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Progress in Medical Physics 2024; 35(4): 73-88

Published online December 31, 2024

https://doi.org/10.14316/pmp.2024.35.4.73

Copyright © Korean Society of Medical Physics.

Principle, Development, and Application of Electrical Conductivity Mapping Using Magnetic Resonance Imaging

Geon-Ho Jahng1 , Mun Bae Lee2 , Oh In Kwon2

1Department of Radiology, Kyung Hee University Hospital at Gangdong, Kyung Hee University College of Medicine, Seoul, 2Department of Mathematics, College of Basic Science, Konkuk University, Seoul, Korea

Correspondence to:Geon-Ho Jahng
(ghjahng@gmail.com)
Tel: 82-2-440-6187
Fax: 82-2-440-6932

Received: August 8, 2024; Revised: November 6, 2024; Accepted: November 12, 2024

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Magnetic resonance imaging (MRI)-related techniques can provide information related to the electrical properties of the body. Understanding the electrical properties of human tissues is crucial for developing diagnostic tools and therapeutic approaches for various medical conditions. This study reviewed the principles, development, and application of electrical conductivity mapping using MRI. To review the magnetic resonance electrical properties tomography (MREPT)-based conductivity mapping technique and its application to brain imaging, first, we explain the definition and fundamental principles of electrical conductivity, some factors that influence changes in ionic conductivity, and the background of mapping cellular conductivities. Second, we explain the concepts and applications of magnetic resonance electrical impedance tomography (MREIT) and MREPT. Third, we describe our recent technical developments and their clinical applications. Finally, we explain the benefits, impacts, and challenges of MRI-based conductivity in clinical practice. MRI techniques, such as MREIT and MREPT, enabled the measurement of conductivity-related properties within the body. MREIT assessed low-frequency conductivity by applying a low-frequency external current, whereas MREPT captured high-frequency conductivity (at the Larmor frequency) without applying an external current. In MREIT, the subject’s safety should be ensured because electrical current is applied, particularly around sensitive areas, such as the brain, or in subjects with implanted electronic devices. Our previous studies have highlighted the potential of conductivity indices as biomarkers for Alzheimer’s disease. MREPT is usually applied to humans rather than MREIT. MREPT holds promise as a noninvasive tool for characterizing tissue properties and understanding pathological conditions.

KeywordsMRI, B1 phase, Conductivity, Brain application

Electrical conductivity in human tissue is a critical concept in medical diagnostics, treatment, and biomedical engineering, among other fields. Human biological tissues conduct electricity because of the presence of ions in bodily fluids. The conductivities of different tissues vary and are influenced by several factors. In human tissues, electrical current is primarily carried by ions. When an electrical field is applied, these ions move, creating a current. This ionic conduction is crucial for various physiological processes, including nerve impulse transmission and muscle contraction. These properties are important because they can provide additional information about tissue structure and function beyond the anatomical details that standard magnetic resonance imaging (MRI) provides.

Imaging electrical conductivity in human tissues involves understanding how ions move through ion channels, how membrane potentials are established, and how electrochemical gradients drive ionic currents. First, ion channels are protein structures embedded in cell membranes that facilitate the movement of ions across the membrane. These channels are selective for specific ions, such as sodium (Na+), potassium (K+), calcium (Ca 2+), and chloride (Cl–) [1]. Ion channels enable ions to flow down their electrochemical gradients, which is essential for generating electrical signals in neurons and muscle cells [2]. Ion channels play crucial roles in various physiological processes, including nerve impulse transmission, muscle contraction, and hormone secretion. Second, the membrane potential is the electrical potential difference across the cell membrane, which results from the distribution of ions on either side of the membrane [3]. In neurons, the resting membrane potential typically ranges from −40 to −90 mV, which are generated by the differential distribution of ions. Action potentials are rapid changes in membrane potential that propagate along neurons and involve sequential opening and closing of voltage-gated Na(+) and K(+) channels, leading to depolarization and repolarization. Finally, electrochemical gradients are the combined effect of chemical gradients, which are differences in ion concentration, and electrical gradients, which are differences in charge, across the membrane [4]. Ions move across membranes as a result of their electrochemical gradients, generating ionic currents. This movement is crucial for the transmission of electrical signals in tissues. Electrochemical gradients are vital to processes such as nutrient uptake, waste removal, and signal transduction. In neurons, they are essential to initiate and propagate action potentials. Electrical impedance tomography (EIT) is a representative technique for imaging electrical conductivity in tissues and measures the impedance of tissue to an applied electrical current, which varies with tissue composition and structure [5,6].

The concept of conductivity is currently being applied in several clinical devices. For example, electrocardiography uses the electrical conductivity of the heart muscles to measure the electrical activity of the heart. Moreover, electroencephalography measures the electrical activity of the brain by assessing the conductivity of neural tissues. Functional electrical stimulation uses electrical current to stimulate muscle contraction during rehabilitation. Transcranial magnetic stimulation indirectly stimulates neural activity by inducing electrical currents in brain tissues. Furthermore, the bioimpedance analysis technique measures the resistance and reactance of body tissues to an applied current to estimate body composition. Finally, MRI can measure conductivity with and without the application of an electrical current in the human body. In this short review, we focused only on the last topic.

The study of electrical properties in human tissues is not only essential for understanding the innate electrical activities of the body but also vital for developing medical devices, diagnostic tools, and treatment approaches for various health conditions. Recently, we have published a series of papers related to conductivity mapping techniques using MRI and their applications in human brains. Based on our preliminary experience, we described the following topics in this short review: 1) the definition and fundamental principles of electrical conductivity, 2) the distinguishing features of electrical conductivity, 3) the factors that influence changes in electrical conductivity, 4) the methodology for measuring electrical conductivity using MRI, and 5) a summary of our key research outcomes.

1. Definition and fundamental principles of ionic conductivity

Electrical conductivity is an essential property of biological tissues and fluids. It determines their ability to transport electrical charges and provides important information about the function of biological tissues. The conductivity in biological tissues is ionic and distinctly different from electron-based conductivity in metals [7]. Ionic conductivity refers to the ability of ions to move through a medium, which can be a liquid, solid, or gel, and to conduct electrical current. Ions are charged particles that can move under the influence of an electrical field [8]. In ionic conductivity, the movement of these ions constitutes the flow of the electrical current. The ionic conductivity can be expressed as follows:

σi=jKNjqjmj

where qj is the charge of an electron of the j-th ions, mj is the mobility of the j-th ions, Nj is the number of the j-th ions, and K is the total number of ions with j=1−K. The SI unit of electric conductance, reciprocal of resistance (ohms, Ω), is Siemens (S), which is equivalent to an ampere per volt (A/V) and measures how easily electricity flows through a material. To express the electrical conductivity of a material, the use of Siemens per meter (S/m), which represents the conductance of a material per unit length, is common.

2. Features of ionic conductivity

In human tissues, muscles and blood are usually good conductors because of their high water content and the presence of various ions, such as Na+, K+, Ca2+, and Cl−, that carry electrical charges. However, bone and fat are relatively poor conductors because of their low water content and high resistance to electrical current flow. Conductivity in the human body can exhibit different conductivities in different directions if their physical structure has an orientation preference—this property is known as anisotropy. MRI can usually characterize conductivity anisotropy by applying diffusivity information [9-11]. Ionic conductivity in biological tissues influences various physiological processes. Biological tissues contain various ions, which are distributed within intracellular and extracellular fluids, contributing to the overall conductivity. Cell membranes act as barriers that separate different ionic environments. Ion channels and transporters in membranes regulate ion movement, thereby influencing conductivity. The extracellular matrix, which is composed of proteins and polysaccharides, affects the diffusion and mobility of ions [12]. The structure of this material can affect the path and speed of ionic conduction. Ionic conductivity is crucial for the generation and propagation of action potentials in neurons [13]. The rapid opening and closing of ion channels lead to changes in membrane potential, which allows electrical signals to travel along nerves. Ionic conductivity helps maintain homeostasis by regulating pH, osmotic balance, and cell volume. Ion transport across membranes is essential for kidney function and fluid balance [14].

3. Factors influencing the changes in ionic conductivity

Electrical conductivity changes due to various factors, reflecting alterations in the internal conditions of the material or the external environment. Altering these factors affects the density and mobility of charge carriers within the material. The common reasons why electrical conductivity can change are as follows: First, temperature is an important factor. Conductivity typically increases with temperature due to enhanced ion mobility. However, extreme temperatures can denature proteins, affecting ion channel function [15]. In human tissues, conductivity also increases with temperature because ions move more rapidly at higher temperatures. Second, the concentration of ions in tissues directly affects conductivity. Imbalances can lead to conditions such as hyperkalemia and hyponatremia, thereby affecting cardiac and neural functions [16]. In human tissues, packed normal tissues are transformed into necrotic tissues. This changes conductivity. Third, changes caused by physiological conditions in human tissues are the most interesting factors for evaluating conductivity. Conductivity is changed by several physiological conditions in human tissues. For example, higher ion concentrations increase conductivity. Tissues with high water content, such as the muscles, lateral ventricle of the brain, and blood, have higher conductivity than those with low water content, such as bone and fat. A brain tumor can disrupt and/or push neuronal bundles, causing a change in the orientation of neuronal fibers, and can cause anisotropic conduction in which the conductivity varies with the direction of current flow through the neuronal fiber. Human tissue conductivity changes with the frequency of the applied current. At low frequencies, the capacitance of cell membranes limits the current flow, whereas, at higher frequencies, the current can pass more easily. Therefore, the conductivity value obtained using magnetic resonance electrical impedance tomography (MREIT) [17-21] is different from that obtained using magnetic resonance electrical properties tomography (MREPT) [22-26]. Understanding how and why electrical conductivity changes is important for the design and use of materials in electronics, sensors, energy devices, and any application in which the flow of electrical current is a critical factor.

