O'Reilly logo

Nonlinear Inverse Problems in Imaging by Eung Je Woo, Jin Keun Seo

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 9

Magnetic Resonance Electrical Impedance Tomography

For high-resolution static imaging of a conductivity distribution inside the human body, there have been strong needs for supplementary data to make the inverse problem well-posed and to overcome the fundamental limitations of the electrical impedance tomography (EIT) imaging methods. To bypass the ill-posed nature of EIT, magnetic resonance electrical impedance tomography (MREIT) was proposed in the early 1990s to take advantage of an MRI scanner as a tool to capture internal magnetic flux density data induced by externally injected currents (Birgul and Ider 1995; Birgul and Ider 1996; Woo et al. 1994; Zhang 1992).

MREIT aims to visualize conductivity images of an electrically conducting object using the current injection MRI technique (Joy et al. 1989; Scott et al. 1991, 1992). To probe the passive material property of the conductivity, low-frequency electrical current is injected into the imaging object through surface electrodes. This induces internal distributions of voltage u, current density J = (Jx, Jy, Jz) and magnetic flux density B = (Bx, By, Bz) dictated by Maxwell's equations. At a low frequency of less than a few kilohertz, we can ignore the effects of permittivity and consider only conductivity. For conductivity image reconstructions, MREIT relies on a set of internal magnetic flux density data, since it is dictated by the conductivity distribution σ according to Ampère's law

where μ0 is the magnetic permeability ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required