Machine learning‐directed electrical impedance tomography to predict metabolically vulnerable plaques - Bioengineering Transla Med - 2023 - Chen - Machine learning‐directed electrical impedance tomography to predict.pdf

RESEARCH ARTICLE

Machine learning-directed electrical impedance tomography

to predict metabolically vulnerable plaques

Justin Chen

| Shaolei Wang

| Kaidong Wang

| Parinaz Abiri

1,2

Zi-Yu Huang

| Junyi Yin

| Alejandro M. Jabalera

| Brian Arianpour

Mehrdad Roustaei

| Enbo Zhu

| Peng Zhao

| Susana Cavallero

2,4

Sandra Duarte-Vogel

| Elena Stark

| Yuan Luo

| Peyman Benharash

Yu-Chong Tai

| Qingyu Cui

| Tzung K. Hsiai

1,2,3,4

Department of Bioengineering, Henry Samueli School of Engineering, University of California, Los Angeles, Los Angeles, California, USA

Division of Cardiology, Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California, U

Department of Medical Engineering, California Institute of Technology, Pasadena, California, USA

Division of Cardiology, Department of Medicine, Greater Los Angeles VA Healthcare System, Los Angeles, California, USA

Division of Laboratory Animal Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California, USA

Division of Anatomy, Department of Pathology and Laboratory Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los A

ngeles,

California, USA

Division of Cardiothoracic Surgery, Department of Surgery, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, Ca

lifornia, USA

Correspondence

Tzung K. Hsiai, Department of Bioengineering,

Henry Samueli School of Engineering,

University of California, Los Angeles, Los

Angeles, CA 90095, USA.

Email:

thsiai@mednet.ucla.edu

Funding information

National Institutes of Health, Grant/Award

Numbers: R01HL118650, R01HL149808;

National Institute of General Medical Sciences,

Grant/Award Number: T32 GM008042; David

Geffen School of Medicine Scholarship; VA

Greater Los Angeles Healthcare System,

Grant/Award Number: I01 BX004356

Abstract

The characterization of atherosclerotic plaques to predict their vulnerability to

rupture remains a diagnostic challenge. Despite existing imaging modalities, none

have proven their abilities to identify metabolically active oxidized low-density

lipoprotein (oxLDL), a marker of plaque vulnerability. To this end, we developed a

machine learning-directed electrochemical impedance spectroscopy (EIS) platform to

analyze oxLDL-rich plaques, with immunohistology serving as the ground truth.

We fabricated the EIS sensor by affixing a six-point microelectrode configuration

onto a silicone balloon catheter and electroplating the surface with platinum black

(PtB) to improve the charge transfer efficiency at the electrochemical interface.

To demonstrate clinical translation, we deployed the EIS sensor to the coronary

arteries of an explanted human heart from a patient undergoing heart transplant

and interrogated the atherosclerotic lesions to reconstruct the 3D EIS profiles of

oxLDL-rich atherosclerotic plaques in both right coronary and left descending

coronary arteries. To establish effective generalization of our methods, we repeated

the reconstruction and training process on the common carotid arteries of an

unembalmed human cadaver specimen. Our findings indicated that our DenseNet

model achieves the most reliable predictions for metabolically vulnerable plaque,

yielding an accuracy of 92.59% after 100 epochs of training.

Received: 30 June 2023 Revised: 5 September 2023 Accepted: 15 October 2023

DOI: 10.1002/btm2.10616

This is an open access article under the terms of the

Creative Commons Attribution

License, which permits use, distribution and reproduction in any medium,

provided the original work is properly cited.

Bioengineering & Translational Medicine

published by Wiley Periodicals LLC on behalf of American Institute of Chemical Engineers.

Bioeng Transl Med.

2024;9:e10616.

wileyonlinelibrary.com/journal/btm2

1of12

https://doi.org/10.1002/btm2.10616

KEYWORDS

atherosclerosis, electrochemical impedance spectroscopy, machine learning, nanomaterials,

oxidized low-density lipoprotein

Translational Impact Statement

We developed a machine learning-directed electrochemical impedance spectroscopy system

and demonstrated its translational potential in the prevention of cardiovascular disease through

its ability to assess the vulnerability of metabolically unstable plaques. The functionality and bio-

compatibility of our system was tested on ex vivo human models, such as an explanted heart.