4. Mapping cellular conductivities

Intra-neurite conductivity (IC) refers to the conductivity within neuron axons and is influenced by the intracellular ion content and the structural integrity of the neuronal cytoskeleton [27]. Extra-neurite conductivity (EC) refers to the conductivity in the space surrounding neurons, including the extracellular matrix and glial cells, and is affected by the ionic composition of the extracellular fluid and the density of the neural tissue [28]. MREIT visualizes internal conductivity distributions by directly injecting direct currents and measuring induced magnetic flux densities using an MRI scanner. This technique can map low-frequency conductivity (LFC) at approximately 10 kHz; however, for its application, placing an electrical current into the human head is required. The details on MREIT will be described in the next section. MREIT reflects only the extracellular effects because the low-frequency current is blocked by the cell membranes. MREPT is a technique used to noninvasively image the electrical properties of tissues, such as conductivity and permittivity, using MRI data. MREPT can visualize high-frequency conductivity (HFC). To overcome MREPT, which cannot directly map cellular-level conductivities, and to investigate cellular or neuronal levels of conductivity without using MREIT, we recently developed a method for decomposing HFC obtained from MREPT into compartment-level conductivity of the human brain without injecting an external current based on information obtained from both HFC and multicompartment diffusivity [10]. The multicompartment diffusivity can separate the diffusion signals from the intra- and extra-neurite spaces. Using the multicompartment diffusivity, the decomposition method can calculate the compartmental conductivities, such as the EC and IC, which are the conductivities in the extra- and intra-neurite spaces, respectively [10,28]. The theoretical background of this development is that the electrical conductivity in biological tissues can be decomposed into the concentration and mobility of charge carriers, such as ions and charged molecules. The mobility of water molecules is related to the water diffusivity of biological tissues. Furthermore, the conductivity tensor imaging technique has been developed using diffusion tensor imaging without externally injected currents [9,11,29-33]. The development of IC and EC measurements for MREPT involves advanced imaging and computational techniques to differentiate and quantify the conductivity within and outside neurons. Neural tissues have a complex microstructure, which makes it challenging to accurately model and measure IC and EC. Efforts are underway to translate these technical developments into clinical practice, providing new tools for diagnosing and monitoring neurological conditions. The technical development of IC and EC for MREPT represents a significant advancement in noninvasive neuroimaging, with the potential to improve our understanding of neural tissue properties and their changes in health and disease.

MRI can measure properties related to conductivity in the human body. Two techniques are used: MREIT and MREPT. The MREIT technique measures LFC by applying low-frequency currents to the human body. However, MREPT maps an HFC at Larmor frequency without applying an external current. We explain these methods in detail below. Table 1 presents a comparison of the advantages and limitations between MREIT and MREPT.

Table 1 Comparison of the MREIT and MREPT techniques

ItemMREITMREPT
DefinitionCan map the electrical conductivity and current density inside the body using MRICan map the electrical properties of tissues at the Larmor frequency of MRI
Primary useTo visualize and monitor physiological and pathological processes in tissues based on their electrical propertiesTo image the electrical properties of tissues, providing information that can be used for diagnosis and treatment planning
Data acquisitionRequire the injection of an external current and measure the resulting magnetic field changesDo not require external current; rely on the knowledge of the complex RF transmit field for the reconstruction of electrical properties
Image reconstructionBased on the measurement of induced voltages or magnetic fields due to the applied currentInvolves the calculation of electrical properties from the distribution of the RF transmit field in the tissue
Spatial resolutionTypically lower than MREPT due to the nature of electrical current application and measurementGenerally higher because it uses the RF field distribution, which can be finely mapped using MRI
SensitivitySensitive to the distribution of electrical currents, which can be affected by tissue composition and pathologySensitive to the intrinsic electrical properties of tissues, which can vary with tissue type and state
ApplicationsUsed in research settings to study tissue conductivity and its changes due to various conditionsExplored for clinical applications, such as characterizing tumors and detecting abnormalities in tissue structure
AdvantagesProvides images of electrical conductivity and current density inside the bodyMeasures the electrical properties of tissues at the Larmor frequency of MRI
Can be used to monitor physiological and pathological processes in tissuesDoes not require external current for mapping, reducing complexity
Noninvasive and does not require external electrodesCan provide high-resolution images of the electrical properties of tissues
LimitationsLower spatial resolution than MREPTSusceptible to noise, particularly in phase images, which can affect accuracy
Sensitive to noise and requires regularization techniques to stabilize the inverse problemThe reconstruction algorithms are complex and computationally intensive
The need for accurate boundary information can be a challengeRequires accurate knowledge of the RF transmit field for electrical properties reconstruction

1. Magnetic resonance electrical impedance tomography

MREIT combines the high spatial resolution of MRI with the sensitivity of EIT to the electrical properties of tissues [17,21,34,35]. MREIT is used to produce high-resolution images of the electrical conductivity and impedance within an object or body by introducing a known electrical current and measuring the resulting magnetic field distortions using MRI [21,23].

Fig. 1 shows a schematic of MREIT. For MREIT, electrodes are attached to the subject’s surface at specified locations, such as in the brain area without hair. Because electrical currents are being used along with strong magnetic fields, safety protocols are established to ensure that there are no risks of burns and adverse effects on the subject. A small known current (usually in the range of milliamps to prevent any sensation or harm) is applied through the electrodes attached to the subject. A special MRI sequence, such as the spin-echo sequence, is used to detect the internal magnetic field. The sequence is sensitive to the magnetic field induced by the electrical current, which causes minute changes in the phase of the MRI signal. Both magnitude and phase images are acquired while the current flows through the subject. The phase image contains information about the phase shift induced by the current. The phase shift is directly associated with the component of the magnetic field that is perpendicular to the main static magnetic field of the MRI scanner [22,36].

Figure 1.Graphical explanation of the MREIT method. In MREIT, electrodes are attached to the subject’s surface at specified locations, such as brain areas without hair. The magnetic resonance imaging phase is used to obtain the Bz Field, which is the component of the magnetic field induced by the applied current. The Bz component is located along the direction of the main magnetic field. After calculating the Bz component, the current density within the subject is calculated by applying Ampere’s Law and/or the Biot–Savart Law. Because the applied current is known, this step allows the reconstruction of the current paths in the tissue. Finally, using mathematical algorithms (e.g., J-substitution algorithm), conductivity images are reconstructed based on the measured magnetic flux density and applied current density. MREIT, magnetic resonance electrical impedance tomography.

To reconstruct the conductivity from the phase images, the Bz Field, which is the primary data of interest in MREIT, is the component of the magnetic field induced by the applied current. The Bz component is located along the direction of the main magnetic field. From the phase images, the Bz Field can be calculated. Then, using the Bz component data and applying Ampere’s Law and/or Biot–Savart Law, the current density within the subject is calculated. Because the applied current is known, this step allows the reconstruction of the current paths in the tissue. Finally, using mathematical algorithms (e.g., J-substitution algorithm), conductivity images are reconstructed based on the measured magnetic flux density and applied current density because the key to MREIT is the relationship between the current density, applied electric field, and conductivity of the tissue. These images show the variations in electrical conductivity across the interior of the subject.

MREIT has applications in medical diagnostics, such as distinguishing between different tissue types (healthy vs. cancerous), due to the contrast in their conductivity properties [9,17,18,32]. Furthermore, it is used in research settings to measure changes in conductivity due to physiological processes or in response to treatment. However, MREIT’s applications face several challenges and limitations. First, accurate conductivity imaging requires precise phase measurements and robust algorithms to solve the ill-posed inverse problem of conductivity reconstruction. Second, noise, subject motion, and other artifacts can significantly affect reconstruction quality. Finally, the safety of the subject must be ensured because current is being directly applied, particularly around sensitive areas, such as the brain, or for subjects with implanted electronic devices. Therefore, the application of this technique in clinical settings has major limitations. Individuals typically apply MREPT to humans.

2. Magnetic resonance electrical properties tomography

MREPT is another method that aims to reconstruct the electrical properties (conductivity and permittivity) of biological tissues, specifically their electrical conductivity and permittivity. Rather than using external currents, MREPT, which is the interaction between radiofrequency (RF) electromagnetic fields and tissues during an MRI scan to infer electrical properties, uses the phase information from standard MRI signals. The phase of the MRI signal is sensitive to the local electrical properties of the tissue, and this information is used to derive maps of electrical conductivity and permittivity.

In MREPT, additional electrodes or external currents are not required, as in MREIT. A standard MRI scan is performed using a sequence that is sensitive to phase information, such as a turbo spin-echo sequence and balanced fast field-echo sequence. The RF electromagnetic waves used in MRI will interact with the electrical properties of tissues, and these interactions affect the phase of the received MRI signal. If the applied sequence is sensitive to the transmit RF field (also known as the B1 field), then the B1 field mapping technique is often used to correct for B1 inhomogeneity. During a scan, the MRI system acquires complex signals, comprising amplitude and phase information. The phase of the MRI signal can be influenced by the local electrical properties (e.g., conductivity and permittivity) of the tissue, similar to MREIT.

