Susceptibility-based functional brain mapping by 3D deconvolution of an MR-phase activation map.

The underlying source of T2*-weighted magnetic resonance imaging (T2*MRI) for brain imaging is magnetic susceptibility (denoted by χ). T2*MRI outputs a complex-valued MR image consisting of magnitude and phase information. Recent research has shown that both the magnitude and the phase images are morphologically different from the source χ, primarily due to 3D convolution, and that the source χ can be reconstructed from complex MR images by computed inverse MRI (CIMRI). Thus, we can obtain a 4D χ dataset from a complex 4D MR dataset acquired from a brain functional MRI study by repeating CIMRI to reconstruct 3D χ volumes at each timepoint. Because the reconstructed χ is a more direct representation of neuronal activity than the MR image, we propose a method for χ-based functional brain mapping, which is numerically characterised by a temporal correlation map of χ responses to a stimulant task. Under the linear imaging conditions used for T2*MRI, we show that the χ activation map can be calculated from the MR phase map by CIMRI. We validate our approach using numerical simulations and Gd-phantom experiments. We also analyse real data from a finger-tapping visuomotor experiment and show that the χ-based functional mapping provides additional activation details (in the form of positive and negative correlation patterns) beyond those generated by conventional MR-magnitude-based mapping.