The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.The work of Yair Censor was supported by the ISF-NSFC joint research plan Grant Number 2874/19. Francisco Aragón and David Torregrosa were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22, and the Generalitat Valenciana (AICO/2021/165). David Torregrosa was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.Comment: Revised version, October 10, 2022; accepted for publication in: Applied Mathematics and Computatio

Simulation of a new respiratory phase sorting method for 4D-imaging using optical surface information towards precision radiotherapy

Background: Respiratory signal detection is critical for 4-dimensional (4D) imaging. This study proposes and evaluates a novel phase sorting method using optical surface imaging (OSI), aiming to improve the precision of radiotherapy. Method: Based on 4D Extended Cardiac-Torso (XCAT) digital phantom, OSI in point cloud format was generated from the body segmentation, and image projections were simulated using the geometries of Varian 4D kV cone-beam-CT (CBCT). Respiratory signals were extracted respectively from the segmented diaphragm image (reference method) and OSI respectively, where Gaussian Mixture Model and Principal Component Analysis (PCA) were used for image registration and dimension reduction respectively. Breathing frequencies were compared using Fast-Fourier-Transform. Consistency of 4DCBCT images reconstructed using Maximum Likelihood Expectation Maximization algorithm was also evaluated quantitatively, where high consistency can be suggested by lower Root-Mean-Square-Error (RMSE), Structural-Similarity-Index (SSIM) value closer to 1, and larger Peak-Signal-To-Noise-Ratio (PSNR) respectively. Results: High consistency of breathing frequencies was observed between the diaphragm-based (0.232 Hz) and OSI-based (0.251 Hz) signals, with a slight discrepancy of 0.019Hz. Using end of expiration (EOE) and end of inspiration (EOI) phases as examples, the mean±1SD values of the 80 transverse, 100 coronal and 120 sagittal planes were 0.967, 0,972, 0.974 (SSIM); 1.657 ± 0.368, 1.464 ± 0.104, 1.479 ± 0.297 (RMSE); and 40.501 ± 1.737, 41.532 ± 1.464, 41.553 ± 1.910 (PSNR) for the EOE; and 0.969, 0.973, 0.973 (SSIM); 1.686 ± 0.278, 1.422 ± 0.089, 1.489 ± 0.238 (RMSE); and 40.535 ± 1.539, 41.605 ± 0.534, 41.401 ± 1.496 (PSNR) for EOI respectively. Conclusions: This work proposed and evaluated a novel respiratory phase sorting approach for 4D imaging using optical surface signals, which can potentially be applied to precision radiotherapy. Its potential advantages were non-ionizing, non-invasive, non-contact, and more compatible with various anatomic regions and treatment/imaging systems

A Free-Breathing Lung Motion Model

Lung cancer has been the leading cause of cancer deaths for decades in the United States. Although radiotherapy is one of the most effective treatments, side effects from error in delivery of radiation due to organ motion during breathing remain a significant issue. To compensate the breathing motion during the treatment, a free breathing lung motion model, x= x0+αv+βf, was developed and discussed, where x is the position of a piece of tissue located at reference position x0. α is a parameter which characterizes the motion due to local air filling: motion as a function of tidal volume) and β is the parameter that accounts for the motion due to the imbalance of dynamical stress distributions during inspiration and exhalation which cause lung motion hysteresis: motion as a function of airflow). The parameters α and β together provide a quantitative characterization of breathing motion that inherently includes the complex hysteresis interplay. The theoretical foundation of the model was built by investigating the stress distribution inside of a lung and the biomechanical properties of the lung tissues. Accuracy of the model was investigated by using 49 free-breathing patient data sets. Applications of the model in localizing lung cancer, monitoring radiation damage and suppressing artifacts in free-breathing PET images were also discussed. This work supported in part by NIHR01CA096679 and NIHR01CA11671

Manned Venus Flyby

This study is one of several being conducted at Bellcomm and in Manned Space Flight whose purpose is to give guidance to the Apollo Applications Program's technical objectives by focusing on a longer range goal. The assumed mission in this case is a three-man flyby of Venus launched in November, 1973 on a single standard Saturn V. The selected flight configuration includes a Command and Service Module similar in some respects to Apollo, an Environmental Support Module which occupies the adapter area and a spent S-IVB stage which is utilized for habitable volume and structural support of a solar cell electrical power system. The total injected weight, 106,775 lbs., is within the capability of a single Saturn V of the early 1970's. The study is focused on the selection of subsystem technologies appropriate to long duration flight. The conclusions are reported in terms of the technical characteristics to be achieved as part of the Apollo Applications Program's long duration objectives

Alternative hull detection techniques for preprocessing in proton computed tomography reconstruction

The purpose of this study was to develop computationally efficient hull detection techniques appropriate for image reconstruction using sparse matrices. The hull detection techniques investigated were space carving (SC), modified space carving (MSC), and space modeling (SM) and these were compared to the cone-beam version of filtered back projection (FBP) algorithm in terms of their computation time and the quality of the object hull they produced