Validation of conductivity tensor imaging using giant vesicle suspensions with different ion mobilities

Estimation of brain tissue response by electrical stimulation in a subject-specific model implemented by conductivity tensor imaging

Electrical stimulation such as transcranial direct current stimulation (tDCS) is widely used to treat neuropsychiatric diseases and neurological disorders. Computational modeling is an important approach to understand the mechanisms underlying tDCS and optimize treatment planning. When applying computational modeling to treatment planning, uncertainties exist due to insufficient conductivity information inside the brain. In this feasibility study, we performed in vivo MR-based conductivity tensor imaging (CTI) experiments on the entire brain to precisely estimate the tissue response to the electrical stimulation. A recent CTI method was applied to obtain low-frequency conductivity tensor images. Subject-specific three-dimensional finite element models (FEMs) of the head were implemented by segmenting anatomical MR images and integrating a conductivity tensor distribution. The electric field and current density of brain tissues following electrical stimulation were calculated using a conductivity tensor-based model and compared to results using an isotropic conductivity model from literature values. The current density by the conductivity tensor was different from the isotropic conductivity model, with an average relative difference |rD| of 52 to 73%, respectively, across two normal volunteers. When applied to two tDCS electrode montages of C3-FP2 and F4-F3, the current density showed a focused distribution with high signal intensity which is consistent with the current flowing from the anode to the cathode electrodes through the white matter. The gray matter tended to carry larger amounts of current densities regardless of directional information. We suggest this CTI-based subject-specific model can provide detailed information on tissue responses for personalized tDCS treatment planning.

High frequency conductivity decomposition by solving physically constraint underdetermined inverse problem in human brain

The developed magnetic resonance electrical properties tomography (MREPT) can visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data from magnetic resonance imaging (MRI). The recovered high-frequency conductivity (HFC) value is highly complex and heterogeneous in a macroscopic imaging voxel. Using high and low b-value diffusion weighted imaging (DWI) data, the multi-compartment spherical mean technique (MC-SMT) characterizes the water molecule movement within and between intra- and extra-neurite compartments by analyzing the microstructures and underlying architectural organization of brain tissues. The proposed method decomposes the recovered HFC into the conductivity values in the intra- and extra-neurite compartments via the recovered intra-neurite volume fraction (IVF) and the diffusion patterns using DWI data. As a form of decomposition of intra- and extra-neurite compartments, the problem to determine the intra- and extra-neurite conductivity values from the HFC is still an underdetermined inverse problem. To solve the underdetermined problem, we use the compartmentalized IVF as a criterion to decompose the electrical properties because the ion-concentration and mobility have different characteristics in the intra- and extra-neurite compartments. The proposed method determines a representative apparent intra- and extra-neurite conductivity values by changing the underdetermined equation for a voxel into an over-determined minimization problem over a local window consisting of surrounding voxels. To suppress the noise amplification and estimate a feasible conductivity, we define a diffusion pattern distance to weight the over-determined system in the local window. To quantify the proposed method, we conducted a simulation experiment. The simulation experiments show the relationships between the noise reduction and the spatial resolution depending on the designed local window sizes and diffusion pattern distance. Human brain experiments (five young healthy volunteers and a patient with brain tumor) were conducted to evaluate and validate the reliability of the proposed method. To quantitatively compare the results with previously developed methods, we analyzed the errors for reconstructed extra-neurite conductivity using existing methods and indirectly verified the feasibility of the proposed method.

Measurement of extracellular volume fraction using magnetic resonance-based conductivity tensor imaging

Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.

Measurement of extracellular volume fraction using magnetic resonance-based conductivity tensor imaging

Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.

