## Abstract

A two-step numerical computation of T_{2}∗ signal weighting maps in gradient echo magnetic resonance imaging in the presence of an object with varied susceptibility property is presented. In the first step, the magnetic scalar potential is computed for an arbitrary 2D magnetic susceptibility distribution using an algebraic solver. The corresponding magnetic field disturbance is computed from the magnetic scalar potential. In the second step, nonlinear operations are used to compute T_{2}∗ from the magnetic field disturbance and then to generate a map of T_{2}∗ signal weighting. The linearity of the first step of the solution process is used to implement a superposition of basis solutions approach that increases computational efficiency. Superposition of basis solutions, computed from a system composed of a single node of differing magnetic susceptibility from the surround, herein referred to as the base system, is found to provide an accurate estimation of the scalar potential for arbitrary susceptibility distributions. Afterwards, nonlinear computation of the T_{2}∗ signal weighting maps can be performed. The properties of the algebraic magnetic scalar potential solver are discussed in this work. Finally, the linearity of the magnetic scalar potential solver is used to estimate the magnetic susceptibility of various objects from in vitro MR-imaging data acquired at 9.4 T.

Original language | English (US) |
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Article number | 045029 |

Journal | Biomedical Physics and Engineering Express |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - Jun 14 2018 |

### Bibliographical note

Funding Information:This work was supported in part by an Institute for Engineering in Medicine (IEM) Group Grant at the University of Minnesota, the University of Minnesota MnDrive RSAM Initiative Grant, the Minnesota Supercomputing Institute (MSI) at the University of Minnesota, NIH grants R01 MH111413, R01 NS070839, R24 MH106049, P41 EB015894, P30 NS076408, the W M Keck Foundation, and NSF-IGERT DGE-1069104.

Publisher Copyright:

© 2018 IOP Publishing Ltd.

## Keywords

- magnetic field distortion
- magnetic susceptibility
- numerical solver