Effect of diffusion in inhomogeneous magnetic fields on balanced steady-state free precession

Abstract

In this work, the effects of susceptibility variation from dilute, micron-sized spherical field perturbers and diffusion on balanced steady-state free precession (bSSFP) are analyzed. Predictions from Monte Carlo simulations are in good agreement with experiments and reveal that, for diffusing protons, susceptibility variation becomes apparent as a reduction in the overall bSSFP signal intensity. This reduction depends on microsphere parameters (radius and susceptibility difference), as well as on sequence-related parameters (repetition time and flip angle) and on relaxation times. Specific Monte Carlo results from one set of parameter values can be extrapolated to another set of values by means of a scaling law and a substitution model. The scaling law, derived from the Bloch-Torrey equation, captures the dependencies of bSSFP signal reduction on susceptibility and diffusion-related changes and on repetition time, whereas the substitution model describes those on flip angle and relaxation times.