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DEPARTMENT OF RADIATION PHYSICS
THE IMPACT OF DIFFERENT DOSE CALCULATION ALGORITHMS AND GRID SIZES ON APERTURE-BASED COMPLEXITY METRICS M.sc. Thesis, Gothenburg spring 2015 Axel Larsson
Supervisors: Anna Bäcka Ph.D. medical physics
Anna Karlsson Hauera Ph.D. medical physics
a) Department of therapeutic radiation physics, Sahlgrenska University Hospital, Gothenburg Email: [email protected] Tel: +46 70 616 48 07
The author is thankful for the great support from his supervisors Anna Bäck and Anna Karlsson Hauer. Special thanks to Magnus Gustavsson, Sahlgrenska University Hospital, for
his support with the film measurement technique and Sebastian Sarudis, Sahlgrenska University Hospital, for the help with the collapsed cone calculations.
Gothenburg, June 2015
Abstract
Background: The use of the IMRT and VMAT technique enables, in many cases, an increased absorbed dose to the tumor, with a more conform dose distribution, compared to conventional radiation therapy. Invers treatment planning is used to create IMRT and VMAT plans. The treatment plan is made up of several, often small or irregular, MLC openings. Small and irregular MLC openings increase the complexity in dose calculation and dose delivery, mainly due to the absence if charge particle equilibrium (CPE). Götstedt et al (2015) developed two different aperture-‐based complexity metrics: converted aperture metric and edge area metric, and evaluated them for 30 different static MLC openings. These metrics provide a complexity score for each MLC opening. The metrics were evaluated for the anisotropy analytical algorithm (AAA) and 0.25 cm calculation grid size using three EPID measurements and one film measurement. A correlation between the complexity scores for both metrics and the difference between calculated and measured dose distribution was found, for both EPID-‐ and film measurements. In this this study it was investigated how the two earlier described metrics correlate with the difference between calculated and measured dose when the dose calculation is made using the dose calculation algorithms pencil beam convolution (PBC), acuros XB advanced calculation algorithm (AXB) and the collapsed cone algorithm (CC). This study is based on film measurements. The previous film measurement made by Götstedt et al (2015) was complemented by two further film measurements in order to take into account the precision in the measurement procedure. The impact of different dose calculation resolutions on the correlation was also investigated. Method: The 30 different MLC openings described in Götstedt et al (2015) were used. These MLC openings were measured on two separate occasions using a 6 MV photon beam and Gafchromic® EBT3 film. The films were calibrated, scanned and analysed in RIT113 (Radiological imaging technology). In the analysis, measured and calculated absorbed dose was compared. The percentage of pixels that did not deviate (calculated vs measured) more than 5 % and 3 % normalized to the calculated maximum absorbed dose in each of the MLC opening (i.e. 5 % and 3 % dose difference pass rate) were used as a measure of the comparision.
Results: High correlation coefficients i.e. pearsons´s r-‐values were found for each metric and all the dose calculation algorithms tested. A lower correlation coefficient was found for Acuros XB. A higher dose calculation resolution generated a better match between calculated and measured dose distribution. The complexity scored for both the metrics correlated with the evaluation results for all examined calculation resolutions. The calculated dose differences for the different MLC openings were dependent on the examined calculation algorithm. The PBC algorithm performed generally worse than other algorithms and AAA performed generally better than the other algorithms. Conclusion: The conclusions from Götstedt et al (2015) were confirmed for AAA. The average spread of the dose difference pass rate values from the three different film measurements, i.e. the standard deviation, was generally within 3 % for the 5 % dose difference pass rate criterion and 4 % for the 3 % dose difference pass rate criterion. The scores for the converted aperture and the edge area metric correlate with the dose difference between measured and calculated dose distribution, also for the PBC, AXB and CC algorithm, as well as for the AAA calculations with different dose calculation resolution. A slightly lower r-‐value was found for AXB compared to the other algorithms.
Abbreviations AAA – Anisotropic analytical algorithm
AXB – Acuros XB
CC – Collapsed cone convolution
CPE – Charge particle equilibrium
DICOM – Digital imaging and communications in medicine
EPID – Electronic portal imaging device
IMRT – Intensity-‐modulated radiation therapy
LBTE – Linear Boltzmann transport equation
MC – Monte carlo
MLC – Multi leaf collimator
MU – Monitor unit
OAR – Organs at risk
OD – Optical density
PBC – Pencil beam convolution
QA – Quality assurance
QC – Quality control
SD – Standard deviation
SNR – Signal to noise ratio
TERMA – Total energy released per unit mass
TPS – Treatment planning system
VMAT – Volumetric-‐modulated arc therapy
List of Contents 1. Introduction ............................................................................................................ 1
1.1 Aim ................................................................................................................................. 3 2. Theory ..................................................................................................................... 4
2.1 Converted aperture metric .............................................................................................. 4 2.2 Edge area metric ............................................................................................................ 5 2.3 Pencil Beam Convolution Algorithm (PBC) .................................................................... 5 2.4 Anisotropy Analytical Algorithm (AAA) ........................................................................... 6 2.5 Acuros XB (AXB) ............................................................................................................ 6 2.6 Collapsed cone convolution (CC) ................................................................................... 7
3. Material and methods ............................................................................................ 8 3.1 The Different MLC Openings .......................................................................................... 8 3.2 Film Measurement .......................................................................................................... 9 3.3 Calculation of Dose Distributions .................................................................................. 11 3.4 Evolution of the Dose Difference .................................................................................. 12
4. Results .................................................................................................................. 14 4.1 Precision of the Film Measurement Procedure ............................................................ 14 4.2 Different Dose Calculation Algorithms .......................................................................... 19 4.3. Different Grid Size ....................................................................................................... 23
5. Discussion ............................................................................................................ 26 6. Conclusions ......................................................................................................... 29 7. References ........................................................................................................... 30 Appendix ................................................................................................................... 32
