Electrodeless conductivity tensor imaging (CTI) using MRI: basic theory and animal experiments

Increased extra-neurite conductivity of brain in patients with Alzheimer's disease: A pilot study

The objectives of this study were to investigate how the extra-neurite conductivity (EC) and intra-neurite conductivity (IC) were reflected in Alzheimer's disease (AD) patients compared with old cognitively normal (CN) people and patients with amnestic mild cognitive impairment (MCI) and to evaluate the association between those conductivity values and cognitive decline. To do this, high-frequency conductivity (HFC) at the Larmor frequency was obtained using MRI-based electrical property tomography (MREPT) and was decomposed into EC and IC using information of multi-shell multi-gradient direction diffusion tensor images. This prospective single-center study included 20 patients with mild or moderate AD, 25 patients with amnestic MCI, and 21 old CN participants. After decomposing EC and IC from HFC for all participants, we performed voxel-based and regions-of-interest analyses to compare conductivity between the three participant groups and to evaluate the association with either age or the Mini-Mental State Examination (MMSE) scores. We found increased EC in AD compared to CN and MCI. EC was significantly negatively associated with MMSE scores in the insula, and middle temporal gyrus. EC might be used as an imaging biomarker for helping to monitor cognitive function.

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.

Neural stochastic differential equations network as uncertainty quantification method for EEG source localization

EEG source localization remains a challenging problem given the uncertain conductivity values of the volume conductor models (VCMs). As uncertain conductivities vary across people, they may considerably impact the forward and inverse solutions of the EEG, leading to an increase in localization mistakes and misdiagnoses of brain disorders. Calibration of conductivity values using uncertainty quantification (UQ) techniques is a promising approach to reduce localization errors. The widely-known UQ methods involve Bayesian approaches, which utilize prior conductivity values to derive their posterior inference and estimate their optimal calibration. However, these approaches have two significant drawbacks: solving for posterior inference is intractable, and choosing inappropriate priors may lead to increased localization mistakes. This study used the Neural Stochastic Differential equations Network (SDE-Net), a combination of dynamical systems and deep learning techniques that utilizes the Wiener process to minimize conductivity uncertainties in the VCM and improve the inverse problem. Results revealed that SDE-Net generated a lower localization error rate in the inverse problem compared to Bayesian techniques. Future studies may employ new stochastic dynamical systems-based techniques as a UQ technique to address further uncertainties in the EEG Source Localization problem. Our code can be found here:https://github.com/rrwabina/SDENet-UQ-ESL.

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.

Correlation analysis between the complex electrical permittivity and relaxation time of tissue mimicking phantoms in 7 T MRI

Dielectric relaxation theory describes the complex permittivity of a material in an alternating field; in particular, Debye theory relates the time it takes for an applied field to achieve the maximum polarization and the electrical properties of the material. Although, Debye’s equations were proposed for electrical polarization, in this study, we investigate the correlation between the magnetic longitudinal relaxation time T1 and the complex electrical permittivity of tissue-mimicking phantoms using a 7 T magnetic resonance scanner. We created phantoms that mimicked several human tissues with specific electrical properties. The electrical properties of the phantoms were measured using bench-test equipment. T1 values were acquired from phantoms using MRI. The measured values were fitted with functions based on dielectric estimations, using relaxation times of electrical polarization, and the mixture theory for dielectrics. The results show that, T1 and the real permittivity are correlated; therefore, the correlation can be approximated with a rational function in the case of water-based phantoms. The correlation between index loss and T1 was determined using a fitting function based on the Debye equation and mixture theory equation, in which the fraction of the materials was taken into account. This phantom study and analysis provide an insight into the application relaxation times used for estimating dielectric properties. Currently, the measurement of electrical properties based on dielectric relaxation theory is based on an antenna, sometimes invasive, that irradiates an electric field into a small sample; thus, it is not possible to create a map of electrical properties for a complex structure such as the human body. This study could be further used to compute the electrical properties maps of tissues by scanning images and measuring T1 maps.

Magnetic Resonance Electrical Impedance Tomography

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a high-resolution bioimpedance imaging technique that has developed over a period beginning in the early 1990s to measure low-frequency (<1 kHz) tissue electrical properties. Low-frequency electrical properties are particularly important because they provide valuable information on cell structures and ionic composition of tissues, which may be very useful for diagnostic purposes. MREIT uses one component of the magnetic flux density data induced due to an exogenous-current administration, measured using an MRI machine, to reconstruct isotropic or anisotropic electrical property distributions. The MREIT technique typically requires two linearly independent current administrations to reconstruct conductivity uniquely. Since its invention, researchers have explored its potential for measuring electrical conductivity in regions such as the brain and muscle tissue. It has also been investigated in disease models, for example, cerebral ischemia and early tumor detection. In this chapter, we aim to provide a solid foundation of the different MREIT image reconstruction algorithms, including both isotropic and anisotropic conductivity reconstruction approaches. We will also explore the newly developed diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method, a practical method for anisotropic tissue property imaging, at the end of the chapter.

