Multidimensional RF pulse design with consideration of concomitant field effects

Purpose: To develop a small-tip multidimensional RF pulse design procedure that incorporates linear time-invariant gradient imperfections and concomitant field effects. This could be particularly important for contemporary low-field MRI systems with high-performance gradients. Theory and Methods: We developed an extension of the small-tip excitation k-space formalism, where concomitant fields were approximated as a Bloch-Siegert shift in the rotating frame. This was evaluated using realistic simulations of 2D selective excitation at various field strengths (0.2T, 0.55T, 1.5T, 3T, and 7T) with single and parallel transmit. Simulated excitation profiles from the original and extended k-space formalisms were compared. Experimental validations were performed at 0.55T with a single-channel transmit. Results: The extended formalism provides improved 2D excitation profiles in all scenarios simulated, compared against the original formalism. The proposed method corrects the concomitant field effects on 2D selective excitations for B-0 > 0.2T when the magnitude of the B-0 is far larger than that of nonrotating concomitant fields. Simulation and phantom experiments at 0.55T match well for both original and proposed methods, with the proposed method providing sharper and more accurate excitation profiles at off-isocenter distances up to 15cm. The impact of the proposed method is greatest in scenarios where concomitant fields are substantial, such as low field strengths and off-isocenter. Conclusion: Concomitant fields can be modeled as a Bloch-Siegert shift in the rotating frame during multidimensional RF pulse design, resulting in improved excitation profiles with sharp edges. This is important to consider for off-isocenter excitations and imaging at low field strengths with strong gradients.