To reconstruct conductivity, the acquired phase information is processed to remove potential artifacts and any contributions not related to the tissue’s electrical properties, such as those resulting from magnetic field inhomogeneities. The spatial distribution of the RF field (B1) is then calculated from the phase images. The electrical (E) field induced by the MRI RF pulse can be calculated from the B1 field using Maxwell’s equations. Once the E-field is known, the local electrical properties (e.g., conductivity and permittivity) are reconstructed by solving a partial differential equation known as the Helmholtz equation, which relates the E-field to conductivity and permittivity. Therefore, the relationship between the B1 field denoted as and the electrical properties are expressed as follows:

2B1=iωμ0τHB1τHτH××B1

where ω is the angular frequency, μ0=4π×10–7 N/A2 is the magnetic permeability of the free space, and τHH+iωϵH at HFC σH and permittivity ϵH [23,25]. The transverse field of B1 can be decomposed into the positively rotating field B1+=12Bx+iByand the negatively rotating field B1=12BxiBy. Using a conventional MRI scanner with a single transmit channel, the magnetic field B1+ component is available. We denoted ϕ+ and ϕ as the phase terms of B1+ and B1, respectively. By assuming σH>>ωϵH, a phase-based MREPT formula was derived as follows:

ϕtr1σH+2ϕtrσH2ωμ0=0

where ϕtr=ϕ++ϕ. To stabilize the formula (3), the MREPT formula based on the convection reaction equation can be derived by adding the regularization coefficient c [37]:

c21σH+ϕtr1σH+2ϕtrσH=2ωμ0

MREPT depends on a relatively weak phase signal from a secondary RF magnetic field, which is induced by the time-varying RF field. Because of the weak phase signal and noise artifacts, a multi-echo spin-echo MRI pulse sequence is advantageous for reducing noise artifacts using the weight for the k-th echo:

ϕtr=k=1NEwkϕk,   wk= ρk 2j=1NE ρj 2

where ϕk and ρk are the phase signal and complex MRI signal, respectively, for the k-th echo. To solve the convection reaction partial differential equation in (4), we used the two-dimensional finite-difference method. For each image matrix, equation (4) can be written as follows:

c2x2+2y2+ϕtrxx+ϕtryy+2ϕtrx2+2ϕtry21σH=2ωμ0

The finite-difference method for solving equation (6) is to find solutions of a linear matrix system Ax=b with the appropriate processing of the Dirichlet boundary conditions. A is a staff matrix, x=1σH1, 1σH2, , 1σHN , and b=2ωμ0, 2ωμ0, , 2ωμ0. We used the finite-difference method to solve the aforementioned matrix system with the regularization coefficient c=0.03 in equation (6) [38]. Several computational algorithms have been developed to perform this inversion from the E-field to the desired electrical properties.

MREPT also has some challenges and limitations. MREPT is sensitive to noise and artifacts, particularly those due to B1 inhomogeneity, and requires phase unwrapping. It relies on sophisticated postprocessing algorithms to correctly resolve the electrical properties from the measured signals, and this is an active area of research. Accurately linking the changes in phase to conductivity and permittivity requires assumptions about tissue properties, and this can introduce errors or uncertainties. MREPT has potential uses in distinguishing healthy from diseased tissues because these properties can differ significantly for conditions such as cancer and inflammation. It could also be particularly helpful in treatment planning for modalities such as hyperthermia therapy and RF ablation, where knowledge of the tissue’s electrical properties can impact the treatment outcomes. We explain the developments and applications of MREPT used for diagnosing Alzheimer’s disease (AD) [38,39]. MREPT has been used in various medical fields to study the properties of brain tissues, tumors, and muscles by providing insights into the tissue’s electrical characteristics [29,40-44].

1. Technical developments

1) Decomposition of HFC into extra- and intra-neurite compartment conductivities

We published a technical development paper to show conductivity tensor images using diffusion tensor images [10]. Fig. 2 summarizes the technical development to map LFC from MREPT using the multicompartment spherical mean technique (MC-SMT) technique [45]. The MC-SMT method was developed to evaluate the microscopic features of the intra- (restricted) and extra-neurite (hindered) compartments in neuronal tissue, which are the two compartments of a neuron. The intra-neurite compartment contains axons and dendrites and can be modeled as a collection of infinitely thin “sticks.” The extra-neurite compartment is everything else in the brain, except for neurites and free water, and can reflect the interactions of water molecules with macromolecules, fibers, and membranes in the brain tissue. The gray matter contains the cell bodies of neurons, dendrites, and axons, and the white matter contains myelinated axons.

Figure 2.Summary of the technical development to map the HFC and low-frequency conductivity using MREPT and MC-SMT images. In MREPT, (a) a standard magnetic resonance imaging scan is performed using a sequence that is sensitive to phase information, such as a turbo spin-echo sequence or balanced fast field-echo sequence. Furthermore, (b) diffusion tensor images with three b-values and multiple gradient directions are acquired to obtain microstructure information. The spatial distribution of the radiofrequency field (B1) is calculated from the phase images. (c) The HFC is calculated with a double derivative of the B1 field by applying a regularization. (d) The MC-SMT is used to map intrinsic diffusion coefficient, intra-neurite volume fraction, and extra-neurite mean diffusivity. (e) The low-frequency conductivity map can be calculated with the recovered HFC and MC-SMT maps. (f) The extra-neurite tensor maps are obtained using MC-SMT maps. (g) The low-frequency conductivity tensor map can be calculated using (c) and (f). HFC, high-frequency conductivity; MREPT, magnetic resonance electrical properties tomography; MC-SMT, multicompartment spherical mean technique.

After calculating the HFC from the B1 phase, the recovered HFC σH was decomposed into the intra- and extra-neurite compartments to calculate the compartmental conductivities [10,45].

σH = σint +σext=νint c¯ intDint+1νint c¯ ext Dext

where σint and σext are the IC and EC, respectively; νint is the intra-neurite volume fraction (IVF); c¯ int  is the intra-neurite ion concentration; c¯  ext and is the extra-neurite ion concentration (EIC). Similarly, Dint and Dext are the intra-neurite diffusivity and the extra-neurite diffusivity (ED), respectively. To obtain νint, Dint and Dext in equation (7), the MC-SMT technique is applied [45]. The key insight into MC-SMT is that for a specified diffusion weighting factor b, the spherical mean of the diffusion signal e¯b over the gradient directions is invariant to the fiber orientation distribution.]

Because the internal current flow at low-frequency (<1 kHz) is only restricted to the extra-neurite space between the cells, the low-frequency dominant average scalar conductivity σL  can be expressed as follows:

σL = 1νint c¯ ext Dext=1vintDextσHvintβDint+1vintDext

The LFC σL  in equation (8) depends on the IVF (νint), apparent EIC (c¯ ext), and extra-neurite mean diffusivity (Dext). Because cerebrospinal fluid (CSF) is a highly conductive liquid without cell membranes, the LFC σL  is almost identical to the HFCs σH in CSF [46].

To measure the anisotropy of conductivity, Dext can be a tensor. We assume that Dext and the water diffusion tensor share the eigenvectors. The eigenvalues of Dext, Dext,d1ext=d2extd3ext, satisfy the following relations:

d1ext+d2ext+d3ext 3=Dext,d1ext=d2ext= (1νint) Dint

Therefore, σL  is also a tensor in which ion mobility is assumed to be proportional to the water molecule diffusion flow [10,28,31,47]. Fig. 3 shows the two slices of the HFC, intrinsic diffusion coefficient (Dint), IVF (νint), ED (Dext), and LFC tensor obtained from a young participant.

Figure 3.Representative maps are obtained from two imaging slices acquired from one young participant. Maps are shown as the high-frequency conductivity (HFC), intrinsic diffusion coefficient (Dint), intra-neurite volume fraction (νint), extra-neurite diffusivity (Dext), and low-frequency conductivity tensor.

2. Clinical applications

1) High-frequency conductivity

We published an article using the HFC of MREPT in patients with AD [38]. This study explored the use of HFC mapping in the brain to differentiate patients with AD from those with amnestic mild cognitive impairment (MCI) and cognitively normal (CN) elderly individuals. Fig. 4 shows a 3D T1-weighted image; the corresponding segmented brain tissues of gray matter volume, white matter volume, and CSF volume; and an HFC map acquired from one CN participant and a patient with AD. In general, the older participant had more brain atrophy than the young participant. This atrophy was caused by brain tissue loss. The atrophy area showed higher conductivity than the normal area, which was caused by the replacement of brain tissues with CSF. The conductivity was higher in patients with AD than in CN participants in several brain areas. An MREPT study was conducted using a clinical 3T MRI system (Ingenia, Philips Medical System) to map the HFC. We identified several key points from the study: First, the HFC values were higher in patients with AD than in the CN and MCI groups. Second, a negative correlation was observed between Mini-Mental State Examination (MMSE) scores and HFC values, indicating that higher HFC values are associated with cognitive decline. Third, age was positively correlated with HFC values. Finally, the HFC value in the insula region of the brain exhibited high potential as a biomarker for differentiating patients with AD from CN participants with high sensitivity and specificity. Our first clinical study concluded that HFC mapping could serve as a noninvasive imaging biomarker for evaluating and differentiating patients with AD from CN individuals, potentially aiding in the early diagnosis and treatment of AD.

Figure 4.3D T1-weighted image (3DT1) and the corresponding segmented brain tissues of gray matter volume (GMV), white matter volume (WMV), and cerebrospinal fluid (CSF) volume and a high-frequency conductivity (HFC) map acquired from one cognitively normal (CN) older participant and a patient with Alzheimer’s disease (AD).

2) Compartmental conductivities to represent a low-frequency conductivity

We recently published a paper to represent compartmental conductivity changes in patients with AD [39]. We obtained MREPT and two-shell diffusion MRI from 21 CN individuals, 25 patients with MCI, and 20 patients with AD. We used MREPT data to obtain the HFC or Larmor frequency conductivity and develop an MC-SMT model to decompose the two-shell diffusion MRI signals into two compartments with distinct diffusion properties: one with restricted diffusion within the neurites and one with hindered diffusion in the extra-neurite space. We focused on the compartments with restricted and hindered diffusion, which do not exactly correspond to the intra- and extracellular spaces. We applied the MC-SMT model based on the ball-and-stick model, which does not account for the diffusion signals originating from the soma or other large cellular domains. The MC-SMT model estimates the microstructural features of the intra- and extra-neurite compartments, rather than the intracellular and extracellular spaces [10,48]. Fig. 5 shows the HFC at the Lamour frequency, EC, and IC acquired from one older CN participant and a patient with AD. We found that HFC and EC were higher in the AD group than in the CN and MCI groups, particularly in the frontal, occipital, parietal, and temporal brain areas. IC was higher in the AD group than in the CN group but lower than in the MCI group. MMSE scores were negatively correlated with HFC and EC but positively correlated with IC. Conductivities increased in areas with lower MMSE scores. Age exhibited no significant correlation with any of the conductivity indices. HFC and EC exhibited good diagnostic performance, particularly in the hippocampus and insular regions. HFC and EC also performed well, with the insular region exhibiting the highest area under the curve for EC. The conductivity indices did not show significant results for differentiating MCI from CN.