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1. Introduction Radiation therapy plays an important role in the treatment of cancer, and it is used as a treatment for more than half of all the cancer patients world wide (IAEA, 2004). The radiation treatment design is simulated in a treatment planning system (TPS) prior delivery to patient. The dose distribution is calculated and optimized in the TPS. Intensity-‐modulated radiation therapy (IMRT) is a radiation technique where the fluence of the beam is non-‐uniform (Kahn, 2010). With IMRT the fluence in a beam at a static gantry angle can be adjusted during radiation delivery based on user-‐defined constrains. This enables higher and more conformal absorbed dose distributions to the tumor with less absorbed dose to OAR. Another radiation technique is the volumetric modulated arc therapy (VMAT). For VMAT the treatment is delivered at the same time as the gantry is rotating around the patients and with a continuously changing MLC shape, dose rate and angle speed of the gantry (O´Daniel et al, 2012). VMAT has the potential to deliver a conformal dose distribution with less monitor units (MU) and shorter treatment time compared to IMRT technique (Younge et al, 2012). Shorter treatment time reduces the risk of patient movement during treatment and gives the patient an increased comfort. Unlike conventional radiation therapy, IMRT and VMAT often have a greater ability to increase the dose to the target with a reduced dose to healthy tissue (McNiven et al, 2010). However, the characteristics of the IMRT/VMAT treatment make higher demands on treatment planning, dose delivery and quality assurance. An IMRT/VMAT treatment plan is created using an optimization algorithm in the TPS. This optimization procedure creates a treatment plan based on user-‐defined constrains that tells the system what the prescribed absorbed dose should be for the target and maximum permissible absorbed dose for the OAR. This generates a treatment plan composed of unique MLC openings with different sizes and shapes (Kahn, 2010). During optimizing of VMAT or IMRT plans the TPS creating more small and irregular shaped MLC openings compared to conventional treatment planning (Younge et al, 2012). Small or irregular MLC openings make it more difficult for the TPS to calculate an accurate dose distribution due to regions lacking charge particle equilibrium (CPE). Fog et al (2011) showed that apertures consisting of small subfields or large fields containing isolated MLC leaves could give rise to significant dose calculation errors. Small MLC openings also lead to a more pronounced dependence on the position of the MLC leafs during delivery and the MLC modeling in the TPS (LoSasso et al, 1998). Because of the complex nature of the IMRT/VMAT technique, it is necessary to confirm that the TPS has calculated the dose distribution correctly and that the insecurities in
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dose delivery from the treatment machine are in tolerance. This is done by quality assurance (QA) (Nelms et al, 2011). The QA includes IMRT quality control (QC). A common way for IMRT QC is to compare the TPS calculated dose distribution with corresponding measured dose distribution in a phantom. Common QC methods that are in use nowadays have been found to miss relevant clinical differences between calculated and delivered dose distributions (Nelms et al, 2011; Götstedt et al, 2015; Nilsson et al, 2013). By taking advantage of complexity metrics that describes the calculation and delivery complexity by calculating a complexity score in the dose calculation process, complex MLC openings can be avoided before the treatment plans are approved (Götstedt et al, 2015). Complexity metrics can also be used as a supplement and simplification of the QA process by giving a signal to the physicist of which QA method that may be required and which treatment plans that need detailed examination. QA measurements require a lot of staff time and demands machine time. Younge et al (2012) showed that highly complex MLC openings are not always needed to create a clinically accepted VMAT plan, instead it is an unwanted effect of the optimizing process in the TPS. Oliver et al (2011) concluded that decreasing the MU:s and creating MLC openings with increased opening area should lead to more stable treatment plans with preserved quality. Complexity metrics can also be used in the optimization procedure to force the optimizer to create treatment plans with less complex apertures (Younge et al, 2012). Younge at el (2012) developed a function that was integrated in the optimization process. The function penalized small and irregular MLC openings. The study verified that penalizing small and irregular MLC openings could give an increased agreement between calculated and measured absorbed dose with negligible changes in the planed dose to target and OAR. The two aperture-‐based metrics evaluated in this study is the converted aperture metric based on the distance between the MLC leave positions and the edge area metric based on the circumference of the MLC opening in relation to the area of the opening. These metrics were developed in a previously study (Götstedt et al, 2015). The study examined the correlation between the metric scores and the difference between calculated and measured absorbed dose. The evaluations were performed with three electronic portal imaging device (EPID) measurements and one film measurement and the calculations were performed with the anisotropic analytical algorithm (AAA). The results indicated a correlation between the metrics and the percentage of pixels that did not deviate more than 3 % or 5 % normalized to the maximum calculated absorbed dose. The correlations were calculated with pearsons´s r-‐value. The pearsons´s r-‐value gives the linear dependence i.e. correlation between two variables by giving a value between
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-‐1 and 1 (Djurfeldt et al, 2010). -‐1 och 1 means a negative or positive correlation respectively. A value close to 0 means that no correlation exists. This project is a complement and an extension of the study by Götstedt et al (2015) for the converted aperture and the edge are metric. The influence on the correlation between the metric scores and the difference between measured and calculated dose distribution were investigated when different dose calculation algorithms and grid sizes were used. 1.1 Aim
§ Reproduce the film measurements from Götstedt el at (2015) to study the precision for the measurement procedure.
§ Evaluate the correlation between the two different complexity metrics, edge area
and converted aperture metric, and the dose difference (i.e. difference between measured and calculated dose distributions) between measured and calculated dose distributions for the pencil beam convolution (PBC), collapsed cone (CC) and acuros XB (AXB) algorithms.
§ Study the impact of the dose calculation grid size on the correlation between the
dose differences and the two complexity metrics when using the AAA algorithm.
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2. Theory
2.1 Converted aperture metric The converted aperture metric is based on the distances between the MLC leaves both parallel and opposed the MLC direction (Götstedt et al, 2015) (figure 1). The metric gives, for a MLC opening, a complexity score value between 0 (non-‐complex) and 1 (complex). The distances are measured every 5 mm.
Figure 1. For the converted aperture metric the distances between MLC leaves are measured both parallel (green solid line) and opposed (red dashed line) the MLC direction. The MLC leaves are 5 mm wide.
The conversion function, f, penalizes smaller distances compared to larger distances (eq. 1).
𝑓(𝑥) = 1− 𝑒−𝑥 (𝐸𝑞. 1)
With the distances (mm) and the equivalent field size as input arguments the function derives a value between 0 (complex) and 1 (non-‐complex). The complexity score is then given by the following equation (Götstedt et al, 2015):
𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑 𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒 𝑚𝑒𝑡𝑟𝑖𝑐 = 1− 𝑓 𝑑! ∙ 𝑓 𝑎!" (𝐸𝑞. 2)
where di is the measured distances and aeq is the equivalent square field size. To get a higher score for increasing complexity, and a lower score for decreasing complexity, the
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score is subtracted from one. The calculations were performed in an in-‐house MatLab® software.
2.2 Edge area metric The edge area metric depends on the length of the edge of the MLC opening (Götstedt et al, 2015). As for the converted aperture metric, the edge area metric calculates a complexity score based on the MLC opening. The MLC opening is divided into two different areas. The first area, Ae, includes 5 mm on both sides of the MLC edge (figure 2). The second area, Ao (mm2), are defined as the rest of the area of the MLC opening. The edge area metric is given by the following equation:
𝐸𝑑𝑔𝑒 𝑎𝑟𝑒𝑎 𝑚𝑒𝑡𝑟𝑖𝑐 =𝐴!
𝐴! + 𝐴! (𝐸𝑞. 3)
As for the converted area metric, a higher score, between zero and one means that the field is more complex.
