A simple theoretical verification of monitor unit calculation for intensity modulated beams using dynamic mini-multileaf collimation

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1 Radiotherapy and Oncology 71 (2004) Technical Note A simple theoretical verification of monitor unit calculation for intensity modulated beams using dynamic mini-multileaf collimation Nadine Linthout*, Dirk Verellen, Swana Van Acker, Guy Storme Department of Radiotherapy, Oncology Center, Academic Hospital Free University Brussels (AZ-VUB), Laarbeeklaan 101, B-1090 Brussels, Belgium Received 31 October 2002; received in revised form 4 November 2003; accepted 26 February Abstract A spreadsheet based program is presented to perform an independent Monitor Unit (MU) calculation verification for the Quality Assurance (QA) of Intensity Modulated Radiation Therapy (IMRT) using Dynamic MultiLeaf Collimation (DMLC). The computed dose value is compared to the planned dose by calculating the percent dose difference per Intensity Modulated Beam (IMB) and absolute dose difference per IMB. The proposed acceptability levels are ^5.0% or ^2.0 cgy for the percent dose difference per IMB and the absolute dose difference per IMB, respectively. For percent dose difference per treatment, an acceptability level of ^2.0% is proposed. The presented program is considered adequate for checking the treatment plans calculated for IMRT treatments using DMLC as a part of the QA procedure. q 2004 Elsevier Ireland Ltd. All rights reserved. Keywords: Monitor unit calculation; Dynamic multileaf collimation; Beam intensity modulation; Quality assurance 1. Introduction Intensity Modulated Radiation Therapy (IMRT) has proven advantages over Conformal Radiation Therapy (CRT) for several clinical cases [1,5,7,8,13,19,21]. The application of IMRT compared to CRT, could improve the target dose uniformity and reduce the dose delivered to the radiosensitive organs close to the target [4,20]. The different possible techniques that have been developed by now to achieve IMRT are grouped together and described by Webb [23]. One of those techniques has received recently increased attention in development and clinical implementation. The technique is Dynamic Multi- Leaf Collimation (DMLC) and uses a MultiLeaf Collimator (MLC) of which the leaves move continuously across the treatment field during irradiation to create the Intensity Modulated Beam (IMB). It is recognized that this technique requires more stringent Quality Assurance (QA) since it is a much more complicated form of treatment compared to conventional treatments. Not only the MLC but also the Treatment Planning System (TPS) must meet more stringent requirements for the delivery of IMRT treatments. If the calculated IMB is accurately converted by the leaf sequencing algorithm incorporated in the TPS into a * Corresponding author. collimation scheme deliverable by the MLC, this collimation scheme will result in the correct intensity modulated treatment field for both geometry and absolute dose. The absolute dose given by an IMB using DMLC is influenced by an important factor being the amount of Monitor Units (MU) that is used to deliver the IMB. The MU verification can, amongst others, be used to check the accuracy of a treatment planning system s dose calculation algorithm for a single point in a target volume. The most accurate yet cumbersome approach is absolute dose measurement. Because an independent MU calculation can in some cases be used as an alternative for these absolute dose measurements, it is considered an important asset in the QA procedure as it can reduce the workload. In CRT, the amount of MU that a treatment field requires can be estimated relatively easy, but in IMRT using DMLC it is very hard to intuitively estimate or evaluate the MUs needed to deliver the IMB. Some previous studies have performed MU calculation verification for DMLC IMRT [3,11] based on programs that require programming skills and specific software to be able to implement the described algorithm. Although meanwhile there is already software commercially available to perform an independent MU calculation verification in IMRT treatments, this work presents an /$ - see front matter q 2004 Elsevier Ireland Ltd. All rights reserved. doi: /j.radonc

2 236 N. Linthout et al. / Radiotherapy and Oncology 71 (2004) in-house developed program using basic formulae and spreadsheet based software to perform a fast and relatively accurate MU calculation verification for IMRT using DMLC. The presented approach to verify the MU calculation is simple and easy to implement in a department. MLC transmission and scattering are taken into account by the program as well as radiation field offset of the segments of the IMB. The original measured beam data are used together with a minimum of output parameters of the treatment plan to recalculate the dose in the normalization point with a calculation algorithm independent from the one used by the TPS. 2. Methods and materials The system that is used in our department to deliver IMRT treatments is the Novalis w system: a single energy (6 MV-photon) linear accelerator (linac) with an integrated mini-multileaf Collimator (mmlc), dedicated for stereotactic radiosurgery. The system offers next to conformal beam and dynamic field shaping rotation therapy [12] also IMRT capable of using Static MultiLeaf Collimation (SMLC) as well as