Evaluation of the AAA Treatment Planning Algorithm for SBRT Lung Treatment: Comparison with Monte Carlo and Homogeneous Pencil Beam Dose Calculations

Transcription

1 Journal of Medical Imaging and Radiation Sciences Journal of Medical Imaging and Radiation Sciences 43 (2012) Journal de l imagerie médicale et des sciences de la radiation Evaluation of the AAA Treatment Planning Algorithm for SBRT Lung Treatment: Comparison with Monte Carlo and Homogeneous Pencil Beam Dose Calculations Ermias Gete, PhD a *, Tony Teke, MSc b and William Kwa, PhD a a British Columbia Cancer Agency-Vancouver Center, Vancouver, BC, Canada b Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada ABSTRACT Purpose: To evaluate the dose calculation accuracy of the Varian Eclipse anisotropic analytical algorithm (AAA) for stereotactic body radiation therapy (SBRT), and to investigate the dosimetric consequences of not applying tissue heterogeneity correction on complex SBRT lung plans. Materials and Methods: Nine cases of non small-cell lung cancer (NSCLC) that were previously treated with SBRT at our center were selected for this study. Following Radiation Therapy Oncology Group 0236, the original plans were calculated using pencil beam without heterogeneity correction (PBNC). For this study, these plans were recalculated by applying tissue heterogeneity correction with the AAA algorithm and with the Monte Carlo (MC) method, keeping the number of monitor units the same as the original plans. Two kinds of plan comparison were made. First, the AAA calculations were compared with MC. Second, the treatment plans that were calculated with AAA were compared with the original PBNC calculations. The following dose-volume parameters were used for the comparison: V 100% ; V 90% ; the maximum, the minimum, and the mean planning target volume (PTV) doses (D max,d min, and D mean, respectively); V 20Gy, V 15Gy,V 10Gy,V 5Gy ;D mean for the lung; and D max for the critical organs. Results: Comparable results were obtained for AAA and MC calculations: except for Dmax, Dmin, and Dmean, the differences in the patient-average values of all of the PTV dose parameters were less than 2%. The largest average difference was observed for Dmin ( %). Average differences in all the lung dose parameters were under 0.2%, and average differences in normal tissue Dmax were under 0.3 Gy, except for the skin dose. There were appreciable differences in the PTV and normal tissue dosevolume parameters when comparing AAA and PBNC calculations. * Corresponding author: Ermias Gete, PhD, British Columbia Cancer Agency-Vancouver Center, 600 W. 10th Ave, Vancouver, BC, V5Z 4E6, Canada. address: egete@bccancer.bc.ca (E. Gete). Except for V 100% and V 90%, PBNC calculations on average underestimated the dose to the PTV. The largest discrepancy was in the PTV maximum dose, with a patient-averaged difference of %. Conclusions: Based on our MC investigation, we conclude that the Eclipse AAA algorithm is sufficiently accurate for dose calculations of lung SBRT plans involving small 6-MV photon fields. Our results also demonstrate that, although dose calculations at the periphery of the PTV showed good agreement when comparing PBNC with both AAA and MC calculations, there is a potential to significantly underestimate the dose inside the PTV and doses to critical structures if tissue heterogeneity correction is not applied to lung SBRT plans. RESUME Objet: Evaluer l exactitude du calcul de la dose de l algorithme d analyse anisotrope (AAA) du systeme de traitement Eclipse de Varian pour le traitement de radiotherapie stereotaxique du corps (SBRT) et etudier les consequences dosimetriques de ne pas appliquer la correction d heterogeneite des tissus sur les plans de traitement SBRT pulmonaires complexes. Materiaux et methodologie: Neuf cas de cancer brochopulmonaire «non a petites cellules» traites anterieurement par SBRT a notre centre ont ete selectionnes pour cette etude. Conformement a RTOG 0236, les plans originaux ont ete calcules sans correction d heterogeneite a l aide de l algorithme de faisceau etroit Varian Eclipse (PBNC). Pour cette etude, les plans de traitement ont ete recalcules en appliquant la correction d heterogeneite des tissus selon l algorithme AAA et la methode Monte Carlo (MC), en conservant le m^eme nombre d unite de monitoring que dans les plans originaux. Deux types de comparaisons ont ete faits. Dans un premier temps, les calculs AAA ont ete compares a la methode MC. Par la suite, les plans de traitement calcules avec l algorithme AAA ont ete compares aux calculs originaux PB-NC. Les parametres de dose-volume suivant ont ete utilises pour la comparaison : V100%, V90%, Dmax, Dmin, Dmoyen et conformite de dose pour PTV; V20Gy, V15Gy, V10Gy, /$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi: /j.jmir

