On the quantification of the dosimetric accuracy of collapsed cone convolution superposition (CCCS) algorithm for small lung volumes using IMRT

Specialized techniques that make use of small field dosimetry are common practice in today's clinics. These new techniques represent a big challenge to the treatment planning systems due to the lack of lateral electronic equilibrium. Because of this, the necessity of planning systems to overcome such difficulties and provide an accurate representation of the true value is of significant importance. Pinnacle3 is one such planning system. During the IMRT optimization process, Pinnacle3 treatment planning system allows the user to specify a minimum segment size which results in multiple beams composed of several subsets of different widths. In this study, the accuracy of the engine dose calculation, collapsed cone convolution superposition algorithm (CCCS) used by Pinnacle3, was quantified by Monte Carlo simulations, ionization chamber, and Kodak extended dose range film (EDR2) measurements for 11 SBRT lung patients. Lesions were < 3.0 cm in maximal diameter and <27.0 cm3 in volume. The Monte Carlo EGSnrc\BEAMnrc and EGS4\MCSIM were used in the comparison. The minimum segment size allowable during optimization had a direct impact on the number of monitor units calculated for each beam. Plans with the smallest minimum segment size (0.1 cm2 to 2.0 cm2) had the largest number of MUs. Although PTV coverage remained unaffected, the segment size did have an effect on the dose to the organs at risk. Pinnacle3‐calculated PTV mean doses were in agreement with Monte Carlo‐calculated mean doses to within 5.6% for all plans. On average, the mean dose difference between Monte Carlo and Pinnacle3 for all 88 plans was 1.38%. The largest discrepancy in maximum dose was 5.8%, and was noted for one of the plans using a minimum segment size of 0.1 cm2. For minimum dose to the PTV, a maximum discrepancy between Monte Carlo and Pinnacle3 was noted of 12.5% for a plan using a 6.0 cm2 minimum segment size. Agreement between point dose measurements and Pinnacle3‐calculated doses were on average within 0.7% in both phantoms. The profiles show a good agreement between Pinnacle3, Monte Carlo, and EDR2 film. The gamma index and the isodose lines support the result. PACS number: 87.56.bd

(IMRT) plans make use of several superimposed small fields to achieve a highly conformal dose distribution to the target volume and spare healthy tissue.
IMRT treatment planning systems calculate an ideal intensity map for each field using optimization routines with physical dose objectives set by the user. (2) Once the optimization completes, the optimized fluence for each field of the plan is realized into several small segments. These segments of small aperture are generated by the segmentation process that produces the delivery sequence of the multileaf collimator. Under such conditions of small field geometries, the electronic equilibrium can be lost, making it challenging for the dose calculation algorithm to accurately predict the dose, especially in the presence of tissue heterogeneities. (1) IMRT planning utilizes iterative optimization techniques, during which the dose needs to be continuously calculated. To improve the efficiency and speed of such implementations, a pencil beam algorithm is typically used for the intermediate (iterative) dose calculation steps, thus introducing convergence errors. (3) It is important to always perform a full 3D dose calculation at the conclusion of the optimization to evaluate the dose the patient will truly receive, especially since it is known that the pencil beam implementations are unreliable in the presence of tissue heterogeneities.
The traditional two-step process of IMRT inverse planning may produce more segments and MUs than necessary-largely due to the conversion of the fluence profiles to deliverable MLC settings. However, with more advance techniques like direct machine parameter optimization (DMPO), the plan will not degrade because of the lack of post processing (no need of fluence profiles conversion to MLC settings). (4) When calculating the dose in a low-density medium such as lung, the use of narrow beams may produce significant perturbations that are energy and density dependent and ultimately affect the accuracy of the dose calculation. This problem is more pronounced when the TPS uses simple, one-dimensional density scaling. (5)(6)(7)(8) The level of accuracy improves with the use of sophisticated treatment planning algorithms (9)(10)(11)(12)(13)(14)(15)(16)(17) where multisource modeling is included, allowing a more accurate dose prediction for small fields and under non-equilibrium conditions. (18,19) It has been shown that the accuracy of small field dosimetry is greatly improved when Monte Carlo simulations are employed, especially for beam sizes less than 3.0 by 3.0 cm 2 in inhomogeneous media. (20)(21)(22)(23) Currently, the model-based dose calculation methods considered most accurate in radiotherapy are Monte Carlo transport and the convolution/superposition method. (24) Researchers have reported various techniques and devices used for obtaining dosimetric input data for small and complicated photon beams. (25)(26)(27)(28)(29) Francescon et al. (30) reported that Pinnacle 3 overestimates the dose by up to 8% for narrow 1.0 cm wide photon segments. Azcona et al. (31) reported an overestimation of calculated dose between 4% and 14% for fields of widths between 1 and 3 cm.
Sophisticated Monte Carlo codes are becoming available in parallel to the emerging use of small field radiotherapy techniques. (32) By explicitly modeling the particle transport, complete Monte Carlo simulations are expected to result in the highest dose calculation accuracy (33) and would become the standard for future planning systems. However, due to the long time required for a MC simulation, clinical implementation is currently not possible.
The quantification of the dose calculation accuracy for treatment planning systems is a matter of high importance in radiotherapy, as inaccuracies may lead to patient complications. This study has a two-fold purpose: first, the dose calculated using the collapsed cone convolution superposition method used in Pinnacle 3 TPS is compared against Monte Carlo dose calculations, ion chamber, and EDR2 film measurements; second, the effect of the smallest segment size allowed during optimization is examined in terms of dose calculation accuracy, and dose to organs at risk and PTV coverage. Although several studies exist that directly compare the CCCS dose calculations against Monte Carlo calculations, there has not been a study to date that includes the above stated purposes.

