Tri M Ngo1, George S K Fung2, Shuo Han1, Min Chen3,4, Jerry L Prince1,5, Benjamin M W Tsui2, Elliot R McVeigh1, Daniel A Herzka1. 1. Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA. 2. Division of Medical Imaging Physics, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins Medical Institutions, Baltimore, Maryland, USA. 3. Image Analysis and Communications Laboratory, Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, Maryland, USA. 4. Translational Neuroradiology Unit, National Institute of Neurological Disorders and Stroke, Bethesda, Maryland, USA. 5. Department of Electrical & Computer Engineering, The Johns Hopkins University, Baltimore, Maryland, USA.
Abstract
PURPOSE: Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing three-dimensional (3D) analytical phantoms are unable to accurately model shapes of biomedical interest. The goal of this study was to demonstrate that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. METHODS: The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D and two-dimensional (2D) MRI acquisitions was described. RESULTS: Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D and 2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing compared with equivalent voxelized/rasterized phantoms. CONCLUSION: Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. Magn Reson Med 76:663-678, 2016.
PURPOSE: Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing three-dimensional (3D) analytical phantoms are unable to accurately model shapes of biomedical interest. The goal of this study was to demonstrate that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. METHODS: The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D and two-dimensional (2D) MRI acquisitions was described. RESULTS: Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D and 2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing compared with equivalent voxelized/rasterized phantoms. CONCLUSION: Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. Magn Reson Med 76:663-678, 2016.
Authors: Ehsan Abadi; William P Segars; Benjamin M W Tsui; Paul E Kinahan; Nick Bottenus; Alejandro F Frangi; Andrew Maidment; Joseph Lo; Ehsan Samei Journal: J Med Imaging (Bellingham) Date: 2020-04-11