Uniform Margin Research Articles

Coverage-based treatment planning to accommodate deformable organ variations in prostate cancer treatment

To compare two coverage-based planning (CP) techniques with standard fixed margin-based planning (FM), considering the dosimetric impact of interfraction deformable organ motion exclusively for high-risk prostate treatments. Nineteen prostate cancer patients with 8-13 prostate CT images of each patient were used to model patient-specific interfraction deformable organ changes. The model was based on the principal component analysis (PCA) method and was used to predict the patient geometries for virtual treatment course simulation. For each patient, an IMRT plan using zero margin on target structures, prostate (CTVprostate) and seminal vesicles (CTVSV), were created, then evaluated by simulating 1000 30-fraction virtual treatment courses. Each fraction was prostate centroid aligned. Patients whose D98 failed to achieve 95% coverage probability objective D98,95 ≥ 78 Gy (CTVprostate) or D98,95 ≥ 66 Gy (CTVSV) were replanned using planning techniques: (1) FM (PTVprostate = CTVprostate + 5 mm, PTVSV = CTVSV + 8 mm), (2) CPOM which optimized uniform PTV margins for CTVprostate and CTVSV to meet the coverage probability objective, and (3) CPCOP which directly optimized coverage probability objectives for all structures of interest. These plans were intercompared by computing probabilistic metrics, including 5% and 95% percentile DVHs (pDVH) and TCP/NTCP distributions. All patients were replanned using FM and two CP techniques. The selected margins used in FM failed to ensure target coverage for 8/19 patients. Twelve CPOM plans and seven CPCOP plans were favored over the other plans by achieving desirable D98,95 while sparing more normal tissues. Coverage-based treatment planning techniques can produce better plans than FM, while relative advantages of CPOM and CPCOP are patient-specific.

Does MLC With Finer Leaf Width Improve the Treatment Plan Quality in Stereotactic Body Radiation Therapy of Lung Cancers

To investigate the impact of leaf width on treatment plan quality in stereotactic body radiation therapy (SBRT) of lung cancers. 4DCT scans were acquired for 10 patients. The GTV was delineated on the maximum intensity projection CT, and it was expended by a uniform margin of 5mm to create the PTV. Volumetric Modulated Arc Therapy (VMAT) treatment plans were generated on the average intensity projection CT. The prescription dose was 48 Gy delivered in 4 fractions. For each patient two VMAT plans were created: the first plan (Plan1cm leave) used the 1 cm leaf width MLCi on Elekta Synergy, and the second plan (Plan0.5cm leave) utilized the 0.5 cm leaf width Agility MLC on Elekta Infinity. The output factors, beam energy and profiles of the two treatment machines were matched to within 1%. The two VMAT plans were analyzed and compared using the following dosimetric parameters: For target dose coverage, Quality of Coverage (QI), Homogeneity Index (HI), and Conformity Index (CI) were calculated; For organs at risk, the maximum dose of cord, heart and ribs, and the mean/V5/V10/V20 for the total lung dose were analyzed; The treatment time in terms of MU was also compared. For the dose coverage of GTV, the averaged CI, HI and QI of Plan1cm leave and Plan0.5cm leave are 0.980±0.046 / 0.970±0.043, 1.079±0.053 / 1.084±0.056, and 0.915±0.218 / 0.960±0.092, respectively. The corresponding p-values between the two plans are 0.250, 0.245 and 0.442. For PTV dose coverage, the averaged CI, HI and QI of Plan1cm leave and Plan0.5cm leave are 0.949±0.079 / 0.953±0.076, 1.142±0.083 / 1.142±0.085 and 0.865±0.141 / 0.862±0.154, respectively. The corresponding p-values are 0.465, 0.943 and 0.594 respectively. The mean MU is 2334.3±395.0 for Plan1cm leave and 2442.8±548.5 Plan0.5cm leave, with the p-value of 0.135. For the total lung, the mean lung dose, V5, V10, and V20 of Plan1cm leave are 4.53±1.88 Gy, 24.83±10.70%, 13.97±6.00%, 6.64±3.53% respectively. The corresponding values for Plan0.5cm leave are 4.48±1.79Gy, 25.06±11.53%, 14.27±6.27%, 6.67±3.65% respectively. The p-values for mean lung dose, V5, V10, and V20 are 0.825, 0.751, 0.410, and 0.864 respectively. The averaged maximum dose for cord, heart and ribs are 8.69±4.40, 16.84±13.68, 42.31±4.06 Gy respectively for Plan1cm leave versus 10.29±5.03, 16.46±13.68, 41.67±3.62 for Plan0.5cm leave. The corresponding p-values are 0.034, 0.530 and 0.322 respectively. Treatment plan quality using 0.5 cm leave width MLC is not statically better than the plan with 1 cm leave MLC. This can be explained by the fact that in most SBRT lung cases the tumor has smooth edge and both 1 cm and 0.5 cm leave MLCs are able to conform to the target edges smoothly. However, the maximum cord dose with Agility MLC is statistically lower than that with MLCi because Agility MLC offers lower MLC transmission.

