An optimal design method for magnetic resonance imaging gradient waveforms

Abstract

A method of using nonlinear constrained optimization to design gradient waveforms for magnetic resonance imaging is described. Artificial constraints on waveform shape imposed by multilobe designs are eliminated by defining the waveform as a set of discrete amplitudes. These amplitudes are the parameters determined in the optimization procedure, subject to the constraints defined by imaging conditions and the specific gradient hardware system of interest. Formulation and solution of the waveform optimization problem are described and example waveforms are presented for a variety of design objectives and constraint sets. Most design objectives can be expressed as linear or quadratic functions of the discrete parameter set, and most constraint functions are linear. Thus, linear and quadratic programming techniques can be utilized to solve the optimization problem. Among the objectives considered are: 1) minimize RMS current; 2) minimize waveform slewing; 3) minimize waveform moments to reduce motion induced dephasing; 4) minimize echo time (TE) for given imaging and motion refocusing conditions; 5) maximize the gradient amplitude during RF application and sampling and the area of the phase encoding waveform to maximize resolution; and 6) minimize or maximize the gradient b factor or diffusion sensitivity. This optimal design procedure produces physically realizable waveforms which optimally achieve specific imaging and motion artifact reduction goals, and it is likely to reduce waveform design time by making it more scientifically (rather than heuristically) based. © 1993 IEEE.