Fast Large-Tip-Angle Multidimensional and Parallel RF Pulse Design in MRI

Abstract

Large-tip-angle multidimensional RF pulse design is a difficult problem, due to the nonlinear response of magnetization to applied RF at large tip-angles. In parallel excitation, multidimensional RF pulse design is further complicated by the possibility for transmit field patterns to change between subjects, requiring pulses to be designed rapidly while a subject lies in the scanner. To accelerate pulse design, we introduce a fast version of the optimal control method for large-tip-angle parallel excitation. The new method is based on a novel approach to analytically linearizing the Bloch equation about a large-tip-angle RF pulse, which results in an approximate linear model for the perturbations created by adding a small-tip-angle pulse to a large-tip-angle pulse. The linear model can be evaluated rapidly using non-uniform fast Fourier transforms, and we apply it iteratively to produce a sequence of pulse updates that improve excitation accuracy. We achieve drastic reductions in design time and memory requirements compared to conventional optimal control, while producing pulses of similar accuracy. The new method can also compensate for non-idealities such as main field inhomogeneties.

Training Schrödinger’s cat: quantum optimal control

“…Motivated by magnetic resonance imaging applications, optimal control pulses for MRI have been developed [88,[324][325][326]330,[397][398][399][400]. Applications include improved spatially selective excitation schemes [106,401,402], pulses with minimal radio-frequency (RF) power and pulses that counteract RF inhomogeneity in parallel transmission at ultra-high field [330,398].…”

“…Applications include improved spatially selective excitation schemes [106,401,402], pulses with minimal radio-frequency (RF) power and pulses that counteract RF inhomogeneity in parallel transmission at ultra-high field [330,398]. For chemical exchange saturation transfer (CEST) imaging, chemical exchange effects were taken into account in pulse sequence optimizaion [403].…”

Time-optimal polarization transfer from an electron spin to a nuclear spin

“…These methods have been successfully applied in NMR [92,93] to designing broad-band [94][95][96] and decoupling pulse sequences [97][98][99][100][101][102]. They have also been utilized in magnetic resonance imaging [25,[103][104][105] and electron paramagnetic resonance [106].…”

Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods

“…[26][27][28] In these areas, OC has demonstrated a great potential to establish experiments adapting well to technical challenges and constraints included in the cost functional, as for example, rf power limitations, 27 rf inhomogeneity, 22,23 and rf envelope "jaggedness." 29,30 Addressing MRI, OC procedures have so far involved gradient-based methods 20,26,27,31 exploiting conjugated gradient optimization. 32 Such methods are known to be robust and convergent within a finite number of iterations.…”

“…Optimization with gradients alone is also prone to convergence towards local optima and may need both plenty of iterations to reach the optimum and may need multiple repetitions to reach a satisfactory optimum without an educated initial starting point. In order to improve these cumbersome steps, Grissom et al 31 have introduced fast optimal control procedures that exploit the nonuniform fast Fourier transform (NUFFT) approximation to the Bloch equation and they demonstrate significant reduction in computation time in the design of pTx MDRF pulses. However, the gradient-based algorithms are still complicated for practical realization and too time consuming for clinical applications.…”