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.

Convection-Enhanced Delivery and Principles of Extracellular Transport in the Brain

Stereotactic neurosurgery involves a targeted intervention based on congruence of image guidance to a reference fiducial system. This discipline has widespread applications in radiosurgery, tumor therapy, drug delivery, functional lesioning, and neuromodulation. In this article, we focused on convection-enhanced delivery to deliver therapeutic agents to the brain addressing areas of research and clinical development. We performed a robust literature review of all relevant articles highlighting current efforts and challenges of making this delivery technique more widely understood. We further described key biophysical properties of molecular transport in the extracellular space that may impact the efficacy and control of drug delivery using stereotactic methods. Understanding these principles is critical for further refinement of predictive models that can inform advances in stereotactic techniques for convection-enhanced delivery of therapeutic agents to the brain.

Decomposition of high-frequency electrical conductivity into extracellular and intracellular compartments based on two-compartment model using low-to-high multi-b diffusion MRI

Background

As an object’s electrical passive property, the electrical conductivity is proportional to the mobility and concentration of charged carriers that reflect the brain micro-structures. The measured multi-b diffusion-weighted imaging (Mb-DWI) data by controlling the degree of applied diffusion weights can quantify the apparent mobility of water molecules within biological tissues. Without any external electrical stimulation, magnetic resonance electrical properties tomography (MREPT) techniques have successfully recovered the conductivity distribution at a Larmor-frequency.

Methods

This work provides a non-invasive method to decompose the high-frequency conductivity into the extracellular medium conductivity based on a two-compartment model using Mb-DWI. To separate the intra- and extracellular micro-structures from the recovered high-frequency conductivity, we include higher b-values DWI and apply the random decision forests to stably determine the micro-structural diffusion parameters.

Results

To demonstrate the proposed method, we conducted phantom and human experiments by comparing the results of reconstructed conductivity of extracellular medium and the conductivity in the intra-neurite and intra-cell body. The phantom and human experiments verify that the proposed method can recover the extracellular electrical properties from the high-frequency conductivity using a routine protocol sequence of MRI scan.

Conclusion

We have proposed a method to decompose the electrical properties in the extracellular, intra-neurite, and soma compartments from the high-frequency conductivity map, reconstructed by solving the electro-magnetic equation with measured B1 phase signals.

Identification of Brain Damage after Seizures Using an MR-Based Electrical Conductivity Imaging Method

Previous imaging studies have shown the morphological malformation and the alterations of ionic mobility, water contents, electrical properties, or metabolites in seizure brains. Magnetic resonance electrical properties tomography (MREPT) is a recently developed technique for the measurement of electrical tissue properties with a high frequency that provides cellular information regardless of the cell membrane. In this study, we examined the possibility of MREPT as an applicable technique to detect seizure-induced functional changes in the brain of rats. Ultra-high field (9.4 T) magnetic resonance imaging (MRI) was performed, 2 h, 2 days, and 1 week after the injection of N-methyl-D-aspartate (NMDA; 75 mg/kg). The conductivity images were reconstructed from B1 phase images using a magnetic resonance conductivity imaging (MRCI) toolbox. The high-frequency conductivity was significantly decreased in the hippocampus among various brain regions of NMDA-treated rats. Nissl staining showed shrunken cell bodies and condensed cytoplasm potently at 2 h after NMDA treatment, and neuronal cell loss at all time points in the hippocampus. These results suggest that the reduced electrical conductivity may be associated with seizure-induced neuronal loss in the hippocampus. Magnetic resonance (MR)-based electrical conductivity imaging may be an applicable technique to non-invasively identify brain damage after a seizure.

