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A. Meijers et al. / Medical Physics in the Baltic States 7 (2009) 56 - 59 1. From freely chosen point vector is drawn to field edge. 2. Intersection point of vector and field edge is found. 3. Length of vector from starting point to intersection point is determined. 4. Determined vector is considered as radius of circular field. 5. SMR for such circular field is determined. 6. Previous five steps are repeated until whole field is covered. Angle between vectors is chosen constant (to ease calculation). In case any vector intersects field edge more than once due to irregular field shape, the vector is divided on several parts as shown in figure 1. Total SMR for such vector is determined by following equation: Fig. 1. EQSQ calculation tool (2) Algorithm as described above was fulfilled in Microsoft Excel spreadsheet, to make it easy accessible and usable. To calculate EQSQ it is necessary to import file from TPS with MLC positions and enter collimator jaw positions as well as SSD. Figure 1 shows example of the calculation. 57 7. SMR for all circular fields is summed. 8. As mentioned above, angle between vectors is constant. Therefore contribution of all circular fields towards SMR of irregular field is considered equal. SMR of irregularly shaped field is determined as average of SMR sum of circular fields. 9. Square field with the same SMR as SMR of irregular field is determined. This square field is considered equivalent square. 3. Analysis and results It is important to determine optimal number of vectors. As a result calculation will be less time consuming. Statistical evaluation was used to find optimal number of vectors. EQSQ was calculated for 32 randomly chosen irregular fields using different number of vectors. Calculated EQSQs for single field were normalized to maximal value, allowing comparing results of different fields. Confidence level was chosen 95%. Results are shown in Table 1.
Table 1. Optimization of number of vectors A. Meijers et al. / Medical Physics in the Baltic States 7 (2009) 56 - 59 vectors average CI error 2 0.900 0.029 3.20% 4 0.930 0.026 2.80% 6 0.964 0.030 3.10% 12 0.963 0.030 3.10% 18 0.963 0.029 3.10% 24 0.962 0.029 3.10% 36 0.962 0.029 3.00% 72 0.963 0.029 3.10% Secondly EQSQ were determined for 25 randomly chosen irregular fields. Same fields were calculated by using Varian TPS Eclipse 6.0 with PBC dose calculation algorithm. Both results were compared. The difference between EQSQ acquired by both methods was 1.83 ± 0.85 % (with confidence level 0.95). Before using described EQSQ calculation tool for manual MU verification, it was necessary to verify the significance of EQSQ error contribution towards calculated MU. By using SSD method (equation 1) necessary MUs were determined to deliver 1 Gy in water, in depth 10 mm, SSD set to 1000 mm. Beam data of Varian Clinac 2100 for 6 MeV were used. Calculation was performed for square fields with the same size as shown in Table 2 using precise EQSQ values. Afterwards MU calculation was repeated using determined EQSQ as shown in Table 2. Test showed that EQSQ values which were determined by developed tool (1.32 ± 0.52 %) introduced error for calculated MU 0.042 ± 0.021 % (confidence level 0.95). Chart 1 Optimal number of vectors 58 According to Chart 1, it is not necessary to use more than 24 vectors, since the calculated result does not change significantly if the number of vectors is further increased. To evaluate error of EQSQ calculation method, two tests were performed. Firstly EQSQ were determined for square fields with size from 4 to 35 cm. EQSQ for square field is square of the same size as given field. Acquired results are shown in Table 2. Maximal error for determined EQSQ is 2.2 %. Table 2. EQSQ determination errors Square field size, cm EQSQ, cm Error 4 3.97 0.80% 6 6.00 0.10% 8 7.83 2.20% 10 9.97 0.30% 12 11.85 1.20% 15 14.76 1.60% 20 19.58 2.10% 25 24.55 1.80% 30 29.60 1.30% 35 34.33 1.90%
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2009 PROCEEDINGS OF THE 7 th INTERN
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Executive editor: D.Adlienė CONFER
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11.15-11.30 Daiva Leščiute, Valda
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