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

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


Introduction
Alzheimer's disease (AD) is a common neurological disorder and is characterized by the progressive loss of memory and other cognitive functions.The main pathophysiology of AD is the accumulation of two abnormal proteins: amyloid-beta (Aβ) protein and tau protein.As the Aβ protein accumulates, oxidative and inflammatory stress induces the loss of synaptic and neuronal integrity.This leads to neuronal loss and brain atrophy (Park and Moon, 2016) which causes an increase in the barriers of diffused proton ions in cells and an increase in ion concentration as a result of the accumulation of proteins and increased mobility caused by neuronal loss and brain atrophy.This subsequently results in increased concentrations of interstitial fluids and/or cerebral spinal fluid (CSF).Furthermore, a previous study showed that metallic ion levels were higher in AD patients compared to age-matched controls because Aβ is a metallic-binding peptide that is altered during disease progression (Gaeta and Hider, 2005).In addition, AD patients have been linked with ion imbalance as AD is associated with impaired glutamate clearance and depressed Na(+)/K(+) ATPase levels in the brain (Vitvitsky et al., 2012), causing a modification of ion concentrations.Furthermore, Abbreviations: 3D T1W, three-dimensional (3D) T1-weighted (T1W); AD, Alzheimer's disease; CDR, clinical dementia rating; CN, cognitively normal; EC, extraneurite conductivity; HFC, high frequency conductivity; IC, intra-neurite conductivity; MCI, mild cognitive impairment; MMSE, mini-mental state examination; MREPT, MRI-based electrical property tomography.
several previous studies showed increased diffusivity caused by demyelination and neurodegeneration in AD patients (Andica et al., 2020;Jahng et al., 2011;Zhang et al., 2007), indicating the increased mobility of protons by microstructural disruptions in AD compared to cognitively normal elderly controls.Mild cognitive impairment (MCI) is a high-risk condition for the development of clinically probable AD or other neurological conditions (Kantarci et al., 2005;Moody et al., 2022;Motovylyak et al., 2022).The amnestic subtype of MCI, which manifests as memory complaints, is generally regarded as a precursor of AD (Griffith et al., 2006).Therefore, the assessment of MCI is beneficial in terms of early AD intervention (Barnett et al., 2014).
The electrical conductivity is a passive material property that mainly depends on the concentrations and mobility of charged carriers.Biological tissues have complicated structures that consist of different types of cells and have different properties and functions depending on their composition and organization.Therefore, the electrical properties of biological tissues such as conductivity are complicated by various factors, such as frequency, ion mobility, ion concentration, cell shapes, and cell membranes.The cell membranes have a high resistance and a high capacitance, which prevent the low-frequency current from passing through them.The low-frequency conductivity of a biological tissue shows electrically anisotropy related with its structural directionality, but Larmor frequency conductivity simultaneously reflects bulk tissue structures (Gabriel et al., 1996a(Gabriel et al., , 1996b, c), c).
Magnetic resonance electrical property tomography (MREPT) has been developed to derive in vivo internal electrical Larmor frequency conductivity using a standard MRI system without applying externally mounted electrodes or currents.In MREPT, a sinusoidal current is applied as the radiofrequency (RF) magnetic field (B1) of the MRI scanner to a human brain and induces a time-harmonic magnetic field that is influenced by the brain's admittivity distribution via Maxwell's equations.Using the positively rotating magnetic field measured by mapping the B1 field, the electrical conductivity can be extracted and this conductivity is called as a high-frequency conductivity (HFC) or the Larmor frequency conductivity.Therefore, HFC is a frequencydependent tissue bulk conductivity.High-frequency current tends to pass through the cell membranes and HFC also does not blocked by the cell membrane.However, the HFC does not distinguish between the different compartments, and it may not capture the subtle changes in the microstructure of the brain tissue that are related to AD.To explore electrical conductivity properties reflecting different compartments, magnetic resonance electrical impedance tomography (MREIT) has been developed by injecting an external low-frequency current in a human body.MREIT visualizes internal conductivity distributions by directly injecting dc currents and measuring induced magnetic flux densities using an MRI scanner.This technique can map low-frequency conductivity, at about 10 kHz, but its application is required for placing an electrical current into the human head to inject the external lowfrequency current.The MREIT reflects only the extracellular effects, as the low frequency current is blocked by the cell membranes.To overcome MREPT, but to investigate cellular or neuronal levels of conductivity without using MREIT, we recently developed a method to decompose HFC into compartment-level conductivity of the human brain without injecting an external current based on information obtained from both HFC and multi-compartment diffusivity (Jahng et al., 2021).The multi-compartment diffusivity can separate the diffusion signals from the intra-and extra-neurite spaces.By using the multi-compartment diffusivity, the decomposition method can calculate the compartmental conductivities, such as the extra-neurite conductivity (EC) and the intra-neurite conductivity (IC), which are the conductivities in the extra-and intra-neurite spaces, respectively (Lee et al., 2021).The theoretical background of this development was 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 