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Magn Reson Imaging. 2015 May;33(4):390-400. doi: 10.1016/j.mri.2015.01.016. Epub 2015 Jan 23.

Nonlinear magnitude and linear phase behaviors of T2* imaging: theoretical approximation and Monte Carlo simulation.

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The Mind Research Network and LBERI, Albuquerque, NM 87106. Electronic address:
The Mind Research Network and LBERI, Albuquerque, NM 87106; University of New Mexico, ECE Dept, Albuquerque, NM 87131.


The underlying source of brain imaging by T2*-weighted magnetic resonance imaging (T2*MRI) is the intracranial inhomogeneous tissue magnetic susceptibility (denoted by χ) that causes an inhomogeneous field map (via magnetization) in a main field. By decomposing T2*MRI into two steps, we understand that the 1st step from a χ source to a field map is a linear but non-isomorphic spatial mapping, and the 2nd step from the field map to a T2* image is a nonlinear mapping due to the trigonometric behavior of spin precession signals. The magnitude and phase calculations from a complex T2* image introduce additional nonlinearities. In this report, we look into the magnitude and phase behaviors of a T2* image (signal) by theoretical approximation and Monte Carlo simulation. We perform the 1st-order Taylor expansion on intravoxel dephasing formula of a T2* signal and show that the T2* magnitude is a quadratic mapping of the field map and T2* phase is a linear isomorphic mapping. By Monte Carlo simulation of T2*MRI for a span of echo times (with B0=3T and TE=[0,120] ms), we first confirm the quadratic magnitude and linear phase behaviors in small phase angle regime (via TE <30ms), and then provide more general magnitude and phase nonlinear behaviors in large phase angle scenarios (via TE >30ms). By solving the inverse problem of T2*MRI, we demonstrate χ tomography and conclude that the χ source can be reliably reconstructed from a T2* phase image in a small phase angle regime.


T2*MRI; complex T2* image (signal); intravoxel dephasing; magnetic susceptibility tomography; small phase angle regime; trigonometric spin signal

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