DMLC. The mmlc M3 w is described in detail by Cosgrove et al. and Xia et al. [6,24]. The linac is capable of generating a variable dose rate up to 800 cgy per minute (calibrated to deliver 1 cgy/mu at depth of maximum dose in fixed SSD configuration). The latter aspect, combined with the zero delay time before the beam is on, makes the machine very suitable to perform IMRT. BrainSCAN w is the Treatment Planning System (TPS) that is combined with the Novalis w system. The software (BrainSCAN w v5.1: BrainLAB AG, Heimstetten, Germany) offers an inverse planning modality for IMRT [22]. In the inverse planning, four plans are optimized with different organ at risk priorities using a Dynamically Penalized Likelihood algorithm [15]. During the optimization the transmission calculation is handled by integrating a quick leaf sequencing from the start of the optimization. The leaf sequencing is based on the theory of Bortfeld et al. [2]. When the inverse planning is finished, the actual leaf sequencing is performed in three parts: the calculation of the leaf movements to deliver the fluence (i.e. the number of segments and the step size), the tongue-and-groove optimization and the transmission calculation. The produced fluence maps are used in the forward calculation of the dose distribution based on the Pencil Beam dose calculation algorithm developed by Mohan et al. [16 18]. One of the four calculated plans can be chosen or the calculation parameters and planning constraints can be changed to achieve the required dose distribution. When one of the four plans is selected for which the MU calculations will be verified, the reference point (normalization point) was defined in accordance with the International Commission on Radiation Units and Measurements (ICRU) 50 report [9] recommendations. In the cases that are verified in this study the normalization point was placed at the isocenter. For each single treatment beam, the relative and absolute dose delivered in the normalization point is calculated by the TPS using the corresponding amount of MU and the calculated segments of the IMB. To verify this MU calculation, a simple spreadsheetbased program is developed. A minimum number of parameters are used from the plan to recalculate the dose predicted by the TPS in the normalization point for each IMB, hereafter called D IMB (TPS). Each segment of a DMLC IMB, defined by the leaf-sequencing algorithm of the TPS, is considered as a uniform intensity beam to calculate the dose delivered by that IMB in the normalization point. This computed dose value will be referred to as D IMB (verif). The variation of the tissue contour of the patient within the treatment fields is neglected in the program and the patient is assumed to be homogeneous and water equivalent. The three parameters that need to be imported in the program from the treatment plan are the MUs for the IMB, the beam shape file of the IMB, and the depth to the normalization point. The MUs for each IMB are copied from the printout of the treatment parameters. The beam shape file includes the shape (determined by the positions of all mmlc leaves) and the relative weight of all segments of that IMB calculated by the TPS. The beam shape file can be exported from the TPS for each IMB used in the treatment plan. The depth to the normalization point for the IMB is defined manually on the TPS because it is not included in the output parameters of the treatment plan. The equivalent depth defined by the TPS is not used in the spreadsheet program because the patient is assumed to be water equivalent. The parameters used in the program that are not imported from the treatment plan are the Tissue Maximum Ratio (TMR) data, the total scatter factors (S c,p ) and the Off Axis Ratios (OAR). These parameters are taken from the original measured beam data. The equivalent square field that corresponds with each segment is calculated with the Sterling formula using the contour of each segment defined by the leaf settings of that segment to calculate the area and the perimeter of that segment. The equivalent square field size is used together with the depth to the normalization point to find the correct TMR value for each segment of the IMB. The corresponding S c,p is determined for the equivalent square field size formed by the leaves of the mmlc. Since all the IMBs are delivered with the jaws positioned at 4.90 cm, the interpolation for the S c,p is only performed between different fields sizes formed by the leaves and for a fixed field size of cm 2 formed by the jaws. To determine the OAR corresponding with every segment, the coordinates of the

