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Monte Carlo calculations of scatter to primary ratios for normalisation of primary and scatter dose

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1990 Phys. Med. Biol. 35 333 (http://iopscience.iop.org/0031-9155/35/3/003) View the table of contents for this issue, or go to the journal homepage for more

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Phys. Med. Biol., 1990, Vol. 35, No 3, 333-338. Printed in the UK

Monte Carlo calculations of scatter to primary ratios for normalisation of primary and scatter dose Roger K Rice? and Lee M Chin$ t UCSD Medical Center, Division of Radiation Oncology, 225 Dickinson Street, San Diego, CA 92103, USA Joint Center for Radiation Therapy, Department of Radiation Therapy, Harvard Medical School, 50 Binney Street, Boston, MA 02115, USA

Received 22 August 1988, in final form 27 September 1989

Abstract. The separation of total absorbed dose into primary and scatter components is a commonly used technique in photon dose calculations. The primary dose component can be characterised by a measured narrow beam attenuation coefficient and a single normalisation value which establishes the relative proportion of the primary to the total dose at some reference depth and field size. The determination of this normalisation value from measured data requires an extrapolation of measured values for finite field sizes to obtain a zero field size value. We have used Monte Carlo simulations to score primary and scatter dose for photon beamsof 4,6, 10, 15 and 24 MV and report values of the scatter to primary ratio at the depth of dose maximum for the circular equivalent of a 10 cm x 10 cm field. These values have an uncertainty of less than 1% and can be used in lieu of extrapolation of measured data to establish the relative magnitude of the primary dose for a wide range of photon beam energies.

1. Introduction

The concept of separation of primary and scatter radiation is commonly used for the calculation of dose distributions from photon beams (Day 1983, Khan er a1 1980). We define primary dose as the dose deposited by electrons generated by photons during their first interaction after entering the phantom. The accuracyof relative contributions of primary and scatter doses becomes important in fields where the scatter doses have to be weighted and modified, e.g. in the presence of beam modifiers (blocked fields) or tissueheterogeneities.The difficulty is that primary or scatterdosecannotbe measured separately, and approximations or extrapolations must be made to extract this information from total dose measurements. There are several techniques to separate approximately the primary and scatter components, using, for example, tissue-to-air ratios (TAR) or tissue-to-maximum ratios (TMR) (Day 1983, Khan et a1 1980). Neglecting effects due to head and collimator scatter, the primary dose P ( d ) is assumed to decrease exponentially with depth d for field sizes large enough to establish lateral electronic equilibrium (Khan er a1 1980). Theonly twoquantitiesneededtodefinetheprimarydosearethenarrowbeam attenuation coefficient ( p ) to define the depth dependence, and a normalisation factor to establish the magnitude of the primary dose, relativetothetotaldoseatsome reference depth and field size. 0031-9155/90/030333+06S03.50

@ 1990 IOP Publishing Ltd

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R K Rice and L M Chin

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From equation (20) of Khan et a1 (1980) it can be shown that S p ( 0 ) = P(dmax)/ D ( d m a x rref)

(1)

where Sp(0)is the phantom scatter correction factor for zero field size and D( dm,, , rref) is the total dose at dm,, in the reference field. The total dose D ( d , r ) , which is the sum of the primary and scatter components, can be written as

D( d, r ) = P ( d ) + S ( d, r )

(2)

or

+ SPR( d, r)]

D ( d, I ) = P ( d ) [1

(3)

where S(d,r ) is thescatterdoseatdepth d for field size r and S P R ( ~r ), is the scatter-to-primary ratio at depth d for field size r and should not be confused with the scatter-phantom ratio referred to in Khan et al. Thus, Sp(0) is given by Sp(O)=P(d,a,)/D(dm,,,

rref)=1/[1+SPR(dmax, rref)l

(4)