2 V5Gy et Dmoyen pour les poumons; et Dmax pour les organes critiques. Resultats: Des resultats comparables ont ete obtenus pour les calculs AAA et MC : sauf pour Dmax, Dmin et Dmoyen, la difference dans les valeurs moyenne des patients de tous les parametres de dose PTV etait inferieure a 2 %. La difference moyenne la plus importante a ete observee pour Dmin (3,85,4) %. Les differences moyennes pour tous les parametres de dose pour les poumons etaient inferieures 2 % et les differences moyennes dans la dose pulmonaire maximale (Dmax) etaient inferieures a 0,3 Gy, sauf pour la dose a la peau. Les differences dans les parametres PTV et les parametres de dosevolume pour les tissus normaux etaient appreciables dans les comparaisons entre les calculs AAA et PB-NC. En moyenne, sauf pour V100 % et V90 %, les calculs PB-NC sous-estiment la dose au PTV. L ecart le plus marque a ete constate dans la dose maximum au PTV avec un ecart moyen entre les patients de 11,14,6 %. Conclusion: A partir de notre etude Monte Carlo, nous concluons que l algorithme AAA Eclipse presente un degredeprecision suffisant pour le calcul de dose des plans de traitement SBRT des poumons avec de petits champs de photons de 6MV. Nos resultats demontrent aussi que, bien que les calculs de dose en peripherie du PTV affichent une bonne conformite dans la comparaison des calculs PB-NC avec les calculs AAA et MC, il existe un potentiel de sous-estimation importante de la dose au PTV et aux structures critiques si aucune correction d heterogeneite des tissus n est appliquee dans le cas des plans de traitement SBRT pulmonaires. Introduction Stereotactic body radiotherapy (SBRT) has been established as an effective treatment modality for inoperable early stage non small-cell lung cancer (NSCLC) [1 4]. At our clinic, the SBRT technique was implemented in September 2008, and more than 40 lung cancer patients have been treated with SBRT since the implementation of this technique. Our SBRT lung treatment protocol closely follows the guidelines set by the Radiation Therapy Oncology Group 0236 (RTOG 0236) [5] for dose prescription, dose calculation, and for setting limits on doses to critical structures. Because of the limitation of the pencil beam algorithm for dose calculation in inhomogeneous media, and following the guideline of RTOG 0236 for dose calculation, tissue heterogeneity correction is not applied to dose calculation of the treatment plans. The limitation of conventional algorithms such as the Pencil Beam and the modified Batho path corrections methods for dose calculations in heterogeneous media is a wellknown problem [6]. The source of the limitation is the inability of these calculation methods to correctly account for the lack of lateral electronic equilibrium and secondary buildup. This problem is even more amplified for dose calculations involving small fields irradiating heterogeneous media, as is typically the case encountered in SBRT lung plans [7]. To address this issue, the authors of RTOG 0236 decided not to allow for tissue heterogeneity correction when calculating monitor unit settings and dose-volume histograms (DVH) that are used to evaluate the dose distribution for the planning target volume (PTV). The Monte Carlo (MC) method, considered to be the gold standard for dose calculation [6, 8], is the only dose calculation algorithm that can properly account for lack of electronic equilibrium and secondary buildup. The long calculation time required for MC calculations with present- day computers, however, makes it impractical for application in a clinical setting, and routine patient dose calculations are performed with model-based algorithms. Advanced model-based dose calculation algorithms such as the convolutionsuperposition method with collapsed cone approximation that is implemented in the Pinnacle planning system [9] and the anisotropic analytic algorithm (AAA) [10] method that is available in the recent versions of Varian Eclipse (Varian Medical Systems Inc., Palo Alto, CA) have been shown to have a more improved accuracy for dose calculation of small photon fields irradiating low density media [11 19]. For this reason, the authors of the AAPM Task Group 101 report [4] recommend that tissue heterogeneity correction be employed for dose calculation of SBRT lung plans. Moreover, two current RTOG trials for SBRT lung, RTOG 0813 [20] and RTOG 0915 [21], now require inhomogeneity correction, with the condition that the dose calculation method used is approved by the RTOG committee. There have been several studies to evaluate the accuracy of the AAA algorithm for dose calculation in low-density media [11 14]. These studies were either phantom-based or they were only focused on dose coverage of the PTV. Ding et al [11] performed MC simulation and measurement on a lung phantom to investigate the accuracy of the AAA algorithm, whereas Rønde and Hoffmann [13] conducted phantombased evaluation of the