Statistical Modeling of CTV Motion and Deformation for IMRT of Early-Stage Rectal Cancer

To derive and validate a statistical model of motion and deformation for the clinical target volume (CTV) of early-stage rectal cancer patients. For 16 patients, 4 to 5 magnetic resonance images (MRI) were acquired before each fraction was administered. The CTV was delineated on each MRI. Using a leave-one-out methodology, we constructed a population-based principal component analysis (PCA) model of the CTV motion and deformation of 15 patients, and we tested the model on the left-out patient. The modeling error was calculated as the amount of the CTV motion-deformation of the left-out-patient that could not be explained by the PCA model. Next, the PCA model was used to construct a PCA target volume (PCA-TV) by accumulating motion-deformations simulated by the model. A PCA planning target volume (PTV) was generated by expanding the PCA-TV by uniform margins. The PCA-PTV was compared with uniform and nonuniform CTV-to-PTV margins. To allow comparison, geometric margins were determined to ensure adequate coverage, and the volume difference between the PTV and the daily CTV (CTV-to-PTV volume) was calculated. The modeling error ranged from 0.9 ± 0.5 to 2.9 ± 2.1 mm, corresponding to a reduction of the CTV motion-deformation between 6% and 60% (average, 23% ± 11%). The reduction correlated with the magnitude of the CTV motion-deformation (P<.001, R=0.66). The PCA-TV and the CTV required 2-mm and 7-mm uniform margins, respectively. The nonuniform CTV-to-PTV margins were 4 mm in the left, right, inferior, superior, and posterior directions and 8 mm in the anterior direction. Compared to uniform and nonuniform CTV-to-PTV margins, the PCA-based PTV significantly decreased (P<.001) the average CTV-to-PTV volume by 128 ± 20 mL (49% ± 4%) and by 35 ± 6 mL (20% ± 3.5%), respectively. The CTV motion-deformation of a new patient can be explained by a population-based PCA model. A PCA model-generated PTV significantly improved sparing of organs at risk compared to uniform and nonuniform CTV-to-PTV margins.

Computed tomography manifestations of histologic subtypes of retroperitoneal liposarcoma.

Liposarcoma (LPS) is the most common soft tissue sarcoma and accounts for approximately 20% of all mesenchymal malignancies, often occurring in deep soft tissue of retroperitoneal space. Accurate preoperative diagnosis is therefore necessary. We explored whether computed tomography (CT) could be used to differentiate between the various types of retroperitoneal liposarcoma (RPLS). Forty-seven cases of RPLS, diagnosed surgically and histologically, were analyzed retrospectively. CT features were correlated with postoperative pathological appearance. The study radiologist identified 29, 11, 2, 2 and 3 RPLS as atypical lipomatous tumor/well-differentiated liposarcoma (ALT/WDL), dedifferentiated liposarcoma (DDL), myxoid/round cell liposarcoma (ML/RCL), pleomorphic liposarcoma (PL) and mixed-type liposarcoma. Analysis of CT scans revealed the following typical findings of the different subtypes of RPLS: ALT/WDL was mainly visible as a well-delineated fatty hypodense tumor with uniform density and integrity margin; DDL was marked by the combination of focal nodular density and hypervascularity. ML/RCL, PL and mixed liposarcoma showed malignant biological behaviour and CT findings need further studies. CT scanning can reveal important details including internal components, margins and surrounding tissues. Based on CT findings, tumor type can be roughly evaluated and biopsy location and therapeutic scheme guided.

Determination of Internal Target Volume for Radiation Treatment Planning of Esophageal Cancer by Using 4-Dimensional Computed Tomography (4DCT)

