Implementation of enhanced dynamic wedge in the focus rtp system

Medical Dosimetry, Vol. 25, No. 2, pp. 81– 86, 2000 Copyright © 2000 American Association of Medical Dosimetrists Printed in the USA. All rights reserved 0958-3947/00/$–see front matter

PII: S0958-3947(00)00033-9

IMPLEMENTATION OF ENHANCED DYNAMIC WEDGE IN THE FOCUS RTP SYSTEM MOYED MIFTEN, PH.D.,1 MARK WIESMEYER, PH.D.,1 ANDY BEAVIS, PH.D.,2 KAZ TAKAHASHI, B.S.,1 and STEVE BROAD, M.S.1 1

Computerized Medical Systems, Inc., St. Louis, MO USA; 2 Princess Royal Hospital and University of Hull, Hull, UK ( Accepted 13 December 1999)

Abstract—The FOCUS RTP system implementation of Varian’s enhanced dynamic wedge (EDW) is presented. Calculations of both dose distributions and wedge factors (WFs) are based on segmented treatment tables (STTs). Calculating dose requires a “transmission matrix” derived from an STT to model the modified fluence from the source. The dose calculation is then performed using either the Clarkson or convolution/superposition algorithms. An initial “primary dose/monitor unit (MU) fraction” WF estimate at the weight point of symmetric and asymmetric fields is calculated from the STT as the ratio of MU delivered on the axis of the weight point divided by total MU delivered for the treatment field. In our approach, we go beyond this initial estimate with a “scatter dose” correction. This requires measured 60° WFs for 5 fields. Scatter corrections derived from measured WFs are interpolated for other wedge angles and field sizes in much the same way as arbitrary wedge angle STTs are derived from a “golden STT” using the “ratio of tangents” formalism. Dose comparisons with measured distributions show good agreement to within 3% or 3 mm for 6-MV beams and all EDW angles. Agreement with measurements to within 1% is obtained for WFs in all symmetric and asymmetric fields for 6- and 10-MV beams. For large wedge angles and field sizes, this represents a significant improvement over the 3% to 4% errors often observed using the MU fraction model alone. © 2000 American Association of Medical Dosimetrists. Key Words: EDW, STT, Dose calculations, Wedge factors.

INTRODUCTION

wedges in the treatment head. In addition, EDW does not harden the beam, and gives the flexibility to plan with more wedge angles. Although no hardening is present through physical attenuation of the beam using EDW, small differences can be seen in depth dose profiles compared to open fields.6 Also, there is additional scatter off the dynamic jaw as it “sweeps” across the beam portal. However, these effects are much smaller than the attenuation and scatter effects of a metal wedge placed in the direction of the beam. Many implementations have modeled the EDW as a “virtual” physical filter in treatment planning systems.3,10 Other models are based on the use of measured data to derive the EDW dosimetric data.4 Methods were proposed to perform dose calculation using transmission matrix generated from Varian’s segmented treatment tables (STTs),7–9 which are energy-dependent tables that describe the dose delivery and jaw position “segments” required to deliver EDW dose. Some authors have proposed using the STTs to calculate wedge factors (WFs) for EDW.3 This monitor unit (MU) fraction model produces WFs for many wedge angles and field sizes to within 1% to 2% of measurements. However, for large field sizes and wedge angles, it produces results within 3% to 4% of measurements.11 Recent published work shows improvements in WF calculations using a dual source model.11 In this work, we describe a universal STT-based