Figure 5.T1-weighted (T1W) image and conductivity maps of the high-frequency conductivity (HFC) and the corresponding extra-neurite conductivity (EC) and intra-neurite conductivity (IC) acquired from one cognitively normal (CN) older participant and a patient with Alzheimer’s disease (AD).

1. Potential benefits of these techniques in clinical applications

MREIT and MREPT are advanced imaging modalities that offer unique insights into the electrical properties of tissues, which can be beneficial in clinical settings. Electrical conductivity can be used to detect and characterize tumors compared with normal tissues [40,41,49-51]. It can help assess stroke by visualizing the impedance changes in brain tissues [42,52]. MREIT may assist in mapping the conduactivity of heart tissues, which can be useful in diagnosing and treating cardiac arrhythmias [53]. MREPT can provide information on tissue composition and structure by measuring electrical properties at high frequencies. It can be used to monitor the effects of thermal and electrical therapies on tissue properties. MREPT may be helpful in differentiating patients with AD from CN older participants and those with amnestic MCI [38,39]. Both techniques are currently under research and development, with ongoing efforts to improve their accuracy, resolution, and clinical relevance [20]. They have the potential to provide noninvasive methods for obtaining electrical property distributions, which could complement existing imaging methods and improve diagnostic and therapeutic outcomes.

Furthermore, both techniques can significantly affect personalized medicine by providing detailed and individualized maps of the electrical properties of tissues [40,41]. By offering precise measurements of tissue conductivity and permittivity, MREIT and MREPT can improve the diagnosis of various conditions, allowing for the development of more tailored treatment plans. These techniques can be used to monitor the effects of treatments in real time, such as observing changes in the electrical properties of cancerous tissue during chemotherapy or radiotherapy [41,54,55]. However, note that these applications are still under research and development, and their clinical use will depend on further validation and refinement of the techniques.

2. Impact of tissue heterogeneity on tissue pathophysiology

It is important to understand how tissue heterogeneity affects the accuracy of measuring electrical properties [53,56]. Tissue heterogeneity can significantly affect the accuracy of electrical property measurements in several ways. Different tissues make different contributions to the measured properties because of differences in depth within the sensing region [57]. The ability to detect and accurately measure the electrical properties of small structures within heterogeneous tissues is limited [51]. Heterogeneous tissues can exhibit spatial variations in electrical properties that are challenging to accurately capture [51]. Many measurement techniques assume homogeneity within the sample, which can lead to errors when applied to heterogeneous tissues [57]. The assumption of average homogeneous thickness distributions in soft tissues can significantly alter the results of biomechanical analyses compared with the inclusion of true spatially varying thickness distributions [53].

Another important issue is the impact of MREIT and MREPT on our understanding of tissue pathophysiology [17,41,58-60]. By imaging at different frequencies, MREIT and MREPT can offer insights into the membrane properties of cells, which is crucial for understanding various diseases at the cellular level [20]. The ability to image low-frequency electrical properties of tissues can lead to better detection and characterization of diseases, such as cancer; ischemic regions from stroke; and other pathologies [61].

3. Challenges in the implementation of MREIT and MREPT in clinical practice

Implementing MREIT and MREPT in clinical practice faces several challenges. First, both techniques require sophisticated hardware and software integration into existing MRI systems, which can be complex and costly [61]. Second, measurements are based very small signals, which can be easily affected by noise and require advanced noise reduction techniques to ensure accuracy [20]. Third, the introduction of electrical currents into the body, as in MREIT, raises safety concerns that must be carefully managed to prevent any harm to patients [61]. Fourth, the electrical properties measured using these techniques are not as widely understood as traditional MRI signals; therefore, there is a learning curve for clinicians to interpret the data effectively [61]. Fifth, extensive clinical trials are necessary to validate the efficacy and safety of these methods before they can be widely adopted in clinical settings [61]. Finally, the conductivity decomposition techniques of MREIT and MREPT cannot be directly transferable to clinics due to several limitations. All current models depend on the diffusion microstructure [10,31,47]. Sajib et al. [31] optimized the volume fraction and water diffusion coefficients of the intracellular space, extracellular matrix space, volume fraction of the free water component, and an offset value. In contrast, Marino et al. [47] optimized the volume fraction of the intracellular, free water, and restricted diffusion compartments in the extracellular space based on the neurite orientation dispersion and density imaging (NODDI) model [62]. It has been demonstrated that cellular microstructure parameters estimated from the NODDI model produce more stable results than that of the method by Sajib et al. [31] Jahng et al. [10] proposed using the MC-SMT to estimate cellular microstructure parameters [45]. Both MREIT and MREPT are sensitive to noise in the measured magnetic fields. This noise can significantly affect the accuracy of the reconstructed conductivity images. These challenges highlight the need for ongoing research and development to refine MREIT and MREPT technologies and establish their practical utility in clinical medicine.

This review highlights the potential of MRI-based techniques to provide detailed information about the electrical properties of the body. These techniques, particularly MREPT, show promise for biomedical applications such as differentiating tissue types and detecting pathological conditions. Our studies have demonstrated the potential of conductivity indices as biomarkers for AD diagnosis. However, both MREIT and MREPT face challenges, including the need for sophisticated hardware, software integration, advanced noise reduction techniques, and patient safety assurance during the procedures. The ongoing research on MREPT aims to address its technical challenges and enhance its accuracy, robustness, and clinical applicability. MREPT is generally applied to humans and holds significant promise as a noninvasive tool for characterizing tissue properties and understanding pathological conditions. In MREIT, the subject’s safety must be ensured because current is applied, particularly around sensitive areas, such as the brain, or for subjects with implanted electronic devices. Future developments and clinical trials are necessary to validate the efficacy and safety of these methods, which could improve their diagnostic capabilities and help develop personalized treatment strategies.

The research was supported by the National Research Foundation of Korea (NRF) grants funded by Ministry of Science and ICT (RS-2024-00335770, G.H.J.; 2020R1A2C1004749, G.H.J; RS-2023-00250977, M.B.L.;2019R1A2C1004660, O.I.K), Republic of Korea.

Conceptualization: Geon-Ho Jahng. Data curation: Geon-Ho Jahng. Formal analysis: Geon-Ho Jahng, Mun Bae Lee. Funding acquisition: Geon-Ho Jahng. Investigation: Geon-Ho Jahng. Methodology: Geon-Ho Jahng, Mun Bae Lee, Oh In Kwon. Resources: Geon-Ho Jahng. Supervision: Oh In Kwon. Visualization: Geon-Ho Jahng. Writing – original draft: Geon-Ho Jahng. Writing – review & editing: Geon-Ho Jahng, Mun Bae Lee, Oh In Kwon.

The study was conducted in accordance with the Declaration of Helsinki. The Institutional Review Board (IRB) of Kyung Hee University Hospital at Gangdong in Seoul, Republic of Korea, approved this cross-sectional prospective study (IRB khnmc2019-07-007) and written informed consent was obtained from the participants.

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Article

Review Article

Progress in Medical Physics 2024; 35(4): 73-88

Published online December 31, 2024 https://doi.org/10.14316/pmp.2024.35.4.73

Copyright © Korean Society of Medical Physics.

Principle, Development, and Application of Electrical Conductivity Mapping Using Magnetic Resonance Imaging

Geon-Ho Jahng1 , Mun Bae Lee2 , Oh In Kwon2

1Department of Radiology, Kyung Hee University Hospital at Gangdong, Kyung Hee University College of Medicine, Seoul, 2Department of Mathematics, College of Basic Science, Konkuk University, Seoul, Korea

Correspondence to:Geon-Ho Jahng
(ghjahng@gmail.com)
Tel: 82-2-440-6187
Fax: 82-2-440-6932

Received: August 8, 2024; Revised: November 6, 2024; Accepted: November 12, 2024

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Magnetic resonance imaging (MRI)-related techniques can provide information related to the electrical properties of the body. Understanding the electrical properties of human tissues is crucial for developing diagnostic tools and therapeutic approaches for various medical conditions. This study reviewed the principles, development, and application of electrical conductivity mapping using MRI. To review the magnetic resonance electrical properties tomography (MREPT)-based conductivity mapping technique and its application to brain imaging, first, we explain the definition and fundamental principles of electrical conductivity, some factors that influence changes in ionic conductivity, and the background of mapping cellular conductivities. Second, we explain the concepts and applications of magnetic resonance electrical impedance tomography (MREIT) and MREPT. Third, we describe our recent technical developments and their clinical applications. Finally, we explain the benefits, impacts, and challenges of MRI-based conductivity in clinical practice. MRI techniques, such as MREIT and MREPT, enabled the measurement of conductivity-related properties within the body. MREIT assessed low-frequency conductivity by applying a low-frequency external current, whereas MREPT captured high-frequency conductivity (at the Larmor frequency) without applying an external current. In MREIT, the subject’s safety should be ensured because electrical current is applied, particularly around sensitive areas, such as the brain, or in subjects with implanted electronic devices. Our previous studies have highlighted the potential of conductivity indices as biomarkers for Alzheimer’s disease. MREPT is usually applied to humans rather than MREIT. MREPT holds promise as a noninvasive tool for characterizing tissue properties and understanding pathological conditions.

Keywords: MRI, B1 phase, Conductivity, Brain application

Introduction

Electrical conductivity in human tissue is a critical concept in medical diagnostics, treatment, and biomedical engineering, among other fields. Human biological tissues conduct electricity because of the presence of ions in bodily fluids. The conductivities of different tissues vary and are influenced by several factors. In human tissues, electrical current is primarily carried by ions. When an electrical field is applied, these ions move, creating a current. This ionic conduction is crucial for various physiological processes, including nerve impulse transmission and muscle contraction. These properties are important because they can provide additional information about tissue structure and function beyond the anatomical details that standard magnetic resonance imaging (MRI) provides.