To determine an efficient strategy for the generation of the internal target volume (ITV) for radiation treatment planning for esophageal cancer using 4-dimensional computed tomography (4DCT). 4DCT sets acquired for 20 patients with esophageal carcinoma were analyzed. Each of the 4DCT sets was binned into 10 respiratory phases. For each patient, the gross tumor volume (GTV) was delineated on the 4DCT set at each phase. Various strategies to derive ITV were explored, including the volume from the maximum intensity projection (MIP; ITV_MIP), unions of the GTVs from selected multiple phases ITV2 (0% and 50% phases), ITV3 (ITV2 plus 80%), and ITV4 (ITV3 plus 60%), as well as the volumes expanded from ITV2 and ITV3 with a uniform margin. These ITVs were compared to ITV10 (the union of the GTVs for all 10 phases) and the differences were measured with the overlap ratio (OR) and relative volume ratio (RVR) relative to ITV10 (ITVx/ITV10). For all patients studied, the average GTV from a single phase was 84.9% of ITV10. The average ORs were 91.2%, 91.3%, 94.5%, and 96.4% for ITV_MIP, ITV2, ITV3, and ITV4, respectively. Low ORs were associated with irregular breathing patterns. ITV3s plus 1 mm uniform margins (ITV3+1) led to an average OR of 98.1% and an average RVR of 106.4%. The ITV generated directly from MIP underestimates the range of the respiration motion for esophageal cancer. The ITV generated from 3 phases (ITV3) may be used for regular breathers, whereas the ITV generated from 4 phases (ITV4) or ITV3 plus a 1-mm uniform margin may be applied for irregular breathers.

TH-C-BRD-03: Determining the Optimal Collimator Position for Collimated Pencil Beam Scanning Proton Therapy

Purpose: There has been a growing interest in applying collimation to pencil beam scanning (PBS) proton therapy in order to sharpen the lateral dose falloff out of the target, especially at low energies. Currently, there is not a method to optimally determine the collimation position or margin around the target. A uniform margin would not be ideal due to the fact that an incoming symmetric pencil beam, after being intercepted by a collimator near the target boundary, will become asymmetric and experience a lateral shift away from its original spot location, leaving the target insufficiently covered. We demonstrate a method that optimally determines the collimator position on a per-spot basis, in order to maximize target dose while minimizing normal tissue dose. Methods: A library of collimated pencil beams were obtained through Monte Carlo simulation with a collimator placed at varying distances from the central axis of an incoming symmetrical pencil beam of 118 MeV and 5 mm sigma-in-air. Two-dimensional treatment plans were then created using this library of collimated pencil beams. For each spot position in a treatment plan, the collimator position was optimally determined in such a way that the resultant pencil beam maximized the ratio of in-target dosemore » and out-of-target dose. For comparison, un-collimated treatment plans were also computed. Results: The spot-by-spot optimally determined collimator positions allowed the reduction of normal tissue dose while maintaining the same target coverage as un-collimated PBS. Quantitatively, the mean dose outside of the target was reduced by approximately 40% as compared to the plan without collimation. Conclusion: The proposed method determines the optimal collimator position for each spot in collimated PBS proton therapy. The use of a collimator will improve PBS dose distributions achievable today and will continue to be the subject of future investigations.« less

SU-E-T-57: Brain SRS Dose Variations Due to TrueBeam STx Isocenter Uncertainty

Purpose: Stereotactic Radiosurgery (SRS) is a valuable option for treatment of cranial melignancies. Well defined isocenter position (uncertainty <1 mm) of Varian TrueBeam STx, HD MLC, linac allows for tighter PTV margins(1mm). We report the effect of daily isocenter fluctuations established by Winston-Lutz test on target and cranial organ at risk (OAR) dosimetric parameters. Methods: 10 patient treatments were prepared using BrainLab iPlan softare. GTV and critical structures were contoured by neurosurgeon. A uniform margin of 1mm was used to expand GTV to PTV. Dose of 18 to 20Gy was prescribed to cover 99% of PTV volume using 3 or 4 dynamic arcs. Winston-Lutz test was performed daily to monitor linac isocenter stability, with 8 images (4 for various gantry angles, 4 for couch angles) analyzed by Standard Imaging PIPSpro software. Singular Value Decomposition method is used to determine the values for isocenter x, y and z coordinate offset, subsequently fed into treatment planning software to evaluate changes in dose coverage. Results: The average displacement (distance from lightfield center) of linac isocenter during 3 months of daily observations was 0.42±0.12mm (max observed displacement 0.656mm), with the average displacement of 0.27mm ptsuperior, 0.22mm pt-right, 0.04mm pt-posterior direction. With all plans normalized (PTV V100=99%) the daily isocenter walk resulted in average loss of V100PTV volume coverage of 4.2%. PTV Dmin dropped 8.9%, while GTV Dmin was 3.1% lower (108.1% planned) on average. Changes for PTV and GTV Dmean and Dmax parameters were less than 1%. Most of the cases showed insignificant changes in OAR dose coverage, with exception of vermis lesion where brainstem Dmax changed 2.4%. Conclusion: Daily monitoring of TrueBeam STx linac isocenter showed that GTV V100 remained at 100% of target volume in all cases. The effect of isocenter uncertainty could be further reduced by Brainlab ExacTrac Xray imaging.