Figure 2. Schematic graph of the areas for the edge area metric. Area Ae (green and light green) includes 5 mm on both sides of the edges of the MLC leaves. The remaining area, Ao, is marked as white. The MLC leves are 5 mm wide.
2.3 Pencil Beam Convolution Algorithm (PBC) The pencil beam convolution algorithm (PBC) is implemented in Eclipse TPS (Varian medical systems, 2010) but similar algorithms are also implemented in other treatment planning systems.
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The absorbed dose is calculated by convolving total energy released by unit mass (TERMA) with a pencil beam kernel. The pencil beam kernels describe the dose deposition from all photons and electrons emerging from an in-‐finite part of the beam. In every voxel the TERMA is calculated based on the beam model. This model describes the fluence from the accelerator and is calculated once and for every unique accelerator. It is based on measured parameters like MLC transmission factors and dose profiles. The irradiated volume is divided into finite voxels. The voxel size is defined by the grid size chosen by the user. The dose calculation resolution i.e. grid size can be chosen to be 0.125 cm, 0.25 cm, 0.5 cm or 1.0 cm for PBC. Reduced grid size improves the dose calculation resolution and vice versa. The convolving process takes place in each voxel. The total dose in a voxel is calculated by superposition of the smaller dose depositions.
2.4 Anisotropy Analytical Algorithm (AAA) The anisotropic analytical algorithm (AAA) is a 3D pencil beam convolution algorithm developed by Varian medical systems (Varian medical systems, 2010). The grid size can be chosen between 0.1 cm and 0.5 cm. The dose calculation model is divided into a beam model and a dose calculation model. The first one describes the beam in the phase space plane by different source models. The source models are the primary-‐, secondary-‐, wedge scattering-‐, and electron contamination source model. Monoenergetic pencil beam kernels are transformed to polyenergetic pencil beam kernels. They are also scaled based on the electron density (heterogenities) along the central axis of the kernel and in six lateral directions. The beam is divided into finite beamlets. Every beamlet is convolved with a kernel. This is done for every source. The total energy in every voxel is given by superposition of the doses from the different source models.
2.5 Acuros XB (AXB) The acuros XB algorithm is implemented in the Eclipse TPS (Varian medical systems, 2010). AXB is considered to be a fast algorithm compared to MC even though the computing time compared to other clinical calculation algorithms is somewhat longer. The grid sizes available to be chosen are between 0.1 cm and 0.3 cm. The beam model is the same as for the anisotropic analytical algorithm (AAA).
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Acuros XB calculates the absorbed dose by solving the linear Boltzmann transport equation (LBTE) (Vassiliev et al, 2010). The LBTE describes macroscopically how ionizing particles for example photons and electrons interact with different matter. LBTE is solved in Eclipse by numerical methods (Varian medical systems, 2010). In the calculations, limitations in accuracy are induced because of the discrete variables in angle, energy and space. Acuros XB calculates absorbed doses in heterogenic material in the same order of accuracy as MC calculations (Fogliata, 2011). The long computing time compared to other calculation algorithm is a disadvantage (Vassiliev et al, 2010).
2.6 Collapsed cone convolution (CC) The collapsed cone convolution (CC) algorithm is implemented in the Oncentra TPS (Nucletron). The grid size can be chosen between 0.1 cm and 0.5 cm. The beam model is made up of two models: one that describes the primary fluence and another that takes into account the fluence of head-‐scatter components. These are stored in separate 2D-‐ matrices. CC uses analytical point kernels to describe the dose deposition from primary photons in the medium (Ahnesjö, 1989). A point kernel gives the dose deposition distribution from primary photons and scattered photons. The absorbed dose is calculated by a 3D convolution/superposition method like the AAA and PBC algorithms. The deposited energy, within a solid angle Ω, is transported to voxels positioned along a line inside a cylindrical coordinate system. Every line defines an axis of a cone. The line is passing thought the middle point of a 3D voxel defined in a cartesian coordinate system. The total energy deposited along the line is transported to this voxel. That means that parallel lines, one for every cartesian voxel, gives the total absorbed dose in the whole radiated volume. CC is an algorithm that effectively takes into account heterogeneities due to the use of a cylindrical coordinate system.
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3. Material and methods
3.1 The Different MLC Openings 30 MLC openings of varying complexity were used in this study. The MLC openings were described in a previous study (Götstedt et al, 2015). The MLC openings have different shapes and sizes and were created in the EclipseTM treatment planning system (v. 11.0.47, Varian Medical Systems). The MLC openings were divided into six series, A-‐F (figure 3). In each series the six openings were numbered 1-‐5. Increased number indicates increased complexity within the series. The circumference and area of series A are decreasing, while the shape of the MLC opening is retaining a square shape. The jaws of series A form a 10 cm x 10 cm large area. In series B the MLC opening area is slightly decreasing with a considerable increased circumference. Series D simulates small subfields. Series D and E have a constant MLC opening area, with an increasing circumference. Series C and F have a constant circumference, with a decreasing MLC opening area.
Figure 3: 30 different MLC openings described by Götstedt et al (2015) were used in this study. The MLC openings were divided into five series A-F. Increased number indicates increased complexity within the series. The MLC leaves are 5 mm wide.
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3.2 Film Measurement Film dosimetry was carried out using Gafchromic® EBT3 film. 70 films were prepared: 60 films for the measurement of the 30 MLC openings in two different occasions and further 10 films for the calibration. Two film measurements were performed in this study. Each film measurement was done on three subsequent days. During day one all the 40 films were scanned with an Epson Expression 1650 Pro scanner to get information about the unique features, such as irregularities and transparency, in each pixel for each film. For each scan the films were placed in the same reproducible way in the scanner and four scans were performed. The first scan was for heating the film and this scan was disregarded in further analysis. The other three directly subsuquent scans, that were made for each of the films during a day of irradiation were averaged to increase signal to noise ratio (SNR). This was made in an in-‐house developed program written in Matlab© (Mathworks). On the same day as the scanning, all films were irradiated to a uniform absorbed dose of 2 Gy. It was done to obtain the radiation sensitivity of each film, which was a part of the calibration. A 6 MeV photon beam was used to deliver the dose (Cliniac® iX linac, Varian medical systems). The films were placed, perpendicular to the beam, at 10 cm depth in a 30 cm × 35 cm solid-‐water phantom. To ensure complete backscatter 7 cm of solid water was placed under the film (figure 4). Two films were placed on top of each other and irradiated at the same time. The gantry angle was set to 0 degrees, the field size to 40 cm × 40 cm and the source to skin distance (SSD) to 90 cm. The treatment table was placed in 90 or 270 degrees during the delivery of the first-‐half of the dose. Then, the table was rotated 180 degrees before the second half of the dose was delivered. This was done to give the films as homogeneous absorbed dose as possible by taking into account possible skewness in the beam from the accelerator. The number of MUs to be delivered was calculated according to equation 4:
𝑀𝑈 =𝐷
(1.172120 )× 𝑀!"#$% (𝐸𝑞. 4)
D (Gy) is the absorbed dose to deliver and !.!"#
!"# (Gy/MU) is the reference output. Mratio is
given by equation 5.
