Multi-echo dipole inversion for magnetic susceptibility mapping.

Purpose: Reconstructing tissue magnetic susceptibility (QSM) from MRI phase data involves solving multiple consecutive ill-posed inverse problems such as phase unwrapping, background field removal, and field-to-source inversion. Multi-echo acquisitions present an additional challenge, as the magnetization field is typically computed from the multiple phase data prior to reconstructing the susceptibility map. Processing the multiple phase data introduces errors during the field estimation, violating assumptions of the subsequent inverse problems, manifesting as streaking artifacts in the susceptibility map. To address this challenge, we propose a multi-echo field-to-source forward model that forgoes the field estimation step. Moreover, we propose a fully general underestimation correction step to recover susceptibility sources that were regularized away during the field-to-source inversion.

Methods: The multi-echo forward model and correction step were validated on the QSM Challenge 2.0 datasets and compared to the standard single field-to-source model in in vivo human brains using different types of deconvolution algorithms.

Results: On the QSM Challenge 2.0 datasets the multi-echo forward model and correction step attain state-of-the-art results on all metrics by a wide margin. Experiments in in vivo brains show that the multi-echo model is in agreement with the single field-to-source model and that the proposed forward model and correction step can be used with any available dipole inversion method.

Conclusion: A multi-echo field-to-source forward model forgoes the need to fit multi-echo phase data and achieves state-of-the-art results on the QSM Challenge 2.0 data. Underestimated low-frequency susceptibility distributions can be partially recovered using a correction step.