Variable slew-rate spiral design: Theory and application to peak B ₁ amplitude reduction in 2D RF pulse design

A new class of spiral trajectories called variable slew-rate spirals is proposed. The governing differential equations for a variable slew-rate spiral are derived, and both numeric and analytic solutions to the equations are given. The primary application of variable slew-rate spirals is peak B₁ amplitude reduction in 2D RF pulse design. The reduction of peak B₁ amplitude is achieved by changing the gradient slew-rate profile, and gradient amplitude and slew-rate constraints are inherently satisfied by the design of variable slew-rate spiral gradient waveforms. A design example of 2D RF pulses is given, which shows that under the same hardware constraints the RF pulse using a properly chosen variable slew-rate spiral trajectory can be much shorter than that using a conventional constant slew-rate spiral trajectory, thus having greater immunity to resonance frequency offsets.