𝑀!"#$% =𝑀 ∙ 𝐾!"𝑀!"#
(𝐸𝑞. 5)
𝑀(C) is the averaged value of three output measurements. The Mratio was calculated before and after the radiation of the films. The second Mratio measurement verified that the Mratio did not change during the film measurements. M was measured with an
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ionizing chamber at 10 cm depth in a solid-‐water phantom with the dimensions 20 cm × 20 cm. The field size was 10 cm × 10 cm and the SSD was 90 cm. The linac was calibrated to deliver 1 Gy at 10 depth in water for a field opening of 10 cm × 10 cm at SSD 90 cm. In each irradiation 120 MU was delivered. Mref is the reference value. Pressure (mmHg) and temperature (oC) were measured at each occurence to give the pressure-‐ and temperature factor KTP.
Day two, more than 18 hours after the first irradiation, the films where scanned again. The scan was performed in the same way as previously describe. Later on the same day, day 2, the measurement started by irradiating each of the 30 films with one of the 30 different MLC openings. The number of MUs for the MLC openings were calculated to deliver about 2 Gy in the center of the MLC opening at 10 cm depth with a SSD of 90 cm. The dose and MU calculations were carried out in EclipseTM. The calculated MUs are listed in table 5, in appendix. Each of the films was placed in the same reproducible way during irradiation. The double exposure method was used to calibrate the films to interconnect the optical density with absorbed dose. The principles are the same as described by Zhu et al (1997). A calibration curve was calculated according to equation 6. The purpose of the calibration procedure was to fit a polynome by tuning the parameters A, B and C to correlate the absorbed dose with the optical density. Parameter A and B applies for every batch and C gives the sensitivity in each pixel of every film. The parameter C is produced from the 2 Gy exposure on day one.
𝑂𝐷 =𝐴×𝑑𝑜𝑠𝑒𝐵×𝑑𝑜𝑠𝑒 + 𝐶×𝑑𝑜𝑠𝑒 (𝐸𝑞. 6)
Figure 4. A photo of the linac and the couch. The gantry angel was at 0 degrees and the couch at 90 or 270 degrees angle during day one. The couch is positioned at 270 degrees in the photo (left). The 40 films were placed at 10 cm depth in a solid-water phantom with 10 cm solid-water on top of the films (right).
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On day two, after the second scan and after the delivery of the 30 MLC openings, 10 films for the calibration were irradiated to a predetermined absorbed dose. One film was left unirradiated. The MUs were calculated as previously describe according to equation 4 and are listed in table 1.
On day three, more than 18 hours after the second irradiation, all the 40 films were scanned again. The optical density for the 10 individual films irradiated with different absorbed doses was measured from a 2.5 cm × 2.5 cm region-‐of-‐interest (ROI) in the center of the 10 films. An in-‐house developed software in Matlab© was used. The parameters A and B were calculated in Excel (Microsoft corporation) and then applied to the films with an in-‐house developed software in Matlab©.
3.3 Calculation of Dose Distributions The dose distributions from the different MLC openings were calculated with the AAA (v.10.0.28), PBC (v.10.0.28) and AXB (v.11.0.31) algorithms in EclipseTM (v.11.0.47, Varian medical systems) and with the CC (v.4.0) in Oncentra© (v.5.3, Nucletron). The phantom used in the TPS was the same as used by Götstedt et al (2015). The dimensions of the phantom were 30 cm × 30 cm × 30 cm (figure 5). The phantom material was set to water in the TPS. The isocenter for the individual MLC openinges were placed at 10 cm depth centrally in the phantom. The chosen dose calculation grid sizes for the AAA algorithm were 0.125 cm, 0.25 cm and 0.5 cm and for the other algorithms the grid size was set to 0.25 cm. The calculated coronal absorbed dose distributions at 10 cm depth, for the individual MLC openings, were exported to RIT113 (v.5.4) for evaluation. The dose distributions exported from the TPS had the dimensions 22.59 cm × 28.39 cm and the resolution in-‐plane was 0.056 cm × 0.056 cm. Thus, the resolution of the exported data was considerably higher than the resolution of any of the calculated grid sizes.
Film Dose (Gy) #MU0 1 0 0 2 0.28 26 3 0.56 52 4 0.75 77 5 1.00 103 6 1.50 155 7 2.01 207 8 3.00 310 9 3.00 413 10 5.00 517
Table 1. Absorbed dose with corresponding number of MU used for the calibration of the films.
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3.4 Evolution of the Dose Difference The film measurements were evaluated pixel-‐by-‐pixel in RIT113 (v.5.4, Radiological Imaging technology INC). The measured absorbed dose data was individually imported and registrered with the corresponding calculated absorbed dose data (DICOM-‐RD) for each MLC opening. When the films were imported, the calibration curve was applied to convert the blackening of the film to absorbed dose. A median 9 pixels × 9 pixels filter was applied for noise reduction of the measured dose data. The registration between the measured and the calculated dose distributions was done with a four-‐point-‐match. The registration points was saved and used when matching the same measured data with another corresponding calculated dose distribution. New templates were created for the films in the second measurement. Orthogonal dose profiles, horizontally and vertically, were used to verify the registration (figure 6). If the dose profiles did not match symmetrically, the points in the four-‐point-‐match were relocated in accordance with the result of the profile evaluations. The normalization was performed in the central part of the individual MLC opening. For D2:D5 a mean value of the individual openings was used for the normalization. In the B-‐series and C-‐series the central part in the largest open part of the MLC opening was used. Normalization was done with a 0.5 cm × 0.5 cm ROI for all openings, except A5, D5 and F5 there a 0.3 cm × 0.3 cm ROI was used because of the small MLC openings, and to avoid placing the normalization ROI in the sharp absorbed dose gradients. The median value within the ROI was used for normalization. A dose cut-‐off threshold of 10 % was used to exclude pixels that had received less than 10 % of the maximum calculated dose in the analysis. Dose difference pass rate was used as a measure of agreement between
Figure 5. The 30 cm × 30 cm × 30 cm phantom used in the calculations of the absorbed dose distributions. The A1 MLC opening is visualized with the corresponding calculated 3D dose distribution in EclipseTM. The phantom material was set to water in the TPS.
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the measured and calculated dose distribution. The dose difference pass rate gives the precentage of evaluated pixels that do not deviate more than a selected precentage. In the evaluation of the dose differences in this study and in the study by Götstedt et al (2015) a 3 % and a 5 % dose difference pass rate criterion was used.
Figure 6. Dose difference analyzes in RIT113. The calculated and the measured coronal dose planes in colored scale (left), the vertical and the horizontal absorbed dose profiles (upper middle and upper right) and the dose difference between the calculated and measured dose data visualized in 3D and 2D (lower middle and lower right).