water molecule mobility relates to the water diffusivity for biological tissues.Water molecular diffusion in biological tissues reflects interactions with macromolecules, fibers, and membranes.Diffusion MRI estimates the neuronal activities in the brain by probing neural tissue micro-structure and analyzing its hindrance to water diffusion based in signal models.Various models of water diffusion in tissue have been proposed to provide quantitative micro-structure information such as the neurite orientation dispersion and density imaging (NODDI) (Kamiya et al., 2020) and multi-compartment spherical mean technique (MC-SMT) (Kaden et al., 2016).In the development, we used the MC-SMT model to evaluate microscopic features of the intra-(restricted) and extra-neurite (hindered) compartments in the neuronal tissue.Extra-neurite and intra-neurite spaces are two different compartments of a neuron.The intra-neurite compartment is the part of a neuron that contains axons and dendrites, which are often referred to together as neurites.This compartment can be modeled as a collection of infinitely thin "sticks" because diffusion in the perpendicular direction is negligible.The extra-neurite compartment is everything else in the brain, except for neurites and free water, such as the cell bodies, glia, and extracellular matrix.The diffusion signals from these compartments can reflect the interactions of water molecules with the macromolecules, fibers, and membranes in the brain tissue.(Kamiya et al., 2020).Gray matter is the tissue of the central nervous system that contains the cell bodies of neurons, as well as dendrites and axons and white matter is the tissue of the central nervous system that contains myelinated axons.The MC-SMT method decomposed HFC into extra-neurite and intra-neurite components to calculate compartmental conductivities called as EC and IC.However, both EC and IC have not been applied to any neurological conditions.The electrical conductivity of tissues regulates how an electromagnetic field, such as the MR radiofrequency field (RF: 64-300 MHz) interacts with the human body (Katscher et al., 2009;Mandija et al., 2021).
A previous study has been used HFC for diagnosing diseases (Park et al., 2022).Although we showed that HFC significantly increased in the AD group compared with the cognitively normal (CN) elderly group (Park et al., 2022), the compartmental conductivities in the extra-neurite and intra-neurite levels of the brain are still unknown, especially in the brain of AD patients.The exact cause of AD-related white matter pathology is still being investigated, but several possible mechanisms have been proposed, including (1) Wallerian degeneration, (2) axonal damage and gliosis and (3) primary myelin degradation (Zerbi et al., 2013).These changes in the neural function are likely to be reflected at the neurite level.Monitoring changes in the neurite level of AD patients in neuronal remodeling during the progression of AD is a crucial step in understanding the progression of AD and determining the efficacy of treatment.There have been previous studies on the changes in gray matter and white matter in AD patients (Bozzali et al., 2002;Weston et al., 2015;Zerbi et al., 2013).However, the changes that may occur in the extra-neurite and intra-neurite compartments at the neuronal unit level in AD have not yet been clearly elucidated.In AD, the loss of neurons due to axonal damage and gliosis leads to a decrease in intra-axonal water and an increase in extra-neurite space, thereby alters the electrical conductivity and diffusivity of the brain tissue, increasing mean diffusivity.Additionally, myelin degeneration further contributes to increased mean diffusivity by reducing neurite density, leading to an expansion of extra-neurite space and a contraction of intra-neurite space.(Burzynska et al., 2010).The decomposition method can detect these changes by comparing the compartmental conductivities and diffusivities of AD patients with those of cognitively normal elderly controls or mild cognitive impairment (MCI) patients, who are at a high risk of developing AD and also evaluate the association between the compartmental conductivities and diffusivities and the cognitive decline, as measured by the Mini-Mental State Examination (MMSE) scores.This study assumed that the progression of AD results in a change of electrical conductivity caused by demyelination and neurodegeneration that are altered compartmental mobilities of protons in the neurons, which can be affected by increasing ion concentrations, misbalance of the cellular ion level, and/or increasing mobilities of protons in the extra-neurite space.Therefore, the objectives of this study were to investigate how the compartmental conductivities were reflected in AD patients compared with old CN people and amnestic MCI patients and to evaluate the association between compartmental conductivities and cognitive decline.
The decomposition of HFC into compartmental conductivities is important because it can reveal the electrical properties of different compartments of the brain tissue, such as the intra-and extra-neurite spaces.These compartmental conductivities can reveal the electrical properties of the brain tissue at the neuronal level, and they may be sensitive to the changes in the microstructure of the brain tissue that are caused by AD.In this pilot study, we obtained MREPT and two-shell diffusion MRI from 21 CN, 25 MCI, and 20AD patients.We used MREPT data to obtain HFC or the Larmor frequency conductivity and the 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 extra-cellular 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 (Chabert and Scifo, 2007;Jahng et al., 2021).We found that EC was higher in AD patients than CN participants, EC values in the insula and middle temporal gyrus decreased with increasing MMSE scores, after adjusting for age, and EC in the hippocampus and insula had high AUC values with high sensitivity and specificity.

