Chamber-quality factors in 60Co for three plane-parallel chambers for the dosimetry of

electrons, protons and heavier charged particles: PENELOPE Monte Carlo simulations

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2008 Phys. Med. Biol. 53 5917

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Phys. Med. Biol. 53 (2008) 5917–5926 doi:10.1088/0031-9155/53/21/002

Chamber-quality factors in 60Co for threeplane-parallel chambers for the dosimetry ofelectrons, protons and heavier charged particles:PENELOPE Monte Carlo simulations

Vanessa Panettieri1, Josep Sempau2,3 and Pedro Andreo1,4

1 Department of Hospital Physics, Karolinska University Hospital, Stockholm, Sweden2 Institut de Tecniques Energetiques, Universitat Politecnica de Catalunya, Barcelona, Spain3 Networking Research Center on Bioengineering, Biomaterials and Nanomedicine(CIBER-BBN), Barcelona, Spain4 Medical Radiation Physics, Stockholm University–Karolinska Institute, Stockholm, Sweden

E-mail: vanessa.panettieri@karolinska.se

Received 13 June 2008, in final form 11 September 2008Published 3 October 2008Online at stacks.iop.org/PMB/53/5917

Abstract

The IBA-Scanditronix NACP-02, IBA-Wellhofer PPC-40 and PPC-05 plane-parallel ionization chambers have been simulated with the Monte Carlo codePENELOPE to obtain their chamber- and quality-dependent factors fc,Qo fora 60Co gamma beam. These are applicable to the determination of kQ beam-quality factors for the dosimetry of electron, protons and heavier chargedparticles beams based on standards of absorbed dose to water. The factorfc,Q is equivalent to the product sw,airp, but it is not subject to the assumedindependence of perturbation factors and stopping power (Sempau et al2004 Phys. Med. Biol. 49 4427–44). The calculations have been carried outusing three different 60Co source models: a monoenergetic point source, apoint source with a realistic 60Co spectrum and the simulated phase spacefrom a radiotherapy 60Co unit. Both the detailed geometries of the ionizationchambers and of the 60Co unit have been obtained from the manufacturers.In the case of the NACP-02 chamber, values of fc,Qo have been comparedwith those in the IAEA TRS-398 Code of Practice and from other authors,results being in excellent agreement. The PPC-05 and PPC-40 chambers areof relatively new design, and their values have not been calculated before.Within the estimated uncertainty, computed at the 2σ level (95% confidencelimit), the results for each of the three chambers appear to be independent ofthe degree of sophistication of the 60Co source model used. For the NACP-02chamber this assumption is justified by the excellent agreement between thevarious models, which occurs at the level of one standard uncertainty. Thissuggests the possibility of adopting the mean value of the three source models,weighted with the inverse of their corresponding uncertainties, as a better

0031-9155/08/215917+10$30.00 © 2008 Institute of Physics and Engineering in Medicine Printed in the UK 5917

5918 V Panettieri et al

estimate of fc,Qo. A consequence of the above conclusions is that the estimateduncertainty of kQ beam-quality factors of all charged particles referred to 60Cocan potentially be decreased considerably using our approach. For example,the estimated relative standard uncertainty of the denominator of kQ, given inTRS-398 as 1.6% for plane-parallel ionization chambers, can be reduced to0.06% for a NACP chamber using the mean value of fc,Qo given in this work.Similar reductions could be obtained for the combined standard uncertainty ofthe kQ beam-quality factors of all charged particles, notably electrons.

1. Introduction

Dosimetry protocols based on absorbed dose to water standards (see, e.g., IAEA TRS-398, byAndreo et al (2000) and AAPM TG-51, by Almond et al (1999)) require the use of ionizationchambers calibrated in a water phantom at a certain beam quality Qo. To account for differentbeam user qualities Q, a beam-quality correction factor kQ,Qo is introduced in the formalism, afactor which is denoted as kQ when the reference quality Qo is 60Co gamma rays. The beam-quality correction factor is evaluated as the ratio, at the qualities Q and Qo, of the productsw,airp, where sw,air is the water-to-air stopping-power ratio, and p is an overall perturbationfactor; sw,air and p are beam-quality dependent and p is, in addition, chamber dependent.

