Volume 27, Issue 1 , Pages 21-29, January 2011
Comparison of monitor units calculated by radiotherapy treatment planning system and an independent monitor unit verification software
Article Outline
- Abstract
- Introduction
- Materials and methods
- Results and discussion
- Conclusion
- Acknowledgements
- References
- Copyright
Abstract
In radiation therapy, the monitor units (MU) needed to deliver a treatment plan are calculated by treatment planning systems (TPS). The essential part of quality assurance is to verify the MU with independent monitor unit calculation to correct any potential errors prior to the start of treatment. In this study, we have compared the MU calculated by TPS and by independent MU verification software. The MU verification software was commissioned and tested for the data integrity to ensure that the correct beam data was considered for MU calculations. The accuracy of the calculations was tested by creating a series of test plans and comparing them with ion chamber measurements. The results show that there is good agreement between the two. The MU difference (MUdiff) between the monitor unit calculations of TPS and independent MU verification system was calculated for 623 fields from 245 patients and was analyzed by treatment site for head & neck, thorax, breast, abdomen and pelvis. The mean MUdiff of −0.838% with a standard deviation of 3.04% was observed for all 623 fields. The site specific standard deviation of MUdiff was as follows: abdomen and pelvis (<1.75%), head & neck (2.5%), thorax (2.32%) and breast (6.01%). The disparities were analyzed and different correction methods were used to reduce the disparity.
Keywords: Independent monitor unit calculations, Quality assurance, Treatment planning
Introduction
The success of radiation therapy depends on the accuracy with which the prescribed dose is delivered to the target volume. The dose prescribed to the target volume is limited by the tolerance of surrounding normal tissues and the margin around the tumor volume. The dose response curves for some tumors and normal tissues may be very steep in the therapeutic dose range i.e., a small change in the prescribed tumor can result in large change in clinical response. So, it is very important that the radiation therapy is accurately planned and properly delivered to the patients.
According to the recommendations of International Commission on Radiation Units and Measurements (ICRU), the delivered dose should not deviate ±5% from the prescribed dose. Since many steps are involved in delivering the prescribed dose to the patient, better than 3% accuracy would be required in each step to achieve the ICRU recommendation [1], [2]. As only a part of the overall uncertainty arises from the process of dose calculation in treatment planning, the tolerance for the accuracy of treatment planning has to be appropriately smaller. Dose errors arising at the treatment planning phase, could potentially affect the whole course of treatment.
American Association of Physicists in Medicine (AAPM) recommends that all graphical treatment plans should be reviewed by the radiation oncology physicist. Further it recommends that this review should occur prior to treatment [3]. When this is not possible, it should occur prior to the third fraction or before 10% of the dose has been delivered, whichever occurs first.
In external beam radiation therapy, monitor units (MU) or beam-on time for a given treatment plan allows the radiotherapy technologists to deliver the actual dose to a patient. Dose errors arising in computing the MU, could potentially affect the whole course of treatment and therefore are of particular concern. So, independent checking of monitor unit calculations, for each radiotherapy treatment plan, is essential for quality assurance. It is considered more than desirable if the beam data set and calculation algorithm are independent of those of the treatment planning system.
AAPM also recommends that there should be a monitor unit check when there is no graphical plan. In addition, it recommends an independent calculation of the dose at one point in the plan, preferably at the isocenter or at a point near the center of the tumor. If the independent calculation differs by more than 5% from the treatment plan, the disparity should be resolved before commencing or continuing treatment [3].
Recently, three-dimensional (3D) treatment planning systems (TPS) have become common in radiotherapy departments offering improved accuracy and enhanced visualization in the radiotherapy treatment planning process. With recent improvement in computing technology, the newer TPS now correctly model the radiation transport properties three dimensionally and estimate the dose deposition precisely. It has changed the traditional MU calculation verification methods. Conventionally, MU calculation verification methods assumed “water phantom geometry” in which the beam was presumed to be incident on a slab of material affording full scatter conditions. Even though the calculation algorithms are tested during the commissioning of TPS and results are achieved with 1–2% accuracy in water phantom geometry, a good quality assurance programme further requires that all monitor units calculated for clinical use should be verified using a second independent calculation method so that any errors due to software faults and improper use of the systems could be identified. Usually the monitor units calculated by the TPS are typically verified using lookup tables of standard beam data, the so called “manual calculations” or by specially designed software packages [4], [5], [6], [7], [8], [9], [10], [11], [12].