Accordingly, we were able to develop 3D reconstructions to describe the radial distributions of

various atherosclerotic elements and implement convolutional neural networks to predict the

likelihood of rupture. All our results were validated with histological data.

INTRODUCTION

Cardiovascular disease (CVD) remains one of the leading causes of

death in developed countries, with over 19 million deaths reported glob-

ally each year.

One of the root causes of CVD is atherosclerosis, or

buildup of plaque, in the coronary arteries. Atherosclerotic lesions typi-

cally contain a necrotic core, a thin fibrous cap, macrophages, and calcifi-

cation (Figure

2,3

The necrotic core largely consists of metabolically

active oxidized low-density lipoprotein (oxLDL) crystals, whereas the

fibrous cap consists of collagenous tissues that effectively serve as a

protective layer to prevent the plaque from rupture. However, biome-

chanical forces, such as shear stress, and inflammatory factors, such as

matrix metalloproteinase, can contribute to the thinning of the fibrous

cap, leading to plaque destabilization and release of the lipid-rich core

into the bloodstream. Ultimately, this leakage can cause blood coagula-

tion, or thrombosis, and hinder the flow of blood in the arteries.

Detecting metabolically active and oxLDL-laden plaques remains

an unmet diagnostic challenge. Several imaging modalities, such as

intravascular ultrasound and optical coherence tomography (OCT),

have facilitated the characterization of atherosclerotic lesions, but

these technologies are limited in their abilities to identify the metabol-

ically active components of the atherosclerotic plaques, which harbor

similar acoustic and scattering properties.

5,6

OCT also requires saline

solution flushing to remove red blood cells in the aorta.

Despite the

ability to characterize oxLDL-laden plaques, near-infrared spectros-

copy requires the injection of contrast agents.

Despite high resolu-

tion to detect intraplaque hemorrhage and presence of lipid-rich

lesions, magnetic resonance imaging is bulky and costly.

Multi-slice

spiral computed tomography allows for high-resolution detection of

calcification, but it exposes patients to radiation.

To overcome these

limitations when patients undergo elective angiograms, we have dem-

onstrated both the theoretical and experimental bases of intravascular

electrical impedance spectroscopy (EIS). This technique can reliably

differentiate between the lipid-rich core, fibrous cap, and calcification;

thus, providing the sensitivity and specificity needed to characterize

the vulnerability of the plaque.

Intravascular EIS can be implemen-

ted by introducing an alternating current (AC) to the atherosclerotic

lesion and measuring its impedance (

) over a range of frequencies,

where

is a complex value consisting of resistance (

) as the real term

and reactance (

) as the imaginary term (

). In addition, the

amplitude of the AC current is typically below 10mV, rendering this

procedure safe and reliable.

RESULTS AND DISCUSSION

2.1

Initial data from pig model

Initial results from the Yucatan mini-pig model revealed several struc-

tural differences between the stable (Figure

) and vulnerable

(Figure

) samples of the right common carotid artery (RCCA). For

instance, the stable segment consisted of a clear lumen with healthy

endothelial tissues, while the vulnerable segment contained bio-

markers of oxLDL-laden plaque, such as a necrotic core and fibrous

cap. Clotted blood was also prevalent in the lumen of the vulnerable

sample, suggesting that an immune reaction was induced by prior

leakage of the necrotic core into the bloodstream. Accordingly, higher

impedances were observed, suggesting that atherosclerotic compo-

nents are more obstructive to current flow when compared to healthy

tissues. Furthermore, finite-element analysis of the oxLDL-laden pla-

que in the RCCA segment revealed that the volume impedance den-

sity (VID) was most concentrated at the endothelial layer, with some

influence at the collagenous tunica media (Figure

Upon measuring each atherosclerotic component of the pig

model, we confirmed that the impedance of lipid-rich cores, fibrous

caps, and calcified tissues were best differentiated at 50 kHz. This

value is a well-accepted critical frequency for distinguishing biological

tissues.

