Multi-echo quantitative susceptibility mapping: how to combine echoes for accuracy and precision at 3 Tesla

Purpose: To compare different multi-echo combination methods for MRI QSM. Given the current lack of consensus, we aimed to elucidate how to optimally combine multi-echo gradient-recalled echo signal phase information, either before or after applying Laplacian-base methods (LBMs) for phase unwrapping or background field removal.

Methods: Multi-echo gradient-recalled echo data were simulated in a numerical head phantom, and multi-echo gradient-recalled echo images were acquired at 3 Tesla in 10 healthy volunteers. To enable image-based estimation of gradient-recalled echo signal noise, 5 volunteers were scanned twice in the same session without repositioning. Five QSM processing pipelines were designed: 1 applied nonlinear phase fitting over TEs before LBMs; 2 applied LBMs to the TE-dependent phase and then combined multiple TEs via either TE-weighted or SNR-weighted averaging; and 2 calculated TE-dependent susceptibility maps via either multi-step or single-step QSM and then combined multiple TEs via magnitude-weighted averaging. Results from different pipelines were compared using visual inspection; summary statistics of susceptibility in deep gray matter, white matter, and venous regions; phase noise maps (error propagation theory); and, in the healthy volunteers, regional fixed bias analysis (Bland-Altman) and regional differences between the means (nonparametric tests).

Results: Nonlinearly fitting the multi-echo phase over TEs before applying LBMs provided the highest regional accuracy of $\chi$ and the lowest phase noise propagation compared to averaging the LBM-processed TE-dependent phase. This result was especially pertinent in high-susceptibility venous regions.

Conclusion: For multi-echo QSM, we recommend combining the signal phase by nonlinear fitting before applying LBMs.