Joint design of kT-points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime.

In Magnetic Resonance Imaging at ultra-high field, kT-points radiofrequency pulses combined with parallel transmission are a promising technique to mitigate the B1 field inhomogeneity in 3D imaging applications. The optimization of the corresponding k-space trajectory for its slice-selective counterpart, i.e. the spokes method, has been shown in various studies to be very valuable but also dependent on the hardware and specific absorption rate constraints. Due to the larger number of degrees of freedom than for spokes excitations, joint design techniques based on the fine discretization (gridding) of the parameter space become hardly tractable for kT-points pulses. In this article, we thus investigate the simultaneous optimization of the 3D blipped k-space trajectory and of the kT-points RF pulses, using a magnitude least squares cost-function, with explicit constraints and in the large flip angle regime. A second-order active-set algorithm is employed due to its demonstrated success and robustness in similar problems. An analysis of global optimality and of the structure of the returned trajectories is proposed. The improvement provided by the k-space trajectory optimization is validated experimentally by measuring the flip angle on a spherical water phantom at 7T and via Quantum Process Tomography.