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4. Results
4.1 Precision of the Film Measurement Procedure Pass rate values calculated for the different MLC openings differed depening on the investigated algorithm. Pass rate values for the criterion of 5 % and 3 % are shown in figure 7 and 8 respectively. The SD was calculated from the three film measurements and is shown in the figures as error bars. The pass rate values decreased with a more complex MLC opening. PBC showed in generall a lower pass rate value regerdless complexity compered to the other algorithms and AAA showed in generall a higher pass rate value regardless complexity. When a part of the field area is complex (series C) it seems to be not so complex for the algorithms, which also emerges for Götstedt et al (2015).
Figure 7. The measured pass rates for the 5 % criterion for the 30 different MLC openings. The pass rates were evaluated for the AAA, PBC, CC and AXB algorithm. The error bars correspond to 1 SD.
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1,#87,19# 2,#87,36# 3,#86,01# 4,#83,63# 5,#80,78#1,#78,11# 2,#76,49#3,#70,99#
4,#64,77#5,#53,58#
1,#85,77# 2,#81,55#3,#74,13#
4,#65,82#5,#60,63#
1,#81,95# 2,#80,92# 3,#77,40# 4,#74,44#5,#68,09#
1# 1,5# 2# 2,5# 3# 3,5# 4# 4,5# 5#
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MLC opening
Series F
1,#87,19# 2,#87,36# 3,#86,01# 4,#83,63# 5,#80,78#1,#78,11# 2,#76,49#3,#70,99#
4,#64,77#5,#53,58#
1,#85,77# 2,#81,55#3,#74,13#
4,#65,82#5,#60,63#
1,#81,95# 2,#80,92# 3,#77,40# 4,#74,44#5,#68,09#
1# 1,5# 2# 2,5# 3# 3,5# 4# 4,5# 5#
E.serien#
AAA# PBC# AcurosXB# CC#
Figure 8. The measured pass rates for the 3 % criterion for the 30 different MLC openings. The pass rates were evaluated for the AAA, PBC, CC and AXB algorithm. The error bars correspond to 1 SD.
16
The dose differences between measured and calculated absorbed dose distributions were larger than 3 % or 5 % exclusively close to the edges of the MLC opening. In figure 9 the colored dose differens maps for the deviations between measured and calculated dose distributions for the B:4 MLC opening are visualized.
AAA PBC AXB CC
B:4
Figure 9. Colored dose difference maps from the comparison of the absorbed dose distribution from a film measurement and the calculated dose distributions from the investigated dose calculation algorithms. The color scale gives the precentage dose differens.
17
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,84
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,90
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,85
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,80
!"!!!!!!!
!10,00!!!!!
!20,00!!!!!
!30,00!!!!!
!40,00!!!!!
!50,00!!!!!
!60,00!!!!!
!70,00!!!!!
!80,00!!!!!
!90,00!!!!!
0,00! 0,10! 0,20! 0,30! 0,40! 0,50! 0,60! 0,70! 0,80! 0,90! 1,00!
5"%"pass"rate"
Converted"Aperture"Metric"
Pencil"Beam"Serie!A! Serie!B! Serie!C! Serie!D! Serie!E! Serie!F!
r"="90,89"
The results for AAA from Götstedt et al (2015) was successfully reproduced for the investigated complexity metrics. Pass rates, with corresponding standard deviation for the evaluated dose differences between the measured and calculated absorbed dose distributions for the 30 MLC openings were plotted against the scores of the complexity metrics (figure 10). The SD was calculated from the three film measurements. The standard deviation, was most often within 3 % for the 5 % dose difference pass rate criteria and 4 % for the 3 % dose difference pass rate criteria. A higher pearsons´s r-‐value was found for all combinations of metrics and pass rate criteria compared to the film measurement by Götstedt et al (2015) (table 2).
Figure 10. The pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for AAA. A dose difference criterion of 5 % (left) and 3% (right) was used. The error bars correspond to 1 SD.
Anisotropic Analytical Algorithm
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,02,$$78,11$$$$$0,03,$$76,49$$$$$0,07,$$70,99$$$$$
0,11,$$64,77$$$$$
0,19,$$53,58$$$$$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,02,$78,10666667$0,03,$76,49$0,07,$70,99$
0,11,$64,77$
0,19,$53,58$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,00$ 0,10$ 0,20$ 0,30$ 0,40$ 0,50$ 0,60$ 0,70$ 0,80$ 0,90$ 1,00$
Pencil'Beam'Series$A$ Series$B$ Series$C$ Series$D$ Series$E$ Series$F$
r'='-0,89'
.
18
Table 2. Persons´s r-values from the evaluation of the pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for AAA. The persons´s r-values in the first column are from one film measurement performed by Götstedt et al (2015) and the persons´s r-values in the second column are from all three film measurements.
Götstedt et al (2015) This study Metric r (5 %) r (3 %) r (5 %) r (3 %) Conv. -‐0.76 -‐0.78 -‐0.80 -‐0.85 Edge. -‐0.79 -‐0.83 -‐0.84 -‐0.90
19
4.2 Different Dose Calculation Algorithms Dose difference pass rates when comparing the measured and calculated absorbed dose distributions was studied individually for PBC (figure 11), AXB (figure 12) and CC (figure 13). Pearson’s r-‐values were calculated for all the individual linear fits of the dose difference pass rates and the complexity metrics scores for the 30 MLC openings (table 3). The SD was calculated from the pass rate values from the three film measurements. High pearsons´s r-‐values were found for all combinations of metrics, pass rate criteria and algorithms.
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,89
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,93
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,95
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,94
Pencil Beam Convolution
Figure 11. The pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for PBC. A dose difference criterion of 5 % (left) and 3 % (right) was used. The error bars correspond to 1 SD.
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,02,$$78,11$$$$$0,03,$$76,49$$$$$0,07,$$70,99$$$$$
0,11,$$64,77$$$$$
0,19,$$53,58$$$$$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,02,$78,10666667$0,03,$76,49$0,07,$70,99$
0,11,$64,77$
0,19,$53,58$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,00$ 0,10$ 0,20$ 0,30$ 0,40$ 0,50$ 0,60$ 0,70$ 0,80$ 0,90$ 1,00$
Pencil'Beam'Series$A$ Series$B$ Series$C$ Series$D$ Series$E$ Series$F$
r'='-0,89'
20
Acuros XB
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,52
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,70
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,71
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,81
Figure 12. The pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for AXB. A dose difference criterion of 5 % (left) and 3% (right) was used. The error bars correspond to 1 SD.
!"!!!!!!!
!10,00!!!!!
!20,00!!!!!
!30,00!!!!!
!40,00!!!!!
!50,00!!!!!