AAA algorithm with a particular focus on lung SBRT treatment plans. Sterpin et al [14] also used a heterogeneous multilayer phantom in their evaluation of the accuracy of AAA for IMRT and small field calculations. In the study by Ding et al [11] and by Xiao et al [12], the dosimetric consequences of applying tissue heterogeneity correction on PTV coverage had been investigated. However, normal tissue doses were not considered in any of these studies. Since the installation of the Eclipse V8.6 treatment planning software at our center, the AAA algorithm has been available and is undergoing testing before it can be released for clinical use. This study was conducted as part of the evaluation of the AAA dose calculation algorithm, with the following objectives: Evaluate the accuracy of the AAA algorithm for dose calculation of SBRT lung plans using the MC method. Study the dosimetric impact of introducing tissue heterogeneity correction on PTV coverage and on doses received by critical organs. This work presents the results of this evaluation. E. Gete et al./journal of Medical Imaging and Radiation Sciences 43 (2012)

3 Materials and Methods Patient Selection and Treatment Planning Nine cases of NSCLC that were previously treated with SBRT at our center were selected for this replanning study. Our selection criteria for the treatment plans were based on the size of the PTV, and the selected patients were representative of the larger cohort with respect to the PTV volume. The original treatment involved the use of 6-MV static conformal fields on a Varian ix Linac (Varian Medical Systems Inc.). During treatment, patients were immobilized with an in-house immobilization system. The clinical target volumes were determined on four-dimensional computed tomography images. The internal target volumes were contoured using the maximum intensity projection images of the four-dimensional computed tomography scans. The PTVs were created by growing the internal target volumes by 5 mm in every direction to account for setup uncertainties. For the patients in this study, the PTV volumes ranged between 18.8 to 62.3 cm 3 with a median value of 40.1 cm 3. Only peripherally located lung tumors were treated (Table 1). In addition to the PTV, the following critical structures were contoured: ipsilateral bronchus, esophagus, trachea, brachial plexus, spinal cord, heart, and skin. The skin was defined as a shell with thickness of 5 mm inside the external contour. An artificial object (known as D2cm) was also created. This is a shell structure that is located at a distance 2 cm away from the PTV. This structure is used to monitor high-dose spillage outside the PTV and to ensure a rapid falloff beyond the PTV [5]. Treatment planning was performed using the Varian Eclipse software version 8.6. The planning technique involved forward planning with multiple static noncoplanar conformal fields. Conformation to the target volume was obtained using the Varian Millennium multileaf collimator, with the collimator leaves automatically fitted to have a 0-mm margin around the PTV. Care was taken not to have a field that enters or exits through either arm. In addition, the fields were spaced as equally as possible around the PTV, avoiding overlap of fields at their entrance and exit through the body. Typically, a plan consisted of seven to nine fields, and delivered a dose of 48 Gy in four fractions to the prescription isodose (note that the dose prescription scheme for RTOG 0236 was 60 Gy in three fractions). The prescription isodose typically varied between 72% and 80% of the dose at the normalization point (Table 1), which is chosen to be the geometric center of the PTV. The following dose-volume constraint set by the RTOG 0236 was followed as a guideline for the PTV coverage: 95% of the PTV should receive the prescription dose (V 100% ¼ 95%). 99% of the PTV should receive 90% of the prescription dose (V 90% ¼ 99%). Whenever it was not possible to meet all the dose-volume constraint criteria for the critical structures, the prescription Table 1 A List Showing the Prescription Dose, the Prescription Isodose, the PTV Volume and Tumor Location Patient No. Prescription Dose (Gy) Prescription Isodose PTV Volume (ml) Tumor Location Left upper lobe Right lower lobe Right upper lobe Left lower lobe Left upper lobe Left upper lobe Right lower lobe Right upper lobe Left lower lobe PTV, planning target volume. dose was lowered so as not to exceed the critical structure dose limits. Dose Calculation For this study, the original plans were copied, anonymized, and recalculated with the three calculation methods described in the following sections. Pencil Beam The original dose calculation was performed using the pencil beam algorithm without tissue heterogeneity correction (PBNC), as per RTOG 0236 recommendation [5]. AAA The original plans were recalculated with the