A.1 Patient selection
Eleven patients (n = 11) were randomly chosen for this study. All the patients were treated using a stereotactic body radiation therapy (SBRT) technique. The patient selections were restricted such that the tumor size was < 3.0 cm in maximum diameter and the volume was < 27.0 cc. The location and target volumes of each patient are shown in Table 1.
All patients were scanned in the supine position using a 16 slice GE LightSpeed (GE Medical, Waukesha WI), and immobilized using the Body Pro-Lok system (CIVCO Medical Solutions, Iowa City IA). A single radiation oncologist delineated the gross tumor volume (GTV) and organs at risk (OAR) using a free breathing scan. CT images and structures were exported to Pinnacle 3 (Philips Medical, Fitchburg WI) treatment planning system through DICOM and DICOM-RT.

A.2 Patients' treatment plans
For each patient, eight optimized plans were created varying the minimum allowable segment size, while maintaining the same optimization dose constraints. The dose prescribed to the target was 45.0 Gy in three fractions (see Table 2). Five coplanar beams were used in all cases; these were optimally placed in order to avoid critical organs. All plans were optimized for delivery using a Varian 2100EX (Varian Medical Systems, Palo Alto, CA) 6 MV photon beam equipped with a 120 Millennium multileaf collimator (MLC). The minimum allowable segment sizes were varied from 0.1 cm 2 to 6.0 cm 2 (0.1, 0.25, 1.0, 2.0, 3.0, 4.0, 5.0, and 6.0 cm 2 ). Smaller segment sizes allow for higher spatial resolution of the optimized fluence map and, thus, permit greater flexibility during optimization. However, the use of smaller segment sizes could introduce unwanted electronic disequilibrium effects. On the other hand, by limiting the maximum size to 6.0 cm 2 , the optimization is more restricted and might fail to provide an optimal solution. It should be noted that the minimum size of the segment also affects the number of segments created and total number of monitor units (MU) required for the delivery.
The direct machine parameter optimization (DMPO) within Pinnacle 3 was used during optimization for all plans. Utilizing the DMPO option eliminates the need for optimization conversion and, beams' fluence generated correspond to deliverable ones.
After optimization, a final dose calculation using the collapsed cone convolution superposition (CCCS) algorithm (9) was performed. Dose grid size used for calculations was 0.2 cm by 0.2 cm by 0.2 cm. Special care was taken during the definition of the dose grid extent in order to ensure complete enclosure of all OARs.