Participants
The Institutional Review Board (IRB) approved this cross-sectional prospective study (IRB khnmc2019-07-007) and informed consent was obtained from the participants between August 2019 and December 2022.Participants provided a detailed medical history and underwent a neurologic examination, standard neuropsychological testing, and an MRI scan.Participants with incomplete MR image, the other neurologic/psychiatric disease, which was the Behcet disease, and brain parenchymal lesions such as severe small vessel disease or previous history of infarction were excluded.Cognitive function was assessed using the full version of a Korean standardized neuropsychological test battery, known as the Seoul Neuropsychological Screening Battery (Ahn et al., 2010).Global cognitive ability was evaluated with the Korean version of the Mini-Mental State Examination (K-MMSE) and the clinical dementia rating (CDR).The study included 20 patients with mild or moderate AD, according to the criteria of the National Institute of Neurological and Communicative Disorders and the Stroke-Alzheimer Disease and Related Disorders Association (Blacker et al., 1994;Dubois et al., 2007), also included 25 participants with amnestic MCI according to the Petersen criteria (Petersen et al., 2014(Petersen et al., , 1999)), and 21 elderly CN participants.Fig. 1 shows the flowchart of the summary of the selection process of participants in the study.Table 1 summarizes the demographic characteristics and the neuropsychological test results of the participant groups.

MRI acquisition
For the brain MREPT images, a multi-echo turbo spin-echo pulse sequence was used (Park et al., 2022) with the following imaging parameters: repetition time (TR) = 3200 ms, first echo time (TE) = 12 ms with 12 ms intervals, flip angle (FA) = 90 • , number of echoes (NE) = 6, number of average (NSA) = 1, slice thickness = 5 mm, number of slices = 20 without a gap between the slices, slice orientation = transverse, and acquired voxel size = 2 × 2 × 5 mm 3 .The scan time of the MREPT sequence was 6 min and 5 s.Real and imaginary images were saved for reconstructing the conductivity map.
For obtaining diffusion MR images to model the MC-SMT (Kaden et al., 2016), a single-shot spin-echo-planner imaging (SS-SE-EPI) pulse sequence was used with two b-shells of nominally 800 and 2000s/mm 2 with 16 and 32 gradient directions, respectively.In addition, b = 0 images were also acquired with six averages.To reduce MR scan time for practical implementation, a relatively small number of diffusion gradient directions was adopted.The imaging parameters were as follows: TR/TE = 15,000/86 ms, FOV = 220 × 220 × 108 mm 3 , voxel size = 2 × 2 × 2 mm 3 , number of slices = 54, EPI factor =37, and the number of excitations = 1.Total scan times were 2 min 15 s, 4 min 45 s, and 8 min 45 s for b-values of 0, 800, and 2000s/mm 2 , respectively.
For image registration and brain tissue segmentation, a sagittal structural three-dimensional (3D) T1-weighted (T1W) image was acquired with the fast field-echo (FFE) sequence, which is similar to the magnetization-prepared rapid acquisition of the gradient echo (MPRAGE) sequence.The imaging parameters were as follows: TR = 8.1 ms, TE = 3.7 ms, FA = 8 • , and voxel size = 1 × 1 × 1 mm 3 .In addition, T2-weighted turbo-spin-echo, fluid-attenuated inversion recovery (FLAIR), and gradient-echo images were also acquired to evaluate any brain abnormalities.MRI was performed using a 3.0 Tesla MRI system equipped with a 32-channel sensitivity encoding head coil (Ingenia, Philips Medical System, Best, The Netherlands).

