- Email: [email protected]
Basic dosimetric verification in water of the anisotropic analytical algorithm for Varian, Elekta and Siemens linacs
ARTICLE IN PRESS TECHNISCHE MITTEILUNG
Basic dosimetric verification in water of the anisotropic analytical algorithm for Varian, Elekta and Siemens linacs Luca Cozzi1,4,, Giorgia Nicolini1, Eugenio Vanetti1, Alessandro Clivio1, Marco Glasho¨rster2, Hans Schiefer3, Antonella Fogliata1 1
Oncology Institute of Southern Switzerland, Medical Physics Unit, Bellinzona, Switzerland Universita¨tspital Mu¨nster, Radiation Oncology Dept., Mu¨nster, Germany 3 Kantonsspital St. Gallen, Klinik fu¨r Radio-Onkologie, St. Gallen, Switzerland 4 University of Lausanne, Faculty of Medicine, Lausanne, Switzerland 2
Received 12 July 2007; accepted 12 September 2007
Since early 2007 a new version of the Anisotropic Analytical Algorithm (AAA) for photon dose calculations was released by Varian Medical Systems for clinical usage on Elekta linacs and also, with some restrictions, for Siemens linacs. Basic validation studies were performed and reported for three beams: 4,6 and 15 MV for an Elekta Synergy, 6 and 15 MV for a Siemens Primus and, as a reference, for 6 and 15 MV from a Varian Clinac 2100C/D. Generally AAA calculations reproduced well measured data and small deviations were observed for open and wedged fields. PDD curves showed in average differences between calculation and measurement smaller than 1% or 1.2 mm for Elekta beams, 1% or 1.8 mm for Siemens beams and 1% or 1 mm for Varian beams. Profiles in the flattened region matched measurements with deviations smaller than 1% for Elekta and Varian beams, 2% for Siemens. Percentage differences in Output Factors were observed as small as 1% in average.
Keywords: Convolution algorithms, Anisotropic Analytical Algorithm, treatment planning systems
Grundlegende dosimetrische Verifizierung des Anisotropic Analytical Algorithm in Was’’ ser fu¨r Varian-, Elekta- und SiemensBeschleuniger ’’
Abstract
Zusammenfassung Seit dem Fru¨hjahr 2007 ist von Varian Medical Systems der neue Algorithmus ‘‘Anisotropic Analytical Algorithm (AAA)’’ fu¨r die Bestrahlungsplanung von Photonen fu¨r Elekta-Beschleuniger fu¨r den klinischen Einsatz sowie mit Einschra¨nkungen auch fu¨r Siemens-Beschleuniger freigegeben. Hier werden grundlegende Parameter untersucht fu¨r drei Strahlenergien: 4,6 und 15 MV eines Elekta Synergy sowie 6 und 15 MV eines Siemens Primus; als Referenz dienen analoge Auswertungen fu¨r 6 und 15 MV eines Varian Clinac 2100C/D. Allgemein kann gesagt werden, dass die AAA-Berechnungen die Messungen gut reproduzieren und sowohl fu¨r offene wie Keilfilterfelder nur geringe Abweichungen zu beobachten sind: Tiefendosiskurven fu¨r Elekta stimmen im Durchschnitt innerhalb von weniger als 1% bzw. 1,2 mm u¨berein; fu¨r Siemens liegen diese Werte bei 1% bzw. 1,8 mm und fu¨r Varian bei 1% bzw. 1 mm. Profile stimmen im flachen Feldbereich fu¨r Elekta und Varian innerhalb 1%, fu¨r Siemens innerhalb von 2% u¨berein. Die Abweichungen bei der Berechnung der Monitoreinheiten liegen im Durchschnitt ebenfalls bei nur 1%. Schlu¨sselwo¨rter: Konvolutions-Algorithmus, Anisotropic Analytical Algorithm, Bestrahlungsplanungssysteme
Corresponding author. Oncology Institute of Southern Switzerland, Radiation Oncology Department, Medical Physics Unit, CH-6504 Bellinzona. Tel.: +41 91 8119202; Fax: +41 91 8118678. E-mail: [email protected] (L. Cozzi).
Z. Med. Phys. 18 (2008) 128–135 doi: 10.1016/j.zemedi.2007.09.003 http://www.elsevier.de/zemedi
ARTICLE IN PRESS L. Cozzi et al. / Z. Med. Phys. 18 (2008) 128–135
Introduction In 2005 the Anisotropic Analytical Algorithm (AAA) for photon dose calculation has been implemented in the Varian Eclipse treatment planning system (Eclipse), and it was clinically released for Varian linacs. The AAA is a 3-D convolution/superposition algorithm that uses Monte Carlo derived kernels. The basic principles of the algorithm can be found in the papers published by Ulmer, Harder and Kaissl [1–3]. Some more details on its implementation in Eclipse, together with the meaning of the parameters used can be found in [4,5]. In its fundamentals, the dose calculation is based on the convolution over the beamlets of multiple radiation sources separately using physical parameters defined for every beamlet. The final dose distribution is obtained from the superposition of all the individual beamlet contributions. The energy deposition kernels account for tissue heterogeneity in an anisotropic way. Preliminary tests on the AAA were published by the developers by Ulmer et al. [6] while other studies [4,5,7] reported about basic verifications, comparisons against measurements, in water and in simple phantoms for Varian linear accelerators; performances of AAA and several other algorithms were reported in [8,9], benchmarked against MonteCarlo simulations, when heterogeneous media are involved in both simple geometrical phantoms and real patients. During the first months of 2007, a new version of the AAA algorithm was released for clinical usage also for Elekta units. For Siemens units, the version used constitutes a preclinical release. The present report is a summary of a basic dosimetric verification for open and wedged fields in water performed on an Elekta linac (with 4,6 and 15 MV photon beams) and for a Siemens unit (with 6 and 15 MV photon beams) and it is intended to give a first comparative overview on the performance of AAA applied to the three main linac models. Aim of this work is to analyse the ability of AAA implementation in Eclipse to reproduce basic data, after the configuration process, for linacs different from the Varian units. The investigation of AAA accuracy in more complex situations (e.g. particular beam settings, MLC, heterogeneities) is beyond the present scope, and it has been already discussed in other papers [4,5,7–9].
Material and methods All dose calculations were performed on a Varian Eclipse system (7.5.51) running the AAA photon dose calculation engine (8.0.05) installed at the Oncology Institute of Southern Switzerland.
