Magnetic Resonance Electrical Impedance Tomography (MREIT)

SIAM Review (Impact Factor: 4.79). 02/2011; 53(1):40-68. DOI: 10.1137/080742932
Source: DBLP

ABSTRACT Magnetic resonance electrical impedance tomography (MREIT) is a recently developed medical imaging modality visualizing conductivity images of an electrically conducting object. MREIT was motivated by the well-known ill-posedness of the image reconstruction problem of electrical impedance tomography (EIT). Numerous experiences have shown that practically measurable data sets in an EIT system are insufficient for a robust reconstruction of a high-resolution static conductivity image due to its ill-posed nature and the influences of errors in forward modeling. To overcome the inherent ill-posed characteristics of EIT, the MREIT system was proposed in the early 1990s to use the internal data of magnetic flux density ${\bf B}=(B_x,B_y,B_z)$, which is induced by an externally injected current. MREIT uses an MRI scanner as a tool to measure the $z$-component $B_z$ of the magnetic flux density, where $z$ is the axial magnetization direction of the MRI scanner. In 2001, a constructive $B_z$-based MREIT algorithm called the harmonic $B_z$ algorithm was developed and its numerical simulations showed that high-resolution conductivity image reconstructions are possible. This novel algorithm is based on the key observation that the Laplacian $\Delta B_z$ probes changes in the log of the conductivity distribution along any equipotential curve having its tangent to the vector field ${\bf J}\times (0,0,1)$, where ${\bf J}=(J_x,J_y,J_z)$ is the induced current density vector. Since then, imaging techniques in MREIT have advanced rapidly and have now reached the stage of in vivo animal and human experiments. This paper reviews MREIT from its mathematical framework to the most recent human experiment outcomes.

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Available from: Eung Je Woo, Dec 18, 2013
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    • "Such methods are also known under the name of " hybrid inverse problems " . Notable examples are the coupling of Magnetic Resonance with Electrical Impedance Tomography [45], Ultrasound and Electrical Impedance Tomography [11], Magnetic Resonance and Elastography [26]. To fix ideas, let us focus on Ultrasound Modulated Electrical Impedance Tomography. "
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    ABSTRACT: We consider $\sigma$-harmonic mappings, that is mappings $U$ whose components $u_i$ solve a divergence structure elliptic equation ${\rm div} (\sigma \nabla u_i)=0$, for $i=1,\ldots,n $. We investigate whether, with suitably prescribed Dirichlet data, the Jacobian determinant can be bounded away from zero. Results of this sort are required in the treatment of the so-called hybrid inverse problems, and also in the field of homogenization studying bounds for the effective properties of composite materials.
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    • "EIT has however a limited spatial resolution, since the surface measurements are less sensitive to conductivity changes in inner regions of the patient [5]. Recently, several hybrid tomography techniques have been developed, which are based on electric and magnetic fields [6], [7], MR signals [8] Corresponding author: N. De Geeter (E-mail: or acoustic modalities [9], [10]. "
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    ABSTRACT: An accurate conductivity estimation of the human brain tissues is important for the correct diagnosis and therapy of neurological diseases. These values are patient-specific and vary naturally with the frequency. Nevertheless, they are often approximated by a constant value. Induced current magnetic resonance - electrical impedance tomography (ICMR-EIT) is a possible technique for non-invasive conductivity reconstruction in the low frequency domain. This paper presents a novel ICMREIT based method that uses the difference of two MR phase images. These images are obtained by gradient echo sequences with and without switching an eddy-current induction gradient. We propose the use of multiple gradients with different time periods, so that only a single parameter per tissue needs to be estimated with conservation of the frequency dependence. A numerical study on a spherical head model with four tissues investigates the feasibility of estimating conductivity values and shows that the proposed technique can successfully reconstruct these conductivity values. Furthermore, the influence of the material model and the number of harmonics associated to the gradient is investigated, together with performance of the proposed technique in the presence of noise.
    IEEE Transactions on Magnetics 03/2013; DOI:10.1109/TMAG.2013.2250985 · 1.21 Impact Factor
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    • "In 2001 [5], an imaging technique of MREIT without mechanical rotation, called harmonic í µí°µ í µí± § algorithm, was developed to provide both conductivity image and current density image. After invention of the harmonic í µí°µ í µí± § algorithm, MREIT has advanced rapidly [6] [7]. However, it still remains a technical problem to reduce the injection current down to a level for routine clinical use while maintaining the spatial resolution of the resulting conductivity images. "
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    ABSTRACT: MR Electric Properties Tomography (EPT) is a lately developed medical imaging modality capable of visualizing both conductivity and permittivity of the patient at the Larmor frequency using B1 maps. The paper discusses the development of EPT reconstructions, EPT sequences, EPT experiments, and challenging issues of EPT.
    Computational and Mathematical Methods in Medicine 03/2013; 2013:546562. DOI:10.1155/2013/546562 · 1.02 Impact Factor
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