13,14

In our experiment, the lipid-rich cores exhibited an imped-

ance on the order of 30 k

, the calcified tissues on the order of

10 k

, and the collagenous tissues on the order of 2 k

(Figure

Phase data also revealed noticeable differences at 50 kHz, with at

least 10

of difference between each element.

2.2

Three-dimensional EIT reconstruction

Combinatorial EIS data obtained from the left anterior descending coro-

nary artery (LAD) and the right coronary artery (RCA) of the explanted

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human heart model, as well as the RCCA of the cadaver specimen

(Figure

), served as the experimental data for our electrical impedance

tomography (EIT) reconstruction. The corresponding Bode plots

(Figure

) generally reported high impedances (>100 k

)fromthe

LAD and low impedances (<10 k

) from both the RCA and RCCA. In

accordance with initial results, 50 kHz was chosen as the critical fre-

quency from which the conductivity values were derived. The 3D EIT

reconstructions of the arterial segments were rendered using a red-

to-yellow gradient colormap (Figure

), where red is indicative of

regions with low electrical conductivity, corresponding to plaque

buildup. Tomographic results suggested a high concentration of oxLDL-

rich plaque distributed between the upper-left and upper-right regions

of the LAD and moderate calcification in the upper region of the RCA.

Additionally, the RCCA of the cadaver specimen was found to be free

of atherosclerosis. All EIT reconstructions aligned with measured EIS

data and the corresponding immunohistology (Figure

2.3

Significance testing and data preprocessing

The results of our skewness test yielded a value of

8972, with

a greater number of stable lesions compared to vulnerable lesions in

our data set. Accordingly, the difference of medians was chosen as

the evaluation parameter for the null hypothesis significance test

(NHST), which yielded a

-value of <0.001 (Figure

). Thus, we

rejected our null hypothesis and determined that there existed a

significant difference between the impedimetric measurements of vul-

nerable and stable plaques. Calculation of the 99% confidence interval

(CI) showed that the difference in median impedances between these

two categories likely fell between 10k

and 17k

. As an additional

data preprocessing step, 3D principal component analysis (PCA) was

able to cluster the impedimetric measurements based on underlying

EIS features (Figure

2.4

Evaluation of model performance

Upon running the three models on a randomly generated testing and

validation data set, DenseNet-9 demonstrated the best performance,

with a minimized loss function (Figure

) and a maximized accuracy

curve (Figure

) when plotted against the number of epochs.

ResNet-7 initially demonstrated a discrepancy between the training

and validation loss, which was indicative of underfitting, but these

metrics began to converge at around 40 epochs. In contrast, the logis-

tic regression model experienced fluctuations in both loss and accu-

racy, indicating that the model was not able to recognize enough

patterns in the data set to achieve optimal results. A histogram com-

paring the validation results of all three models is shown in Figure

Next, receiver operating characteristic (ROC) curves revealed that

100 epochs of training resulted in the greatest amount of separability

for each of the three models (Figure

). After running for this dura-

tion, DenseNet-9 and ResNet-7 achieved an area under the curve

FIGURE 1

Initial data obtained from the RCCA of the Yucatan mini-pig model. (a) The stable arterial sample consisted of healthy tissues, with

no biomarkers of atherosclerosis. Its corresponding impedance heatmap suggests little obstruction to current flow. Scale bar: 1 mm. (b) Evidence

of atherosclerosis, such as a necrotic core and fibrous cap, were present in the vulnerable sample. The presence of clotted blood, or thrombus,

signifies a prior immune reaction. Moreover, the corresponding impedance heatmap suggests major obstructions to current flow. Scale bar: 1 mm.

