended by TRS430 [5] and in IAEA-TECDOC-1583 [6].

For Monte Carlo simulation validation of 6 MV photon beam produced by Var-

Materials and2100, methods: ian Clinac the gamma index values, which were ≤ 1, defined the agree-

ment between the measured and the calculated dose distribution along the depth I. Monte Carlo simulation validation: in the water phantom, and the gamma index acceptance rate was determined. For Monte Carlo simulation validation of 6 MV photon beam produced by Varian Figures 1 and 2 show the PDD distribution comparison and gamma index evalClinac 2100, The gamma index values which were ≤1 defined the agreement between a uation, and dose profile comparison and gamma index evaluation, respectively measured and calculated dose distribution along the depth in the water phantom and the for the field size of 10 × 10 cm2 , the photon beam energy of 6 MV and SSD of gamma index acceptance rate was determined.

100 cm.

The figure 3, and 4 shown the PDD distribution comparison and gamma index evaluation, and dose profile comparison and gamma index evaluation respectively for the field size of 10×10 cm2, the photon beam energy of 6 MV and SSD of 100 cm. Calculated PDD

Gamma index 10 9 8 7 6 5 4 3 2 1 0

PDD (%)

100 80 60 40 20 0 0

50

100

150

200

250

300

Gamma index

Measured PDD 120

350

Depth (mm) 1: Measured calculated and gamma as a function of depth FigureFigure 1. Measured PDD, PDD, calculated PDD,PDD, and gamma indexindex as a function of depth on on the beam central axis in the water phantom. The 6 MV photon beam produced by the beam central axis in the water phantom. The 6 MV photon beam produced by Varian 2 Clinac size cmSSD andwas the SSD ClinacVarian 2100, the field2100, size the wasfield 10 × 10was cm210×10 and the 100 was cm. 100 cm. The gamma index acceptance rate was 99 % for the criteria (3%/3mm) for the PDD 56 distribution; in the next, the Monte Carlo simulation was validated for the dose profiles at a depth of maximum dose (Dmax) and at a depth of 10 cm, the field size was 10×10 cm2.

Photon Beam Fluence and Energy at the Phantom Surface as a Function of...

Gamma index

Dose profile (%)

100 80 60 40 20 -100

-50

0

50

Off-axis distance (mm)

100

150

10 9 8 7 6 5 4 3 2 1 0

100 Dose profile (%)

10 9 8 7 6 5 4 3 2 1 0

0 -150

Measured dose profile Calculated dose Profile Gamma index 120

B

Gamma index

Measured dose profile Calculated dose profile Gamma index 120

A

80 60 40 20

0 -150

-100

-50

0

50

100

150

Off-axis distance (mm)

Figure 2. 2: Measured index as as a function of Measured dose doseprofile, profile,calculated calculateddose doseprofile, profile,and andgamma gamma index a function off axis distance at a depth of Dmax (A) and a depth of 10 cm (B) on the beam central axis in of off axis distance at: a depth of Dmax (A); and a depth of 10 cm (B) on the beam central the water The 6 MV produced by Varianby Clinac 2100, the 2100, field size axis in thephantom. water phantom. Thephoton 6 MVbeam photon beam produced Varian Clinac the was 10×10 cm210 and field size was × the 10 SSD cm2 was and 100 the cm. SSD was 100 cm. The gamma index passing rate was found for the criteria (3%, 3mm) at 97 % for the dose profile distribution at a depth ofrate Dmax % for dose profile distribution The gamma index acceptance wasand9998,62 % for thethe criteria (3%/3mm) for at thea depth of 10 cm, thus the Varian Clinac 2100 Monte Carlo simulation was validated with PDD distribution; in the next, the Monte Carlo simulation was validated for the accuracy and as realistically as possible. Our results revealed that the PDDs and beam profiles dose profiles at a depth of maximum dose (Dmax ) and at a depth of 10 cm, the agreed by almost 99% and 97% respectively and within the tolerance limit recommended by field size was 10 × 10 cm2 . TRS430 [5] and in IAEA-TECDOC-1583 [6]. The gamma index found shown the good The gamma passing in rate was found the criteria mm) at 97% calculation andindex more developed comparison withfor previous study as (3%, it was 3done by Kadman et al.the [7]. dose profile distribution at a depth of Dmax and 98,62% for the dose for

