Purpose: 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.
Keywords: B1+; Dielectric shimming; electromagnetic scattering; integral equations; inverse problem.
© 2015 Wiley Periodicals, Inc.