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Title: SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

Abstract

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction, we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when theymore » are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.« less

Authors:
 [1];  [2]; ;  [3];  [1]
  1. Stanford University, Stanford, CA (United States)
  2. (United States)
  3. Stanford University School of Medicine, Stanford, CA (United States)
Publication Date:
OSTI Identifier:
22648943
Resource Type:
Journal Article
Resource Relation:
Journal Name: Medical Physics; Journal Volume: 43; Journal Issue: 6; Other Information: (c) 2016 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
60 APPLIED LIFE SCIENCES; 61 RADIATION PROTECTION AND DOSIMETRY; ALGORITHMS; COMPUTER CODES; LIMITING VALUES; MATHEMATICAL SOLUTIONS; PLANNING; RADIATION DOSES; RADIOTHERAPY

Citation Formats

Ungun, B, Stanford University School of Medicine, Stanford, CA, Fu, A, Xing, L, and Boyd, S. SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints. United States: N. p., 2016. Web. doi:10.1118/1.4956525.
Ungun, B, Stanford University School of Medicine, Stanford, CA, Fu, A, Xing, L, & Boyd, S. SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints. United States. doi:10.1118/1.4956525.
Ungun, B, Stanford University School of Medicine, Stanford, CA, Fu, A, Xing, L, and Boyd, S. 2016. "SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints". United States. doi:10.1118/1.4956525.
@article{osti_22648943,
title = {SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints},
author = {Ungun, B and Stanford University School of Medicine, Stanford, CA and Fu, A and Xing, L and Boyd, S},
abstractNote = {Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction, we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.},
doi = {10.1118/1.4956525},
journal = {Medical Physics},
number = 6,
volume = 43,
place = {United States},
year = 2016,
month = 6
}
  • Several reports have dealt with correlations of late rectal toxicity with rectal dose-volume histograms (DVHs) for high dose levels. There are 2 techniques to assess rectal volume for reception of a specific dose: relative-DVH (R-DVH, %) that indicates relative volume for a vertical axis, and absolute-DVH (A-DVH, cc) with its vertical axis showing absolute volume of the rectum. The parameters of DVH vary depending on the rectum delineation method, but the literature does not present any standardization of such methods. The aim of the present study was to evaluate the effects of different delineation methods on rectal DVHs. The enrollmentmore » for this study comprised 28 patients with high-risk localized prostate cancer, who had undergone intensity-modulated radiation therapy (IMRT) with the prescription dose of 78 Gy. The rectum was contoured with 4 different methods using 2 lengths, short (Sh) and long (Lg), and 2 cross sections, rectum (Rec) and rectal wall (Rw). Sh means the length from 1 cm above the seminal vesicles to 1 cm below the prostate and Lg the length from the rectosigmoid junction to the anus. Rec represents the entire rectal volume including the rectal contents and Rw the rectal volume of the area with a wall thickness of 4 mm. We compared dose-volume parameters by using 4 rectal contour methods for the same plan with the R-DVHs as well as the A-DVHs. For the high dose levels, the R-DVH parameters varied widely. The mean of V{sub 70} for Sh-Rw was the highest (19.4%) and nearly twice as high as that for Lg-Rec (10.4%). On the contrary, only small variations were observed in the A-DVH parameters (4.3, 4.3, 5.5, and 5.5 cc for Sh-Rw, Lg-Rw, Sh-Rec, and Lg-Rec, respectively). As for R-DVHs, the parameters of V{sub 70} varied depending on the rectal lengths (Sh-Rec vs Lg-Rec: R = 0.76; Sh-Rw vs Lg-Rw: R = 0.85) and cross sections (Sh-Rec vs Sh-Rw: R = 0.49; Lg-Rec vs Lg-Rw: R = 0.65). For A-DVHs, however, the parameters of Sh rectal A-DVHs hardly changed regardless of differences in rectal length at all dose levels. Moreover, at high dose levels (V{sub 70}), the parameters of A-DVHs showed less dependence on rectal cross sections (Sh-Rec vs Sh-Rw: R = 0.66; Lg-Rec vs Lg-Rw: R = 0.59). This study showed that A-DVHs were less dependent on the delineation methods than R-DVHs, especially for evaluating the rectal dose at higher dose levels. It can therefore be assumed that, in addition to R-DVHs, A-DVHs can be used for evaluating rectal toxicity.« less
