Inverse Mapping of BOLD fMRI: 4D Magnetic Susceptibility (χ) Tomography

Background: A brain magnetic state (in terms of magnetic susceptibility distribution χ) can be detected by T2*-weighted MRI (T2*MRI) undergoing a cascade of data transformations. The MRI transformations cause distortions (or spatial morphing), which may be undone by solving the inverse imaging or mapping problem. Upon having a dataset acquired from Blood Oxygenation Level-Dependent (BOLD) functional MRI, we can reconstruct the dynamic brain χ source by inverse mapping called 4D χ tomography. This chapter is to address the imaging and inverse imaging aspects of BOLD fMRI from the perspective of data mapping. Methods: T2*MRI is described by a mathematical mapping from a real-valued continuous χ source to a complex-valued discrete T2* image, of which the T2* magnitude imaging implements a mapping from a set of real numbers (R = (-∞, ∞)) to a set of nonnegative numbers (R+ = [0, ∞)) that is irreversible; whereas the T2* phase imaging (with unwrapped phase) is a mapping of R → R that is reversible. A 3D χ map is reconstructed from a 3D T2* phase image by a Computed Inverse MRI (CIMRI) method. The dynamic 4D χ source is reconstructed by 4D χ tomography, implementing a spatiotemporal inverse mapping of BOLD fMRI. Zikuan Chen1,2* 1Zinv LLC, Albuquerque, NM 87108, USA 2The Mind Research Network, Albuquerque, NM 87106, USA *Corresponding author: Zikuan Chen, The Mind Research Network, Albuquerque, NM 87106, USA, Email: [email protected] Published Date: June 30, 2016