A.3 Monte Carlo calculations
Monte Carlo calculations for each of the optimized fluence plans were performed using both patient geometry and two phantom geometries. CT scans from each patient and the CT scans of the two phantoms were converted to Monte Carlo geometry. A total of 3 by 88 = 264 Monte Carlo dose calculations were performed. Monte Carlo calculations were performed in two steps. First, a phase space file of the linear accelerator was created using the EGSnrc/BEAMnrc system. (34) Geometry and material composition used in the simulation were based on the specifications of the linear accelerator treatment head as provided by the manufacturer. The cutoff energies used for the simulations were 700 keV for electrons and 10 keV for photons. Energy thresholds for X-ray production (AE) and for bremsstrahlung production (AP) were 700 keV and 10 keV, respectively. Results of the LINAC simulation were in agreement (± 1% or within 1 mm) with the measured PDD curves and the dose profiles at various depths in water obtained with a 0.125 cc PTW-Freiburg ion chamber. After the Monte Carlo commissioning of the linear accelerator, a phase space file was created before the jaws in order to be used in the dose calculation simulations (Fig. 1).
The Monte Carlo dose calculations were performed using the EGS4/MCSIM user code. The EGS4/MCSIM code system can accurately calculate patient dose distributions by simulating the accelerator head leakage, MLC leaf leakage and scatter, and the effect of beam modifiers such as collimator jaws, wedges, and blocks. Furthermore, calculation times are 10-30 times faster than other widely available general-purpose Monte Carlo codes. (35)   The EGS4/MCSIM code was used in this work due to its extended functionality. The code is capable of calculating dose in a patient given the intensity map (ODM) or the Radiation Therapy Plan (RTP) file, which includes patient setup parameters and beam and leaf-sequence information. The ODM files generated by Pinnacle 3 were used as input for EGS4/MCSIM. Based on the dose per incident particle, as derived from calculations using calibration conditions, EGS4/MCSIM can calculate the absolute dose to the patient. Moreover, if contours exist in the patient geometry from computed tomography (CT) images, doses to each organ may be calculated and DVHs generated for all contoured organs.

A. 4 Ion chamber and film measurements
For each of the resulting 88 plans, two IMRT QA verification plans were created using a homogenous and heterogeneous phantom (Fig. 2). The heterogeneous phantom (Standard Imaging, Middleton WI) was used in order to mimic the patient geometry during radiation delivery. Each phantom was structured so that ionization chamber could be incorporated, as well as an extended dose radiographic (EDR2) film (Kodak Inc., Rochester NY). The film was placed within the phantom to measure the planar dose distribution. Verification plans were calculated and delivered with all of the beams positioned in planned angles. This resulted in 176 verification plans.
A vented cylindrical ionization chamber (PTW N31003, New York NY) with a sensitive volume of 0.3 cc was used for all measurements. Measured point doses from the ion chamber were compared against their respective calculated point dose from the TPS. The film dose measurements were compared to their respective calculated planar doses exported from Pinnacle 3 . Film calibration was performed by exposing films to a dose range of 0.1 to 4.0 Gy using a step wedge with known dose values at the center of each step. (36) All films were scanned on a Vidar 16-bit scanner (VIDAR Systems Corporation Herndon, VA) and analyzed using the RIT113v5 (Radiological Imaging Technology, Colorado Springs, CO), software platform.

A.1 Effect of minimum segment size on plan quality
The minimum segment size allowable during optimization had a direct impact on the number of monitor units calculated for each beam. Plans with the smallest minimum segment size (0.1 cm 2 to 2.0 cm 2 ) had the largest number of MUs per field (Table 3). Dose statistics for the planning target volumes of all of the patients are shown in Table 4. Small variations in the PTV dose statistics were noted, leading to the conclusion that there is no significant dependence of the PTV coverage on the minimum allowable segment size. Although PTV coverage remained unaffected, the segment size did have an effect on the dose to the organs at risk. When segment sizes are large, the minimum segment shape is comparable to the aperture size and thereby limits the spatial resolution of the deliverable fluence. This limitation affects the sparing of critical structures, particularly those adjacent to the target volume. The dose to the organs at risk was shown to increase overall for very small and large minimum segment sizes allowable (Table 5).
Small differences were noted in the DVHs as the minimum segment sizes were varied for the target volumes (Fig. 3). Larger discrepancies were witnessed in the DVHs for the organs at risk with the exception of the lung. The DVH of the lung for each patient was not significantly different among the various optimized plans. Different results were observed for the spinal cord, esophagus, and trachea DVHs in which it can be observed that the segment size had an influence in the dose. The location of the tumor relative to the heart for the sample patient makes it difficult to draw any conclusive results. Similar results can be observed for the rest of the patients. Figure 3 shows the DVHs of all eight plans for patient 1 for: (1) the PTV, (2) the lung, (3) spinal cord, (4) the esophagus, (5) the trachea, and (6) the heart. Table 3. Mean MU per field as a function of minimum segment size for each patient calculated using the CCCS algorithm.  378  357  381  294  270  263  258  Patient 2  325  324  313  307  288  275  282  271  Patient 3  362  366  372  320  318  301  295  287  Patient 4  391  391  402  462  355  321  314  285  Patient 5  365  368  347  371  320  314  303  298  Patient 6  334  335  324  405  294  288  287  274  Patient 7  344  345  334  308  304  300  289  276  Patient 8  359  357  344  433  327  318  313  298  Patient 9  368  341  358  365  337  336  336  321  Patient 10  355  356  357  366  311  303  299  282  Patient 11  368  370  332  401  326  324  314  298   Mean  358  357  349  374  316  305 300 286

