USING VARIAN PHOTON BEAM SOURCE MODEL FOR DOSE CALCULATION OF SMALL FIELDSTuomas Torsti, Laura Korhonen, Viljo Petäjä

Varian Medical Systems Finland Oy, Paciuksenkatu 21, FIN-00270 Helsinki, Finland (Dated: September 2013)

Abstract

The use of small fi elds in radiotherapy techniques has increased substantially, in particular in stereotactic treatments and large uniform or nonuniform fi elds that are composed of small fi elds, such as for intensity-modulated radiation therapy (IMRT). This clinical perspective will focus on an experimental evaluation of the dose calculation accuracy of the anisotropic analytical algorithm (AAA) and Acuros® XB advanced dose calculation (Acuros XB) for small fi eld sizes. All measurements were performed with fi lm, as well as with point dose detectors suitable for small fi eld aperture.

Clinical perspectives | Varian Photon Beam Source Model

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Contents

I. Introduction 3

II. Materials and methods 3

A. Source model, dose deposition engine, confi guration program 3

1. Collimator backscatter factors 4

2. Version history 5

B. Beam data confi guration 7

1. Recommended measurements for open beam 8

2. Tuning of eff ective spot size parameters 9

III. Results 10

A. Basic beam data measurements 10

B. Verifi cation measurements and results 10

IV. Summary and conclusions 11

V. Acknowledgements 12

References 14

Clinical perspectives | Varian Photon Beam Source Model

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I. INTRODUCTION

Treatment using small photon fi elds has been an established practice in stereotactic radiotherapy for many years. On the other hand, the Eclipse™ treatment planning system was originally designed mainly for planning treatments based on conventional, broad photon fi elds — enhancements required for planning treatments using small fi elds have been made incrementally in the newer Eclipse versions only. Also, experimental determination of small fi eld dosimetric data is a challenging task, requiring specialized expertise and extra care in the choice of the detectors used [1]. The goal of this clinical perspective is twofold. First, we present a version his-tory of the fi nal dose calculation algorithms AAA and Acuros XB, detailing the most important incremental improvements from the point of view of accurate dose calculation for small fi elds. Second, we present an experimental evaluation of the dose calculation accuracy of AAA and Acuros XB for small fi eld sizes. For independent evaluations of the accuracy of these algorithms, see for example Refs. [2, 3].

This clinical perspective is organized as follows: In Section IIA, we introduce the reader to the Varian Photon Beam Source Model (VPBSM), an integral part of AAA and Acuros XB algorithms. We discuss the limitations aff ecting the accuracy of small fi eld dose calculation from two points of view: 1) analyzing the diff erences of the physical collimator backscatter factors on the one hand and the residual correc-tion term of the source model that carries the same name. 2) we list several improvements since version 8.6 that have been made in the system aff ecting the accuracy of small fi eld dose calculation. Then in Section IIB, we discuss the mea-surements and manual optimization procedures that help improve the accuracy of the dose calculation for small fi elds using the VPBSM. In Section III, we present the results of comparing calculated dose to fi lm measurements of several small static multileaf collimator (MLC) openings. Finally in Section IV, we present the summary and conclusions.

Throughout this paper, we make several comparisons between versions 8.6, 8.9, 10.0 and 11.0 of AAA and versions 10.0 and 11.0 of Acuros XB to illustrate the plurality of changes made aff ecting the accuracy of modeling of small fi elds. The results with versions 10.0 and 11.0 are very similar, and are not always shown separately. The diff erence between the two versions is discussed in the text.

All measurements presented in this paper, unless otherwise stated, have been performed by Ann Van Esch and Dominique Huyskens from the 7Sigma QA-team in Namur, Belgium using a C-series Varian machine, 6X energy mode. More information about the measurements is given in Section III.

II. MATERIALS AND METHODS

A. Source model, dose deposition engine, confi guration program

Accuracy of dose calculation is aff ected by three separate features in the treatment planning system: 1) an accurate source model for the radiation output of the linear accel-erator, capable of reproducing a suffi ciently wide range of machine types and variations between individual machines; 2) an accurate phantom scatter model, or dose deposition engine, capable of modeling the radiation transport (and con-version to absorbed dose) in the phantom; and 3) a process to optimize, or confi gure, the source model parameters in order to reproduce the actual beam data measurements and verifi cation measurements in a wide range of conditions.

An integral part of source modeling is the calculation of the opening ratio matrix (ORM) for the primary beam, commonly referred to as fl uence (not to be confused with energy fl u-ence). For a static jaw-delimited fi eld, ORM simply equals 1.0 inside and 0.0 (or jaw transmission) outside the jaw opening. For AAA versions prior to version 10.0, ORM was calculated in the Eclipse client* with a fi xed 2.5 mm resolution. For small fi elds, this was a signifi cant limitation which was improved by high resolution fl uence calculation (in version 10.0) and by unifi ed fl uence calculation (UFC) (in version 11.0).

The AAA and Acuros XB algorithms are logically separated into: 1) the source model (VPBSM), 2) the confi guration program, 3) the AAA dose deposition engine, and 4) the Acuros XB dose deposition engine. In confi guring the beam data for AAA or Acuros XB, the confi guration program optimizes the source model parameters using either the AAA or Acuros XB dose deposition engine, respectively. For more information on the source model and its confi guration program, the reader is referred to Ref. [4]. For information on the AAA dose deposition engine, Ref. [5] is useful. For information on the Acuros XB dose deposition engine, consult Ref. [6].