profile distribution at a depth of 10 cm, thus the Varian Clinac 2100 Monte Carlo For the validated Monte Carlo simulation, the primary electron source above the target simulation was validated with accuracy and as realistically as possible. Our was elliptical form and it had the Gaussian spread. Its characterizations were X and Y results revealed that the PDDs and beam profiles agreed by almost 99% and coordinates equal to 1,4 mm, the mean angle spread of primary electrons was 1° and the 97%, within the tolerance limit recommended by TRS430 [5] electronrespectively, source energyand was 6,52 MeV. and in IAEA-TECDOC-1583 [6]. The gamma index found marked a good and II. developed Primary electron assumptions: more calculation in comparison with previous study as it was done by Kadman al. [7]. Theetinitial electron energy is not clearly provided by the manufacturer and varies among of theMonte same model 24]. Based on the primary For thelinacs validated Carlo [17-21, simulation, the primary electronelectron sourceenergy above was the validated above, the electron beam energy was selected surrounding the energy validated of target was elliptical form and it had the Gaussian spread. Its characterizations 6.52 MeV. The Monte Carlo calculation was performed for a monodirectional electron point were X- and Y-coordinates equal to 1.4 mm, the mean angle spread of primary source uponwas the 1target electronsource energiesenergy varied was from 6.52 6,1 toMeV. 6,7 MeV with 0,2 MeV ◦ electrons andand thethe electron

step and the PDD were calculated, the results of measurements and calculations were compared to validated within gamma index acceptance rate tolerance of 95% . The gamma 2.2 Primary electron assumptions index technique was used for the quantitative evaluation for comparing the measured and calculated PDDs, the acceptance gamma index criterions were 3% for the dose deviation The electron energy is not clearly provided by the manufacturer and varies (DD)initial and 3 mm for distance to agreement (DTA).

among linacs of the same model [17-21,24]. Based on the primary electron enIII. validated PDD validation: ergy above, the electron beam energy was selected surrounding the energy validated of 6.52 MeV. The Monte Carlo calculation was performed for a monodirectional electron point source upon the target and the electron energies 4 varied from 6.1 to 6.7 MeV with 0.2 MeV step, and the PDD were calculated,

57

M. Bencheikh, A. Maghnouj, J. Tajmouati the results of measurements and calculations were compared to validated within gamma index acceptance rate tolerance of 95%. The gamma index technique was used for the quantitative evaluation for comparing the measured and calculated PDDs, the acceptance gamma index criterions were 3% for the dose deviation (DD) and 3 mm for distance to agreement (DTA). 2.3

PDD validation

The percentage depth dose was validated by acceptance by gamma index criterions; the photon beam characterization was investigated depending on the primary electron energy above the target. The measured PDD and the calculated the PDD were plotted for each value of primary electron energy. Figure 3 presents the measured PDD and the calculated PDDs as a function of depth on the beam central axis for each value of primary electron energy. The field size is 10 × 10 cm2 , the photon beam energy of 6 MV produced by Varian Clinac 2100, and the SSD is 100 cm. The SP file was recorded at z=100 cm at the water The percentage depth dose was validated by acceptance by gamma index criterions; phantom surface and directly under the air gap.

the photon beam characterization was investigated depending on the primary electron energy Fortarget. all primary electron gamma was plotted determined to value compare above the The measured PDDenergy, and the the calculated theindex PDD were for each the electron calculated PDDs measured PDD. 4 presents index curve of primary energy. Thetofigure 1 presents theFigure measured PDD andthe thegamma calculated PDDs as function on the beam percentage ofenergy. acceptance as a function of depthofondepth the beam central axiscentral for eachaxis. valueThe of primary electron The of gamma index for all by primary energy field size is 10×10 cm², criterions the photon was beammore energythan of 6 95 MV%produced Varian electron Clinac 2100, and thestudied. SSD is 100 cm. The SP file was recorded at z=100 cm at the water phantom surface and directly under the air gap. Measured PDD Calculated PDD - 6,3 MeV Calculated PDD - 6,7 MeV

120

Calculated PDD - 6,1 MeV Calculated PDD - 6,5 MeV

PDD (%)

100 80 60 40 20 0 0

50

100

150

200

250

300

350

Depth (mm)

3: Measured MeasuredPDD PDDand andcalculated calculatedPDDs PDDs a function of depth a water Figure 3. as as a function of depth in ain water phantom phantom on the beam central axisvalue for each value of primary electron (6,1MeV; on the beam central axis for each of primary electron energy (6.1 energy MeV; 6.3 MeV; 6,3 MeV; 6,5MeV). MeV; The and 6,7 MeV). Theenergy photon of beam energy of 6 MV 6.5 MeV; and 6.7 photon beam 6 MV produced by produced Varian Clinac 2 by Varian Clinac 2100, size 10×10 cm², is and thecm. SSD is 100 cm. 2100, the field size is 10the×field 10 cm , isand the SSD 100 For all primary electron energy, the gamma index was determined to compare the calculated PDDs to measured PDD. The figure 2 presents the gamma index curve as function of depth on the beam central axis. The percentage of acceptance of gamma index criterions 58than 95 % for all primary electron energy studied. was more

