1
ol.:ȋͬͭͮͯͰͱͲͳʹ͵Ȍ
Scientific Reports
| (2021) 11:19859
|
https://doi.org/10.1038/s41598-021-99132-z
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Electrical impedance tomography
for non‑invasive identification
of fatty liver infiltrate in
overweight
individuals
Chih‑Chiang
Chang
1,4,13
, Zi‑Yu Huang
2,13
, Shu‑Fu Shih
1,3
, Yuan Luo
2
, Arthur Ko
4
, Qingyu Cui
4
,
Jennifer Sumner
5
, Susana Cavallero
4
, Swarna Das
1
, Wei Gao
2
, Janet Sinsheimer
6,7,8
,
Alex Bui
1,3
, Jonathan P.
Jacobs
4,9,10
, Päivi Pajukanta
7,11
, Holden Wu
1,3
, Yu‑Chong
Tai
2
,
Zhaoping Li
4,10,12
& Tzung K. Hsiai
1,2,4,10
*
Non‑alcoholic fatty liver disease (NAFLD) is one of the most common causes of cardiometabolic
diseases in overweight individuals. While liver biopsy is the current gold standard to diagnose NAFLD
and magnetic resonance imaging (MRI) is a non‑invasive alternative still under clinical trials, the
former is invasive and the latter costly. We demonstrate electrical impedance tomography (EIT)
as a portable method for detecting fatty infiltrate. We enrolled 19 overweight subjects to undergo
liver MRI scans, followed by EIT measurements. The MRI images provided the a priori knowledge
of the liver boundary conditions for EIT reconstruction, and the multi‑echo MRI data quantified
liver proton‑density fat fraction (PDFF%) to validate fat infiltrate. Using the EIT electrode belts,
we circumferentially injected pairwise current to the upper abdomen, followed by acquiring the
resulting surface‑voltage to reconstruct the liver conductivity. Pearson’s correlation analyses
compared EIT conductivity or MRI PDFF with body mass index, age, waist circumference, height,
and weight variables. We reveal that the correlation between liver EIT conductivity or MRI PDFF with
demographics is statistically insignificant, whereas liver EIT conductivity is inversely correlated with
MRI PDFF (
R
= −0.69,
p
= 0.003, n = 16). As a pilot study, EIT conductivity provides a portable method
for operator
‑independent and cost
‑effective detection of hepatic steatosis.
Obesity is the major risk factor associated with the development of nonalcoholic fatty liver disease (NAFLD),
affecting more than a third of American adults, and the prevalence of severe obesity (BMI
≥ 35 kg
m
−2
) is con
-
tinuing to rise
nationwide
1
. NAFLD is now one of the most common causes of cirrhosis requiring liver trans
-
plantation in the Western
world
2
,
3
. A clinical challenge in the management of NAFLD resides in non-invasively
detecting fatty liver (i.e., simple hepatic steatosis) at an early stage for intervention and monitoring its progres
-
sion to steatohepatitis (hepatic inflammation), fibrosis (liver scarring), and ultimately
cirrhosis
4
,
5
. While liver
biopsy remains the gold standard for diagnosis of NAFLD, it carries substantial risks, including bleeding and is
confounded by sampling bias and inter-observer
variability
6
. While liver MRI proton-density fat fraction (PDFF)
is recognized as the non-invasive reference standard for validating liver fat
infiltrate
7
,
8
, it is cost-prohibitive
for underserved communities and requires access to a scanner. Ultrasound elastography is also non-invasive,
OPEN
1
Department of Bioengineering, UCLA, Los Angeles, CA, USA.
2
Department of Medical Engineering, California
Institute of Technology, Pasadena, CA, USA.
3
Department of Radiological Sciences, David Geffen School
of Medicine at UCLA, Los Angeles, CA, USA.
4
Department of Medicine, David Geffen School of Medicine at
UCLA, Los Angeles, CA, USA.
5
Department of Psychology, College of Life Sciences, UCLA, Los Angeles, CA,
USA.
6
Department of Biostatistics, Fielding School of Public Health, UCLA, Los Angeles, CA, USA.
7
Department
of Human Genetics, David Geffen School of Medicine at UCLA, Los Angeles, CA, USA.
8
Computational Medicine,
David Geffen School of Medicine at UCLA, Los Angeles, CA, USA.