Low-frequency conductivity tensor imaging with a single current injection using DT-MREIT

Diffusion tensor-magnetic resonance electrical impedance tomography (DT-MREIT) is an imaging modality to obtain low-frequency anisotropic conductivity distribution employing diffusion tensor imaging and MREIT techniques. DT-MREIT is based on the linear relationship between the conductivity and water self-diffusion tensors in a porous medium, like the brain white matter. Several DT-MREIT studies in the literature provide cross-sectional anisotropic conductivity images of tissue phantoms, canine brain, and the human brain. In these studies, the conductivity tensor images are reconstructed using the diffusion tensor and current density data acquired by injecting two linearly independent current patterns. In this study, a novel reconstruction algorithm is devised for DT-MREIT to reconstruct the conductivity tensor images using a single current injection. Therefore, the clinical applicability of DT-MREIT can be improved by reducing the total acquisition time, the number of current injection cables, and contact electrodes to half by decreasing the number of current injection patterns to one. The proposed method is evaluated utilizing simulated measurements and physical experiments. The results obtained show the successful reconstruction of the anisotropic conductivity distribution using the proposed single current DT-MREIT.

Low-frequency dominant electrical conductivity imaging of in vivo human brain using high-frequency conductivity at Larmor-frequency and spherical mean diffusivity without external injection current

Diffusion weighted imaging based on random Brownian motion of water molecules within a voxel provides information on the micro-structure of biological tissues through water molecule diffusivity. As the electrical conductivity is primarily determined by the concentration and mobility of ionic charge carriers, the macroscopic electrical conductivity of biological tissues is also related to the diffusion of electrical ions. This paper aims to investigate the low-frequency electrical conductivity by relying on a pre-defined biological model that separates the brain into the intracellular (restricted) and extracellular (hindered) compartments. The proposed method uses B1 mapping technique, which provides a high-frequency conductivity distribution at Larmor frequency, and the spherical mean technique, which directly estimates the microscopic tissue structure based on the water molecule diffusivity and neurite orientation distribution. The total extracellular ion concentration, which is separated from the high-frequency conductivity, is recovered using the estimated diffusivity parameters and volume fraction in each compartment. We propose a method to reconstruct the low-frequency dominant conductivity tensor by taking into consideration the extracted extracellular diffusion tensor map and the reconstructed electrical parameters. To demonstrate the reliability of the proposed method, we conducted two phantom experiments. The first one used a cylindrical acrylic cage filled with an agar in the background region and four anomalies for the effect of ion concentration on the electrical conductivity. The other experiment, in which the effect of ion mobility on the conductivity was verified, used cell-like materials with thin insulating membranes suspended in an electrolyte. Animal and human brain experiments were conducted to visualize the low-frequency dominant conductivity tensor images. The proposed method using a conventional MRI scanner can predict the internal current density map in the brain without directly injected external currents.

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

Background

Electrical conductivity of a biological tissue at low frequencies can be approximately expressed as a tensor. Noting that cross-sectional imaging of a low-frequency conductivity tensor distribution inside the human body has wide clinical applications of many bioelectromagnetic phenomena, a new conductivity tensor imaging (CTI) technique has been lately developed using an MRI scanner. Since the technique is based on a few assumptions between mobility and diffusivity of ions and water molecules, experimental validations are needed before applying it to clinical studies.

Methods

We designed two conductivity phantoms each with three compartments. The compartments were filled with electrolytes and/or giant vesicle suspensions. The giant vesicles were cell-like materials with thin insulating membranes. We controlled viscosity of the electrolytes and the giant vesicle suspensions to change ion mobility and therefore conductivity values. The conductivity values of the electrolytes and giant vesicle suspensions were measured using an impedance analyzer before CTI experiments. A 9.4-T research MRI scanner was used to reconstruct conductivity tensor images of the phantoms.

Results

The CTI technique successfully reconstructed conductivity tensor images of the phantoms with a voxel size of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5\times 0.5\times 0.5\hbox { mm}^3$$\end{document}0.5×0.5×0.5mm3. The relative \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}L2 errors between the conductivity values measured by the impedance analyzer and those reconstructed by the MRI scanner was between 1.1 and 11.5.

Conclusions

The accuracy of the new CTI technique was estimated to be high enough for most clinical applications. Future studies of animal models and human subjects should be pursued to show the clinical efficacy of the CTI technique.

Statistical analysis of the accuracy of water content-based electrical properties tomography

Water content-based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water content maps, thereby eliminating the need for B₁ field measurement in the traditional magnetic resonance electrical properties tomography method. The wEPT is performed by conventional MR scanning, such as T₁ -weighted spin-echo imaging, and thus can be directly applied to clinical settings. However, the random noise propagation involved in wEPT causes inaccuracy in EP mapping. To guarantee the EP estimates desired for clinical practice, this study statically investigates the noise-specific uncertainty of wEPT through probability density function models. We calculated the probability distribution of EP maps with different noise levels and examined the effects of scan parameters on reconstruction accuracy with various flip angles (FAs) and repetition time (TR) settings. The theoretical derivation was validated by Monte Carlo simulations and human imaging experiment at 3 T. Results showed that a serious deviation could occur in tissues with large conductivity value at a low signal-to-noise ratio and quantitatively demonstrate that such deviation could be mitigated by increased FAs or TRs. This study provided useful information for the setup of scan parameters, evaluation of accuracy of the wEPT under specific SNR levels, and promote its clinical applications.