Photon Beam Fluence and Energy at the Phantom Surface as a Function of... 6

Gamma index - 6,1 MeV

6

Gamma index

Gamma index

3





5 5 4




4 3

2 2 1 1 0

00

0

50

50

100

100

150

200

150 Depth (mm)

250

200

300

250

350

300

350

Depth (mm) Figure onon thethe beam central Figure 4: 4. Gamma Gamma index indexas asfunction functionofofdepth depthininwater waterphantom phantom beam central axis axis for each value of primary electron energy (6,1 MeV; 6,3 MeV; 6,5 MeV; and 6,7MeV). for each value of primary electron energy (6.1 MeV; 6.3 MeV; 6.5 MeV; and 6.7 Figure 4: Gamma index as function of depth in water phantom on the beam central MeV).

axis for each value of primary electron energy (6,1 MeV; 6,3 MeV; 6,5 MeV; and 6,7

Results and discussion: MeV).

3

Results and Discussion

I. Photon fluence profile: Results and discussion:

Planar fluence profile - 6,3 MeV

3,50E-05 5,00E-05 3,00E-05 2,50E-05 4,50E-05 2,00E-05 4,00E-05 1,50E-05 3,50E-05 1,00E-05 3,00E-05 5,00E-06 2,50E-05 0,00E+00 2,00E-05 0,00

Planar fluence/incident particle particle

Planar fluence/incident

3.1 Photon fluence profile Based on PS file at the water phantom surface, the planar photon fluence profiles were I. Photon fluence profile: determined as a function of the off axis distance, the figure 3 presents the planar photon Based on PS file at the water phantom surface, the planar photon fluence profiles fluence profiles for each value of the primary electron energy. Baseddetermined on PS file at water phantom planar photon profiles were as the a function of the surface, off axis the distance, Figure fluence 5 presents the were determined a function of profiles the off for axiseach distance, thethefigure 3 presents the planar photon planaras5,00E-05 photon fluence value of primary electron energy. Planar fluence profile - 6,1 MeV 4,50E-05 fluence profiles for each value of the primary electron energy. 4,00E-05 Planar fluence profile - 6,5 MeV Planar fluence profile - 6,7 profile MeV - 6,1 MeV Planar fluence

Planar fluence profile - 6,3 MeV Planar fluence profile - 6,5 MeV Planar fluence profile - 6,7 MeV 5,00

10,00

15,00

1,50E-05 Off-axis ditance (cm) 1,00E-05 5,00E-06 Figure 5: The planar photon fluence profiles as a function of off axis distance at the 0,00E+00 water phantom surface for a 10×10 cm2 field size for each value of primary electron 0,00 5,00 10,00 15,00 energy (6,1 MeV; 6,3 MeV; 6,5 MeV; and 6,7 MeV). The photon beam of 6 MV Off-axis and ditance (cm) produced by Varian Clinac 2100 accelerator, the SSD is100 cm.

Figure The planar photon fluence profilesprofiles as a function of off axisofdistance the water at the Figure5. 5: The planar photon fluence as a function off axisat distance 2 2 for each value of primary electron energy phantom surface for a 10 × 10 cm field size water phantom surface for a 10×10 cm field size for each value of primary electron (6,1 MeV; 6,3 MeV; 6,5 MeV; and 6,7 MeV). The photon beam of 6 MV produced by energy (6,1 MeV; 6,3 MeV; 6,56 MeV; and 6,7 MeV). The photon beam of 6 MV Varian Clinac 2100 accelerator, and the SSD is 100 cm.

produced by Varian Clinac 2100 accelerator, and the SSD is100 cm.

59 6

off-axis range from 0 to 5 cm and all planar photon fluence profiles have zero at the beam edge.

Planar photon fluence maximum/incident particle

It can be seen that the photon fluence maximum for each planar photon fluence profile increased with the primary electron energy and moved in the increasing primary electron energy as a linear manner. For this purpose, the photon fluence profile maximum was determined for each planar photon fluence curve, and the figure 4 shown the variation of photon fluence profile maximum as a function of the primary electron energy above the linac M. Bencheikh, A. Maghnouj, J. Tajmouati target. 5,00E-05 4,00E-05 3,00E-05

Planar photon fluence maximum

2,00E-05 1,00E-05

0,00E+00 6

6,2

6,4

6,6

6,8

7

Primary electron energy (MeV) Figure 6. The of photon a function of primary electron The figure 6: variation The variation offluence photonmaximum fluenceasmaximum asthe a function of the primary energy at the water phantom surface. electron energy at the water phantom surface.