and is the normalisation factor which establishes the magnitude of the primary dose relative to the total dose. Once the primary dose is determined, the scatter dose for all depths and field sizes wherechargedparticleequilibriumexists is obtained by subtracting the primary dose from the measured total dose. While this formalism is strictly valid only for the limited geometry of a semi-infinite water phantom, it can be used as a basisforextending to morecomplexgeometrieswiththeuse of scatter integration techniques (Khan et a1 1980). The narrow beam attenuation coefficient ( p ) ,which defines the depth dependence for the primary component, can be accurately determined from a well defined set of measurements (Day 1983, Khan et al 1980). The only other parameter necessary for the accurate separation of the primary and scatter components at all depths and field sizes where electronic equilibrium exists is the SPR at dm,, in the referetlce field. This is usually determined by extrapolation of measured total dose data for arange of field sizes.However,this procedure is subject toconsiderableuncertainty,ashasbeen discussed by several investigators, especially for 6oCobeams (Ahuja et a1 1978, Bjarngard and Petti 1988, Henry 1982, Kijewski et a1 1986, Pfalzner 1981). This uncertainty arises because we aretryingtodetermine the primary component ina field where lateral electronic equilibrium exists by extrapolating to a zero field size. Since lateral equilibrium does not exist forvery small field sizes, measurements made in these fields cannot be used in the extrapolation. 2. Materials and methods

We define primary dose as the dose deposited by electrons which were generated by photons undergoing their first interaction after entering the phantom. Scatter dose is the dose depositedby all other electrons. By scoring primary and scatter dose separately as a function of depth and field size, S P R ( ~r ), can be calculated directly as the ratio of scatter to primary dose for any field radius r and depthd. According to thisdefinition SPR(~,,,, rref) can bedetermined with noextrapolationsandthe accuracy is only determined by the uncertainty in extracting the relevant quantities from the Monte Carlo results. The typical normalisation point for measured databases is a 10 cm x 10 cm field at the depth of maximum dose dm,,.

