Algebraic reconstraction 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

Model based analysis of the variation in Korotkoff sound onset time during exercise

In this study, a minimal mathematical model of the cardiovascular system is used to study the effects of changes in arterial compliance and cardiac contractility on the onset time of Korotkoff sounds during an auscultatory procedure. The model provides blood pressure waveforms in the ventricle, the aorta and the brachial artery. From these waveforms, pre-ejection time, pulse propagation time and rise time of the blood pressure at the brachial artery can be computed. The time delay between onset time of ECG Q wave and onset time of Korotkoff sound is the sum of these three times. Rise time is zero and the time delay is minimal when the cuff pressure is slightly above the diastolic pressure. This minimum time delay is represented by QKD. Simulation results suggest that during the Bruce exercise protocol QKD decreases to one-third of its pre-exercise value if the cardiac contractility increases threefold. The effect of arterial compliance is not as significant as that of the cardiac contractility. From data recorded during an exercise test, it is observed that QKD decreases considerably as the test load is increased. We show in this study that the amount of decrease in QKD can be used as an index of the amount of increase in cardiac contractility during an exercise ECG test. Use of signal averaging for reducing the effect of motion artifacts during an exercise test is also shown to be very instrumental for making accurate QKD measurements

Feasibility of conductivity imaging using subject eddy currents induced by switching of MRI gradients

Purpose: To investigate the feasibility of low-frequency conductivity imaging based on measuring the magnetic field due to subject eddy currents induced by switching of MRI z-gradients. Methods: We developed a simulation model for calculating subject eddy currents and the magnetic fields they generate (subject eddy fields). The inverse problem of obtaining conductivity distribution from subject eddy fields was formulated as a convection-reaction partial differential equation. For measuring subject eddy fields, a modified spin-echo pulse sequence was used to determine the contribution of subject eddy fields to MR phase images. Results: In the simulations, successful conductivity reconstructions were obtained by solving the derived convection-reaction equation, suggesting that the proposed reconstruction algorithm performs well under ideal conditions. However, the level of the calculated phase due to the subject eddy field in a representative object indicates that this phase is below the noise level and cannot be measured with an uncertainty sufficiently low for accurate conductivity reconstruction. Furthermore, some artifacts other than random noise were observed in the measured phases, which are discussed in relation to the effects of system imperfections during readout. Conclusion: Low-frequency conductivity imaging does not seem feasible using basic pulse sequences such as spin-echo on a clinical MRI scanner. Magn Reson Med 77:1926–1937, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicin

Numerical methods and software tools for simulation, design, and resonant mode analysis of radio frequency birdcage coils used in MRI

Design of magnetic resonance imaging (MRI) radiofrequency (RF) coils using lumped circuit modeling based techniques begins to fail at high frequencies, and therefore more accurate models based on the electromagnetic field calculations must be used. Field calculations are also necessary to understand the interactions between the RF field and the subject inside the coil. Furthermore, observing the resonance behavior of the coil and the fields at the resonance frequencies have importance for design and analysis. In this study, finite element method (FEM) based methods have been proposed for accurate time-harmonic electromagnetic simulations, estimation of the tuning capacitors on the rungs or end rings, and the resonant mode analysis of the birdcage coils. Capacitance estimation was achieved by maximizing the magnitude of the port impedance at the desired frequency while simultaneously minimizing the variance of RF magnetic field in the region of interest. In order for the proposed methods to be conveniently applicable, two software tools, resonant mode and frequency domain analyzer (RM-FDA) and Optimum Capacitance Finder (OptiCF), were developed. Simulation results for the validation and verification of the software tools are provided for different cases including human head simulations. Additionally, two handmade birdcage coils (low-pass and high-pass) were built and resonance mode measurements were made. Results of the software tools are compared with the measurement results as well as with the results of the lumped circuit modeling based method. It has been shown that the proposed software tools can be used for accurate simulation and design of birdcage coils. © 2015 Wiley Periodicals, Inc

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. © 2005 IOP Publishing Ltd

Gradient-based electrical conductivity imaging using MR phase

Purpose: To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise. Theory: Starting from the Maxwell's equations, a new electrical conductivity imaging method that is based solely on the MR transceive phase has been proposed. Different from the previous phase based electrical properties tomography (EPT) method, a new formulation was derived by including the gradients of the conductivity into the equations. Methods: The governing partial differential equation, which is in the form of a convection-reaction-diffusion equation, was solved using a three-dimensional finite-difference scheme. To evaluate the performance of the proposed method numerical simulations, phantom and in vivo human experiments have been conducted at 3T. Results: Simulation and experimental results of the proposed method and the conventional phase–based EPT method were illustrated to show the superiority of the proposed method over the conventional method, especially in the transition regions and under noisy data. Conclusion: With the contributions of the proposed method to the phase-based EPT approach, a fast and reliable electrical conductivity imaging appears to be feasible, which is promising for clinical diagnoses and local SAR estimation. Magn Reson Med 77:137–150, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc

Model based and experimental investigation of respiratory effect on the HRV power spectrum

The role of respiration in the genesis of heart rate variability (HRV) has been the subject matter of many experimental and modeling studies. It is widely accepted that the high frequency (HF) peak of a HRV power spectrum, which is centered at the average respiratory frequency, is caused by mechanisms activated by respiration. On the other hand, there is a debate on the possible role of respiration in the genesis of the low frequency (LF) peak which is usually centered around 0.1 Hz. In this study, a comprehensive cardiorespiratory interaction model is used to test various hypotheses regarding the role of respiration in the LF peak of HRV. In this model, chest and abdomen circumference signals and lung volume signal are used as respiratory inputs. Simulations are made for periodic, spontaneous and slightly irregular respiratory patterns, and it is observed that the more low frequency (LF) power there in the respiratory signals, the more LF power there in the model-predicted HRV. Experiments on nine volunteers are also performed for the same respiratory patterns and similar results are observed. Furthermore, the actual measured respiratory signals are input to the model and the model predicted and the actual HRVs are compared both in time domain and also with respect to their power spectra. It is concluded in general that respiration not only is the major contributor to the genesis of the HF peak in the HRV power spectrum, but also plays an important role in the genesis of its LF peak. Thus, the LF/HF ratio, which is used to assess sympathovagal balance, cannot be correctly utilized in the absence of simultaneous monitoring of respiration during an HRV test. © 2006 IOP Publishing Ltd

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

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

Electrical Impedance Tomography of Translationally Uniform Cylindrical Objects with General Cross-Sectional Boundaries

An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane,- therefore the axial variation of the boundary conditions and also the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems and it is shown that the Fourier series can be truncated to provide substantial saving in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. For a given cross-sectional boundary, the ratios of the gradients calculated for both 2-D and 3-D homogeneous objects are formed. The actual measurements from the 3-D object are multiplied by these ratios and thereafter the tomographic image is obtained by the 2-D iterative equipotential lines method. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated. The method is also applied to humans and satisfactory images are obtained. It is argued that the method finds an “equivalent” translationally uniform object, the calculated gradients for which are the same as the actual measurements collected. In the absence of any other information about the translational variation of conductance this method is especially suitable for body parts with some translational uniformity. © 1990 IEE