The varied a linearelectron mannerenergy as a function Thephoton photonfluence fluence profile profilesmaximum increased with theinprimary above of the -05 primary electron energy and the slope of the line was 1,285 10 photon per incident the linac target, and the planar photon fluence profiles kept the same difference particle per MeV.between The photon maximum of primary energy electron themfluence in the off-axis rangeincreased from 0 towith 5 cmincreasing and all planar photon fluence above theprofiles target. have zero at the beam edge. II.

It can be seen that the photon fluence maximum for each planar photon fluence

Photon fluence profile: profile energy increased with the primary electron energy and moved in the increasing primary electron energy in a linear manner. For this purpose, the photon fluence

The photon energy fluence has the interesting role in dosimetry study of external profile maximum was determined for each planar photon fluence curve, and Figradiotherapy in the deep tumor oftreatment [1-5, profile 47]. The energyasfluence profiles were ure 6and shows variation photon fluence maximum a function of determined as a function of off-axis distance. The figure 5 gives the photon energy fluence the primary electron energy above the linac target. profiles for each valuefluence of the profile primarymaximum electron energy. The photon varied in a linear manner as a function of the primary electron energy and the slope of the line was 1,285 10−05 photon per incident particle per MeV. The photon fluence maximum increased with increasing of primary energy electron above the target. 3.2

Photon energy fluence profile

The photon energy fluence has an interesting role in dosimetry study of external radiotherapy and in deep tumor treatment [1-5,47]. The energy fluence profiles were determined as a function of off-axis distance. Figure 7 gives the photon energy fluence profiles for each value of the primary electron energy. The photon energy fluence profiles increased with the primary electron energy above the target, and the planar photon fluence profiles kept the same difference between them in off-axis range from 0 to beam edge (almost at 5 cm) and all 7 planar photon energy fluence profiles have zero at the beam edge. It can be seen that the photon energy fluence maximum for each planar photon energy fluence profiles increased with the primary electron energy and moved in 60

Planar photon energy Planar photon energy fluence/incident particle fluence/incident particle

Planar energy fluence profile - 6,1 MeV Planar energy fluence profile - 6,3 MeV Planar energy fluence profile - 6,5 MeV Planar energy fluence profile - 6,7 MeV

8,00E-05 7,00E-05 6,00E-05

Photon Beam Fluence and Energy at the Phantom Surface as a Function of... 5,00E-05 4,00E-05

Planar energy fluence profile - 6,1 MeV Planar energy fluence profile - 6,3 MeV Planar energy fluence profile - 6,5 MeV Planar energy fluence profile - 6,7 MeV

3,00E-05 2,00E-05 8,00E-05 1,00E-05 7,00E-05 0,00E+00 6,00E-05 0,00 5,00E-05 4,00E-05

5,00

10,00

15,00

Off axis distance (mm)

3,00E-05

Figure 7:2,00E-05 The planar photon energy fluence profiles as a function of off axis distance at the water phantom surface for a 10×10 cm2 field size for each value of primary 1,00E-05 electron energy 0,00E+00(6,1 MeV; 6,3 MeV; 6,5 MeV; and 6,7 MeV). The photon beam of 6 5,00 10,00 15,00 MV produced by 0,00 Varian Clinac 2100 accelerator, and the SSD is100 cm. Off axis distance (mm) The photon energy fluence profiles increased with the primary electron energy above the target, and the planar photon fluence profiles kept the same difference between them in Figure 7.7:The planar photon energyenergy fluencefluence profiles as a function off axis distance at distance Figure The planar photon profiles as aof function of off axis 2 off-axistherange from 0 surface to beam edge (almost at size 5 cm) andvalue all planar photon energy fluence 2 each water phantom for a 10 × 10 cm field for of primary electron at the water phantom surface for a 10×10 cm field size for each value of primary 6.3beam MeV; 6.5 MeV; and 6.7 MeV). The photon beam of 6 MV produced profilesenergy have (6.1 zeroMeV; at the edge. electron energy2100 (6,1accelerator, MeV; 6,3andMeV; 6,5is.100 MeV;cm. and 6,7 MeV). The photon beam of 6 by Varian Clinac the SSD MV produced Varian Clinacenergy 2100 accelerator, and the for SSDeach is100 cm. photon energy It can be seenby that the photon fluence maximum planar fluencethe profiles increased with the energy primary energy The andphoton movedenergy in the increasing primary electron in aelectron linearwith manner. Theincreasing photon energy fluence profiles increased the primary electron energy above primaryfluence electron energyvaried as a depending linear manner. photon energy fluence maximum varied on theThe primary electron energy above the the target, and maximum the planar photon fluence profiles kept the same difference between them in depending on the primary electron energy above the target. The figure 6 presents target. Figure 8 presents the photon energy fluence maximum as a function of the photon off-axis range from 0 to beam edge (almost at 5 cm) and all planar photon energy fluence the primary electron as energy. energy maximum aedge. function of the primary electron energy. profilesfluence have zero at the beam Planar photon energy Planar photon energy fluence maximum/incident fluence maximum/incident particle particle

