Magnetic resonance-based reconstruction method of conductivity and permittivity distributions at the Larmor frequency

Magnetic resonance electrical property tomography 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 systems the eddy currents induced by the radio-frequency magnetic fields reflect the conductivity ($\sigma$) and permittivity ($\epsilon$) distributions inside the tissues through Maxwell's equations. The corresponding inverse problem consists of reconstructing the admittivity distribution ($\gamma=\sigma+i\omega\epsilon$) at the Larmor frequency ($\omega/2\pi=$128 MHz for a 3 tesla MRI machine) from the positive circularly polarized component of the magnetic field ${\bf H}=(H_x,H_y,H_z)$. Previous methods are usually based on an assumption of local homogeneity ($\nabla\gamma\approx 0$) which simplifies the governing equation. However, previous methods that include the assumption of homogeneity are prone to artifacts in the region where $\gamma$ varies. Hence, recent work has sought a reconstruction method that does not assume local-homogeneity. This paper presents a new magnetic resonance electrical property tomography reconstruction method which does not require any local homogeneity assumption on $\gamma$. We find that $\gamma$ is a solution of a semi-elliptic partial differential equation with its coefficients depending only on the measured data $H^+$, which enable us to compute a blurred version of $\gamma$. 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 $\gamma$. Numerical simulations are presented to illustrate the potential of the proposed reconstruction method

A Local Region of Interest Imaging Method for Electrical Impedance Tomography with Internal Electrodes

Electrical Impedance Tomography (EIT) is a very attractive functional imaging method despite the low sensitivity and resolution. The use of internal electrodes with the conventional reconstruction algorithms was not enough to enhance image resolution and accuracy in the region of interest (ROI). We propose a local ROI imaging method with internal electrodes developed from careful analysis of the sensitivity matrix that is designed to reduce the sensitivity of the voxels outside the local region and optimize the sensitivity of the voxel inside the local region. We perform numerical simulations and physical measurements to demonstrate the localized EIT imaging method. In preliminary results with multiple objects we show the benefits of using an internal electrode and the improved resolution due to the local ROI image reconstruction method. The sensitivity is further increased by allowing the surface electrodes to be unevenly spaced with a higher density of surface electrodes near the ROI. Also, we analyse how much the image quality is improved using several performance parameters for comparison. While these have not yet been studied in depth, it convincingly shows an improvement in local sensitivity in images obtained with an internal electrode in comparison to a standard reconstruction method

Electrical Impedance Tomography-Based Abdominal Subcutaneous Fat Estimation Method Using Deep Learning

This paper proposes a deep learning method based on electrical impedance tomography (EIT) to estimate the thickness of abdominal subcutaneous fat. EIT for evaluating the thickness of abdominal subcutaneous fat is an absolute imaging problem that aims at reconstructing conductivity distributions from current-to-voltage data. Existing reconstruction methods based on EIT have difficulty handling the inherent drawbacks of strong nonlinearity and severe ill-posedness of EIT; hence, absolute imaging may not be possible using linearized methods. To handle nonlinearity and ill-posedness, we propose a deep learning method that finds useful solutions within a restricted admissible set by accounting for prior information regarding abdominal anatomy. We determined that a specially designed training dataset used during the deep learning process significantly reduces ill-posedness in the absolute EIT problem. In the preprocessing stage, we normalize current-voltage data to alleviate the effects of electrodeposition and body geometry by exploiting knowledge regarding electrode positions and body geometry. The performance of the proposed method is demonstrated through numerical simulations and phantom experiments using a 10 channel EIT system and a human-like domain

A Point Crack Source Location Method without Velocity Information in Anisotropic Plates

Locating cracks in a solid object using acoustic emission (AE) is useful both for detecting defects during safety monitoring and for basic laboratory studies of fractures. We developed an acoustic source location (ASL) method without the use of velocity information with AE in anisotropics plates, such as carbon fiber-reinforced polymers. Assuming that the propagation velocity of an unknown elastic wave is constant in anisotropic materials, the objective function to be minimized is defined based on the elliptic wavefront shape-based technique. The objective function is minimized using an iterative method, such as the gradient descent method. As a result of the numerical experiments and PLB testing on a carbon fiber-reinforced polymer plate, the method is accurate within 5% and is stable against noise

A Point Crack Source Location Method without Velocity Information in Anisotropic Plates

Locating cracks in a solid object using acoustic emission (AE) is useful both for detecting defects during safety monitoring and for basic laboratory studies of fractures. We developed an acoustic source location (ASL) method without the use of velocity information with AE in anisotropics plates, such as carbon fiber-reinforced polymers. Assuming that the propagation velocity of an unknown elastic wave is constant in anisotropic materials, the objective function to be minimized is defined based on the elliptic wavefront shape-based technique. The objective function is minimized using an iterative method, such as the gradient descent method. As a result of the numerical experiments and PLB testing on a carbon fiber-reinforced polymer plate, the method is accurate within 5% and is stable against noise

Effective Admittivity of Biological Tissues as a Coefficient of Elliptic PDE

The electrical properties of biological tissues can be described by a complex tensor comprising a simple expression of the effective admittivity. The effective admittivities of biological tissues depend on scale, applied frequency, proportions of extra- and intracellular fluids, and membrane structures. The effective admittivity spectra of biological tissue can be used as a means of characterizing tissue structural information relating to the biological cell suspensions, and therefore measuring the frequency-dependent effective conductivity is important for understanding tissue’s physiological conditions and structure. Although the concept of effective admittivity has been used widely, it seems that its precise definition has been overlooked. We consider how we can determine the effective admittivity for a cube-shaped object with several different biologically relevant compositions. These precise definitions of effective admittivity may suggest the ways of measuring it from boundary current and voltage data. As in the homogenization theory, the effective admittivity can be computed from pointwise admittivity by solving Maxwell equations. We compute the effective admittivity of simple models as a function of frequency to obtain Maxwell-Wagner interface effects and Debye relaxation starting from mathematical formulations. Finally, layer potentials are used to obtain the Maxwell-Wagner-Fricke expression for a dilute suspension of ellipses and membrane-covered spheres