Reconstruction of MREPT and SMT data
In the reconstruction step, we first mapped HFC from MREPT, then applied MC-SMT to derive extra-neurite and intra-neurite compartment information from multi-shell DTI data, and calculated compartmental conductivities and diffusivities.Detailed theories and algorithms are described in our previous paper (Jahng et al., 2021).The reconstruction processing steps were as follows: First, to obtain HFC, we used the following double derivative of the B1 field equation: where B 1 is the B1 field, ω is the angular frequency, μ 0 = 4π × 10 − 7 N/A 2 is the magnetic permeability of the free space, and τ H = σ H + iωϵ H is the high-frequency electrical tissue properties of HFC σ H and permittivity ϵ H (Katscher et al., 2009).With the phase term ϕ + (ϕ − ) of the positive (negative) rotating component of the transverse field of B 1 , a phase-based MREPT formula with the regularization coefficient c, was derived as where ϕ tr = ϕ + + ϕ − is the measurable transceiver phase using MRI (Gurler and Ider, 2017).Through the numerical approximation, Eq. [2] leads to the matrix system Ax = b using the known boundary information, where , and b = (2ωμ 0 , ⋯ , 2ωμ 0 ), respectively.We used the finite-difference method to solve the above matrix system with regularization coefficient c = 0.03 in Eq. [2].Second, to calculate the compartmental conductivities and ion concentration information, the recovered HFC σ H was decomposed into the intra-neurite and extra-neurite compartments where σ int and σ ext are the intra-neurite conductivity (IC) and the extraneurite conductivity (EC), respectively, ν int is the intra-neurite volume fraction (IVF), c int is the intra-neurite ion concentration, and c ext is the extra-neurite ion concentration (EIC).Similarly, D int and D ext are the intra-neurite diffusivity (ID) and the extra-neurite diffusivity (ED), respectively.To obtain ν int , D int and D ext in Eq.[3], we used the multicompartment spherical mean technique (MC-SMT) (Kaden et al., 2016).The key insight of MC-SMT is that for a specified diffusion weighting factor b, the spherical mean of the diffusion signal ēb over the gradient directions is invariant with respect to the fiber orientation distribution, and hence the mean diffusion signal can be expressed as \ where h b is the microscopic diffusion signal and θ is the angle between the gradient direction and microdomain orientation.MC-SMT adopts a microscopic diffusion model for a microscopic environment of brain tissue with the normalized gradient direction g and orientation w ∈ S 2 = {w ∈ R 3 : ‖ w ‖ = 1} as where [4] and [5], the mean diffusion signal takes the form where erf is the error function.The mean diffusion signals ēb are approximated by taking the average of normalized diffusion MR signals obtained from two b-shells of nominally 800 and 2000s/mm 2 , each acquired with 16 and 32 gradient directions, respectively.The parameters v int and D int can be determined through a least-squares technique that fits Eq. [6].
Now, extra-neurite diffusivity was defined as Using the reference value β= 0.41 (Sajib et al., 2018), the ratio of ion concentrations in the intra-and extra-compartments was set as c int = β c ext and then by using Eq.[3], c ext can be expressed as the following form: Finally, from this reconstruction step, we obtained the following parameter maps: HFC (σ H ) and two separated conductivities of EC (σ ext ) and IC (σ int ).These maps were further processed with the 3D T1W image in the following step.

Post-processing of all reconstructed maps
To process the reconstructed maps of each participant, the Statistical Results reflect the significant difference between the cognitively normal (CN) and Alzheimer disease (AD) groups (1:3), between the CN and mild cognitive impairment (MCI) groups (1:2), and between the MCI and AD groups (2:3).Abbreviation: CDR, clinical dementia rating.
Parametric Mapping version 12 (SPM12) software (http://www.fil.ion.ucl.ac.uk/spm/software/spm12/) was used and the following postprocessing steps were performed.First, the 3D T1W image and all reconstructed maps for each participant were co-registered.Second, the 3D T1W image was spatially normalized into an AD-specific brain template (Guo et al., 2021) and segmented into gray matter, white matter, and CSF using the computational anatomy toolbox (CAT12) tool (http://www.neuro.uni-jena.de/cat/).Third, all maps were then spatially normalized into the brain template using the deformation field information from the 3D T1W image.After all the maps were normalized, areas of less than 5 % IVF in EC were masked out because those areas, such as ventricles, are usually free diffusion.The voxel size difference between the two sequences should be affected in small CSF regions.EC IVF values less than 5 % in each voxel should be masked out.If not, IVF must be larger than 5 %.Finally, Gaussian smoothing using the full-width at half maximum (FWHM) of 10×10×10 mm3 was applied to all parameter maps for voxel-based statistical analyses.

Statistical analysis of maps 2.5.1. Demographic data
Both age and the K-MMSE score were compared between the three participant groups using the Kruskal-Wallis test.Sex was compared using the chi-squared test.