8,00E-05 It can be seen that the photon energy fluence maximum for each planar photon energy 7,00E-05 with the primary electron energy and moved in the increasing fluence profiles increased primary electron 6,00E-05 energy as a linear manner. The photon energy fluence maximum varied depending on the 5,00E-05 primary electron energy above the target. figure 6 presents the photon PlanarThe photon energy 4,00E-05 fluence maximum energy fluence maximum as a function of the primary electron energy. 3,00E-05 2,00E-05 8,00E-05 1,00E-05 7,00E-05 0,00E+00 6,00E-05

6,2 6,4 6,6 6,8 7 5,00E-05 6 Planar photon energy Primary electron energyfluence (MeV) 4,00E-05 maximum 3,00E-05 2,00E-05 Figure 8. The of the photon maximum a function as of a thefunction The figure 8: variation The variation of the energy photonfluence energy fluenceasmaximum 1,00E-05 primary electron energy at the water phantom surface. primary electron 0,00E+00 energy at the water phantom surface. 6 6,2 6,4 6,6 6,8 7

Primary electron energy (MeV)

of the

61

8

The figure 8: The variation of the photon energy fluence maximum as a function of the

M. Bencheikh, A. Maghnouj, J. Tajmouati The photon energy fluence maximum varied in a linear manner as a function of The photonelectron energy energy fluence and maximum varied in line a linear manner a function −05 the primary the slope of the was-05 2,861 10as MeV perof the primary electron energy and the slope of the line was 2,861 10 MeV per incident particle incident particle per MeV per MeV Photon energy distribution III. 3.3 Photon energy fluencefluence distribution: We Wehave haveinvestigated investigatedalso alsothe theenergy energyfluence fluencedistribution distributiondepending dependingon onthe thepriprimary mary electron energy above the Varian Clinac 2100 target. Figure 9 shows the electron energy above the Varian Clinac 2100 target. The figure 7 shows the variation of the of the energy distribution as a function of the energy. energyvariation fluence distribution as fluence a function of the energy. Planar energy fluence distribution - 6,1 MeV Planar energy fluence distribution - 6,3 MeV Planar energy fluence distribution - 6,5 MeV Planar energy fluence distribution - 6,7 MeV

Planar energy fluence/MeV/incident particle

3,50E-06 3,00E-06 2,50E-06 2,00E-06 1,50E-06 1,00E-06 5,00E-07 0,00E+00

-5,00E-07 0,00

2,00

4,00

6,00

8,00

Energy (MeV) Figure 9. 9: The planar photon energy fluence distributions as a function of theofenergy at Figure The planar photon energy fluence distributions as a function the energy at 2 for each value of primary electron the water phantom surface for a 10 × 10 cm2 fieldcm size the water phantom surface for a 10×10 field size for each value of primary energy (6,1 energy MeV; 6,3 MeV; 6,5 MeV; and 6,7 beam of 6 MV produced electron (6,1 MeV; 6,3 MeV; 6,5MeV). MeV;The andphoton 6,7 MeV). The photon beam of 6 by Varian Clinac 2100 accelerator, and the SSD is 100 cm.

MV produced by Varian Clinac 2100 accelerator, and the SSD is100 cm.

The energy fluence distribution increased withwith the increasing of primary Thephoton photon energy fluence distribution increased the increasing of primary electron energy above the target, and the photon fluence distribution kept the electron energy above the target, and the photon fluence distribution kept the same difference same difference between them in the energy range from 0.5 MeV to 6 MeV, and between them in the energy range from 0,5 MeV to 6 MeV, and the most of the photons have the most of the photons have an energy of 1.24 MeV. an energy of 1,24 MeV. It can be seen that the photon energy fluence maximum for each photon energy It can distribution be seen thatincreases the photon fluence for eachenergy photon fluence withenergy increasing of maximum primary electron andenergy fluence distribution increase with increasing of primary electron energy and moved moved in the increasing primary electron energy as a linear manner. The photonin the increasing primary energy as adepending linear manner. photon energyenergy fluenceabove maximum energy fluenceelectron maximum varied on theThe primary electron variedthe depending on the 10 primary electron energyenergy above fluence the target. The figure 8 presents the target. Figure presents the photon maximum distribution photonasenergy fluence maximum as a function of the primary electron energy. a function of the primarydistribution electron energy. The planar photon energy fluence distribution maximum varied in a linear manner as a function of the primary electron energy and the slope of the line was 6,49 10−07 MeV per incident particle per MeV. It can be seen from Figure 5, Figure 7, and Figure 9, the photon fluence profile, the photon energy fluence profile and the photon energy fluence distribution 62

Planar energy fluence maximum /MeV/incident particle

Photon Beam Fluence and Energy at the Phantom Surface as a Function of... 3,50E-06 3,00E-06 2,50E-06 2,00E-06

Planar energy fluence distribution maximum

1,50E-06 1,00E-06 5,00E-07

0,00E+00 6

6,2

6,4

6,6

6,8

7

Primary electron energy (MeV) Figure 10. The of photon maximum as maximum a function of The figure 10:variation The variation ofenergy photondistribution energy distribution asthe a function of primary electron energy at the water phantom surface. the primary electron energy at the water phantom surface.