  • Purpose: Determine equivalent Organ at Risk (OAR) tolerance dose (TD) constraints for MV x-rays and particle therapy. Methods: Equivalent TD estimates for MV x-rays are determined from an isoeffect, regression-analysis of published and in-house constraints for various fractionation schedules (n fractions). The analysis yields an estimate of (α/β) for an OAR. To determine equivalent particle therapy constraints, the MV x-ray TD(n) values are divided by the RBE for DSB induction (RBE{sub DSB}) or cell survival (RBE{sub S}). Estimates of (RBE{sub DSB}) are computed using the Monte Carlo Damage Simulation, and estimates of RBES are computed using the Repair-Misrepair-Fixation (RMF) model.more » A research build of the RayStation™ treatment planning system implementing the above model is used to estimate (RBE{sub DSB}) for OARs of interest in 16 proton therapy patient plans (head and neck, thorax, prostate and brain). Results: The analysis gives an (α/β) estimate of about 20 Gy for the trachea and heart and 2–4 Gy for the esophagus, spine, and brachial plexus. Extrapolation of MV x-ray constraints (n = 1) to fast neutrons using RBE{sub DSB} = 2.7 are in excellent agreement with clinical experience (n = 10 to 20). When conventional (n > 30) x-ray treatments are used as the reference radiation, fast neutron RBE increased to a maximum of 6. For comparison to a constant RBE of 1.1, the RayStation™ analysis gave estimates of proton RBE{sub DSB} from 1.03 to 1.33 for OARs of interest. Conclusion: The presented system of models is a convenient formalism to synthesize from multiple sources of information a set of self-consistent plan constraints for MV x-ray and hadron therapy treatments. Estimates of RBE{sub DSB} from the RayStation™ analysis differ substantially from 1.1 and vary among patients and treatment sites. A treatment planning system that incorporates patient and anatomy-specific corrections in proton RBE would create opportunities to increase the therapeutic ratio. The research build of the RayStation used in the study was made available to the University of Washington free of charge. RaySearch Laboratories did not provide any monetary support for the reported studies.« less
  • Purpose: To identify an anatomic structure predictive for acute (AUT) and late (LUT) urinary toxicity in patients with prostate cancer treated with low-dose-rate brachytherapy (LDR) with or without external beam radiation therapy (EBRT). Methods and Materials: From July 2002 to January 2013, 927 patients with prostate cancer (median age, 66 years) underwent LDR brachytherapy with Iodine 125 (n=753) or Palladium 103 (n=174) as definitive treatment (n=478) and as a boost (n=449) followed by supplemental EBRT (median dose, 50.4 Gy). Structures contoured on the computed tomographic (CT) scan on day 0 after implantation included prostate, urethra, bladder, and the bladder neck, defined asmore » 5 mm around the urethra between the catheter balloon and the prostatic urethra. AUT and LUT were assessed with the Common Terminology Criteria for Adverse Events, version4. Clinical and dosimetric factors associated with AUT and LUT were analyzed with Cox regression and receiver operating characteristic analysis to calculate area under the receiver operator curve (ROC) (AUC). Results: Grade ≥2 AUT and grade ≥2 LUT occurred in 520 patients (56%) and 154 patients (20%), respectively. No grade 4 toxicities were observed. Bladder neck D2cc retained a significant association with AUT (hazard ratio [HR], 1.03; 95% confidence interval [CI], 1.03-1.04; P<.0001) and LUT (HR, 1.01; 95% CI, 1.00-1.03; P=.014) on multivariable analysis. In a comparison of bladder neck with the standard dosimetric variables by use of ROC analysis (prostate V100 >90%, D90 >100%, V150 >60%, urethra D20 >130%), bladder neck D2cc >50% was shown to have the strongest prognostic power for AUT (AUC, 0.697; P<.0001) and LUT (AUC, 0.620; P<.001). Conclusions: Bladder neck D2cc >50% was the strongest predictor for grade ≥2 AUT and LUT in patients treated with LDR brachytherapy. These data support inclusion of bladder neck constraints into brachytherapy planning to decrease urinary toxicity.« less
