skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

Abstract

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimization and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases.more » Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.« less

Authors:
; ;  [1]
  1. The University of Chicago, Chicago, IL (United States)
Publication Date:
OSTI Identifier:
22653905
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; COMPUTERS; GRAPH THEORY; LIMITING VALUES; OPTIMIZATION; PLANNING; RADIOTHERAPY

Citation Formats

Liu, X, Belcher, AH, and Wiersma, R. MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning. United States: N. p., 2016. Web. doi:10.1118/1.4957359.
Liu, X, Belcher, AH, & Wiersma, R. MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning. United States. doi:10.1118/1.4957359.
Liu, X, Belcher, AH, and Wiersma, R. 2016. "MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning". United States. doi:10.1118/1.4957359.
@article{osti_22653905,
title = {MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning},
author = {Liu, X and Belcher, AH and Wiersma, R},
abstractNote = {Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimization and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.},
doi = {10.1118/1.4957359},
journal = {Medical Physics},
number = 6,
volume = 43,
place = {United States},
year = 2016,
month = 6
}
  • Purpose: Radiosurgery of multiple (n>4) brain metastasis lesions requires 3–4 noncoplanar VMAT arcs with excessively high monitor units and long delivery time. We investigated whether an improved optimization technique would decrease the needed arc numbers and increase the delivery efficiency, while improving or maintaining the plan quality. Methods: The proposed 4pi arc space optimization algorithm consists of two steps: automatic couch angle selection followed by aperture generation for each arc with optimized control points distribution. We use a greedy algorithm to select the couch angles. Starting from a single coplanar arc plan we search through the candidate noncoplanar arcs tomore » pick a single noncoplanar arc that will bring the best plan quality when added into the existing treatment plan. Each time, only one additional noncoplanar arc is considered making the calculation time tractable. This process repeats itself until desired number of arc is reached. The technique is first evaluated in coplanar arc delivery scheme with testing cases and then applied to noncoplanar treatments of a case with 12 brain metastasis lesions. Results: Clinically acceptable plans are created within minutes. For the coplanar testing cases the algorithm yields singlearc plans with better dose distributions than that of two-arc VMAT, simultaneously with a 12–17% reduction in the delivery time and a 14–21% reduction in MUs. For the treatment of 12 brain mets while Paddick conformity indexes of the two plans were comparable the SCG-optimization with 2 arcs (1 noncoplanar and 1 coplanar) significantly improved the conventional VMAT with 3 arcs (2 noncoplanar and 1 coplanar). Specifically V16 V10 and V5 of the brain were reduced by 11%, 11% and 12% respectively. The beam delivery time was shortened by approximately 30%. Conclusion: The proposed 4pi arc space optimization technique promises to significantly reduce the brain toxicity while greatly improving the treatment efficiency.« less
  • Purpose: To evaluate the use of post-irradiation changes in respiratory rate and CBCT-based morphology as predictors of survival in mice. Methods: C57L/J mice underwent whole-thorax irradiation with a Co-60 beam to four different doses [0Gy (n=3), 9Gy (n=5), 11Gy (n=7), and 13Gy (n=5)] in order to induce varying levels of pneumonitis. Respiratory rate measurements, breath-hold CBCTs, and free-breathing CBCTs were acquired pre-irradiation and at six time points between two and seven months post-irradiation. For respiratory rate measurements, we developed a novel computer-vision-based technique. We recorded mice sleeping in standard laboratory cages with a 30 fps, 1080p webcam (Logitech C920). Wemore » calculated respiratory rate using corner detection and optical flow to track cyclical motion in the fur in the recorded video. Breath-hold and free-breathing CBCTs were acquired on the X-RAD225Cx system. For breathhold imaging, the mice were intubated and their breath was held at full-inhale for 20 seconds. Healthy lung tissue was delineated in the scans using auto-threshold contouring (0–0.7 g/cm{sup 3}). The volume of healthy lung was measured in each of the scans. Next, lung density was measured in a 6-mm{sup 2} ROI in a fixed anatomic location in each of the scans. Results: Day-to-day variability in respiratory rate with our technique was 13%. All metrics except for breath-hold lung volume were correlated with survival: lung density on free-breathing (r=−0.7482,p<0.01) and breath-hold images (r=−0.5864,p<0.01), free-breathing lung volume (r=0.7179,p<0.01), and respiratory rate (r= 0.6953,p<0.01). Lung density on free-breathing scans was correlated with respiratory rate (r=0.7142,p<0.01) and lung density on breath-hold scans (r=0.5543,p<0.01). One significant practical hurdle in the CBCT measurements was that at least one lobe of the lung was collapsed in 36% of free-breathing scans and 45% of breath-hold scans. Conclusion: Lung density and lung volume on free-breathing CBCTs and respiratory rate outperform breath-hold CBCT measurements as indicators for survival from radiation-induced pneumonitis. This work was partially funded by Elekta.« less
