### 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) |
---|---|

Article number | 045029 |

Journal | Biomedical Physics and Engineering Express |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - Jun 14 2018 |

### Fingerprint

### Keywords

- magnetic field distortion
- magnetic susceptibility
- numerical solver

### PubMed: MeSH publication types

- Journal Article

### Cite this

_{2}∗-weighted MRI, with Applications to Magnetic Susceptibility Parameter Estimation.

*Biomedical Physics and Engineering Express*,

*4*(4), [045029]. https://doi.org/10.1088/2057-1976/aaca02

**Computation of Magnetic Field Distortions and Impact on T _{2}∗-weighted MRI, with Applications to Magnetic Susceptibility Parameter Estimation.** / Cruttenden, Corey E.; Zhu, Xiao Hong; Chen, Wei; Rajamani, Rajesh.

Research output: Contribution to journal › Article

_{2}∗-weighted MRI, with Applications to Magnetic Susceptibility Parameter Estimation',

*Biomedical Physics and Engineering Express*, vol. 4, no. 4, 045029. https://doi.org/10.1088/2057-1976/aaca02

}

TY - JOUR

T1 - Computation of Magnetic Field Distortions and Impact on T2∗-weighted MRI, with Applications to Magnetic Susceptibility Parameter Estimation

AU - Cruttenden, Corey E.

AU - Zhu, Xiao Hong

AU - Chen, Wei

AU - Rajamani, Rajesh

PY - 2018/6/14

Y1 - 2018/6/14

N2 - A two-step numerical computation of T2∗ 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 T2∗ from the magnetic field disturbance and then to generate a map of T2∗ 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 T2∗ 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.

AB - A two-step numerical computation of T2∗ 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 T2∗ from the magnetic field disturbance and then to generate a map of T2∗ 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 T2∗ 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.

KW - magnetic field distortion

KW - magnetic susceptibility

KW - numerical solver

UR - http://www.scopus.com/inward/record.url?scp=85053135196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053135196&partnerID=8YFLogxK

U2 - 10.1088/2057-1976/aaca02

DO - 10.1088/2057-1976/aaca02

M3 - Article

C2 - 31179012

AN - SCOPUS:85053135196

VL - 4

JO - Biomedical Physics and Engineering Express

JF - Biomedical Physics and Engineering Express

SN - 2057-1976

IS - 4

M1 - 045029

ER -