Radiotherapy planning for glioblastoma based on a tumor growth model: improving target volume delineation

Glioblastoma differ from many other tumors in the sense that they grow infiltratively into the brain tissue instead of forming a solid tumor mass with a defined boundary. Only the part of the tumor with high tumor cell density can be localized through imaging directly. In contrast, brain tissue infiltrated by tumor cells at low density appears normal on current imaging modalities. In current clinical practice, a uniform margin, typically two centimeters, is applied to account for microscopic spread of disease that is not directly assessable through imaging. The current treatment planning procedure can potentially be improved by accounting for the anisotropy of tumor growth, which arises from different factors: anatomical barriers such as the falx cerebri represent boundaries for migrating tumor cells. In addition, tumor cells primarily spread in white matter and infiltrate gray matter at lower rate. We investigate the use of a phenomenological tumor growth model for treatment planning. The model is based on the Fisher–Kolmogorov equation, which formalizes these growth characteristics and estimates the spatial distribution of tumor cells in normal appearing regions of the brain. The target volume for radiotherapy planning can be defined as an isoline of the simulated tumor cell density. This paper analyzes the model with respect to implications for target volume definition and identifies its most critical components. A retrospective study involving ten glioblastoma patients treated at our institution has been performed. To illustrate the main findings of the study, a detailed case study is presented for a glioblastoma located close to the falx. In this situation, the falx represents a boundary for migrating tumor cells, whereas the corpus callosum provides a route for the tumor to spread to the contralateral hemisphere. We further discuss the sensitivity of the model with respect to the input parameters. Correct segmentation of the brain appears to be the most crucial model input. We conclude that the tumor growth model provides a method to account for anisotropic growth patterns of glioma, and may therefore provide a tool to make target delineation more objective and automated.

A study on planning organ at risk volume for the rectum using cone beam computed tomography in the treatment of prostate cancer

In this study, we analyzed planning organ at risk volume (PRV) for the rectum using a series of cone beam computed tomographies (CBCTs) acquired during the treatment of prostate cancer and evaluated the dosimetric effect of different PRV definitions. Overall, 21 patients with prostate cancer were treated radically with 78Gy in 39 fractions had in total 418 CBCTs, each acquired at the end of the first 5 fractions and then every alternate fraction. The PRV was generated from the Boolean sum volume of the rectum obtained from first 5 fractions (PRV-CBCT-5) and from all CBCTs (PRV-CBCT-All). The PRV margin was compared at the superior, middle, and inferior slices of the contoured rectum to compare PRV-CBCT-5 and PRV-CBCT-All. We also compared the dose received by the planned rectum (Rectum-computed tomography [CT]), PRV-CBCT-5, PRV-CBCT-All, and average rectum (CBCT-AV-dose-volume histogram [DVH]) at critical dose levels. The average measured rectal volume for all 21 patients for Rectum-CT, PRV-CBCT-5, and PRV-CBCT-All was 44.3 ± 15.0, 92.8 ± 40.40, and 121.5 ± 36.7cm3, respectively. For PRV-CBCT-All, the mean ± standard deviation displacement in the anterior, posterior, right, and left lateral directions in centimeters was 2.1 ± 1.1, 0.9 ± 0.5, 0.9 ± 0.8, and 1.1 ± 0.7 for the superior rectum; 0.8 ± 0.5, 1.1 ± 0.5, 1.0 ± 0.5, and 1.0 ± 0.5 for the middle rectum; and 0.3 ± 0.3; 0.9 ± 0.5; 0.4 ± 0.2, and 0.5 ± 0.3 for the inferior rectum, respectively. The first 5 CBCTs did not predict the PRV for individual patients. Our study shows that the PRV margin is different for superior, middle, and the inferior parts of the rectum, it is wider superiorly and narrower inferiorly. A uniform PRV margin does not represent the actual rectal variations during treatment for all treatment fractions. The large variation in interpatient rectal size implies a potential role for adaptive radiotherapy for prostate cancer.

Dosimetric Comparison of Different Prescription Modes in Lung Stereotactic Body Radiation Therapy

The purpose of this study was to compare the dose-volume statistics of stereotactic body radiotherapy (SBRT) for lung cancer between planning target volume (PTV): D95 and gross tumor volume (GTV): D99 dose prescriptions using Monte Carlo (MC) calculation. Plans for 183 patients treated between October 2010 and April 2013 were generated based on four-dimensional (4D) computed tomography (CT) under free breathing. A uniform margin of 8 mm was added to the internal target volume (ITV) to generate PTV. A leaf margin of 2 mm was added to the PTV. The plans were calculated with two different dose prescription methods: 40 Gy to cover 95% of the PTV (PTV prescription) and 44 Gy to cover 99% of the GTV (GTV prescription). A 6-MV photon beam was used. A dose-volume histogram (DVH) analysis was performed for dose to the GTV using PTV and GTV dose prescriptions. For each treatment plan, we evaluated the minimum dose to 99% of the GTV (D99). The D99 of GTV was 44.5 ± 1.9 Gy and 44.0 ± 0.0 Gy for PTV and GTV prescriptions, respectively. The dose to the GTV had wide variations with PTV prescription. We recommend that GTV based dose prescription should be used to standardize dose to the tumor and to achieve highly conformal dose distributions in SBRT for lung cancer.