Section III will show that it is possible to confi gure the latest versions (AAA versions 10.0 and 11.0, Acuros XB versions 10.0 and 11.0) of the source model for both dose deposition engines so that accurate results for small static MLC- and jaw openings (5 x 5 mm2 ... 20 x 20 mm2) are obtained.

* Recall the distinction between the Eclipse client and the dose calculation algorithm (or servant): the user interacts directly with the Eclipse client. When dose calculation is requested, the client prepares and sends input data to the servant, and later receives calculated dose. In versions prior to 11.0, the opening ratio matrix (ORM), often referred to simply as “fl uence”, was a part of that input data.

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1. Collimator backscatter factors

Figure 1 shows calculated backscatter factors for symmetric and square jaw-delimited fi elds from the source model beam data confi gured for use in conjunction with AAA and Acuros XB dose deposition engines. The graph also shows data from Figure 9 or Ref [7], showing measured collimator backscatter factor (CBSF) data based on counting the electron pulses or charge from the electron target of an accelerator.

The calculated CBSF is not expected to agree exactly with the measured, physical collimator backscatter factor. This is due to the fact that the CBSF factor in the source model beam data is a residual correction factor taking into account all phenomena of phantom scatter and head scatter that are not otherwise accounted for by the source model or the dose deposition engine. However, the diff erences between the physical back scatter factor and the confi gured values reveal interesting information about the remaining limitations of the source model and the dose deposition engines:

1. The CBSF value for the 1 x 1 cm2 fi eld diff ers mark-edly from the trend followed by CBSF factors for other fi eld sizes for both dose deposition engines.

2. For fi eld sizes smaller than 10 x 10 cm2, the con-fi gured CBSF values follow a rising trend, steeper than the measured one. For the 2 x 2 cm2 fi eld size, the confi gured value is about 4% higher than the measured value.

3. For the largest fi eld sizes Acuros XB CBSF follows the measured values better than AAA CBSF. At 40 x 40 cm2 fi eld size, the diff erence for AAA is about 1%.

Limitations 2 and 3 for AAA are inherent in the detailed implementation of the AAA phantom model. As limitation 1 occurs for both AAA and Acuros XB dose deposition engines, we can conclude that this is a source model limitation. The

phase space of the head scatter source is approximated as a planar distributed source with a Gaussian shape located at the bottom of the fl attening fi lter [4]. According to Monte Carlo simulations performed by Fix et al. [8], a second important source of scattered radiation in the treatment head is located at the edge of the primary collimator. Another approximation is that the source model parameters are optimized using symmetric jaw-delimited fi elds. In the future, introducing MLC-delimited or asymmetric fi elds as input to the confi guration program, the optimization process could produce the source model parameters that will produce realistic CBSF in this fi eld size range.

As discussed above in connection to limitation 2, the CBSF for fi eld sizes smaller than 3 x 3 cm2 appear unphysical, based on comparison with direct measurements. However, by defi nition (as a residual correction factor) these result in a correct abso-lute dose level for jaw-delimited fi eld sizes smaller than 3 x 3 cm2 (in the output factor measurement geometry). Therefore, when small jaw-delimited fi eld sizes are used, it is important to include accurate output factor measurements for the minimum fi eld size used when confi guring the beam data.

However, because accurate output factor measurements for such small fi eld sizes are a challenge, it is worthwhile to con-sider the alternative of leaving the jaws at the 3 x 3 cm2 posi-tion, and instead use the MLC to shape the smallest apertures. One rationalization for this approach is also the fact that the positional accuracy of the MLC leaves is greater than that of the collimator jaws. In this paper, we present several compari-sons of measured and calculated absolute dose for small MLC apertures with variable jaw settings that can shed some light on the optimal combination of jaw- and MLC apertures.

Figure 2 shows results that are obtained for a 1 x 1 cm2 fi eld size delimited either by jaw or the MLC. In the case of jaw-delimited fi eld, also the eff ect of including the fi eld size 1 x 1 cm2 to the output factor table is seen. In the upper panel, we see that a 1 x 1 cm2 MLC-delimited fi eld does not suff er from either source model limitations or limitations of dose deposition engine when the jaws are set at 4 x 4 cm2 and Acuros XB is used as the dose deposition engine. On the other hand, AAA dose deposition engine underestimates the dose by about 2% of maximum dose (about 3% of local dose). As seen in the middle panel, at 5 cm depth all algo-rithm versions yield a good result for the absolute dose of a 1 x 1 cm2 jaw-delimited fi eld when the output factor for this fi eld size is included, provided that the 1 x 1 cm2 output factor measurement is of good quality and the jaw calibration is perfect in both beam data measurement and deliverysession. The lower panel shows that the error for a 1 x 1 cm2 jaw-delimited fi eld may be acceptable for both AAA and Acuros XB even when the smallest fi eld size in the output factor table is 3 x 3 cm2. All calculated results are obtained using a 1 mm grid size.

FIGURE 1: Collimator backscatter factors for symmetric and square jaw-limited fi elds for a Varian C-series machine. The measured data is from Figure 9 of Ref. [7].

