Optimal diffusion-gradient waveforms for measuring axon diameter

Introduction: Measuring microstructure parameters of brain tissue, such as axon radius, in vivo is a challenge in diffusion MRI. Current approaches typically use pulsed-gradient spin-echo (PGSE) [1] or stimulated-echo (STEAM) [2] sequences, both of which use a rectangular diffusion-gradient pulse. However other shapes of diffusion-gradient pulses such as oscillating [3] or chirped [4] may provide more sensitivity to microstructure features, particularly at low gradient strengths available on clinical scanners. Here, we optimize the shape of the diffusion-gradient waveform, constrained only by hardware limits and to have fixed orientation, to give the best estimate of axon radius based on a simple model of the diffusion within white matter.