The planarwith photon energyoffluence maximum varied in linear manner as a increased increasing primarydistribution electron energy. To illustrate thea primary functionelectron of the energy primary electron energy and the slope of the line was 6,49 10-07 MeV per effects on the photon beam characterizations, we have calculated incidentthe particle per MeV. deviation characterization quantity maximum relative to those of 6.1 MeV as formula below:

It can be seen from the figure 4, the figure 6, and the figure 8, the photon fluence Max(Xprimary electron energy ) − Max(X6,1 ) profile, the photon energy=fluence Deviation 100 × profile and the photon energy fluence distribution , (1) increased Max(X6,1 ) with increasing of primary electron energy. To illustrate the primary electron energy effects on the where photon characterizations, we haveat calculated the deviation characterization X:beam phhoton characterization quantity the photon surface. quantityFigure maximum relative to those of 6,1 MeV as formula below 11 presents the variation of deviation of photon beam: characterization maximum relative to photon beam characterization at primary electron energy 𝑀𝑎𝑥 (𝑋𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 )−Max(𝑋6,1 ) 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = primary 100 × electron 6.1 MeV as a function of the energy. Max(𝑋 ) 6,1

(1)

The photon energy fluence maximum increased more than both photon fluence

Where, maximum and energy fluence distribution maximum as a function of the primary electron energy. For primary electron energy at 6.7 MeV, the percentage of

X : Photon characterization photon surface. photon fluence maximum wasquantity 23.22% at of the photon fluence maximum at 6.1 MeV, the percentage of photon energy fluence maximum was 32.69% of photon energy

The figure 9 presents the variation of deviation of photon characterization fluence maximum at 6.1 MeV, and the percentage of photon energy beam distribution maximum relativewas to 19.39% photon beam characterization at primary electron maximum of photon energy distribution maximum at 6.1energy MeV. 6,1 MeV as a functionThe of the primary electron energy. photon energy maximum increased as a function of the primary electron that striking the target for producing the photons by bremsstrahlung effects and the photon energy varied up to the electron energy above the target. Our study illustrates the relationship between the both variations of photon fluence and photon energy fluence as function of the primary electron energy above the Varian Clinac 2100 target using the Monte Carlo method.

63

M. Bencheikh, A. Maghnouj, J. Tajmouati 45,00 40,00

Deviation

35,00

Planar photon fluence profile maximum (%)

30,00 25,00 20,00

Planar photon energy fluence profile maximum (%)

15,00 10,00 5,00

Planar energy fluence distribution maximum (%)

0,00 6

6,2

6,4

6,6

6,8

7

Primary electron energy (MeV) The figure 11: Variation Percentage of photon maximum to fluence photon Figure 11. Variation percentage of photon fluencefluence maximum relativerelative to photon maximum at 6.1 MeV, photon energy fluenceenergy maximum relative to phofluence maximum at the 6,1 percentage MeV, the of percentage of photon fluence maximum ton energy fluence energy maximum at 6.1maximum MeV, andatthe photon energyofdistriburelative to photon fluence 6,1percentage MeV, andofthe percentage photon tion maximum relative to photon energyto distribution maximum at 6.1 MeV as a function energy distribution maximum relative photon energy distribution maximum at 6,1 of theas primary electron energy. MeV a function of the primary electron energy. The photon energy fluence maximum increased more than both the photon fluence 3.4andThe statistical uncertainty maximum the energy fluence distribution maximum as a function of the primary electron energy. For primary electron energy at 6,7 MeV, the percentage of photon fluence maximum The statistical uncertainty of Monte Carlo simulation of 6 MV photon beam was 23,22 % of photon fluence maximum at 6,1 MeV, the percentage of photon energy produced by Varian Clinac 2100 was 1 at the maximum dose as found by M. fluence maximum was 32,69 % of photon energy fluence maximum at 6,1 MeV, and the Aljamal et al. [40]. percentage of photon energy distribution maximum was 19,39 % of photon energy distribution maximum at 6,1 MeV.