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2. Version history

Several fi gures illustrate the changes in algorithms and Eclipse client aff ecting the accuracy of dose calculation for small fi elds since version 8.6.

1. In Figure 2, it can be seen that at depths smaller than 2 cm the depth dose curve for AAA 8.6 diff ers markedly from the newer versions as a result of an improved build-up and build-down correction mechanism [13].

2. In AAA version 8.9, the origin of the internal calcu-lation grid in the AAA dose calculation algorithm was aligned with the origin of the low resolution fl uence grid (resolution 2.5 mm) sent by the Eclipse client. This change caused a sharpening to the cal-culated penumbra compared to earlier versions for jaw-delimited fi elds when the calculation resolution of 2.5 mm was used. For 1 mm grid size, there was no signifi cant diff erence in the penumbra width between the two versions. Figures 3 and 4 illustrate this change.

FIGURE 2: Depth dose curves for 1 x 1 cm2 fi eld delivered and calculated in various ways. Upper panel: The fi eld is delimited by the multileaf collimator, jaws are at 4 x 4 cm2. Middle panel: the fi eld is delimited by jaws, and output factor for 1 x 1 cm2-fi eld size is included in beam data measurements. Lower panel: The fi eld is delimited by jaws, while smallest fi eld size included in output factor table is the 3 x 3 cm2. All calculated results are obtained using 1 mm grid size. See also discussion in Sections IIA1 and IIA2.

FIGURE 3: Left: An AAA 8.9 X-profi le for a 4 x 4 cm2 fi eld calculated with a 2.5 mm grid size matches better with a fi lm measurement than AAA 8.6 calculated with a 2.5 mm grid size. With a 1 mm grid size both match well. Right: A profi le calculated with AAA 8.6 using 2.5 mm grid size matches better with a PTW 125 mm3 ion chamber measurement than a profi le calculated with an AAA 8.9 using a 2.5 mm grid size. With 1 mm resolution both disagree more with the measurement, revealing the smoothing eff ect of ion chamber.

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3. Also, in AAA version 8.9, bilinear interpolation from the low resolution opening ratio matrix (ORM) to the internally used ORM was replaced by an energy-conserving histogram (constant value within the pixel - no interpolation). See Figure 4.

4. Eclipse client 10.0 sends the fl uence for static MLC fi elds and volumetric modulated arc therapy (VMAT) fi elds for AAA and Acuros XB 10.0 with a resolution of 0.3125 mm, if calculation option “VMAT Fluence Resolution” is set to value “High”.

• AAA then resamples this fl uence into its inter-nally used fl uence, which has a resolution given by the calculation option Calculation Grid Size at the isocenter plane.

• Acuros XB then resamples this fl uence into its internally used fl uence, which has a resolution given by half of the value of the calculation op-tion Calculation Grid Size at the isocenter plane.

For earlier algorithm versions (and in version 10.0, if the low resolution fl uence setting is used), the Eclipse client fi rst calculates a binary fl uence with resolution 2.5 mm / 8 = 0.3125 mm for these fi elds, and then downsamples the fl uence to the resolution of 2.5 mm. As a result, the boundaries of MLC-delimited fi elds are not sharp in the fl uence but are blurred due to tongue-and-groove eff ect in the collimator-Y direction and the imperfect alignment of the MLC-leaf tip with fl uence pixel boundary in the collimator-X-direction. Compared to earlier versions, the calculated penumbra is sharper and the calculated absolute dose level for small MLC-delimited fi eld sizes is higher. See Figures 5, 6 and 8.

5. When AAA or Acuros XB version 11.0 is used, the UFC is used, resulting in equivalent accuracy. ORMs for static MLC fi elds, VMAT fi elds, and intensity-modulated radiation therapy (IMRT) fi elds are calculated by the source model itself, instead of the Eclipse client, at the required resolution. For

FIGURE 4: A low-resolution fi eld fl uence (sent by Eclipse client 8.9 and older) for the 5 x 5 mm2 MLC opening. The opening ratio matrix for a 1 mm calculation grid used by AAA versions 8.6 and 8.9 also illustrates an intermediate version where only the bilinear interpolation is replaced by histogram interpretation and energy-conserving resampling of the fl uence. In addition in version 8.9, the pixel boundaries of the two fl uences have been aligned. The calculation grid size is 1 mm in all cases shown.

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AAA, the fl uence resolution at the isocenter plane is determined by the calculation option Calculation Grid Size, while for Acuros XB, it is given by half of this value.

B. Beam data confi guration

A single beam data set containing both small and large fi eld measurements produces accurate results for all fi eld sizes. There should be no need to create separate models for the calculation of small and large fi eld sizes. If a beam data set is expected to be used for calculation of dose for small fi eld sizes, the most important aspect to consider is the manual adjustment of the spot size parameters in collimator X- and Y-directions, in order to obtain good agreement with mea-sured absolute dose levels for small MLC-delimited apertures. These spot size parameters also aff ect the penumbra width, which can be considered as the secondary goal in optimiz-ing these parameters. In both cases, notice the paramount importance of the careful selection of the detector. If small jaw-delimited fi eld sizes are needed, it is also important

to carefully measure the output factors for these. Relative profi les or depth dose curves for fi eld sizes smaller than 3 x 3 cm2 are not needed, and those for fi eld sizes smaller than 2 x 2 cm2 are in fact not used by the confi guration program even if they are included in the input data.

