Exploiting gradient-echo frequency evolution: Probing white matter microstructure and extracting bulk susceptibility-induced frequency for quantitative susceptibility mapping

Abstract

Purpose: This work is to investigate the microstructure-induced frequency shift in white matter (WM) with crossing fibers and to separate the microstructure-related frequency shift from the bulk susceptibility-induced frequency shift by model fitting the gradient-echo (GRE) frequency evolution for potentially more accurate quantitative susceptibility mapping (QSM).

Methods: A hollow-cylinder fiber model (HCFM) with two fiber populations was developed to investigate GRE frequency evolutions in WM voxels with microstructural orientation dispersion. The simulated and experimentally measured TE-dependent local frequency shift was then fitted to a simplified frequency evolution model to obtain a microstructure-related frequency difference parameter ( $∆f$ ) and a TE-independent bulk susceptibility-induced frequency shift ( $C_f$ ). The obtained $C_f$ was then used for QSM reconstruction. Reconstruction performances were evaluated using a numerical head phantom and in vivo data and then compared to other multi-echo combination methods.

Results: GRE frequency evolutions and $∆f$ -based tissue parameters in both parallel and crossing fibers determined from our simulations were comparable to those observed in vivo. The TE-dependent frequency fitting method outperformed other multi-echo combination methods in estimating $C_f$ in simulations. The fitted $∆f$ , $C_f$ , and QSM could be improved further by navigator-based B₀ fluctuation correction.

Conclusion: A HCFM with two fiber populations can be used to characterize microstructure-induced frequency shifts in WM regions with crossing fibers. HCFM-based TE-dependent frequency fitting provides tissue contrast related to microstructure ( $∆f$ ) and in addition may help improve the quantification accuracy of $C_f$ and the corresponding QSM.

Keywords: QSM; TE-dependent frequency; bulk susceptibility-induced frequency; gradient-echo frequency evolution; microstructure-induced frequency.