(c) A finite-element model constructed from plaque-laden histological segments shows the volume impedance density in 3D, representing the

spatial distribution of oxLDL. Scale bar: 1 mm. (d) Averaged Bode plots (

6) of the three major atherosclerotic components confirm that they

are best distinguished at the critical frequency (

crit

) of 50 kHz. A greater weight was placed on impedance magnitude to simplify the training

process of the machine learning models. However, phase data may also provide useful information regarding the electrical interactions between

the atherosclerotic elements and the extracellular environment. oxLDL, oxidized low-density lipoprotein; RCCA, right common carotid artery.

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(AUC) of 1.00 and 0.96, respectively, signifying a low number of incor-

rect predictions within our validation data sets. The logistic regression

model, on the other hand, produced a greater number of false posi-

tives, contributing an AUC of 0.75. Nonetheless, the AUC of all three

models far exceeded that of a random classifier (AUC

0.5), indicat-

ing their potentials in interpreting EIS data in the context of athero-

sclerotic vulnerability.

Further analysis of the confusion matrices (Figure

) suggested

that DenseNet-9 outperformed the other models in terms of accu-

racy, misclassification rate, sensitivity, and F

score (Table

), yielding

92.59% of correct classifications and no false negative predictions in

the validation data set. ResNet-7 also resulted in promising outcomes,

yielding the most optimal specificity, false positive rate, and precision

rates. In contrast, the logistic regression model generated inferior

results across all metrics.

Taken together, we determined DenseNet-9 and ResNet-7 to

be the most appropriate models for evaluation of EIS data.

DenseNet-9 accumulated four incorrect predictions from our valida-

tion data set (

54), all attributed to false positives, while

ResNet-7 accrued nine incorrect predictions, which were all false

negatives. However, the clinical context must be further investi-

gated to determine whether DenseNet-9 or ResNet-7 is favorable.

For instance, sensitivity is more desirable when performing EIS in

essential arteries that supply blood to vital organs.

–

Hence,

DenseNet-9 would be an appropriate model for such applications, as

it maximizes sensitivity, which

does not depend on the number of

false positives. On the contrary, specificity is more desirable for non-

critical arteries, especially in instances where secondary blood ves-

sels are still able to deliver a sufficient blood supply to the target

tissue.

The number of false positive errors should be minimized, as

they may lead to unnecessary medical interventions, posing a burden

for the patient. Hence, ResNet-7 would serve as the ideal model for

this case, as it resulted in a lower number of false positive predic-

tions compared to its counterparts.

FIGURE 2

Three-dimensional EIT reconstructions of EIS data. (a) EIS data were measured in the LAD and RCA of the explanted heart model,

as well as the RCCA of the cadaver specimen. (b) Bode plots were acquired by iterating through the 15 combinations of electrode pairs, showing

the impedimetric dependence on frequency. (c) Results from the well-posed forward algorithm were used to render 3D conductivity maps, where

red indicates regions of plaque buildup. Tomographic results predicted the presence of two lipid cores surrounded by fibrous caps in the LAD

segment, prominent calcification in the RCA, and no signs of atherosclerosis in the RCCA. L: lipid core; FC: fibrous cap; Ca

: calcification. (d) All

histological results correlated with their corresponding EIT reconstructions, supporting intravascular EIS as a viable technique for plaque

characterization. All scale bars: 1 mm. EIS, electrochemical impedance spectroscopy; EIT, electrical impedance tomography; LAD, left anterior

descending coronary artery; RCA, right coronary artery; RCCA, right common carotid artery.

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2.5

Limitations and future directions

Despite the novel aspects of our machine learning-guided EIS system,

we acknowledge that there remains a need for continuous monitoring

during interventional procedures, improving the signal-to-noise ratio

(SNR), and clinical testing on patients. Currently, our reconstruction

algorithm is limited to processing one set of data at a time, but future

work could involve an iterative version of the reconstruction algo-

rithm to continuously sample the tissue impedance and render a

dynamic finite element model (FEM). To improve the SNR, we can

investigate other nanomaterials, such as reduced graphene quantum

dots (rGQDs), as a method of increasing the effective surface area at

the electrode

–

tissue interface.

