Abstract. The results of an investigation of the accuracy of monitor unit (MU) calculation in clinical shaped beams are presented. Measured doses at the ...
T he British Journal of Radiology, 70 (1997 ), 638–644 © 1997 The British Institute of Radiology
Short communication
Monitor unit calculation in 6 MV irregularly shaped beams—accuracy in clinical practice P LOMBARDI, C FIORINO, G M CATTANEO and R CALANDRINO Servizio di Fisica Sanitaria, H S Raffaele, Via Olgettina 60, 20132 Milano, Italy Abstract. The results of an investigation of the accuracy of monitor unit (MU) calculation in clinical shaped beams are presented. Measured doses at the reference depth on the beam central axis (isocentre) or on a beam axis representative of the irradiated area (when the isocentre lies under a block or near the edges of the block’s shadow) were compared with the expected doses when calculating MUs, by applying dierent methods normally used in clinical practice. Empirical (areas weighted, Wrede) and scatter summation (Clarkson) methods as well as a pencil-beam based algorithm were applied. 40 irregular fields (6 MV X-rays, CLinac, Varian 6/100), divided into six categories, were considered. Dose measurements were performed with a NE2571 ionization chamber in an acrylic 30×30×30 cm3 phantom. The depths in acrylic were converted into waterequivalent depths through a correction factor derived from TMR measurements. The method of dose measurements in acrylic was found to be suciently accurate for the purpose of this study by comparing expected and measured doses in open square and rectangular fields (mean deviation +0.2%, SD=0.5%). Results show that all the considered methods are suciently reliable in calculating MUs in clinical situations. Mean deviations between measured and expected dose values are around 0 for all the methods; standard deviations range from 1% for the Wrede method to 0.75% for the pencil-beam method. The dierences between expected and measured doses were within 1% for about 3/4 of the fields when calculating MUs with all the considered methods. Maximum deviations range from 1.6% (pencil-beam) to 3% (Wrede). Slight dierences among the methods of MU calculation were revealed within the dierent categories of blocked fields analysed. The surprising agreement between measured and expected dose values obtained by using empirical methods (area weighted and Wrede) is probably due to the fact that the reference points were positioned in a ‘‘central’’ region of the unblocked areas.
Introduction The need for high accuracy in the calculation of dose distributions in external radiotherapy is an important prerequisite for the successful treatment of cancer. Monitor unit (MU) calculation is a very important step, MUs being related to the dose delivered at a certain reference point within the patient (the International Commission on Radiological Units and Measurements (ICRU ) reference point [1 ]). Great care has to be given to the procedures of calculating MUs, which must also take into account the presence of beam modifiers interposed between the source and the patient. For this reason and to avoid systematic errors, many centres perform the MU calculation manually with independent check protocols as a vital part of quality assurance programmes [2 ]. The problem of correctly assessing the influence of scattered radiation on the dose distribution Received 13 September 1996 and in revised form 31 January 1997, accepted 10 February 1997. Address correspondence to C Fiorino. 638
delivered in the presence of shaping blocks has been widely investigated. Several methods have been developed and are routinely applied [ 3–11 ]. However, little experimental work on the accuracy of these methods when calculating MUs in clinical conditions have been reported. Moreover, the wide use of computer calculation could be dangerous if some preventive tests on the reliability of the algorithms implemented on the treatment planning system (TPS) are not performed. So, the verification of accuracy in the calculation of MUs in irregularly shaped ‘‘clinical’’ beams is suggested within a protocol of quality assurance (QA) of TPS [12 ]. In this paper, the results of an investigation of the accuracy of some of the methods generally used when calculating MUs in blocked 6 MV X-ray beams are presented. Measured doses in the reference point (in isocentric geometry) in an acrylic phantom were compared with expected doses when calculating MUs by applying dierent methods: empirical (equivalent field based), analytic (a home-made simplified version of the Clarkson–Cunningham T he British Journal of Radiology, June 1997
Short communication: Monitor unit calculation in 6 MV irregular fields
method [3, 4 ]) as well as pencil-beam based [13] (implemented on our treatment planning system, Cadplan 3D Varian-Dosetek Oy) methods were considered. An acrylic phantom was preferred to water phantom to simplify the set-up procedures. 40 ‘‘clinical’’ blocked fields were considered and divided into six categories (‘‘large’’ lateral neck fields, ‘‘boosts’’ lateral neck fields, suvraclavicular anteroposterior fields, lung anteroposterior fields, mantle fields, large pelvic-abdominal fields). The accuracy of the measurements was verified to be within 1% (2 SD) by comparing expected vs measured doses in open square and rectangular fields (after correcting the depths in acrylic into water equivalent depths).
to W ×Y . S and S had been previously measured c p in agreement with the methods proposed by Van Gasteren et al [16 ]. If the isocentre lies under or near the edge of a block, following the ICRU formalism, a reference o-axis point on the same plane (at 100 cm from the source) has to be chosen as representative of the dose within the irradiated area. In this case we can again apply Formula (1 ) by correcting the denominator with an o-axis ratio measured or interpolated from water phantom measurements (‘‘o-axis ratio correction’’). In this investigation, we considered four dierent methods for calculating MUs in irregular fields.
