Signatures of microstructure in gradient‐echo and spin‐echo signals

Abstract Purpose To determine whether the spatial scale and magnetic susceptibility of microstructure can be evaluated robustly from the decay of gradient‐echo and spin‐echo signals. Theory and Methods Gradient‐echo and spin‐echo images were acquired from suspensions of spherical polystyrene microbeads of 10, 20, and 40 μm nominal diameter. The sizes of the beads and their magnetic susceptibility relative to the medium were estimated from the signal decay curves, using a lookup table generated from Monte Carlo simulations and an analytic model based on the Gaussian phase approximation. Results Fitting Monte Carlo predictions to spin‐echo data yielded acceptable estimates of microstructural parameters for the 20 and 40 μm microbeads. Using gradient‐echo data, the Monte Carlo lookup table provided satisfactory parameter estimates for the 20 μm beads but unstable results for the diameter of the largest beads. Neither spin‐echo nor gradient‐echo data allowed accurate parameter estimation for the smallest beads. The analytic model performed poorly over all bead sizes. Conclusions Microstructural sources of magnetic susceptibility produce distinctive non‐exponential signatures in the decay of gradient‐echo and spin‐echo signals. However, inverting the problem to extract microstructural parameters from the signals is nontrivial and, in certain regimes, ill‐conditioned. For microstructure with small characteristic length scales, parameter estimation is hampered by the difficulty of acquiring accurate data at very short echo times. For microstructure with large characteristic lengths, the gradient‐echo signal approaches the static‐dephasing regime, where it becomes insensitive to size. Applicability of the analytic model was further limited by failure of the Gaussian phase approximation for all but the smallest beads.