SNR-Enhanced, Rapid Electrical Conductivity Mapping Using Echo-Shifted MRI

Magnetic resonance electrical impedance tomography (MREIT) permits high-spatial resolution electrical conductivity mapping of biological tissues, and its quantification accuracy hinges on the signal-to-noise ratio (SNR) of the current-induced magnetic flux density (B_z). The purpose of this work was to achieve B_z SNR-enhanced rapid conductivity imaging by developing an echo-shifted steady-state incoherent imaging-based MREIT technique. In the proposed pulse sequence, the free-induction-decay signal is shifted in time over multiple imaging slices, and as a result is exposed to a plurality of injecting current pulses before forming an echo. Thus, the proposed multi-slice echo-shifting strategy allows a high SNR for B_z for a given number of current injections. However, with increasing the time of echo formation, the B_z SNR will also be compromised by T₂*-related signal loss. Hence, numerical simulations were performed to evaluate the relationship between the echo-shifting and the B_z SNR, and subsequently to determine the optimal imaging parameters. Experimental studies were conducted to evaluate the effectiveness of the proposed method over conventional spin-echo-based MREIT. Compared with the reference spin-echo MREIT, the proposed echo-shifting-based method improves the efficiency in both data acquisition and current injection while retaining the accuracy of conductivity quantification. The results suggest the feasibility of the proposed MREIT method as a practical means for conductivity mapping.

Comparison of Five Conductivity Tensor Models and Image Reconstruction Methods Using MRI

Imaging of the electrical conductivity distribution inside the human body has been investigated for numerous clinical applications. The conductivity tensors of biological tissue have been obtained from water diffusion tensors by applying several models, which may not cover the entire phenomenon. Recently, a new conductivity tensor imaging (CTI) method was developed through a combination of B1 mapping, and multi-b diffusion weighted imaging. In this study, we compared the most recent CTI method with the four existing models of conductivity tensors reconstruction. Two conductivity phantoms were designed to evaluate the accuracy of the models. Applied to five human brains, the conductivity tensors using the four existing models and CTI were imaged and compared with the values from the literature. The conductivity image of the phantoms by the CTI method showed relative errors between 1.10% and 5.26%. The images by the four models using DTI could not measure the effects of different ion concentrations subsequently due to prior information of the mean conductivity values. The conductivity tensor images obtained from five human brains through the CTI method were comparable to previously reported literature values. The images by the four methods using DTI were highly correlated with the diffusion tensor images, showing a coefficient of determination (R2) value of 0.65 to 1.00. However, the images by the CTI method were less correlated with the diffusion tensor images and exhibited an averaged R2 value of 0.51. The CTI method could handle the effects of different ion concentrations as well as mobilities and extracellular volume fractions by collecting and processing additional B1 map data. It is necessary to select an application-specific model taking into account the pros and cons of each model. Future studies are essential to confirm the usefulness of these conductivity tensor imaging methods in clinical applications, such as tumor characterization, EEG source imaging, and treatment planning for electrical stimulation.

Conductivity Tensor Imaging of the Human Brain Using Water Mapping Techniques

Conductivity tensor imaging (CTI) has been recently proposed to map the conductivity tensor in 3D using magnetic resonance imaging (MRI) at the frequency range of the brain at rest, i.e., low-frequencies. Conventional CTI mapping methods process the trans-receiver phase of the MRI signal using the MR electric properties tomography (MR-EPT) technique, which in turn involves the application of the Laplace operator. This results in CTI maps with a low signal-to-noise ratio (SNR), artifacts at tissue boundaries and a limited spatial resolution. In order to improve on these aspects, a methodology independent from the MR-EPT method is proposed. This relies on the strong assumption for which electrical conductivity is univocally pre-determined by water concentration. In particular, CTI maps are calculated by combining high-frequency conductivity derived from water maps and multi b-value diffusion tensor imaging (DTI) data. Following the implementation of a pipeline to optimize the pre-processing of diffusion data and the fitting routine of a multi-compartment diffusivity model, reconstructed conductivity images were evaluated in terms of the achieved spatial resolution in five healthy subjects scanned at rest. We found that the pre-processing of diffusion data and the optimization of the fitting procedure improve the quality of conductivity maps. We achieve reproducible measurements across healthy participants and, in particular, we report conductivity values across subjects of 0.55 ± 0.01Sm, 0.3 ± 0.01Sm and 2.15 ± 0.02Sm for gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), respectively. By attaining an actual spatial resolution of the conductivity tensor close to 1 mm in-plane isotropic, partial volume effects are reduced leading to good discrimination of tissues with similar conductivity values, such as GM and WM. The application of the proposed framework may contribute to a better definition of the head tissue compartments in electroencephalograpy/magnetoencephalography (EEG/MEG) source imaging and be used as biomarker for assessing conductivity changes in pathological conditions, such as stroke and brain tumors.

