Journal of BUON 8: 55-59, 2003 2003 Zerbinis Medical Publications. Printed in Greece ORIGINAL ARTICLE Field size and depth dependence of wedge factor for internal wedge of dual energy linear accelerator G. Kemikler Istanbul University, Oncology Institute, Department of Medical Radiophysics, Istanbul, Turkey Summary Purpose: To investigate the field size and depth dependence of wedge factors for internal wedge in the isocentrical setup for 6 and 15 MV photon beams. Materials and methods: Measurements were performed at d max 5, 10, and 15 cm depths for fields 5 5 cm 2 to 20 20 cm 2. The source-isocenter distance (SID was 100 cm. Relative wedge factors (s were calculated to describe the dependence of the wedge factor on the field size and depth. Results: The dependence of wedge factors on field size and depth were less than 2% at 6 MV and 1% at 15 MV X- ray beams for 15 0 and 30 0 wedges. When the field size increased from 5 5 to 20 20 cm 2, the field size dependence increased by 2.7% and 5.2% for 45 0 and 60 0 wedge, respectively, at 6 MV. The dependence on the field size was less than 2.5% for 45 0 and 60 0 wedges at 15 MV. The depth dependence of 60 0 wedge was up to 6.5% for large field size at the depths at 6 MV. For 15 MV beam, s showed only a small change with increasing depth. Conclusion: The magnitude of error in using a single wedge factor was minimal for thin wedges. However, for 6 MV use of a single wedge factor produced errors up to 6% with 60 0 wedge filter. Therefore, in the presence of 45 0 and 60 0 wedges in the beam, a field size and depth dependence wedge factor or a separate output factor (OF curve for wedged beams should be used. Key words: depth dependence, field size dependence, internal wedge, wedge transmission factor, X-ray beam Introduction Received 17-12-2002; Accepted 12-01-2003 Author and address for correspondence: Gönül Kemikler, PhD Istanbul University Oncology Institute Department of Medical Radiophysics 34390, Topkapi Istanbul Turkey Tel: +90 212 5313100 ext: 145-196 Fax: +90 212 5348078 E-mail: gkemikler@ixir.com In external photon beam treatment, beam modifiers including wedges, blocks, or compensators are frequently used to shape the treatment fields and to modify dose distributions in photon fields. Wedge filters have been commonly used in radiation oncology to improve the dose uniformity in the target volume [1]. The wedge shaped isodoses have been achieved by physical wedges, universal motorized wedges, and dynamic wedges. Universal motorized wedge of 60 0 is used for a portion of the treatment to achieve the effective desired wedge angle [2]. When a wedge is present in a photon field, a wedge factor is used conventionally to describe a reduction of the radiation dose in a wedged field compared to the open field, due to the wedge attenuation. Wedge factors are usually measured at a fixed depth along the central axis in a reference field, such as 10 10 cm 2 at 100 cm source-skin distance (SSD. These factors are used directly in dose calculations based on the calibrated dose in the reference open field. However, wedges not only attenuate but also harden the original photon beams. They also produce additional scattered radiation downstream. Therefore, dose in a wedged field is more complicated than a single wedge factor could describe. The reported wedge factor variations with field size are up to 10% [3-5]. Wedge factors are affected by many factors including photon beam energy, wedge material, field geometry and depth. Therefore, measurements of wedge factors for various fields and depths
56 should be done. However, wedge factors for several treatment conditions such as asymmetric fields or different SSDs for a SID technique also may be required. The purpose of this study was to investigate the field size and depth dependence of wedge factors for internal motorized wedge in the isocentrically setup for 6 and 15 MV photon energies. Materials and methods All measurements were performed with 6-15 MV X-ray beams (GE- Saturne 42, General Electric. The Saturne 42 accelerator uses an internal motorized wedge with 60 0 nominal wedge angle. This internal wedge (0 0-60 0 made of tungsten can be positioned by remote control. The wedge angles ranged from 15 0 to 60 0 and were obtained by weighed superposition of the wedged and open beams [2]. Measurements were made in a RWA solid water phantom