Computational methods and optimization strategies for parallel transmission in ultra high field MRI
Keywords: Electrical Engineering.

Magnetic resonance imaging (MRI) is a powerful imaging modality that is widely used in medicine for both clinical and research purposes. Despite its success, there is still a demand for improved image quality in the form of higher SNR and resolution and a promising approach to achieve this is with higher static field strengths (7 Tesla and above) corresponding to the ultra high frequency (UHF) regime of the RF pulse. At these frequencies, wavelength effects and complex interactions with biological tissue become problematic leading to field inhomogeneity artifacts and tissue heating concerns quantified by the specific absorption rate (SAR). This dissertation will focus on the excitation portion of the imaging process with parallel transmission (pTx) that involves using a transmit RF coil with multiple independent transmit channels. pTx is an effective way to address the challenges of ultra high field MRI through optimization of the transmitted pulse in a patient-specific way. We introduce the Iterative Minimization Procedure with Uncompressed Local SAR Estimate (IMPULSE) which is a novel distributed optimization algorithm that has favorable scaling properties and eliminates the need for virtual observation points (VOPs) thus resulting in superior SAR performance and shorter computation time. The optimization problem is to minimize SAR over a pulse sequence consisting of multiple slice excitations while ensuring that the flip angle inhomogeneity (FAI) for each excited slice is within some user specified tolerance. IMPULSE uses the alternating direction method of mulitpliers (ADMM) to split the optimization into two subproblems, a SAR-update and a FAI-update, that are solved at each iteration until convergence. The SAR-update can be formulated as an unconstrained minimization of a piecewise quadratic function which can be solved efficiently by using a bundle method to build a piecewise linear surrogate that can easily be minimized. The computation time for the FAI-update can be reduced by exploiting parallelization and using an efficient algorithm for projection of a point onto an ellipsoid. IMPULSE achieves superior SAR performance and reduced computation time compared to a conventional approach using virtual observation points or compared to using a generic sequential quadratic programming (SQP) solver in MATLAB. Using the Duke head model consisting of over six million voxels, minimum SAR pTx pulses were designed for 120 slices within 45 seconds with an FAI tolerance of 5\% at each slice. IMPULSE combined with variable rate selective excitation (VERSE) can also be used to improve SAR performance and reduce computation time for simultaneous multislice (SMS) excitation with a pTx-SMS pulse. This method (IMPULSE-SMS) was used for the pTx-SMS task of the ISMRM RF Pulse Design competition in 2016 and resulted in a pulse that was about 20\% shorter than the second best submission and about 10 times shorter than a conventional approach (SAR-unaware pulse design without VERSE). Increasing the number of transmit channels in a coil can give more degrees of freedom to achieve flip angle uniformity and reduce SAR but also increases cost and complexity of the hardware. Studying the performance of massively parallel transmit arrays in simulation can help determine whether investment in these arrays is justified based on new applications that are enabled. An 84 channel loop array for 10.5T with 6 rows and 14 columns was simulated using the Ella body model and applied to two novel applications: power independent of number of slices (PINS) pulses combined with pTx for SMS excitation and SAR focusing for therapeutic hyperthermia. Using this coil in addition to an insertable head gradient (slew rate of 1500 T/m/s), a pulse duration of about 13ms for a 16 slice coronal excitation with 0.4mm slice thickness with 10\% FAI was achieved. SAR focusing is possible for a range of locations throughout the head (although focusing is better at the periphery than at the center). A solution to a simplified bioheat equation indicates that achievable temperature rise would be within acceptable range for some forms of hyperthermia (but not high enough to achieve for ablation). A significant concern in SAR-aware pTx is mismatch between the patient and the tissue model used for SAR estimation since running the optimization on a mismatched model can result in significantly higher SAR compared to a perfect match. One technique to introduce robustness to this mismatch is to use the SAR terms for voxels of multiple tissue models (rather than a single model) in the cost function of IMPULSE. Results indicate that using multiple poorly matched models can achieve similar SAR performance compared to using a single closely matched model indicating that the multiple model approach is a way to get by with a sparse model library that doesn't fully represent the entire human population. A more sophisticated approach is to use deep learning to predict the 3D SAR maps from measured magnetic field maps. An initial implementation of this concept shows promise but is still inconclusive.