Estimating microstructural parameters from gradient-echo and spin-echo data: a test of the strong collision approximation

Motivation: To develop noninvasive methods to interrogate magnetic microstructure. Goal(s): To test whether the strong collision approximation can accurately characterize microstructure of known geometry and magnetic susceptibility from gradient-echo and spin-echo signals. Approach: Experimental data were acquired from phantoms containing polystyrene microbeads of 10$$$\mu$$$m, 20$$$\mu$$$m and 40$$$\mu$$$m diameter suspended in gadolinium-doped gelatin. Data were fitted using a published model based on the strong collision approximation and a lookup table prepared from Monte Carlo simulations. Results: The strong collision approximation overestimated bead size and underestimated magnetic susceptibility from gradient-echo data. For spin-echo data, it yielded poor estimates of susceptibility and was insensitive to bead size. Impact: The strong collision approximation is a non-perturbative approach for predicting gradient-echo and spin-echo signals in the presence of magnetic microstructure. It employs the Krogh construction and a simplified diffusion propagator. We show how those simplifications affect estimates of microstructural parameters.