A harmonic -based conductivity reconstruction method in MREIT with influence of non-transversal current density

Abstract

Magnetic resonance electrical impedance tomography (MREIT) is a high-resolution conductivity imaging method utilizing measured magnetic flux density data induced by externally injected currents. Most MREIT image reconstruction methods including the harmonic $B_z$ algorithm adopt iterative schemes to handle the non-linear relation between conductivity and magnetic flux density. Iterative methods, however, may not guarantee a reliable conductivity reconstruction when the measured magnetic flux density data are contaminated with a significant amount of noise. In this paper, we propose a new image reconstruction method which alleviates the technical difficulties of the iterative harmonic $B_z$ algorithm. It effectively reduces the number of iterations by two at most. To improve the image quality, it incorporates the influence of non-transversal current densities. Providing theoretical observations and details of the proposed algorithm, we present results of numerical simulations and phantom experiments for its validation.

Keywords:

• MREIT
• $B_z$-based algorithm
• conductivity and current density reconstruction
• non-transversal current density
• phantom experiment

Notes

No potential conflict of interest was reported by the authors.

2 Friedrichs’ inequality [35]: Suppose that ${\mathrm{\Omega }}_s$ is a simply connected bounded Lipschitz domain in ${\mathbf{R}}^2$. Then every function $\mathbf{u}$ of ${\left[H_1({\mathrm{\Omega }}_s)\right]}^2$ with $\mathbf{u}·\mathbf{n}=0$ on $\mathit{\partial }{\mathrm{\Omega }}_s$ satisfies that ${\Vert \mathbf{u}\Vert }_{{\mathbf{L}}^2({\mathrm{\Omega }}_s)}\le C\left(\Vert {\mathrm{\nabla }}_{xy}{·\mathbf{u}\Vert }_{L^2({\mathrm{\Omega }}_s)}+{\Vert {\mathrm{\nabla }}_{xy}^{\perp }·\mathbf{u}\Vert }_{L^2({\mathrm{\Omega }}_s)}\right)$ where the constant $C>0$ depends only on ${\mathrm{\Omega }}_s$.

Additional information

Funding

Kiwan Jeon was supported by the National Institute for Mathematical Sciences (NIMS) grant funded by the Korean government [number A21300000]. Chang-Ock Lee was supported by the NRF grant funded by MSIP (NRF-2014R1A2A2A01006497). Eung Je Woo was supported by the NRF grant (NRF-2014R1A2A1A09006320).