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The Eclipse system was configured to enable AAA calculations for: i) Elekta Synergy linac, equipped with Motorized Wedge, producing the following beams: 4 MV (4X_E) with dmax ¼ 1.0 cm and TPR20/10 ¼ 0.634 6 MV (6X_E) with dmax ¼ 1.5 cm and TPR20/10 ¼ 0.679 15 MV (15X_E) with dmax ¼ 2.9 cm and TPR20/10 ¼ 0.754 For this linac, profiles and depth dose curves used for configuration and verification were acquired in water at SSD ¼ 100 cm. Field sizes ranged from 3 3 to 40 40 cm2 for open fields, and from 3 3 to 30 30 cm2 for the 601 Motorized Wedge. Output factors were defined at 10 cm depth, SSD ¼ 100 cm. ii) Siemens Primus, equipped with Hard Wedges (15, 30, 45 and 601), producing the following beams: 6 MV (6X_S) with dmax ¼ 1.5 cm and TPR20/10 ¼ 0.668 15 MV (15X_S) with dmax ¼ 2.9 cm and TPR20/10 ¼ 0.758 In this case, profiles and depth dose curves used for configuration and verification were acquired at SSD ¼ 100 cm. Field sizes ranged from 2 2 to 40 40 cm2 for open fields, from 2 2 to 25 25 cm2 (maximum allowed 30 25 cm2) for Hard Wedges from 15 to 451, and from 2 2 to 20 20 cm2 (maximum allowed field size 30 20 cm2) for the 601 Wedge. Output factors were defined at dmax, SSD ¼ 100 cm. iii) As a reference, AAA computations for Elekta and Siemens beams were compared against corresponding calculations for a Varian Clinac 2100 C/D unit with: 6 MV (6X_V) with dmax ¼ 1.5 cm and TPR20/10 ¼ 0.669 15 MV (15X_V) with dmax ¼ 2.7 cm and TPR20/10 ¼ 0.759 In the present publication, the results for Varian refer to calculations performed with the AAA 8.0.05 release while in [4] the 7.5.14.3 release was used; in both cases the same linacs were used. The new results shall be considered as an update of the previous findings and as a quality assurance test on the basic stability of AAA between releases in absence of expected performance improvements. Reference calibration conditions were: 10 10 cm2 field size, depth in water equal to dmax, SSD ¼ 100 cm, 1 Gy for 100 MU for both Elekta and Siemens, while for Varian d ¼ 10 cm and SSD ¼ 90 cm (isocentric configuration).
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Measurements were performed in water with conventional small volume ion chambers according to local standards and conventions for the Elekta linac with steps of 1 to 2.5 mm for profiles and ranging from 1 to 5 mm for depth doses; for Siemens unit measurements were acquired with steps of 2.5 mm for profiles and 5 mm for depth doses; for Varian unit, resolutions varying from 1 mm to 2.5 mm were applied as described in [4]. Calculations in Eclipse were performed using a grid size of 2.5 mm (allowed range: 2 to 5 mm). As known, the AAA implementation in Eclipse is divided in two parts, the dose calculation algorithm and the configuration algorithm. The configuration algorithm determines the fundamental physical parameters needed to model linear accelerators and to divide broad beams into finite-size beamlets with pointing geometry to be used for final calculations. The clinical beam is described by three components (multiple sources): a primary source modeling the bremsstrahlung photons from the target not interacting in the linac head; an extra-focal source, modeling photons scattered, mainly in the flattening filter and in the primary collimators and a third source modeling mostly contaminant electrons. The starting point of AAA configuration is the selection of generic parameters from a library of the most common treatment heads. These generic parameters are then tailored, to any actual specific linac that will be used clinically. The user’s input to the configuration phase consists of dosimetric data and parameters describing geometrical and physical characteristics of the real beams. Most of the geometrical data are read from defaults stored in the built-in libraries but some of them can be manually edited and adjusted to site specific needs. Dosimetric data needed for the configuration are: depth dose curves along beam central axis, lateral profiles at different depths, and output factors for open and wedged fields. For open beams, also diagonal profiles are needed while for wedges a profile transverse to the wedge direction is required. Minimal settings are defined by Varian while larger datasets are allowed or recommended. To optimize generic parameters and calculation kernels against measured beam data, objective functions include the g index [10] and penalty factors to prevent unphysical results or to minimize effect of noise in the measurements. As output from the configuration process, the following data are generated for use in the AAA photon dose calculation: mean radial energy curves, intensity profile curves, electron contamination curves and smoothing factor (sigmas of the Gaussians), spectrum, calculated diagonal profiles, lateral profiles, depth doses, collimator back scatter tables, final open (wedged) beam parameters (including absolute calibration). In addition, for wedges the transmission curves and specific wedge parameters are added.
Algorithm validation was based on the comparison of calculations and measurements of:
Depth dose curves (PDD): SSD ¼ 100 cm for Elekta and Siemens, SSD ¼ 90 cm for Varian, field size ranging from minimum to maximum allowed per linac type. Profiles: SSD ¼ 100 cm for Elekta and Siemens, SSD ¼ 90 cm for Varian, depths ¼ dmax, 5, 10, 20 and 30 cm, field size ranging from minimum to maximum allowed as above. Output Factors (OF): SSD ¼ 100 cm, d ¼ 10 cm for Elekta, d ¼ dmax for Siemens, and SSD ¼ 90 cm with d ¼ 10 cm for Varian, field size ranging from minimum to maximum allowed as above, for square and rectangular fields. Wedge Transmission Factors (WF): SSD ¼ 100 cm, d ¼ 10 cm for Elekta, d ¼ dmax for Siemens, and SSD ¼ 90 cm with d ¼ 10 cm for Varian, field size 10 10 cm2. MU computation in calibration conditions.
For the analysis, measured and calculated curves were linearly interpolated in order to have all data sampled with the finest grid size available between the two sets. Analysis of PDD and profiles was carried out as differences, point by point, between calculations and measurements. Statistical parameters, as mean, standard deviation, minimum and maximum values were computed. The PDDs analysis was divided into two regions: i) after dmax, as dose difference between calculation and measurement. More precisely, the curve where the dose after dmax was smaller than 95% of the maximum dose for each PDD was included to avoid the ‘flat’ buildup region. PDDs in those cases were normalized to 100% at 10 cm depth; ii) in the build-up region, as difference in mm at fixed dose levels; for this last analysis PDDs were normalized to 100% at dmax. The analysis for profiles was performed: i) in the ‘flattened’ region, defined as the region were the dose is greater than 95% for open fields, and within the central 90% of the geometrical field size for wedge beams, and ii) in the ‘penumbra region’ defined as the region between the 20% and 80% dose levels. For both cases results and statistical parameters were recorded in terms of differences as for PDDs. Each profile (orthogonal to the beam axis) was normalized to 100% at the beam central axis. Output Factor results were analyzed as percentage difference between computed and measured OF: mean, standard deviation and range were reported. The MU calculations were compared to measurements, and reported as percentage difference for the standard linac calibration conditions for open beams, while for
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wedge beams they were reported as WF (wedge transmission factors) percentage difference for a 10 10 cm2 field.
