Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)

Cataloged from PDF version of article.Images of electrical conductivity and permittivity of tissues may be used for diagnostic purposes as well as for estimating local specific absorption rate distributions. Magnetic resonance electrical properties tomography (MREPT) aims at noninvasively obtaining conductivity and permittivity images at radio-frequency frequencies of magnetic resonance imaging systems. MREPT algorithms are based on measuring the B1 field which is perturbed by the electrical properties of the imaged object. In this study, the relation between the electrical properties and the measured B1 field is formulated for the first time as a well-known convection-reaction equation. The suggested novel algorithm, called “cr-MREPT,” is based on the solution of this equation on a triangular mesh, and in contrast to previously proposed algorithms, it is applicable in practice not only for regions where electrical properties are relatively constant but also for regions where they vary. The convective field of the convection-reaction equation depends on the spatial derivatives of the B1 field, and in the regions where its magnitude is low, a spot-like artifact is observed in the reconstructed electrical properties images. For eliminating this artifact, two different methods are developed, namely “constrained cr-MREPT” and “double-excitation cr-MREPT.” Successful reconstructions are obtained using noisy and noise-free simulated data, and experimental data from phantoms

Fourier transform magnetic resonance current density imaging (FT-MRCDI) from one component of magnetic flux density

Fourier transform (FT)-based algorithms for magnetic resonance current density imaging (MRCDI) from one component of magnetic flux density have been developed for 2D and 3D problems. For 2D problems, where current is confined to the xy-plane and z-component of the magnetic flux density is measured also on the xy-plane inside the object, an iterative FT-MRCDI algorithm is developed by which both the current distribution inside the object and the z-component of the magnetic flux density on the xy-plane outside the object are reconstructed. The method is applied to simulated as well as actual data from phantoms. The effect of measurement error on the spatial resolution of the current density reconstruction is also investigated. For 3D objects an iterative FT-based algorithm is developed whereby the projected current is reconstructed on any slice using as data the Laplacian of the z-component of magnetic flux density measured for that slice. In an injected current MRCDI scenario, the current is not divergence free on the boundary of the object. The method developed in this study also handles this situation. © 2010 Institute of Physics and Engineering in Medicine

Oscillatory surface rheotaxis of swimming E. coli bacteria

Bacterial contamination of biological conducts, catheters or water resources is a major threat to public health and can be amplified by the ability of bacteria to swim upstream. The mechanisms of this rheotaxis, the reorientation with respect to flow gradients, often in complex and confined environments, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow with two complementary experimental assays, based on 3D Lagrangian tracking and fluorescent flagellar labelling and we develop a theoretical model for their rheotactic motion. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A full theoretical analysis explains these regimes and predicts the corresponding critical shear rates. The predicted transitions as well as the oscillation dynamics are in good agreement with experimental observations. Our results shed new light on bacterial transport and reveal new strategies for contamination prevention.Comment: 12 pages, 5 figure

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization

Cataloged from PDF version of article.Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (del B-2(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this del B-2(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is testedwith simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial

Electrical impedance tomography using the magnetic field generated by injected currents

In 2D EIT imaging, the internal distribution of the injected currents generate a magnetic field in the imaging region which can be measured by magnetic resonance imaging techniques. This magnetic field is perpendicular to the imaging region on the imaging region and it can be used in reconstructing the conductivity distribution inside the imaging region. For this purpose, internal current distribution is found using the finite element method. The magnetic fields due to this current is found using Biot-Savart law. Sensitivity of magnetic field distribution to inner conductivity perturbations for different current injection profiles is studied. it is found that, to achieve a uniform spatial resolution, a current profile which generates uniform current inside the imaging region is to be applied. The condition number of the sensitivity matrix obtained for this case is found to be very low. Several images are obtained using simulation data

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

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

Magnetic resonance-conductivity imaging using 0.15 Tesla MRI scanner

A novel imaging method for electrical impedance tomography is implemented. In this method, the magnetic flux density generated by current flowing in a 2D slice is measured using MRI scanner and recorded data is used to reconstruct relative conductivity images. The measurements are done from all parts of the imaging region, and therefore sensitivity is space independent. The magnetic flux density is extracted from phase images of the MRI image and a sensitivity based image reconstruction algorithm is used to reconstruct relative conductivity images. The magnetic flux density measured and the conductivity image reconstructed for an insulator object placed in the middle of the imaging region 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

Imaging electrical current density using 0.15T Magnetic Resonance Imaging system

In this study, imaging of electrical current density in conducting objects, which contain nuclear magnetic resonance (NMR) active nuclei is planned using 0.15T Magnetic Resonance Imaging (MRI) system. Current to be imaged is externally applied to the object in synchrony with a standard spin-echo pulse sequence. Applied current is a bipolar DC current pulse, which creates a DC current density at each cycle within the object. The applied current pulse creates a measurable magnetic flux density. The component of magnetic flux density parallel to the main magnetic field accumulates an additional phase in the phase of the complex MR image. Magnetic flux density can be extracted using two phase images acquired with and without the current pulse. Measurement of all three components of magnetic flux density makes the reconstruction of current density possible with a spatial resolution equal to the half of the MR resolution. Experiments performed on several phantoms and the results are presented