The Ritz Adjoint Method for MRI Pulse Design.

High-field magnetic resonance imaging (MRI) suffers from pronounced magnetic field inhomogeneities and subject-specific field variations, motivating the in-scanner design of individually tailored excitation pulses to exploit the full capabilities of high-field MRI. Contemporary methods may employ piecewise-constant (PWC) waveform parameterizations to design excitation pulses, which require many optimization variables and hinder rapid, in-scanner customization. We represent the radiofrequency (RF) and gradient waveforms in a global waveform basis, demonstrated using a Chebyshev polynomial basis, to reduce problem dimensionality and accelerate convergence, while ensuring waveform smoothness. The adjoint method efficiently computes derivatives of the excitation objective function with respect to the basis coefficients, which each influence an entire waveform. Graphics processing unit (GPU) acceleration of derivative computation further reduces computation time, while system and safety constraints are enforced throughout the optimization. Using this global waveform basis yields an approximate five- to ten-fold speedup in subject-specific (tailored) pulse optimization for non-selective excitations and, in the best case, comparable gains for slice-selective designs, making real-time, subject-specific pulse optimization feasible even for advanced pulse types.