Simple but reliable solutions for spiral MRI gradient design

The efficiency of gradient design in MRI is limited by the simple fact that the gradient coil current and slew rate cannot exceed hardware threshold values. In spiral MRI, which requires gradients to be very rapidly switched between positive and negative values, minimization of the acquisition time is achieved by maintaining the current and slew rate as high as possible during the entire measurement. Since the current and slew rate compete against each other, an efficient gradient design consists of two parts in which current and slew rate are pushed alternatively to their limits. Values for these types of gradients can be obtained by solving numerically the equation of motion for the spiral trajectory. This paper shows that simple but reasonable mathematical approximations deliver reliable analytical solutions. Images obtained using these analytical solutions do not show evident distortions when compared with images obtained with numerical solutions.