Extracellular electrical conductivity property imaging by decomposition of high-frequency conductivity at Larmor-frequency using multi-b-value diffusion-weighted imaging

Magnetic resonance electrical properties tomography (MREPT) uses the B1 mapping technique to provide the high-frequency conductivity distribution at Larmor frequency that simultaneously reflects the intracellular and extracellular effects. In biological tissues, the electrical conductivity can be described as the concentration and mobility of charge carriers. For the water molecule diffusivity, diffusion weighted imaging (DWI) measures the random Brownian motion of water molecules within biological tissues. The DWI data can quantitatively access the mobility of microscopic water molecules within biological tissues. By measuring multi-b-value DWI data and the recovered high-frequency conductivity at Larmor frequency, we propose a new method to decompose the conductivity into the total ion concentration and mobility in the extracellular space (ECS) within a routinely applicable MR scan time. Using the measured multi-b-value DWI data, a constrained compartment model is designed to estimate the extracellular volume fraction and extracellular mean diffusivity. With the extracted extracellular volume fraction and water molecule diffusivity, we directly reconstruct the low-frequency electrical properties including the extracellular mean conductivity and extracellular conductivity tensor. To demonstrate the proposed method by comparing the ion concentration and the ion mobility, we conducted human experiments for the proposed low-frequency conductivity imaging. Human experiments verify that the proposed method can recover the low-frequency electrical properties using a conventional MRI scanner.

In Vivo Measurement of Brain Tissue Response After Irradiation: Comparison of T2 Relaxation, Apparent Diffusion Coefficient, and Electrical Conductivity

Radiation therapy (RT) has been widely used as a powerful treatment tool to address cancerous tissues because of its ability to control cell growth. Its ionizing radiation damages the DNA of cancerous tissues, leading to cell death. Medical imaging, however, still has limitations regarding the reliability of its assessment of tissue response and in predicting the treatment effect because of its inability to provide contrast information on the gradual, minute tissue changes after RT. A recently developed magnetic resonance (MR)-based conductivity imaging method may provide direct, highly sensitive information on this tissue response because its contrast mechanism is based on the concentration and mobility of ions in intracellular and extracellular spaces. In this feasibility study, we applied T2-weighted, diffusion-weighted, and electrical conductivity imaging to mouse brain, thus, using the MR imaging to map the tissue response after radiation exposure. To evaluate the degree of response, we measured the T2 relaxation, apparent diffusion coefficient (ADC), and electrical conductivity of brain tissues before and after irradiation. The conductivity images, which showed significantly higher sensitivity than other MR imaging methods, indicated that the contrast is distinguishable in different ways at different areas of the brain. Future studies will focus on verifying these results and the long-term evaluation of conductivity changes using various irradiation methods for clinical applications.

Electrical conductivity-based contrast imaging for characterizing prostatic tissues: in vivo animal feasibility study

Background

Electrical conductivity-based magnetic resonance (MR) imaging may provide unique information on tissue condition because its contrast originates from the concentration and mobility of ions in the cellular space. We imaged the conductivity of normal canine prostate in vivo and evaluated tissue contrast in terms of both the conductivity distribution and anatomical significance.

Methods

Five healthy laboratory beagles were used. After clipping the pelvis hair, we attached electrodes and placed each dog inside the bore of an MRI scanner. During MR scanning, we injected imaging currents into two mutually orthogonal directions between two pairs of electrodes. A multi spin echo pulse sequence was used to obtain the MR magnitude and magnetic flux density images. The projected current density algorithm was used to reconstruct the conductivity image.

Results

Conductivity images showed unique contrast depending on the prostatic tissues. From the conductivity distribution, conductivity was highest in the center area and lower in the order of the middle and outer areas of prostatic tissues. The middle and outer areas were, respectively, 11.2 and 25.5% lower than the center area. Considering anatomical significance, conductivity was highest in the central zone and lower in the order of the transitional and peripheral zones in all prostates. The transitional and peripheral zones were, respectively, 7.5 and 17.8% lower than the central zone.

Conclusions

Current conductivity-based MR imaging can differentiate prostatic tissues without using any contrast media or additional MR scans. The electrical conductivity images with unique contrast to tissue condition can provide a prior information on tissues in situ to be used for human imaging.