Results and discussions Configuration Configuration parameters defining beam characteristics after tailoring to measured beam data in the configuration algorithm are not presented in this report for space reason, but they could be sent by the authors on request. As a quality assurance tool, the AAA configuration process generates, in output, histograms of the g index calculated for each processed measured curve against calculations. Table 1 shows the average of the resulting g values together with the percentage of points failing the
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pass fail test (g larger than 1). The thresholds used to compute g are fixed in Eclipse and not tunable by the user, and set as distance to agreement DTA ¼ 3 mm and dose difference DD ¼ 1%. The criterion of 1% in dose difference is quite stringent, while 3 mm of distance to agreement is possibly too coarse to check algorithm accuracy in high dose gradient regions, like the build up and penumbra areas. For example, the penumbra region presents for all units and energies, no points with g41 while, as it will be shown later, for Siemens units the differences between calculations and measurements are not negligible. Depth-dose curves Table 2 presents a summary of the analysis on depth dose data for open and wedged fields. Values refer to
Table 1 Gamma error histogram results: average gamma error and, in brakets, the percentage of point not respecting the criteria (DTA ¼ 3 mm, DD ¼ 1%). Parameter
4X_E
6X_E
15X_E
6X_S
15X_S
6X_V
15X_V
Depth dose curves: Before dmax After dmax
0.63 (11.5%) 0.11 (0.2%)
0.21 (0.0%) 0.11 (0.0%)
0.36 (2.0%) 0.17 (0.0%)
0.32 (0.0%) 0.10 (0.0%)
0.34 (3.1%) 0.16 (0.7%)
0.19 (0.0%) 0.08 (0.0%)
0.22 (0.0%) 0.12 (0.0%)
Profiles: Inside field In penumbra region Outside field
0.19 (1.4%) 0.18 (0.0%) 0.23 (2.2%)
0.12 (0.0%) 0.15 (0.0%) 0.23 (1.5%)
0.13 (0.0%) 0.16 (0.0%) 0.20 (0.0%)
0.18 (0.1%) 0.37 (0.0%) 0.33 (2.2%)
0.17 (0.2%) 0.33 (0.0%) 0.29 (0.3%)
0.12 (0.1%) 0.18 (0.0%) 0.35 (0.9%)
0.13 (0.3%) 0.19 (0.0%) 0.24 (0.0%)
Table 2 Differences between calculated (AAA) and measured depth dose curves, profiles and output factors for the different beams, open and wedges. Reported are the mean, standard deviation and range over all curves (point by point) and for all analysed field sizes. 4X_E
6X_E
15X_E
6X_S
15X_S
6X_V
15X_V
Before dmax Calc-Meas [mm]
Depth doses Open
1.270.3 [0.2, 1.6]
0.670.1 [0.2, 1.0]
0.570.5 [1.3, 1.0]
0.470.1 [0.2, 1.0]
0.570.5 [1.4, 0.9]
0.570.1 [0.0, 1.2]
0.270.5 [1.2, 1.6]
W15
–
–
–
0.870.2 [0.2, 1.3]
0.470.9 [1.8, 2.3]
0.270.2 [0.4, 0.5]
0.270.7 [1.8, 2.1]
W30
–
–
–
0.170.3 [1.2, 0.8]
1.170.9 [2.8, 1.5]
0.170.3 [0.4, 0.9]
0.170.7 [2.0, 2.1]
W45
–
–
–
0.570.1 [1.5, 0.4]
1.571.1 [4.1, 1.4]
0.470.1 [0.5, 0.1]
0.370.9 [1.7, 2.9]
W60/MW
0.770.2 [0.3, 1.7]
0.270.1 [0.4, 0.6]
1.070.5 [2.2, 0.2]
0.770.2 [2.0, 0.2]
1.871.0 [3.9, 1.0]
0.670.1 [1.2, 0.0]
0.171.1 [1.9, 2.7]
After dmax Calc-Meas [%] Open
0.270.2 [0.8, 1.1]
0.070.2 [0.8, 0.8]
0.070.2 [1.0, 1.2]
0.170.1 [0.7, 1.7]
0.170.2 [1.5, 2.8]
0.170.1 [0.4, 1.0]
0.070.2 [0.8, 1.2]
W15
–
–
–
0.170.2 [1.1, 2.5]
0.170.3 [1.4, 2.7]
0.070.1 [0.7, 1.6]
0.070.2 [0.8, 1.3]
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Table 2 (continued ) 4X_E
6X_E
15X_E
6X_S
15X_S
6X_V
15X_V
W30
–
–
–
0.070.3 [1.2, 3.6]
0.170.2 [1.6, 2.3]
0.070.1 [0.5, 1.3]
0.070.2 [0.8, 1.1]
W45
–
–
–
0.170.3 [1.8, 3.9]
0.270.3 [2.3, 3.0]
0.170.1 [1.0, 2.2]
0.470.1 [0.9, 1.1]
W60/MW
0.170.2 [1.5, 2.5]
0.070.2 [1.0, 1.5]
0.370.3 [1.1, 1.6]
0.270.3 [1.5, 2.7]
0.070.2 [1.4, 3.0]
0.170.1 [0.8, 1.7]
0.470.1 [1.3, 1.2]
Profiles All field sizes Open
0.070.3 [1.4, 5.4]
0.070.2 [1.1, 4.5]
0.170.2 [1.2, 2.0]
0.270.6 [2.0, 11.1]
0.570.4 [1.7, 7.1]
0.070.3 [1.9, 4.2]
0.170.2 [6.5, 3.0]
W15
–
–
–
1.972.0 [2.3, 24.6]
1.871.6 [1.2, 20.4]
0.770.6 [10.8, 16.2]
0.270.5 [9.2, 11.4]
W30
–
–
–
1.671.9 [2.5, 25.6]
1.771.6 [3.4, 21.9]
0.770.6 [9.6, 17.2]
0.370.6 [9.1, 12.1]
W45
–
–
–
1.872.2 [5.4, 29.8]
1.671.8 [5.2, 24.7]
0.770.6 [8.4, 18.5]
0.370.6 [11.5, 13.0]
W60/MW
0.470.5 [5.0, 8.3]
0.270.4 [7.5, 14.0]
0.070.4 [6.1, 7.0]
1.972.4 [7.9, 28.3]
1.871.9 [4.9, 24.3]
0.870.8 [10.8, 21.9]
0.270.7 [17.5, 13.3]
Field sizes X 5 5 cm2 Open
0.070.3 [1.4, 4.9]
0.070.2 [1.1, 4.5]
0.170.2 [1.2, 2.0]
0.170.5 [2.0, 11.1]
0.470.3 [1.7, 7.1]
0.170.3 [1.9, 4.2]
0.270.2 [6.5, 2.5]
W15
–
–
–
1.070.8 [2.3, 24.6]
1.170.7 [1.2, 19.1]
0.570.4 [10.8, 13.5]
0.170.4 [9.2, 8.7]
W30
–
–
–
0.870.8 [2.5, 23.9]
1.070.7 [3.4, 19.4]
0.570.4 [9.6, 15.5]
0.170.4 [9.1, 9.2]
W45
–
–
–
0.870.8 [5.4, 25.0]
0.870.8 [5.2, 23.4]
0.570.5 [8.4, 17.3]
0.170.5 [11.5, 10.4]
W60/MW
0.470.5 [5.0, 7.4]
0.270.4 [7.5, 14.0]
0.070.4 [6.1, 6.4]
0.870.9 [7.9, 22.8]
0.970.8 [4.2, 21.8]
0.670.7 [10.8, 21.9]
0.070.6 [17.5, 11.6]
Open
0.070.3 [0.5, 0.5]
0.170.3 [0.6, 0.3]
0.270.4 [1.2, 0.2]
0.270.5 [1.5, 0.4]
0.670.9 [3.1, 0.1]
0.170.3 [0.6, 0.3]
0.370.4 [1.2, 0.2]
W15
–
–
–
0.270.6 [1.7, 1.2]
0.771.1 [3.3, 0.3]
0.270.3 [0.7, 0.4]
0.370.4 [1.1, 0.3]
W30
–
–
–
0.370.6 [1.9, 0.5]
0.771.1 [3.4, 0.4]
0.270.3 [0.8, 0.3]
0.370.5 [1.2, 0.1]
W45
–
–
–
0.270.5 [1.7, 0.5]
0.771.0 [3.1, 0.7]
0.370.3 [0.9, 0.3]
0.370.4 [1.1, 0.1]
W60/MW
0.170.8 [1.6, 1.6]
0.271.3 [2.5, 1.8]
0.370.8 [1.7, 1.6]
0.370.6 [1.8, 0.6]
0.771.0 [3.0, 0.5]
0.470.5 [1.5, 0.7]
0.570.4 [1.4, 0.1]
Output Factors
mean7standard deviation of the differences between calculated and measured PDDs. The first group of results shows the findings (in mm) for the build-up region, while the second section reports dose differences (as percentage, with normalization to 100% for each curve at 10 cm depth) after dmax. Ranges (maximum and mini-
mum differences through the whole dataset) are also reported. The lowest energy (4 MV of the Elekta unit) presents mean differences in the build-up region of more than 1 mm.This effect is visualized in (Fig. 1), where depth doses of a 15 15 cm2 field for all analyzed beams are
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Figure 1. Examples of PDD (two left columns) and Profiles (two right columns) for AAA (solid) and measurements (points). Data are shown at 10 cm depth and 15 15 cm2, for open and 601 wedged fields. Differences between calculations and measurements are also shown.