Radiation therapy treatment planning for many clinical situations requires wedge-shaped isodose distributions. The wedged dose distributions can be generated through the use of physical wedges, motorized wedges, and the synchronization of jaw or multileaf collimator dynamic motion with accelerator dose output. The varian enhanced dynamic wedge (EDW) (Varian Oncology Systems, Palo Alto, CA) delivers wedged-shaped dose distributions by combining computer controlled dose delivery with collimator motion.1 The EDW fields are generated by combining open and 60° fields with the relative weights of the 2 fields calculated using the “ratio of tangents” formalism. Seven angles (10°, 15°, 20°, 25°, 30°, 45°, and 60°) and asymmetric capability are available with the EDW. The wedge plane is restricted to the Y (upper) jaws with a maximum field size of 30 cm (Y1 ⫽ 20 cm, Y2 ⫽ 10) or (Y1 ⫽ 10 cm, Y2 ⫽ 20 cm). The clinical advantages of using dynamic wedges have been reported by many investigators.2–7 Unlike physical wedges, EDW is not limited in length and does not create additional low energy electron and photon scatter, which could increase both surface and peripheral dose. The use of EDW results in faster treatment times and fewer hazards when compared to physically placing Reprint requests to: Moyed Miften, Ph.D., Computerized Medical Systems, Inc., 1195 Corporate Lake Drive, St. Louis, MO 63132. 81

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model to calculate dose for EDW using either the Clarkson12 or convolution/superposition13 algorithms and describe a new approach to calculate WFs for symmetric and asymmetric fields. An initial “primary dose/MU fraction” WF estimate at the weight point of symmetric and asymmetric fields is calculated from the STT as the ratio of MU delivered on the axis of the weight point divided by total MU delivered for the treatment field. We improve this initial estimate with a “scatter dose” correction. This correction requires measured 60° WFs for 5 fields. Scatter corrections derived from measured WFs are interpolated for other wedge angles and field sizes in much the same way as arbitrary wedge angle STTs are derived from a “golden STT” using the “ratio of tangents” formalism. The methods proposed in this paper generate WFs to within 1% and isodose distributions to within 3% or 3 mm, compared to measurements for a full range of symmetric and asymmetric field sizes. METHODS AND MATERIALS The EDW model is implemented in the FOCUS RTP system (Computerized Medical Systems, St. Louis, MO). Calculated dose distributions are compared to data measured on Varian Clinac accelerators (Varian). Measurements were acquired with an RFA-300 water scanning system using a LDA-25 diode array (Scanditronix AB, Uppsala, Sweden). The isocenter of the accelerator is 100-cm and the surface of the water was placed at 100-cm source to skin distance. Profiles for a 6-MV beam are measured at 0.5-cm depth spacing for a range of EDW angles and field sizes. Wedge factors for 6- and 10-MV beams were calculated and compared to ion chamber measurements for a range of EDW angles and for a range of both symmetric and asymmetric field sizes. Three-dimensional dose distributions were calculated with 0.4-cm resolution using the Clarkson and convolution/superposition algorithms on HP-C3000 workstation (Hewlett Packard, Palo Alto, CA). Isodose distributions of both the calculated and measured data were superimposed using common axes and scales. The plotted isodose values were used for the assessment of the accuracy of the calculation data. In addition, isodifference values, which are the difference between the calculated and measured doses as a fraction of the normalization dose were generated. The results were used to identify the regions where the calculation and measurement difference is more than 3% and 3 mm (distance to agreement to the nearest point exhibiting the same dose level). Generating a segmented treatment table The Varian EDW is based on the concept of an energy-specific “golden STT.” By definition, the golden STT describes the sequence of jaw positions and doses for each fraction of the MU delivered for a 60° EDW for the largest field size. Generating a segmented treatment

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table for an arbitrary angle and field size, require a series of operations on the golden STT.1 The golden STT is first modified to deliver dose for the wedge angle that is to be delivered. The modification process employs the “ratio of tangents” method,1 and is performed as follows:

冋

D ␪ (y) ⫽ 1 ⫺

册

tan ␪ tan ␪ D (0) ⫹ D (y) tan 600 0 tan 600 60

(1)

where D0(0) is the open field dose, D60(y) is the cumulative dose delivered at dynamic collimator position y in the golden STT, and ␪ is the wedge angle to be delivered. The next step in producing an STT for a treatment, called “truncation,” is composed of linearly interpolating the cumulative dose from the STT calculated using Eq. (1) to a new evenly-spaced set of one hundred segments throughout the desired field. The result of these manipulations is an STT for the specified field and wedge angle; it is this modified STT that is used in dose calculation. Dose calculation The delivery of an EDW treatment is a simple one-dimensional intensity modulation. Two parameters are modulated, as specified by the STT, during the course of the delivery: the jaw positions and the beam intensity. Together these modulations produce a fluence profile similar to that generated by physical wedges. Both modulations occur in real time when implemented by a Varian linear accelerator. However, because photon dose calculations are time-independent, calculating dose for EDW requires that these modulations must be described in a way that is also independent of time. Segmented treatment tables suit this need well. They specify the relative cumulative dose delivered for various dynamic collimator positions. The increase in cumulative dose, delivered in the interval between 2 specified dynamic collimator positions, is linear:1 D (y) ⫽ (D b ⫺ D a)