Normalisation of primary scatter dose and

335

The simulations were done with the user code I N H O M P , written by D W 0 Rogers, and is a version of I N H O M which uses the E G S ~(Nelson et a1 1985) Monte Carlo radiation transport system and the PRESTA (Bielajew and Rogers 1987) algorithm. The code was modified at our institution to score total and primary dose to a semi-infinite water phantom as a function of depth and field size. Dose was scored to a region of 1 cm2 area on the central axis with a depth resolution of0.125cm in the build-up region and 1 cm resolution at depths beyond dm,,. Electrons were transported down to 10 keV with a maximum energy loss per step of 4%. Simulations were done for circular incident parallel photon beams of 4,6, 10, 15 and 24 MV using published spectra (Mohan etal 1985)for the relativeenergycomposition of eachbeam with spectral component intervals of 0.25 MeV for the 4 MV spectra up to 1.5 MeV for the 25 MV spectra. Each simulation used 2.5 x lo5 to lo6 incident photons in 10 batches to assess the statistical uncertainty in the results (< 1%). Values of dm,, and the primary beam attenuation coefficients from the simulations agreed well with measured values forexistingbeamsat ourinstitutions with energies of 4,6, 10 and 15MV. These measured values are given in table 1. Table 1.

~~~

6Oc 0 0.066 4 MV 6 MV 10 MV 15 MV 24 MV

0.5 1.04 (1.0) (0.049) 0.048 (1.5)1.43 2.08 (2.5) 2.99 0.034(0.035) (3.0) 5.93

0.058 (0.059)

0.041 (0.040) 0.020

0.065 *0.015 0.085 0.92210.013 10.015 0.078 0.015 0.079 0.015 0.077 0.015 0.064i0.015

* * *

~~

*

0.939 0.013 0.928 *0.013 0.927 0.013 0.929 0.013 0.940 0.013

* * *

+ Measured values from clinical beams are shown in parentheses.

3. Results

Figure 1 shows the primary dose as a functionof depth for each beam energy studied. Data for 6oCo are also shown from the calculations of Kijewski et a1 (1986). Each curve is normalised to the total dose at dm,, for a field of radius 5.64 cm (equivalent square of 10 cm X 10 cm). The data show that the assumption of simple exponential attenuation beyond dm,, is adequate. The narrow beam attenuation coefficient determined by a least-squares fit to the data beyond dm,, for each energy is given in table 1. Figure 2 shows theSPR for a circular field of radius 5.64 cm as a function of d l d , , , for each beam energy studied. The dm,, for each energy was determined by fitting the total dose for a large field ( r = 22.5 cm) to the form

The depth of maximum dose is then given by drnax=ln(plA)l(p"A)*

(6)

The values of dm,, determined in this way are listed in table 1. The value of the SPR, at d l d , , , = 1.0, for each photon energy, gives SPR(dm,, , rref).These values are also

336

R K Rice and L M Chin

Figure 1. Primary dose as a function of depth along with central axis calculated for incident parallel beams of radius 5.64 cm and a range of incident photon beam energies. All values are relative to the total dose at dm,, for a beam of radius5.64 cm for each beam energy. Data for6oCoare from the calculations of Kijewski et a/ (1986).

SPR

0

1

0

l

~

l

l

5

1

l

l

1

1

10

l

1

l

1

15

d/dmox

Figure 2. Scatter-to-primary ratio ( S P R ) along the central axis as a function of did,,, for a rangeof incident beam energies. Data for 6oCoare from the calculations of Kijewski et a / (1986).

given in table 1. The numbers showlittle change with beam energy and have an average value of 0.076*0,01. The relative magnitude of the primary to the total dose at dm,, and rref are given in the last column of table 1. The average value is 0.93 1% for all energies studied.

*

4. Discussion

Values of SPR for a reference field of radius r = 5.64 cm, at dm,,,generated from Monte Carlo simulations for a wide range of clinically relevant photon beams are reported. The quantity S,(O), defined as the magnitude of the primary dose relative to the total dose at dm,, in a 10 cm X 10 cm field, ranges from 0.92 to 0.94 for the range of photon beam energies from4 to 24 MV. This suggests that for thiswide range of beam energies we may use an average value of 0.93. The quantity S,(O) is identical to the quantity

Normalisation of primary scatter dose and

337

NPSF, from Day (1983). These two quantities are normally defined by extrapolating measureddatatozero field sizes. However, no suggestions aremade of how the extrapolations should be done. In addition, no actual values of S,(O) or NPSFo are published except for a single example in figure E3 of Day (1983) which gives a value of NPSF, for 8 MV x-rays of 0.960. When S,(O) is combined with experimentally determined narrow beam attenuation coefficients and measured total doses relative to the total dose in the reference field at dm,,, the separation of primary and scatter can be done without extrapolation of measured data to zero field size. In practice SPR onlyinfluences the relativemagnitude of primaryandscatter components in a radiationfield. For calculations in a homogeneous medium for regular fields where charged particle equilibrium exists an error in SPR will not affect the total dose calculation since the sum of primary and scatter componentsis based on measurements of the total dose. However, in caseswhere thescatterradiation has to beweighted or modified because of blocked fields or the presence of heterogeneities, the SPR does affect the accuracy of the total dose. The average value of S,(O) = 0.93 1% can be applied in the primary and scatter dose separation according to the model presented in Khan et a1 (1980) for beam energies ranging from 4 to 24 MV to achieve acceptable accuracy.