  • Purpose: Cerium oxide nanoparticles (CONPs) have unique pH dependent properties such that they act as a radical modulator. These properties may be used in radiation therapy (RT) to protect normal tissue. This work investigates the selective radioprotection of CONPs in-vitro and potential for in-situ delivery of CONPs in prostate cancer RT. Methods: i) Normal human umbilical vein endothelial cells (HUVEC) and human prostate cancer cells (PC-3) were treated with 0 or 2 ng/mL CONPs (NP size: 5 nm). 2 Gy of 100 kVp radiation was delivered to the cells 4 hours after the CONP treatment. Cell viability was checked 48more » hours later using MTS assays. ii) A prostate tumor was modeled as a 2-cm diameter sphere. CONPs were proposed to be loaded in a hollow radiotherapy fiducial marker. The concentration profile for the CONPs within the tumor was modeled with a previously validated diffusion equation employed in other studies for nanoparticles 10 nm or less. Results: i) Without radiation, cell viability was above 90% when treated with 2 ng/mL CONPs for both HUVEC and PC-3. After irradiation, a slightly higher viability was observed in HUVEC with CONPs than the ones without CONPs, and this effect was not observed in PC-3. ii) Based on the calculations, 2 ng/mL of CONPs could be delivered to normal cells by diffusion with a 1 µg/mL initial concentration within two weeks. Conclusion: We conclude that CONPs can provide selective radioprotection. The delivery of needed concentrations of CONPs is feasible via in-situ release from radiotherapy biomaterials (e.g. fiducials) loaded with the CONPs.« less
  • Purpose: Automatically derive electron density of tissues using MR images and generate a pseudo-CT for MR-only treatment planning of brain tumours. Methods: 20 stereotactic radiosurgery (SRS) patients’ T1-weighted MR images and CT images were retrospectively acquired. First, a semi-automated tissue segmentation algorithm was developed to differentiate tissues with similar MR intensities and large differences in electron densities. The method started with approximately 12 slices of manually contoured spatial regions containing sinuses and airways, then air, bone, brain, cerebrospinal fluid (CSF) and eyes were automatically segmented using edge detection and anatomical information including location, shape, tissue uniformity and relative intensity distribution.more » Next, soft tissues - muscle and fat were segmented based on their relative intensity histogram. Finally, intensities of voxels in each segmented tissue were mapped into their electron density range to generate pseudo-CT by linearly fitting their relative intensity histograms. Co-registered CT was used as a ground truth. The bone segmentations of pseudo-CT were compared with those of co-registered CT obtained by using a 300HU threshold. The average distances between voxels on external edges of the skull of pseudo-CT and CT in three axial, coronal and sagittal slices with the largest width of skull were calculated. The mean absolute electron density (in Hounsfield unit) difference of voxels in each segmented tissues was calculated. Results: The average of distances between voxels on external skull from pseudo-CT and CT were 0.6±1.1mm (mean±1SD). The mean absolute electron density differences for bone, brain, CSF, muscle and fat are 78±114 HU, and 21±8 HU, 14±29 HU, 57±37 HU, and 31±63 HU, respectively. Conclusion: The semi-automated MR electron density mapping technique was developed using T1-weighted MR images. The generated pseudo-CT is comparable to that of CT in terms of anatomical position of tissues and similarity of electron density assignment. This method can allow MR-only treatment planning.« less
  • Purpose: Metal in patients creates streak artifacts in CT images. When used for radiation treatment planning, these artifacts make it difficult to identify internal structures and affects radiation dose calculations, which depend on HU numbers for inhomogeneity correction. This work quantitatively evaluates a new metal artifact reduction (MAR) CT image reconstruction algorithm (GE Healthcare CT-0521-04.13-EN-US DOC1381483) when metal is present. Methods: A Gammex Model 467 Tissue Characterization phantom was used. CT images were taken of this phantom on a GE Optima580RT CT scanner with and without steel and titanium plugs using both the standard and MAR reconstruction algorithms. HU valuesmore » were compared pixel by pixel to determine if the MAR algorithm altered the HUs of normal tissues when no metal is present, and to evaluate the effect of using the MAR algorithm when metal is present. Also, CT images of patients with internal metal objects using standard and MAR reconstruction algorithms were compared. Results: Comparing the standard and MAR reconstructed images of the phantom without metal, 95.0% of pixels were within ±35 HU and 98.0% of pixels were within ±85 HU. Also, the MAR reconstruction algorithm showed significant improvement in maintaining HUs of non-metallic regions in the images taken of the phantom with metal. HU Gamma analysis (2%, 2mm) of metal vs. non-metal phantom imaging using standard reconstruction resulted in an 84.8% pass rate compared to 96.6% for the MAR reconstructed images. CT images of patients with metal show significant artifact reduction when reconstructed with the MAR algorithm. Conclusion: CT imaging using the MAR reconstruction algorithm provides improved visualization of internal anatomy and more accurate HUs when metal is present compared to the standard reconstruction algorithm. MAR reconstructed CT images provide qualitative and quantitative improvements over current reconstruction algorithms, thus improving radiation treatment planning accuracy.« less