Voxel-based analyses
Each parameter map was compared among the three participant groups using the voxel-wised full factorial design of one-way analysis of covariance (ANCOVA) with age as a covariate.Furthermore, the association between the voxel value of each map and either age or the K-MMSE score, with age as a covariate, was evaluated using the voxelbased multiple regression analysis.For the voxel-based analyses, a significance level of α = 0.05 was applied with correction for multiple comparisons using the false-discovery rate (FDR) method and clusters with at least 100 contiguous voxels.

Region-of-interest (ROI)-based analyses
To obtain a value for each map in a specific brain area, we defined the four atlas-based region-of-interest (ROI) areas of the hippocampus and middle temporal gyrus (MTG) areas based on knowledge of the affected locations in AD patients, the insular area based on our previous finding (Park et al., 2022), and the corpus callosum area which is the main white matter region in the brain using wfu pickatlas software (http://fmri.wfubmc.edu/software/PickAtlas).The mean values of each map were extracted from both sides of the selected ROIs and the following statistical analyses were performed using this data.First, a group comparison of the ROI value was performed using ANCOVA, with age as a covariate, to evaluate the differences in ROI values between the three participant groups using the Bonferroni post-hoc test.Second, the correlation coefficient test was performed to analyze the degree of association between the ROI values and the participant's age using all three groups.We also repeated this analysis using only the CN group.In addition, we performed a partial correlation analysis between the ROI values and K-MMSE scores using all three groups, with adjustments for the participant's age.We also repeated this analysis using both MCI and AD groups.Finally, a receiver operating characteristic (ROC) curve analysis was performed for each conductivity index for each ROI to differentiate between the groups.For ROI data, α < 0.05 was used to determine the significance level.The statistical analysis was performed using the Medcalc (MedCalc Software, Acacialaan, Ostend, Belgium) statistical program.

Characteristics of participants
Demographic information of the participants is shown in Table 1.Among the 83 recruited participants, 17 patients were excluded from analysis for reasons summarized in the flowchart (Fig 1).Finally, total 66 participants were included in this study as 20 CE patients, 25 amnestic MCI patients, and 21 CN elderly people.The statistical results of baseline patient characteristics are shown in Table 1.Age and sex were not significantly different between the participant groups.K-MMSE score were significantly different between CN and MCI (p = 0.001), between CN and AD (p < 0.001), and between MCI and AD (p < 0.001).
Fig 2 shows the representative T1-weighted images and the corresponding maps of HFC, EC, and IC obtained from the brain of one CN participant (a 72-year-old female), one MCI patient (a 77-year-old female), and one AD patient (a 73-year-old female).Both the HFC and EC appear brighter in the AD patient compared to the CN participant and the MCI patient at the overall slice.The quantitative assessment of the conductivity maps from all participants was listed in Tables.IC is heavily dependent on IVF, Since IVF is low not only in the CSF but also in its adjacent areas such as the lateral ventricle, IVF is low in the regions adjacent to CSF (for example, the areas marked by the red arrows in Fig. 2. Additionally, demyelination and neurodegeneration in AD patients have led to a reduction in IVF which results in lower IC, as shown in the areas marked with blue arrows in Fig. 2.

Group comparison
Compared with the CN and MCI groups, HFC and EC were higher in the AD group (Fig 3).The conductivities of both HFC and EC were increased in the AD group in the large brain areas, including the frontal, occipital, parietal, and temporal areas (Supplementary Table S1).The IC was increased in AD compared with CN, but decreased in AD compared with MCI.Compared with the CN group, all three conductivity indices were increased in the MCI group.

Association with age or K-MMSE scores
The K-MMSE score was negatively associated with both HFC and EC but positively associated with IC (Fig 4).The conductivities of both HFC and EC were increased in the low MMSE score in the brain areas of the temporal, insular, occipital gyrus and frontal white matter (Supplementary Table S2).IC was increased with increased MMSE scores at frontal and precentral and cingulate white matter.Age was not significantly associated with any conductivity indices.

Group comparison
The statistical results of the group comparisons for each ROI value, comprising of mean values with the standard deviation, are listed in Table 2.
Compared with the CN group, HFC was significantly higher in the AD group at the hippocampus (p = 0.003), insular (p = 0.001), and MTG (p = 0.018).EC was also significantly higher in the AD group at the hippocampus (p = 0.009) and insular (p = 0.020).IC was not significantly different among the groups for all four ROIs.
Compared with the MCI group, HFC was significantly higher in the AD group at the insular (p = 0.005).EC was also significantly higher in the AD group at the insular (p = 0.018).IC was not significantly different among the groups for all four ROIs.

