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The Discrete Orthogonal Polynomial Least Squares Method for Approximation and Solving Partial Differential Equations

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Communications in Computational Physics 2008年第3期3卷 734-758页

作者： Anne Gelb Rodrigo B.Platte w.steven rosenthal Department of Mathematics and Statistics Arizona State UniversityTempeArizona 85287USA

we investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential *** focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential *** results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in *** time stability,small corrections near the ends of the interval are computed using local polynomial *** numerical experiments illustrate the performance of the method.

关键词： Discrete least-squares orthogonal polynomials spectralmethods high order numerical methods uniform grid.

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Treatment-Plan Comparison of Three Advanced Radiation Treatment Modalities for Fractionated Stereotactic Radiotherapy to the Head and Neck

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International Journal of Medical Physics, Clinical Engineering and Radiation Oncology 2019年第2期8卷 106-120页

作者： He wang James N. Yang Xiaodong Zhang Jing Li steven J. Frank Zhongxiang Zhao Dershan Luo Xiaorong Zhu Congjun wang Samuel Tung Adam S. Garden David I. rosenthal Clifton David Fuller Gary Brandon Gunn Amol J. Ghia Jay P. Reddy Shaan M. Raza Franco De Monte Mark S. Chambers Paul D. Brown Shirley Su Jack Phan Department of Radiation Physics The University of Texas MD Anderson Cancer Center Houston TX USA Department of Radiation Oncology The University of Texas MD Anderson Cancer Center Houston TX USA Department of Neurosurgery The University of Texas MD Anderson Cancer Center Houston TX USA Department of Oncologic Dentistry Prosthodontics Thoracic/Head &Neck Surgery The University of Texas MD Anderson Cancer Center Houston TX USA Department of Radiation Oncology The Mayo Clinic Rochester MN USA

Purpose: Fractionated stereotactic radiosurgery (FSRS) can be given with at least three modalities: Gamma Knife, with the noninvasive frameless extend system (GKE);linear accelerator-based volumetric modulated arc therapy (VMAT);and intensity-modulated proton therapy (IMPT). we extracted treatment plans for patients who had received FSRS with GKE for recurrent skull base or intracranial tumors, created corresponding plans for VMAT and IMPT, and compared the quality of the three sets of plans. Methods and materials: Plans were extracted for 9 patients with recurrent malignant skull-base tumors (n = 6) or large intracranial tumors (n = 3) who had received FSRS with GKE (median dose 24 Gy in 3 fractions) in 2013 through 2015. Plans for VMAT were generated with a TrueBeam STx LINAC machine using 6-MV photons, and plans for IMPT were generated with multi-field optimization. The optimized VMAT and IMPT plans were normalized to achieve the best possible target coverage while meeting the same dose-volume constraints on organs at risk (OARs) as the GKE plans. Plans were evaluated on the basis of target coverage, conformity index, homogeneity index, gradient index, and treatment efficiency. Results: The median target volume was 10.2 cm3 (range 1.9 - 33.8 cm3). The VMAT and IMPT plans met all OAR constraints, and target coverage and conformity were comparable among all plans. VMAT and IMPT plans showed significantly better target uniformity and treatment delivery efficiency (P P Conclusion: FSRS for skull base and large intracranial lesions delivered by VMAT and IMPT can achieve comparable target coverage, conformity, and sparing of critical structure as the GKE while providing superior target uniformity and treatment delivery efficiency. The GKE had superior high-dose gradients outside the target and thus better protected surrounding normal structures.

关键词： Gamma Knife Extend System Stereotactic Radiosurgery Volumetric Modulated Arc Therapy Intensity-Modulated Proton Therapy Spot Scanning Proton Therapy

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