Both TRS-398 and TG-51 recommend the use of plane-parallel ionization chambersfor electron beam dosimetry and, in addition, TRS-398 recommends this type of chambersfor protons and heavier charged particles dosimetry5. In the case of electrons, a preferredrecommendation is to cross-calibrate plane-parallel chambers (versus a cylindrical chamber)at a high electron energy, mainly to circumvent the use of 60Co quality for which the uncertaintyof the overall perturbation factor p poses the largest contribution to the final estimate of theuncertainty for kQ. The recommendation, however, is not made in the case of protons andheavier charged particles, even if a similar argument on uncertainties applies (limited bythose of stopping-power ratios and Wair/e), and kQ values are always referred to 60Co. Inaddition, many users and standard laboratories still prefer that the calibration of plane-parallelionization chambers is made at the reference 60Co beam of the calibration lab in order tomaintain the same type of traceability as for high-energy photon beams, which might havelegal implications.

There is then a need for generating numerical data at 60Co quality entering into the kQ

values for the various radiotherapy beam types for plane-parallel ionization chambers in wideuse, as well as for new chambers recently developed for which no values exist. The presentwork aims at this goal.

Different authors (see, e.g., Aldana et al 2003, Sempau et al 2004, Capote et al 2004),introduced an alternative approach based on Monte Carlo (MC) methods to obtain kQ,Qo

for electron beams that did not rely on the commonly assumed independence of perturbationfactors and stopping-power ratios at a given quality. Instead, a chamber- and quality-dependentfactor fc,Q (here abbreviated as chamber-quality factor) was defined for a given quality, as

5 The terminology recommended jointly by the International Commission on Radiation Units and Measurements(ICRU) and the International Atomic Energy Agency (IAEA) is used here, where the term ‘light ions’ is used fornuclei with atomic number equal or smaller than 10 (neon), whereas the term ‘heavy ions’ is used for numbers above10 (for example, silicon or argon). The general recommendation is to refer to ‘protons and heavier charged particles’(Wambersie et al 2004).

Chamber-quality factors in 60Co 5919

the ratio of the MC-calculated absorbed dose to water at the reference depth and the averageabsorbed dose in the ionization chamber (i.e. in its air cavity) when its reference point is placedat the reference depth, that is

fc,Q ≡ Dw

Dair, (1)

and then kQ,Qo can be simply evaluated as

kQ,Qo = fc,Q

fc,Qo. (2)

This type of approach is now commonly used in MC calculations of chamber correctionfactors (Sanchez-Doblado et al 2005, Zink and Wulff 2008), and in the present work it hasbeen applied to obtain the values of fc,Qo for 60Co for the three plane-parallel ionizationchambers studied in the previous work (Sempau et al 2004), namely, the IBA-ScanditronixNACP-02, the IBA-Wellhofer PPC-05 and PPC-40.

2. Monte Carlo simulations

MC simulations of the absorbed dose in the air cavity of the three ion chambers analysedwere performed by using the PENELOPE code system (Salvat et al 2006). Three differentsource models were employed, as described in section 2.1. The absorbed dose to water underthe same irradiation conditions was also calculated so that the ratio in equation 1 could bedetermined.

PENELOPE is a subroutine package that requires a steering main program. We relied onthe general-purpose main program provided with the PENEASY package (Sempau and Badal2008), which includes several source models and tallies. This code had to be adapted to fitour needs, mainly to implement the variance reduction techniques described below.