  • Monte Carlo (MC) simulation is currently the most accurate dose calculation algorithm in radiotherapy planning but requires relatively long processing time. Faster model-based algorithms such as the anisotropic analytical algorithm (AAA) by the Eclipse treatment planning system and multigrid superposition (MGS) by the XiO treatment planning system are 2 commonly used algorithms. This study compared AAA and MGS against MC, as the gold standard, on brain, nasopharynx, lung, and prostate cancer patients. Computed tomography of 6 patients of each cancer type was used. The same hypothetical treatment plan using the same machine and treatment prescription was computed for each casemore » by each planning system using their respective dose calculation algorithm. The doses at reference points including (1) soft tissues only, (2) bones only, (3) air cavities only, (4) soft tissue-bone boundary (Soft/Bone), (5) soft tissue-air boundary (Soft/Air), and (6) bone-air boundary (Bone/Air), were measured and compared using the mean absolute percentage error (MAPE), which was a function of the percentage dose deviations from MC. Besides, the computation time of each treatment plan was recorded and compared. The MAPEs of MGS were significantly lower than AAA in all types of cancers (p<0.001). With regards to body density combinations, the MAPE of AAA ranged from 1.8% (soft tissue) to 4.9% (Bone/Air), whereas that of MGS from 1.6% (air cavities) to 2.9% (Soft/Bone). The MAPEs of MGS (2.6%±2.1) were significantly lower than that of AAA (3.7%±2.5) in all tissue density combinations (p<0.001). The mean computation time of AAA for all treatment plans was significantly lower than that of the MGS (p<0.001). Both AAA and MGS algorithms demonstrated dose deviations of less than 4.0% in most clinical cases and their performance was better in homogeneous tissues than at tissue boundaries. In general, MGS demonstrated relatively smaller dose deviations than AAA but required longer computation time.« less
  • Purpose: Advanced stereotactic radiotherapy (SRT) treatments require accurate dose calculation for treatment planning especially for treatment sites involving heterogeneous patient anatomy. The purpose of this study was to evaluate the accuracy of dose calculation algorithms, Raytracing and Monte Carlo (MC), implemented in the MultiPlan treatment planning system (TPS) in presence of heterogeneities. Methods: First, the LINAC of a CyberKnife radiotherapy facility was modeled with the PENELOPE MC code. A protocol for the measurement of dose distributions with EBT3 films was established and validated thanks to comparison between experimental dose distributions and calculated dose distributions obtained with MultiPlan Raytracing and MCmore » algorithms as well as with the PENELOPE MC model for treatments planned with the homogenous Easycube phantom. Finally, bones and lungs inserts were used to set up a heterogeneous Easycube phantom. Treatment plans with the 10, 7.5 or the 5 mm field sizes were generated in Multiplan TPS with different tumor localizations (in the lung and at the lung/bone/soft tissue interface). Experimental dose distributions were compared to the PENELOPE MC and Multiplan calculations using the gamma index method. Results: Regarding the experiment in the homogenous phantom, 100% of the points passed for the 3%/3mm tolerance criteria. These criteria include the global error of the method (CT-scan resolution, EBT3 dosimetry, LINAC positionning …), and were used afterwards to estimate the accuracy of the MultiPlan algorithms in heterogeneous media. Comparison of the dose distributions obtained in the heterogeneous phantom is in progress. Conclusion: This work has led to the development of numerical and experimental dosimetric tools for small beam dosimetry. Raytracing and MC algorithms implemented in MultiPlan TPS were evaluated in heterogeneous media.« less