Monte Carlo calculations of the absorbed dose and energy dependence of plasticscintillatorsA. Sam Beddar, Tina Marie Briere, Firas A. Mourtada, Oleg N. Vassiliev, H. Helen Liu, and Radhe Mohan Citation: Medical Physics 32, 1265 (2005); doi: 10.1118/1.1897465 View online: http://dx.doi.org/10.1118/1.1897465 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/32/5?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Verification of TG-61 dose for synchrotron-produced monochromatic x-ray beams using fluence-normalizedMCNP5 calculations Med. Phys. 39, 7462 (2012); 10.1118/1.4761870 Monte Carlo simulation of a novel water-equivalent electronic portal imaging device using plastic scintillatingfibers Med. Phys. 39, 1518 (2012); 10.1118/1.3687163 Monte Carlo study of the energy and angular dependence of the response of plastic scintillation detectors inphoton beams Med. Phys. 37, 5279 (2010); 10.1118/1.3488904 Extraction of depth-dependent perturbation factors for parallel-plate chambers in electron beams using a plasticscintillation detector Med. Phys. 37, 4331 (2010); 10.1118/1.3463383 Towards two-dimensional brachytherapy dosimetry using plastic scintillator: New highly efficient water equivalentplastic scintillator materials Med. Phys. 26, 1515 (1999); 10.1118/1.598647

Monte Carlo calculations of the absorbed dose and energy dependenceof plastic scintillators

A. Sam Beddar,a! Tina Marie Briere, Firas A. Mourtada, Oleg N. Vassiliev,H. Helen Liu, and Radhe MohanDepartment of Radiation Physics, Division of Radiation Oncology, The University of Texas M. D. AndersonCancer Center, Houston, Texas 77030

sReceived 6 January 2005; revised 15 February 2005; accepted for publication 7 March 2005;published 13 April 2005d

Detector systems using plastic scintillators can provide instantaneous measurements with highspatial resolution in many applications including small field and high dose gradient field applica-tions. Energy independence and water equivalence are important dosimetric properties that deter-mine whether a detector will be useful in a clinical setting. Using Monte Carlo simulations, wecalculated the energy dependence of plastic scintillators when exposed to photon beams in theradiotherapeutic range. These calculations were performed for a detector comprised of a BC-400plastic scintillator surrounded by a polystyrene wall. Our results showed the plastic scintillationdetector to be nearly energy independent over a range of energies from 0.5 to 20 MeV. The ratio ofthe dose absorbed by the scintillator to that absorbed by water was nearly a constant, approximatelyequal to 0.98 over the entire energy range of interest. These results confirm the water equivalenceof the plastic scintillation detector and are in very good agreement with earlier results obtainedusing Burlin cavity theory. ©2005 American Association of Physicists in Medicine.fDOI: 10.1118/1.1897465g

Key words: Monte Carlo, Burlin cavity theory, plastic scintillation dosimetry, scintillator, waterequivalence

I. INTRODUCTION

Detector systems using plastic scintillators can provide in-stantaneous measurements with high spatial resolution insmall field and high dose gradient field applications. Thesesmall-volume detectors offer reproducibility, linear response,resistance to radiation damage, temperature independence,and superior spatial resolution. Applications using plasticscintillation detectors include dosimetry of high-energy pho-ton and electron beams,1,2 quality assurance of60Co andhigh-energy therapy machines,3 ophthalmic plaquedosimetry,4,5 and stereotactic radiosurgery dosimetry.6,7 Plas-tic scintillators have even been used forin vivo b-particledetection in the brains of small animals8,9 and intravascularbrachytherapy for in stent restenosis.10

Energy independence and water equivalence are impor-tant dosimetric properties that determine whether a detectorcan be widely used in a clinical setting or languish on alaboratory shelf. The material that comprises a plastic scin-tillator has previously been shown to be a good match towater in the mega electron volt energy range.1 The meanmass-energy absorption coefficients of the plastic scintillatorare quite close to those of water above 100 keV, as are themass collision stopping powers and the mass angular scatter-ing powers. The dose absorbed by plastic scintillators haspreviously been calculated using Burlin cavity theory,1 andthe results showed near energy independence for photonswithin the megavoltage energy range. Kirovet al.11 andWilliamson et al.12 studied the same scintillator material forphoton energies under 1 MeV. The results of both MonteCarlo calculations and experiment showed a steep drop in the

absorbed dose with decreasing energy, making the unadulter-ated plastic scintillator less than ideal for brachytherapy andother low-energy applications.