2.1. Radiation sources

In order to investigate the importance of an accurate description of the radiation source,three source models were used, namely, (i) a monoenergetic point source emitting 1.25 MeVphotons, (ii) a point source with the spectrum of a cobalt unit obtained with the EGS4 code(Nelson et al 1985, Rogers et al 1988), and (iii) a phase-space file (PSF) obtained by simulatinga cobalt therapy unit with PENELOPE. In all cases, the source-surface distance (SSD) was100 cm, and the beam defined a 10 × 10 cm2 field on the phantom surface.

In the PSF case, the radiation field was obtained by modelling a Nordion MDS Eldorado-78 machine (MDS Nordion, Kanata, Canada) according to the manufacturer’s specifications.To get a reasonably low statistical uncertainty in the dose calculations, the PSF must containa relatively large number of particles, which implies a long computation time. In order toreduce this time, two variance reduction (VR) techniques, Russian roulette and source biasing(Bielajew and Rogers 1988, Rogers et al 1995), were implemented in the main program. Thecomputation was also parallelized, as explained later.

Russian roulette speeds up the calculation by discarding particles that are unlikely toproduce any relevant contribution to the sought tally. In our case, it was applied for electronsand positrons entering the brass and lead casing surrounding the source. The killing probabilityP was set to 0.95 and, in consequence, simulation results were kept unbiased by increasingthe statistical weight of the surviving particles by a factor 1/(1 − P) equal to 20.

5920 V Panettieri et al

Source biasing (Briesmeister 1993) was implemented by changing the probabilitydistribution of the direction of emission of the source. The standard source routine in PENEASY

provides an emission with uniform probability per unit solid angle and limited to a cone withan user-defined aperture. Instead, to increase the number of particles reaching the scoringplane, the isotropic distribution was replaced by a distribution per unit solid angle given by twodifferent constant values in two different intervals of the polar angle of emission θ . The firstinterval was defined by having cos θ between 1 (pointing downstream and corresponding to anangle of 0◦) and 0.995 (corresponding to an angle of 5.73◦), and it was assigned an emissionprobability of 50%. The other interval covered the rest of polar angles and the remaining50% of probability. These values resulted from the optimization of the simulation efficiencyassociated with the lateral profiles obtained in a homogenous water phantom. The statisticalweight of the particles was modified accordingly.

Overall, the combination of Russian roulette and particle splitting increased the numberof particles written to the PSF per unit time by a factor of ∼16. The generated PSF containedapproximately three million particles, which represents about 10% of the number of primarycobalt photons simulated. Although this may seem like a modest size for a PSF, it should beborne in mind that the application of the source-biasing technique described above impliesthat the density of particles per unit surface (and their statistical weight) was not uniformthroughout the field. Indeed, more particles were located in the region directly upstream ofthe ion chamber and its close surroundings than in the rest of the radiation field. It should alsobe mentioned that particle splitting was applied, so that each particle in the PSF was clonedinto 100 identical copies with a statistical weight reduced by a factor of 0.01.

To validate the PSF a series of simulations was carried out in a homogenous water phantomto obtain percentage depth doses (PDD) and lateral profiles. PDDs were calculated in thecentral axis, and the lateral profiles were simulated at a depth of 5 cm in the water phantom. MCresults were compared with experimental measurements carried out, under the same conditions,with an ionization chamber. For the PDD, the difference between MC and experimental datawas always less than the standard statistical uncertainty of the simulation (about 0.5% at 1σ ).For lateral profiles, the maximum in-field discrepancy between experiment and simulation was∼2%, which is of the same order of magnitude as the recommended tolerance level in mostTPS quality assurance protocols (Fraas et al 1998). Since our simulations were performedwith the chambers placed in the central axis, this validation was considered sufficient for thepurpose of this work.

All computations were parallelized using a cluster with 16 CPUs (Intel Pentium IV at3.0 GHz clock speed) with the package CLONEASY (Badal and Sempau 2005). To ensurestatistical independence, various CPUs were supplied with non-overlapping sequences ofpseudo-random numbers. With this hardware, the generation of the PSF took less than a weekto complete.