One widely used and acceptable approach for measuring profi les uses a diode detector for fi eld sizes smaller than 5 x 5 cm2 and an ion chamber for larger fi eld sizes. Measur-ing all profi les with a diode is equally acceptable, as long as care is taken for the accuracy of the measured profi le outside the fi eld in the profi le tail region as well as inside the fi eld — the absolute dose level in the tail region directly aff ects the second source weight when the source model parameters are optimized. The recommended detector for all profi le measurements is the ion chamber.

Accurate representation of the penumbrae in the measured relative profi les does not aff ect the quality of the confi gura-tion result; it only makes direct comparison of the measured and calculated profi les easier.

FIGURE 5: High-resolution fi eld fl uence (sent by Eclipse client 10.0) for the 5 x 5 mm2 MLC opening. Resampled opening ratio matrix (ORM) with 1 mm resolution as seen by AAA 10.0. Also shown are the blurred ORMs when the fi nite spot size is applied. Note that AAA 11.0 and Acuros XB 11.0 will generate similar ORMs directly from the UFC. Fig. 7 shows X- and Y- profi les through these fl uences.

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1. Recommended measurements for open beam

Basic beam data measurements should include depth dose curves and profi les from 3 x 3 cm2 up to a maximum fi eld size deliverable with the machine (e.g., 40 x 40 cm2), as well as diagonal profi les for the maximum fi eld size. Inclusion of measurements for smaller fi eld sizes does not have a signifi -cant impact on the calculated beam data parameters. Beam model will be accurate even though measurement data does not contain very small fi eld sizes (1 x 1 cm2 and 2 x 2 cm2).

Output factors from 3 x 3 cm2 up to a maximum fi eld size deliverable with the machine shall be measured. Output factors for small fi eld sizes 1 cm ≤ X ≤ 3 cm or 1 cm ≤Y ≤ 3 cm can be included, if desired. However, these will not aff ect the calculation results for small MLC-collimated fi elds in treatment units where MLC is located below the jaws (e.g., Varian), if the jaw opening remains 3 x 3 cm2 or larger. This is because the backscatter in these cases is determined from the size of the jaw opening. If small jaw-openings are used in the treatments, the inclusion of output factor measurements for these fi eld sizes may improve the accuracy.

If measurements for very small fi eld sizes are included in the beam data, the selected detector needs to be suitable for the measurement of small fi elds. The positioning of the phantom and detector needs to be done carefully.

FIGURE 6: X- and Y- profi les through the opening ratio matrices of a 5 x 5 mm2 MLC opening shown in Figures 4 and 5. Note that the fi eld size in X-direction is enlarged by the dosimetric leaf gap (DLG) of 1.4 mm, and in Y-direction it is reduced as a result of the tongue and groove eff ect (TnG) by 0.625 mm. Calculation grid size is 1 mm in all cases shown. Note that the low resolution fl uence from Eclipse client nowhere exceeds the value of 7/8 within the area of this fi eld. Each of the four bright fl uence pixels in upper left corner of Figure 4 are shadowed by the TnG eff ect, reducing the fl uence value by 12.5. Note also the spurious blurring eff ect in AAA 8.6 due to misalignment of the internal fl uence and the fl uence sent by Eclipse client, as well as bilinear interpolation from the low resolution fl uence. These eff ects lead to a noticable under-estimation of absolute dose for this case for older versions, as will be further discussed by means of the results shown in Figure 8.

FIGURE 7: X- and Y- profi les through some of the opening ratio matrices of a 5 x 5 mm2 MLC opening shown in Figure 5. Adjust-ing the spot size has a user-controllable blurring eff ect on the primary fl uence. This can be used to adjust the absolute dose level for very small fi elds, as well as the penumbra width. The calculation grid size is 1 mm in all cases shown.

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2. Tuning of eff ective spot size parameters

The beam data includes parameters “Eff ective target spot size in X-direction” and “Eff ective target spot size in Y-direction”, which have a signifi cant eff ect on the calculated absolute dose level for very small fi eld sizes (≤ 1 x 1 cm2) and for the shape of the calculated penumbra for all fi eld sizes. These parameters can be manually adjusted for each treatment unit based on high-resolution measurements (such as fi lm). Note that contrary to what the names of these parameters suggest,

they are not suitable for modeling a highly elliptic target spot size; these parameters are given in the collimator coordinate system. For MLC-delimited fi elds, the optimal value for eff ec-tive target spot size in the X-direction may be higher than the optimal value for the eff ective target spot size in the Y-direc-tion, because the former can be used to model the rounded shape of the MLC leaf tip. Figure 9 illustrates the performance of the four diff erent spot sizes discussed in the results-section of the present work: “MLC-spot” and “jaw spot” for

FIGURE 8: Comparing calculated and measured dose for the 5 x 5 mm2 MLC-delimited fi eld (jaws at 40 x 40 mm2) between diff erent versions (AAA 8.6, AAA 8.9, AAA 11.0). Spot Size X = Spot Size Y = 0. The transition from low-resolution fi eld fl uence to high-resolution fl uence in version 10.0 (or alternatively to UFC in version 11.0 which provides equivalent accuracy) was the key factor in enabling good accuracy for such small openings.