using a NE 2571, 1007 serial number, 0.6 cc ion chamber with a PTW Unidos electrometer. The reference point for the cylindrical chamber was at the chamber centre. Measurements were performed at d max 5, 10, and 15 cm depths in solid water phantom for field sizes (defined at SID ranging from 5 5 cm 2 to the maximum square field size available for a particular wedge. The maximum-wedged field size was 20 20 cm. Sourcechamber distance (SCD or SID was 100 cm for all measurements. So, phantom SSDs were 85-98.5 cm for 6 MV and 85-97 cm for 15 MV photon beam when the depth of interest in the patient varied from d max to 15 cm for isocentrical treatment. The long axis of the chamber was always along the nonwedged plan. Measurements were made for two collimator orientations (180º apart and determined the average of the two measurements. The calculated wedge transmission factor (WTF was the ratio of the average ionization with the wedge in place to the average open field ionization: Dwdg ( d, fs WTF ( d, fs = (1 Dopen ( d, fs where D wdg and D open are the doses in a wedged field and in open field, respectively. d, and f s are depth and field size, respectively. In this study, s also were calculated to describe the dependence of the wedge factor on the field size and depth. f was defined as a ratio of the WTF at various depths to that under the reference conditions for field size dependence. For a specific wedge, f was calculated as: (, s f( d, fs = WTF d f WTF ( d, f (2 ref sref where reference depth and field size are d ref =5 cm for 6 MV, d ref =10 cm for 15 MV, and f ref =10 10 cm 2. These reference depths have been chosen because daily dose calibrations have been performed at these depths. Relative wedge factors ( d also were calculated to describe the dependence of the wedge factor on the depth. d was defined as: WTF ( d, fs d( d, fs = WTF ( d, f (3 where d is the ratio of the WTF at various depths to that at the depth of maximum dose (1.5 cm and 3 cm for 6 and 15 MV, respectively. The equation (2 can be rewritten as max Dwdg ( d, fs Dwdg ( dref, fsref f( d, fs = / D ( d, f D ( d, f open s open ref sref Dwdg ( d, fs Dopen( d, fs f( d, fs = / D ( d, f D ( d, f s wdg ref sref open ref sref OFwdg ( d, fs f( d, fs = OF ( d, f (4 open This equation (4 shows that f is a ratio of the OF of a wedged field to the relative OF of an open field. For OFs, doses for both open fields and wedged fields were normalized to the dose at the reference depth in the 10 10 cm 2 field size. The dose at the depth of 5 cm and 10 cm in the 10 10 cm 2 field was used as the reference dose at 6 and 15 MV, respectively. Thus, attenuation of the dose with depth is also included by the OF. Results The field size and depth dependence of the internal wedge transmission factors were determined for 6 and 15 MV beams for isocentrical setup. Wedge transmission measurements at 15 0 and 30 0 and relative wedge calculations indicated that the dependence of wedge factors on field size and depth were less than 2% at 6 MV and 1% at 15 MV X-ray beams. Therefore, only 45 0 and 60 0 wedge data are shown. Figures 1 and 2 present the f, which shows the dependence on the field size for 6 and 15 MV X-ray beams. The wedge factors were normalized to the wedge factors at the depth of 5 cm and 10 cm of the 10x10 cm 2 for 6 and 15 MV, respectively. Figure 3 presents a comparison of depth dependence of d for 45 0 and 60 0 for the 6 MV beam. s
57 Figure 1. A comparison of field size dependence of relative wedge factors (f for the 45 0 (A and 60 0 (B wedge for the 6 MV beam. Wedge factors are normalized to that at the depth of 5 cm in the 10 10 cm 2 field. SID=100 cm. Figure 2. A comparison of field size dependence of relative wedge factors (f for the 45 0 (A and 60 0 (B wedge for the 15 MV beam. Wedge factors are normalized to that at the depth of 10 cm in the 10 10 cm 2 field. SID=100 cm. Figure 3. The relative output factors as a function of field size and depth in open and wedged fields for the 45 0 (A and 60 0 (B wedge for the 6 MV beam. Output factors are normalized to that at the depth of 5 cm in the 10 10 cm 2 field. SID=100 cm. Figure 4. The relative output factors as a function of field size and depth in open and wedged fields for the 45 0 (A and 60 0 (B wedge for the 15 MV beam. Output factors are normalized to that at the depth of 10 cm in the 10 10 cm 2 field. SID=100 cm.