2.2. Plane-parallel chambers

The three chambers studied were the IBA-Scanditronix NACP-02, and the IBA-WellhoferPPC-05 and PPC-40. A very detailed description of their geometry and material compositionwas prepared using data provided by the manufacturer, as discussed in a previous work bySempau et al (2004). Their characteristics are given in table 1 and to illustrate the degree ofdetail of our model, the geometry used in the simulation of the NACP-02 chamber is shownin figure 1. All the calculations were performed by positioning the chambers’ inner surfaceof the front window under reference conditions in a semi-infinite water phantom, i.e., at 5 cmdepth in water and at an SSD of 100 cm.

Chamber-quality factors in 60Co 5921

Figure 1. Geometry model employed for the Scanditronix NACP-02 chamber. Each colourrepresents a different material, as follows: the purple region (1) is a mylar foil, yellow is graphite(2), red is rexolite, (3) and cyan (visible in the cavity) is a graphite liner (4). The 2.05 mm thickchamber cavity is filled with air.

(This figure is in colour only in the electronic version)

Table 1. Characteristics of the three plane-parallel chambers used in this study as presented in theprevious work by Sempau et al (2004).

Chamber Electrode Collecting Guardtype Materials spacing (height) diameter ring width thickness Window

NACP-02 Maylar foil and graphite window 2 mm 10 mm 3 mm 104 mg cm−2

Graphited rexolite electrode 0.6 mmGraphite body (back wall)rexolite housing

PPC-40 Window and body PMMA 2 mm 16 mm 4 mm 118 mg cm−2

Graphited PMMA electrode 1 mm

PPC-05 Window and body Shonka C-552 0.6 mm 9.9 mm 3.5 mm 176 mg cm−2

Graphited PEEK electrode 1 mm

In PENELOPE, photon transport is simulated by means of a detailed simulation scheme,i.e., interaction by interaction. Electron and positron histories are generated on the basisof a mixed procedure, which combines detailed simulation of hard events (those involvingenergy losses or angular deflections above certain user-defined cutoffs) with fully condensedsimulation of soft interactions. For a more detailed description of the transport algorithmsimplemented in this code system, the interested reader is referred to its accompanyingdocumentation (Salvat et al 2006).

The transport algorithm of PENELOPE is governed by eight user-defined simulationparameters for each material. Briefly, these parameters are three absorption energies (EABS),one for each particle type (i.e., photons, electrons or positrons), at which transport isdiscontinued, and the remaining kinetic energy is locally absorbed; C1 (average elasticangular deflection, 1 − cos θ , in a step) and C2 (average fractional energy loss in a step),which determine the cutoff angle that separates hard from soft elastic interactions; WCCand WCR, the cutoff energies for the production of hard inelastic and bremsstralung events,respectively; and the distance DSMAX, an upper limit to the allowed step length. As described

5922 V Panettieri et al

by Sempau and Andreo (2006), the use of smaller simulation parameters implies shorter pathlengths and, hence, a higher accuracy at the expense of a slower computation.

In our case, the intention is to select an increasing degree of detail in the transport ofcharged particles as these approach the chamber sensitive volume by selecting progressivelysmaller values of the simulation parameters. To obtain the highest accuracy, detailed (i.e.collision-by-collision) simulation was used inside the air cavity, both in the sensitive part,where the deposited energy is scored, and in the remaining air. This was done by settingWCC, WCR, C1 and C2 to zero. In addition, thin ‘skin’ regions with relatively smallparameters (WCC and WCR equal to 0.1 keV, and C1 and C2 equal to 0.01) were defined inboth the graphite and the rexolite surrounding the cavity. In all the other regions, electrontransport parameters were chosen to be less conservative (WCC and WCR depending of theemployed EABS and C1 and C2 equal to 0.1). Absorption energies were set to 1 keV for allparticles in the cavity neighbourhood—this value was chosen so that electron transport in theproximity of the cavity is terminated at an energy which is smaller than the energy necessaryto span the air. Larger EABS values were used for more distant regions where the probabilityof lower energy electrons reaching the cavity is negligibly small.

