title: Realistic analytical polyhedral MRI phantoms.
abstract: 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.
  
  
  
  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.
  
  
  
  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.
  
  
  
  Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. Magn Reson Med 76:663-678, 2016. © 2015 Wiley Periodicals, Inc.
authors.affiliation: Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.
authors.forename: Tri M
authors.initials: TM
authors.lastname: Ngo
authors.affiliation: Division of Medical Imaging Physics, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins Medical Institutions, Baltimore, Maryland, USA.
authors.forename: George S K
authors.initials: GS
authors.lastname: Fung
authors.affiliation: Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.
authors.forename: Shuo
authors.initials: S
authors.lastname: Han
authors.affiliation: Image Analysis and Communications Laboratory, Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, Maryland, USA.|Translational Neuroradiology Unit, National Institute of Neurological Disorders and Stroke, Bethesda, Maryland, USA.
authors.forename: Min
authors.initials: M
authors.lastname: Chen
authors.affiliation: Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.|Department of Electrical & Computer Engineering, The Johns Hopkins University, Baltimore, Maryland, USA.
authors.forename: Jerry L
authors.initials: JL
authors.lastname: Prince
authors.affiliation: Division of Medical Imaging Physics, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins Medical Institutions, Baltimore, Maryland, USA.
authors.forename: Benjamin M W
authors.initials: BM
authors.lastname: Tsui
authors.affiliation: Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.
authors.forename: Elliot R
authors.initials: ER
authors.lastname: McVeigh
authors.affiliation: Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Herzka
mesh_terms: D000818:Animals; D032701:Biomimetics / Q000379:methods*; D003198:Computer Simulation; D005583:Fourier Analysis; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D008954:Models, Biological; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Fourier transform; analytical phantom; magnetic resonance imaging; simulation