A simple analytical expression for the gradient induced potential on active implants during MRI.

During magnetic resonance imaging, there is an interaction between the time-varying magnetic fields and the active implantable medical devices (AIMD). In this study, in order to express the nature of this interaction, simplified analytical expressions for the electric fields induced by time-varying magnetic fields are derived inside a homogeneous cylindrical volume. With these analytical expressions, the gradient induced potential on the electrodes of the AIMD can be approximately calculated if the position of the lead inside the body is known. By utilizing the fact that gradient coils produce linear magnetic field in a volume of interest, the simplified closed form electric field expressions are defined. Using these simplified expressions, the induced potential on an implant electrode has been computed approximately for various lead positions on a cylindrical phantom and verified by comparing with the measured potentials for these sample conditions. In addition, the validity of the method was tested with isolated frog leg stimulation experiments. As a result, these simplified expressions may help in assessing the gradient-induced stimulation risk to the patients with implants.

Induced current magnetic resonance-electrical impedance tomography.

Magnetic resonance-electrical impedance tomography (MR-EIT) is a conductivity imaging method based on injecting currents into the object. In this study, a new MR-EIT method, whereby currents are induced inside the object by using external coils, is proposed. This new method is called induced current magnetic resonance-electrical impedance tomography. In induced current MR-EIT surface electrodes are not used and thereby artifacts due to electrodes are eliminated. The reconstruction algorithm is based on the measurement of only one component of the secondary magnetic flux density. The algorithm is an iterative one, is 3D and is based on the solution of a linear matrix equation at each iteration. For the measurement of secondary magnetic flux density, a pulse sequence to be used in the MRI system is proposed. Numerical simulations are performed to test the algorithm for both noise-free and noisy cases. The singular value behavior of the matrix is monitored and it is observed that at least two current induction profiles improve the images significantly. It is shown that induced current MR-EIT can be used to reconstruct absolute conductivity images without the need for any additional peripheral voltage measurement.

Algebraic reconstruction for 3D magnetic resonance-electrical impedance tomography (MREIT) using one component of magnetic flux density.

Magnetic resonance-electrical impedance tomography (MREIT) algorithms fall into two categories: those utilizing internal current density and those utilizing only one component of measured magnetic flux density. The latter group of algorithms have the advantage that the object does not have to be rotated in the magnetic resonance imaging (MRI) system. A new algorithm which uses only one component of measured magnetic flux density is developed. In this method, the imaging problem is formulated as the solution of a non-linear matrix equation which is solved iteratively to reconstruct resistivity. Numerical simulations are performed to test the algorithm both for noise-free and noisy cases. The uniqueness of the solution is monitored by looking at the singular value behavior of the matrix and it is shown that at least two current injection profiles are necessary. The method is also modified to handle region-of-interest reconstructions. In particular it is shown that, if the image of a certain xy-slice is sought for, then it suffices to measure the z-component of magnetic flux density up to a distance above and below that slice. The method is robust and has good convergence behavior for the simulation phantoms used.

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.

Uniqueness and reconstruction in magnetic resonance-electrical impedance tomography (MR-EIT).

Magnetic resonance-electrical impedance tomography (MR-EIT) was first proposed in 1992. Since then various reconstruction algorithms have been suggested and applied. These algorithms use peripheral voltage measurements and internal current density measurements in different combinations. In this study the problem of MR-EIT is treated as a hyperbolic system of first-order partial differential equations, and three numerical methods are proposed for its solution. This approach is not utilized in any of the algorithms proposed earlier. The numerical solution methods are integration along equipotential surfaces (method of characteristics), integration on a Cartesian grid, and inversion of a system matrix derived by a finite difference formulation. It is shown that if some uniqueness conditions are satisfied, then using at least two injected current patterns, resistivity can be reconstructed apart from a multiplicative constant. This constant can then be identified using a single voltage measurement. The methods proposed are direct, non-iterative, and valid and feasible for 3D reconstructions. They can also be used to easily obtain slice and field-of-view images from a 3D object. 2D simulations are made to illustrate the performance of the algorithms.

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 Ohm's 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.