Jackson Chan et al. compared the monitor unit calculated by Pinnacle planning system with hand calculations from lookup tables for nearly 13,500 treatment fields without considering the tissue inhomogenity and reported average systematic difference of 1% between the TPS and the “hand” monitor unit calculations [13]. Similarly, Starkschall et al. reported the systematic difference of 0.5–1% with Pinnacle planning system for calculating the monitor units [14]. Leszczynski et al. have created an independent monitor unit calculation in an MS-Excel spreadsheet and shown that this method is sufficiently sensitive to identify significant errors and is consistent on the magnitude of uncertainties in clinical dosimetry. They have reported that using straightforward but detailed computer based verification calculations, it is possible to achieve a precision of 1% when compared with a 3D TPS monitor unit calculation [15].
The manual calculations are expected to be less accurate than those performed by the TPS because factors such as patient surface convexity, tissue heterogeneity or beam obliquity are not considered. Moreover, with the introduction of Intensity Modulation Radiation Therapy (IMRT), an independent manual calculation of MU becomes difficult due to the complex relationship between the MU and the beam shape as well as the technique used to generate the intensity modulation [16], [17], [18], [19], [20]. Currently, a variety of new monitor unit verification software packages have been introduced in the market and are claimed to be capable of accurately calculating the monitor units even for IMRT.
In this paper, we have compared the monitor units of 245 patients' treatment plans consisting of 623 treatment fields calculated by the 3D Plato Sunrise planning system with commercially available RadCalc monitor unit verification software from Lifeline Software, Inc., and we have evaluated the accuracy and utility of the RadCalc calculation as a verification tool in several treatment sites covering a range of treatment complexity.
Materials and methods
Commissioning of RadCalc for MU calculation
The RadCalc monitor unit verification software package was installed in a stand-alone computer system and the patients planning data were imported from Plato Sunrise planning system through local area network system. The accuracy of the data transfer was confirmed by importing several patients' treatment plans and the geometric parameters like gantry angle, collimator angle, wedge angle, wedge orientation, jaw positions, MLC leaf positions, prescribed dose, photon energies etc., were tested for each plan. No discrepancy was detected during the import process but it was found that only one plan could be imported at a time for a patient and this caused an inconvenience in routine clinical workflow for multiple phase plans.
After the complete installation of RadCalc, the measured data required to determine the monitor unit like percentage depth dose, collimator scatter factors, phantom scatter factors, wedge factors, beam profiles at different depths, MLC transmission and dose per MU were measured using Wellhofer Scanditronix systems (RFA 200 system and 0.65
cc farmer type chamber). The measured data were transferred to RadCalc system.
Once the dosimetric data were transferred to RadCalc system, series of 52 tests were performed for each energies (6 and 15
MV photon) and documented in order to assess the accuracy of MU calculations according to the procedures described in technical report series (TRS) 430 by creating a series of test plans [4], [5], [21]. Different square and rectangular fields, asymmetric fields, fields with wedge, field with central block and fields with different oblique angle of incidence were generated in RadCalc and the monitor units required to deliver 100
cGy at calculation points on the central axis and on the off axis were calculated. The monitor units calculated in RadCalc were delivered with Siemens Primus linear accelerator. All the measurements were carried out with RW3 solid phantom and 0.65
cc farmer type chamber at SSD
=
90
cm. The measurements were repeated thrice and the mean value was considered. The plan details, measurement setup and the results are tabulated in Table 1, Table 2.
Table 1. Setup details and the results of measurements used to access the accuracy of RadCalc system for 6
MV photon beam.