A strong limitation in the MC simulations of ionization chambers is related to the factthat the physical dimensions of the chambers are relatively small compared with the typicalradiation fields used in the clinical practice (for example, the NACP chamber has a sensitivevolume of 0.16 cm3) and, therefore, only a very small fraction of the interactions will occurin the vicinity of the air cavity. This could lead to very inefficient simulations. To overcomethis limitation we again relied on the use of VR techniques and parallel computing. First,particle splitting (Bielajew and Rogers 1988) was applied to particles reaching the chamberouter boundary. Additionally, for positrons and electrons, range rejection was applied inthe water surrounding the chamber. This latter method is equivalent to selecting differentabsorption energies (EABS) according to the distance of the particle to the sensitive volume.For photons, Russian roulette and interaction forcing were employed. By interaction forcingwe mean the method, implemented in the standard PENELOPE distribution, that consists inartificially increasing the interaction probability per unit path length of the process of interestand reducing the statistical weight accordingly. This increase in the interaction probabilityaffects only the production of secondary particles, but it does not alter, on average, the stateof the primary particle. In our case, this technique was applied in the sensitive air and in theskin regions around it. Russian roulette, in turn, was applied to photons that interacted withthe water at a point located far from the chamber.

The introduction of these VR techniques allowed a reduction in the simulation time bya factor of ∼200. The energy deposited (and hence the absorbed dose Dair) per MC history6

in the sensitive air of each chamber was obtained with the aid of the corresponding tally ofPENEASY, which is based on the so-called collision estimator.

The next task was to evaluate the absorbed dose to water Dw. In principle, this quantityshould be determined at the point of interest. However, this is unfeasible in any MC simulation;instead, a very small, but finite, volume (3 × 10−4 cm high with a radius of 0.5 cm) aroundthe point of interest was considered. This layer of water was chosen thin enough so that theabsorbed dose was approximately independent of its size. The radius was chosen to be similarto the radius of the sensitive region of the studied ion chambers. To verify the suitability ofthis configuration, simulations were carried out in a water phantom with two different scoringvolumes, namely, a cylinder with a radius of 0.5 cm and a parallelepiped with a square base

6 MC history is understood to be a primary photon emerging from the 60Co source and all the electromagnetic showergenerated by it.

Chamber-quality factors in 60Co 5923

1.14

1.15

1.16

1.17

1.18

IAEATRS-398

PALM2000

Stewart2002

Mainegra2003

SPE MONOPENELOPE

PSF

f c,Q

o

Figure 2. fc,Qo for the Scanditronix NACP-02 chamber. The PENELOPE data correspond to thethree source models analysed, namely, a point source with 60Co spectrum (SPE), a monoenergeticpoint source (MONO) and a PSF source. Other data are as follows: IAEA TRS-398 (Andreoet al 2000, Palm et al 2000, Stewart and Seuntjens 2002) obtained with experimental measurementsand Mainegra-Hing et al (2003) obtained with the EGSnrc MC code using a point source with arealistic 60Co spectrum source. All uncertainty bars are at 1σ .

of 0.4 cm of side. All of them were 3 × 10−4 cm high. The results of the two cases agreedwithin 0.5%, acceptable for our purposes and well within the associated uncertainties.

3. Results and discussion

Simulations were run until the standard statistical uncertainty (1σ ) of fc,Qo was of the orderof 0.1–0.2%. The total calculation time for each chamber would have been of the order of50 days if it had been run on a single CPU, except for the PPC-05, which would take almosttwice as much time due to its smaller active volume—0.046 cm3 compared to the 0.16 cm3 ofthe NACP-02. The use of parallel computation reduced the simulation time to about 3 daysfor the NACP-02 and PPC-40 and about 5–6 days for the PPC-05.