Electrical Conductivity of a Stretching Viscoelastic Filament

Long polymeric chains highly stretched and aligned with the flow confer a strong mechanical anisotropy on a viscoelastic solution. The electrically-driven transport of free ions under such conditions is far from being understood. In this paper, we determine experimentally whether the above-mentioned deviation from isotropy affects the electric charge transport across the liquid. To this end, we measure the electrical conductivity in the flow (stretching) direction of the cylindrical liquid filament formed in the elasto-capillary thinning that arises during the breakup of a viscoelastic liquid bridge. First, we examine the behavior of monodisperse solutions of polyethylene oxide (PEO) in a mixture of glycerine and water. For all the concentrations and molecular weights considered, the filament conductivity remains practically the same as the isotropic conductivity measured under hydrostatic conditions. However, we observe a decrease in the electric current at the end of elasto-capillary regime which may partially be attributed to the reduction of the liquid conductivity. Then, we measure the conductivity of bidisperse solutions of PEO with very different molecular weights. In this case, a significant decrease in conductivity is observed as the filament radius decreases. This constitutes the first experimental evidence of ion mobility reduction in stretching viscoelastic filaments, a relevant effect in applications such as electrospinning.

MR-Based Electrical Conductivity Imaging of Liver Fibrosis in an Experimental Rat Model

BACKGROUND

Liver fibrosis is characterized by the excessive accumulation of extracellular matrix proteins. Electrical conductivity imaging at low frequency can provide novel contrast because the contrast mechanisms originate from the changes in the concentration and mobility of ions in the extracellular space.

PURPOSE

To evaluate the feasibility of an MR-based electrical conductivity imaging that can detect the changes in a tissue condition associated with the progression of liver fibrosis.

STUDY TYPE

Prospective phantom and animal study.

ANIMAL MODEL

Fibrosis was induced by weekly intraperitoneal injection of dimethylnitrosamine (DMN) in 45 male Sprague-Dawley rats.

FIELD STRENGTH/SEQUENCE

3T MRI with a multispin-echo pulse sequence.

ASSESSMENT

The percentage change of conductivity (Δσ, %) in the same region-of-interest (ROI) was calculated from the DMN-treated rats based on the values of the normal control rats. The percentage change was also calculated between the ROIs in each DMN-treated group.

STATISTICAL TESTS

One-way analysis of variance (ANOVA) and a two-sample t-test were performed.

RESULTS

Liver tissues in normal control rats showed a uniform conductivity distribution of 56.6 ± 4.4 (mS/m). In rats more than 5 weeks after induction, the fibrous region showed an increased conductivity of ≥12% compared to that of the corresponding normal control rats. From regional comparisons in the same liver, the fibrous region showed an increased conductivity of ≥11% compared to the opposite, less induced region of rats more than 5 weeks after induction. Liver samples from the fibrous region represent tissue damages such as diffuse centrilobular congestion with marked dilatation of central veins from the histological findings. Immunohistochemistry revealed significant levels of attenuated fibrosis and increased inflammatory response.

DATA CONCLUSION

The increased conductivity in the fibrous region is related to the changes of the extracellular space. The correlation between the collagen deposition and conductivity changes is essential for future clinical studies. Level of Evidence 2 Technical Efficacy Stage 2 J. MAGN. RESON. IMAGING 2021;53:554-563.