RF B₁ field localization through convex optimization

A 9-cm wavelength in the human brain at the 400-MHz Larmor frequency for 9.4-T leads to pronounced B₁ field contours and consequential image inhomogeneity. The objective of this study was to develop a new technique to control this nonuniformity by designing the phase and magnitude of radiofrequency (RF) power emanating from RF coil antenna elements in a multichannel transceiver array. Nonuniformity was used to steer a constructively interfering B₁ field node to spatially correlate with an anatomic region of interest. This work outlines a convex (quadratically constrained quadratic problem) formulation of the B₁ localization problem and the benefits of such a formulation. This convex formulation was used to design antenna excitation magnitude and phase. Localization is demonstrated in simulated finite difference time domain (FDTD) B₁ field human head distributions and human head phantom measurement.