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AAA and Acuros XB: both of these two spot sizes result in excellent agreement with the measured absolute dose level for the 5 x 5 mm2 MLC-delimited fi eld, as discussed in the results section.

III. RESULTS

A. Basic beam data measurements

The measurements were obtained for the 6X energy mode of a Varian C-series treatment unit located in the Clinique Ste Elisabeth in Namur, Belgium by Ann Van Esch and Dominique Huyskens from the 7Sigma QA-team. Beam data measure-ments included: depth dose curves for fi eld sizes 4 x 4 cm2, . . . , 40 x 40 cm2; profi les for fi eld sizes 4 x 4 cm2, . . . , 40 x 40 cm2 and depths 1.5, 5, 10, 20 and 30 cm; Diagonal profi les for fi eld size 40 x 40 cm2 and depths 1.5, 5, 10, 20 and 30 cm.

The detector used for all percentage depth doses (PDDs) and profi les was the PTW 125 mm3 ion chamber. Output factors were measured for a table of rectangular fi eld sizes with X and Y ranging from 1, 2, 3, ..., 40 cm (SSD = 95 cm, depth = 5 cm). For jaw positions exceeding 4 cm, the PTW 0.125 cc ion chamber was used. For smaller fi eld sizes (X or Y < 4 cm), output factor measurements were obtained and cross-checked by means of two detectors: the PTW 3D Pin-Point ion chamber and the Wellhofer stereotactic diode. The accurate jaw calibration as well as the precise positioning of the detector was verifi ed through short profi le scans preced-ing the output factor measurements. An overlap between the large and small fi eld size regime measurements assured a seamless transition between the diff erent detectors in the output factor table.

Eff ective spot size in X-direction (Spot Size X) and eff ective spot size in Y-direction (Spot Size Y) were separately chosen for AAA and Acuros XB with two diff erent objectives in mind:

• For AAA, a good match for the penumbra width of jaw-delimited fi elds (while simultaneously constraining the search for good agreement with absolute dose levels for the smallest 5 x 5 mm2 MLC-delimited fi eld) was found for the choice Spot Size X = Spot Size Y = 0 mm (AAA jaw spot). Similarly, the Acuros XB jaw spot was found to be characterized by parameter values Spot Size X = Spot Size Y = 1 mm.

• If, instead of the penumbra of jaw-delimited fi elds, the penumbra of MLC-delimited fi elds is of interest, it was found that the following choice yields better results while still maintaining good agreement for the absolute dose level for all measured MLC-delimited fi eld sizes: AAA MLC spot (Spot Size X = 1 mm, Spot Size Y = 0 mm) and the Acuros XB MLC spot (Spot Size X = 1.5 mm, Spot Size Y = 1 mm).

Figure 9 illustrates the performance of these four diff erent spot sizes.

B. Verifi cation measurements and results

Film measurements for the 12 combinations of jaw openings and MLC openings shown in the fi rst two columns of Table I were made using Gafchromic fi lm, which was calibrated to give absolute dose. The absolute dose levels were confi rmed by the point dose measurements for all but the smallest fi elds. The measurements were made at depth 5 cm, at SSD = 95 cm. The Millennium™ 120 MLC was used.

Measurements and calculations were compared using the gamma index measure [9]. The units in gamma error measure were 2% of calculated dose maximum and 1 mm in distance to agreement. The gamma index pass rate (GIPR) — i.e., the percentage of points with Γ(2%; 1 mm) less than one — was recorded separately for the high dose region (GIPRhigh= GIPR (D > 0.2 Dmaxmeas; Γ(2%; 1 mm))) and the global dose region (GIPRglobal= GIPR (D > 0.02 Dmaxcalc; Γ(2%; 1 mm)) [14]). Table I shows results for AAA and Acuros XB 10.0 using the “jaw spot”, while Table II gives the results for AAA and Acuros XB 11.0 with the “MLC spot”. In the remain-der of this discussion, we assume that results shown in Table I apply also to algorithm versions 11.0 and those in Table II apply to versions 10.0 (this assumption is supported by the internal tests, confi rming agreement between a few tenths of a percent).

For Acuros XB, both versions, therefore, we can recommend using the “MLC spot” for the modeling of the MLC-delimited fi elds. Out of the 24 pass rates reported in Table 2, every one exceeds 95%, and all but two exceed 97%. For AAA, the same recommendation applies; all but two pass rates exceed 95%, and all but three exceed 97%. However, the 1 x 1 cm2 MLC fi eld in 2 x 2 cm2 jaw opening is an exception, falling slightly below the 90% pass rate. This is not a problem, however, if jaw openings smaller than 3 x 3 cm2 are avoided. Even though the results presented in Table 2 are slightly inferior to the data shown in Table 1, they are still of good quality and all exceed the 90% level.

Statistics for versions earlier than 10.0 are not quite as good, the main reason being the low-resolution fl uence calculation in the Eclipse client for these versions. The results for AAA 8.6 and AAA 8.9 (with the “jaw spot”) are shown in Table 3. Even for these versions only four (8.6) and three (8.9) cases have pass rates lower than 90%. See also Figure 8: the dose level for MLC openings of the order of 5 x 5 mm2 is underes-timated by a large percentage by these versions because of the low-resolution fl uence.