12,18,19

Transmission electron micros-

copy performed in tangent to our initial animal experiments has

FIGURE 3

Performance metrics to evaluate the efficacy of logistic regression, ResNet-7, and DenseNet-9 in EIS classification. (a) Loss

functions of all three models suggest that DenseNet-9 yielded predictions with the most minimal error. ResNet-7 also resulted in low error, but

underfitting was experienced until 40 epochs of training. (b) Similarly, accuracy curves suggest that DenseNet-9 yielded the most optimal

predictions, with ResNet-7 also converging after 40 epochs. (c) ROC curves were obtained over 10, 20, 40, and 100 epochs of training. One

hundred epochs were sufficient to achieve AUCs of 0.75, 0.96, and 1.00 for the logistic regression, ResNet-7, and DenseNet-9 models,

respectively. (d) Each prediction instance was categorized as a true positive, false positive, false negative, or true negative in the form of a

confusion matrix. Percentages are rounded to the nearest tenth. AUC, area under the curve; EIS, electrochemical impedance spectroscopy; ROC,

receiver operating characteristic.

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verified the increased roughness of composite rGQD-coated elec-

trodes, resulting in an impedimetric reduction and a greater capaci-

tance (Figure

). Lastly, we must consider the biocompatibility of our

system to ensure its successful translation to clinical use. Materials

used in our EIS catheter, such as PtB, gold, polyimide (PI), and silicone,

have all been found by previous studies to be safe for in vivo

applications.

–

No adverse responses were observed in this study,

and to the best of our knowledge, no immunogenic responses were

reported in prior literature that tested similarly constructed EIS

devices in vivo on animal models.

–

Despite the promising outlook

of the materials implemented in our catheter, approval by the Food

and Drug Administration (FDA) is still required to proceed with Phase

I clinical study of our device.

It is also important to note that only male Yucatan mini-pigs were

available during the time of experimentation. Thus, the data acquired

during the initial portion of our study may not be entirely reflective of

the female population. There are a few studies that suggest differ-

ences in atherosclerotic formation between males and females

because of hormonal or dietary factors.

29,30

Hence, future studies

should involve more rigorous testing of both sexes to fully examine

the diagnostic capabilities of intravascular EIS sensors.

EXPERIMENTAL SECTION

3.1

Translational objectives

Previous EIS studies have largely been limited to the New Zealand white

rabbit and mini-pig models of atherosclerosis.

–

To demonstrate clini-

cal translation in preparation for FDA-regulated safety studies, we

sought to interrogate the EIS profiles of the coronary arteries from the

explanted hearts of patients undergoing heart transplant (Figures

and

) and the carotid arteries from unembalmed human cadavers. We per-

formed histological analyses as the ground truth (Figure

) to corrobo-

rate the 3D EIT profiles with the oxLDL-laden plaques.

3.2

Electrode fabrication

In this study, a six-point microelectrode-based EIS sensor was devel-

oped around a silicone balloon catheter, with the eventual goal of

delivery through the femoral artery (Figure

The EIS sensor con-

sisted of a 2-by-3 arrangement of gold (Au) electrodes that were elec-

troplated with PtB, spaced 1.4 mm apart, and placed on top of a

flexible PI substrate (Figure

). Copper (Cu) wires were also embed-

ded within the PI substrate to establish a direct connection to the

electrochemical workstation. By increasing the surface roughness of

the electrodes at the nanoscopic level, electroplating serves to reduce

the parasitic impedance at the low-frequency regime (Figure

which is primarily driven by the diffusion of ions at the electrode

–

tissue interface.

27,31

This phenomenon is known as the electrochemi-

cal double layer (Figure

), and its impedimetric effects are modeled

by Randle's equivalent circuit (Figure

). The nonlinear behavior of

the interface is described by the constant phase element (CPE).

Equation (

) represents its impedance, with

and

serving as tun-

able parameters.

CPE

ðÞ

≤

≤

A value of

1 denotes an ideal capacitor with capacitance

, while

a value of

0 denotes an ideal resistor with resistance 1

The

Warburg diffusion element (

) is a specific case of the CPE where

5. The impedance of the Warburg element can be derived from

Fick's second law of diffusion, capturing the passive transport of ions

through the electrochemical double-layer.