9
Division of Digestive Diseases, David Geffen
School of Medicine at UCLA, Los Angeles, CA, USA.
10
Greater Los Angeles VA Healthcare System, Los Angeles, CA,
USA.
11
Institute for Precision Health, David Geffen School of Medicine at UCLA, Los Angeles, CA, USA.
12
Center for
Human Nutrition, David Geffen School of Medicine at UCLA, Los Angeles, CA, USA.
13
These authors contributed
equally: Chih-Chiang Chang and Zi-Yu Huang
*
email: Thsiai@mednet.ucla.edu
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however, it is operator-dependent and resolution is limited
9
,
10
. Thus, there remains an unmet clinical need to
develop a cost-effective and portable method for early and operator-independent detection of fatty liver disease.
We have previously established the theoretical and experimental basis of electrical impedance tomography
(EIT) for measuring liver fat content in the New Zealand White Rabbit model of fatty liver
disease
11
. By virtue
of tissue-specific electrical conductivity, fatty infiltrate in the liver is characterized by its frequency-dependent
electrical impedance (Z) in response to applied alternating current (AC)
11
. At low frequencies, the lipid-bilayers
impede the current flow, resulting in high conductivity, whereas, at high frequency, the bilayers serve as imperfect
capacitors, resulting in tissue- and fluid-dependent impedance. This impedimetric property provides the basis
for applying the multi-electrode array to measure tissue-specific conductivity, morphology, and
volume
12
–
15
.For
this reason, a body of literature has demonstrated brain EIT for functional studies, cardiac EIT for stroke volume,
and transthoracic impedance pneumography for respiratory
ventilation
16
–
19
.
In this context, we applied a portable multi-electrode belt to perform pairwise injection of alternating current
(AC) to the liver in the upper abdomen, and we recorded the corresponding surface voltage to reconstruct the
conductivity distribution for liver EIT
11
. Specifically, we performed EIT voltage measurements by injecting elec-
trical currents from 1–4 mA at 50 and 250 kHz. The current penetrated the abdomen to varying depths, and the
resulting surface voltage was acquired by the multi-electrode array. Due to the varying free ion content, muscle
and blood are more conductive than fat, bone, or lung
tissue
12
,
20
. Fat-free tissue such as skeletal muscle carries
high water (~
73%), ions and proteins content, allowing for efficient electrical conductivity (S·m
−1
), whereas
fat-infiltrated tissue such as fatty liver is anhydrous (steatosis)
21
, resulting in a reduction in
conductivity
22
. This
impedimetric property provides the basis to apply a liver EIT for the identification of fatty liver infiltrate. Unlike
EIT for cardiopulmonary function focusing on the differential
conductivity
12
–
19
, we solved the non-linear prob-
lem to reconstruct the absolute liver conductivity.
As a pilot study, we recruited overweight subjects (BMI
> 25) to undergo liver 3 T MRI scans, followed by the
portable EIT belt measurements. MRIs were acquired to provide the a priori knowledge of the liver boundary
condition to solve the inverse problem for EIT reconstruction. We further compared and validated the subject-
specific EIT conductivity with the liver MRI proton-density fat fraction (PDFF) as a reference standard for fatty
liver
infiltrate
23
. Next, we performed Pearson’s correlation analyses between the liver EIT or MRI PDFF with
different parameters, including BMI (kg·m
−2
), age (years), waist circumference (cm), height (cm), and weight
(kg). Following Bonferroni correction for multi-testing, correlation analyses revealed that neither EIT conduc
-
tivity (S·m
−1
) nor MRI PDFF was correlated with these variables; but the liver EIT conductivity was inversely
correlated with MRI PDFF. This inverse correlation holds promises for developing non-invasive and portable
liver EIT for early detection of fatty liver content in the overweight individuals.
Results
Schematic workflow to compare and validate EIT reconstruction with MRI.
The subject recruit-
ment complied with the guidelines of the UCLA Human Subjects Protection Committee, as described in the
method section. The workflow and schematic setup (Fig.
1
) depicted the individual subjects undergoing the liver
MRI scans and MRI multi-echo imaging to acquire the PDFF, followed by the EIT measurements and recon-
structions. The average liver MRI PDFF and the absolute EIT conductivity were quantified for the correlation
analyses.
Comparison between MRI multi‑echo imaging and EIT images.
