Phys. Med. Biol.42 (1997) 1505–1514. Printed in the UK PII: S0031-9155(97)81132-3

Practical approach to electron beam dosimetry at extendedSSD

Joanna Cygler, X Allen Li, George X Ding and Edward LawrenceDepartment of Medical Physics, Ottawa Regional Cancer Centre, Civic Division,190 Melrose Avenue, Ottawa, Ontario K1Y 4K7, Canada

Received 20 January 1997

Abstract. This paper presents a practical approach to clinical dosimetry for electron beams atextended source-to-surface distance (SSD). Characteristics of electron beams from a SiemensMD-2 accelerator are presented at a nominal SSD of 100 cm and an extended SSD of 115 cm.Relative output factors are measured at both 100 and 115 cm SSDs for a range of square fieldsizes for each beam energy. The change of output with SSD does not follow the inverse squarelaw, if the nominal SSD is used. This deviation is larger for lower beam energy and smallerfield sizes. An effective SSD, SSDeff, has been determined atdmax for each beam energy as afunction of field size. A comprehensive approach to treatment time calculations is proposed.

1. Introduction

The characteristics of clinical electron beams depend on the primary beam’s parametersas well as on the scattering materials present in the beam. Electron interactions with theaccelerator head components and the field defining apertures affect the dose distribution inthe phantom not only at a standard source-to-surface distance (SSD) but also at extendedtreatment distances. The fraction of electrons scattered from the applicator walls andreaching the phantom has an influence on the percentage depth–dose curve (%DD), fieldflatness, penumbra and relative output factors (ROF). These beam characteristics changewhen the SSD increases.

It has been noted before that corrections to dose rate at extended SSD do not followthe inverse square law (ISL) if the nominal value of SSD (usually 100 cm) is used (Khanet al 1978). This is due to the fact that the nominal SSD is often defined as the distancefrom the accelerator exit window to the phantom surface, while the apparent source is infact positioned not at the window but at various distances downstream from the window,depending on the amount of scattering material present in the beam (ICRU 1984). Severalapproaches have been proposed to describe the electron source in a clinical accelerator:effective extended source (ICRU 1984), virtual source (Khanet al 1991) and effectivesource (Khanet al 1978). They all have their merit for various applications but also havetheir limitations.

For the purpose of ISL corrections to the dose rate in clinical situations, the effectivesource approach proposed by Khanet al (1978) is the most practical one, since it properlypredicts the distance dependence of the output of clinical beams. The effective SSD is thedistance from the phantom surface to the effective source. The effective SSD is known todepend on beam energy and field size (Khanet al 1978, Sweeneyet al 1981, Jamshidiet al

0031-9155/97/081505+10$19.50c© 1997 IOP Publishing Ltd 1505

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1986, Robacket al 1995). This complicates the treatment time calculations at extendedSSDs, since a large number of clinical data are needed.

In our clinic we have recently commissioned a new Siemens MD-2 accelerator. Thiswas an occasion to review our electron beam dosimetry and define a more comprehensiveapproach to everyday clinical problems. In this paper we discuss the effects of extendedSSD on electron beams characteristics as well as our approach to treatment time calculations.

2. Experiment

A Siemens MD-2 accelerator produces electron beams in the energy range of 5–15 MeV. Theunit has various applicators with nominal source to applicator-end-distance of 95 cm. Thisintroduces a 5 cm air gapbetween the applicator end and the nominal SSD (100 cm) plane.The detailed description of this applicator has been given elsewhere (Ebert and Hoban 1995).A variety of field-shaping cerrobend cut-outs were designed and inserted in the applicatorsto define irregular fields. An RFA 300 dosimetry system (Therados) with a p-type silicondiode was used to measure lateral beam profiles and depth–dose curves in water for allfield sizes defined by open applicators and cut-outs. The output factors for each applicatorand cut-out were measured atdmax for each field size using an RK cylindrical chamber(0.12 cc) supplied by Scanditronix. The relative output factors for applicators (ROFapp)were defined in reference to open 10× 10 cm2 applicator. The relative output factors forcerrobend cut-outs (ROFcut) were defined in reference to open applicators. Measurementswere performed at various SSDs ranging from 95 to 125 cm. The measurement uncertaintywas±0.3%.

3. Results

3.1. Depth–dose curves

The parameters of the %DD curves for electron beams for 100 cm SSD and open 10×10 cm2

applicator are presented as a function of the nominal beam energy in table 1. For a givenfield size these parameters depend strongly on the beam energy. For a given energy, thedepth–dose curve depends on the field size. For smaller field sizes the maximum of the%DD curve shifts towards the surface of the phantom, as shown in table 2. This shift ismore pronounced for higher energies.