In figure 2, our results for the NACP-02 chamber are compared with experimental (Palmet al (2000), Stewart and Seuntjens (2002)) and MC (Mainegra-Hing et al (2003)) datafrom other authors. Comparison is also given with the value provided by the IAEA TRS-398 obtained by the product sw,airp (Andreo et al 2000). The results are also presented innumerical form in table 2, and the weighted mean of fc,Qo given by the three different sourceswith its combined uncertainty is also provided. The weight of each source component wasassigned to be the inverse of its variance. As can be seen, the MC calculations performedwith PENELOPE using the direct method yield values of Dw/Dair that are in agreementwith those published by the other authors and, in particular, with the value from the IAEATRS-398 Code of Practice, although our result has a considerably lower statistical uncertainty.It is emphasized that for this chamber the three 60Co source models employed in this studyprovide essentially the same results within the estimated statistical uncertainty (see table 2 andfigure 2), thus suggesting that simple models can be used in the determination of fc,Qo forother chambers in the future.

5924 V Panettieri et al

1.135

1.14

1.145

1.15

SPE MONO PSF

f cQ

o

1.135

1.14

1.145

1.15

SPE MONO PSF

f c,Q

o

Figure 3. MC values of fc,Qo for the Wellhofer PPC-05 (circles) and PPC-40 (triangles) chambers.Results are given for a point source with 60Co spectrum (SPE), a monoenergetic point source(MONO) and a PSF. Statistical uncertainty bars are at 1σ .

Table 2. fc,Qo for the Scanditronix NACP-02 chamber. The correction factors obtained witha point source with 60Co spectrum (SPE), a monoenergetic point source (MONO) and a PSFare given. In the third and fourth columns, respectively, the absolute (u) and the relative (u%)statistical standard uncertainties (1σ) associated with each datum are shown. The weighted meanvalue (WEIGHTED MEAN) of the fc,Qo calculated with the three different sources is also given,as well as the corresponding standard uncertainty.

Type of source fc,Qo u(1σ) u% (1σ)

SPECTRUM 1.1575 0.0012 0.10MONO 1.1579 0.0010 0.09PSF 1.1588 0.0024 0.21WEIGHTED MEAN 1.1578 0.0007 0.06

Table 3. fc,Qo for the Wellhofer PPC-05 chamber. See table 2 for details.

Type of source fc,Qo u(1σ) u% (1σ)

SPECTRUM 1.1374 0.0025 0.22MONO 1.1405 0.0011 0.10PSF 1.1461 0.0030 0.26WEIGHTED MEAN 1.1410 0.0010 0.09

Figure 3 shows the results of the present study for the PPC-05 and PPC-40 chambers.The same data are presented in tables 3 and 4 in numerical form. The Wellhofer chambers arerelatively new, and to the best of our knowledge, they have not been studied in detail before;therefore, we present only data obtained with our three source models. Here, the equivalenceamong the three source models is not as good as in the previous case, but they agree withintwo standard deviations (2σ), i.e., the estimated expanded uncertainty with a coverage factorof 2 (95% confidence limit).

Chamber-quality factors in 60Co 5925

Table 4. fc,Qo for the Wellhofer PPC-40 chamber. Same details as in table 2.

Type of source fc,Qo u(1σ) u% (1σ)

SPECTRUM 1.1466 0.0010 0.09MONO 1.1452 0.0010 0.09PSF 1.1418 0.0023 0.20WEIGHTED MEAN 1.1455 0.0007 0.06

4. Conclusions

Values of the chamber-quality factor, fc,Qo, have been calculated for 60Co for the three plane-parallel ionization chambers IBA-Scanditronix NACP-02, the IBA-Wellhofer PPC-05 andPPC-40. These values are of use for the dosimetry of electron, protons and heavier chargedparticles based on standards of absorbed dose to water with kQ,Qo beam-quality factors referredto the reference 60Co beam of a calibration laboratory (kQ).

