B. Murat Eyuboglu

Current constrained voltage scaled reconstruction (CCVSR) algorithm for MR-EIT and its performance with different probing current patterns.

Conventional injected-current electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) techniques can be combined to reconstruct high resolution true conductivity images. The magnetic flux density distribution generated by the internal current density distribution is extracted from MR phase images. This information is used to form a fine detailed conductivity image using an Ohms law based update equation. The reconstructed conductivity image is assumed to differ from the true image by a scale factor. EIT surface potential measurements are then used to scale the reconstructed image in order to find the true conductivity values. This process is iterated until a stopping criterion is met. Several simulations are carried out for opposite and cosine current injection patterns to select the best current injection pattern for a 2D thorax model. The contrast resolution and accuracy of the proposed algorithm are also studied. In all simulation studies, realistic noise models for voltage and magnetic flux density measurements are used. It is shown that, in contrast to the conventional EIT techniques, the proposed method has the capability of reconstructing conductivity images with uniform and high spatial resolution. The spatial resolution is limited by the larger element size of the finite element mesh and twice the magnetic resonance image pixel size.

Experimental results for 2D magnetic resonance electrical impedance tomography (MR-EIT) using magnetic flux density in one direction

Magnetic resonance electrical impedance tomography (MR-EIT) is an emerging imaging technique that reconstructs conductivity images using magnetic flux density measurements acquired employing MRI together with conventional EIT measurements. In this study, experimental MR-EIT images from phantoms with conducting and insulator objects are presented. The technique is implemented using the 0.15 T Middle East Technical University MRI system. The dc current method used in magnetic resonance current density imaging is adopted. A reconstruction algorithm based on the sensitivity matrix relation between conductivity and only one component of magnetic flux distribution is used. Therefore, the requirement for object rotation is eliminated. Once the relative conductivity distribution is found, it is scaled using the peripheral voltage measurements to obtain the absolute conductivity distribution. Images of several insulator and conductor objects in saline filled phantoms are reconstructed. The L2 norm of relative error in conductivity values is found to be 13%, 17% and 14% for three different conductivity distributions.

Equipotential projection-based magnetic resonance electrical impedance tomography and experimental realization

In this study, a direct, fast image reconstruction algorithm, based on the fact that equipotential lines are perpendicular to current lines in a volume conductor, is proposed for magnetic resonance electrical impedance tomography (MR-EIT). The proposed technique is evaluated both on simulated and measured data for conductor and insulator objects.

Anisotropic conductivity imaging with MREIT using equipotential projection algorithm

Magnetic resonance electrical impedance tomography (MREIT) combines magnetic flux or current density measurements obtained by magnetic resonance imaging (MRI) and surface potential measurements to reconstruct images of true conductivity with high spatial resolution. Most of the biological tissues have anisotropic conductivity; therefore, anisotropy should be taken into account in conductivity image reconstruction. Almost all of the MREIT reconstruction algorithms proposed to date assume isotropic conductivity distribution. In this study, a novel MREIT image reconstruction algorithm is proposed to image anisotropic conductivity. Relative anisotropic conductivity values are reconstructed iteratively, using only current density measurements without any potential measurement. In order to obtain true conductivity values, only either one potential or conductivity measurement is sufficient to determine a scaling factor. The proposed technique is evaluated on simulated data for isotropic and anisotropic conductivity distributions, with and without measurement noise. Simulation results show that the images of both anisotropic and isotropic conductivity distributions can be reconstructed successfully.

Distinguishability analysis of an induced current EIT system using discrete coils

The distinguishability of a discrete coil induced current electrical impedance tomography system is analysed. The solution methodology of the forward problem of this system is explained. An optimization procedure using this forward problem solution is developed to find optimum currents that maximize the distinguishability. For the concentric inhomogeneity problem, it is shown that the coil currents can be optimized to focus the current density in any desired location, in the field of view. Optimum coil currents under the constraints of limited peak coil currents and limited total power are determined. Examples that demonstrate the performance of the system are presented.

