Papers
Analysis and Blocking of Error Propagation by Region-Dependent Noisy Data in MREIT
- AuthorYizhuang Song, Hyeuknam Kwon, Kiwan Jeon, Yoon Mo Jung, Jin Keun Seo, Eung Je Woo
- JournalSIAM Journal on Scientific Computing 35(4) (2013
- Link https://doi.org/10.1137/120889034
- Classification of papersSCI
Magnetic resonance electrical impedance tomography (MREIT) aims to visualize a conductivity distribution inside the human body. In MREIT, we inject current to produce a current density $\mathbf{J}$ and magnetic flux density $\mathbf{B}$ inside the body, and we measure $B_z$, which is the $z$-component of $\mathbf{B}$, using an MRI scanner with its main field in the $z$ direction. Using fundamental relations between the measured $B_z$ and the conductivity, we can reconstruct cross-sectional images of the internal conductivity distribution. In this paper, we adopt the harmonic $B_z$ algorithm, which is based on the key observation that $\nabla^2 B_z$ reveals changes in the log of the conductivity distribution along any equipotential curve on an imaging slice. When we apply the method to measured $B_z$ data from animal or human subjects, however, there occur a few technical difficulties that are mainly related to measurement errors in $B_z$ data, especially in a local region where MR signals are very small. This demands innovative data processing methods based on a rigorous mathematical analysis of such defective data. We carefully investigate sources of the error and its adverse effects on the image reconstruction process. We suggest a new error propagation blocking algorithm to prevent defective data at one local region from negatively influencing conductivity images of other regions. We experimentally examine the performance of the proposed method by comparing reconstructed images with and without applying the error propagation blocking algorithm. We found that the error blocking algorithm improves the accuracy of reconstructed conductivity images.
Magnetic resonance electrical impedance tomography (MREIT) aims to visualize a conductivity distribution inside the human body. In MREIT, we inject current to produce a current density $\mathbf{J}$ and magnetic flux density $\mathbf{B}$ inside the body, and we measure $B_z$, which is the $z$-component of $\mathbf{B}$, using an MRI scanner with its main field in the $z$ direction. Using fundamental relations between the measured $B_z$ and the conductivity, we can reconstruct cross-sectional images of the internal conductivity distribution. In this paper, we adopt the harmonic $B_z$ algorithm, which is based on the key observation that $\nabla^2 B_z$ reveals changes in the log of the conductivity distribution along any equipotential curve on an imaging slice. When we apply the method to measured $B_z$ data from animal or human subjects, however, there occur a few technical difficulties that are mainly related to measurement errors in $B_z$ data, especially in a local region where MR signals are very small. This demands innovative data processing methods based on a rigorous mathematical analysis of such defective data. We carefully investigate sources of the error and its adverse effects on the image reconstruction process. We suggest a new error propagation blocking algorithm to prevent defective data at one local region from negatively influencing conductivity images of other regions. We experimentally examine the performance of the proposed method by comparing reconstructed images with and without applying the error propagation blocking algorithm. We found that the error blocking algorithm improves the accuracy of reconstructed conductivity images.