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4X_E
1 0 -1 -2 -3 0
10
20
30
40
3
6X_E
d=1.5 cm d=10 cm d=30 cm
2 1 0 -1 -2 -3 -4
0
10
20
30
40
6X_S
1 0 -1 -2 -3 -4
0
10
1 0 -1 -2 -3 0
10
20
30
15X_S
30
40
1 0 -1 -2 -3 -4
40
d=2.9 cm d=10 cm d=30 cm
2
0
10
Field Size [cm]
20
30
40
30
40
Field Size [cm]
4
4 d=1.4 cm d=10 cm d=30 cm
2
6X_V Calc-Meas Pen [mm]
3 1 0 -1 -2 -3 -4
20 Field Size [cm]
3
d=1.5 cm d=10 cm d=30 cm
2
Calc-Meas Pen [mm]
3
-4
15X_E
d=2.9 cm d=10 cm d=30 cm
2
4
4
Calc-Meas Pen [mm]
3
Field Size [cm]
Field Size [cm]
Calc-Meas Pen [mm]
Calc-Meas Pen [mm]
d=1 cm d=10 cm d=30 cm
2
-4
4
4
3
Calc-Meas Pen [mm]
Calc-Meas Pen [mm]
4
0
10
20
30
Field Size [cm]
40
3
d=2.7 cm d=10 cm d=30 cm
2
15X_V
1 0 -1 -2 -3 -4
0
10
20 Field Size [cm]
Figure 2. Differences between computed and measured penumbras as a function of field size at different depths.
presented (together with a zoom box inside to better appraise the build-up region differences) with the dose differences superimposed. In the case of Elekta, results are comparable for both open and motorized wedge beams. For the Siemens beams, instead, a decreasing quality of the agreement between calculations and measurements in the build-up region was observed when wedges are used. The discrepancy increases with wedge angle. For Varian beams, results are fully consistent and compatible with the analysis performed on the previous AAA release.
Profiles Table 2, reports also results from profile’s analysis. Findings are given for the whole dataset of fields analyzed and also for the sub-group of fields larger or equal than
5 5 cm2. No substantial differences are shown between the two groups for Elekta beams while, for Siemens beams, the agreement between AAA calculations and measurement is systematically better when analysis is restricted to larger fields only with the obvious implication that efforts should be put in improving the agreement in the small fields group, particularly for wedged beams. In (Fig. 1) profiles for a 15 15 cm2 open and 60 degree wedge beams are plot; dose differences are also superimposed. Figure 2 summarizes the analysis carried out in the penumbra region as a function of measurement depth and field size. There is no clear trend in penumbra differences with respect to field size or depth, and there is a clear underestimation of the penumbra values with AAA in almost all cases for Elekta and Siemens beams, qualitatively different from what observed for Varian beams. Quantitatively, the mean difference among all Elekta open beams
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(independently from energy, field size and depth) is 0.770.6 mm, it is 1.770.8 mm for Siemens unit, and 0.270.6 mm for Varian. As anticipated, also the profiles shown in (Fig. 2) evidentiate pictorially this effect while in the Varian case the agreement is much better. Since the relatively high difference observed for Siemens beams is not well detected in the g analysis if the threshold of 3 mm of DTA is used in the optimization process, it would be advisable to improve that part of the AAA system in order to either allow an user’s interface to define DTA and DD or to present results with different thresholds applied (e.g. 3 mm in the flattened region and 1 or 2 mm in the dose gradient region). Such an evolution of the AAA configuration algorithm would allow users to better appraise the reliability of the algorithm when applied to their local photon beams.
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Conclusions The present report was limited to an analysis of calculations performed by the AAA configuration algorithm and therefore investigates only a limited number of geometrical conditions. As an example no data are presented for asymmetric fields or for MLC shaped fields and this should be part of a detailed commissioning study for any center. As a conclusion, the study proved that AAA, in its release 8.0.05, confirm the quality already observed for Varian linacs and published also by other groups and anticipate a satisfactory agreement between calculations and measurements for other linac models, structurally very different one from the other in both geometrical and physical aspects. Validation of AAA under more clinical, special and complex situations to evaluate the degree of accuracy of the algorithm itselft have already been published.
MU calculation: Output and Wedge Transmission Factors and absolute calibration Table 2 presents finally the summary of the analysis of the Output Factors (OF) for open and wedged fields. Good agreement in MU computation is shown for the newly analyzed beams. For Elekta beams, the OF difference never exceed 2%, except very few cases of very small (3 3 cm2) or highly elongated beams (4 20 cm2) with Motorized Wedge, 6 MV. For Siemens beams, results of OF agree within 2% except for the fields with jaw X set to 4 cm (the largest deviation is for the 4 4 cm2 fields), with open and wedge 15 MV, where an almost systematic underestimation is found. For Varian unit, all OF deviations are kept within 1.5% (mostly within 1%). Wedge Transmission Factors computed with AAA differ from measurements in a range of 70.3% despite of the machine, the energy and the wedge angle. The absolute dose calculation in terms of MU computation was checked at reference conditions for each open beam, with 2 mm of calculation grid, where 100 MU/Gy are expected. The Eclipse results were as follows:
4X_E: 6X_E: 15X_E: 6X_S: 15X_S: 6X_V: 15X_V:
100.01 MU/Gy 100.36 MU/Gy 100.04 MU/Gy 100.38 MU/Gy 100.04 MU/Gy 99.90 MU/Gy 99.87 MU/Gy
(SSD ¼ 100 cm, d ¼ 1.0 cm) (SSD ¼ 100 cm, d ¼ 1.5 cm) (SSD ¼ 100 cm, d ¼ 2.9 cm) (SSD ¼ 100 cm, d ¼ 1.5 cm) (SSD ¼ 100 cm, d ¼ 2.9 cm) (SSD ¼ 90 cm, d ¼ 10 cm) (SSD ¼ 90 cm, d ¼ 10 cm)
References [1] Ulmer W, Harder D. A triple Gaussian pencil beam model for photon beam treatment planning. Z Med Phys 1995;5:25–30. [2] Ulmer W, Harder D. Applications of a triple Gaussian pencil beam model for photon beam treatment planning. Z Med Phys 1996;6:68–74. [3] Ulmer W, Kaissl W. The inverse problem of a gaussian convolution and its application to the finite size of the measurement chambers/ detectors in photon and proton dosimetry. Phys Med Biol 2003;48:707–27. [4] Fogliata A, Nicolini G, Vanetti E, Clivio A, Cozzi L. Dosimetric validation of the anisotropic analytical algorithm for photon dose calculation: fundamental characterization in water. Phys Med Biol 2006;51:1421–38. [5] Van Esch A, Tillikainen L, Pyykkonen J, Tenhunen M, Helminen H, Siljamaki S, et al. Testing of the analytical anisotropic algorithm for photon dose calculation. Med Phys 2006;33:4130–48. [6] Ulmer W, Pyyry J, Kaissl W. A 3D photon superposition/convolution algorithm and its foundation on results of Monte Carlo calculations. Phys Med Biol 2005;50:1767–90. [7] Bragg CM, Conway J. Dosimetric verification of the anisotropic analytical algorithm for radiotherapy treatment planning. Radiother Oncol 2006;81:315–23. [8] Fogliata A, Vanetti E, Albers D, Brink C, Clivio A, Kno¨o¨s T, et al. On the dosimetric behaviour of photon dose calculation algorithms in the presence of simple geometric heterogeneities: comparison with Monte Carlo calculations. Phys Med Biol 2007;52:1363–85. [9] Kno¨o¨s T, Wieslander E, Cozzi L, Brink C, Fogliata A, Albers D, et al. Comparison of dose calculation algorithms for treatment planning in external photon beam therapy for clinical situations. Phys Med Biol 2006;51:5785–807. [10] Low DA, Harms WB, Mutic S, Purdy JA. A technique for the quantitative evaluation of dose distributions. Med Phys 1998;25:656–61.