AAA algorithm by applying heterogeneity correction. The number of monitor units for each field was kept the same as the number of monitor units for the original plan calculated with PBNC. MC MC calculations of the doses were performed on the same treatment plans. The BEAMnrc/DOSXYZnrc MC system [22, 23] was used to simulate dose to the patients. MC particle transport through the multileaf collimator was simulated using the code developed by Siebers et al [24]. The information required for the MC simulations was extracted from the TPS DICOM RT files using codes developed by Zavgorodni et al [25]. The following MC transport parameters were used: AP ¼ PCUT ¼ MeV and AE ¼ ECUT ¼ MeV [26]. This choice of electron transport cutoff energy for simulations in lung was also suggested by Ma et al [27]. The accelerator model simulated was a Varian Clinac ix, and the physical parameters were defined according to manufacturer specifications. Simulations were performed on a cluster of dedicated computers. A phase space above the jaws was obtained using initial electrons incident on the target and contains particles. The number of histories used in DOSXYZnrc was selected for each simulation, such that the statistical uncertainty in the high dose voxels was 1%. We used the MC simulation setup described by 28 E. Gete et al./journal of Medical Imaging and Radiation Sciences 43 (2012) 26-33

4 Popescu et al [28], which allows a rigorous calculation of the absolute dose delivered to the patient for the planned number of monitor units. Dosimetric Comparison For each treatment plan, relevant dose volume quantities for the PTV, lung tissue, and critical organs were calculated using the three dose calculation methods. These dosimetric quantities were manually recorded from the DVH of the treatment plans and compared. The comparisons were based on the differences of the dosimetric quantities calculated with the different algorithms. The mean, maximum, and average of the differences over the nine patients were calculated for the comparison. PTV The PTV dose comparison was based on the two dose prescription parameters of RTOG 0236 (V 100% and V 90% ) as well as on the maximum, minimum, and mean PTV doses. In addition, target conformalities at the prescription dose (R 100% ), at 105% of the prescription dose (R 105% ), and at 50% of the prescription dose (R 50% ) were also evaluated. prescription iodose volume R 100% ¼ PTV volume 50% of prescription iodose volume R 50% ¼ PTV volume 150% of prescription iodose volume R 150% ¼ PTV volume Lung and Critical Organs Dose to the lungs was evaluated by calculating the absolute dose-volume parameters such as the V 20Gy,V 15Gy,V 10Gy, and V 5Gy as well as the mean lung dose. Doses to the critical structures are reported in accordance with the metrics set by the RTOG Results Two kinds of plan comparisons were made with different purpose. First, the plans that were calculated with AAA were compared with MC calculations. The purpose of this comparison was to evaluate the accuracy of the AAA dose calculation algorithm for lung SBRT plans. Second, the original plans that were calculated with PBNC were compared with the plans that were calculated with AAA. The purpose of this comparison was to investigate the dosimetric consequences of applying tissue heterogeneity correction to lung SBRT treatment plans that were calculated without tissue heterogeneity correction. The results of these comparisons are presented in the following sections. Comparison between AAA and MC Figure 1 shows a DVH comparison of calculations with MC (dashed lines) and AAA (solid lines) for patient 4. Patient 4 is chosen because the results are typical of the cohort. One could see from Figure 1 that there is a good agreement between MC and AAA calculations of the DVHs for the PTV as well as for the critical organs. It has been shown in this work that such an agreement was observed for all the patient plans that were analyzed in this study. Details of the analyses for PTV and the critical organ dose comparisons are given in the following section. PTV Coverage A list of patient-averaged dose parameters for the PTV calculated with AAA, MC, and PBNC is given in Table 2. These dose-volume parameters are: the volume of the PTV covered by the 100% and the 90% of the prescription isodose (V 100% and V 90%, respectively); the maximum, the minimum, and the mean PTV doses (D max,d min, and D mean, respectively); and PTV dose conformalities at three dose levels (R 100%,R 50%, and R 105% ). Comparisons between AAA and MC are given as the maximum, the minimum, and the average of the differences between AAA and MC calculations of these quantities (columns 5 to 7). As could be seen from Table 2, a good agreement was observed between AAA and MC calculations for V 100%,V 90%, the mean PTV dose, as well as for the dose conformalities at the 50%, 100%, and 