(A) Empirical areas weighted method
Materials and methods MU calculation: algorithms When calculating MUs to deliver an arbitrary dose at the isocentre (source-to-axis distance (SAD), equal to 100 cm) we apply a well known formula, based on a fixed source-to-skin distance (SSD) output calibration set-up. If the output of the accelerator is calibrated to deliver 1 Gy 100 MU−1 at d (1.5 cm for our 6 MV beam) for max a 10×10 cm2 field when SSD=100 cm, the MUs to deliver 1 Gy at the isocentre (MU(100)) in a W ×Y field (at the SAD) with a certain SSD and at depth p, can be calculated from the following formula [14]: MU(100 )=100/[S (Z)×S (W ×Y )×F ×F p c t w ×PDD(100, Z, p)×I2×(1+F)/2 ] (1 )
where: Z=2[W ×Y /(W +Y )]×(SSD/SAD) is the equivalent square beam of the W ×Y field at the phantom surface, given by Sterling’s formula [ 15]; S (Z) is the phantom scatter factor for the field Z p (field dimension at the SSD and referred to d ); max S (W ×Y ) is the collimator scatter factor, defined c by the collimator setting; F and F are, respectt w ively, the tray and the wedge factors; PDD(100, Z, p) is the measured percentage depth dose at a depth p with an SSD=100 cm in a square field with a beam width equal to Z at the phantom surface; I2 is the inverse square correction factor ([(100+d )/(SSD+d )]2 ) and F is the max max Mayneord factor: (1+F )/2 is the term which converts the PDD from SSD=100 to another SSD [ 14]. In the case of an irregular field, one could take into account the modification of scattering due to the presence of the blocks through the estimation of an equivalent field size L (at the SSD). In this familiar approach one can calculate MUs for a blocked field by applying Formula (1 ) and considering PDD and S referred to L and S referred p c T he British Journal of Radiology, June 1997
In this empirical approach the unblocked area A of the beam is considered to be composed of a ‘‘central’’ area A1 around the reference point (approximately describing the major scattering contribution) and of smaller areas all around A1 (A2, A3…). The equivalent field size L is assumed to be the mean value between the square root of A and the square root of the ratio between the quadratic sum of A and A. All dimensions must be intended at i the SSD. The assessment of the areas is carried out manually by the physicist on the simulation films.
(B) Area-to-perimeter ratio or Wrede method [6] L is calculated from the ratio 4A/P where P r r is the perimeter of the unblocked area at the SSD.
(C ) Simplified Clarkson scatter summation method 12 radii are drawn from the reference point to the edges of the unblocked area (at the SAD) to divide it into elementary sectors. The lengths of these radii are measured on the simulation film and reported at the isocentre level (by demagnification). Then, the mean value of the scatter maximum ratios (SMRs) corresponding to the length of the radii (corrected to take into account the fact that we use square fields data instead of circular fields data) is calculated (SMR ). To maintain the m formalism of Formula (1 ), an equivalent field size L is assessed from the square field (at the SAD) having the value of SMR nearest to SMR and m deriving the corresponding value of L at the SSD (by the correction factor SSD/SAD). The method has been implemented on a PC and only requires the introduction of the measured radii on the simulation film. The method does not 639
P L ombardi, C Fiorino, G M Cattaneo and R Calandrino
consider scatter contributions from open areas which are beyond blocks when they are seen from the reference point. This could lead to underestimation of dose for mantle fields. However, because of the central position of the reference point (i.e. the central beam axis), this underestimate is expected to be almost insignificant.
(D) Pencil-beam method (Cadplan) The algorithm calculates the dose distribution before deriving the PDD referred to an axis representative of the ‘‘maximum scatter’’ region of the blocked field. The incident irregularly shaped beam fluence is convolved with a ‘‘scatter’’ kernel. Oaxis values are calculated by convolving the incident fluence with a ‘‘boundary’’ kernel, taking into account the influence of the blocks in three dimensions. Both ‘‘scatter’’ and ‘‘boundary’’ kernels are derived directly by the treatment planning system from measured input data (PDD and dose profiles of open fields). As this convolution is performed only at some depths, calculation times are dramatically reduced. For more information the reader could refer to the paper of Storchi and Woudstra [ 13]. Methods A and B are empirical and do not take into account accurately the position of the reference point with respect to the position of the blocks, assessing an equivalent field size value just through geometrical measurements and estimating the dose in the ‘‘central’’ part of the unshielded area. They are expected to give acceptable results only if the reference point is positioned in the ‘‘central’’ region of the irradiated area. These methods are generally used to calculate MUs for fields delivered with palliative intent. They do not require particular procedures to be implemented, being necessary to calculate equivalent field sizes for each beam manually. Methods C and D also take into account the position of the reference point with respect to the position of the blocks. Method C can be easily implemented on a PC in few days, once the appropriate dosimetric data are available. Method D is automatically implemented in the Cadplan program, being the pencil-beam kernels calculated directly from measured data. Regarding methods A, B and C, MUs were calculated manually by applying Formula (1) (and possible ‘‘o-axis-ratio correction’’), once having assessed the equivalent field size value L (at the SSD). When applying method D, MU calculation is performed directly by the computer after having renormalized the calculated dose distribution to the dose in the reference point (at which the chamber measurement is referred ). 640