Simultaneous modulated accelerated radiation therapy for esophageal cancer: A feasibility study

To establish the feasibility of simultaneous modulated accelerated radiation therapy (SMART) in esophageal cancer (EC). Computed tomography (CT) datasets of 10 patients with upper or middle thoracic squamous cell EC undergoing chemoradiotherapy were used to generate SMART, conventionally-fractionated three-dimensional conformal radiotherapy (3DCRT) and intensity-modulated radiation therapy (cf-IMRT) plans, respectively. The gross target volume (GTV) of the esophagus, positive regional lymph nodes (LN), and suspected lymph nodes (LN ±) were contoured for each patient. The clinical target volume (CTV) was delineated with 2-cm longitudinal and 0.5- to 1.0-cm radial margins with respect to the GTV and with 0.5-cm uniform margins for LN and LN(±). For the SMART plans, there were two planning target volumes (PTVs): PTV66 = (GTV + LN) + 0.5 cm and PTV54 = CTV + 0.5 cm. For the 3DCRT and cf-IMRT plans, there was only a single PTV: PTV60 = CTV + 0.5 cm. The prescribed dose for the SMART plans was 66 Gy/30 F to PTV66 and 54 Gy/30 F to PTV54. The dose prescription to the PTV60 for both the 3DCRT and cf-IMRT plans was set to 60 Gy/30 F. All the plans were generated on the Eclipse 10.0 treatment planning system. Fulfillment of the dose criteria for the PTVs received the highest priority, followed by the spinal cord, heart, and lungs. The dose-volume histograms were compared. Clinically acceptable plans were achieved for all the SMART, cf-IMRT, and 3DCRT plans. Compared with the 3DCRT plans, the SMART plans increased the dose delivered to the primary tumor (66 Gy vs 60 Gy), with improved sparing of normal tissues in all patients. The Dmax of the spinal cord, V20 of the lungs, and Dmean and V50 of the heart for the SMART and 3DCRT plans were as follows: 38.5 ± 2.0 vs 44.7 ± 0.8 (P = 0.002), 17.1 ± 4.0 vs 25.8 ± 5.0 (P = 0.000), 14.4 ± 7.5 vs 21.4 ± 11.1 (P = 0.000), and 4.9 ± 3.4 vs 12.9 ± 7.6 (P = 0.000), respectively. In contrast to the cf-IMRT plans, the SMART plans permitted a simultaneous dose escalation (6 Gy) to the primary tumor while demonstrating a significant trend of a lower irradiation dose to all organs at risk except the spinal cord, for which no significant difference was found. SMART offers the potential for a 6 Gy simultaneous escalation in the irradiation dose delivered to the primary tumor of EC and improves the sparing of normal tissues.

An assessment of PTV margin based on actual accumulated dose for prostate cancer radiotherapy

The purpose of this work is to present the results of a margin reduction study involving dosimetric and radiobiologic assessment of cumulative dose distributions, computed using an image guided adaptive radiotherapy based framework. Eight prostate cancer patients, treated with 7–9, 6 MV, intensity modulated radiation therapy (IMRT) fields, were included in this study. The workflow consists of cone beam CT (CBCT) based localization, deformable image registration of the CBCT to simulation CT image datasets (SIM-CT), dose reconstruction and dose accumulation on the SIM-CT, and plan evaluation using radiobiological models. For each patient, three IMRT plans were generated with different margins applied to the CTV. The PTV margin for the original plan was 10 mm and 6 mm at the prostate/anterior rectal wall interface (10/6 mm) and was reduced to: (a) 5/3 mm, and (b) 3 mm uniformly. The average percent reductions in predicted tumor control probability (TCP) in the accumulated (actual) plans in comparison to the original plans over eight patients were 0.4%, 0.7% and 11.0% with 10/6 mm, 5/3 mm and 3 mm uniform margin respectively. The mean increase in predicted normal tissue complication probability (NTCP) for grades 2/3 rectal bleeding for the actual plans in comparison to the static plans with margins of 10/6, 5/3 and 3 mm uniformly was 3.5%, 2.8% and 2.4% respectively. For the actual dose distributions, predicted NTCP for late rectal bleeding was reduced by 3.6% on average when the margin was reduced from 10/6 mm to 5/3 mm, and further reduced by 1.0% on average when the margin was reduced to 3 mm. The average reduction in complication free tumor control probability (P+) in the actual plans in comparison to the original plans with margins of 10/6, 5/3 and 3 mm was 3.7%, 2.4% and 13.6% correspondingly. The significant reduction of TCP and P+ in the actual plan with 3 mm margin came from one outlier, where individualizing patient treatment plans through margin adaptation based on biological models, might yield higher quality treatments.