*

5. Conclusions For high-energy photon beams the extrapolation of measured data to small fields may become inaccurate. Alternatively, in view of the insensitivity of SPR, at dm,, , to photon energy, the SPR and, hence, S,(O) values reported in this work can be used directly without introducing significant errors in the dose calculation. Acknowledgments

This work was supported in part by Public Health Service Grants Numbers CA-09234 and CA-34964, awarded by the National Cancer Institute, DHHS. The authors would like to thank H Kooy for helpful suggestions pertaining to the MonteCarlo calculations. Resume Simulations de type Monte Carlo des rapports diffuse/primaire pour normaliser et diffuse de la dose.

les composantes primaire

La dtcomposition de la dose absorbee totale en composantes primaire et diffuse est une technique courante pour le calcul de dose dans les faisceaux de photons. La composante primaire dela dose peut itre caracttriste par un coefficient d’atttnuation mesure dans un faisceau itroit et un coefficient de normalisation unique, qui etablit la valeur relative du primaire par rapport i la dose totale pour une profondeur et des dimensions de champ de reference.La determination de ce coefficienta partir de mesures necessite I’extrapolation pour un champ de dimensions nulles des valeurs mesurees avec des champs de dimensions finies. Les auteurs ont utilise des simulations de type Monte Carlo pour Cvaluer les composantes primaire et diffuse de la dose pour des faisceaux de photons de4,6,10, 15 et 24 MV; ils presentent les valeurs du rapport diffust/primaire 51 la profondeur du maximum de dose pour un champ circulaire equivalent B un champ carre de 10 cm x 10 cm. L’incertitude sur ces valeurs est infirieure B 1% et elles peuvent donc etre utilisees a la place des extrapolations de donndes mesurees pour Cvaluer la valeur relative de la composante primaire de la dose dans une large gamme d’energies de faisceaux de photons.

Zusammenfassung Monte CarIo-Berechnungen der Verhaltnisse Primar- und Streustrahlendosen.

von Streustrahlung zu Primarstrahlung zur Normierung der

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R K Rice and L M Chin

Die Trennung der Gesamtenergiedosisin Primar- und Streukomponentenist ein haufig venvandtes Verfahren bei Berechnungen der Photonendosis. Die Dosiskomponente durch Primarstrahlung kann charakterisiert werden durch einen gemessenen Narrow-Beam-Schwachungskoeffizienten und einen einzigen Normierungswert, der den relativen Anteil der Primarstrahlendosis an der Gesamtdosis in einer Referenztiefe und bei einer gegebenen FeldgroBe bestimmt. Die Bestimmung dieses Normierungswertes aus gemessenen Daten erfordert eine Extrapolation der gemessenen Werte fur endliche FeldgroBen, um einen Wert fur die FeldgroBe Null zu erhalten.MitHilfevonMonteCarlo-SimulationenwurdenPrimar-undStreustrahlendosenfur Photonenstrahlen von 4,6, 10, 15 und 24 MV bestimmt, sowie Werte des VerhaltnissesStreu- zu Primarstrahlung in der Tiefe des Dosismaximums fur ein Kreisfeld, aquivalent einem 10 cm x 10 cm Feld. Diese Werte habeneineUnsicherheitvon < l % undkonnenanstattderExtrapolationgemessenerDatenverwendet zu werden, um die relative GroBe der Primarstrahlendosis fur einen weiten Bereich von Photonenenergien bestimmen.

References Ahuja A S, Dubuque G L and Hendee W R 1978 Output factors and scatter ratios for radiotherapy units Phys. Med. Biol. 23 968-71 Bielajew A F and Rogers D W 0 1987 PRESTA: the parameter, reduced electron-step transport algorithm for electron Monte Carlo transport Nucl. Instrum. Methods B18 165-81 Phys. Med. Bjarngard B E and Petti P L 1988 Description of the scatter component in photon beam data Bid. 33 21-32 Day M J 1983 The normalized peak scatter factor and normalized scatter functions for high energy photon beams Br. J. Radiol. suppl. 17 131-6 Phps. Med. Biol. Henry W H 1982 Tissue-air ratio and its associated ‘in-air’ reference minimal phantoms 27 153-4 Khan F M, Sewchand W, Lee J and Williamson J F 1980 Revision of tissue-maximum-ratio and scattermaximum-ratio concepts for cobalt-60 and higher energy x-ray beams Med. Phys. 7 230-7 Kijewski P K, Bjarngard B E and Petti P L 1986 Monte Carlo calculations of scatter dose for small field sizes in a 6oCo beam Med. Phys. 13 74-7 Mohan R, Chui C and Lidofsky L 1985 Energy and angular distributions of photons from medical linear accelerators Med. Phys. 12 592-7 NelsonW R, HirayamaAandRogers D W 0 1985 The E G S ~codesystem StanfordLinearAccelerator Report 265 (Stanford, CA: SLAC) Pfalzner P M1981 A revised equation relating tissue-air ratio to percent depth dose Phys. Med. Biol. 26 510- 13

Monte Carlo calculations of scatter to primary ratios for normalisation of primary and scatter dose.

The separation of total absorbed dose into primary and scatter components is a commonly used technique in photon dose calculations. The primary dose c...
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