| Dose prescription | SSD | Energy | |||
|---|---|---|---|---|---|
| Field size (cm2) | Depth (cm) | Off-axis distance (cm) | Gantry angle | Measured dose in cGy | % Diff |
| 5 | dmax | 0 | 0° | 100.3 | 0.30 |
| 5 | 5 | 0 | 0° | 100.1 | 0.10 |
| 5 | 10 | 0 | 0° | 100.7 | 0.70 |
| 5 | 20 | 0 | 0° | 100.4 | 0.40 |
| 10 | dmax | 0 | 0° | 100.5 | 0.50 |
| 10 | 5 | 0 | 0° | 100.4 | 0.40 |
| 10 | 10 | 0 | 0° | 100.5 | 0.50 |
| 10 | 20 | 0 | 0° | 100.7 | 0.70 |
| 30 | dmax | 0 | 0° | 99.64 | −0.36 |
| 30 | 5 | 0 | 0° | 100.5 | 0.50 |
| 30 | 10 | 0 | 0° | 100.2 | 0.20 |
| 30 | 20 | 0 | 0° | 100.4 | 0.40 |
| 20 | dmax | 0 | 0° | 99.40 | −0.60 |
| 20 | 5 | 0 | 0° | 99.70 | −0.30 |
| 20 | 10 | 0 | 0° | 99.30 | −0.70 |
| 20 | 20 | 0 | 0° | 100.1 | 0.10 |
| 5 | dmax | 0 | 0° | 99.60 | −0.40 |
| 5 | 5 | 0 | 0° | 99.70 | −0.30 |
| 5 | 10 | 0 | 0° | 99.34 | −0.66 |
| 5 | 20 | 0 | 0° | 99.63 | −0.37 |
| (5,10) | dmax | 0 | 0° | 99.83 | −0.17 |
| (5,10) | 5 | 0 | 0° | 99.40 | −0.60 |
| (5,10) | 10 | 0 | 0° | 99.63 | −0.37 |
| (5,10) | 20 | 0 | 0° | 99.75 | −0.25 |
| (17,3) | dmax | 0 | 0° | 99.37 | −0.63 |
| (17,3) | 5 | 0 | 0° | 99.47 | −0.53 |
| (17,3) | 10 | 0 | 0° | 99.48 | −0.52 |
| (17,3) | 20 | 0 | 0° | 99.16 | −0.84 |
| 10 | dmax | 2 | 0° | 99.15 | −0.85 |
| 10 | 5 | 2 | 0° | 98.86 | −1.14 |
| 10 | 10 | 2 | 0° | 98.54 | −1.46 |
| 10 | 20 | 2 | 0° | 98.35 | −1.65 |
| 30 | dmax | 5 | 0° | 98.75 | −1.25 |
| 30 | 5 | 5 | 0° | 98.67 | −1.33 |
| 30 | 10 | 5 | 0° | 98.45 | −1.55 |
| 30 | 20 | 5 | 0° | 98.16 | −1.84 |
| 20 | 5 | 5 | 0° | 100.41 | 0.41 |
| 20 | 5 | 5 | 0° | 100.61 | 0.61 |
| 20 | 10 | 5 | 0° | 100.65 | 0.65 |
| 20 | 10 | 5 | 0° | 100.55 | 0.55 |
| 10 | 5 | 0 | 0° | 100.30 | 0.30 |
| 10 | 5 | 0 | 0° | 100.70 | 0.70 |
| 10 | 5 | 0 | 0° | 100.40 | 0.40 |
| 10 | 5 | 0 | 0° | 99.94 | −0.06 |
| 5 | 5 | 0 | 15° | 100.14 | 0.14 |
| 5 | 5 | 0 | 30° | 99.13 | −0.87 |
| 5 | 5 | 0 | 45° | 98.23 | −1.77 |
| 5 | 5 | 0 | 60° | 98.05 | −1.95 |
| 30 | 5 | 0 | 15° | 99.97 | −0.03 |
| 30 | 5 | 0 | 30° | 99.14 | −0.86 |
| 30 | 5 | 0 | 45° | 98.32 | −1.68 |
| 30 | 5 | 0 | 60° | 98.15 | −1.85 |
Table 2. Setup details and the results of measurements used to access the accuracy of RadCalc system for 15
MV photon beam.