4

Conclusion

The photon energy maximum increased as a function of the primary electron that strikingThis the target producing the photons by effects energy and theon photon energy studyfor presents an investigation onBremsstrahlung the primary electron the photon varied beam up to characterization the electron energy above the target. Our study illustrates the relationship at the water phantom surface, according to photon beam betweencharacterization the both variations of photon photonenergy energy above fluencethe as target function of sethe required; the fluence primaryand electron was primarylected, electronthis energy above the Varian Clinac 2100 target using the Monte Carlo method. study also illustrates that optimal beams will have high fluence and IV.

low energy fluence that recommended by IAEA in TRS-398 [49]. The statistical uncertainty: The variation of photon fluence, photon energy fluence, and photon energy flu-

The uncertainty of Monte of 6 MV photon produced encestatistical distribution were varied in a Carlo linearsimulation manner depending on the beam primary elecby Varian Clinac 2100 was 1 at the maximum dose as found by Aljamal M. et al [40]. tron energy [9]. Our study can be useful to improve photon beam dosimetry,

radiotherapy treatment and to design new accelerators more efficient and of

Conclusion: high quality in the photon external beam radiotherapy; the optimal photon beam

can be found as high photon fluence and low photon energy fluence to save the

This study presents an investigation on the primary electron energy on the photon healthy cells surrounding the tumor volume treatment [5]. beam characterization at the water phantom surface, according to photon beam characterization required; the primary electron energy above the target was selected, this study also illustrate that optimal beams will have high fluence and low energy fluence that recommended by IAEA in TRS-398 [49].

64 11

Photon Beam Fluence and Energy at the Phantom Surface as a Function of... Acknowledgement The authors would like to thank VARIAN Medical Systems to provide us the Varian Clinac 2100 geometry data and give us this opportunity to study the VARIAN linear accelerator technology and to participate in its future development, our study is one among many study over the world in this field. References [1] P. Mayles, A. Nahum, and J.C. Rosenwald (2007) “Handbook of Radiotherapy Physics Theory and Practice” (Taylor & Francis group, LCC, USA) pp. 452-480. [2] D.S. Chang, F.D. Lasley, I.J. Das, M.S. Mendonca, and J.R. Dynlacht (2014) “Basic Radiotherapy Physics and Biology” (Springer, New York) pp 77-92. [3] E.B. Podgorsak (2005) “Radiation Oncology Physics: A Handbook for Teachers and Students” (IAEA, Vienna) pp 161-216. [4] J. Palta, S. Kim, J. Li, and C. Liu (2003) In: “Intensity-Modulated Radiation Therapy: The State of the Art”, Proceeding of the AAPM 2003 Summer School, eds. J.R. Palta and T.R. Mackie (Madison, WI: Medical Physics) pp 593-612. [5] Technical Reports Series No.430 (2004) Commissioning and Quality Assurance of Computerized Planning Systems for Radiation Treatment of Cancer (IAEA, Vienna). [6] IAEA-TECDOC-1540 (2007) Specification and Acceptance Testing of Radiotherapy Treatment Planning Systems (IAEA, Vienna). [7] B. Kadman, N. Chawapun, S. Ua-Apisitwong, T. Asakit, N. Chumpu, and J. Rueansri (2016,J. Phys. Conf. Ser. 694 012023. [8] D.M. Lovelock, C.S. Chui, and R. Mohan (1995) Med. Phys. 22 1387-1394. [9] H.H. Liu, T.R. Mackie, and E.C. McCullough (1997) Med. Phys. 24 1960-1974. [10] B. Libby, J. Siebers, and R. Mohan (1999) Med. Phys. 26 1476-1483. [11] C.M. Ma, E. Mok, A. Kapur, T. Pawlicki, D. Findley, S. Brain, K. Forster, and A.L. Boyer (1999) Med. Phys. 26 2133-2143. [12] A.E. Schach von Wittenau, L.J. Cox, P.M. Bergstrom, W.P. Chandler, C.L. Hartmann Siantar, and R. Mohan (1999) Med. Phys. 26 1196-2110. [13] J.V. Siebers, P.J. Keall, B. Libby, and R. Mohan (1999) Phys. Med. Biol. 44 30093026. [14] I. Chetty, J.J. DeMarco, and T.D. Solberg (2000) Med. Phys. 27 166-172. [15] S.B. Jiang, A. Kapur, J. Li, T. Pawlicki, and C.M. Ma (2000) Phys. Med. Biol. 45 411-427. [16] W. Van der Zee, and J. Welleweerd (1999) Med. Phys. 26 1883-1892. [17] C.M. Ma (1998) Radiat. Phys. Chem. 53 329-344. [18] M.K. Fix, H. Keller, P. Ruegsegger, and E.J. Born (2000) Med. Phys. 27 2739-2747. [19] M.K. Fix, M. Stampanoni, P. Manser, E.J. Born, R. Mini, and P. Ruegsegger (2001) Phys. Med. Biol. 46 1407-1427. [20] D.A. Low, J.F. Dempsey (2003) Med. Phys. 30 2455-2464. [21] M.K. Fix, P.J. Keall, K. Dawson, and J.V. Siebers (2004) Med. Phys. 31 3106-3121.