Figures 10-15 contain more information about the gamma error maps for the 11.0 versions with “MLC spot”, as well as measured and calculated profi les for these cases.

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IV. SUMMARY AND CONCLUSIONS

We have shown that versions AAA 10.0 and Acuros XB 10.0 can be confi gured to produce excellent accuracy for small MLC-delimited static fi elds in water by comparing calculated dose with measurements performed by means of Gafchromic

fi lm and point dose detectors. In all our calculations we have used a 1 mm calculation grid size. We have manually opti-mized the spot size with special care towards accuracy of the smallest MLC-delimited opening (5 x 5 mm2) and the penum-bra width of either jaw-delimited or MLC-delimited fi elds.

FIGURE 9: Illustrating the choice of the spot size for 10 x 10 mm2 MLC-delimited fi eld in a 60 x 60 mm2 jaw-opening. All calculations performed with 11.0 versions and 1 mm calculation grid size.

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We have also discussed the limitations that the earlier Eclipse versions and AAA algorithm versions have exhibited in small fi eld dose calculation. We have shown how the major limita-tions have been overcome, mainly in the 10.0 release. While Acuros XB dose deposition algorithm brings an important improvement for small fi elds, the most important improve-ment was the introduction of high-resolution fl uence in this version of the Eclipse client. Version 11.0, for its part, replaces this feature with the unifi ed fl uence calculation (which also improves accuracy for IMRT fi elds and has many other technical advantages over the approach in version 10.0).

Even if there have been made several important and eff ective improvements into the AAA and Acuros XB source model versions 10.0 and later, it must be emphasized that the results for the previous versions may be useful for typical clinical plans, e.g., IMRT and RapidArc® radiotherapy technology fi elds consisting of several small MLC-delimited openings. For earlier versions, even if the height of a dose distribution for a single small MLC opening is not as accurate as for the later versions, the integral of the dose is correct, and thus the total energy deposited. This leads to correct total dose in an IMRT or RapidArc case consisting of several such openings except in the most extreme cases.

We have also introduced the reader to the remaining, albeit less signifi cant, limitations in the source model and the AAA dose deposition engine for small fi elds in water, with the help of Figure 1. This fi gure does show that the dose deposition engines behave somewhat anomalously for the 1 x 1 cm2 fi eld size (while however, still retaining its usefulness for the 5 x 5 mm2 fi eld size as shown in Section III, and the magnitude of the anomaly even for the 1 x 1 cm2 fi eld size appears to be only in the range of 2% - see for example Figure 2). This issue either

does not appear for the Acuros XB dose deposition engine, or is of smaller magnitude there. The remaining limitation of the source model (unphysical CBSF values) also appears to not present a major obstacle for the fi nal dose calculation ac-curacy, although the reader is advised to validate MLC and jaw combinations such as the ones shown in Tables 1 and 2 when deciding on the combination of jaw opening and MLC opening to use clinically for maximum dose calculation accuracy.

Finally, this paper did not address the question of small fi eld dose calculation in heterogeneous phantoms, such as lung. This aspect has been addressed elsewhere [10, 11], and it has been shown that the AAA dose deposition engine has some signifi cant limitations in this area. The Acuros XB dose deposi-tion engine, as a Monte Carlo equivalent transport calculator, has been shown to overcome these limitations. Combining the excellent transport capabilities of the Acuros XB dose deposi-tion engine with the accuracy of the Varian Photon Beam Source Model for small fi elds demonstrated in this paper is expected to result in a dose calculation package well adapted for clinical usage in small-fi eld dosimetry.

V. ACKNOWLEDGEMENTS

We are grateful for the measurements and related valuable insights of Ann Van Esch and Dominique Huyskens from the 7Sigma QA-team. Ann Van Esch also contributed signifi -cantly to the process of improving this clinical perspective. Valuable comments regarding this document were also received from Henna Hietala, Mu Young Lee, Marko Rusanen, Tuomas Lunttila, and Joakim Pyyry. Yves Archambault and Helen Phillips are acknowledged for their introduction of the concept of the gamma index pass rate (GIPR) for the analy-sis of dose calculation accuracy at Varian Medical Systems.

MLC (mm2) Jaw (mm2) GIPR AAA10.0high (%) GIPR AAA10.0

global (%) GIPR AXB10.0high (%) GIPR AXB10.0

global (%)

- 10 x 10 99.9 100.0 100.0 100.0

- 10 x 20 100.0 99.5 100.0 99.4

- 20 x 20 99.3 99.7 99.5 99.7

10 x 10 20 x 20 91.9 96.3 98.9 96.8

10 x 10 40 x 40 95.6 96.8 99.9 95.6

10 x 10 60 x 60 99.8 97.5 99.1 95.3

10 x 10 100 x 100 98.9 99.3 93.5 96.6

5 x 5 40 x 40 100.0 99.8 100.0 99.8

10 x 20 60 x 60 99.4 99.0 95.7 94.3

10 x 20 100 x 100 98.5 98.4 92.6 93.6

15 x 20 50 x 50 99.7 99.4 99.1 96.4

15 x 20 100 x 100 97.7 98.9 92.2 94.6

TABLE I: Gamma index pass rate (GIPR) in high dose region (GIPRhigh=GIPR(D > 0.2 Dmaxmeas; Γ(2%; 1 mm))) and global dose region (GIPRglobal = GIPR(D > 0.02 Dmaxcalc; Γ(2%; 1 mm))) for AAA version 10.0 using “AAA jaw spot”: Spot Size X = Spot Size Y = 0 mm and Acuros XB version 10.0 using “Acuros XB jaw spot”: Spot Size X = Spot Size Y = 1 mm. Pass rates higher than 90% and lower than 97% are shown in cyan color, while pass rates lower than 90% are shown in red color.