!60,00!!!!!
!70,00!!!!!
!80,00!!!!!
!90,00!!!!!
0,00! 0,10! 0,20! 0,30! 0,40! 0,50! 0,60! 0,70! 0,80! 0,90! 1,00!
5"%"pass"rate"
Converted"Aperture"Metric"
Pencil"Beam"Serie!A! Serie!B! Serie!C! Serie!D! Serie!E! Serie!F!
r"="90,89"
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,02,$$78,11$$$$$0,03,$$76,49$$$$$0,07,$$70,99$$$$$
0,11,$$64,77$$$$$
0,19,$$53,58$$$$$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,02,$78,10666667$0,03,$76,49$0,07,$70,99$
0,11,$64,77$
0,19,$53,58$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,00$ 0,10$ 0,20$ 0,30$ 0,40$ 0,50$ 0,60$ 0,70$ 0,80$ 0,90$ 1,00$
Pencil'Beam'Series$A$ Series$B$ Series$C$ Series$D$ Series$E$ Series$F$
r'='-0,89'
21
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
r = -‐0,73
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00 3 %-‐ d
d pa
ss ra
te (%
) Converted aperture metric.
r = -‐0,85
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,85
0
20
40
60
80
100
0,00 0,20 0,40 0,60 0,80 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
r = -‐0,91
!"!!!!!!!
!10,00!!!!!
!20,00!!!!!
!30,00!!!!!
!40,00!!!!!
!50,00!!!!!
!60,00!!!!!
!70,00!!!!!
!80,00!!!!!
!90,00!!!!!
0,00! 0,10! 0,20! 0,30! 0,40! 0,50! 0,60! 0,70! 0,80! 0,90! 1,00!
5"%"pass"rate"
Converted"Aperture"Metric"
Pencil"Beam"Serie!A! Serie!B! Serie!C! Serie!D! Serie!E! Serie!F!
r"="90,89"
Collapsed Cone Convolution
Figure 13. The pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for CC. A dose difference criterion of 5 % (left) and 3% (right) was used. The error bars correspond to 1 SD.
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,01,$$76,45$$$$$
0,10,$$65,45$$$$$0,25,$$61,69$$$$$
0,40,$$51,74$$$$$
0,60,$$36,63$$$$$
0,02,$$74,86$$$$$0,07,$$69,93$$$$$
0,13,$$61,77$$$$$
0,18,$$54,79$$$$$
0,31,$$38,46$$$$$
0,01,$79,28$0,02,$78,29$0,04,$77,30$0,06,$74,48$0,10,$73,60$0,01,$$74,99$$$$$
0,05,$$65,69$$$$$
0,11,$$56,65$$$$$0,17,$$50,86$$$$$
0,27,$$45,74$$$$$
0,02,$$78,11$$$$$0,03,$$76,49$$$$$0,07,$$70,99$$$$$
0,11,$$64,77$$$$$
0,19,$$53,58$$$$$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,02,$78,10666667$0,03,$76,49$0,07,$70,99$
0,11,$64,77$
0,19,$53,58$
0,00,$$84,21$$$$$0,01,$$81,37$$$$$
0,04,$$76,88$$$$$
0,11,$$67,40$$$$$
0,35,$$47,91$$$$$
0,00$ 0,10$ 0,20$ 0,30$ 0,40$ 0,50$ 0,60$ 0,70$ 0,80$ 0,90$ 1,00$
Pencil'Beam'Series$A$ Series$B$ Series$C$ Series$D$ Series$E$ Series$F$
r'='-0,89'
22
Pearsons´s r-‐values for the dose difference comparisions between measured and calculated absorbed dose distributions for the different algorithms were calculated (table 3).
Algorithm Metric r (5 %) r (3 %) AAA Conv. -‐0.80 -‐0.85 AAA Edge. -‐0.84 -‐0.90 PBC Conv. -‐0.89 -‐0.93 PBC Edge. -‐0.94 -‐0.95 AXB Conv. -‐0.52 -‐0.70 AXB Edge. -‐0.71 -‐0.81 CC Conv. -‐0.73 -‐0.85 CC Edge -‐0.85 -‐0.91
Table 3. The pearson´s r-values for the different algorithms and metrics.
23
4.3. Different Grid Size The impact of different dose calculation resolution on the correlation between metric score and dose difference passrate was examined. This is shown for the converted aperture metric and edge area metric in figure 14 and 15 respectively. The SD was calculated from the three film measurements and is shown as error bars in the figures. A correlation was found for all combinations of metrics, pass rate criteria and dose calculation resolution. The pass rates for the evaluated dose distributions were genereally increased for higher dose calculation resolutions. However, only minor differences in the correlation values for the two investigated metrics versus the evaluated pass rates were observed when altering the calculated dose resolution (table 4).
0 10 20 30 40 50 60 70 80 90
100
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00
5 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
0 10 20 30 40 50 60 70 80 90
100
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Converted aperture metric
Anisotropic Analytical Algorithm Converted Aperture Metric
Figure 14. The pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for different grid sizes. A dose difference criterion of 5 % and 3 % was used. The error bars correspond to 1 SD.
0,56,%72,61%
0,75,%52,10% 0,89,%48,64%0,96,%42,67%
1,00,%30,02%
0,5,%69,76%0,64,%62,75%
0,74,%50,43%
0,75,%37,99% 0,85,%35,43%
0,44,%77,28%0,47,%66,90%
0,49,%74,36%0,51,%69,84%0,53,%70,66%0,52,%62,76%
0,67,%57,73%0,77,%48,07%
0,90,%36,04%1,00,%28,83%
0,54,%66,16%0,56,%69,30%0,65,%62,52%
0,74,%51,07%
0,90,%34,65%
0,42,%79,78%0,47,%69,99%
0,56,%65,04%
0,70,%53,23%
1,00,%35,83%
0,56,%89,41% 0,75,%88,62% 0,89,%84,74%0,96,%78,96%1,00,%71,18%
0,5,%89,21% 0,64,%86,02% 0,74,%86,26%0,75,%83,85% 0,85,%79,65%0,44,%90,38%0,47,%91,56%0,49,%90,27%0,51,%86,27%0,53,%89,83%
0,52,%96,07%0,67,%89,47% 0,77,%87,38% 0,90,%85,58%
1,00,%79,61%
0,54,%93,09%0,56,%92,63%0,65,%90,18%0,74,%91,99% 0,9,%87,55%0,42,%93,28%0,47,%94,27%0,56,%93,61% 0,70,%92,42% 1,00,%90,13%0,56,%90,85%
0,75,%84,55% 0,89,%80,72%0,96,%76,28%1,00,%71,11%
0,50,%86,39% 0,64,%84,57% 0,74,%82,10%0,75,%77,32%
0,85,%59,00%
0,44,%90,31%0,47,%90,12%0,49,%88,74%0,51,%85,33%0,53,%87,74%0,52,%88,11%0,67,%81,48% 0,77,%79,35%
0,90,%71,86%1,00,%69,24%
0,54,%87,19%0,56,%87,36%0,65,%86,01%0,74,%83,63% 0,90,%80,78%0,42,%91,24%0,47,%89,73%0,56,%88,46%
0,70,%82,74%1,00,%73,93%
0,00% 0,10% 0,20% 0,30% 0,40% 0,50% 0,60% 0,70% 0,80% 0,90% 1,00%
DOSMATRISINVERKAN-5%0-PASSRATE-
0,5%cm% 0,125%cm% 0,25%cm%
24
Anisotropic Analytical Algorithm Edge Area Metric
Figure 15. The pass rates for the dose difference evaluation of the measured and calculated dose distributions versus the complexity metric scores for different grid sizes. A dose difference criterion of5 % and 3 % was used. The error bars correspond to 1 SD.