From the six-point configuration, 15 different combinations of

impedimetric measurements (Figure

) can be obtained for each arte-

rial segment, allowing for the subsequent 3D EIT reconstruction.

While the number of microelectrodes can be increased for future EIS

designs, six points were chosen for this study because the proximity

of the microelectrodes to each other would lead to an inherent trade-

off between EIT resolution and parasitic capacitance.

3.3

Initial testing on the mini-pig model of carotid

atherosclerosis

To demonstrate the theoretical and experimental bases of EIS prior to

human studies, we conducted a series of initial experiments using seg-

ments of the right carotid artery isolated from male Yucatan mini-pigs

(

6). Surgical ligation was performed, followed by feeding with a

TABLE 1

Performance metrics for

the evaluation of classification models.

Logistic regression

ResNet-7

DenseNet-9

Accuracy

0.7593

0.8333

0.9259*

Misclassification rate

0.2407

0.1667

0.0741*

Sensitivity

0.6000

0.6786

1.0000*

Specificity

0.8529

1.0000*

0.8919

False positive rate

0.1471

0.0000*

0.1081

Precision

0.7059

1.0000*

0.8095

score

0.6486

0.8085

0.8947*

Note

: For each performance metric, the model with the desirable outcome is denoted with an asterisk (*).

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high-fat diet for 16 weeks to develop atherosclerotic lesions in com-

pliance with the protocol approved by the UCLA Institutional Animal

Care and Use Committee (IACUC) #2014-059. Statistical significance

for this sample size was shown by a previous study, which yielded a

value of less than 0.05.

As a proof-of-concept experiment, EIS data

was acquired using a 10-mV amplitude signal and swept across a fre-

quency range of 1 kHz to 300 kHz at 10 points per decade. It was

expected that the metabolically active and vulnerable atherosclerotic

plaques are oxLDL-rich and that these plaques would yield higher

impedances throughout this range.

Next, a computational model was developed to visualize how

impedance is distributed among the three tunics of the artery.

Methods from Abiri et al. (2022) were implemented to create a

three-dimensional reconstruction (Figure

) based on a set of

11 histological cross sections from an oxLDL plaque laden RCCA,

each spaced 0.4 mm apart. The corresponding model was imported

onto the AC/DC module of COMSOL Multiphysics, where each

layer was assigned a conductivity (

) and relative permittivity (

)

(Table

). Then, a pair of electrodes were made in contact with the

endoluminal wall, conforming to the same geometry as the EIS cathe-

ter, and activated with a peak-to-peak AC voltage of 25mV across a

frequency sweep of 1kHz to 300kHz. The VID was evaluated using

Equation (

), where

and

denotes the current densities measured

at the electrodes,

represents the resistivity, and

denotes the

injected current.

VID

The VID was mapped onto the 3D model using a finite-element

solver. Four

cross sections were obtained from the geometry to

enhance the visualization of the interior impedimetric distribution,

each spaced 0.5mm apart with respect to the

-axis.

3.4

Differentiation of atherosclerotic

components

To demonstrate the 3D EIT data for the oxLDL-laden endoluminal

wall, we calibrated a frequency at which maximum differentiation was

established between the main components of an atherosclerotic pla-

que. We isolated the three main components: namely, lipid-rich cores,

fibrous caps, and calcified sections of the arterial wall from the carotid

arteries of the mini-pig model of atherosclerosis (

6). EIS measure-

ments of the endoluminal wall were obtained within a frequency

sweep from 1 kHz to 1000 kHz, a wide experimental range to

FIGURE 4

Experimental design and microelectrode configuration. (a) The explanted human heart used for this study. LAD: left anterior

descending artery; Ao: aorta; LV: left ventricle; RV: right ventricle. Scale bar: 2 cm. (b) The corresponding immunohistology from the LAD reveals