The calculated fc,Qo factors, equivalent to the product sw,airp but not subject to theassumed independence of perturbation factors and stopping-power ratios, have been comparedwith existing similar data for the NACP-02 chamber, finding excellent agreement among allthe MC calculations and experimental data. This provides reliability on the robustness ofthe approach and methodology of the present work, which can then be used for the otherplane-parallel chambers of new design.

Within the estimated uncertainty, computed at the 2σ level (95% confidence limit), theresults for each of the three chambers appear to be independent of the degree of sophisticationof the 60Co source model used. For the NACP-02 chamber this assumption is justified by theexcellent agreement between the various models, which occurs at the level of one standarduncertainty. Note that the maximum difference is 0.11%, which is not far from the combineduncertainty of the mean, 0.06%. This observation seems to suggest the possibility of adoptingthe mean value of the three source models, weighted with the inverse of their correspondinguncertainties, as a better estimate of fc,Qo. For the PPC chambers the agreement is not asgood. For the PPC-05 chamber the maximum difference is 0.76%, whereas the uncertainty ofthe mean is 0.09%. For the PPC-40, the difference is 0.42%, and the mean has an uncertaintyof 0.06%. This may not rule out the possibility of the different models being equivalent, butsheds a doubt on the validity of this assumption. We have included the mean values in tables2, 3 and 4 for completeness, in case the reader deems it appropriate to accept the assumedindependence.

A consequence of the above conclusions is that the estimated uncertainty of kQ

beam-quality factors of all charged particles referred to 60Co can potentially be decreasedconsiderably using our approach. For example, the estimated relative standard uncertainty uof the denominator of kQ given in TRS-398 as 1.6% for plane-parallel ionization chambers(cf table 38 therein) can be reduced to 0.06% for a NACP chamber using the mean valueof table 2 of the present work while maintaining the estimated uncertainties of TRS-398 forthe assignment of sw,air to beam quality and Wair/e. If it is further assumed that the effectof the uncertainties in the cross sections employed in the computations can be approximatedby the relative uncertainty, also employed in TRS-398, for the stopping-power ratio sw,air

7

which equals 0.5%, the resulting u is below 0.6%, still much lower than the currently acceptedvalue. Similar reductions could be obtained for the combined standard uncertainty of the kQ

beam-quality factors of all charged particles, notably electrons. In the case of protons, and

7 It should be noted that this uncertainty accounts for variations in the mean excitation energies and density effectcorrections of ion chamber materials.

5926 V Panettieri et al

especially of heavier charged particles, the reduction is limited by the current knowledge ofthe relevant stopping-power ratios, Wair/e and their associated uncertainties.

Acknowledgments

Scanditronix–Wellhofer (IBA) is gratefully acknowledged for the support provided to thisinvestigation. JS acknowledges financial support from the Fondo de Investigacion Sanitaria ofthe Spanish Ministerio de Sanidad y Consumo, project no FIS 01/0093 and from the SpanishMinisterio de Educacion y Ciencia, project no FIS2006-07016.

References

Aldana J, Sempau J, Mazurier J, Andreo P and Salvat F 2003 Monte Carlo determination of electron beam qualitycorrection factors for plane-parallel ionization chambers Rad. Oncol. 68 561

Almond P R, Biggs P J, Coursey B M, Hanson W F, Huq M S, Nath R and Rogers D W O 1999 AAPM’s TG-51protocol for clinical reference dosimetry of high-energy photon and electron beams Med. Phys. 26 1847–70

Andreo P, Burns D T, Hohlfeld K, Huq M S, Kanai T, Laitano F, Smyth V and Vynckier S 2000 Absorbed DoseDetermination in External Beam Radiotherapy: An International Code of Practice for Dosimetry Based onStandards of Absorbed Dose to Water Technical Report TRS 398 International Atomic Energy Agency