58 This Figure shows that the wedge factors increased with depth. For the 15 MV beam, the s showed only a small change with increasing depth (Figure 4. Figures 5 and 6 show the OF in the wedged and open fields at 6 MV and 15 MV beams, respectively. OF wdg increased more significantly with field size than OF open at all depths. Discussion Figure 1 implies that when the field size increases from 5 5 to 20 20 cm 2, the f increases by 2.7% and 5.2% for 45 0 and 60 0 wedge at 6 MV, respectively. This is consistent with the literature data, showing an increase of wedge field with field size [4, 6-9]. Also, Figure 1B shows that the wedge factor increases with field size pre-eminently at the shorter SSD due to the increase of the wedge scatter. The increase of the wedgegenerated dose with SSD can be clinically important particularly for a SID treatment. In general, field size dependence of wedge factors is attributed to the introduction of scattered-photon fluence by the wedge [9]. The number of scattered photons increases with the irradiated wedge volume that increases with the field size. As shown in Figure 2 the dependence of wedge factor on field size is 1% and 2.5% for 45 0 and 60 0 wedge, respectively, at 15 MV for large field at the depth of 15 cm. Figure 3 presents a variation of depth dependence of d for 45 0 and 60 0 for the 6 MV, and shows that the wedge factors increase with depth. McCullough et al. found that these d related to the percent depth doses [3]. In this study, the SID setup was used for the measurements. Therefore, the d related to the tissue-maximum ratio (TMR. The d accounts for TMR differences between those for wedged and open fields. Figure 3 shows that the wedge factors have a linear dependence with depths for 45 0 and 60 0 wedges at 6 MV, respectively. The linear increase in wedge factors with depth arises from beam hardening [8]. The s at a depth greater than 10 cm differs by up to 3% from that measured at d max for 45 0 wedge. The variation for depths greater than 10 cm is up to 6.5% for large field size with 60 0 wedge. This would be an error more than 6% in dose calculation, if the single wedge factor measured at d max is used. These variations are related to TMRs which increase with increasing depth and wedge angle. An increase in beam penetration for wedge fields is expected in view of the beam hardening which results from the much more attenuation of low energy photon Figure 5. A comparison of depth size dependence of relative wedge factors for the 45 0 (A and 60 0 (B wedge for the 15 MV beam. Wedge factors are normalized to that at the depth of 1.5 cm (d max in the 10 10 cm 2 field. Figure 6. A comparison of depth size dependence of relative wedge factors, d for the 45 0 (A and 60 0 (B wedge for the 15 MV beam. Wedge factors are normalized to that at the depth of 3 cm (d max in the 10 10 cm 2 field.