a lipid-rich necrotic core surrounded by calcified tissue. Scale bar: 1 mm. (c) A six-point microelectrode system was designed to be deployed from

the femoral artery to the coronary arteries, which supply blood perfusion to the myocardium. (d) The gold (Au) microelectrodes were

electroplated with platinum black (PtB) and deposited on a polyimide (PI) substrate. Copper (Cu) wires were embedded within the polyimide

substrate to establish a direct connection to the electrochemical system. Here,

and

represent the recorded voltage signals. Scale bars (left to

right): 1cm, 1mm. (e) An impedance spectrum illustrates a significant reduction in impedance at the low-frequency regime after electroplating

with platinum black. (f) The Randle's circuit serves as a well-recognized model for electrophysiological stimulation, capturing the parasitic eff

ects

at the electrode

–

tissue interface. It is important to note that the electrodes are in contact with the endoluminal layer of the blood vessel wall.

(g) The six-point microelectrode configuration yields 15 different combinations of impedimetric measurements, which can be combined to form a

3D EIT reconstruction. EIT, electrical impedance tomography.

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interrogate the characteristics of the impedance spectra of the three

main components. A critical frequency was identified such that the

resulting impedance magnitudes (

) and phases (

) of the lipid-rich

cores, fibrous caps, and calcified tissues were most distinguishable.

However, to simplify the training process, a greater weight was placed

on differentiating the magnitudes.

3.5

Reconstruction of the EIT

3D EIT was performed on 18 arterial segments of two ex vivo human

models: an explanted heart and a cadaver. Vessels containing signifi-

cant atherosclerotic buildup or stenosis were grounds for inclusion,

while poorly preserved samples were excluded. Eight of the segments

were acquired from the RCA and LAD of the explanted heart, while

10 of the segments were taken from the RCCA of the cadaver speci-

men. This study was approved by UCLA Institutional Review Board

#17-001112, with patient consent acquired prior to the research. To

visualize the distribution of plaque within these human samples, we

designed a cylindrical FEM, consisting of 3 coaxial layers, 8 rows, and

36 elements per row for a total of 864 elements. The coaxial layers

represent the tunica adventitia, tunica media, and the plaque laden

tunica intima. Unlike traditional EIT solvers that utilize the ill-posed

inverse problem, we implemented a well-posed forward algorithm

(Figure

) based on EIDORS (version 3.11) to solve for the conductiv-

ity matrix corresponding to each of the 864 elements, thereby

enabling the 3D rendering of a plaque distribution map.

The algo-

rithm begins with an initial guess of the conductivity matrix, which

was obtained by evaluating each of the 15 impedance functions at the

critical frequency and by solving for the equations in

Methods S1

Then, Gaussian-distributed noise was added to the initial guess,

thereby yielding the first set of candidates for the conductivity map

. We defined a fitness function

, as shown in Equation (

), and iter-

ated through a

“

genetic algorithm

”

until its minima no longer

exceeded our predefined error threshold

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

≠

,measured

,sim

Once this condition was met, the values of the final conductivity

matrix

σ

were chosen as the basis for the 3D EIT reconstruction. To

automate the process, we developed a MATLAB program that pro-

cesses the conductivity matrix from a spreadsheet file and renders the

corresponding FEM in a single step.

3.6

Establishment of the ground truth and data

preprocessing

After obtaining the EIT reconstruction of the intravascular space,

three classification models (logistic regression, ResNet-7, and

DenseNet-9) were designed to predict the vulnerability of an

FIGURE 5

Architectures of algorithms and classification models for the analysis of EIS data. (a) The 3D EIT reconstruction algorithm consists

of iterating the candidate pool through a genetic algorithm until its error function converges to a value below a predetermined threshold. Once

this condition is reached, a separate program processes the final conductivity matrix and renders the corresponding model in a single step. (b

–

Model architectures of logistic regression, ResNet-7, and DenseNet-9, respectively. These models were evaluated against each other to

determine the best architecture for EIS plaque classification. EIS, electrochemical impedance spectroscopy; EIT, electrical impedance tomograp

hy.

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