y⫺a ⫹ Da b⫺a

(2)

where a, b are adjacent dynamic collimator positions listed on the STT, a ⬍ y ⬍ b, and Da, Db are the values of the cumulative dose delivered that are paired with dynamic collimator positions a, b, respectively. Thus, it is possible to calculate the cumulative dose delivered to any given dynamic collimator position that is part of an EDW treatment. The information is now written in a format that is independent of time by converting the modified STT to a transmission matrix. Note that the use of this transmission matrix is conceptually different for the Clarkson and convolution/superposition algorithms. In the Clarkson algorithm, the transmission matrix is used to modulate primary dose, whereas in the convolution/superposition algorithms, the transmission matrix is used to modulate fluence.

Implementation of EDW in the FOCUS RTP system ● M. MIFTEN et al.

Consider a point in a patient who is going to be treated with EDW, the “weight” of any element of the transmission matrix is: D(y) W(y) ⫽ D total

which the weight point occurs) to the total MU delivered in the wedged treatment: WF primary (y) ⫽

D(y) D total

(5)

(3)

where D( y) is determined as described in Eq. (2), above, and Dtotal is the total MU delivered during the treatment. Notice that the table is a function only of y, due to the one-dimensional aspect of EDW fluence modulation. The complete two-dimensional transmission matrix used in the dose calculation algorithms can be constructed for each fluence (convolution/superposition) or primary dose (Clarkson) “fan” using the weight ratio described in Eq. (3): T(m,n) ⫽ W(y(m,n))

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(4)

where the fan under consideration is the m,nth fan in the matrix, m is the width, and n is the length, and y(m,n) is the position of the dynamic collimator jaw when it is coincident upon the m,nth fan in the matrix. The derived transmission matrix is used in the dose calculation algorithms, and the calculation can be performed using either the Clarkson or convolution/superposition algorithms. Wedge factor calculation Another algorithm calculates a WF, analogous to the wedge attenuation factor for a physical wedge, for each beam setup that uses an EDW. The STTs used for calculating WFs must be identical to the STTs controlling the delivery of the EDW treatment. If this correspondence is maintained, a first approximation to the WF can be derived directly from the STT. For any treatment setup, this approximate “primary dose” WF is the ratio of the MU delivered on the axis of the weight point divided by the total MU delivered for the treatment field, both are quantities that are found in the STT. The implementation goes beyond this simple first approximation, however, with a “scatter dose” correction for WF. This correction requires measured 60° WFs for 5 field sizes at the geometric field-center. The measured field sizes are a symmetric 4 ⫻ 4 cm, 10 ⫻ 10 cm, 15 ⫻ 15 cm, 20 ⫻ 20 cm, and an asymmetric 30 ⫻ 30 cm. For the other 60° wedged field sizes, we use linear interpolation to calculate WFs from the 5 measured WFs. These scatter dose corrections derived from the measured WFs are scaled for non-measurement conditions (i.e., angles other than 60°) in much the same way that arbitrary wedge angle STT tables are derived from the golden STT. An approximate WF, one that only accounts for primary dose, may be computed as the ratio of the MU delivered at the weight fan (the calculation fan along

where y is the dynamic collimator position coincident with the weight point. Note this formula is similar to Eq. (3), which was used to derive the transmission matrix. After calculating the primary WF, a correction for “scatter dose” is calculated by comparing approximate WFs calculated for calibration setups to measured wedge factors for the same setups for a 60° EDW. This produces the following correction factor: CF 60 (fc) ⫽

WF measured,60 (fc) WF primary,60 (fc)