105% isodose levels. However, larger differences were observed for the maximum and the minimum PTV doses. The largest difference observed was in the minimum PTV dose, where the AAA calculation gave 12.8% higher dose than MC for one patient plan. The average of the differences in the minimum and maximum PTV doses were % and %, respectively. Dose to Critical Organs A comparison of the maximum doses (in Gy) received by the critical organs calculated with AAA and MC are listed in Figure 1. Planning target volume (PTV) and normal tissue dose-volume histograms of patient #4 calculated with anisotropic analytical algorithm (AAA; solid lines) and Monte Carlo (MC; dashed lines). Patient #4 is used because the treatment plan is typical of the cohort. E. Gete et al./journal of Medical Imaging and Radiation Sciences 43 (2012)

5 Table 2 Dose-volume Parameters for the PTV Calculated with AAA, MC, and PBNC Planning Comparison AAA-MC AAA-PB (NC) PTV AAA avr MC avr PB avr Diff max Diff min Diff avr SD Diff max Diff min Diff avr SD V V D max D min D mean R R R AAA, anisotropic analytical algorithm; MC, Monte Carlo; PBNC, pencil beam without heterogeneity correction; PTV, planning target volume. Note that the doses are normalized with respect to the prescription isodose. columns 2 4 of Table 3. The comparisons are given in terms of the minimum, the maximum, and the average of the differences in the maximum doses the organs received (D max ) calculated over the nine patient plans. It could be seen from the third column of Table 3 that on average, there was a good agreement in the maximum normal tissue doses calculated, except for the dose to the skin where the difference was Gy. When looking at the differences in D max for individual patient plans, large differences were observed for some of the critical organs. For example, the largest difference observed for the maximum dose to the skin was 4.1 Gy. Dose to the Lung Table 4 (columns 2 4) lists comparisons of percent lung volumes irradiated to different dose levels (V 20Gy, V 15Gy, V 10Gy,andV 5Gy ), and the mean lung dose (D mean ) as calculated by AAA and MC. The comparison is presented in terms of the maximum, the minimum, and average of the differences of these values calculated over the nine patient plans. It can be seen from Table 4 that there was a very good agreement between the AAA and MC calculations for all of the lung dose parameters compared, where the patient-averaged Table 3 Differences in Maximum Doses to Critical Structures between AAA and MC (Columns 2 4) and between PBNC and AAA (Columns 5 7) Planning Comparison AAA-MC AAA-PB (NC) Critical organs Diff max (Gy) Diff min (Gy) Diff avr SD (Gy) Diff max (Gy) Diff min (Gy) Diff avr SD (Gy) Skin Spinal cord Heart Esophagus Brachial Plexus Trachea Ipsilateral bronchus AAA, anisotropic analytical algorithm; MC, Monte Carlo; PBNC, pencil beam without heterogeneity correction; PTV, planning target volume. The maximum, minimum, and average values are calculated over the nine patient plans. values of the differences between AAA and MC calculations were well within the statistical error of MC calculation (column 4). For individual patient plans, the largest observed difference was for V 5Gy (1.9%). Comparison of Calculations between AAA and PBNC PTV Coverage Figure 2a shows the dose distribution for the plan of patient 4 calculated on an axial isocentric slice with PBNC. Plots of dose profiles along a line in the AP direction (dashed vertical line in Figure 2a) calculated with PBNC, AAA, and MC are shown in Figure 2b. As can be seen from Figure 2b, the dose inside the PTV is underestimated by the PBNC calculation. This is to be expected since heterogeneity correction is not applied for the PB calculation. However, all the three calculation methods show a good agreement for the dose profiles near the edge of the PTV. A comparison of the following PTV dose-volume parameters between AAA and PBNC calculations is given in Table 2: the volume of the PTV covered by the 100% and the 90% of the prescription isodose (V 100% and V 90%, respectively); the maximum, minimum, and mean PTV doses (D max,d min, and D mean, respectively); and PTV dose conformalities at three dose levels (R 100%,R 50%, and R 105% ). The comparisons are given in terms of patient-averaged values (columns 1 and Table 4 A Comparison of Dose-volume Parameters for the Lung Tissue Planning Comparison AAA-MC AAA-PB (NC) Lung dose Diff max Diff min Diff avr SD Diff max Diff min Diff avr SD V V V V D mean (Gy) Gy AAA, anisotropic analytical algorithm; MC, Monte Carlo; PBNC, pencil beam without heterogeneity correction. Comparison between AAA and MC are listed in columns 2 4. Comparisons between AAA and PBNC are listed in columns 5 7. The comparisons are presented in terms of maximum, minimum, and average of the differences calculated over the nine patient plans. 30 E. Gete et al./journal of Medical Imaging and Radiation Sciences 43 (2012) 26-33

