Practical design of diffusion MRI based on the decay of spatial modulations in a steady-state

Abstract Purpose To determine the precision achievable and identify optimal protocols for imaging diffusion using the decay of a spatial modulation of longitudinal magnetization in a spoiled gradient-echo train, for MR microscopy, clinical 3T imaging and low-field systems. Theory and Methods: A modulation of longitudinal magnetization at spatial frequency k decays at a rate Λ = R 1 − ln(cos α)/TR + Dk² during a steady state sequence, and D can be obtained from measuring the rates at two spatial frequencies. We derive the constraints that gradient limitations place on image acquisitions and extend the analysis to encoding modules that write several harmonics simultaneously. We calculate the Cramér–Rao bound on D for realistic experimental measurements on typical systems. Protocols were optimized considering modulation period, flip angle, TR, train length and recovery delay at fixed scan time, and checked with Monte Carlo and Bloch–Torrey simulations. Results Optimal modulation periods were 65–75 µm at 3 T, near 75 µm at 64 mT and 20–25 µm for microscopy, with shallow optima. Predicted precision was 3.8% per voxel in six minutes at 3 T with a single-shot readout, 13.6% at 64 mT and 18.7% in microscopy, or 0.4–1.9% over a region of 100 voxels. A single 1–1 module is optimal when a recall gradient is needed; a 1-3-3-1 module is better when its harmonics can be resolved. Away from boundaries D was mapped to within 0.3%. Conclusion Precise diffusion measurements are feasible with weak gradients on clinical and low-field scanners. The controlling design constraint is that the recall gradient must fit inside TR.