59 beam than the high energy one [8, 10, 11]. Depth dependence of wedge factors has been observed, particularly for the 6 MV photon beam with a large wedge angle and large field sizes. It is generally accepted that the depth dependence of wedge factors is due to beam hardening, especially for low energy megavolt photon beams such as 6 MV [8, 9]. For the 15 MV beam, s show only a small change with increasing depth (Figure 4. The variation with depth is within 1% for both 45 0 and 60 0 wedge. At a high photon energy the wedge scatter becomes more significant, thus the effects of the beam hardening are completely overcome by the wedge scatter. Thus, the variation of the wedge factor with depth at all field sizes is decreased [12]. OF wdg changes more significantly than OF open because s increase with depth. For 45 0 wedge, the OFs for open small field are either equal or larger than that of the wedged field at smaller depth. However, as the depth increases, the OF for wedged field comes bigger than that of the open field. This is especially more obvious for 60º wedged fields, where large variations of output ratios with field size are observed. Figure 5B shows that OF wdg increases more significantly with field size than OF open at all depths except for depths less than 5 cm. This increase is a result of wedge-generated dose [12]. On the other hand, the effect of beam hardening by the wedge can be seen in Figure 5. The beam output changes in the presence of wedge filter is due to changes in fluence of scattered photons reaching the isocenter [4]. At 15 MV the variation of the relative OFs is less than that of the 6 MV (Figure 6. Knöss et al. claimed that at this energy, decreasing beam hardening can be the eventual result after heavy filtration in wedge, and this was often the case for dual-energy machine equipped with one permanent install wedge (60º [11]. Conclusion In this study, field and depth dependence of motorized wedge was examined in 6 MV and 15 MV photon beam for the SID setup. For 6 MV, the dependence of 45 0 wedge on field size and depth was 3% at maximum field size and 15 cm depth, while the dependence of 60 0 wedge on field size and depth was about 5%. This variation of the wedge factor can result in large errors for many of the SID treatments, especially involving obese patients. For 15 MV, field size dependence was between 1% and 2% for 45 0 and 60 0 wedge filters, respectively. At 6 MV, it had the stronger depth dependence because of beam hardening with a large wedge angle and large field sizes. The depth dependence of the wedge factor was related to differences in percent depth dose (PDD or TMR between open and wedged fields in relation to SSD and SID setup. The results have shown that OFs increased more significantly with wedged field size than in the open fields. s have indicated that there are significant differences in PDD (or TMR and OFs between open and wedged fields, especially for 6 MV beam with large field sizes and large wedge. Thus, severe errors could be done in dose calculation if the depth dose data for open field are use for wedged field. It may not be valid to use a single wedge factor in combination with the open beam OF for dose calculation. The magnitude of error in using single wedge factor measured at reference depth for a 10x10 cm field is minimal for thin wedges. Nevertheless, for 6 MV X-rays the use of a single wedge factor introduces error of up to 6% with 60 0 wedge filter. Therefore, in the presence of a 45º and 60º wedge filters in the beam, a field size and depth dependence wedge factor or a separate OF curve for wedged beams should be used for treatment planning, especially at 6 MV photon beams. References 1. Bentel EG, Nelson CE, Noell KT (eds. Treatment planning and dose calculation in Radiation Oncology. Pergamon Press, 1989. 2. Tatcher M. A method for varying effective angle of wedge filters. Radiology 1970; 97: 132. 3. McCullough EC, Gortney J, Blackwell CR. A depth dependence determination of the wedge transmission factor for 4-10 MV photon beams. Med Phys 1988; 15: 621-623. 4. Palta JR, Daftari I, Suntharalingam N. Field size dependence of wedge factors. Med Phys 1988; 15: 624-626. 5. Thomas SL. The variation of wedge factors with field size on a linear accelerator. Br J Radiol 1990; 63: 355-356. 6. Georg D, Garibaldi C, Dutreix A. Measurements of basic parameters in wedged high- energy photon beams using a miniphantom. Phys Med Biol 1997; 42: 1821-1831. 7. Niroomand-Rad A, Haleem M, Rodgers J, Obcemea C. Wedge factor dependence on depth and field size for various beam energies using symmetric and half-collimated asymmetric jaw settings. Med Phys 1992; 19: 1445-1450. 8. Popescu A, Lai K, Singer K, Phillips M. Wedge factor dependence with depth, field size, and nominal distance. A general computational rule. Med Phys 1999; 26: 541-549. 9. Tailor RC, Followill S, Hanson WF. A first order approximation of field- size and depth dependence on wedge transmission. Med Phys 1998; 25: 241-244. 10. Kalend AM, Wu A, Yoder V, Maitz A. Separation of dosegradient effect from beam-hardening effect on wedge factors in photon fields. Med Phys 1990; 1: 701-704. 11. Knöss T, Wittgren L. Which depth dose data should be used for dose planning when wedge filters are used to modify the photon beams? Phys Med Biol 1991; 36: 255-267. 12. Liu HH, Mackie TR, McCullough EC. Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method. Med Phys 1997; 24: 1714-1728..