Basic dosimetric verification in water of the anisotropic analytical algorithm for Varian, Elekta and Siemens linacs Luca Cozzi1,4,, Giorgia Nicolini1, Eugenio Vanetti1, Alessandro Clivio1, Marco Glasho¨rster2, Hans Schiefer3, Antonella Fogliata1 1
Oncology Institute of Southern Switzerland, Medical Physics Unit, Bellinzona, Switzerland Universita¨tspital Mu¨nster, Radiation Oncology Dept., Mu¨nster, Germany 3 Kantonsspital St. Gallen, Klinik fu¨r Radio-Onkologie, St. Gallen, Switzerland 4 University of Lausanne, Faculty of Medicine, Lausanne, Switzerland 2
Received 12 July 2007; accepted 12 September 2007
Since early 2007 a new version of the Anisotropic Analytical Algorithm (AAA) for photon dose calculations was released by Varian Medical Systems for clinical usage on Elekta linacs and also, with some restrictions, for Siemens linacs. Basic validation studies were performed and reported for three beams: 4,6 and 15 MV for an Elekta Synergy, 6 and 15 MV for a Siemens Primus and, as a reference, for 6 and 15 MV from a Varian Clinac 2100C/D. Generally AAA calculations reproduced well measured data and small deviations were observed for open and wedged fields. PDD curves showed in average differences between calculation and measurement smaller than 1% or 1.2 mm for Elekta beams, 1% or 1.8 mm for Siemens beams and 1% or 1 mm for Varian beams. Profiles in the flattened region matched measurements with deviations smaller than 1% for Elekta and Varian beams, 2% for Siemens. Percentage differences in Output Factors were observed as small as 1% in average.
Keywords: Convolution algorithms, Anisotropic Analytical Algorithm, treatment planning systems
Grundlegende dosimetrische Verifizierung des Anisotropic Analytical Algorithm in Was’’ ser fu¨r Varian-, Elekta- und SiemensBeschleuniger ’’
Abstract
Zusammenfassung Seit dem Fru¨hjahr 2007 ist von Varian Medical Systems der neue Algorithmus ‘‘Anisotropic Analytical Algorithm (AAA)’’ fu¨r die Bestrahlungsplanung von Photonen fu¨r Elekta-Beschleuniger fu¨r den klinischen Einsatz sowie mit Einschra¨nkungen auch fu¨r Siemens-Beschleuniger freigegeben. Hier werden grundlegende Parameter untersucht fu¨r drei Strahlenergien: 4,6 und 15 MV eines Elekta Synergy sowie 6 und 15 MV eines Siemens Primus; als Referenz dienen analoge Auswertungen fu¨r 6 und 15 MV eines Varian Clinac 2100C/D. Allgemein kann gesagt werden, dass die AAA-Berechnungen die Messungen gut reproduzieren und sowohl fu¨r offene wie Keilfilterfelder nur geringe Abweichungen zu beobachten sind: Tiefendosiskurven fu¨r Elekta stimmen im Durchschnitt innerhalb von weniger als 1% bzw. 1,2 mm u¨berein; fu¨r Siemens liegen diese Werte bei 1% bzw. 1,8 mm und fu¨r Varian bei 1% bzw. 1 mm. Profile stimmen im flachen Feldbereich fu¨r Elekta und Varian innerhalb 1%, fu¨r Siemens innerhalb von 2% u¨berein. Die Abweichungen bei der Berechnung der Monitoreinheiten liegen im Durchschnitt ebenfalls bei nur 1%. Schlu¨sselwo¨rter: Konvolutions-Algorithmus, Anisotropic Analytical Algorithm, Bestrahlungsplanungssysteme
Corresponding author. Oncology Institute of Southern Switzerland, Radiation Oncology Department, Medical Physics Unit, CH-6504 Bellinzona. Tel.: +41 91 8119202; Fax: +41 91 8118678. E-mail: [email protected] (L. Cozzi).
Z. Med. Phys. 18 (2008) 128–135 doi: 10.1016/j.zemedi.2007.09.003 http://www.elsevier.de/zemedi
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Introduction In 2005 the Anisotropic Analytical Algorithm (AAA) for photon dose calculation has been implemented in the Varian Eclipse treatment planning system (Eclipse), and it was clinically released for Varian linacs. The AAA is a 3-D convolution/superposition algorithm that uses Monte Carlo derived kernels. The basic principles of the algorithm can be found in the papers published by Ulmer, Harder and Kaissl [1–3]. Some more details on its implementation in Eclipse, together with the meaning of the parameters used can be found in [4,5]. In its fundamentals, the dose calculation is based on the convolution over the beamlets of multiple radiation sources separately using physical parameters defined for every beamlet. The final dose distribution is obtained from the superposition of all the individual beamlet contributions. The energy deposition kernels account for tissue heterogeneity in an anisotropic way. Preliminary tests on the AAA were published by the developers by Ulmer et al. [6] while other studies [4,5,7] reported about basic verifications, comparisons against measurements, in water and in simple phantoms for Varian linear accelerators; performances of AAA and several other algorithms were reported in [8,9], benchmarked against MonteCarlo simulations, when heterogeneous media are involved in both simple geometrical phantoms and real patients. During the first months of 2007, a new version of the AAA algorithm was released for clinical usage also for Elekta units. For Siemens units, the version used constitutes a preclinical release. The present report is a summary of a basic dosimetric verification for open and wedged fields in water performed on an Elekta linac (with 4,6 and 15 MV photon beams) and for a Siemens unit (with 6 and 15 MV photon beams) and it is intended to give a first comparative overview on the performance of AAA applied to the three main linac models. Aim of this work is to analyse the ability of AAA implementation in Eclipse to reproduce basic data, after the configuration process, for linacs different from the Varian units. The investigation of AAA accuracy in more complex situations (e.g. particular beam settings, MLC, heterogeneities) is beyond the present scope, and it has been already discussed in other papers [4,5,7–9].