Badal A and Sempau J 2005 A package of Linux scripts for the parallelization of Monte Carlo simulations Comp.Phys. Comm. 175 440–50

Bielajew A F and Rogers D W O 1988 Variance reduction techniques Monte Carlo transport of Electrons and Photonsed T M Jenkins, W R Nelson and A Rindi (New York: Plenum)

Briesmeister J F 1993 MCNP—A General Monte Carlo N-Particle Transport Code, Version 4A, Los Alamos NationalLaboratory Report LA-12625

Capote R, Sanchez-Doblado F, Leal A, Arrans R and Hartmann G H 2004 An EGSnrc Monte Carlo study of themicroionization chamber for reference dosimetry of narrow irregular IMRT beamlets Med. Phys. 31 2416–22

Fraas B, Doppke K and Hunt M 1998 Quality assurance for clinical radiotherapy treatement planning, AAPMRadiation Therapy committee TG53 Med. Phys. 25 1773, 1829

Mainegra-Hing E, Kawrakow I and Rogers D W O 2003 Calculations for plane-parallel ion chambers in Co-60 beamsusing the EGSnrc Monte Carlo code Med. Phys. 30 179–89

Nelson W R, Hirayama H and Rogers D W O 1985 The EGS4 code system Technical Report SLAC-265 (StanfordLinear Accelerator Center)

Palm A, Mattsson O and Andreo P 2000 Calibration of plane-parallel chambers and determination of pwall for theNACP and Roos chambers for Co-60 gamma-rays beams Phys. Med. Biol. 45 971–81

Rogers D W O, Ewart G M, Bielajew A F and van Dyk G 1988 Calculation of electron contamination in a 60Cotherapy beam Proc. IAEA Int. Symp. Dosimetry in Radiotherapy (Vienna)

Rogers D W O, Faddegon B A, Ding G X, Ma C M, We J and Mackie T R 1995 BEAM: A Monte Carlo code tosimulate radiotherapy treatments units Med. Phys. 22 503–24

Salvat F, Fernandez-Varea J M and Sempau J 2006 PENELOPE-2006: A Code System for Monte Carlo Simulationof Electron and Photon Transport (Issy-les-Moulineaux, France: OECD Nuclear Energy Agency) (available inpdf format at http://www.nea.fr)

Sanchez-Doblado F, Capote R, Leal A, Rosello J, Lagares J, Arrans R and Hartmann G H 2005 Microionizationchamber for reference dosimetry in IMRT verification: clinical implications on OAR dosimetric errors Phys.Med. Biol. 50 959–70

Sempau J and Andreo P 2006 Configuration of the electron transport algorithm of PENELOPE to simulate ionchambers Phys. Med. Biol. 51 3533–48

Sempau J, Andreo P, Aldana J, Mazurier J and Salvat F 2004 Electron beam quality correction factors for plane-parallelionization chambers: Monte Carlo calculations using the PENELOPE system Phys. Med. Biol. 49 4427–44

Sempau J and Badal A 2008 PENEASY, a modular main program and voxelised geometry package for PENELOPEfreely available at (http://www.upc.edu/inte/downloads/penEasy.htm)

Stewart K J and Seuntjens P J 2002 Comparing calibration methods of electron beams using plane-parallel chamberswith absorbed-dose to water based protocols Med. Phys. 29 284–9

Wambersie A, DeLuca P M, Andreo P and Hendry J H 2004 ‘Light’ or ‘heavy’ ions: a debate of terminology Rad.Oncol. 73 iiii (Suppl S2)

Zink K and Wulff J 2008 Monte Carlo calculations of beam quality correction factors kQ for electron dosimetry witha parallel-plate Roos chamber Phys. Med. Biol. 53 1595–607