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Traditionally, brain function analysis is based on the magnitude data of complex-valued spatiotemporal (4D) functional magnetic resonance imaging (fMRI). Since an MRI signal is formed from the underlying brain tissue magnetic property through a cascade of transformations (such as dipole magnetization), the fMRI data (either magnitude or phase) do not directly capture the original magnetic source. In principle, upon solving an inverse fMRI problem, we can reconstruct the magnetic source (specifically magnetic susceptibility, denoted by χ and analyze brain function in the reconstructed χ dataspace at a stage closer to the origin of brain function neurophysiology. Our recent research has shown that the magnetic χ source can be reconstructed from the fMRI phase through a computational inverse MRI solution (CIMRI). Together with the fMRI output data, we can compare three aspects of the data, the magnitude, the phase, and the susceptibility, each of which provides a different perspective. Given a 4D dataset, we analyze the data via independent component analysis (ICA), applicable to both single-subject and multi-subject data. In this study, we addressed the following points: 1) brain function ICA decomposition of magnitude (mICA), phase (pICA), and susceptibility (χICA); 2) comparison of brain function network connectivity matrices (FC) for each of these, namely {mFC, pFC, and χFC} matrices; and 3) applications to a task fMRI experiment (fingertapping, 20 subjects). In theory, we show that the fMRI phase is approximately linearly related to the reconstructed χ source data (different by a spatial dipole convolution), while fMRI magnitude has a nonlinear relationship. Therefore, we conclude that pFC is more similar to χFC than mFC. Through experimental data analyses, we have verified this conclusion.
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