Table 1. Siemens MD2 electron beam parameters, measured in water with silicon p-type diodes.10× 10 cm2 applicator, SSD= 100 cm.

Nominalenergy (MeV) dmax (cm) R85 (cm) R50 (cm) R20 (cm) Rp (cm)

6 1.45 1.95 2.40 2.76 2.949 2.10 2.94 3.59 4.11 4.33

11 2.60 3.63 4.43 5.05 5.3713 2.90 4.20 5.13 5.86 6.21

For field sizes greater than 5×5 cm2, it is found that as the SSD increases the percentagesurface dose and dose in the build-up region decrease, but the %DD curves beyond the depthof maximum dose are not practically affected. The effects of extended SSD become moreobservable for higher electron-beam energies. It is found that the variation in the %DD

Electron beam dosimetry at extended SSD 1507

Table 2. Dependence ofdmax (cm) on the cut-out size. 10×10 cm2 applicator, SSD= 100 cm.

Square cut-out(cm2)

Energy 10× 10(MeV) open 8× 8 7× 7 6× 6 5× 5 4× 4 3× 3 2× 2

6 1.45 1.45 1.45 1.40 1.40 1.40 1.25 1.009 2.10 2.10 2.10 2.10 2.10 2.00 1.70 1.10

11 2.60 2.60 2.60 2.60 2.45 2.25 1.95 1.2013 2.90 2.90 2.90 2.90 2.70 2.50 2.00 1.30

curves is up to 6% as SSD increases from 100 to 115 cm for a 13 MeV electron beam and10× 10 cm2 open applicator. The extended SSD effects observed at present for field sizesgreater than 5× 5 cm2 agree generally with those reported previously (Sawet al 1994,1995) for a similar machine.

For cut-out sizes less than 5×5 cm2, the extended SSD affects the entire %DD curves.Figure 1 shows the extended SSD effects on the %DD curves for the 6 and 13 MeV beamswith the 2× 2 cm2 cut-out in the 10× 10 cm2 applicator. It is seen from figure 1 thatthe change in the %DD curves is up to 10% as SSD increases from 100 to 115 cm for the6 MeV electron beam with the 2× 2 cm2 cut-out. The data presented here for small fieldsizes for the Siemens MD2 linac show comparable effects to those observed for a VarianClinac-2100C unit (Daset al 1995).

It should be noted that the biggest change due to extended SSD for a 10× 10 cm2

field occurs at the surface. Unlike the conclusions reported by the previous studies (Sawet al 1994, 1995, Daset al 1995), in the present work the percentage surface dose doesnot always decrease as the SSD increases. The percentage surface dose increases in thesesmall-field cases for whichdmax shifts towards the surface. The percentage surface dosedecreases whendmax shifts away from the surface or does not change.

Note that the AAPM TG-25 (Khanet al 1991) suggests using a 1/r2 divergence factor(TG25, equation (29)) to correct %DD at extended SSD. We find that this divergence factor istoo small to modify the %DD curves for all the field sizes for our machine. For comparison,figure 1 includes the %DD curve for the 6 MeV, 2× 2 cm2 cut-out, at SSD= 115 cm,corrected using the divergence factor.

3.2. Lateral profiles

The extended SSD effects on profiles are represented by a loss of field flatness and anenlargement of the penumbra. Figures 2 and 3 show beam penumbra and flatness againstelectron beam energy for different cone and cut-out sizes at SSD of 100 and 115 cm. Thepenumbra is typically defined as the distance between 20 and 80% of maximum intensityseen in the profile at the depth of maximum dose (ICRU 1984). The flatness is specifiedas the percentage difference between maximum and minimum intensity seen in 80% of thefield width on the beam profile at depth of maximum dose, where the field width is definedas width of 50% intensity (ICRU 1984). It is seen from figure 2 that the electron fieldpenumbra increases at extended SSD for all cone and cut-out sizes studied. This effectbecomes more severe for lower electron energies. This is because electron scattering poweris much higher for lower energies (ICRU 1984, Li and Rogers 1995). The loss of electronbeam flatness, which is represented by a rounded shape profile, depends slightly on coneor cut-out size and beam energy as seen from figure 3. This loss may be explained by the

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Figure 1. Percent depth–dose curves for a 2× 2 cm2 cut-out in a 10× 10 cm2 cone at 100 and115 cm SSD for (a) 6 MeV and (b) 13 MeV electron beams.

fact that the electrons scattered at large angles from the sides of the cone or the cut-outcontribute to the dose at the edges of the field at standard SSD. These electrons are lostfrom the beam at extended SSD and thus the beams are less flat.