Material and methods All dose calculations were performed on a Varian Eclipse system (7.5.51) running the AAA photon dose calculation engine (8.0.05) installed at the Oncology Institute of Southern Switzerland.
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The Eclipse system was configured to enable AAA calculations for: i) Elekta Synergy linac, equipped with Motorized Wedge, producing the following beams: 4 MV (4X_E) with dmax ¼ 1.0 cm and TPR20/10 ¼ 0.634 6 MV (6X_E) with dmax ¼ 1.5 cm and TPR20/10 ¼ 0.679 15 MV (15X_E) with dmax ¼ 2.9 cm and TPR20/10 ¼ 0.754 For this linac, profiles and depth dose curves used for configuration and verification were acquired in water at SSD ¼ 100 cm. Field sizes ranged from 3 3 to 40 40 cm2 for open fields, and from 3 3 to 30 30 cm2 for the 601 Motorized Wedge. Output factors were defined at 10 cm depth, SSD ¼ 100 cm. ii) Siemens Primus, equipped with Hard Wedges (15, 30, 45 and 601), producing the following beams: 6 MV (6X_S) with dmax ¼ 1.5 cm and TPR20/10 ¼ 0.668 15 MV (15X_S) with dmax ¼ 2.9 cm and TPR20/10 ¼ 0.758 In this case, profiles and depth dose curves used for configuration and verification were acquired at SSD ¼ 100 cm. Field sizes ranged from 2 2 to 40 40 cm2 for open fields, from 2 2 to 25 25 cm2 (maximum allowed 30 25 cm2) for Hard Wedges from 15 to 451, and from 2 2 to 20 20 cm2 (maximum allowed field size 30 20 cm2) for the 601 Wedge. Output factors were defined at dmax, SSD ¼ 100 cm. iii) As a reference, AAA computations for Elekta and Siemens beams were compared against corresponding calculations for a Varian Clinac 2100 C/D unit with: 6 MV (6X_V) with dmax ¼ 1.5 cm and TPR20/10 ¼ 0.669 15 MV (15X_V) with dmax ¼ 2.7 cm and TPR20/10 ¼ 0.759 In the present publication, the results for Varian refer to calculations performed with the AAA 8.0.05 release while in [4] the 7.5.14.3 release was used; in both cases the same linacs were used. The new results shall be considered as an update of the previous findings and as a quality assurance test on the basic stability of AAA between releases in absence of expected performance improvements. Reference calibration conditions were: 10 10 cm2 field size, depth in water equal to dmax, SSD ¼ 100 cm, 1 Gy for 100 MU for both Elekta and Siemens, while for Varian d ¼ 10 cm and SSD ¼ 90 cm (isocentric configuration).
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Measurements were performed in water with conventional small volume ion chambers according to local standards and conventions for the Elekta linac with steps of 1 to 2.5 mm for profiles and ranging from 1 to 5 mm for depth doses; for Siemens unit measurements were acquired with steps of 2.5 mm for profiles and 5 mm for depth doses; for Varian unit, resolutions varying from 1 mm to 2.5 mm were applied as described in [4]. Calculations in Eclipse were performed using a grid size of 2.5 mm (allowed range: 2 to 5 mm). As known, the AAA implementation in Eclipse is divided in two parts, the dose calculation algorithm and the configuration algorithm. The configuration algorithm determines the fundamental physical parameters needed to model linear accelerators and to divide broad beams into finite-size beamlets with pointing geometry to be used for final calculations. The clinical beam is described by three components (multiple sources): a primary source modeling the bremsstrahlung photons from the target not interacting in the linac head; an extra-focal source, modeling photons scattered, mainly in the flattening filter and in the primary collimators and a third source modeling mostly contaminant electrons. The starting point of AAA configuration is the selection of generic parameters from a library of the most common treatment heads. These generic parameters are then tailored, to any actual specific linac that will be used clinically. The user’s input to the configuration phase consists of dosimetric data and parameters describing geometrical and physical characteristics of the real beams. Most of the geometrical data are read from defaults stored in the built-in libraries but some of them can be manually edited and adjusted to site specific needs. Dosimetric data needed for the configuration are: depth dose curves along beam central axis, lateral profiles at different depths, and output factors for open and wedged fields. For open beams, also diagonal profiles are needed while for wedges a profile transverse to the wedge direction is required. Minimal settings are defined by Varian while larger datasets are allowed or recommended. To optimize generic parameters and calculation kernels against measured beam data, objective functions include the g index [10] and penalty factors to prevent unphysical results or to minimize effect of noise in the measurements. As output from the configuration process, the following data are generated for use in the AAA photon dose calculation: mean radial energy curves, intensity profile curves, electron contamination curves and smoothing factor (sigmas of the Gaussians), spectrum, calculated diagonal profiles, lateral profiles, depth doses, collimator back scatter tables, final open (wedged) beam parameters (including absolute calibration). In addition, for wedges the transmission curves and specific wedge parameters are added.
Algorithm validation was based on the comparison of calculations and measurements of:
Depth dose curves (PDD): SSD ¼ 100 cm for Elekta and Siemens, SSD ¼ 90 cm for Varian, field size ranging from minimum to maximum allowed per linac type. Profiles: SSD ¼ 100 cm for Elekta and Siemens, SSD ¼ 90 cm for Varian, depths ¼ dmax, 5, 10, 20 and 30 cm, field size ranging from minimum to maximum allowed as above. Output Factors (OF): SSD ¼ 100 cm, d ¼ 10 cm for Elekta, d ¼ dmax for Siemens, and SSD ¼ 90 cm with d ¼ 10 cm for Varian, field size ranging from minimum to maximum allowed as above, for square and rectangular fields. Wedge Transmission Factors (WF): SSD ¼ 100 cm, d ¼ 10 cm for Elekta, d ¼ dmax for Siemens, and SSD ¼ 90 cm with d ¼ 10 cm for Varian, field size 10 10 cm2. MU computation in calibration conditions.
For the analysis, measured and calculated curves were linearly interpolated in order to have all data sampled with the finest grid size available between the two sets. Analysis of PDD and profiles was carried out as differences, point by point, between calculations and measurements. Statistical parameters, as mean, standard deviation, minimum and maximum values were computed. The PDDs analysis was divided into two regions: i) after dmax, as dose difference between calculation and measurement. More precisely, the curve where the dose after dmax was smaller than 95% of the maximum dose for each PDD was included to avoid the ‘flat’ buildup region. PDDs in those cases were normalized to 100% at 10 cm depth; ii) in the build-up region, as difference in mm at fixed dose levels; for this last analysis PDDs were normalized to 100% at dmax. The analysis for profiles was performed: i) in the ‘flattened’ region, defined as the region were the dose is greater than 95% for open fields, and within the central 90% of the geometrical field size for wedge beams, and ii) in the ‘penumbra region’ defined as the region between the 20% and 80% dose levels. For both cases results and statistical parameters were recorded in terms of differences as for PDDs. Each profile (orthogonal to the beam axis) was normalized to 100% at the beam central axis. Output Factor results were analyzed as percentage difference between computed and measured OF: mean, standard deviation and range were reported. The MU calculations were compared to measurements, and reported as percentage difference for the standard linac calibration conditions for open beams, while for
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wedge beams they were reported as WF (wedge transmission factors) percentage difference for a 10 10 cm2 field.