Flexible Copula Density Estimation with Penalized Hierarchical B‐splines

ABSTRACTThe paper introduces a new method for flexible spline fitting for copula density estimation. Spline coefficients are penalized to achieve a smooth fit. To weaken the curse of dimensionality, instead of a full tensor spline basis, a reduced tensor product based on so called sparse grids (Notes Numer. Fluid Mech. Multidiscip. Des., 31, 1991, 241‐251) is used. To achieve uniform margins of the copula density, linear constraints are placed on the spline coefficients, and quadratic programming is used to fit the model. Simulations and practical examples accompany the presentation.

SU‐E‐T‐665: Investigation of Uniform Planning Margin for Intensity Modulated Proton Therapy of Pediatric Brain Tumors

Purpose: Determine if a uniform planning target volume (PTV) margin can be used for intensity modulated proton therapy (IMPT) of centrally located pediatric brain tumors and determine the most appropriate value. Methods: Treatment planning data from three pediatric patients with centrally located brain tumors were used in this study. For each patient, two IMPT plan types, a 3 field multi‐field‐optimized (MFO) and a 3 field single‐field‐optimized (SFO), and a 5 field IMRT plan were created for 7 uniform PTV margins that ranged from 0 to 10mm. The IMPT plans did not use robust optimization. For all plan types, the target coverage was held constant (98% of CTV received 54Gy and 95% of PTV received &gt;53Gy) and normal tissue doses were minimized. Four error types, each with numerous variations, were simulated and their effect were recorded. The four error types were: systematic plan position error, systematic field position error, systematic range error, and random position error. Results: Regarding normal tissues, there was no notable difference between MFO and SFO, both were substantially better than IMRT, e.g. mean cochlea dose was 14Gy for IMRT with 3mm margin and 5Gy for the IMPT plans. In general, smaller margins gave better normal tissue sparring. For both IMPT plan types and IMRT, PTV margins less than 3mm lead to target coverage deficits under the various errors. For position errors, the IMPT and IMRT plans gave similar results as a function of margin size. For density and systematic field errors, the SFO plans maintained target coverage better than MFO. Conclusions: A uniform PTV margin is not suitable for MFO planning. However, a uniform PTV margin of 3mm is appropriate for SFO planning when considering the above uncertainties (excluding large errors). At 3mm, which is also required for IMRT, the SFO plans had superior normal tissue sparing. Varian Medical Systems

SU‐E‐T‐649: Planning Margins Validation for Concurrent Treatment of Prostate and Pelvic Lymph Nodes Under Daily Image Guided Delivery

Purpose: To validate prostate planning margins for concurrent treatment of the prostate and pelvic lymph nodes (PLN) under daily kilo‐voltage cone beam (KV‐CBCT) imaging guidance while applying MLC and iso‐center shifting methods to compensate for inter‐fractional prostate motion. Methods and Materials: Ninety‐four daily KV‐CBCTs from five patients, who received IMRT treatment with a clinical planning margin to the prostate of 8mm/6mm posterior (M(8,6)) and 5mm to the PLN, were selected. Three additional IMRT plans were created for each patient with the prostate planning margins of 6mm/4mm posterior (M(6,4)), 4mm/2mm posterior (M(4,2)) and 2mm uniform margin (M(2,2)). The PLN planning margin remained 5mm. Subsequently, each plan was applied to the daily KV‐CBCT using MLC and iso‐center shifting methods. Daily D95 of the prostate and D95 of the PLN, and D5 of the rectum and D5 of the bladder were evaluated for adequate planning margins. Results: For both the MLC and iso‐center shifting methods, D95 of the prostate was greater than or equal 97% of the prescription dose in 97.8% (100%), 98.9% (97.9%), 95.8% (97.9%), and 93.7%(96.8%) of 94 fractions, for M(8,6), M(6,4), M(4,2), and M(2,2) respectively. Accordingly, D95 of the PLN was greater than or equal 97% of the prescription dose in 98.9%(100%), 100%(98.9%), 98.9%(98.9%), and 100%(98.9%), for M(8,6), M(6,4), M(4,2), and M(2,2) respectively. For the rectum, D5 exceeded 105% of the original IMRT D5 for the MLC‐shift (and iso‐center shift) plans in 16%(14.9%), 14.9%(16.4%), 5.4%(12.2%) and 4.3%(12.2%) for these four planning margins respectively. For the bladder, D5 exceeded 105% of the original IMRT D5 for the MLC‐shift (and iso‐center shift) plans in 0%(1.1%), 6.4% 3.2%), 13.9%(4.3%), and 8.6%(4.3%), respectively. Conclusion: With 5 mm planning margin to the PLN, both MLC and iso‐center shifting methods can reduce the prostate planning margin to 4mm/2mm posterior while achieving adequate targets coverage. This research was supported by the United States Army Medical Research and Materiel Command (USAMRMC) (Grant No. W81XWH‐080‐0358)