Correlation with age
Results of the correlation analysis between conductivity measures and ages with all participants are listed in Table 3 and Supplementary  S4.In summary, there were no significant correlation between conductivity indices and CN age in any brain ROI areas.

Correlation with K-MMSE scores
Results of the correlation analysis between conductivity measures and K-MMSE scores with all participants are listed in Table 3 and Supplementary Fig S2 .The K-MMSE scores in the insular were significantly negatively correlated with HFC (rho r = − 0.427, p = 0.0004) and EC (rho r = − 0.426, p = 0.0004).The K-MMSE scores in the MTG were significantly negatively correlated with HFC (rho r = − 0.438, p = 0.0003) and EC (rho r = − 0.365, p = 0.003).The K-MMSE scores in the corpus callosum were significantly positively correlated with IC (rho r = 0.370, p = 0.002).Additional results of the correlation analysis between conductivity measures and K-MMSE scores with both MCI and AD participants are listed in Supplementary Table S4.The patterns of significant correlations were the same as results with using all participants.

ROC curve analysis of conductivity indices
Table 4 shows results of the ROC curve analysis of conductivity indices obtained in the specific brain areas.To differentiate AD from CN, in the hippocampus, HFC had area-under-curve (AUC)=0.792with sensitivity (SE)=80 and specificity (SP)=71 and EC had AUC=0.788with SE=85 and SP=76, which was highest sensitivity with high specificity.In the insular, HFC had AUC=0.786with SE=65 and SP=100 and EC also had high AUC =0.765 with high SE=70 and SP=95.Finally, in MTG, HFC had AUC=0.736with SE=50 and SP=95 and EC also had AUC =0.732 with high SE=90 and SP=52.
To differentiate AD from MCI, in the hippocampus, HFC had AUC=0.694with SE=75 and SP=64 and EC had AUC=0.699with SE=75 and SP=72.In the insular, HFC had AUC=0.719with SE=65 and SP=84 and EC also had high AUC =0.746, which was the highest AUC value, with SE=65 and SP=9.Finally, in MTG, EC had AUC =0.717 with high SE=75 and SP=68.To differentiate MCI from CN, any conductivity indices from any defined ROIs were not significant.

Discussion
We separated HFC into EC and IC compartments using MC-SMT, examined how EC and IC were reflected in AD patients compared with CN elderly people and patients with amnestic MCI, and evaluated the association between conductivity measures and cognitive decline.We found that EC was increased in AD patients compared with CN elderly people and both EC in the insula and middle temporal gyrus and IC in the corpus callosum were significantly associated with MMSE scores.EC in the hippocampus and insula had high AUC values with high sensitivity and specificity.

