### Abstract

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 B_{0}=3T and T_{E}=[0,120] ms), we first confirm the quadratic magnitude and linear phase behaviors in small phase angle regime (via T_{E} <30ms), and then provide more general magnitude and phase nonlinear behaviors in large phase angle scenarios (via T_{E} >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.

Original language | English (US) |
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Pages (from-to) | 390-400 |

Number of pages | 11 |

Journal | Magnetic Resonance Imaging |

Volume | 33 |

Issue number | 4 |

DOIs | |

State | Published - May 1 2015 |

Externally published | Yes |

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### Keywords

- Complex T2 image (signal)
- Intravoxel dephasing
- Magnetic susceptibility tomography
- Small phase angle regime
- T2*MRI
- Trigonometric spin signal

### ASJC Scopus subject areas

- Biophysics
- Biomedical Engineering
- Radiology Nuclear Medicine and imaging