TU‐E‐141‐02: Coverage‐Based Treatment Planning to Accommodate Deformable Organ Variations in Prostate Cancer Treatment

Purpose: To (1) investigate the dosimetric impact of interfraction deformable organ motion for high‐risk prostate cancer treatments and (2) compare two coverage‐based planning (CP) techniques with the fixed margin‐based planning (FM).Methods: 19 patients with 8–13 prostate CT images were used to model interfraction deformable organ changes using principal component analysis (PCA). Displacement vector fields (DVFs) that map from each of the 8–13 images to the reference image were analyzed with PCA to determine the dominant eigenmodes, which were then used to predict the synthetic patient geometries for virtual treatment course simulation. For each patient, an intensity modulated radiation therapy (IMRT) plan with zero PTV margin on target structures (CTVprostate and CTVseminalVesicles) was created, then evaluated by simulating 1000 30‐fraction virtual treatment courses. Each fraction was prostate centroid aligned. Probabilistic metrics, including 5% and 95% percentile DVHs (pDVH) and TCP/NTCP distributions, were computed. Patients whose D98 failed to achieve 95% coverage probability objective D98,95&gt;=78Gy (CTVprostate) or D98,95&gt;=66Gy (CTVseminalVesicles) were replanned using (1) FM (PTVprostate = CTVprostate + 5mm, PTVseminalVesicles = CTVseminalVesicles + 8mm), (2) CPOM which optimized uniform margins for CTVprostate and CTVseminalVesicles to meet the CP objective, and (3) CPCOP which directly optimized coverage‐based objectives for all structures of interest. Results: For zero‐PTV‐margin plans, 0/19 patients satisfied objective D98,95 for both CTVprostate and CTVseminalVesicles. The selected margins used in FM failed to ensure target coverage for 8/19 patients. 11 CPOM plans and 8 CPCOP plans were favored over the other plans by achieving desirable D98,95 while sparing more normal tissues. Conclusion: The dosimetric impact of deformable organ motions for prostate centroid alignment treatment is not insignificant. Coverage‐based treatment planning techniques can produce better plans than FM, while relative advantages of CPOM and CPCOP are patient specific. Supported by NIH P01‐CA‐116602 and Philips Medical Systems. Supported by NIH P01‐CA‐116602 and Philips Medical Systems; NIH P01‐CA‐116602 and Philips Medical Systems

Bayesian Inference of Pair-Copula Constriction for Multivariate Dependency Modeling of Iran’s Macroeconomic Variables