Results and discussions Configuration Configuration parameters defining beam characteristics after tailoring to measured beam data in the configuration algorithm are not presented in this report for space reason, but they could be sent by the authors on request. As a quality assurance tool, the AAA configuration process generates, in output, histograms of the g index calculated for each processed measured curve against calculations. Table 1 shows the average of the resulting g values together with the percentage of points failing the
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pass fail test (g larger than 1). The thresholds used to compute g are fixed in Eclipse and not tunable by the user, and set as distance to agreement DTA ¼ 3 mm and dose difference DD ¼ 1%. The criterion of 1% in dose difference is quite stringent, while 3 mm of distance to agreement is possibly too coarse to check algorithm accuracy in high dose gradient regions, like the build up and penumbra areas. For example, the penumbra region presents for all units and energies, no points with g41 while, as it will be shown later, for Siemens units the differences between calculations and measurements are not negligible. Depth-dose curves Table 2 presents a summary of the analysis on depth dose data for open and wedged fields. Values refer to
Table 1 Gamma error histogram results: average gamma error and, in brakets, the percentage of point not respecting the criteria (DTA ¼ 3 mm, DD ¼ 1%). Parameter
4X_E
6X_E
15X_E
6X_S
15X_S
6X_V
15X_V
Depth dose curves: Before dmax After dmax
0.63 (11.5%) 0.11 (0.2%)
0.21 (0.0%) 0.11 (0.0%)
0.36 (2.0%) 0.17 (0.0%)
0.32 (0.0%) 0.10 (0.0%)
0.34 (3.1%) 0.16 (0.7%)
0.19 (0.0%) 0.08 (0.0%)
0.22 (0.0%) 0.12 (0.0%)
Profiles: Inside field In penumbra region Outside field
0.19 (1.4%) 0.18 (0.0%) 0.23 (2.2%)
0.12 (0.0%) 0.15 (0.0%) 0.23 (1.5%)
0.13 (0.0%) 0.16 (0.0%) 0.20 (0.0%)
0.18 (0.1%) 0.37 (0.0%) 0.33 (2.2%)
0.17 (0.2%) 0.33 (0.0%) 0.29 (0.3%)
0.12 (0.1%) 0.18 (0.0%) 0.35 (0.9%)
0.13 (0.3%) 0.19 (0.0%) 0.24 (0.0%)
Table 2 Differences between calculated (AAA) and measured depth dose curves, profiles and output factors for the different beams, open and wedges. Reported are the mean, standard deviation and range over all curves (point by point) and for all analysed field sizes. 4X_E
6X_E
15X_E
6X_S
15X_S
6X_V
15X_V
Before dmax Calc-Meas [mm]
Depth doses Open
1.270.3 [0.2, 1.6]
0.670.1 [0.2, 1.0]
0.570.5 [1.3, 1.0]
0.470.1 [0.2, 1.0]
0.570.5 [1.4, 0.9]
0.570.1 [0.0, 1.2]
0.270.5 [1.2, 1.6]
W15
–
–
–
0.870.2 [0.2, 1.3]
0.470.9 [1.8, 2.3]
0.270.2 [0.4, 0.5]
0.270.7 [1.8, 2.1]
W30
–
–
–
0.170.3 [1.2, 0.8]
1.170.9 [2.8, 1.5]
0.170.3 [0.4, 0.9]
0.170.7 [2.0, 2.1]
W45
–
–
–
0.570.1 [1.5, 0.4]
1.571.1 [4.1, 1.4]
0.470.1 [0.5, 0.1]
0.370.9 [1.7, 2.9]
W60/MW
0.770.2 [0.3, 1.7]
0.270.1 [0.4, 0.6]
1.070.5 [2.2, 0.2]
0.770.2 [2.0, 0.2]
1.871.0 [3.9, 1.0]
0.670.1 [1.2, 0.0]
0.171.1 [1.9, 2.7]
After dmax Calc-Meas [%] Open
0.270.2 [0.8, 1.1]
0.070.2 [0.8, 0.8]
0.070.2 [1.0, 1.2]
0.170.1 [0.7, 1.7]
0.170.2 [1.5, 2.8]
0.170.1 [0.4, 1.0]
0.070.2 [0.8, 1.2]
W15
–
–
–
0.170.2 [1.1, 2.5]
0.170.3 [1.4, 2.7]
0.070.1 [0.7, 1.6]
0.070.2 [0.8, 1.3]
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Table 2 (continued ) 4X_E
6X_E
15X_E
6X_S
15X_S
6X_V
15X_V
W30
–
–
–
0.070.3 [1.2, 3.6]
0.170.2 [1.6, 2.3]
0.070.1 [0.5, 1.3]
0.070.2 [0.8, 1.1]
W45
–
–
–
0.170.3 [1.8, 3.9]
0.270.3 [2.3, 3.0]
0.170.1 [1.0, 2.2]
0.470.1 [0.9, 1.1]
W60/MW
0.170.2 [1.5, 2.5]
0.070.2 [1.0, 1.5]
0.370.3 [1.1, 1.6]
0.270.3 [1.5, 2.7]
0.070.2 [1.4, 3.0]
0.170.1 [0.8, 1.7]
0.470.1 [1.3, 1.2]
Profiles All field sizes Open
0.070.3 [1.4, 5.4]
0.070.2 [1.1, 4.5]
0.170.2 [1.2, 2.0]
0.270.6 [2.0, 11.1]
0.570.4 [1.7, 7.1]
0.070.3 [1.9, 4.2]
0.170.2 [6.5, 3.0]
W15
–
–
–
1.972.0 [2.3, 24.6]
1.871.6 [1.2, 20.4]
0.770.6 [10.8, 16.2]
0.270.5 [9.2, 11.4]
W30
–
–
–
1.671.9 [2.5, 25.6]
1.771.6 [3.4, 21.9]
0.770.6 [9.6, 17.2]
0.370.6 [9.1, 12.1]
W45
–
–
–
1.872.2 [5.4, 29.8]
1.671.8 [5.2, 24.7]
0.770.6 [8.4, 18.5]
0.370.6 [11.5, 13.0]
W60/MW
0.470.5 [5.0, 8.3]
0.270.4 [7.5, 14.0]
0.070.4 [6.1, 7.0]
1.972.4 [7.9, 28.3]
1.871.9 [4.9, 24.3]
0.870.8 [10.8, 21.9]
0.270.7 [17.5, 13.3]
Field sizes X 5 5 cm2 Open
0.070.3 [1.4, 4.9]
0.070.2 [1.1, 4.5]
0.170.2 [1.2, 2.0]
0.170.5 [2.0, 11.1]
0.470.3 [1.7, 7.1]
0.170.3 [1.9, 4.2]
0.270.2 [6.5, 2.5]
W15
–
–
–
1.070.8 [2.3, 24.6]
1.170.7 [1.2, 19.1]
0.570.4 [10.8, 13.5]
0.170.4 [9.2, 8.7]
W30
–
–
–
0.870.8 [2.5, 23.9]
1.070.7 [3.4, 19.4]
0.570.4 [9.6, 15.5]
0.170.4 [9.1, 9.2]
W45
–
–
–
0.870.8 [5.4, 25.0]
0.870.8 [5.2, 23.4]
0.570.5 [8.4, 17.3]
0.170.5 [11.5, 10.4]
W60/MW
0.470.5 [5.0, 7.4]
0.270.4 [7.5, 14.0]
0.070.4 [6.1, 6.4]
0.870.9 [7.9, 22.8]
0.970.8 [4.2, 21.8]
0.670.7 [10.8, 21.9]
0.070.6 [17.5, 11.6]
Open
0.070.3 [0.5, 0.5]
0.170.3 [0.6, 0.3]
0.270.4 [1.2, 0.2]
0.270.5 [1.5, 0.4]
0.670.9 [3.1, 0.1]
0.170.3 [0.6, 0.3]
0.370.4 [1.2, 0.2]
W15
–
–
–
0.270.6 [1.7, 1.2]
0.771.1 [3.3, 0.3]
0.270.3 [0.7, 0.4]
0.370.4 [1.1, 0.3]
W30
–
–
–
0.370.6 [1.9, 0.5]
0.771.1 [3.4, 0.4]
0.270.3 [0.8, 0.3]
0.370.5 [1.2, 0.1]
W45
–
–
–
0.270.5 [1.7, 0.5]
0.771.0 [3.1, 0.7]
0.370.3 [0.9, 0.3]
0.370.4 [1.1, 0.1]
W60/MW
0.170.8 [1.6, 1.6]
0.271.3 [2.5, 1.8]
0.370.8 [1.7, 1.6]
0.370.6 [1.8, 0.6]
0.771.0 [3.0, 0.5]
0.470.5 [1.5, 0.7]
0.570.4 [1.4, 0.1]
Output Factors
mean7standard deviation of the differences between calculated and measured PDDs. The first group of results shows the findings (in mm) for the build-up region, while the second section reports dose differences (as percentage, with normalization to 100% for each curve at 10 cm depth) after dmax. Ranges (maximum and mini-
mum differences through the whole dataset) are also reported. The lowest energy (4 MV of the Elekta unit) presents mean differences in the build-up region of more than 1 mm.This effect is visualized in (Fig. 1), where depth doses of a 15 15 cm2 field for all analyzed beams are
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Figure 1. Examples of PDD (two left columns) and Profiles (two right columns) for AAA (solid) and measurements (points). Data are shown at 10 cm depth and 15 15 cm2, for open and 601 wedged fields. Differences between calculations and measurements are also shown.
