With the recent proposal of using magnetic fields that are nonlinear by design for spatial encoding, new flexibility has been introduced to MR imaging. The new degrees of freedom in shaping the spatially encoding magnetic fields (SEMs) can be used to locally adapt the imaging resolution to features of the imaged object, e.g., anatomical structures, to reduce peripheral nerve stimulation during in vivo experiments or to increase the gradient switching speed by reducing the inductance of the coils producing the SEMs and thus accelerate the imaging process. In this work, the potential of nonlinear and nonbijective SEMs for spatial encoding during transmission in multidimensional spatially selective excitation is explored. Methods for multidimensional spatially selective excitation radiofrequency pulse design based on nonlinear encoding fields are introduced, and it is shown how encoding ambiguities can be resolved using parallel transmission. In simulations and phantom experiments, the feasibility of selective excitation using nonlinear, nonbijective SEMs is demonstrated, and it is shown that the spatial resolution with which the target distribution of the transverse magnetization can be realized varies locally. Thus, the resolution of the target pattern can be increased in some regions compared with conventional linear encoding. Furthermore, experimental proof of principle of accelerated two-dimensional spatially selective excitation using nonlinear SEMs is provided in this study. Magn Reson Med 70:1220-1228, 2013. (c) 2012 Wiley Periodicals, Inc.