Shahid Chamran University, Ahvaz, Iran Bayesian inference of pair-copula constriction (PCC) is used for multivariate dependency modeling of Iran’s macroeconomics variables: oil revenue, economic growth, total consumption and investment. These constructions are based on bivariate t-copulas as building blocks and can model the nature of extreme events in bivariate margins individually. The model parameter was estimated based on Markov chain Monte Carlo (MCMC) methods. A MCMC algorithm reveals unconditional as well as conditional independence in Iran’s macroeconomic variables, which can simplify resulting PCC’s for these data. Key words: Monte Carlo Markov Chain Method, pair-copula construction, vine. Introduction Multivariate data usually exhibit a complex pattern of dependency. Methods such as graphical model and Bayesian networks are available to investigate dependency structures in multivariate data. One increasingly popular approach for constructing high dimensional dependency is based on copulas. Copulas are multivariate distribution functions with uniform margins which allow representation of joint distribution functions as a function of marginal distributions and a copula (Sklar, 1959). Copulas are used in various fields of applied sciences, but are most widely used in economics, finance and risk management (Embrechts, et al., 2003; Patton, 2004; Nolte, 2008). The class of copulas for bivariate data is rich in comparison to the one for �−dimensional data with � ≥ 3. Untilrecently, Gaussian and t-copulas or, more M. R. Zadkarami is a associated professor on the Faculty of Mathematics and Computer Sciences in the Statistics Department. Email him at: zadkarami@yahoo.co.uk. O. Chatrabgoun is a PhD student on the Faculty of Mathematics and Computer Sciences in the Statistics Department. Email him at: o-chatrabgoun@phdstu.scu.ac.ir. generally, elliptical copulas, have been used for multivariate data (Frahm, et al., 2003). The generalization of bivariate copulas to multivariate copulas of dimensions larger than 2 is not straightforward, however there is one simple generalization for Archimedean copulas known as exchangeable Archimedean copulas (Frey & McNeil, 2003). It should be noted that not all bivariate Archimedean copulas have a corresponding multivariate exchangeable version (Nelsen, 1999). Approaches for constructing multivariate Archimedean copulas of more than 2 have dimensions been developed by Joe (1997), Embrechts, et al. (2003), Whelan, (2004), McNeil, et al. (2006), Savu and Trede (2006) and McNeil (2007). Joe (1996) and Bedford and Cooke (2001, 2002) constructed flexible higher-dimensional copulas by using only bivariate copulas as building blocks, which they termed vines. Kurowicka and Cooke (2006) discussed Gaussian vine constructions in details. Aas, et al. (2007) first recognized the general construction principle for deriving multivariate copulas; they used more general bivariate copulas than the Gaussian copula and applied these construction methods to financial risk data using more appropriate pair-copulas such as the bivariate t Clayton and Gumbel copulas. According to recent empirical investigations of Berg and Aas (2007) and Fischer, et al. (2007), the vine constructions based on bivariate t-

Dosimetric comparison of patient setup strategies in stereotactic body radiation therapy for lung cancer

In this work, the authors retrospectively compared the accumulated dose over the treatment course for stereotactic body radiation therapy (SBRT) of lung cancer for three patient setup strategies. Ten patients who underwent lung SBRT were selected for this study. At each fraction, patients were immobilized using a vacuum cushion and were CT scanned. Treatment plans were performed on the simulation CT. The planning target volume (PTV) was created by adding a 5-mm uniform margin to the internal target volume derived from the 4DCT. All plans were normalized such that 99% of the PTV received 60 Gy. The plan parameters were copied onto the daily CT images for dose recalculation under three setup scenarios: skin marker, bony structure, and soft tissue based alignments. The accumulated dose was calculated by summing the dose at each fraction along the trajectory of a voxel over the treatment course through deformable image registration of each CT with the planning CT. The accumulated doses were analyzed for the comparison of setup accuracy. The tumor volume receiving 60 Gy was 91.7 ± 17.9%, 74.1 ± 39.1%, and 99.6 ± 1.3% for setup using skin marks, bony structures, and soft tissue, respectively. The isodose line covering 100% of the GTV was 55.5 ± 7.1, 42.1 ± 16.0, and 64.3 ± 7.1 Gy, respectively. The corresponding average biologically effective dose of the tumor was 237.3 ± 29.4, 207.4 ± 61.2, and 258.3 ± 17.7 Gy, respectively. The differences in lung biologically effective dose, mean dose, and V20 between the setup scenarios were insignificant. The authors' results suggest that skin marks and bony structure are insufficient for aligning patients in lung SBRT. Soft tissue based alignment is needed to match the prescribed dose delivered to the tumors.

Polar codes for distributed source coding

A polar coding method to construct a distributed source coding scheme which can achieve any point on the dominant face of the Slepian-Wolf rate region for sources with uniform marginals is proposed. Source encoding and decoding operations are performed using efficient algorithms which makes practical implementation feasible. Simulation results are given to exhibit the performance of the presented method.

A comparison between the Gumbel-Hougaard and distorted Frank copulas for drought frequency analysis

Drought is a global phenomenon and is a common characteristic of extreme climate. It is widely considered as the world’s costliest natural disaster since their effects are especially devastating to the agricultural and social economy. Effective water resource infrastructure and management is required for the mitigation of drought, and this requires drought risk assessment. Essential characteristics of drought are severity, average intensity and duration, which are highly correlated. Copulas are multivariate uniform distribution functions with uniform marginals, which provide a flexible approach to model their relationship. For an extreme drought event to be modelled, the upper-tail dependence must be investigated. The construction of an alternative copula form is introduced through a transformation called a distortion, to allow for more versatile modelling of tail dependence. Data from a rainfall district in New South Wales is considered and the Gumbel-Hougaard copula and distorted Frank copulas are fitted to the drought characteristics. Goodness-of-fit and upper tail correlations of these copulas are analysed and discussed. Finally, conditional annual drought recurrence intervals are calculated and compared for these fitted copulas.