Magnetic Resonance Electrical Impedance Tomography

Magnetic resonance electrical impedance tomography (MREIT) is an imaging technique of reconstructing the cross-sectional conductivity distribution of a human body by means of the EIT technique integrated with the MRI technique.

In MREIT, one uses a magnetic resonance imaging scanner to measure the induced magnetic flux density due to an injection current. When one injects a current into a subject, it produces a magnetic field as well as an electric field. In EIT, one utilizes only the electrical quantities. Furthermore, since there is no noninvasive way of getting measurements of electrical quantities from inside the subject, we are limited in EIT by the boundary current-voltage data which is insensitive to internal conductivity perturbations. However, one can enrich the data by measuring the internal magnetic flux density. This can be done using a magnetic resonance imaging scanner as a tool to capture the internal magnetic flux density images. This technique is called magnetic resonance current density imaging (MRCDI). Combining EIT and MRCDI, MREIT perceives the distortion of current pathways due to the conductivity distribution to be imaged and overcomes the severe ill-posedness character of EIT.

In this chapter, we first formulate the forward and inverse problem in MREIT utilizing the internal magnetic flux density in conductivity image reconstructions. Then we discuss the uniqueness issue in MREIT. We show that one should use at least two appropriate injection currents for the uniqueness of reconstructed conductivity image. After that, we describe the J-substitution algorithm which provides a high-resolution conductivity image. This algorithm is involved with a nonlinear partial differential equation instead of the linear conductivity equation.