6 Figure 2. (a) Dose distribution of the plan for patient 4 on an axial isocentric slice calculated with pencil beam without heterogeneity correction (PBNC). The planning target volume (PTV) is represented by the orange contour. (b) Dose profiles of the plan for patient 4 across a line in the anteroposterior direction (red dashed line shown in 2a) calculated with the three algorithms anisotropic analytical algorithm (AAA), Monte Carlo (MC), and PBNC. Note that a reasonable agreement in dose is observed at the planning target volume (PTV) edge for all the three calculations. 3), as well the maximum, the minimum, and the average of the differences between AAA and PBNC calculations of these quantities (columns 8 10). When looking at the patientaveraged values, a good agreement was observed between AAA and PBNC calculations for V 100% and V 90%. However, larger differences were observed for the mean, maximum, and minimum PTV doses. The largest difference observed was in the maximum PTV dose where the AAA calculation gave 18.3% higher dose than PBNC for one patient plan. The average of the differences in the maximum, minimum and mean PTV doses between AAA and PBNC calculations were %, %, and %, respectively. This observation is consistent with the plots of the PTV dose profiles shown in Figure 2b where the doses calculated with AAA and PBNC show a good agreement at the edge of the PTV, but show large discrepancies inside the PTV. Large differences were observed for the conformalities at the 50% and 100% prescription isodoses, where the averaged of the differences in R 100% and R 50% were and , respectively. Dose to Critical Organs Figures 3a and3b show DVHs for the critical organs of patient 4 calculated with AAA and PBNC. It can be seen from Figures 3a and 3b that doses calculated by AAA are consistently larger than PBNC calculations for all the organs shown. A comparison of the maximum doses (in Gy) received by the critical organs calculated with AAA and PBNC are listed in columns 5 7 of Table 3. The comparisons are given in terms of the minimum, maximum, and average of the differences in the maximum doses the organs received (D max ) calculated over the nine patient plans. When looking at the patient average differences of D max (last column of Table 3), one could see that AAA calculations gave consistently larger values for D max than the values calculated with PBNC for all the critical organs considered. When looking at differences in dose for individual patient plans, the differences observed ranged from 1.8 Gy (trachea and ipsilateral bronchus) to 6.0 Gy (esophagus). Dose to the Lung A comparison of the lung volumes irradiated to different dose levels (V 20Gy,V 15Gy,V 10Gy, and V 5Gy ), and the mean lung dose for AAA and PBNC calculation are listed in the last three columns of Table 4. The comparisons are presented in terms of the maximum, minimum, and average of the differences between AAA and PBNC calculations. Similar to the critical organ dose comparisons, it could be seen from Table 4 that AAA calculations gave consistently larger values than PBNC calculation for all the lung dose volume parameters considered. The largest difference observed was in the value of V 5Gy with patient-averaged difference of % and largest difference (5.6%). The average and maximum difference in the mean lung dose were Gy and 0.91 Gy, respectively. Discussion Comparison between AAA and MC Agreements between the AAA and MC dose calculations for the PTV were generally good. With the exception of the minimum and the maximum PTV doses, AAA calculations slightly underestimated all the PTV dose quantities that were compared, with the average of the differences ranging between 0.2% and 2.6%. These findings are in agreement with the results of the study by Sterpin et al [14] in which they compared AAA and MC calculations for a single plan involving a small lung tumor. In their study, they report a difference in the mean PTV dose of 2.1% between MC and AAA calculations. Our results are also consistent with the findings of previous phantom based studies by Ding et al [11] and by Rønde and Hoffmann [14] that were able to E. Gete et al./journal of Medical Imaging and Radiation Sciences 43 (2012)