New technique for high-resolution absolute conductivity imaging using magnetic-resonance electrical impedance tomography (MR-EIT)

A novel MR-EIT imaging modality has been developed to reconstruct high-resolution conductivity images with true conductivity value. In this new technique, electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) techniques are simultaneously used. Peripheral voltages are measured using EIT and magnetic flux density measurements are determined using MRI. The image reconstruction algorithm used is an iterative one, based on minimizing the difference between two current density distributions calculated from voltage and magnetic flux density measurements separately. The performance of the proposed method and the suggested reconstruction algorithm are tested on simulated data. A finite element model with 1089 nodes and 2048 triangular elements is used to generate the simulated potential and magnetic field measurements. A 16 electrode opposite drive EIT strategy is adopted. The spatial resolution is space independent and limited by either the finite element size or half the MR resolution. The worst of the two defines the spatial resolution. The rms error in reconstructed conductivity for a concentric inhomogeneity is calculated as 5.35% and this error increases to 13.22% when 10% uniformly distributed random noise is added to potential and magnetic flux density measurements. The performance of the algorithm for more complex models will also be presented.

A quasi-static analysis for a class of induced-current EIT systems using discrete coils

A discrete coil EIT system is investigated for the general case of an eccentric circular inhomogeneity. The solution methodology of the forward problem of this system is explained. An optimization procedure using this forward problem solution is developed to find optimum currents that maximize the distinguishability. For an eccentric inhomogeneity problem, it is shown that the coil currents can be optimized to focus the current density in a region of interest. Optimum coil currents under limited peak coil currents constraint and limited total power constraint are obtained. Representative examples that demonstrate the performance of the system are presented.

Use of a priori information in estimating tissue resistivities: a simulation study

Accurate estimation of tissue resistivities in vivo is needed to construct reliable human body volume conductor models in solving forward and inverse bioelectric field problems. The necessary data for the estimation can be obtained by using the four-electrode impedance measurement technique, usually employed in electrical impedance tomography. In this study, a priori geometrical information with statistical properties of regional resistivities and linearization error as well as instrumentation noise has been incorporated into a new resistivity estimation algorithm which is called a statistically constrained minimum mean squares error estimator (MiMSEE) to improve estimation accuracy. MiMSEE intakes geometrical information from the image which is obtained by using a high-resolution imaging modality. This study is an extension of earlier work by Eyüboğlu et al and obtains simulated measurements from two numerical models containing five and six regions on a background region. Also, estimations are repeated by using up to eight multiple current electrode pairs, in order to observe the effect of estimation performance while increasing the number of measurements up to 96. The results are compared with a conventional least squares error estimator (LSEE) which is used in one-pass algorithms. It is shown that the MiMSEE estimation error is up to 27 times smaller than the LSEE error which is realized for a small, high-contrast region, for example the aorta. In estimating the regional resistivities, the MiMSEE algorithm requires 25.8 (for the five-region resistivity distribution) and 22.2 (for the six-region resistivity distribution) times more computational time than the LSEE. This gap between the computational times of the two algorithms decreases as the number of regions increases.

Induced current magnetic resonance electrical impedance tomography with z-gradient coil

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a medical imaging method that provides images of electrical conductivity at low frequencies (0-1 kHz). In MREIT, electrical current is applied to the body via surface electrodes and corresponding magnetic flux density is measured by means of Magnetic Resonance (MR) phase imaging techniques. By utilizing the magnetic flux density measurements and surface potential measurements images of true conductivity distribution can be reconstructed. In order to overcome difficulties regarding current application via surface electrodes, Induced Current MREIT (ICMREIT) have been proposed in the past. In ICMREIT, electrical currents and corresponding magnetic flux density are generated in the object through electromagnetic induction by means of externally placed coils driven with time varying currents. In this study, use of z-gradient, z-Helmholtz, and circular coil configurations in ICMREIT are proposed and investigated. Finite Element Method (FEM) is used to solve the forward problem of ICMREIT. Consequently, excitation performances and clinical applicability of different coil configurations are analyzed.

J-substitution and equipotential-projection based hybrid MREIT reconstruction algorithm

Magnetic Resonance Electrical Impedance Tomography is an imaging modality which reconstructs true conductivity images by using current density distribution and surface potential measurements. In this study, two current based algorithms, namely equipotential projection [1] and J-substitution image reconstruction [2] algorithms are compared. A novel reconstruction technique, J-substitution and equipotential-projection based hybrid reconstruction algorithm, is proposed. In this technique, the image which is reconstructed with equipotential projection algorithm is assigned as the starting conductivity distribution for J-substitution algorithm. Moreover, true conductivity values can be reconstructed with two surface potential measurements. Simulation results on a thorax phantom show that the proposed method has a better performance in some regions.