| Dose prescription | SSD | Energy | |||
|---|---|---|---|---|---|
| Field size (cm2) | Depth (cm) | Off-axis distance (cm) | Gantry angle | Measured dose in cGy | % Diff |
| 5 | dmax | 0 | 0° | 100.27 | 0.27 |
| 5 | 5 | 0 | 0° | 99.98 | −0.02 |
| 5 | 10 | 0 | 0° | 99.46 | −0.54 |
| 5 | 20 | 0 | 0° | 100.56 | 0.56 |
| 10 | dmax | 0 | 0° | 100.87 | 0.87 |
| 10 | 5 | 0 | 0° | 100.76 | 0.76 |
| 10 | 10 | 0 | 0° | 100.34 | 0.34 |
| 10 | 20 | 0 | 0° | 99.78 | −0.22 |
| 30 | dmax | 0 | 0° | 99.56 | −0.44 |
| 30 | 5 | 0 | 0° | 100.46 | 0.46 |
| 30 | 10 | 0 | 0° | 100.98 | 0.98 |
| 30 | 20 | 0 | 0° | 99.79 | −0.21 |
| 20 | dmax | 0 | 0° | 99.23 | −0.77 |
| 20 | 5 | 0 | 0° | 100.28 | 0.28 |
| 20 | 10 | 0 | 0° | 100.34 | 0.34 |
| 20 | 20 | 0 | 0° | 99.56 | −0.44 |
| 5 | dmax | 0 | 0° | 99.75 | −0.25 |
| 5 | 5 | 0 | 0° | 100.78 | 0.78 |
| 5 | 10 | 0 | 0° | 99.78 | −0.22 |
| 5 | 20 | 0 | 0° | 100.87 | 0.87 |
| (5,10) | dmax | 0 | 0° | 99.54 | −0.46 |
| (5,10) | 5 | 0 | 0° | 99.37 | −0.63 |
| (5,10) | 10 | 0 | 0° | 99.46 | −0.54 |
| (5,10) | 20 | 0 | 0° | 99.67 | −0.33 |
| (17,3) | dmax | 0 | 0° | 99.76 | −0.24 |
| (17,3) | 5 | 0 | 0° | 99.01 | −0.99 |
| (17,3) | 10 | 0 | 0° | 99.23 | −0.77 |
| (17,3) | 20 | 0 | 0° | 99.45 | −0.55 |
| 10 | dmax | 2 | 0° | 99.68 | −0.32 |
| 10 | 5 | 2 | 0° | 99.23 | −0.77 |
| 10 | 10 | 2 | 0° | 98.56 | −1.44 |
| 10 | 20 | 2 | 0° | 98.23 | −1.77 |
| 30 | dmax | 5 | 0° | 99.43 | −0.57 |
| 30 | 5 | 5 | 0° | 99.10 | −0.90 |
| 30 | 10 | 5 | 0° | 98.59 | −1.41 |
| 30 | 20 | 5 | 0° | 98.23 | −1.77 |
| 20 | 5 | 5 | 0° | 100.10 | 0.10 |
| 20 | 5 | 5 | 0° | 99.98 | −0.02 |
| 20 | 10 | 5 | 0° | 100.23 | 0.23 |
| 20 | 10 | 5 | 0° | 100.28 | 0.28 |
| 10 | 5 | 0 | 0° | 100.78 | 0.78 |
| 10 | 5 | 0 | 0° | 99.46 | −0.54 |
| 10 | 5 | 0 | 0° | 99.79 | −0.21 |
| 10 | 5 | 0 | 0° | 100.23 | 0.23 |
| 5 | 5 | 0 | 15° | 99.94 | −0.06 |
| 5 | 5 | 0 | 30° | 99.23 | −0.77 |
| 5 | 5 | 0 | 45° | 98.65 | −1.35 |
| 5 | 5 | 0 | 60° | 98.33 | −1.67 |
| 30 | 5 | 0 | 15° | 100.10 | 0.10 |
| 30 | 5 | 0 | 30° | 99.38 | −0.62 |
| 30 | 5 | 0 | 45° | 98.56 | −1.44 |
| 30 | 5 | 0 | 60° | 98.32 | −1.68 |
Treatment planning and validation of RadCalc system
In order to validate the accuracy of RadCalc MU verification system, we randomly selected 245 treatment plans which consist of 623 treatment fields and they were grouped into the following categories by site: head and neck (92 patients and 210 fields), thorax (41 patients and 102 fields), breast (43 patients and 120 fields), abdomen (27 patients and 60 fields) and pelvis (42 patients and 131 fields). Initially, the patient data was acquired using Siemens Somatom Emotion CT scanner with slice thickness of 5
mm and it was transferred to TPS. For all patients, critical structures and target volumes were delineated. Treatment plans were generated in commercially available Plato Sunrise treatment planning system. Monitor units required to deliver the prescribed dose were calculated in Plato TPS using pencil beam algorithm and tissue inhomogenity was considered. Beam data sets used to calculate the monitor units is independent from the beam data sets used for RadCalc MU verification system and the Plato calculations were tested in accordance with TRS-430 protocol. Once the treatment plans were approved by radiation oncologist, the treatment plan was exported to local area network therapy information system (LANTIS) for patient treatment delivery and to RadCalc system for MU verification.