0 10 20 30 40 50 60 70 80 90 100
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00
3 %-‐ d
d pa
ss ra
te (%
)
Edge area metric
0
10
20
30
40
50
60
70
80
90
100
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00
5 %-‐ d
d pa
ss ra
te(%
)
Edge area metric
0,56,%72,61%
0,75,%52,10% 0,89,%48,64%0,96,%42,67%
1,00,%30,02%
0,5,%69,76%0,64,%62,75%
0,74,%50,43%
0,75,%37,99% 0,85,%35,43%
0,44,%77,28%0,47,%66,90%
0,49,%74,36%0,51,%69,84%0,53,%70,66%0,52,%62,76%
0,67,%57,73%0,77,%48,07%
0,90,%36,04%1,00,%28,83%
0,54,%66,16%0,56,%69,30%0,65,%62,52%
0,74,%51,07%
0,90,%34,65%
0,42,%79,78%0,47,%69,99%
0,56,%65,04%
0,70,%53,23%
1,00,%35,83%
0,56,%89,41% 0,75,%88,62% 0,89,%84,74%0,96,%78,96%1,00,%71,18%
0,5,%89,21% 0,64,%86,02% 0,74,%86,26%0,75,%83,85% 0,85,%79,65%0,44,%90,38%0,47,%91,56%0,49,%90,27%0,51,%86,27%0,53,%89,83%
0,52,%96,07%0,67,%89,47% 0,77,%87,38% 0,90,%85,58%
1,00,%79,61%
0,54,%93,09%0,56,%92,63%0,65,%90,18%0,74,%91,99% 0,9,%87,55%0,42,%93,28%0,47,%94,27%0,56,%93,61% 0,70,%92,42% 1,00,%90,13%0,56,%90,85%
0,75,%84,55% 0,89,%80,72%0,96,%76,28%1,00,%71,11%
0,50,%86,39% 0,64,%84,57% 0,74,%82,10%0,75,%77,32%
0,85,%59,00%
0,44,%90,31%0,47,%90,12%0,49,%88,74%0,51,%85,33%0,53,%87,74%0,52,%88,11%0,67,%81,48% 0,77,%79,35%
0,90,%71,86%1,00,%69,24%
0,54,%87,19%0,56,%87,36%0,65,%86,01%0,74,%83,63% 0,90,%80,78%0,42,%91,24%0,47,%89,73%0,56,%88,46%
0,70,%82,74%1,00,%73,93%
0,00% 0,10% 0,20% 0,30% 0,40% 0,50% 0,60% 0,70% 0,80% 0,90% 1,00%
DOSMATRISINVERKAN-5%0-PASSRATE-
0,5%cm% 0,125%cm% 0,25%cm%
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The persons´s r-‐values from the dose difference comparision between measured and calculated absorbed dose distributions for different grid sizes were calculated (table 4). The highest pearsons´s r-‐value (r = -‐0.98) was calculated between edge area metric and 3 % dose difference for 0.5 cm dose calculation resolution. The lowest pearsons´s r-‐value was found between the edge of the area index and 5 % dose difference for 0.125 cm grid size.
Pearsons´s r-values
Metric Grid size (cm) 5 % pass rate 3 % pass rate
Conv. 0.5 -‐0.82 -‐0.85
Edge. 0.5 -‐0.95 -‐0.98
Conv. 0.25 -‐0.80 -‐0.85
Edge. 0.25 -‐0.84 -‐0.90
Conv. 0.125 -‐0.85 -‐0.86
Edge. 0.125 -‐0.72 -‐0.73
Table 4. Persons´s r-values for the correlation between the metrics and the pass rates for different grid sizes. Dose difference criteria of 5 % and 3 % were used.
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5. Discussion Compared with the film measurement in the study of Götstedt et al (2015), this study demonstrated a stronger correlation between both metrics and pass rate criteria. Reasons for the stronger correlation demonstrated in this study for the AAA algorithm can be because of a more comprehensive statistical data. The study by Götstedt et al (2015) was based on one film measurement, while this study was instead based on three measurements. The spread of the pass rate values could arise from the different film calibrations that have been used in the first measurement of Götstedt et al (2015) and in this study, due to the use of different film batches. Another thing, that could affect the pass rate, is the user-‐dependent registration of the measured and the calculated dose distribution. For the 3 % pass rate criteria, the spread in the result is greater than for the 5 % pass rate criteria. The dose difference histogram for the measured and the calculated dose ditributions are visually shown to be close to normally distributed. The 3 % criterion is generally placed in the steep gradient of the normal distribution, while the 5 % criterion is positioned further out in a more flat part of the distribution. It leads to a greater dependance on how well the film and the calculated dose distribution matched for the number of pixels that fall within 5 %. One reason for the difference in the correlation coefficients between the different dose calculation algorithms can be related to the quadratic fields of series A. With respect to the linear fit it can been seen that the pass rate for the MLC openings in series A deviates compared to the other MLC openings. Exclusion of series A gave an equivalent correlation for all algorithms (table 6 appendix). This could be due to 1) Each metric assigns the square fields a too high complexity score, 2) The MLC openings receives a higher pass rate value than what they should have.