Imaging electrical conductivity in human tissues involves understanding how ions move through ion channels, how membrane potentials are established, and how electrochemical gradients drive ionic currents. First, ion channels are protein structures embedded in cell membranes that facilitate the movement of ions across the membrane. These channels are selective for specific ions, such as sodium (Na+), potassium (K+), calcium (Ca 2+), and chloride (Cl–) [1]. Ion channels enable ions to flow down their electrochemical gradients, which is essential for generating electrical signals in neurons and muscle cells [2]. Ion channels play crucial roles in various physiological processes, including nerve impulse transmission, muscle contraction, and hormone secretion. Second, the membrane potential is the electrical potential difference across the cell membrane, which results from the distribution of ions on either side of the membrane [3]. In neurons, the resting membrane potential typically ranges from −40 to −90 mV, which are generated by the differential distribution of ions. Action potentials are rapid changes in membrane potential that propagate along neurons and involve sequential opening and closing of voltage-gated Na(+) and K(+) channels, leading to depolarization and repolarization. Finally, electrochemical gradients are the combined effect of chemical gradients, which are differences in ion concentration, and electrical gradients, which are differences in charge, across the membrane [4]. Ions move across membranes as a result of their electrochemical gradients, generating ionic currents. This movement is crucial for the transmission of electrical signals in tissues. Electrochemical gradients are vital to processes such as nutrient uptake, waste removal, and signal transduction. In neurons, they are essential to initiate and propagate action potentials. Electrical impedance tomography (EIT) is a representative technique for imaging electrical conductivity in tissues and measures the impedance of tissue to an applied electrical current, which varies with tissue composition and structure [5,6].

The concept of conductivity is currently being applied in several clinical devices. For example, electrocardiography uses the electrical conductivity of the heart muscles to measure the electrical activity of the heart. Moreover, electroencephalography measures the electrical activity of the brain by assessing the conductivity of neural tissues. Functional electrical stimulation uses electrical current to stimulate muscle contraction during rehabilitation. Transcranial magnetic stimulation indirectly stimulates neural activity by inducing electrical currents in brain tissues. Furthermore, the bioimpedance analysis technique measures the resistance and reactance of body tissues to an applied current to estimate body composition. Finally, MRI can measure conductivity with and without the application of an electrical current in the human body. In this short review, we focused only on the last topic.

The study of electrical properties in human tissues is not only essential for understanding the innate electrical activities of the body but also vital for developing medical devices, diagnostic tools, and treatment approaches for various health conditions. Recently, we have published a series of papers related to conductivity mapping techniques using MRI and their applications in human brains. Based on our preliminary experience, we described the following topics in this short review: 1) the definition and fundamental principles of electrical conductivity, 2) the distinguishing features of electrical conductivity, 3) the factors that influence changes in electrical conductivity, 4) the methodology for measuring electrical conductivity using MRI, and 5) a summary of our key research outcomes.

Electrical Conductivity

1. Definition and fundamental principles of ionic conductivity

Electrical conductivity is an essential property of biological tissues and fluids. It determines their ability to transport electrical charges and provides important information about the function of biological tissues. The conductivity in biological tissues is ionic and distinctly different from electron-based conductivity in metals [7]. Ionic conductivity refers to the ability of ions to move through a medium, which can be a liquid, solid, or gel, and to conduct electrical current. Ions are charged particles that can move under the influence of an electrical field [8]. In ionic conductivity, the movement of these ions constitutes the flow of the electrical current. The ionic conductivity can be expressed as follows:

σi=jKNjqjmj

where qj is the charge of an electron of the j-th ions, mj is the mobility of the j-th ions, Nj is the number of the j-th ions, and K is the total number of ions with j=1−K. The SI unit of electric conductance, reciprocal of resistance (ohms, Ω), is Siemens (S), which is equivalent to an ampere per volt (A/V) and measures how easily electricity flows through a material. To express the electrical conductivity of a material, the use of Siemens per meter (S/m), which represents the conductance of a material per unit length, is common.

2. Features of ionic conductivity

In human tissues, muscles and blood are usually good conductors because of their high water content and the presence of various ions, such as Na+, K+, Ca2+, and Cl−, that carry electrical charges. However, bone and fat are relatively poor conductors because of their low water content and high resistance to electrical current flow. Conductivity in the human body can exhibit different conductivities in different directions if their physical structure has an orientation preference—this property is known as anisotropy. MRI can usually characterize conductivity anisotropy by applying diffusivity information [9-11]. Ionic conductivity in biological tissues influences various physiological processes. Biological tissues contain various ions, which are distributed within intracellular and extracellular fluids, contributing to the overall conductivity. Cell membranes act as barriers that separate different ionic environments. Ion channels and transporters in membranes regulate ion movement, thereby influencing conductivity. The extracellular matrix, which is composed of proteins and polysaccharides, affects the diffusion and mobility of ions [12]. The structure of this material can affect the path and speed of ionic conduction. Ionic conductivity is crucial for the generation and propagation of action potentials in neurons [13]. The rapid opening and closing of ion channels lead to changes in membrane potential, which allows electrical signals to travel along nerves. Ionic conductivity helps maintain homeostasis by regulating pH, osmotic balance, and cell volume. Ion transport across membranes is essential for kidney function and fluid balance [14].

3. Factors influencing the changes in ionic conductivity

Electrical conductivity changes due to various factors, reflecting alterations in the internal conditions of the material or the external environment. Altering these factors affects the density and mobility of charge carriers within the material. The common reasons why electrical conductivity can change are as follows: First, temperature is an important factor. Conductivity typically increases with temperature due to enhanced ion mobility. However, extreme temperatures can denature proteins, affecting ion channel function [15]. In human tissues, conductivity also increases with temperature because ions move more rapidly at higher temperatures. Second, the concentration of ions in tissues directly affects conductivity. Imbalances can lead to conditions such as hyperkalemia and hyponatremia, thereby affecting cardiac and neural functions [16]. In human tissues, packed normal tissues are transformed into necrotic tissues. This changes conductivity. Third, changes caused by physiological conditions in human tissues are the most interesting factors for evaluating conductivity. Conductivity is changed by several physiological conditions in human tissues. For example, higher ion concentrations increase conductivity. Tissues with high water content, such as the muscles, lateral ventricle of the brain, and blood, have higher conductivity than those with low water content, such as bone and fat. A brain tumor can disrupt and/or push neuronal bundles, causing a change in the orientation of neuronal fibers, and can cause anisotropic conduction in which the conductivity varies with the direction of current flow through the neuronal fiber. Human tissue conductivity changes with the frequency of the applied current. At low frequencies, the capacitance of cell membranes limits the current flow, whereas, at higher frequencies, the current can pass more easily. Therefore, the conductivity value obtained using magnetic resonance electrical impedance tomography (MREIT) [17-21] is different from that obtained using magnetic resonance electrical properties tomography (MREPT) [22-26]. Understanding how and why electrical conductivity changes is important for the design and use of materials in electronics, sensors, energy devices, and any application in which the flow of electrical current is a critical factor.

4. Mapping cellular conductivities

Intra-neurite conductivity (IC) refers to the conductivity within neuron axons and is influenced by the intracellular ion content and the structural integrity of the neuronal cytoskeleton [27]. Extra-neurite conductivity (EC) refers to the conductivity in the space surrounding neurons, including the extracellular matrix and glial cells, and is affected by the ionic composition of the extracellular fluid and the density of the neural tissue [28]. MREIT visualizes internal conductivity distributions by directly injecting direct currents and measuring induced magnetic flux densities using an MRI scanner. This technique can map low-frequency conductivity (LFC) at approximately 10 kHz; however, for its application, placing an electrical current into the human head is required. The details on MREIT will be described in the next section. MREIT reflects only the extracellular effects because the low-frequency current is blocked by the cell membranes. MREPT is a technique used to noninvasively image the electrical properties of tissues, such as conductivity and permittivity, using MRI data. MREPT can visualize high-frequency conductivity (HFC). To overcome MREPT, which cannot directly map cellular-level conductivities, and to investigate cellular or neuronal levels of conductivity without using MREIT, we recently developed a method for decomposing HFC obtained from MREPT into compartment-level conductivity of the human brain without injecting an external current based on information obtained from both HFC and multicompartment diffusivity [10]. The multicompartment diffusivity can separate the diffusion signals from the intra- and extra-neurite spaces. Using the multicompartment diffusivity, the decomposition method can calculate the compartmental conductivities, such as the EC and IC, which are the conductivities in the extra- and intra-neurite spaces, respectively [10,28]. The theoretical background of this development is that the electrical conductivity in biological tissues can be decomposed into the concentration and mobility of charge carriers, such as ions and charged molecules. The mobility of water molecules is related to the water diffusivity of biological tissues. Furthermore, the conductivity tensor imaging technique has been developed using diffusion tensor imaging without externally injected currents [9,11,29-33]. The development of IC and EC measurements for MREPT involves advanced imaging and computational techniques to differentiate and quantify the conductivity within and outside neurons. Neural tissues have a complex microstructure, which makes it challenging to accurately model and measure IC and EC. Efforts are underway to translate these technical developments into clinical practice, providing new tools for diagnosing and monitoring neurological conditions. The technical development of IC and EC for MREPT represents a significant advancement in noninvasive neuroimaging, with the potential to improve our understanding of neural tissue properties and their changes in health and disease.

Methodologies for Measuring Electrical Conductivity Using MRI

MRI can measure properties related to conductivity in the human body. Two techniques are used: MREIT and MREPT. The MREIT technique measures LFC by applying low-frequency currents to the human body. However, MREPT maps an HFC at Larmor frequency without applying an external current. We explain these methods in detail below. Table 1 presents a comparison of the advantages and limitations between MREIT and MREPT.

Table 1 . Comparison of the MREIT and MREPT techniques.

