### Abstract

Magnetic resonance electric properties tomography (MREPT) is a recent medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. It uses the fact that in magnetic resonance imaging (MRI) systems the eddy currents induced by the radio-frequency magnetic fields reflect the conductivity (σ) and permittivity (ε) distributions inside the tissues through Maxwell's equations. The corresponding inverse problem consists of reconstructing the admittivity distribution (γ = σ + iωε)at the Larmor frequency (ω/2π = MHz for a 3 Tesla MRI machine) from the positive circularly polarized component of the magnetic field H =(H_{x}, H_{y}, H_{z}. Previous methods are usually based on an assumption of local homogeneity (∀_{γ} ≈0)which simplifies the governing equation. However, previous methods that include the assumption of homogeneity are prone to artifacts in the region where γ varies. Hence, recent work has sought a reconstruction method that does not assume local-homogeneity. This paper presents a new MREPT reconstruction method which does not require any local homogeneity assumption on γ. We find that γ is a solution of a semi-elliptic partial differential equation with its coefficients depending only on the measured data H^{+}:= (H_{x}+iH_{y})/2, which enable us to compute a blurred version of γ. To improve the resolution of the reconstructed image, we developed a new optimization algorithm that minimizes the mismatch between the data and the model data as a highly nonlinear function of γ. Numerical simulations are presented to illustrate the potential of the proposed reconstruction method.

Original language | English |
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Article number | 105001 |

Journal | Inverse Problems |

Volume | 31 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2015 Sep 8 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics

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## Cite this

*Inverse Problems*,

*31*(10), [105001]. https://doi.org/10.1088/0266-5611/31/10/105001