The first reason could be due to the leakage between the edges of the closed MLC leaves (figure 16 appendix). However analysis made for the series A when the leakage is excluded has not affected the result substantially. The closed MLC leaf pairs are not included in the complexity score calculation process which could contradict to higher complexity scores. The leakage between the MLC leaves is not measured in this study due to the 10 % cut-‐off. That can be a reason a too high pass rate value. The other reason is probably due to something in the film and evaluation process. Götstedt et al (2015) found that the film measurements generated higher pass rate values compared to EPID measurements. This was assumed to come from that the EPID measurements were not normalized compared to the film measurement. In their results, the difference between the pass rates for EPID and film measurement was greatest in series A. In the evaluation of the films the registration has been based on the AAA algorithm. It could have penalized the other algorithms because of the dependance of the shortcomings of AAA. This has been investigated by calculating all openings with Acuros
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XB (0.1 cm grid size) and creating an independent registration template for AXB. It turned out that match with Acuros XB differed 0-‐3 pixels (1 pixel = 0.0169 cm) against the original AAA registration, which was adopted as negligible. The evaluation of some fields with the new AXB template showed only negligible increase or decrease of the pass rates. The evaluation of the edge area metric showed slightly higher Pearson’s r-‐values than the evaluation of the converted aperure metric. One explanation for this may be that a large part of the calculation and MLC position errors occur in edges of the MLC opening, i.e. the penumbra region (figure 9 and figure 16, appendix). Götstedt et al (2015) have also shown by EPID measurements that the edges of the fields contribute most to the calculation errors. Edge area metric is based on the ratio of the edge area and the total area and could perhaps provide a better measure of the proportion of penumbra, since it takes the MLC opening edges more into account compared to converted aperture metric. The latter metric is based on the distance between the MLC leafs and does not specifically take penumbras into account. This needs to be investigated further in order to draw any conclusions. The edge area metric has proved to give a higher r-‐value for EPID measurements as well (Götstedt et al, 2015). When evaluated the pass rate two different dose differens criteria have been used. Pixels that have received a absorbed dose that deviate more than 5 % or 3 % of the estimated maximum dose does not pass the criteria. The Pearson’s r-‐vaulues are slightly higher for the 3 % pass rate, compared with the 5 % pass rate. One explanation can be due to the fact that fewer pixels manages the 3 % dose difference critera which indicates a bigger fail rate. When the metric is made to just give one measure of the error, it could be that the 3 % criterion give a fairer picture of the complexity. This needs to be further investigated. The better correlation of the 3 % criterion has not been demonstrated for EPID measurements (Götstedt et al, 2015). In this study EBT3 film measurements have been used as dosimetry system. It is important to note the uncertainties in the film measurement for example in the calibration and registration processes. The advantage of film measurements is the very high detection resolution. The highest pearsons´s r-‐value i.e. correlation coefficient was calculated for the lowest resolution i.e. highest grid size because of the steeper line. The lower correlation coefficient was between the edge area metric and 5 % dose difference of 0.125 cm grid size because of the steeper line. The reason for the different slopes may have to do with more and less smeared penumbras. Less smeared penumbras appears with higher dose calculation resolution and more smeared penumbras appears with lower dose calculation resolution. Dose difference, i.e. calculation and delivery errors, is present mainly at the edges there the edge area metric is working. The edge area that has a static area of 10 mm along the edges could maybe overestimate the area of error. One could
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imagine that the edge area metric would perform better if the edge area was chosen less to be less than 10 mm when using the 0.125 cm grid size. This would need to be further investigated in future studies. That higher dose calculation resolution reduces the error in the estimated absorbed dose has been shown in a previous study by Ong et al (2011). The study was based on film measurements in polysterene and cork with square shaped MLC openings. The conclusion was that a 0.10 cm grid size compared with 0.25 cm grid size in some situations gave a 20 % better agreement between the calculated and measured dose distribution. Calculations were performed with the AAA (V.8). A later version of the algorithm AAA (v.10) was found to further reduce the error. It may be that this also applies to other field shapes and later versions of the AAA, but it must be investigated further in order to be confirmed The pass rate values for the 0.5 cm grid size has the highest spread i.e. standard devidation. It may be due to that a lower dose calculation resolution provides a more stretched dose profile which makes it more difficult to register the calculated and measured dose profile in the evaluation process. However, this has not been investigated. In future studies, it would be interesting to compare the measured dose distributions with MC simulations.. MC is often considered as a gold standard for estimation of absorbed dose (referens) It would also be interesting to use 0.5 cm and 0.125 cm grid size for the PBC, CC and AXB algorithms.
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6. Conclusions The conclusions from Götstedt et al (2015) were confirmed for AAA. The average spread of the dose difference pass rate values from the three different film measurements, i.e. the standard deviation, was most often within 3 % for the 5 % dose difference pass rate criteria and 4 % for the 3 % dose difference pass rate criteria. The scores for converted aperture metric and edge area metric correlate with the difference between measured and calculated dose distribution, also for the PBC, CC, and AXB algorithm, as well as for the AAA calculations with different dose calculation resolution.
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Appendix
MLC opening Depth (cm)
SSD (cm) MU Dose (Gy)
A1 10 90 261 2 A2 10 90 276 2 A3 10 90 290 2 A4 10 90 304 2 A5 10 90 303 2 B1 10 90 250 2 B2 10 90 254 2 B3 10 90 257 2 B4 10 90 257 2 B5 10 90 258 2 C1 10 90 249 2 C2 10 90 250 2 C3 10 90 251 2 C4 10 90 252 2 C5 10 90 253 2 D1 10 90 246 2 D2 10 90 247 2 D3 10 90 249 2 D4 10 90 249 2 D5 10 90 250 2 E1 10 90 256 2 E2 10 90 256 2 E3 10 90 257 2 E4 10 90 259 2 E5 10 90 263 2 F1 10 90 241 2 F2 10 90 245 2 F3 10 90 250 2 F4 10 90 259 2 F5 10 90 279 2
Table 5. Parameters at the radiation of the 30 different MLC openings.
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With serie A Without serie A Algorithm Metric Pass rate
(5 %) Pass rate
(3%) Pass rate
(5 %)
Pass rate (3 %)
Difference (5 %)
Difference (3 %)
AAA Conv. -‐0.80 -‐0.85 -‐0.89 -‐0.9 11.89 6.08 AAA Edge. -‐0.84 -‐0.90 -‐0.85 -‐0.87 1.20 -‐3.68 PBC Conv. -‐0.89 -‐0.93 -‐0.94 -‐0.83 5.59 -‐10.27 PBC Edge. -‐0.94 -‐0.95 -‐0.94 -‐0.95 0.36 -‐0.39 AXB Conv. -‐0.52 -‐0.70 -‐0.88 -‐0.87 69.10 23.79 AXB Edge. -‐0.71 -‐0.81 -‐0.89 -‐0.86 25.26 6.29 CC Conv. -‐0.73 -‐0.85 -‐0.9 -‐0.89 23.10 4.87 CC Edge. -‐0.85 -‐0.91 -‐0.88 -‐0.89 3.75 -‐1.79
Table 6. The Pearsons´s r-values for the correlation between pass rates and metrics. Different algorithms were investigated. The correlation was evaluated with and without the a-serie.
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Comparisons between Calculated Dose Distributions with AAA as Reference
AAA Vs. PBC
AAA Vs. CC
AAA Vs. AXB
A:1 A:5
Figure 16. Colored dose difference maps from the comparison of the calculated absorbed dose distribution from AAA and the calculated dose distributions from the other investigated dose calculation algorithms.