Methods of measurements To investigate the accuracy of the methods in realistic conditions, a number of irregular clinical 6 MV beams were considered. Expected doses at the reference point when calculating MU(100) with the four considered methods were compared with the corresponding measured doses (with an irradiation time equal to 100 MUs). Doses were measured in an acrylic 30×30×30 cm3 phantom at the corresponding water-equivalent depth with an NE2571 cylindrical ionization chamber (connected to an electrometer IONEX NE2534). The chamber was always positioned with its eective measurement point at 100 cm from the source. The reference point was coincident with the isocentre for most fields. For a few fields the reference point was not positioned on the beam axis, but in a central point with respect to the irradiated area (e.g. in the case of shaped beams with a central block). In any case, the measurement point was relatively distant from the nearest edge of the blocks (at least 2 cm, projected at the SAD). At each set of measurements the calibration of the output of the accelerator was checked and measured doses were corrected to take into account daily variations of the output (i.e. the dose measured at d with SSD=100 cm in a 10×10 cm2 max beam with an irradiation time equal to 100 MUs). This procedure was necessary to compare measured doses with the corresponding expected doses (1/MU(100)). An acrylic phantom was preferred to a water phantom to minimize the set-up time. The factor which translates the depths in acrylic to depths in water was carefully assessed by comparing tissue maximum ratio (TMR) values in acrylic with TMR values previously measured in water ( by a computerized water phantom (Cadscan VarianDosetek) in a 10×10 cm2 field. This factor was found to vary with the depth, but it can be considered practically constant (1.21±0.010) for the clinically relevant range of depths (3–10 cm of acrylic) considered in this investigation. To estimate the accuracy of the method, we compared estimated and measured doses with an irradiation time equal to 100 MUs for a number of rectangular/square fields (from 5×5 to 20×20) and depths (3–10 cm in acrylic). A mean deviation (on 15 measurements) equal to +0.2% [(expected−measured)/measured] with a standard deviation equal to 0.5% were found. Maximum deviations were −0.5 and +1.0%. These values are indicative of the overall accuracy of the method. Other causes of inaccuracy are (1) the intrinsic approximations of Formula (1); (2 ) the interpolation of PDD, S and S data (which are not p c measured for all field sizes); and (3) assessment of T he British Journal of Radiology, June 1997
Short communication: Monitor unit calculation in 6 MV irregular fields
the equivalent square field of a rectangular field through Sterling’s formula.
Clinical shaped beams The irregularly shaped beams considered in this investigation are a significant sample of typical isocentric irregular beams encountered in clinical practice. They were divided into the following categories: (a) Lateral ‘‘large’’ neck fields (n=9): including the whole neck with shielding of some critical structures such as skull base, mandibula and eyes. ( b) Lateral ‘‘small’’ neck fields (n=4): boosts to the tumour with sparing of spinal cord and/or brain stem. (c) Supraclavicular hemiblocked anteroposterior fields (n=5): including supraclavicular nodes with sparing of lung apex with or without a central block. (d) Anteroposterior lung-mediastinum fields (n= 10 ): variable shape depending on the location of the tumour. (e) ‘‘Mantle’’ fields for Hodgkin’s disease treatment (n=3). (f ) Anteroposterior pelvic fields: large fields for pelvic disease treatment (n=5). On assessment four further fields could not be included in these categories and were considered separately. These were: (g) A lateral brain boost field with a large shielded area. ( h) A large lateral whole brain field of a craniospinal treatment. (i) A large antero-posterior beam for lombo-aortic nodes irradiation. ( l) A brain lateral field. For each field the ‘‘true’’ depth at which the isocentre was located within the patient was set (range 3–12 cm). The mean degree of blocking (i.e. percentage of the area blocked against total area) of the first six categories was as follows: (a) 10–20%; (b) 20–50%; (c) around 60%; (d) 10–30%; (e) around 25–30%; (f ) from 5–15%. No wedged beams have been considered.
Results and discussion In Table 1 a summary of the data obtained is given. Mean and maximum percentage dierences between expected and measured doses, as well as the standard deviations, were calculated for the T he British Journal of Radiology, June 1997
four considered methods. In each case the number of fields analysed is also specified. The overall mean values of the deviations between expected and measured doses are: 0.01%, 0.08%, −0.05%, −0.02%, for the area weighed, the Wrede, the PC based Clarkson and the pencilbeam methods, respectively. The corresponding percentage overall global standard deviations are 0.86, 0.99, 0.83, 0.75, respectively. None of the methods applied is significantly better than any other, even if the pencilbeam algorithm gives the best performance. In Figure 1 the results are visualized by means of four graphs, one for each method, reporting the number of fields versus the percentage deviation between expected and measured dose values. Figure 2 shows the percentage of fields showing a dierence between expected and measured dose within a certain percentage value, reported on x axes. A further analysis of the results was carried out using the data obtained within the dierent categories of shaped fields. The only important dierence ( p