A.3 Ion chamber and film measurements
Using both phantoms, measurements were acquired using a PTW 0.3 cc ionization chamber and radiographic EDR2 film. Point absolute dose measurements using the ionization chamber were made for all plans. Agreement between point dose measurements and Pinnacle 3 calculated doses were on average within 0.7% in both phantoms (see Table 7). Coronal planar doses at the level of the film were also exported. The dose to the center of the planar dose was compared between measurements and calculations. The agreement in this case was inferior to the point measurements. This is probably due to uncertainties in the film calibration curve and inaccuracy in determining the "center" of each step. Observing the absolute film doses at the center between the solid and lung phantom measurements and the respective TPS calculations, it is clear that better agreement is achieved in the case where the solid phantom was used. This is due to the difference in the phantoms composition and to the inhomogeneities embedded in the lung phantom (Solid Acrylic (Virtual Water, StandardImaging, Middleton, WI)) and two wood slabs lung tissue equivalent. This heterogeneous phantom gives the closest representation of a real clinical case in comparison to the solid water phantom in which case the difference in the results gives a significant representation of the actual plan delivered in a patient. These results are summarized in Table 7 Planar doses exported from Pinnacle 3 were compared against their respective film measurements. The isodose distribution, gamma index using 2 mm DTA and 3% dose difference, and profiles were used for the evaluation of the TPS performance ( Figs. 7 and 8). The figures show a good agreement between Pinnacle 3 and film measurements in the high-dose region, in which case the result is confirmed with the isodose lines and gamma index. Small differences can be seen in the low-dose regions which can be explained by the reasons stated above.

IV. dISCuSSIOn
The average values of the percent difference between Pinnacle 3 and MC for the minimum, maximum, and mean doses characterizes the ability of Pinnacle 3 to accurately spare organs at risk while at the same time cover the PTV. The results showed that Pinnacle 3 is able to match the predictions made by the Monte Carlo simulations to within a few percent differences with the understanding that structures such as the spinal cord, trachea, and esophagus-typically small in volume-may in some circumstances be misleading. This is partly due to small differences in the conversion of the contours from Pinnacle 3 to Monte Carlo phantoms because of voxel size limitations which create potential discrepancies in the calculated volume. However, overall, high-dose regions were accurately predicted by Pinnacle 3 .
Superimpositions of the DVHs showed that Pinnacle 3 is able to obtain good coverage of the PTV independent of the segment size used. For the organs at risk, the TPS showed good agreement in the coverage of the total lung; as for the spinal cord, the location of the tumor influenced the dose statistics. Pinnacle 3 is able to deliver the prescribed dose to the PTV independent of the segment size used indicating that the planning system is able to model the difficulties associated with small fields.
The Monte Carlo codes EGSnrc\BEAMnrc and EGS4\MCSIM were used to calculate the particle transport to obtain the absorbed dose with the help of the ODMs by Pinnacle 3 . These codes were used because they have shown that they provide the feasibility and flexibility to give accurate results. The number of histories used was chosen to provide a standard deviation of less than 2%. The improved Monte Carlo statistics lead to confirmation of good agreement among Pinnacle 3 , MC and ion chamber measurements as shown in Table 7.
Agreement between point dose measurements and Pinnacle 3 calculated doses were, on average, within 0.7% in both phantom geometries. Better agreement was observed between Pinnacle 3 and the solid phantom as opposed to the inhomogeneous phantom. This is due probably to the difference in the phantom's composition and to the inhomogeneities embedded in the lung phantom. Using the inhomogeneous phantom, however, provides a closer representation of real patient anatomy.

V. COnCLuSIOnS
Agreement between Pinnacle 3 and Monte Carlo was within ± 2% for the target mean dose, while higher discrepancies (up to 4%) were observed for the minimum and maximum doses. For the ipsilateral lung, a difference in the maximum dose of up to 7%, and 2% for the mean dose was noted. Small differences in the total coverage of the PTV were found for all cases as a function of segment size. Good agreement between Pinnacle 3 and MC using dose profiles, isodose distributions, and Gamma Index analysis verified the results-particularly in the high dose region.