ItemMREITMREPT
DefinitionCan map the electrical conductivity and current density inside the body using MRICan map the electrical properties of tissues at the Larmor frequency of MRI
Primary useTo visualize and monitor physiological and pathological processes in tissues based on their electrical propertiesTo image the electrical properties of tissues, providing information that can be used for diagnosis and treatment planning
Data acquisitionRequire the injection of an external current and measure the resulting magnetic field changesDo not require external current; rely on the knowledge of the complex RF transmit field for the reconstruction of electrical properties
Image reconstructionBased on the measurement of induced voltages or magnetic fields due to the applied currentInvolves the calculation of electrical properties from the distribution of the RF transmit field in the tissue
Spatial resolutionTypically lower than MREPT due to the nature of electrical current application and measurementGenerally higher because it uses the RF field distribution, which can be finely mapped using MRI
SensitivitySensitive to the distribution of electrical currents, which can be affected by tissue composition and pathologySensitive to the intrinsic electrical properties of tissues, which can vary with tissue type and state
ApplicationsUsed in research settings to study tissue conductivity and its changes due to various conditionsExplored for clinical applications, such as characterizing tumors and detecting abnormalities in tissue structure
AdvantagesProvides images of electrical conductivity and current density inside the bodyMeasures the electrical properties of tissues at the Larmor frequency of MRI
Can be used to monitor physiological and pathological processes in tissuesDoes not require external current for mapping, reducing complexity
Noninvasive and does not require external electrodesCan provide high-resolution images of the electrical properties of tissues
LimitationsLower spatial resolution than MREPTSusceptible to noise, particularly in phase images, which can affect accuracy
Sensitive to noise and requires regularization techniques to stabilize the inverse problemThe reconstruction algorithms are complex and computationally intensive
The need for accurate boundary information can be a challengeRequires accurate knowledge of the RF transmit field for electrical properties reconstruction


1. Magnetic resonance electrical impedance tomography

MREIT combines the high spatial resolution of MRI with the sensitivity of EIT to the electrical properties of tissues [17,21,34,35]. MREIT is used to produce high-resolution images of the electrical conductivity and impedance within an object or body by introducing a known electrical current and measuring the resulting magnetic field distortions using MRI [21,23].

Fig. 1 shows a schematic of MREIT. For MREIT, electrodes are attached to the subject’s surface at specified locations, such as in the brain area without hair. Because electrical currents are being used along with strong magnetic fields, safety protocols are established to ensure that there are no risks of burns and adverse effects on the subject. A small known current (usually in the range of milliamps to prevent any sensation or harm) is applied through the electrodes attached to the subject. A special MRI sequence, such as the spin-echo sequence, is used to detect the internal magnetic field. The sequence is sensitive to the magnetic field induced by the electrical current, which causes minute changes in the phase of the MRI signal. Both magnitude and phase images are acquired while the current flows through the subject. The phase image contains information about the phase shift induced by the current. The phase shift is directly associated with the component of the magnetic field that is perpendicular to the main static magnetic field of the MRI scanner [22,36].

Figure 1. Graphical explanation of the MREIT method. In MREIT, electrodes are attached to the subject’s surface at specified locations, such as brain areas without hair. The magnetic resonance imaging phase is used to obtain the Bz Field, which is the component of the magnetic field induced by the applied current. The Bz component is located along the direction of the main magnetic field. After calculating the Bz component, the current density within the subject is calculated by applying Ampere’s Law and/or the Biot–Savart Law. Because the applied current is known, this step allows the reconstruction of the current paths in the tissue. Finally, using mathematical algorithms (e.g., J-substitution algorithm), conductivity images are reconstructed based on the measured magnetic flux density and applied current density. MREIT, magnetic resonance electrical impedance tomography.

To reconstruct the conductivity from the phase images, the Bz Field, which is the primary data of interest in MREIT, is the component of the magnetic field induced by the applied current. The Bz component is located along the direction of the main magnetic field. From the phase images, the Bz Field can be calculated. Then, using the Bz component data and applying Ampere’s Law and/or Biot–Savart Law, the current density within the subject is calculated. Because the applied current is known, this step allows the reconstruction of the current paths in the tissue. Finally, using mathematical algorithms (e.g., J-substitution algorithm), conductivity images are reconstructed based on the measured magnetic flux density and applied current density because the key to MREIT is the relationship between the current density, applied electric field, and conductivity of the tissue. These images show the variations in electrical conductivity across the interior of the subject.

MREIT has applications in medical diagnostics, such as distinguishing between different tissue types (healthy vs. cancerous), due to the contrast in their conductivity properties [9,17,18,32]. Furthermore, it is used in research settings to measure changes in conductivity due to physiological processes or in response to treatment. However, MREIT’s applications face several challenges and limitations. First, accurate conductivity imaging requires precise phase measurements and robust algorithms to solve the ill-posed inverse problem of conductivity reconstruction. Second, noise, subject motion, and other artifacts can significantly affect reconstruction quality. Finally, the safety of the subject must be ensured because current is being directly applied, particularly around sensitive areas, such as the brain, or for subjects with implanted electronic devices. Therefore, the application of this technique in clinical settings has major limitations. Individuals typically apply MREPT to humans.

2. Magnetic resonance electrical properties tomography

MREPT is another method that aims to reconstruct the electrical properties (conductivity and permittivity) of biological tissues, specifically their electrical conductivity and permittivity. Rather than using external currents, MREPT, which is the interaction between radiofrequency (RF) electromagnetic fields and tissues during an MRI scan to infer electrical properties, uses the phase information from standard MRI signals. The phase of the MRI signal is sensitive to the local electrical properties of the tissue, and this information is used to derive maps of electrical conductivity and permittivity.

In MREPT, additional electrodes or external currents are not required, as in MREIT. A standard MRI scan is performed using a sequence that is sensitive to phase information, such as a turbo spin-echo sequence and balanced fast field-echo sequence. The RF electromagnetic waves used in MRI will interact with the electrical properties of tissues, and these interactions affect the phase of the received MRI signal. If the applied sequence is sensitive to the transmit RF field (also known as the B1 field), then the B1 field mapping technique is often used to correct for B1 inhomogeneity. During a scan, the MRI system acquires complex signals, comprising amplitude and phase information. The phase of the MRI signal can be influenced by the local electrical properties (e.g., conductivity and permittivity) of the tissue, similar to MREIT.

To reconstruct conductivity, the acquired phase information is processed to remove potential artifacts and any contributions not related to the tissue’s electrical properties, such as those resulting from magnetic field inhomogeneities. The spatial distribution of the RF field (B1) is then calculated from the phase images. The electrical (E) field induced by the MRI RF pulse can be calculated from the B1 field using Maxwell’s equations. Once the E-field is known, the local electrical properties (e.g., conductivity and permittivity) are reconstructed by solving a partial differential equation known as the Helmholtz equation, which relates the E-field to conductivity and permittivity. Therefore, the relationship between the B1 field denoted as and the electrical properties are expressed as follows:

2B1=iωμ0τHB1τHτH××B1

where ω is the angular frequency, μ0=4π×10–7 N/A2 is the magnetic permeability of the free space, and τHH+iωϵH at HFC σH and permittivity ϵH [23,25]. The transverse field of B1 can be decomposed into the positively rotating field B1+=12Bx+iByand the negatively rotating field B1=12BxiBy. Using a conventional MRI scanner with a single transmit channel, the magnetic field B1+ component is available. We denoted ϕ+ and ϕ as the phase terms of B1+ and B1, respectively. By assuming σH>>ωϵH, a phase-based MREPT formula was derived as follows:

ϕtr1σH+2ϕtrσH2ωμ0=0

where ϕtr=ϕ++ϕ. To stabilize the formula (3), the MREPT formula based on the convection reaction equation can be derived by adding the regularization coefficient c [37]:

c21σH+ϕtr1σH+2ϕtrσH=2ωμ0

MREPT depends on a relatively weak phase signal from a secondary RF magnetic field, which is induced by the time-varying RF field. Because of the weak phase signal and noise artifacts, a multi-echo spin-echo MRI pulse sequence is advantageous for reducing noise artifacts using the weight for the k-th echo:

ϕtr=k=1NEwkϕk,   wk= ρk 2j=1NE ρj 2

where ϕk and ρk are the phase signal and complex MRI signal, respectively, for the k-th echo. To solve the convection reaction partial differential equation in (4), we used the two-dimensional finite-difference method. For each image matrix, equation (4) can be written as follows:

c2x2+2y2+ϕtrxx+ϕtryy+2ϕtrx2+2ϕtry21σH=2ωμ0

The finite-difference method for solving equation (6) is to find solutions of a linear matrix system Ax=b with the appropriate processing of the Dirichlet boundary conditions. A is a staff matrix, x=1σH1, 1σH2, , 1σHN , and b=2ωμ0, 2ωμ0, , 2ωμ0. We used the finite-difference method to solve the aforementioned matrix system with the regularization coefficient c=0.03 in equation (6) [38]. Several computational algorithms have been developed to perform this inversion from the E-field to the desired electrical properties.

MREPT also has some challenges and limitations. MREPT is sensitive to noise and artifacts, particularly those due to B1 inhomogeneity, and requires phase unwrapping. It relies on sophisticated postprocessing algorithms to correctly resolve the electrical properties from the measured signals, and this is an active area of research. Accurately linking the changes in phase to conductivity and permittivity requires assumptions about tissue properties, and this can introduce errors or uncertainties. MREPT has potential uses in distinguishing healthy from diseased tissues because these properties can differ significantly for conditions such as cancer and inflammation. It could also be particularly helpful in treatment planning for modalities such as hyperthermia therapy and RF ablation, where knowledge of the tissue’s electrical properties can impact the treatment outcomes. We explain the developments and applications of MREPT used for diagnosing Alzheimer’s disease (AD) [38,39]. MREPT has been used in various medical fields to study the properties of brain tissues, tumors, and muscles by providing insights into the tissue’s electrical characteristics [29,40-44].

