title: A theoretical approach based on electromagnetic scattering for analysing dielectric shimming in high-field MRI.
abstract: OBJECTIVE
  In this study, we analyzed dielectric shimming by formulating it as an electromagnetic scattering problem using integral equations.
  
  
  METHODS
  Three-dimensional simulations of the radiofrequency field in two configurations using different materials were analyzed in terms of induced currents and secondary fields. A two-dimensional integral equation method with different backgrounds was used to identify the underlying physical mechanisms. This framework was then used to develop an inversion method for the design of dielectric pads.
  
  
  RESULTS
  The effects of a dielectric pad can be attributed to the interference of a secondary field that is produced by the currents induced in the dielectric pad, radiating in an inhomogeneous background. The integral equation method with inhomogeneous background reduces the complexity of the forward and inverse problem significantly and can be used to optimize the permittivity distribution for a desired B1+ field. Agreement with experimental B1+ maps was obtained in a cylindrical phantom, demonstrating the validity of the method.
  
  
  CONCLUSIONS
  The integral equation method with inhomogeneous background yields an efficient numerical framework for the analysis and inverse design of dielectric shimming materials.
authors.affiliation: C. J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, Netherlands.
authors.forename: Wyger M
authors.initials: WM
authors.lastname: Brink
authors.affiliation: Circuits and Systems Group, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands.
authors.forename: Rob F
authors.initials: RF
authors.lastname: Remis
authors.affiliation: C. J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, Netherlands.
authors.forename: Andrew G
authors.initials: AG
authors.lastname: Webb
mesh_terms: D000465:Algorithms; D017609:Barium Compounds / Q000737:chemistry; D001921:Brain / Q000000981:diagnostic imaging; D002118:Calcium / Q000737:chemistry; D003198:Computer Simulation; D004553:Electric Conductivity; D004574:Electromagnetic Fields; D060733:Electromagnetic Radiation; D004867:Equipment Design; D006257:Head / Q000000981:diagnostic imaging; D006801:Humans; D021621:Imaging, Three-Dimensional; D008279:Magnetic Resonance Imaging; D008297:Male; D015233:Models, Statistical; D059906:Neuroimaging / Q000379:methods*; D011846:Radio Waves; D015203:Reproducibility of Results; D012542:Scattering, Radiation; D014025:Titanium / Q000737:chemistry
chemical_list: D017609:Barium Compounds; C024547:barium titanate(IV); C000592180:calcium titanate; D014025:Titanium; D002118:Calcium
keywords: B1+; Dielectric shimming; electromagnetic scattering; integral equations; inverse problem