3 N. Linthout et al. / Radiotherapy and Oncology 71 (2004) gravitation point of every segment are calculated using Eqs (1) and (2): x g ¼ y g ¼ xydx ydx 1 2 y 2 dx ydx Based on these coordinates, the radial distance between the gravitation point of the segment and the normalization point is determined. This diagonal radius and the depth to the normalization point allow one to define the OAR that corresponds with every segment based on the original measured beam data. The total amount of MUs of the IMB is distributed over the segments of the IMB. Therefore, the relative weight of every segment ðw i Þ is calculated by subtracting the indices from the successive segments in the exported beam shape file. There is no threshold value defined to eliminate segments with a low relative weight, every segment of the IMB is taken in consideration. The contribution of each segment (con i ) to the dose delivered in the normalization point is defined by determination of the degree to which the segment covers the normalization point. If the normalization point is located within and at least 0.50 cm from the borders of the segment, the contribution of the dose delivered by that segment to the normalization point dose is considered maximal (con i ¼ 1). For the segments where the normalization point is blocked by the mmlc leaves by at least 0.50 cm in both the inplane and crossplane direction, only the mmlc transmission dose to the normalization point dose is taken into account (con i ¼ 0.02). When the normalization point is positioned between the two previous margins (^0.50 cm), the contribution of that segment to the normalization point dose is calculated by linear interpolation depending on the position of the normalization point with respect to the mmlc leaves. This interpolation interval covers the penumbra as well as the shoulder and the heel of the field border. By multiplying the relative weight and the contribution with the total amount of MUs of the IMB, the MUs of the IMB are distributed over all segments: MU i ¼ MU IMB ðtpsþ w i con i ð3þ with MU IMB (TPS) representing the total amount of MUs calculated by the TPS for that IMB, MU i the MUs for segment i that contribute to the dose delivered in the normalization point, w i the relative weight of segment i and con i the contribution of the dose delivered by segment i to the normalization point dose. ð1þ ð2þ The dose that every segment delivers to the normalization point is calculated with the formula: D i ¼ MU i TMR i S c;pi OAR i ð4þ CF SAD where D i is the dose delivered by segment i; MU i, the MUs for segment i; TMR i, the tissue maximum ratio for segment i corresponding with the depth and the field size of segment i; S c,pi the total scatter factor for segment i corresponding with the field size of segment i; OAR i the off axis ratio for segment i based on the position of the gravitation point of segment i and CF SAD the conversion factor for isocentric treatments since the linac is calibrated to deliver 1 cgy/mu at depth of maximum dose with a fixed SSD geometry that is calculated with Eq. (5). CF SAD ¼ððSSD norm þ d norm Þ=SIDÞ 2 with SSD norm representing the source surface distance used for dose monitor calibration of the linac performed at a defined depth d norm and SID the source isocenter distance. The dose delivered by that IMB in the normalization point is calculated by summing the doses of all segments of the IMB together: D IMB ðverifþ ¼ X D i ð6þ i The calculated doses D IMB (verif) are compared with the predicted doses by the BrainSCAN software D IMB (TPS). The relative difference is reported as percent dose differences per IMB and is computed using: %diff ¼ ðd IMBðverifÞ 2 D IMB ðtpsþþ 100 ð7þ D IMB ðtpsþ The absolute difference between the two doses per IMB is also defined: diffðcgyþ ¼D IMB ðtpsþ 2 D IMB ðverifþ 3. Results In order to test the program, 166 IMBs have been generated by the BrainSCAN w TPS and have been verified with the spreadsheet program. The IMRT plans that are used for this study included 11 prostate cases, 9 brain and 6 head and neck cases and three imaginary targets defined in a homogeneous phantom to cover different degrees of treatment complexities. The average number of IMBs of the 29 verified treatment plans was 5.5 with a standard deviation (SD) of 1.1 (range 4 9). The delivered dose per treatment had a mean value of cgy with a SD of 73.8 cgy (range cgy). The average amount of ð5þ ð8þ

4 238 N. Linthout et al. / Radiotherapy and Oncology 71 (2004) Fig. 1. The frequency of the discrepancies between the planned doses and the dose values computed with the spreadsheet-based program expressed in percent dose differences per DMLC IMB. The curve is the normal distribution curve fitted to the resulting frequencies. MUs per treatment was 825 MU with a SD of 376 MU (range MU). In Fig. 1, the frequency is displayed of the percent dose differences per IMB calculated with Eq. (7). The mean percent difference per IMB was 21.1% with a SD of 6.5% (range þ 20.7%). The percent differences between the total dose calculated by the TPS in the normalization point per treatment and the total dose value computed by the spreadsheet program for the same treatment are also calculated. The mean percent dose difference per treatment was 20.6% with a SD of 2.9% (range 25.2 þ 5.6%). The frequency of the absolute dose differences per IMB calculated with Eq. (8) is shown in Fig. 2. The mean absolute dose difference was 20.2 cgy with a SD of 2.0 cgy (range þ 7.5 cgy). 