Direct design of 2D RF pulses using matrix inversion

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.