Monte Carlo simulations have not previously been used tocalculate the dose absorbed by plastic scintillators for ener-gies above 1 MeV. Our purpose, therefore, was to calculate,using Monte Carlo simulations, the absorbed dose to a plas-tic scintillator embedded in a polystyrene probe. The calcu-lations were performed for a range of energies typically usedin accelerator beam radiation therapy, and both monoener-getic and polyenergetic beams were used. Finally, we com-pared the results of our Monte Carlo calculations with thosedetermined using Burlin cavity theory.

II. METHODS AND MATERIALS

A. Monte Carlo calculations with monoenergeticbeams

Dose to the scintillator and water was calculated usingMonte Carlo simulations with the Monte Carlo N-particletransport codesMCNPX, version 2.4.k, Los Alamos NationalLaboratory, Los Alamos, NMd. The most important featuresof MCNPX relevant to electron-photon transport are the up-grades to the Integrated Tiger SeriessITSd version 3.0 elec-tron physics. The electron-physics enhancements includechanges to the density-effect calculation for collisionselec-tronicd stopping power, radiative stopping power, brems-strahlung productionsspectra and angular distributiond, andelectron-impact ionization.13 The plastic scintillation detectorsystem was modeled on a system designed by Beddaret al.1,2

1265 1265Med. Phys. 32 „5…, May 2005 0094-2405/2005/32„5…/1265/5/$22.50 © 2005 Am. Assoc. Phys. Med.

and consisted of a plastic scintillator embedded in a polysty-rene probesFig. 1d. The chemical composition of the scintil-lator was based on the BC-400 plastic scintillatorsBicronCorporation, Newbury, OHd, which is made from polyvinyl-toluene doped with organic fluors. The scintillator detectingvolume was 1 mm in diameter and 4 mm in length, and thepolystyrene probe was 4 mm in diameter and 7 mm inlength. The probe was surrounded by a 20320320 cm3 wa-ter bath to simulate immersion in a water phantom. Table Ilists the density and composition by weight of the materialsused in these simulations. Monoenergetic photon beam simu-lations with energies of 0.2, 0.5, 1, 2, 4, 6, 8, 10, 15, and20 MeV were placed at the topmost surface of the waterphantom, and the center of the scintillator was placed 5 cmbelow. Both the scintillator and the polystyrene probe werereplaced by water, and the absorbed dose was calculated forthe same volume as the plastic scintillator.

All coupled photon–electron simulations were performedon a Pentium 42.0 GHz laptop computer operatingWINDOWS

2000 PROFESSIONAL. Each calculation took, on average, 14 hto complete. The electron energy cutoff was set to 100 keV,while the photon energy cutoff was set to 10 keV. This wasthought to be a valid cutoff energy because the detector di-ameter of 1 mm is larger than the range of a 100 keV elec-tron in the media investigated. The defaultMCNP4C andMCNPX 2.4 energy-indexing algorithm was changed to theITS-style algorithm, as discussed in the literature.14,15 TheMCNPX electron step sizes were chosen as a default to resultin an average energy loss of 8.3% per step, as recommended

by Berger.16 These steps were further broken into a numberof equal-length substeps, the default electron substeps perenergy step of 3 for water, polystyrene, and polyvinyltoluenewere used.15 The absorbed dose was obtained by tallying theenergy within the scintillator or equivalent water volume anddividing the result by the mass of the scintillator or water toconvert to dose. For each energy simulation, 200 millionhistories were transported to obtain a statistical relative errorof 2%–4%s1 s.d.d, with higher percentages of errors occur-ring for the lower photon energies. The statistical error in thecalculation of absorbed dose to the scintillator was about thesame as that for the calculation of absorbed dose to water atthe same energy. All ten statistical checks provided by theMCNPX output indicated convergence at the completion of thesimulation.