4. Discussion and conclusion All used IMBs are typically composed of 29 segments, corresponding with the root-mean-square (RMS) error that is set to 1.0 in the treatment plan optimization parameters. All segments are imported at the same time in the program when the beam shape file is imported. Therefore, the number of segments of the IMB does not influence the workload of using the program. The spread of the percent dose differences per IMB was rather wide due to a not completely optimized program to calculate the dose values. Some of the imperfections of the program can be found in: (a) the linear approximation of the shape of the field border of the treatment beam, (b) the scatter in the patient that is not taken into account because a homogeneous patient is assumed, (c) no changes in the outer contour of the patient are taken into account, (d) borderline situations where the normalization point is blocked by the majority of the segments of the IMB, may not be fully covered. (a) The change of the penumbra with the field size and the position of the field border, which is less than 0.02 cm for the Novalis w system, is not taken into account with the linear approximation of the shape of the field border. The interpolation is always performed between a contribution of 1 and 0.02 for a leaf position ranging from 0.50 cm (open field) to cm (overtravel). The relative leaf position of ^ 0.50 cm with respect to the position of the normalization point is chosen as interpolation margin because the penumbra (lateral distance between the 80% and the 20% isodose line) of the largest possible treatment field of the Novalis w system ( cm 2 ) is 0.43 cm while the smallest treatment field ( cm 2 ) has a penumbra of 0.41 cm. The penumbra as well as the shoulder and the heel of the field border are covered in the linear interpolation range. The calculated dose to the normalization point can be underestimated due to the linear approximation of the field border compared to the planned dose if the normalization point is located between the 50 and 100% isodose line of the treatment field. Similar, if the normalization point is located between the 0.02 and the 50% isodose line of the treatment field the dose to the normalization point is overestimated by the program.

5 N. Linthout et al. / Radiotherapy and Oncology 71 (2004) Fig. 2. The frequency of the discrepancies between the planned doses and the dose values computed with the spreadsheet-based program expressed in absolute dose differences per DMLC IMB. The curve is the normal distribution curve fitted to the resulting frequencies. (b) Deviations between planned and computed dose values can be introduced due to the assumed homogeneous patient when large changes in electron density appeared in the area traversed by the IMB. While air cavities will cause the computed dose value to underestimate the actual or planned dose [14], bony structures will introduce the opposite effect. If a large negative difference is observed during the verification of the dose and a large air cavity is traversed by the treatment beam before the normalization point is reached, one can recalculate the dose value with the equivalent depth to evaluate the observed difference. Similar, a large positive difference could be observed when a lot of bony structures appear in the pathway of the treatment beam before the normalization point, if the equivalent depth is used for the calculation of the dose value instead of the manually measured depth. An observed difference for the verification of the calculated dose of an IMB can of course also be evaluated based on the absolute dose measurement of that IMB. (c) The changes in the outer contour of the patient within the geometrical limits of the IMB can cause the actual distance between the central entrance point of a segment and the normalization point to differ from the measured depth to the normalization point. The TMR, S c,p and OAR values for that segment will be altered by the difference in depth. (d) Borderline situations are found in IMBs where very little segments contribute to the dose in the normalization point. For instance, in the IMB for which the percent dose difference amounts to 224.8% the normalization point is covered partially by only 2 out of 29 segments. Large percent dose differences can be introduced by this fact in combination with the linear approximation of the penumbra shape. The spreadsheet program is not optimized to account for these borderline situations in order to keep the program simple because it is only used for double-checking the calculated plan. If the percent dose difference of an IMB is extremely high or low, a closer look has to be taken at the separate segments of the IMB to verify if their shape can cause the large discrepancy between the doses. If the latter is not the case, a deviation might be found in one of the other treatment parameters in either the value used by the TPS or the value imported in the spreadsheet program. Due to these limitations of the presented program, an accuracy of ^ 5.0% is found acceptable for the calculated percent dose difference per IMB. At the moment there is no general protocol established that defines the required accuracy for the 3-dimensional computer planning of IMRT treatments. This protocol would refer to the agreement between the calculated and the measured dose in a point under the same irradiation conditions. Therefore an accuracy of ^5.0% is proposed as accuracy level of the for the percent dose difference per IMB. Because the spread of the percent dose differences per IMB was considered wide, the percent dose difference per treatment was also calculated to allow an evaluation of the entire treatment plan. These results had a much smaller spread. In the ICRU 42 report [10] a relative accuracy of 2.0% is prescribed for the dose calculated by the TPS. In this report is not referred to IMRT treatments but the same accuracy level can be used as an acceptability level for the percent dose difference per treatment calculated with the presented program since it refers to a dose difference

