T2∗ phase imaging and processing for brain functional magnetic susceptibility (χ) mapping

Purpose. To provide a review on T2∗-weighted magnetic resonance imaging (T2∗MRI) for T2∗ phase imaging and on a computed inverse MRI (CIMRI) model for magnetic susceptibility (χ) reconstruction. To compare two different phase unwrapping methods (in the time domain and in the space domain) for χreconstruction and χ-based functional mapping. Methods. T2∗MRI and CIMRI are modeled as twostep spatial mappings. A task-evoked blood oxygenation level dependent functional MRI study produces a timeseries of T2∗ magnitude and phase images. A complex division is performed on a 4D phase dataset to extract the temporal phase changes (δP), implementing time-domain phase unwrapping. A 4D δχ dataset is reconstructed from 4D δP by CIMRI. Mean while, T2∗ phase images are subject to Laplacian phase unwrapping and homodyne high-pass filtering. The processed phase images are used for 4Dχ dataset reconstruction. Finally, independent component analysis (ICA) is performed to different 4D datasets to extract task-evoked functional maps from different perspectives. Results. A 7T finger tapping experiment provided a pair of 4D T2∗ magnitude and phase datasets. A 4Dχ dataset was reconstructed from spatially unwrapped phase images (P), and a 4Dδχ dataset froma temporally-unwrapped phase images (δP). The ICA-extracted functional maps from five different 4D dataspaces {'A', 'P', 'δP', 'χ', 'δχ'} exhibited correlative responses (via ICA-extracted temporal modes) to the task stimuli with maximal temporal correlations of {0.93, 0.85, 0.90, 0.87, 0.91} respectively. Conclusion. A time series of T2∗ phase images can be effectively temporally unwrapped by a complex division algorithm that extracts the phase changes in relative to baseline. The small phase changes facilitate the pure brain χ response reconstruction by a linear CIMRI model. In comparison, the phase unwrapping in the space domain retains the baseline for full brain χ state reconstruction at a compromise of CIMRI linearity.