Concerto per MRI: A Mathematical Orchestration of RF Fields for pTx Systems

The Bloch equation describes the MR excitation process in terms of classical mechanics. A closed form solution in case of small tip angle (STA) excitation can be derived and exploited for RF pulse design. After discretization, the resulting linear system has to be solved to find the RF pulse which, simultaneously with the prescribed gradient waveform, excites the magnetic spins in the desired way. The same STA formalism has been extended to the case of parallel excitation, when several RF coils simultaneously transmit independent RF fields modulated in time by the designed waveform functions. In this work, an efficient numerical solution of the STA equation for the transmit SENSE pulse design has been presented. Particularly at high field strengths, the coil's transmit sensitivities are not homogeneous, and knowledge of each individual transmit profile is needed to obtain accurate magnetization profiles and/or shorten the RF pulse length by undersampling the k-space. Transmit RF coil sensitivity maps are thus needed for the RF design process as the receive RF coil sensitivity maps are needed for parallel imaging techniques. The way to acquire these two kind of maps has been, up to this moment, performed with two distinct measurements. In this work, a unifying approach for fast and simultaneous mapping of transmit and receive fields is introduced. Finally, not only the global but also the local power deposition in the tissue can be controlled in the design process by extending the model equation to include terms which correspond to local SAR. The extended model requires lengthy computations to be solved. The final part of this thesis is dedicated to the fast solution of this problem. The outlined points have prevented so far the implementation of the transmit SENSE RF pulse design process into clinical application. This thesis addresses these issues and indicates solution strategies which could pave the way to clinical implementation