3.3. Relative output factors

For clinical purposes relative output factors are needed for all applicators, cut-outs and SSDs.The applicator factors, ROFapp, defined as the ratio of the chamber reading atdmax for agiven applicator at an SSD of 100 cm to the chamber reading atdmax for the 10× 10 cm2

applicator at an SSD of 100 cm, are shown in table 3 for various beam energies. The ROFcut

values for the cut-outs were normalized to the detector reading for the given open applicator

Electron beam dosimetry at extended SSD 1509

Figure 2. Electron field penumbra versus electron energy for 2×2, 3×3 and 5×5 cm2 cut-outsin a 10×10 cm2 applicator and for 10×10 and 15×15 cm2 open applicators at 100 and 115 cmSSD. The penumbra is defined as the distance between 20 and 80% of maximum intensity seenin the profile at the depth of maximum dose.

Table 3. Siemens MD2 applicator factors, ROFapp (measured with RK chamber, normalized to10× 10 cm2 applicator at the standard SSD of 100 cm). Measurement uncertainty was±0.3%.

Energy (MeV) Circular 5 cm∅ 10× 10 cm2 15× 15 cm2 20× 20 cm2

6 0.834 1.000 1.013 1.0229 0.924 1.000 0.995 0.974

11 0.938 1.000 0.993 0.97213 0.954 1.000 0.993 0.965

at a given SSD. The data for cut-outs in the 10× 10 cm2 applicator for SSDs of 100 and115 cm are presented in figures 4(a) and (b) for 6 and 13 MeV respectively. The ROFcut

values decrease for smaller cut-outs. The decrease is more pronounced for lower-energybeams. For the same beam energy, the decrease of ROF values, with the field size is morepronounced for larger SSD. This is due to the loss from the beam of electrons scattered atlarger angles. This loss is larger for longer SSDs. Similar data have been collected andsimilar trends have been observed for other applicators.

3.4. Effective source position and inverse square law

To check the application of the inverse square law, and to find the effective source position,measurements were performed at various SSD values ranging from 95 to 125 cm. Themethod we use to find the effective SSD was proposed by Khanet al (1984). If Q0 isthe ionization charge reading atdmax at the standard nominal SSD (100 cm) andQg is the

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Figure 3. Electron field flatness versus electron energy for 2× 2, 3× 3 and 5× 5 cm2 cut-outsin a 10×10 cm2 cone and for 10×10 and 15×15 cm2 open cones at 100 and 115 cm SSD. Theflatness is specified as percentage difference between maximum and minimum intensity seen in80% of the field width on the beam profile at depth of maximum dose, where the field width isdefined as the width of 50% intensity.

reading atdmax with the extra gap, then(Q0

Qg

)1/2

= g

SSDeff + dmax+ 1 (1)

where the gap,g, is the difference between the extended and nominal SSD. From the slopeof the straight line described by equation (1), one can calculate the effective SSD by

SSDeff = 1

slope− dmax. (2)

Figure 5 presents(Q0/Qg)1/2 as a function of the air gap introduced between the nominal

and extended SSD for a 10× 10 cm2 open applicator. The measured data follow a straightline for each electron energy; however, the slopes of the lines are different leading todifferent effective SSDs for different electron beams defined by the 10× 10 cm2 openapplicator. Figure 6 plots the effective SSD as function of field size. It is found that, for6 MeV electrons, the value of SSDeff is 82 cm for the open 10× 10 cm2 applicator andonly 31 cm for the 3× 3 cut-out.

4. Discussion

Electron interactions with the accelerator head components and the field-defining aperturesaffect the dose distribution in the phantom. The effect of extended SSD on %DD curvesdepends on the field size. For large field sizes, there are only small effects observed inthe build-up region. The percentage dose in the build-up region is lower at extended thanat the standard SSD. However, these differences which are at most 2% are not clinically

Electron beam dosimetry at extended SSD 1511

Figure 4. Cut-out factors (ROFcut) for (a) 6 MeV and (b) 13 MeV for cut-outs in a 10×10 cm2

applicator at 100 cm SSD. The measurement uncertainty was±0.3%.

significant. More pronounced changes in %DD curves at extended SSD are observed forsmall field sizes (figure 1). The curve is modified over the entire depth range. The changein %DD curve is specially apparent for lower energies. The observed effect suggests thatbeams defined by small cut-outs are more monodirectional and monoenergetic at largerSSDs than at shorter SSDs.