EC was increased in AD patients compared with CN elderly people
Our results showed that EC in the ROI-based analysis was significantly higher in the AD group at the hippocampus, insular, and MTG (Table 2).In addition, in the voxel-based analysis, it was found that EC increased in the AD group in the large brain areas, including the frontal, occipital, parietal, and temporal areas.EC discriminated AD from others with high sensitivity and specificity at the hippocampus, insular, and MTG (Table 4).Conductivity in the extra-neurite compartment is highly sensitive to evaluate AD.Demyelination and neurodegeneration in AD patients resulted in increased diffusivity, as shown by the greater mobility of protons due to microstructural abnormalities, increasing anisotropic diffusivity into the axonal direction.Although we can differentiate extra-neurite from extracellular in the brain tissue, we know that extracellular areas in the AD brain change due to several extracellular environmental factors.For example, firstly, the hallmark   Lendel, 2021).Finally, AD causes an imbalance of ions since AD is linked to decreased levels of Na(+)/K(+) ATPase and reduced glutamate clearance in the brain (Vitvitsky et al., 2012).These cellular-level changes result in a difference in conductivity, which explains the higher EC value in the AD group compared with the other groups.Our previous study also showed that HFC increased in the hippocampus and insular of an AD group compared to other groups and is similar to previous findings (Park et al., 2022).
EC may be a good candidate to use as an imaging biomarker to differentiate AD from others (Table 4).EC was sensitively discriminated AD from CN with high sensitivity and specificity at the hippocampus, insular, and MTG.To differentiate AD from MCI, EC in the insular had the highest AUC value with a good sensitivity and specificity.Our previous study showed that HFC value in the insular had a high AUC value to differentiate from other (Park et al., 2022).The sensitivity and specificity of HFC were higher than the gray matter volume measurement in the hippocampus.
Our results showed that IC in the ROI-based analysis was not significantly different between the groups (Table 2).However, in the voxel-based analysis, it was found that IC also increased in the AD group compared with the CN group in the frontal, occipital, and parietal white matter areas, but decreased in the AD group compared with the MCI group in the frontal, temporal, and parietal white matter areas (Supplementary Table S1).Since the diffusion signal is decomposed into two compartments with distinct diffusion properties: one with restricted diffusion within the neurites and one with hindered diffusion in the extra-neurite space, IC is the conductivity value mainly in the white matter and in the intra-neurite site (Kaden et al., 2016;Kamiya et al., 2020).We defined IC as the conductivity value in the intra-neurite site.The definition of intra-neurite was based on the MC-SMT model (Kaden et al., 2016), which was also used in NODDI model (Kamiya et al., 2020).Supplementary Figure 3 shows values of the IVF (a) and ID (b) measured in the bilateral CC area for the CN elderly, amnestic(MCI, and AD groups.Mean value of IVF is gradually decreased from CN to AD. Mean value of ID is higher in AD than CN and MCI.The neuronal cytoskeletal degeneration course is distinct to six stages in disease propagation (transentorhinal I-II: clinically silent cases; limbic III-IV: incipient Alzheimer's disease; neocortical V-VI: fully-developed Alzheimer's disease) (Braak and Braak, 1998).Such an intraneuronal change can induce increase of IC value in AD and MCI groups compared with the CN group, but slight decrease of IC value in AD who shows cytoskeletal degradation continues to worsen without remission nor recovery compared with the MCI group.IC value in corpus callosum which is the area of the white matte buddle was slightly lower in AD than MCI (Table 2).
The clinical application perspective of using EC and IC is that they can provide a non-invasive and comprehensive way of measuring the electrical properties of the brain tissue at different levels, and that they can help to understand the pathophysiology and progression of AD and other neurological disorders.AD is a common neurodegenerative disorder that is characterized by the accumulation of abnormal proteins, such as amyloid-beta and tau, which can induce oxidative and inflammatory stress, and lead to the loss of synaptic and neuronal integrity, neuronal loss, and brain atrophy.These changes can affect the electrical conductivity and diffusivity of the brain tissue, and thus alter the EC and IC values.By using EC and IC, clinicians and researchers can assess the microstructural changes in the brain tissue that are related to AD, and

EC and IC values were associated with K-MMSE scores
The K-MMSE scores were significantly negatively correlated with EC in the insular and MTG areas (Table 3, Fig. 4), indicating that the conductivity value increased with increasing disease severity.However, the K-MMSE scores were significantly positively correlated with IC in the corpus callosum, which is a major white matter bundle that connects the two hemispheres of the brain.
For HFC, our finding is similar to our recent study (Park et al., 2022) which showed that HFC was negatively associated with K-MMSE scores.The K-MMSE is the most well-known, widely used screening tool for providing an overall measure of cognitive impairment in clinical, research, and community settings (Ahn et al., 2010;Arevalo-Rodriguez et al., 2015).The brain of AD patients often shows at least moderate cortical atrophy, most evident in multimodal association structures in the cortical and limbic lobes.The K-MMSE is sensitive to the severity of dementia in patients with AD.Although the MMSE cannot be used as the sole diagnostic tool for dementia due to non-neurological reasons that lead to low scores, a previous study has shown that patients with AD generally lose three points per year on the MMSE (Bernard and Goldman, 2010).This result shows the possibility that EC might be considered as an imaging biomarker for monitoring cognitive function and the progression of AD, as it can capture the changes in the intra-neurite space that are caused by AD, such as the neuronal cytoskeletal degeneration, the demyelination and neurodegeneration, and the reduction of intra-axonal water.Atrophy involving not only the frontal and temporal cortices but also the medial temporal lobe affecting the amygdala and hippocampus is typical of AD, but can be seen in other age-related disorders (DeTure and Dickson, 2019).As a result of this atrophy, most affected patients show a loss of brain weight, which together with increases in ion concentrations and diffusivity can explain the result that age in the insula and MTG was significantly positively correlated with CSF volume.A previous study reported significant correlation between fractional anisotropy (FA) and MMSE score in entire white matter areas, and showed higher mean diffusivity and lower fractional anisotropy (FA) in the corpus callosum and white matter of the frontal, temporal and parietal lobes of AD compared to healthy controls (Bozzali et al., 2002).However, it is still controversial with conflicting results.Other previous studies reported there was no correlation between DTI indices of affected white matter in AD and MMSE (Ibrahim et al., 2009) (Patil and Ramakrishnan, 2014).

