High-Permittivity Pad Design for Dielectric Shimming in Magnetic Resonance Imaging Using Projection-Based Model Reduction and a Nonlinear Optimization Scheme

Inhomogeneities in the transmit radio frequency magnetic field (<inline-formula> <tex-math notation="LaTeX">${\text{B}}_{1}^{+}$ </tex-math></inline-formula>) reduce the quality of magnetic resonance (MR) images. This quality can be improved by using high-permittivity pads that tailor the <inline-formula> <tex-math notation="LaTeX">${\text{B}}_{1}^{+}$ </tex-math></inline-formula> fields. The design of an optimal pad is application-specific and not straightforward and would therefore benefit from a systematic optimization approach. In this paper, we propose such a method to efficiently design dielectric pads. To this end, a projection-based model order reduction technique is used that significantly decreases the dimension of the design problem. Subsequently, the resulting reduced-order model is incorporated in an optimization method in which a desired field in a region of interest can be set. The method is validated by designing a pad for imaging the cerebellum at 7 T. The optimal pad that is found is used in an MR measurement to demonstrate its effectiveness in improving the image quality.