B. Monte Carlo calculations with a polyenergeticbeam

For the Monte Carlo calculations using polyenergetic pho-ton beams, radiation transport in the accelerator was modeledusing the BEAMnrc Monte Carlo code.17–20 The acceleratorgeometry and materials were obtained from the manufactur-er’s data for the Varian Clinac 2100 series acceleratorsVarianMedical Systems, Palo Alto, CAd. The study was limited tothe 6 and 18 MV photon modes. The accelerator model wasbuilt using the standard BEAMnrc component modules,which include a bremsstrahlung target, a primary collimator,a flattening filter, and two movable collimatorssjawsd. Prop-erties of the electron beam incident on the target are notknown with sufficient accuracy; therefore, on the basis ofprevious studies,21,22 the beam was assumed to be parallel,and the energy spectrum and lateral spread of the electronfluence were assumed to be Gaussian. The three parametersdescribing the electron beam, the center and width of theenergy distribution and the width of the lateral spread, weredetermined by comparing simulation results with dosimetrydata for a water phantom. The experimental data includeddepth-dose data, dose profiles, and output factors. Bestagreement between simulation results and dosimetry data forthe 6 MV beam was achieved for an electron beam with anenergy spectrum centered at 6.2 MeV, a full width at halfmaximum sFWHMd of 3%, and a lateral spread of FWHM=1 mm. In the 18 MV mode, the spectrum was centered at18.0 MeV and had the same FWHM values, 3% and 1 mm.The bulk of the data agree to within 2%, or 2 mm. Largerdiscrepancies were found mainly in low-dose regionssout-side the penumbrad and in data for a 40340 cm2 field. For-tunately, these cases are of little relevance to the presentstudy.

Calculations were performed for a 10310 cm2 field. Thenumber of simulated histories was set to 1.53108 s6 MVdand 43107 s18 MVd. To improve efficiency, selectivebremsstrahlung splitting was used, with respective minimumand maximum splitting numbers of 20 and 200 and an effec-tive field size of 20320 cm2. Phase space coordinates of allparticles reaching a plane located at a source-to-surface dis-tancesSSDd of 100 cm were recorded in a file. The data were

FIG. 1. Diagram of the polystyrene probe containing the scintillator.

TABLE I. Physical properties of the scintillator, polystyrene, and water.

Parameter Scintillator Polystyrene Water

Density sg/cm3d 1.032 1.060 1.000Ratio of the number ofe− inthe compound to themolecular weightkZ/Al

0.5414 0.5377 0.5551

Electron densitys1023 e−/gd 3.272 3.238 3.343Compositionswt %d H: 8.47

C: 91.53H: 7.74C: 92.26

H: 11.19O: 88.81

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then processed by theBEAMDP program23 to obtain the en-ergy and angular distributions of the photon fluence. Thesedistributions generally showed planar variation and weretherefore averaged over a 10310 cm2 square located at theSSD and centered on the beam central axis. This approachreduces statistical errors and simplifies further calculations.The distributions were then used as a source for theMCNPX

calculations, using the same method as described earlier.

C. Burlin cavity theory

Burlin cavity theory was previously applied to comparethe dose absorbed by the plastic scintillator to that absorbedby water,1 and we briefly review the method here. The theoryis appropriate for cavities of intermediate size and bridgesthe gap between small cavities, for which the Bragg–Graytheory applies, and large cavities, for which the influence ofthe cavity walls is negligible. Burlin cavity theory may beexpressed as1,24,25

D̄scin

Dwater= dmsS̄dwater

scin + s1 − ddS m̄en

rD

water

scin

, s1d

whereD̄scin is the average absorbed dose in the scintillator,Dwater is the dose in charged-particle equilibrium at the same

location in water,msS̄dwaterscin is the mean ratio of mass collision

stopping powers for the plastic scintillator and water,sm̄en/rdwater

scin is the mean ratio of the mass energy absorptioncoefficients, andd accounts for the attenuation of electronsentering the cavity and the build-up of electrons generatedinside the cavity. For diffuse fields of electrons whose flu-ence is approximately the same in both materials,d is givenby

d = s1 − e−bLd/bL, s2d

where b is the effective absorption coefficient of the elec-trons in the cavity andL is the mean path length of theelectrons across the cavity. For small cavities, the value ofdapproaches unity, whereas for large cavities, it approacheszero. The value ofd for the plastic scintillator was found to

FIG. 2. sad Ratio of absorbed dose inthe plastic scintillator to that in water.Results for Monte Carlo calculationswith a range of monoenergetic photonbeams and 6 and 18 MV polyenergeticbeams are shown. Calculations usingBurlin cavity theory assumed a zero-thickness polystyrene wall. The solidline represents the average value ofMonte Carlo calculations for monoen-ergetic beams, while the dashed linesare at ±1% of the average.sbd Resultsof Burlin cavity theory calculations forthe plastic scintillator and equivalentvolumes of airsfor ion chambersd andLiF sfor TLDsd. Si sfor diodesd wasmodeled using Bragg–Gray cavitytheory.