6 240 N. Linthout et al. / Radiotherapy and Oncology 71 (2004) resulting from an entire treatment plan. This acceptability level of ^ 2.0% should provide a reasonable guarantee that the treatment preparation of the IMRT treatment is performed within the uncertainties of all involved parameters. Nevertheless, the verification of the MU calculation of the IMBs separately is necessary to give supplementary information about the treatment compared to the verification of the MU calculation for the entire treatment plan because the latter can obscure large deviations in the verification of the IMBs separately that need to be looked at in detail. During commissioning of IMRT with the Novalis w system, the agreement between the dose to a point calculated by the TPS and the absolute measured dose in that point was found within 2.0% in a waterphantom, as recommended by the ICRU42 report [10]. During the pretreatment verification of a patient treatment the delivered dose of the entire treatment plan is verified absolutely and the fluence patterns of all IMBs of the treatment plan are verified. The results of these verifications are beyond the scope of this study and not reported here. The agreement between D IMB (verif) and the actual dose delivered by a single IMB was not verified for all IMBs in this study, but for all IMBs the computed dose values and planned doses are compared absolutely. The comparison of the absolute doses has given another, sometimes more relevant, appreciation of the differences between the doses. Especially when the planned dose for a certain IMB is very small, e.g. 5.0 cgy, a deviation of 0.4 cgy (mean absolute dose difference) results in a percent dose difference of 8.0%, what exceeds the proposed accuracy level of ^ 5.0%. For the absolute dose verification an accuracy of ^ 2.0 cgy is proposed as acceptability level, that takes the uncertainties of the involved parameters into account. If the example of the IMB with a percent dose difference of % is reviewed, the absolute dose difference for this IMB amounts to 21.5 cgy what is within the accuracy of the absolute dose verification. When the percent dose difference per IMB exceeds the acceptability level but the absolute dose difference per IMB does not, the comparison of the absolute doses eliminates a further evaluation of the IMB segments. Therefore the absolute dose verification is considered a complementary tool in the MU calculation verification program. For IMBs, where neither of the acceptability criteria were fulfilled (what happened in about 10% of the verified IMBs) a further investigation of the dose delivered by that IMB was required. Performing an absolute dose measurement for these IMBs covered the latter. The discrepancies in the outcome of the program have proved that a MU calculation verification can certainly not be used as the only verification that is performed for IMRT treatments. A program like the presented one could be used to reduce the workload of IMRT treatment verification because it is not longer required to verify all IMBs by absolute dose measurement. The proposed accuracy levels for both percent dose and absolute dose differences per IMB are found stringent enough to indicate important errors in the treatment plan. For instance, if another beam data file is used for the calculations of the IMRT plan, all the IMBs used in that plan will result in a percent dose and an absolute dose difference per IMB that exceeds the proposed accuracy levels. Any possible uncertainty embedded by the recalculation of the measured TMR data to PDD data that the TPS uses for the treatment plan calculations is avoided by using the original TMR data for the calculation verification. Since all treatments performed with the Novalis w system are isocentric treatments, it is found reasonable to compute the dose values based on the originally measured TMR data. The BrainSCAN w software uses also a MU calibration factor, the Nominal Linac Output factor (NOF), that defines the dose delivered at calibration depth using the calibration setup for 100 MUs. This factor does not need to be included in the calculation program because the linac is calibrated to deliver 1 cgy/mu at a depth of maximum dose in a fixed SSD configuration, the original measured TMR beam data are normalized to 100% at depth of maximum dose and the conversion factor CF SAD is used to take the fact that the linac is not calibrated in SAD geometry into consideration. In this way, a minimum number of parameters are used from the MU calculation performed by the TPS making the presented program an independent MU calculation verification that can be implemented in the QA procedure for IMRT treatments using DMLC. The achieved accuracy of the presented program has shown that it is not always necessary to have the programming skills to write a computer program or to buy software that performs the MU calculation verification in the QA procedure. A more simple approach can, notwithstanding some loss of accuracy, be sufficient to result in an adequate QA for IMRT treatments. References [1] Benedict SH, Cardinale RM, Wu Q, Zwicker RD, Broaddus WC, Mohan R. Intensity-modulated stereotactic radiosurgery using dynamic micro-multileaf collimation. Int J Radiat Oncol Biol Phys 2001;50(3): [2] Bortfeld TR, Kahler DL, Waldron TJ, Boyer AL. X-ray field compensation with multileaf collimators. 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