Conductivity Tensor Imaging of In Vivo Human Brain and Experimental Validation Using Giant Vesicle Suspension

Human brain mapping of low-frequency electrical conductivity tensors can realize patient-specific volume conductor models for neuroimaging and electrical stimulation. We report experimental validation and in vivo human experiments of a new electrodeless conductivity tensor imaging (CTI) method. From CTI imaging of a giant vesicle suspension using a 9.4-T MRI scanner, the relative error in the reconstructed conductivity tensor image was found to be less than 1.7% compared with the measured value using an impedance analyzer. In vivo human brain imaging experiments of five subjects were followed using a 3-T clinical MRI scanner. With the spatial resolution of 1.87 mm, the white matter conductivity showed considerably more position dependency compared with the gray matter and cerebrospinal fluid (CSF). The anisotropy ratio of the white matter was in the range of 1.96-3.25 with a mean value of 2.43, whereas that of the gray matter was in the range of 1.12-1.19 with a mean value of 1.16. The three diagonal components of the reconstructed conductivity tensors were from 0.08 to 0.27 S/m for the white matter, from 0.20 to 0.30 S/m for the gray matter, and from 1.55 to 1.82 S/m for the CSF. The reconstructed conductivity tensor images exhibited significant inter-subject variabilities in terms of frequency and position dependencies. The high-frequency and low-frequency conductivity values can quantify the total and extracellular water contents, respectively, at every pixel. Their difference can quantify the intracellular water content at every pixel. The CTI method can separately quantify the contributions of ion concentrations and mobility to the conductivity tensor.

FPGA-Based Interface of Digital DAQ System for Double-Scattering Compton Camera

Purpose

The double-scattering Compton camera (DSCC) is a radiation imaging system that can provide both unknown source energy spectra and 3D spatial source distributions. The energies and detection locations measured in coincidence with three CdZnTe (CZT) detectors contribute to reconstructing emission energies and a spatial image based on conical surface integrals. In this study, we developed a digital data acquisition (DAQ) board to support our research into coincidence detection in the DSCC.

Methods

The main components of the digital DAQ board were 12 ADCs and one field programmable gate array (FPGA). The ADCs digitized the analog 96-channel CZT signals at a sampling rate of 50 MHz and transferred the serialized ADC samples and the bit and frame clocks to the FPGA. In order to correctly capture the ADC sample bits in the FPGA, we conducted individual sync calibrations for all the ADC channels to align the bit and frame clocks to the right positions of the ADC sample bits. The FPGA logic design was composed of IDELAY and IDDR components, six shift registers, and bit slip buffer resources.

Results

Using a Deskew test pattern, the delay value of the IDELAY component was determined to align the bit clock to the center of each sample bit. We determined the bit slip in the 12-bit ADC sample using an MSB test pattern by checking where the MSB value of one is located in the captured parallel data.

Conclusions

After sync calibration, we tested the interface between the ADCs and the FPGA with a synthetic analog Gaussian signal. The 96 ADC channels yielded a mean R ² goodness-of-fit value of 0.95 between the Gaussian curve and the captured 12-bit parallel data.

Achieving reliable coincidence resolving time measurement of PET detectors using multichannel waveform digitizer based on DRS4 chip

Coincidence resolving time (CRT) is one of the most important physical-performance measures for positron emission tomography (PET), as reconstruction with accurate time-of-flight information enhances the lesion detectability in patient studies. Accordingly, various PET detector designs and high-performance front-end readout circuits have been actively investigated to improve timing performance. The resulting PET detectors are often evaluated using multichannel waveform digitizers for versatile data analysis of the output signals. However, we have found that inappropriate data acquisition (DAQ) using a multichannel waveform digitizer based on the domino-ring-sampler 4 (DRS4) chip can lead to a considerable error when determining CRT. To address this issue, we performed CRT measurements using a pair of Hamamatsu R9800 photomultiplier tube based PET detectors. Then, considering intra- and inter-chip sampling, we employed four different combinations of input channels into the CAEN DT5742B waveform digitizer and obtained 2D CRT maps according to the leading-edge discriminator threshold for assessing each DAQ scheme. The intra-chip CRT measurement exhibited unusual streak patterns in the 2D CRT map and yielded the artificially-low CRT information in PET detector pairs, whereas the inter-chip CRT measurement provided the reliable estimation of timing resolution. Further, we could prevent the high-frequency signal crosstalk among input channels within the DRS4 chip using the inter-chip CRT measurement. We expect that our findings will also be useful for achieving the reliable CRT measurements when using other single-chip-based multichannel waveform digitizers.