Study limitations
First, the number of participants in each group is relatively small.Therefore, a large population study is required in the future.Second, in ROI analysis, there was no significant difference in the IC value between the AD and other groups, which is inconsistent to the result of the voxelbased analysis.Therefore, further investigation is required regarding intra-and extra-compartment modeling to clarify the result.Third, in this study, the conductivity difference between amyloid plaques and other types of amyloid such as monomer or oligomer forms was not investigated.Since smaller ions are more conductive than larger ions, because small ions can move through a solution with less hydrodynamic resistance, it can be expected that conductivity values among different forms of amyloid may differ.Therefore, it may be necessary to investigate amyloid-related conductivity to clarify these results.Finally, the separated components of EC and IC results were not verified with another technique, such as magnetic resonance electrical impedance tomography, which is obtained by injecting an external low-frequency current.However, it may be impossible to inject a current into the brains of AD patients during a routine clinical evaluation.Therefore, animal studies may be required to verify the results.

Conclusion
This study was a first-time trial to decompose high-frequency conductivity into extra-neurite conductivity and intra-neurite conductivity in the brain of AD patients.For AD patients, the electrical properties of the extra-neurite compartment were sensitively changed.The EC value was higher in patients with AD than CN elderly people and patients with amnestic MCI.The EC value decreased with increasing K-MMSE scores after adjusting for age in the insula and middle temporal gyrus.This study showed the possibility that the EC value might be used as an imaging biomarker for helping to monitor cognitive function.Because the EC value may be associated with extra-neurite ion concentration and diffusivity, MREPT may reflect neuronal loss and ion changes in AD patients.This pilot study proposes that alterations in the conductivity in AD brains might serve as imaging biomarkers with clinical significance, aiding in the early detection and/or monitoring of disease progression.Animal studies may be required to verify our results.

Table 4
Results of a receiver operating characteristic (ROC) curve analysis of conductivity measures obtained in the specific brain areas.

Fig. 1 .
Fig. 1.Flow chart shows summary of selection process of participants in the study.One CN participant in the exclusion due to other neurologic/psychiatric disease was the Behcet disease.Abbreviations: CN, cognitively normal; MCI, amnestic mild cognitive impairment patient; AD, Alzheimer's disease; MR, magnetic resonance.

Fig S1 .
Fig S1.Age was positively significantly correlated with HFC in only the corpus callosum (rho r = 0.313, p = 0.011).EC and IC had a trend positively correlation with age in MTG (rho r = 0.244, p = 0.049) and the corpus callosum (rho r = 0.294, p = 0.017) for EC and negatively correlation with age in hippocampus (rho r = − 0.267, p = 0.030) for IC.Additional results of the correlation analysis between conductivity measures and ages with only the CN participants are listed in Supplementary TableS4.In summary, there were no significant correlation between conductivity indices and CN age in any brain ROI areas.

Fig. 3 .
Fig. 3. Group comparison result using the voxel-based analysis of covariance of high-frequency conductivity (HFC), extra-neurite conductivity (EC), and intraneurite conductivity (IC) between the three participant groups.The red color indicates higher in the AD group than the CN and MCI groups.The blue color indicates higher in the MCI group than the AD group.The color bar indicates the significant level of T-score in each comparison.

Fig. 4 .
Fig. 4. Result of the voxel-based multiple regression analysis of high-frequency conductivity (HFC), extra-neurite conductivity (EC), and intra-neurite conductivity (IC) with K-MMSE scores using all participant data.The red and blue colors indicate positive and negative associations between values of each map with K-MMSE scores.Age was not significantly associated with HFC, EC, and IC.The color bar indicates the significant level of T-score in each comparison.

Table 1
Summary of the statistical results of the demographic data.Age and the Korean version of Mini-Mental State Examination (K-MMSE) were evaluated by the Kruskal-Wallis test (*p-value) with a Mann-Whitney post-hoc test if significant.Sex was tested by the chi-squared test.

Table 2
Results of comparisons of MRI measures among the three participant groups at the specific brain areas.

Table 3
Results of correlation analyses of MRI measures with ages or K-MMSE scores in the specific brain areas.the cognitive decline and the efficacy of treatment.EC and IC can also be used to differentiate AD from CN and MCI, and to identify the brain regions that are most affected by AD.Therefore, EC and IC can give am added value to provide a more comprehensive and accurate diagnosis and prognosis of AD.
Data are listed as Pearson correlation coefficient (r) by correlation coefficient analysis with p-value, except *adjMMSE which is the result of the partial correlation analysis between the Korean version of Mini-Mental State Examination (MMSE) scores and MRI measures with adjusting age.Statistical significance was defined as p = 0.05/4 = 0.0125.Abbreviation: ROI, regions-of-interest; MGT, middle temporal gyrus; HFC, high-frequency conductivity; EC, extra-neurite conductivity; IC, intra-neurite conductivity;.monitor