Saurav Z. K. Sajib

Electrical tissue property imaging using MRI at dc and Larmor frequency

Cross-sectional imaging of conductivity and permittivity distributions inside thehumanbodyhasbeenactivelyinvestigatedinimpedanceimagingareassuch as electrical impedance tomography (EIT) and magnetic induction tomography (MIT). Since the conductivity and permittivity values exhibit frequencydependent changes, it is worthwhile to perform spectroscopic imaging from almost dc to hundreds of MHz. To probe the human body, we may inject current using surface electrodes or induce current using external coils. In EIT and MIT, measured data are only available on the boundary or exterior of the body unless we invasively place sensors inside the body. Their image reconstruction problems are nonlinear and ill-posed to result in images with a relatively low spatial resolution. Noting that an MRI scanner can noninvasively measure magnetic fields inside the human body, electrical tissue property imaging methods using MRI have lately been proposed. Magnetic resonance EIT (MREIT) performs conductivity imaging at dc or below 1 kHz by externallyinjectingcurrentintothehumanbodyandmeasuringinducedinternal magneticfluxdensitydatausinganMRIscanner.Magneticresonanceelectrical property tomography (MREPT) produces both conductivity and permittivity images at the Larmor frequency of an MRI scanner based on B1-mapping techniques. Since internal data are only available in MREIT and MREPT, we may formulate well-posed inverse problems for image reconstructions. To develop related imaging techniques, we should clearly understand the basic principles of MREIT and MREPT, which are based on coupled physics of bioelectromagnetism and MRI as well as associated mathematical methods. In this paper, we describe the physical principles of MREIT and MREPT in a unified way and associate measurable quantities with the conductivity and permittivity. Clarifying the key relations among them, we examine existing image reconstruction algorithms to reveal their capabilities and limitations. We discuss technical issues in MREIT and MREPT and suggest future research

Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions.

Regional absolute conductivity reconstruction using projected current density in MREIT

Magnetic resonance electrical impedance tomography (MREIT) is a non-invasive technique for imaging the internal conductivity distribution in tissue within an MRI scanner, utilizing the magnetic flux density, which is introduced when a current is injected into the tissue from external electrodes. This magnetic flux alters the MRI signal, so that appropriate reconstruction can provide a map of the additional z-component of the magnetic field (B(z)) as well as the internal current density distribution that created it. To extract the internal electrical properties of the subject, including the conductivity and/or the current density distribution, MREIT techniques use the relationship between the external injection current and the z-component of the magnetic flux density B = (B(x), B(y), B(z)). The tissue studied typically contains defective regions, regions with a low MRI signal and/or low MRI signal-to-noise-ratio, due to the low density of nuclear magnetic resonance spins, short T(2) or T*(2) relaxation times, as well as regions with very low electrical conductivity, through which very little current traverses. These defective regions provide noisy B(z) data, which can severely degrade the overall reconstructed conductivity distribution. Injecting two independent currents through surface electrodes, this paper proposes a new direct method to reconstruct a regional absolute isotropic conductivity distribution in a region of interest (ROI) while avoiding the defective regions. First, the proposed method reconstructs the contrast of conductivity using the transversal J-substitution algorithm, which blocks the propagation of severe accumulated noise from the defective region to the ROI. Second, the proposed method reconstructs the regional projected current density using the relationships between the internal current density, which stems from a current injection on the surface, and the measured B(z) data. Combining the contrast conductivity distribution in the entire imaging slice and the reconstructed regional projected current density, we propose a direct non-iterative algorithm to reconstruct the absolute conductivity in the ROI. The numerical simulations in the presence of various degrees of noise, as well as a phantom MRI imaging experiment showed that the proposed method reconstructs the regional absolute conductivity in a ROI within a subject including the defective regions. In the simulation experiment, the relative L₂-mode errors of the reconstructed regional and global conductivities were 0.79 and 0.43, respectively, using a noise level of 50 db in the defective region.