The penumbra width increases dramatically at extended SSD, specially for lower beamenergies (figure 2). This should be taken into account during treatment planning either byaddition of an appropriately larger margin around the tumour volume or by putting the finalfield-defining cut-out directly on the patient’s skin. At the standard SSD the beam flatnessfor a given field size is practically independent of energy (figure 3). For a given energy,the flatness is worse for smaller field sizes.

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Figure 5. Determination of effective SSD (equation (1)) for an open 10× 10 cm2 applicator.The estimated uncertainty was±0.5%.

Figure 6. Effective SSD as a function of cut-out size for beam energies 6–13 MeV. Themeasurement uncertainty was±0.5%.

Based on graphs similar to figure 5, the effective SSD is found for all beam energies. Thedata are presented in figure 6. For a given energy, the effective SSD depends strongly on thecollimation opening. For larger collimation openings the effective source position appearsto deviate less from the nominal value of 100 cm. Small cut-outs introduce more electronsscattered at larger angles. Therefore the angular distribution of electrons immediately below

Electron beam dosimetry at extended SSD 1513

Figure 7. Applicator gap factors, defined as the ratio of the chamber readings for a givenopen applicator atdmax at an SSD of 115 cm to the chamber reading for this applicator atSSD= 100 cm.

the cut-out is wider. This moves the effective source position closer to the phantom surfaceas compared to the larger field size. For a given collimation opening, the effective SSDdepends on the energy of the beam. The lower the beam energy, the shorter the valueof effective SSD for all field sizes below 15× 15 cm2. For field sizes 15× 15 cm2 andlarger, the effective SSD is practically independent of energy. This behaviour can also beexplained in terms of the angular distribution of the beam. The lower the energy, the widerthe angular distribution of the beam and the shorter the effective SSD. For large field sizes(>15× 15 cm2) the electrons scattered at large angles from the field defining apertures donot reach the central axis atdmax. This causes the angular distribution of electrons on thecentral axis to be narrower and the effective source of the beam appears to be right at theexit window of the accelerator for all beam energies.

The error committed if the nominal SSD is used in the inverse square law correctionsof the dose rate at extended SSD is larger for smaller energies and field sizes. To reducethe chance of errors in treatment time calculations, we have decided to limit the numberof dosimetric data for standard clinical use. Only one value of extended SSD is allowed,equal to 115 cm. Since our machine’s applicators are at 95 cm from the nominal sourceposition, 115 cm SSD gives a 20 cm air gap between the end of the applicator and thepatient surface. This is sufficient for all clinical situations. The treatment time is calculatedbased on the following formula:

#MU = D

RDR× ROFapp×GF× ROFcut

whereD is the dose per fraction, RDR is the reference dose rate for 10× 10 cm openapplicator atdmax and standard SSD of 100 cm, ROFapp is the applicator factor, GF is theapplicator gap factor (GF= 1 at an SSD of 100 cm), and ROFcut is the cut-out factor for agiven applicator at a given SSD. The applicator gap factors, GF, defined as the ratio of thechamber readings for a given open applicator atdmax at an SSD of 115 cm to the chamber

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reading for this applicator at an SSD of 100 cm are presented in figure 7. The cut-outfactors, ROFcut, are presented in figure 4 for 6 and 13 MeV. It is seen from figure 4 thatthe cut-out factors are smaller at 115 cm than at 100 cm SSD. This effect is much morepronounced for 6 than for 13 MeV. It can be explained by a larger fraction of electronswith wider angular distribution in the 6 than in the 13 MeV beam. For a given cut-outsize these electrons are lost from the beam when the air gap between the cut-out and thephantom surface is larger, leading to smaller ROFcut at extended SSD.

5. Conclusions

Electron interactions with the accelerator head components and additional beam-definingcut-outs are complex and result in different values of effective SSD, SSDeff, for differentenergies and field sizes. The inverse square law does apply to dose rate corrections at therange of studied distances, provided the proper value of SSDeff is used. Since this wouldrequire a rather large set of data, it is practical to limit the range of treatment distances forclinical use. It should be noted that the percentage depth–dose is modified over the entirerange of the beam at extended SSD for small field sizes. For the given depth, penumbraincreases with the increase of the treatment distance. All considerations about penumbrasizes should be passed to the physician, to make sure that adequate tumour coverage isachieved.

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