7 Figure 3. (a) Normal tissue dose-volume histograms (skin, lung, esophagus, and D2cm ) of patient 4 calculated with anisotropic analytical algorithm (AAA; solid lines) and pencil beam without heterogeneity correction (PBNC; dashed lines). AAA calculations in general gave larger normal tissue doses when compared with PBNC values. (b) Normal tissue dose-volume histograms (heart, spinal cord, brachial plexus, and trachea) of patient 4 calculated with AAA (solid lines) and PBNC (dashed lines). AAA calculations in general gave larger normal tissue doses when compared with PBNC values. demonstrate the accuracy of AAA for dose calculation of small 6-MV photon beams irradiating inhomogeneous media. A good agreement was observed in the shape of the DVHs for normal tissue between AAA and MC calculations, as illustrated in Figure 1. However, larger differences were observed when comparing the maximum critical organ doses (Table 3). For example, differences as large as 3.3 Gy and 4.1 Gy were observed for the maximum doses received by the spinal cord and the skin, respectively. These differences are significant, and one possible source of the discrepancy could be the inability of AAA to accurately calculate doses for materials with high atomic number such as bone, as reported by Bush et al [29]. There was a good agreement between AAA and MC calculations for all the lung dose parameters that were compared, and the differences observed were well within the statistical uncertainty of MC calculations (1%). Comparison of Dose Calculation between AAA and PBNC When comparing PBNC with AAA calculations for PTV dose-volume parameters, the following was observed consistently. First, the maximum dose to the PTV increased significantly (by as large as 18%) when tissue heterogeneity correction was applied, showing that PBNC calculation underestimates the dose inside the PTV. Second, there was a good agreement between AAA and PBNC calculations for the volume of the PTV covered by the prescription isodose V 100% : The patient averaged values of V 100% for the AAA and PBNC plans were very close (95.6% and 95.7%), respectively, whereas the largest observed difference in V 100% was 2.7%. The implication of this second observation is that, the calculated number of monitor units (which is directly related to the magnitude of the prescription dose), does not change significantly when inhomogeneity correction is applied to lung SBRT plans calculated with AAA. Another consequence of applying inhomogeneity correction is an increase in the PTV dose conformalities at 100% and 50% isodose. As a consequence of this, the PTV dose conformality constraints set by RTOG 0236 can no longer be satisfied when tissue heterogeneity correction is applied, and dose conformality constraints published by RTOG 0915 should be used [21] when evaluating the quality of a plan calculated with tissue heterogeneity correction. As shown in Figures 3a and b, critical organ and lung doses calculated with AAA were generally higher than PBNC calculation. This is expected because the PBNC calculation does not account for the reduction of attenuation of the photon beam because of the presence of lung as a beam is exiting through the critical organ considered. The increase in dose to critical organs varied significantly from patient to patient (Table 3), and it is difficult to predict because it depends on the beam arrangement, location of the tumor, and the location of the normal tissue considered. As far as we are aware, there is no publication to- date that has investigated the dosimetric consequences of applying tissue inhomogeneity correction on normal tissue doses for lung SBRT plans. A rigorous statistical analysis of the data was not performed in this study because the sample size used is too small for performing such an analysis. We had to limit the sample size to nine mainly because of the scarcity of resources to perform MC simulation. We do not expect the dosimetric results obtained for the PTV to be different if we used a larger sample size. However, a larger sample size could reveal a more complete picture on the differences in normal tissue doses since significant variation was observed in the normal tissue dose comparisons. Conclusion We have conducted a retrospective treatment planning study to evaluate the accuracy of the AAA algorithm, and to investigate the dosimetric consequences of applying tissue heterogeneity correction to lung SBRT treatment plans that were originally calculated without tissue heterogeneity correction. 32 E. Gete et al./journal of Medical Imaging and Radiation Sciences 43 (2012) 26-33

8 Comparison of AAA calculations with MC shows that the AAA algorithm is capable of accounting for inhomogeneities accurately for lung SBRT plans, confirming findings by other studies [11, 13, 14]. Appreciable differences were observed between PBNC and AAA calculations on the PTV and normal tissue doses. Except for V 100% and V 90%, PBNC calculations on average underestimated the dose to the PTV. The largest discrepancy was in the PTV maximum dose with an average difference of %. Normal tissue doses were also underestimated by PBNC calculations, and difference in dose that is as large as 6 Gy was observed for individual patient plans. This highlights the fact that if tissue heterogeneity correction is not applied, there is a potential for underestimating the dose given to normal tissue. 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