Current Density Imaging During Transcranial Direct Current Stimulation Using DT-MRI and MREIT: Algorithm Development and Numerical Simulations

Objective: Transcranial direct current stimulation (tDCS) is a neuromodulatory technique for neuropsychiatric diseases and neurological disorders. In the tDCS treatment, dc current is injected into the head through a pair of electrodes attached on the scalp over a target region. A current density imaging method is needed to quantitatively visualize the internal current density distribution during the tDCS treatment. Methods: We developed a novel current density image reconstruction algorithm using 1) a subject specific segmented 3-D head model, 2) diffusion tensor data, and 3) magnetic flux density data induced by the tDCS current. We acquired T1 weighted and diffusion tensor images of the head using the MRI scanner before the treatment. During the treatment, we can measure the induced magnetic flux density data using a magnetic resonance electrical impedance tomography (MREIT) pulse sequence. In this paper, the magnetic flux density data were numerically generated. Results: Numerical simulation results show that the proposed method successfully recovers the current density distribution including the effects of the anisotropic, as well as isotropic conductivity values of different tissues in the head. Conclusion: The proposed current density imaging method using DT-MRI and MREIT can reliably recover cross-sectional images of the current density distribution during the tDCS treatment. Significance: Success of the tDCS treatment depends on a precise determination of the induced current density distribution within different anatomical structures of the brain. Quantitative visualization of the current density distribution in the brain will play an important role in understanding the effects of the electrical stimulation.

Simultaneous imaging of dual‐frequency electrical conductivity using a combination of MREIT and MREPT

To propose a single magnetic resonance scan conductivity imaging technique providing dual‐frequency characteristics of tissue conductivity.

Simulations and phantom evaluations of magnetic resonance electrical impedance tomography (MREIT) for breast cancer detection

MREIT is a new imaging modality that can be used to reconstruct high-resolution conductivity images of the human body. Since conductivity values of cancerous tissues in the breast are significantly higher than those of surrounding normal tissues, breast imaging using MREIT may provide a new noninvasive way of detecting early stage of cancer. In this paper, we present results of experimental and numerical simulation studies of breast MREIT. We built a realistic three-dimensional model of the human breast connected to a simplified model of the chest including the heart and evaluated the ability of MREIT to detect cancerous anomalies in a background material with similar electrical properties to breast tissue. We performed numerical simulations of various scenarios in breast MREIT including assessment of the effects of fat inclusions and effects related to noise levels, such as changing the amplitude of injected currents, effect of added noise and number of averages. Phantom results showed straightforward detection of cancerous anomalies in a background was possible with low currents and few averages. The simulation results showed it should be possible to detect a cancerous anomaly in the breast, while restricting the maximal current density in the heart below published levels for nerve excitation.

Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT

We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.

Analysis of local projected current density from one component of magnetic flux density in MREIT

Magnetic resonance electrical impedance tomography is a new modality capable of imaging the static electrical conductivity of an object by measuring Bz data, a component of the magnetic flux density B = (Bx, By, Bz), perturbed by an external injection current. In an imaging area, the current density J induced by the external injection current can be uniquely decomposed into a recoverable component JP and an invisible component from the measured Bz data. In the case of in vivo animal and human imaging experiments, the imaging area frequently includes local defective regions with a low signal-to-noise ratio. As a result, the measured Bz data in the defective regions include serious noise due to rapid T2 decay, a small amount of internal current density and weak MR signals. In this paper, we propose an algorithm to reconstruct a recoverable current density from the measured Bz data in a local region avoiding the defective regions. We estimate the L2-norm of the difference between the induced internal current density J and the locally recovered from the measured Bz data in the local region . The difference only depends on the z-components of J and J0 and the values of Bx and By on the boundary , where J0 is the background current density by the injected current. Numerical simulations and phantom experiments demonstrate that the proposed method directly reconstructs a local current density avoiding noise effects in defective regions.

Numerical simulations of MREIT conductivity imaging for brain tumor detection.

Magnetic resonance electrical impedance tomography (MREIT) is a new modality capable of imaging the electrical properties of human body using MRI phase information in conjunction with external current injection. Recent in vivo animal and human MREIT studies have revealed unique conductivity contrasts related to different physiological and pathological conditions of tissues or organs. When performing in vivo brain imaging, small imaging currents must be injected so as not to stimulate peripheral nerves in the skin, while delivery of imaging currents to the brain is relatively small due to the skulls low conductivity. As a result, injected imaging currents may induce small phase signals and the overall low phase SNR in brain tissues. In this study, we present numerical simulation results of the use of head MREIT for brain tumor detection. We used a realistic three-dimensional head model to compute signal levels produced as a consequence of a predicted doubling of conductivity occurring within simulated tumorous brain tissues. We determined the feasibility of measuring these changes in a time acceptable to human subjects by adding realistic noise levels measured from a candidate 3 T system. We also reconstructed conductivity contrast images, showing that such conductivity differences can be both detected and imaged.

Experimental evaluation of electrical conductivity imaging of anisotropic brain tissues using a combination of diffusion tensor imaging and magnetic resonance electrical impedance tomography

Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At low frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.