To compare the MU calculated by Plato TPS with RadCalc MU verification system, dose per field, prescribed isodose line and prescription point were entered carefully for each patients. In MU calculations, the beam data sets that were used assume that the calculation point is located in a homogeneous medium. In clinical situations, most of the times, the prescription point is in or behind the inhomogeneous medium. So the attenuation of the primary beam and the scatter dose deposition at the prescription point will not be the same as for the homogeneous medium. In this study equivalent path length method was considered to account for tissue inhomogeneity effects. For each beam, the MUdiff i.e., percent difference between MU calculated by Plato TPS and RadCalc system was calculated by using the expression

Results and discussion
The results of the tests carried out to access the accuracy of RadCalc system were shown in Table 1, Table 2 and Fig. 1. For symmetric and asymmetric fields, the RadCalc system accurately calculates the MU unit, which is required to deliver the prescription dose of 100
cGy at the calculation point on the central axis within the range of ±0.98%. However RadCalc system underestimates the MU for asymmetric fields. It was observed that for off-axis calculation the RadCalc system underestimates the dose by maximum of −1.84%. It was also observed that for fields with wedge and block, RadCalc calculates the dose with the maximum deviation of 0.78%. For different angle of incidence, the magnitude of the maximum difference observed was about 1.95%.
The MUdiff of all 623 treatment fields were characterized in terms of mean and standard deviation of the MUdiff between TPS and RadCalc system in each site. In each site, histograms between the MUdiff and number of patients also were plotted. In the study of 623 treatment fields, for all sites the mean MUdiff was −0.838% with a standard deviation of 3.04%. A histogram of the MUdiff for these 623 treatment fields is shown in Fig. 2.

Figure 2
Histogram of percentage difference in MU calculated by RadCalc system compared to Plato TPS for all 623 fields showing the mean MUdiff of −0.838% with a standard deviation of 3.04%.
Histograms of the MUdiff for each site are shown in Figure 3, Figure 4, Figure 5, Figure 6, Figure 7 respectively. From the Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, it was evident that except for the sites head & neck, thorax and breast in all the other treatment sites standard deviation of MUdiff were lesser than 1.75% whereas in head & neck region standard deviation was 2.5%, in thorax region the standard deviation was 2.32% and in breast region the standard deviation was 6.01%. The variations were larger than what was expected to be due to more tissue inhomogeneity, surface irregularity, missing tissue, point of prescription etc, [11], [12], [22], [23], [24], [25], [26].

Figure 3
Histogram of percentage difference in MU between RadCalc and Plato TPS for 92 patients' 210 head & neck treatment fields showing the mean MUdiff of −0.10% with a standard deviation of 2.50%.

Figure 4
Histogram of percentage difference in MU between RadCalc and Plato TPS for 41 patients' 102 thorax treatment fields showing the mean MUdiff of 2.36% with a standard deviation of 2.32%.

Figure 5
Histogram of percentage difference in MU between RadCalc and Plato TPS for 43 patients' 120 breast treatment fields showing the mean MUdiff of −1.93% with a standard deviation of 6.01%.

Figure 6
Histogram of percentage difference in MU between RadCalc and Plato TPS for 27 patients' 60 abdomen treatment fields showing the mean MUdiff of 2.40% with a standard deviation of 1.74%.

Figure 7
Histogram of percentage difference in MU between RadCalc and Plato TPS for 42 patients' 131 pelvic treatment fields showing the mean MUdiff of 0.70% with a standard deviation of 1.37%.
In head & neck and thorax region, we could expect that the larger standard deviation was due to tissue inhomogeneity, whereas in breast it could be attributed to tissue inhomogenity, missing tissue and also due to placement of prescription point. The over/under estimation of MU in RadCalc system due to tissue inhomogenity was reduced to 1% by considering radiological effective path length which was given by Plato planning system. But in this method the standard deviation of MUdiff increased from 2.32% to 2.43% in thorax and from 6.01% to 6.46% in breast. Even though the standard deviation of MUdiff increased in thorax and breast sites, we have decided to use this method to account for tissue inhomogenity for all patients systematically.