65

M. Bencheikh, A. Maghnouj, J. Tajmouati [22] C.L. Hartmann Siantar, R.S. Walling, T.P. Daly, B. Faddegon, N. Albright, P. Bergstrom, A.F. Bielajew, C. Chuang, D. Garrett, R.K. House, D. Knapp, D.J. Wieczorek, and L.J. Verhey (2001) Med. Phys. 28 1322-1337. [23] P. Francescon, C. Cavedon, S. Reccanello, and S. Cora (2000) Med. Phys. 27 15791587. [24] D. Sheikh-Bagheri, D.W. Rogers (2002) Med. Phys. 29 391-402. [25] P.J. Keall, J.V. Siebers, B. Libby, and R. Mohan (2003) Med. Phys. 30 574-582. [26] R.D. Lewis, S.J. Ryde, D.A. Hancock, and C.J. Evans (1999) Phys. Med. Biol. 44 1219-1230. [27] B.T. Sichani and M. Sohrabpour (2004) Phys. Med. Biol. 49 807-818. [28] M. Dumitrache and A. Tanase (2012) A Comparative Study On 6 MV Photon Beam Percentage Depth Dose Of VARIAN Clinac 2300 C/D, ELEKTA Synergy Platform, and Siemens Primus Linacs, Sofia, European Medical Physics and Engineering Conference, October 18-20. [29] R. Popa, M. Dumitrache, and A. Ciovlica (2012) Rom. Rep. Phys. 64 997-1010. [30] A. Mesbahi, P. Mehnati, and A. Keshtkar (2007) Iran. J. Radiat. Res. 23-30. [31] A. Mesbahi, M. Fix, M. Allahverdi, E. Grein, and H. Garaati (2005) Appl. Radiat. Isot. 62 469-477. [32] L. Apipunyasopon, S. Srisatit, and N. Phaisangittisakul (2013) J. Radiat. Res. 54 374-382. [33] D.W.O. Rogers, B. Walters, and I. Kawrakow (2013) “em BEAMnrc Users Manual” (NRCC Report, Ottawa) pp 12-254. [34] B. Walters, I. Kawrakow, and D.W.O. Rogers (2013) “DOSXYZnrc Users Manual (NRCC Report, Ottawa) pp 9-103. [35] D.W.O. Rogers, I. Kawrakow, J.P. Seuntjens, B. Walters, and H.E. Mainegra (2013) “NRC User Codes for EGSnrc” (NRCC Report, Ottawa) pp 6-83. [36] C.M. Ma and D.W.O. Rogers (2013) “BEAMDP Users Manual” (National Research Council of Canada, NRCC Report, Ottawa) pp 3-24. [37] M. Asghar, M. Parinaz, K. Ahmad, F. Alireza (2007) Radiat. Med. 25 315-324. [38] J.K. Paul, V.S. Jeffrey, L. Bruce, and M. Radhe (2003) Med. Phys. 30 574-582. [39] A. Mesbahi (2006) Iran. J. Radiat. Res. 4 7-14. [40] D. Sheikh-Bagheri and D.W. Rogers (2002) Med. Phys. 29 379-390. [41] M. Oprea, C. Constantin, D. Mihailescu, C. Borcia (2012) U.P.B. Sci. Bull. Ser. A 74 153-166. [42] F. Verhaegen, J. Seuntjens (2003) Phys. Med. Biol. 48 3401-58. [43] K. Aljarrah, G.C. Sharp, T. Neicu, and S.B. Jiang (2006) Med. Phys. 33 850-858. [44] O. Chibani, B. Moftah, C.M. Ma (2011) Med. Phys. 38 188-201. [45] S.B. Jiang, A.L. Boyer, and C.M. Ma (2001) Med. Phys. 28 55-66. [46] D.A. Low, W.B. Harms, S. Mutic, and J.A. Purdy (1998) Med. Phys. 25 656-661. [47] H.C.E. McGowan, B.A. Faddegon, and C.M. Ma (2013) STATDOSE for 3D dose distributions (NRCC Report, Ottawa) pp 1-10. [48] M. Aljamal and A. Zakaria (2013) Aust. J. Basic Appl. Sci. 7 340-346. [49] IAEA (2000) Absorbed dose determination in external beam radiotherapy (Technical reports series no. 398, Vienna) pp 110-133.

66