Direct design of 2D RF pulses using matrix inversion

Abstract

Multi-dimensional pulses are frequently used in MRI for applications such as targeted excitation, fat–water separation or metabolic imaging with hyperpolarised 13C compounds. For the design, the problem is typically separated into the different dimensions. In this work, a method to directly design two-dimensional pulses using the small-tip angle approximation is introduced based on a direct matrix representation. The numerical problem is solved in a single step directly in two dimensions by matrix inversion. Exemplary spectral–spatial excitation and spatio-temporal encoding (SPEN) pulses are designed and validated. The main benefits of the direct design approach include a reduction of artefacts in case of spectral–spatial pulses, a simple and straightforward computer implementation and high flexibility in the pulse design.