In tangential treatment field for breast, always there is a significant amount of “missing tissue” due to complex external contours and field borders outside the body. Monitor unit verification is usually performed with simple algorithms that assume full scatter conditions. The result is an overestimate of scatter dose to the calculation point and an underestimate of the monitor units required to deliver the desired dose. So in this study further we have tried for the equivalent triangle and equivalent rectangle method for the breast cases to account for the missing tissue. The different equivalent methods to account for missing tissues were described elsewhere [12], [22], [23], [24], [25]. By following these methods, the results were positive i.e. the standard deviation of MUdiff was reduced to 6.13%.
The corrections for discrepancies due to irregular field were made using blocked equivalent square method in the RadCalc software. A modal value of 0.2% that is getting closer to the MU calculated by the TPS was observed.
A common error found in the RadCalc was that the differences of around 10–12% were found in breast cases if the calculation/prescription point falls near/within lung or any air cavity. The reason for this systematic error is that the planning system is trying to compute the dose to prescription points located in areas where electronic equilibrium exists while RadCalc cannot take it into account. The solution given by the RadCalc system would be to try and find a point in the patient where there is enough build-up material. But in most of our breast case study the point of normalization was usually placed on the lung/chest wall interface. In Plato TPS the inhomogeneity correction was applied based on equivalent tissue air ratio (ETAR) method for dose calculations. The effects described above are not taken into account in both the Batho and ETAR methods, which in turn results in requirement of more MUs to deliver the prescribed dose at the normalized point. The results of several studies show that materials with densities that deviate substantially from water present difficulties for these inhomogeneity correction algorithms due to their inability in lateral and longitudinal electron transport model [11], [22], [24].
Smulders et al. have concluded that the depth dose characteristics for symmetric wedged fields differ from those for wedged asymmetric fields perpendicular to the wedge direction and are smaller than those on the central beam axis due to the wedge hardening effects at off-axis distance [26], [27]. Hence, an attempt was made to measure an off-axis wedge correction factor and to use it for the RadCalc MU calculation for breast fields. This reduced the standard deviation of MUdiff from 6.13% to 5.98%. Statistics of disparity between the MU calculations using RadCalc systems and Plato TPS for different sites are shown in Table 3.
Table 3. Statistics of disparity between the MU calculations using RadCalc systems and Plato TPS.
| Treatment site | Before correction | After accounting tissue inhomogenity | After accounting missing tissue | After accounting wedge hardening effects | ||||
|---|---|---|---|---|---|---|---|---|
| Mean MUdiff | SD % | Mean MUdiff | SD % | Mean MUdiff | SD % | Mean MUdiff | SD % | |
| Head and neck | −0.10 | 2.50 | 0.10 | 1.82 | – | – | – | – |
| Abdomen | 2.40 | 1.74 | 0.86 | 0.94 | – | – | – | – |
| Pelvis | 0.70 | 1.37 | 0.74 | 1.04 | – | – | – | – |
| Thorax | 2.36 | 2.32 | 1.86 | 2.43 | – | – | – | – |
| Breast | −1.93 | 6.01 | 1.45 | 6.46 | 1.38 | 6.13 | 1.33 | 5.98 |
Conclusion
In this paper, we have done a comprehensive analysis of differences between the monitor unit calculations of the Plato treatment planning system and monitor unit calculated in RadCalc system for different treatment sites as described. The results of this study indicate that the MU calculated by RadCalc software program agreed well with that calculated by the Plato planning system. We also have identified some systematic differences in the calculation methods and determined the range of dose variations for each site. These systematic differences were due to complex treatment geometry and limitations in the calculation methods. Since multiple factors are used in the calculation, these systematic differences can build up to produce large net differences. Based on this study we have determined that the action levels for implementing this MU validation method in clinical routine depend on treatment site and treatment geometry. The action levels were 5% for tangent beams in breast region, 4% for beams in thorax region and 3% for beams in all other sites. For the plans showing deviations larger than the action levels, the cause of discrepancy should be further investigated. If needed, the prescription point may be repositioned and calculations may be repeated. If the discrepancies still occur, the phantom measurement should be performed with ion chamber.
Acknowledgements
The authors would like to thank Sun Nuclear Corporation for providing the RadCalc software package to carry out this study.
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PII: S1120-1797(10)00008-6
doi:10.1016/j.ejmp.2010.01.006
© 2010 Associazione Italiana di Fisica Medica. Published by Elsevier Inc. All rights reserved.
Volume 27, Issue 1 , Pages 21-29, January 2011