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4X_E
1 0 -1 -2 -3 0
10
20
30
40
3
6X_E
d=1.5 cm d=10 cm d=30 cm
2 1 0 -1 -2 -3 -4
0
10
20
30
40
6X_S
1 0 -1 -2 -3 -4
0
10
1 0 -1 -2 -3 0
10
20
30
15X_S
30
40
1 0 -1 -2 -3 -4
40
d=2.9 cm d=10 cm d=30 cm
2
0
10
Field Size [cm]
20
30
40
30
40
Field Size [cm]
4
4 d=1.4 cm d=10 cm d=30 cm
2
6X_V Calc-Meas Pen [mm]
3 1 0 -1 -2 -3 -4
20 Field Size [cm]
3
d=1.5 cm d=10 cm d=30 cm
2
Calc-Meas Pen [mm]
3
-4
15X_E
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Figure 2. Differences between computed and measured penumbras as a function of field size at different depths.
presented (together with a zoom box inside to better appraise the build-up region differences) with the dose differences superimposed. In the case of Elekta, results are comparable for both open and motorized wedge beams. For the Siemens beams, instead, a decreasing quality of the agreement between calculations and measurements in the build-up region was observed when wedges are used. The discrepancy increases with wedge angle. For Varian beams, results are fully consistent and compatible with the analysis performed on the previous AAA release.
Profiles Table 2, reports also results from profile’s analysis. Findings are given for the whole dataset of fields analyzed and also for the sub-group of fields larger or equal than
5 5 cm2. No substantial differences are shown between the two groups for Elekta beams while, for Siemens beams, the agreement between AAA calculations and measurement is systematically better when analysis is restricted to larger fields only with the obvious implication that efforts should be put in improving the agreement in the small fields group, particularly for wedged beams. In (Fig. 1) profiles for a 15 15 cm2 open and 60 degree wedge beams are plot; dose differences are also superimposed. Figure 2 summarizes the analysis carried out in the penumbra region as a function of measurement depth and field size. There is no clear trend in penumbra differences with respect to field size or depth, and there is a clear underestimation of the penumbra values with AAA in almost all cases for Elekta and Siemens beams, qualitatively different from what observed for Varian beams. Quantitatively, the mean difference among all Elekta open beams
ARTICLE IN PRESS L. Cozzi et al. / Z. Med. Phys. 18 (2008) 128–135
(independently from energy, field size and depth) is 0.770.6 mm, it is 1.770.8 mm for Siemens unit, and 0.270.6 mm for Varian. As anticipated, also the profiles shown in (Fig. 2) evidentiate pictorially this effect while in the Varian case the agreement is much better. Since the relatively high difference observed for Siemens beams is not well detected in the g analysis if the threshold of 3 mm of DTA is used in the optimization process, it would be advisable to improve that part of the AAA system in order to either allow an user’s interface to define DTA and DD or to present results with different thresholds applied (e.g. 3 mm in the flattened region and 1 or 2 mm in the dose gradient region). Such an evolution of the AAA configuration algorithm would allow users to better appraise the reliability of the algorithm when applied to their local photon beams.
135
Conclusions The present report was limited to an analysis of calculations performed by the AAA configuration algorithm and therefore investigates only a limited number of geometrical conditions. As an example no data are presented for asymmetric fields or for MLC shaped fields and this should be part of a detailed commissioning study for any center. As a conclusion, the study proved that AAA, in its release 8.0.05, confirm the quality already observed for Varian linacs and published also by other groups and anticipate a satisfactory agreement between calculations and measurements for other linac models, structurally very different one from the other in both geometrical and physical aspects. Validation of AAA under more clinical, special and complex situations to evaluate the degree of accuracy of the algorithm itselft have already been published.
MU calculation: Output and Wedge Transmission Factors and absolute calibration Table 2 presents finally the summary of the analysis of the Output Factors (OF) for open and wedged fields. Good agreement in MU computation is shown for the newly analyzed beams. For Elekta beams, the OF difference never exceed 2%, except very few cases of very small (3 3 cm2) or highly elongated beams (4 20 cm2) with Motorized Wedge, 6 MV. For Siemens beams, results of OF agree within 2% except for the fields with jaw X set to 4 cm (the largest deviation is for the 4 4 cm2 fields), with open and wedge 15 MV, where an almost systematic underestimation is found. For Varian unit, all OF deviations are kept within 1.5% (mostly within 1%). Wedge Transmission Factors computed with AAA differ from measurements in a range of 70.3% despite of the machine, the energy and the wedge angle. The absolute dose calculation in terms of MU computation was checked at reference conditions for each open beam, with 2 mm of calculation grid, where 100 MU/Gy are expected. The Eclipse results were as follows:
4X_E: 6X_E: 15X_E: 6X_S: 15X_S: 6X_V: 15X_V:
100.01 MU/Gy 100.36 MU/Gy 100.04 MU/Gy 100.38 MU/Gy 100.04 MU/Gy 99.90 MU/Gy 99.87 MU/Gy
(SSD ¼ 100 cm, d ¼ 1.0 cm) (SSD ¼ 100 cm, d ¼ 1.5 cm) (SSD ¼ 100 cm, d ¼ 2.9 cm) (SSD ¼ 100 cm, d ¼ 1.5 cm) (SSD ¼ 100 cm, d ¼ 2.9 cm) (SSD ¼ 90 cm, d ¼ 10 cm) (SSD ¼ 90 cm, d ¼ 10 cm)
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