Summary of the Key Research Outcomes

1. Technical developments

1) Decomposition of HFC into extra- and intra-neurite compartment conductivities

We published a technical development paper to show conductivity tensor images using diffusion tensor images [10]. Fig. 2 summarizes the technical development to map LFC from MREPT using the multicompartment spherical mean technique (MC-SMT) technique [45]. The MC-SMT method was developed to evaluate the microscopic features of the intra- (restricted) and extra-neurite (hindered) compartments in neuronal tissue, which are the two compartments of a neuron. The intra-neurite compartment contains axons and dendrites and can be modeled as a collection of infinitely thin “sticks.” The extra-neurite compartment is everything else in the brain, except for neurites and free water, and can reflect the interactions of water molecules with macromolecules, fibers, and membranes in the brain tissue. The gray matter contains the cell bodies of neurons, dendrites, and axons, and the white matter contains myelinated axons.

Figure 2. Summary of the technical development to map the HFC and low-frequency conductivity using MREPT and MC-SMT images. In MREPT, (a) a standard magnetic resonance imaging scan is performed using a sequence that is sensitive to phase information, such as a turbo spin-echo sequence or balanced fast field-echo sequence. Furthermore, (b) diffusion tensor images with three b-values and multiple gradient directions are acquired to obtain microstructure information. The spatial distribution of the radiofrequency field (B1) is calculated from the phase images. (c) The HFC is calculated with a double derivative of the B1 field by applying a regularization. (d) The MC-SMT is used to map intrinsic diffusion coefficient, intra-neurite volume fraction, and extra-neurite mean diffusivity. (e) The low-frequency conductivity map can be calculated with the recovered HFC and MC-SMT maps. (f) The extra-neurite tensor maps are obtained using MC-SMT maps. (g) The low-frequency conductivity tensor map can be calculated using (c) and (f). HFC, high-frequency conductivity; MREPT, magnetic resonance electrical properties tomography; MC-SMT, multicompartment spherical mean technique.

After calculating the HFC from the B1 phase, the recovered HFC σH was decomposed into the intra- and extra-neurite compartments to calculate the compartmental conductivities [10,45].

σH = σint +σext=νint c¯ intDint+1νint c¯ ext Dext

where σint and σext are the IC and EC, respectively; νint is the intra-neurite volume fraction (IVF); c¯ int  is the intra-neurite ion concentration; c¯  ext and is the extra-neurite ion concentration (EIC). Similarly, Dint and Dext are the intra-neurite diffusivity and the extra-neurite diffusivity (ED), respectively. To obtain νint, Dint and Dext in equation (7), the MC-SMT technique is applied [45]. The key insight into MC-SMT is that for a specified diffusion weighting factor b, the spherical mean of the diffusion signal e¯b over the gradient directions is invariant to the fiber orientation distribution.]

Because the internal current flow at low-frequency (<1 kHz) is only restricted to the extra-neurite space between the cells, the low-frequency dominant average scalar conductivity σL  can be expressed as follows:

σL = 1νint c¯ ext Dext=1vintDextσHvintβDint+1vintDext

The LFC σL  in equation (8) depends on the IVF (νint), apparent EIC (c¯ ext), and extra-neurite mean diffusivity (Dext). Because cerebrospinal fluid (CSF) is a highly conductive liquid without cell membranes, the LFC σL  is almost identical to the HFCs σH in CSF [46].

To measure the anisotropy of conductivity, Dext can be a tensor. We assume that Dext and the water diffusion tensor share the eigenvectors. The eigenvalues of Dext, Dext,d1ext=d2extd3ext, satisfy the following relations:

d1ext+d2ext+d3ext 3=Dext,d1ext=d2ext= (1νint) Dint

Therefore, σL  is also a tensor in which ion mobility is assumed to be proportional to the water molecule diffusion flow [10,28,31,47]. Fig. 3 shows the two slices of the HFC, intrinsic diffusion coefficient (Dint), IVF (νint), ED (Dext), and LFC tensor obtained from a young participant.

Figure 3. Representative maps are obtained from two imaging slices acquired from one young participant. Maps are shown as the high-frequency conductivity (HFC), intrinsic diffusion coefficient (Dint), intra-neurite volume fraction (νint), extra-neurite diffusivity (Dext), and low-frequency conductivity tensor.

2. Clinical applications

1) High-frequency conductivity

We published an article using the HFC of MREPT in patients with AD [38]. This study explored the use of HFC mapping in the brain to differentiate patients with AD from those with amnestic mild cognitive impairment (MCI) and cognitively normal (CN) elderly individuals. Fig. 4 shows a 3D T1-weighted image; the corresponding segmented brain tissues of gray matter volume, white matter volume, and CSF volume; and an HFC map acquired from one CN participant and a patient with AD. In general, the older participant had more brain atrophy than the young participant. This atrophy was caused by brain tissue loss. The atrophy area showed higher conductivity than the normal area, which was caused by the replacement of brain tissues with CSF. The conductivity was higher in patients with AD than in CN participants in several brain areas. An MREPT study was conducted using a clinical 3T MRI system (Ingenia, Philips Medical System) to map the HFC. We identified several key points from the study: First, the HFC values were higher in patients with AD than in the CN and MCI groups. Second, a negative correlation was observed between Mini-Mental State Examination (MMSE) scores and HFC values, indicating that higher HFC values are associated with cognitive decline. Third, age was positively correlated with HFC values. Finally, the HFC value in the insula region of the brain exhibited high potential as a biomarker for differentiating patients with AD from CN participants with high sensitivity and specificity. Our first clinical study concluded that HFC mapping could serve as a noninvasive imaging biomarker for evaluating and differentiating patients with AD from CN individuals, potentially aiding in the early diagnosis and treatment of AD.

Figure 4. 3D T1-weighted image (3DT1) and the corresponding segmented brain tissues of gray matter volume (GMV), white matter volume (WMV), and cerebrospinal fluid (CSF) volume and a high-frequency conductivity (HFC) map acquired from one cognitively normal (CN) older participant and a patient with Alzheimer’s disease (AD).

2) Compartmental conductivities to represent a low-frequency conductivity

We recently published a paper to represent compartmental conductivity changes in patients with AD [39]. We obtained MREPT and two-shell diffusion MRI from 21 CN individuals, 25 patients with MCI, and 20 patients with AD. We used MREPT data to obtain the HFC or Larmor frequency conductivity and develop an MC-SMT model to decompose the two-shell diffusion MRI signals into two compartments with distinct diffusion properties: one with restricted diffusion within the neurites and one with hindered diffusion in the extra-neurite space. We focused on the compartments with restricted and hindered diffusion, which do not exactly correspond to the intra- and extracellular spaces. We applied the MC-SMT model based on the ball-and-stick model, which does not account for the diffusion signals originating from the soma or other large cellular domains. The MC-SMT model estimates the microstructural features of the intra- and extra-neurite compartments, rather than the intracellular and extracellular spaces [10,48]. Fig. 5 shows the HFC at the Lamour frequency, EC, and IC acquired from one older CN participant and a patient with AD. We found that HFC and EC were higher in the AD group than in the CN and MCI groups, particularly in the frontal, occipital, parietal, and temporal brain areas. IC was higher in the AD group than in the CN group but lower than in the MCI group. MMSE scores were negatively correlated with HFC and EC but positively correlated with IC. Conductivities increased in areas with lower MMSE scores. Age exhibited no significant correlation with any of the conductivity indices. HFC and EC exhibited good diagnostic performance, particularly in the hippocampus and insular regions. HFC and EC also performed well, with the insular region exhibiting the highest area under the curve for EC. The conductivity indices did not show significant results for differentiating MCI from CN.

Figure 5. T1-weighted (T1W) image and conductivity maps of the high-frequency conductivity (HFC) and the corresponding extra-neurite conductivity (EC) and intra-neurite conductivity (IC) acquired from one cognitively normal (CN) older participant and a patient with Alzheimer’s disease (AD).

Benefits, Impacts, and Challenges of MREIT and MREPT in Clinical Practice

1. Potential benefits of these techniques in clinical applications

MREIT and MREPT are advanced imaging modalities that offer unique insights into the electrical properties of tissues, which can be beneficial in clinical settings. Electrical conductivity can be used to detect and characterize tumors compared with normal tissues [40,41,49-51]. It can help assess stroke by visualizing the impedance changes in brain tissues [42,52]. MREIT may assist in mapping the conduactivity of heart tissues, which can be useful in diagnosing and treating cardiac arrhythmias [53]. MREPT can provide information on tissue composition and structure by measuring electrical properties at high frequencies. It can be used to monitor the effects of thermal and electrical therapies on tissue properties. MREPT may be helpful in differentiating patients with AD from CN older participants and those with amnestic MCI [38,39]. Both techniques are currently under research and development, with ongoing efforts to improve their accuracy, resolution, and clinical relevance [20]. They have the potential to provide noninvasive methods for obtaining electrical property distributions, which could complement existing imaging methods and improve diagnostic and therapeutic outcomes.

Furthermore, both techniques can significantly affect personalized medicine by providing detailed and individualized maps of the electrical properties of tissues [40,41]. By offering precise measurements of tissue conductivity and permittivity, MREIT and MREPT can improve the diagnosis of various conditions, allowing for the development of more tailored treatment plans. These techniques can be used to monitor the effects of treatments in real time, such as observing changes in the electrical properties of cancerous tissue during chemotherapy or radiotherapy [41,54,55]. However, note that these applications are still under research and development, and their clinical use will depend on further validation and refinement of the techniques.

2. Impact of tissue heterogeneity on tissue pathophysiology

It is important to understand how tissue heterogeneity affects the accuracy of measuring electrical properties [53,56]. Tissue heterogeneity can significantly affect the accuracy of electrical property measurements in several ways. Different tissues make different contributions to the measured properties because of differences in depth within the sensing region [57]. The ability to detect and accurately measure the electrical properties of small structures within heterogeneous tissues is limited [51]. Heterogeneous tissues can exhibit spatial variations in electrical properties that are challenging to accurately capture [51]. Many measurement techniques assume homogeneity within the sample, which can lead to errors when applied to heterogeneous tissues [57]. The assumption of average homogeneous thickness distributions in soft tissues can significantly alter the results of biomechanical analyses compared with the inclusion of true spatially varying thickness distributions [53].