Clinical perspectives | Varian Photon Beam Source Model

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MLC (mm2) Jaw (mm2) GIPR AAA11.0high (%) GIPR AAA11.0

global (%) GIPR AXB11.0high (%) GIPR AXB11.0

global (%)

- 10 x 10 98.5 99.5 100.0 99.9

- 10 x 20 98.4 98.9 99.6 99.2

- 20 x 20 99.4 99.7 99.4 99.7

10 x 10 20 x 20 86.8 95.6 98.0 99.3

10 x 10 40 x 40 92.5 98.0 99.4 98.9

10 x 10 60 x 60 99.7 99.4 99.7 99.4

10 x 10 100 x 100 99.8 99.8 95.7 99.4

5 x 5 40 x 40 100.00 99.8 100.00 99.9

10 x 20 60 x 60 99.8 99.8 99.1 99.4

10 x 20 100 x 100 99.4 99.6 97.2 98.6

15 x 20 50 x 50 99,8 99.8 99.6 99.3

15 x 20 100 x 100 98.7 99.6 95.2 98.3

TABLE 2: Gamma index pass rate (GIPR) in high dose region (GIPRhigh=GIPR(D > 0.2 Dmaxmeas; Γ(2%; 1 mm))) and global dose region (GIPRglobal = GIPR(D > 0.02 Dmaxcalc; Γ(2%; 1 mm))) for AAA version 11.0 using “AAA MLC spot”: Spot Size X = 1 mm, Spot Size Y = 0 mm and Acuros XB version 11.0 using “Acuros XB MLC spot”: Spot Size X = 1.5 mm, Spot Size Y = 0 mm. Pass rates higher than 90% and lower than 97% are shown in cyan color, while pass rates lower than 90% are shown in red color.

MLC (mm2) Jaw (mm2) GIPR AAA8.6high (%) GIPR AAA8.6

global (%) GIPR AXB8.9high (%) GIPR AXB8.9

global (%)

- 10 x 10 97.9 99.2 99.4 99.8

- 10 x 10 99.0 99.2 99.5 99.3

- 20 x 20 99.3 99.7 99.4 99.7

10 x 10 20 x 20 69.1 89.0 79.9 93.0

10 x 10 40 x 40 74.8 95.6 86.1 97.5

10 x 10 60 x 60 92.9 99.2 99.1 99.7

10 x 10 100 x 100 99.9 99.8 100.0 99.8

5 x 5 40 x 40 79.0 98.2 85.0 98.8

10 x 20 60 x 60 99.2 99.8 99.9 99.9

10 x 20 100 x 100 99.4 99.8 99.8 99.8

15 x 20 50 x 50 98.3 99.5 99.8 99.8

15 x 20 100 x 100 97.5 99.3 98.9 99.6

TABLE 3: Gamma index pass rate (GIPR) in high dose region (GIPRhigh=GIPR(D > 0.2 Dmaxmeas; Γ(2%; 1 mm))) and global dose region (GIPRglobal = GIPR(D > 0.02 Dmaxcalc; Γ(2%; 1 mm))) for AAA version 8.6 using “AAA jaw spot”: Spot Size X = 0 mm, Spot Size Y = 0 mm and AAA version 8.9 using “AAA jaw spot”: Spot Size X = 0 mm, Spot Size Y = 0 mm. Pass rates higher than 90% and lower than 97% are shown in cyan color, while pass rates lower than 90% are shown in red color.

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REFERENCES

[1] M. Aspradakis, J. Byrne, H. Palmans, J. Conway, K. Rosser, J. Warrington, and S. Duane, Small Field MV Photon Dosim-etry. Fairmont House, 230 Tadcaster Road, York YO24 1ES: Institute of Physics and Engineering in Medicine, 2010.

[2] L. Fog, J. Rasmussen, M. Aznar, F. Kjaer-Kristoff ersen, I. Vogelius, S. A. Engelholm, and J. Bangsgaard, “A closer look at RapidArc radiosurgery plans using very small fi elds,” Physics in Medicine and Biology, vol. 56, no. 6, pp. 1853-1863, 2011.

[3] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti, and L. Cozzi, “Accuracy of Acuros XB and AAA dose calculation for small fi elds with reference to RapidArc stereotactic treatments,” Medical Physics, vol. 38, no. 11, pp. 6228-6237, 2011.

[4] L. Tillikainen, S. Siljamäki, H. Helminen, J. Alakuijala, and J. Pyyry, “Determination of parameters for a multiple-source model of megavoltage photon beams using optimization methods,” Physics in Medicine and Biology, vol. 52, no. 5, pp. 1441-1467, 2007.

