Magnetic resonance-based reconstruction method of conductivity and permittivity distributions at the Larmor frequency. (8th September 2015)

• Record Type: Journal Article
• Authors: Ammari, Habib; Kwon, Hyeuknam; Lee, Yoonseop; Kang, Kyungkeun; Seo, Jin Keun
• Is Part Of: Inverse problems. Volume 31:Number 10(2015:Oct.)
• Publication Date: 2015-09-08
• Subjects: inverse problems -- electrical property tomography -- optimal control -- MRI -- Maxwell's equations; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/10/105001
• Languages: English
• ISSNs: 0266-5611

Abstract

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 distributions inside the tissues through Maxwell's equations. The corresponding inverse problem consists of reconstructing the admittivity distribution at the Larmor frequency ( MHz for a 3 Tesla MRI machine) from the positive circularly polarized component of the magnetic field . Previous methods are usually based on an assumption of local homogeneity 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, 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.