(6)

where WFmeasured,60 (fc) is the measured 60° WF for a square field at the geometric field center (fc). The correction factor for any angle can be obtained using the ratio of tangents formula: CF ␪ (fc) ⫽ (CF 60 (fc) ⫺ 1)

tan (␪ ) ⫹1 tan (60)

(7)

where ␪ is the wedge angle to be delivered. The correction factor is used to correct the original approximated, primary WF: WF (y) ⫽ WF primary (y) CF ␪ (fc)

(8)

The result of Eq. (8) is the final WF to be used in the time/MU calculation. One limitation of this approach is that the WF may be overestimated for weight points away from the geometric field center. Scatter dose decreases with off-axis distance and this decrease is not modeled in this approach, because the CF is calculated at the field center. RESULTS AND DISCUSSION We have performed dose calculations for 6-MV beams using the Clarkson and convolution/superposition algorithms. Figure 1(a) displays the measured and Clarkson calculated isodose distributions in a water phantom for a 6-MV 10 ⫻ 10-cm 60° EDW field. Figure 1(b) shows the measured and the convolution/ superposition calculated isodose distributions for the same setup. Figure 2 displays the measured and calculated dose profiles for a 6-MV beam at depth of maximum dose (dmax) for a 60° wedge 30 ⫻ 20-cm (maximum field length) asymmetric field. The maximum field length 60° profiles were measured using ion chambers. We observe good agreement to within 3% or 3 mm between calculations and measurements for 10 ⫻ 10-cm case using the convolution/superposition algorithm. Similar results were observed for other wedges angles. This shows that performing the dose

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Fig. 2. Relative measured and calculated dose profiles at dmax for a 60° EDW 6-MV beam, maximum field length. The wedge field is 30-cm long (Y1 ⫽ 20 cm, Y2 ⫽ 10 cm) and 20-cm wide.

Fig. 1. Superimposed measured and calculated relative isodose distributions along a central-axis transverse plane in a water phantom for a 10 ⫻ 10-cm 60° EDW 6-MV beam. (a) Measurements (solid lines) and Clarkson (dashed lines). (b) Measurements (solid lines) and convolution/superposition (dashed lines).

calculation with a transmission matrix generated from the STT produce accurate results. The results show that using the STTs to generate an intensity map yields improved dose results, without the need for measured data, compared to modeling the EDW as a physical filter. Unlike the STT-based models, the EDW filter model results in large hot spots along the toe region for large fields,3 which usually require modification of the filter thickness to minimize the difference. In addition, such an approach requires measured data for each wedge angle to derive the filter thickness. Figures 3 and 4 show calculated and measured wedge factors for 15°, 30°, 45°, and 60° EDW 6- and 10-MV beams, respectively. Figure 5 shows the wedge factors for asymmetric 6-MV 60° EDW fields. Excellent agreement with measurements is obtained for WFs in all

symmetric and asymmetric fields. The agreement is achieved due to the use of scatter dose correction factors in the WF calculation. To quantify the magnitude of this correction, we show, in Fig. 6, the scatter dose correction factors for 15°, 30°, 45°, and 60° EDW 6-MV beam and for a range of field sizes. We observe that the scatter dose correction factor increases with large field sizes and large wedge angles to a maximum of 3% for the 20 ⫻ 20-cm 60° wedged field. The approach of using the ratio of tangents to derive corrections from the 60° corrections for all field sizes and wedge angles resulted in WFs values to within 1% of measurements. For large wedge angles and field sizes, this represents a significant improvement over the 3% to 4% errors observed using the MU fraction model alone without correction.

Fig. 3. Central-axis measured and calculated WFs for 15°, 30°, 45°, and 60° EDW 6-MV beam over a range of square field sizes.

Implementation of EDW in the FOCUS RTP system ● M. MIFTEN et al.

Fig. 4. Central-axis measured and calculated WFs for 15°, 30°, 45°, and 60° EDW 10-MV beam over a range of square field sizes.