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be nearly zero for low photon energies and close to one forenergies above 10 MeV. Thus, the large cavity approxima-tion is justified for orthovoltage energies, while the smallcavity approximation is applicable to high energies. In therange of most radiotherapy beams,d was found to lie in theintermediate region, justifying the use of Burlin cavitytheory.

III. RESULTS AND DISCUSSION

The ratio of absorbed dose in the scintillator to that inwater is shown in Fig. 2sad. Looking first at the results forthe monoenergetic photon beams, we can see that for ener-gies of 0.5 MeV and above, the ratio is nearly a constant, andthe value is close to 0.98 throughout the megavoltage radio-therapeutic energy range for experimental conditions close tothat selected in this work. At 0.2 MeV, the ratio drops toabout 0.94, and as shown previously,11,12 the plastic scintil-lator begins to show strong energy dependence at lower en-ergies.

Beam fluence as a function of photon energy for the poly-energetic 6 and 18 MV photon beams is shown in Fig. 3,where the average photon energies were 1.7 and 4.5 MeV,respectively. Looking back at Fig. 2sad, we can see that theresults of Monte Carlo calculations for the polyenergeticbeams are similar to those obtained for the monoenergeticbeams. It is clear that the plastic scintillator is both waterequivalent and energy independent in the megavoltage en-ergy range. Thus, a plastic scintillation detector could becalibrated in a60Co teletherapy beam, for instance, and thenused without any correction factors to measure a polyener-getic beam produced by a high-energy accelerator for experi-mental conditions close to those selected in this work.

The results of Burlin cavity theory are in close agreementwith those obtained from the Monte Carlo calculationsfFig.2sadg. This demonstrates that the assumption of anintermediate-sized cavity is appropriate. Furthermore, be-cause the polystyrene probe has radiological properties simi-lar to those of both water and the plastic scintillator, thezero-thickness wall approximation is valid. The results alsosuggest that Burlin cavity theory could be used to validate

new detectors of a similar size to the one studied, unlessconditions necessitate the use of Monte Carlo calculationssfor example, use of a detector made from high-Z materiald.Considering the consistency in energy response, the scintil-lation detector can be expected to outperform many com-monly used detectors, including ion chambers, thermolumi-nescent devicessTLDsd, and silicon diodes. This isdemonstrated in Fig. 2sbd, where Burlin cavity theory wasused for the detector materials airsion chambersd, LiFsTLDsd, and Si sdiodesd.1 Typical Si diodes have effectivethicknesses of the order of 50mm, and therefore the Burlinparameterd was taken as unity, which reduces to Bragg–Gray theory. Whereas the plastic scintillator is energy inde-pendent in the megavoltage energy range, the other detectorsshow somewhat stronger energy dependence.

Aside from energy independence, the plastic scintillationdetector has many attractive dosimetric characteristics, in-cluding reproducibility, linear response to dose, temperatureindependence, and resistance to radiation damage.1–4,6,26Thedetector can accurately measure the depth dose profiles foreither x rays or electron beams in the megavoltage energyrange. Its spatial resolution is superior to many traditionaldetectors, including ionization chambers, radiographic film,and silicon diodes.2,7 One important issue still facing thedetector is its signal-to-noise ratio, particularly when ex-posed to electron beams, where Cerenkov radiation cannotbe ignored. It is hoped that improvement in signal collectionefficiency and reduction in background will make these de-tectors more widely utilized for clinical applications.27–30

IV. CONCLUSIONS

Monte Carlo calculations show the plastic scintillator tobe energy independent and water equivalent in the energyrange of megavoltage radiotherapeutic photon beams. A plas-tic scintillation detector could thus be calibrated at an energyabove 1 MeV and then be used over the megavoltage energyrange without any energy correction. The good agreementbetween Monte Carlo and Burlin cavity theory calculationsvalidates the approximations used in this application to Bur-lin cavity theory. Monte Carlo calculations can be a useful

FIG. 3. Beam fluence as a function of energy for the6 MV sblackd and 18 MV sgrayd polyenergetic photonbeams.

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tool to determine the energy dependence of new materialsthat could potentially be used as detecting media for radia-tion detectors.

adAuthor to whom correspondence should be addressed. Electronic mail:abeddar@mdanderson.org

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