Another important issue is the impact of MREIT and MREPT on our understanding of tissue pathophysiology [17,41,58-60]. By imaging at different frequencies, MREIT and MREPT can offer insights into the membrane properties of cells, which is crucial for understanding various diseases at the cellular level [20]. The ability to image low-frequency electrical properties of tissues can lead to better detection and characterization of diseases, such as cancer; ischemic regions from stroke; and other pathologies [61].

3. Challenges in the implementation of MREIT and MREPT in clinical practice

Implementing MREIT and MREPT in clinical practice faces several challenges. First, both techniques require sophisticated hardware and software integration into existing MRI systems, which can be complex and costly [61]. Second, measurements are based very small signals, which can be easily affected by noise and require advanced noise reduction techniques to ensure accuracy [20]. Third, the introduction of electrical currents into the body, as in MREIT, raises safety concerns that must be carefully managed to prevent any harm to patients [61]. Fourth, the electrical properties measured using these techniques are not as widely understood as traditional MRI signals; therefore, there is a learning curve for clinicians to interpret the data effectively [61]. Fifth, extensive clinical trials are necessary to validate the efficacy and safety of these methods before they can be widely adopted in clinical settings [61]. Finally, the conductivity decomposition techniques of MREIT and MREPT cannot be directly transferable to clinics due to several limitations. All current models depend on the diffusion microstructure [10,31,47]. Sajib et al. [31] optimized the volume fraction and water diffusion coefficients of the intracellular space, extracellular matrix space, volume fraction of the free water component, and an offset value. In contrast, Marino et al. [47] optimized the volume fraction of the intracellular, free water, and restricted diffusion compartments in the extracellular space based on the neurite orientation dispersion and density imaging (NODDI) model [62]. It has been demonstrated that cellular microstructure parameters estimated from the NODDI model produce more stable results than that of the method by Sajib et al. [31] Jahng et al. [10] proposed using the MC-SMT to estimate cellular microstructure parameters [45]. Both MREIT and MREPT are sensitive to noise in the measured magnetic fields. This noise can significantly affect the accuracy of the reconstructed conductivity images. These challenges highlight the need for ongoing research and development to refine MREIT and MREPT technologies and establish their practical utility in clinical medicine.

Conclusions

This review highlights the potential of MRI-based techniques to provide detailed information about the electrical properties of the body. These techniques, particularly MREPT, show promise for biomedical applications such as differentiating tissue types and detecting pathological conditions. Our studies have demonstrated the potential of conductivity indices as biomarkers for AD diagnosis. However, both MREIT and MREPT face challenges, including the need for sophisticated hardware, software integration, advanced noise reduction techniques, and patient safety assurance during the procedures. The ongoing research on MREPT aims to address its technical challenges and enhance its accuracy, robustness, and clinical applicability. MREPT is generally applied to humans and holds significant promise as a noninvasive tool for characterizing tissue properties and understanding pathological conditions. In MREIT, the subject’s safety must be ensured because current is applied, particularly around sensitive areas, such as the brain, or for subjects with implanted electronic devices. Future developments and clinical trials are necessary to validate the efficacy and safety of these methods, which could improve their diagnostic capabilities and help develop personalized treatment strategies.

Funding

The research was supported by the National Research Foundation of Korea (NRF) grants funded by Ministry of Science and ICT (RS-2024-00335770, G.H.J.; 2020R1A2C1004749, G.H.J; RS-2023-00250977, M.B.L.;2019R1A2C1004660, O.I.K), Republic of Korea.

Conflicts of Interest

The authors have nothing to disclose.

Availability of Data and Materials

The datasets used and/or analyzed in the current study are available from the corresponding author upon reasonable request.

Author Contributions

Conceptualization: Geon-Ho Jahng. Data curation: Geon-Ho Jahng. Formal analysis: Geon-Ho Jahng, Mun Bae Lee. Funding acquisition: Geon-Ho Jahng. Investigation: Geon-Ho Jahng. Methodology: Geon-Ho Jahng, Mun Bae Lee, Oh In Kwon. Resources: Geon-Ho Jahng. Supervision: Oh In Kwon. Visualization: Geon-Ho Jahng. Writing – original draft: Geon-Ho Jahng. Writing – review & editing: Geon-Ho Jahng, Mun Bae Lee, Oh In Kwon.

Ethics Approval and Consent to Participate

The study was conducted in accordance with the Declaration of Helsinki. The Institutional Review Board (IRB) of Kyung Hee University Hospital at Gangdong in Seoul, Republic of Korea, approved this cross-sectional prospective study (IRB khnmc2019-07-007) and written informed consent was obtained from the participants.

Fig 1.

Figure 1.Graphical explanation of the MREIT method. In MREIT, electrodes are attached to the subject’s surface at specified locations, such as brain areas without hair. The magnetic resonance imaging phase is used to obtain the Bz Field, which is the component of the magnetic field induced by the applied current. The Bz component is located along the direction of the main magnetic field. After calculating the Bz component, the current density within the subject is calculated by applying Ampere’s Law and/or the Biot–Savart Law. Because the applied current is known, this step allows the reconstruction of the current paths in the tissue. Finally, using mathematical algorithms (e.g., J-substitution algorithm), conductivity images are reconstructed based on the measured magnetic flux density and applied current density. MREIT, magnetic resonance electrical impedance tomography.
Progress in Medical Physics 2024; 35: 73-88https://doi.org/10.14316/pmp.2024.35.4.73

Fig 2.

Figure 2.Summary of the technical development to map the HFC and low-frequency conductivity using MREPT and MC-SMT images. In MREPT, (a) a standard magnetic resonance imaging scan is performed using a sequence that is sensitive to phase information, such as a turbo spin-echo sequence or balanced fast field-echo sequence. Furthermore, (b) diffusion tensor images with three b-values and multiple gradient directions are acquired to obtain microstructure information. The spatial distribution of the radiofrequency field (B1) is calculated from the phase images. (c) The HFC is calculated with a double derivative of the B1 field by applying a regularization. (d) The MC-SMT is used to map intrinsic diffusion coefficient, intra-neurite volume fraction, and extra-neurite mean diffusivity. (e) The low-frequency conductivity map can be calculated with the recovered HFC and MC-SMT maps. (f) The extra-neurite tensor maps are obtained using MC-SMT maps. (g) The low-frequency conductivity tensor map can be calculated using (c) and (f). HFC, high-frequency conductivity; MREPT, magnetic resonance electrical properties tomography; MC-SMT, multicompartment spherical mean technique.
Progress in Medical Physics 2024; 35: 73-88https://doi.org/10.14316/pmp.2024.35.4.73

Fig 3.

Figure 3.Representative maps are obtained from two imaging slices acquired from one young participant. Maps are shown as the high-frequency conductivity (HFC), intrinsic diffusion coefficient (Dint), intra-neurite volume fraction (νint), extra-neurite diffusivity (Dext), and low-frequency conductivity tensor.
Progress in Medical Physics 2024; 35: 73-88https://doi.org/10.14316/pmp.2024.35.4.73

Fig 4.

Figure 4.3D T1-weighted image (3DT1) and the corresponding segmented brain tissues of gray matter volume (GMV), white matter volume (WMV), and cerebrospinal fluid (CSF) volume and a high-frequency conductivity (HFC) map acquired from one cognitively normal (CN) older participant and a patient with Alzheimer’s disease (AD).
Progress in Medical Physics 2024; 35: 73-88https://doi.org/10.14316/pmp.2024.35.4.73

Fig 5.

Figure 5.T1-weighted (T1W) image and conductivity maps of the high-frequency conductivity (HFC) and the corresponding extra-neurite conductivity (EC) and intra-neurite conductivity (IC) acquired from one cognitively normal (CN) older participant and a patient with Alzheimer’s disease (AD).
Progress in Medical Physics 2024; 35: 73-88https://doi.org/10.14316/pmp.2024.35.4.73

Table 1 Comparison of the MREIT and MREPT techniques

ItemMREITMREPT
DefinitionCan map the electrical conductivity and current density inside the body using MRICan map the electrical properties of tissues at the Larmor frequency of MRI
Primary useTo visualize and monitor physiological and pathological processes in tissues based on their electrical propertiesTo image the electrical properties of tissues, providing information that can be used for diagnosis and treatment planning
Data acquisitionRequire the injection of an external current and measure the resulting magnetic field changesDo not require external current; rely on the knowledge of the complex RF transmit field for the reconstruction of electrical properties
Image reconstructionBased on the measurement of induced voltages or magnetic fields due to the applied currentInvolves the calculation of electrical properties from the distribution of the RF transmit field in the tissue
Spatial resolutionTypically lower than MREPT due to the nature of electrical current application and measurementGenerally higher because it uses the RF field distribution, which can be finely mapped using MRI
SensitivitySensitive to the distribution of electrical currents, which can be affected by tissue composition and pathologySensitive to the intrinsic electrical properties of tissues, which can vary with tissue type and state
ApplicationsUsed in research settings to study tissue conductivity and its changes due to various conditionsExplored for clinical applications, such as characterizing tumors and detecting abnormalities in tissue structure
AdvantagesProvides images of electrical conductivity and current density inside the bodyMeasures the electrical properties of tissues at the Larmor frequency of MRI
Can be used to monitor physiological and pathological processes in tissuesDoes not require external current for mapping, reducing complexity
Noninvasive and does not require external electrodesCan provide high-resolution images of the electrical properties of tissues
LimitationsLower spatial resolution than MREPTSusceptible to noise, particularly in phase images, which can affect accuracy
Sensitive to noise and requires regularization techniques to stabilize the inverse problemThe reconstruction algorithms are complex and computationally intensive
The need for accurate boundary information can be a challengeRequires accurate knowledge of the RF transmit field for electrical properties reconstruction

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Korean Society of Medical Physics

Vol.35 No.4
December 2024

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