CONCLUSIONS The implementation of EDW in RTP systems provides clinics with an additional effective tool for conformal radiotherapy treatment planning. Furthermore, the use of such computer-controlled dose modulators improves efficiency by removing the need to mount and un-mount physical devices. Using such a tool requires accurate dose and wedge factor calculations. We have

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Fig. 6. Scatter dose correction factors for 15°, 30°, 45°, and 60° EDW 6-MV beam over a range of square field sizes.

presented a model, which relies on the STT, to accurately calculate dose and WFs for EDW. The results show that a transmission matrix calculated from STT can be used to generate accurate dose calculations using the empirically-based Clarkson algorithm or model-based convolution/superposition algorithm. Finally, we demonstrated accurate WF calculations, for a full range of beam setups, based on STT and correction factors derived from the 60° measured WFs using the ratio of tangents formalism.

Acknowledgments—We would like to thank Shaun Baggerly and Eric Klein for providing us with the measured data. We also thank Eric Klein for helpful discussions.

REFERENCES

Fig. 5. Geometric field center measured and calculated WFs with field asymmetry for a 60° EDW 6-MV beam. The field width was held constant at 20 cm, the Y2 static jaw at 10 cm and the initial position of the Y1 dynamic jaw was varied between 0 cm and 10 cm. The width of the asymmetric field is given by the Y1 ⫹ Y2 position. The WFs are normalized to the 20 ⫻ 20-cm field WF.

1. Varian Oncology Systems C-Series, Clinac Enhanced Dynamic Wedge Implementation Guide; 1996. 2. Leavitt, D.D.; Martin, M.; Moeller, J.H.; et al. Dynamic wedge field techniques through computer-controlled motion and dose delivery. Med. Phys. 17:87–91; 1990. 3. Klein, E.E.; Low, D.S.; Meigooni, A.S.; et al. Dosimetry and clinical implementation of dynamic wedge. Int. J. Radiat. Oncol. Biol. Phys. 31:583–592; 1995. 4. Leavitt, D.D.; Lee, W.L.; Gafney, D.K.; et al. Dosimetric parameters of enhanced dynamic wedge for treatment planning and verification. Med. Dosim. 22:177–183; 1997. 5. Bidmead, A.M.; Garton, A.J.; Childs, P.J. Beam data measurements for dynamic wedges on Varian 600C (6 MV) and 2100C (6 and 10 MV) linear accelerators. Phys. Med. Biol. 40:393– 411; 1995. 6. Beavis, A.W.; Weston, S.J.; Whitton, V.J. Implementation of the Varian EDW into a commercial RTP system. Phys. Med. Biol. 41:1691–1704; 1996. 7. Papatheodorou, S.; Zefkili, S.; Rosenwald, J-C. The ‘equivalent wedge’ implementation of the Varian Enhanced Dynamic Wedge (EDW) into a treatment planning system. Phys. Med. Biol. 44: 509 –524; 1999. 8. Storchi, P.; Woudstra, E.; Johansson, K.A.; et al. Calculation of

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absorbed dose distributions for dynamic wedges. Phys. Med. Biol. 43:1497–1506; 1998. 9. Weber, L.; Ahnesjo¨, A.; Nilsson, P.; et al. Verification and implementation of dynamic wedge calculations in a treatment planning system based on a dose-to-energy-fluence formalism. Med. Phys. 23:307–316; 1996. 10. Klein, E.E.; Gerber, R.; Zhu, X.R.; et al. Multiple machine implementation of enhanced dynamic wedge. Int. J. Radiat. Oncol. Biol. Phys. 40:977–985; 1998.

Volume 25, Number 2, 2000 11. Gibbons, J.P. Calculation of enhanced dynamic wedge factors for symmetric and asymmetric photon fields. Med. Phys. 25:1411– 1418; 1998. 12. Cunningham, J.R.; Shrivastava, P.N.; Wilkinson, J.M. Program IRREG-calculation of dose from irregularly shaped radiation beams. Comp. Prog. Biomed. 2:192; 1972. 13. Miften, M.; Wiesmeyer, M.; Monthofer, S.; et al. Implementation of FFT convolution and multigrid superposition models in the FOCUS RTP system. Phys. Med. Biol. 45:817– 833; 2000.