[5] L. Tillikainen, H. Helminen, T. Torsti, S. Siljamäki, J. Alakuijala, J. Pyyry, and W. Ulmer, “A 3D pencil-beam-based superposition algorithm for photon dose calculation in heterogeneous media,” Physics in Medicine and Biology, vol. 52, pp. 3821-3839, 2008.

[6] O. Vassiliev, T. Wareing, J. McGhee, G. Failla, M. Salehpour, and F. Mourtada, “Validation of a new grid-based Bolzmann equation solver for dose calculation in radiotherapy with photon beams,” Physics in Medicine and Biology, vol. 55, no. 3, pp. 581-598, 2010.

[7] H. H. Liu, T. R. Mackie, and E. C. McCullough, “Modeling photon output caused by backscattered radiation into the monitor chamber from collimator jaws using a Monte Carlo technique,” Medical Physics, vol. 27, no. 4, pp. 737-744, 2000.

[8] M. K. Fix, P. J. Keall, K. Dawson, and J. V. Siebers, “Monte Carlo source model for photon beam radiotherapy: photon source characteristics,” Medical Physics, vol. 31, no. 11, pp. 3106-3121, 2004.

[9] T. Ju, T. Simpson, O. Deasy, and D. A. Low, “Geometric interpretation of the gamma dose distribution comparison technique: interpolation-free calculation,” Medical Physics, vol. 5, no. 3, pp. 879-897, 2008.

[10] T. Han, J. Mikell, M. Salehpour, and F. Mourtada, “Dosimetric comparison of Acuros XB deterministic radiation transport method with Monte Carlo and model-based convolution methods in heterogeneous media,” Medical Physics, vol. 38, no. 5, 2651-2664, 2011.

[11] G. X. Ding, D. M. Duggan, B. Lu, D. E. Hallahan, A. Cmelak, A. Malcolm, J. Newton, M. Deeley, and C. W. Coff ey, “Impact of inhomogeneity corrections on dose coverage in the treatment of lung cancer using stereotactic body radiation therapy,” Medical Physics, vol. 34, no. 7, 2985-2994, 2007.

[12] In fact, for Eclipse versions older than 11.0, an important part of the source model (calculation of the opening ratio matrix (ORM) often referred to as “fl uence calculation”) re-sides in the Eclipse client instead of the algorithm. In Eclipse version 11.0, the fl uence calculation is performed by the uni-fi ed fl uence calculation (UFC), an integral part of VPBSM.

[13] The following sentence in Ref. [5] on page 3827, four lines after Eq. (16) describes the implementation in AAA 8.6 and older: “Hence, it is necessary to pre-compensate for it either in the original Monte Carlo kernel in (2) or in the I function in (4). For simplicity, we have chosen the latter approach.” The latter approach, however, has the drawback shown in Figure 2. Therefore, it has been replaced with the former approach in AAA 8.9 and later.

[14] Points where both measured and calculated doses are so small that the gamma index test passes trivially are not included in the global region. Therefore it is sometimes referred to as the “non-small dose region”.

Clinical perspectives | Varian Photon Beam Source Model

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FIGURE 10: MLC 10 x 10 mm2 opening in following jaw opening sizes: 20 x 20 mm2, 40 x 40 mm2, 60 x 60 mm2, 100 x 100 mm2. Results for AAA version 11.0, “AAA MLC spot”: Spot Size X = 1 mm, Spot Size Y = 0 mm

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FIGURE 11: Various MLC openings in various jaw openings. Results for AAA 11.0, “AAA MLC spot”: Spot Size X = 1 mm, Spot Size Y = 0 mm.

Clinical perspectives | Varian Photon Beam Source Model

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FIGURE 12: Small jaw openings: 10 x 10 mm2, 10 x 20 mm2, 20 x 20 mm2. Results for AAA version 11.0, “AAA MLC spot”: Spot Size X = 1 mm, Spot Size Y = 0 mm

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FIGURE 13: MLC 10 x 10 mm2 opening in following jaw opening sizes: 20 x 20 mm2, 40 x 40 mm2, 60 x 60 mm2, 100 x 100 mm2. Results for Acuros XB version 11.0, “Acuros XB MLC spot”: Spot Size X = 1.5 mm, Spot Size Y = 0 mm

Clinical perspectives | Varian Photon Beam Source Model

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FIGURE 14: Various small MLC openings in various jaw openings. Results for Acuros XB 11.0, “AcurosXB MLC spot”: Spot Size X = 1.5 mm, Spot Size Y = 0 mm.

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FIGURE 15: Small jaw openings: 10 x 10 mm2, 10 x 20 mm2, 20 x 20 mm2. Results for Acuros XB version 11.0, “Acuros XB MLC spot”: Spot Size X = 1.5 mm, Spot Size Y = 0 mm

Intended Use SummaryVarian Medical Systems’ linear accelerators are intended to provide stereotactic radiosurgery and precision radiotherapy for lesions, tumors, and conditions anywhere in the body where radiation treatment is indicated.

SafetyRadiation treatments may cause side eff ects that can vary depending on the part of the body being treated. The most frequent ones are typically tempo-rary and may include, but are not limited to, irritation to the respiratory, digestive, urinary or reproductive systems, fatigue, nausea, skin irritation, and hair loss. In some patients, they can be severe. Treatment sessions may vary in complexity and time. Radiation treatment is not appropriate for all cancers.