Liver MRI images provide the a
priori geometric knowledge to reconstruct 2-D EIT images. This information includes the boundary conditions
Figure 1.
Schematic workflow of the comparison and validation of the MRI and EIT. Volunteers were
recruited in line with the UCLA Institutional Human Subjects Protection Committee. Multi-echo MRI scans
were performed to provide the liver anatomy and proton density fat fraction (PDFF), followed by the EIT
measurements. Finally, the EIT conductivity maps were reconstructed and the MRI PDFF was used to quantify
fatty liver infiltrate and to compare with EIT liver conductivity.
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for: (1) the abdominal cross-section, (2) the peripheral tissues consisting of the skin, subcutaneous fat, and
the ribs, and (3) the liver in the upper abdomen. For each subject, EIT liver conductivity and MRI PDFF were
compared with the corresponding BMI value (Table
1
). Furthermore, the representative abdomen MRI images
for liver anatomy and PDFF, liver segmentation (annotation), and liver EIT conductivity distribution (S·m
−1
)
were compared (Fig.
2
). There was no significant correlation between the MRI PDFF and BMI or liver EIT and
BMI. Subject 17 with a relatively lower BMI (BMI
= 27.1 kg·
m
−2
, PDFF = 6.2%, EIT = 0.3243 S·m
−1
) had a higher
MRI PDFF than that of Subject 3 with a much higher BMI (BMI
= 39.0 kg·m
−2
, PDFF = 3.82%, EIT = 0.3296
S·m
−1
). However, subject 11 with a low BMI value (BMI
= 27.9 kg·m
−2
, MRI PDFF = 3.62%, EIT = 0.3473 S·m
−1
)
had a lower MRI PDFF than that of Subject 10 with a higher BMI (BMI
= 34.3 kg·m
−2
, MRI PDFF = 16.44%,
EIT = 0.3007 S·m
−1
). Furthermore, despite similar BMI (27.1 kg·
m
−2
vs. 27.9 kg·m
−2
), the MRI PDFF of Subject
17 was around two times higher than that of Subject 11 (6.20 vs. 3.62%). Notably, the MRI PDFF for Subject 10
(BMI = 34.3 kg·m
−2
) was 4 times higher than that of Subject 3 (BMI
= 39.0 kg
m
−2
). These inconsistent relations
support the notion that BMI is an inaccurate index to predict the levels of fatty liver infiltrate in the overweight
individuals.
EIT conductivity versus MRI PDFF.
Using the MRI PDFF and EIT conductivity data from Table
1
, we
performed Pearson’s correlation analyses to determine if the BMI correlates with MRI PDFF or EIT conductivity.
We observed that the correlation between BMI and MRI PDFF (
R
= − 0.037,
p
= 0.89, n = 16) or between BMI
and EIT (
R
= −0.19,
p
= 0.47, n
= 16) was statistically insignificant (Fig.
3
A-B). However, the confidence interval
plot revealed inverse correlation between EIT and MRI PDFF (
R
= −0.69,
p
= 0.003, n = 16) (Fig.
3
C). This finding
supports the use of EIT conductivity as an index for non-invasive detection of liver fatty infiltrate.
Correlation analyses with the demographic and anthropometric parameters, MRI PDFF, and
EIT conductivity.
To identify fatty liver infiltrate in the enrolled subjects (BMI
> 25), we performed indi-
vidual correlation analyses with waist circumference, height, and weight (Table
2
). We compared the correlation
coefficients between MRI PDFF and demographic as well as anthropometric parameters in 16 subjects (Fig.
4
).
Following the Bonferroni correction for multi-testing, the correlations with age (
R
= −0.13,
p
= 0.64, n = 16), waist
circumference (
R
= −0.23,
p
= 0.4, n = 16), height (
R
= −0.59,
p
= 0.016, n = 16) and weight (
R
= −0.41,
p
= 0.12,
n = 16) were statistically insignificant when multiple testing was considered, albeit height was significant at the
nominal cut off of 0.05. We further compared the correlation coefficients between liver EIT and demographic
and anthropometric parameters in 16 subjects (Fig.
5
). The correlation with age (
R
= −0.1,
p
= 0.71, n = 16), waist
circumference (
R
= −0.05,
p
= 0.85, n = 16), height (
R
= 0.63,
p
= 0.0092, n = 16) and weight (
R
= 0.19,
p
= 0.47,
n = 16) were statistically insignificant when multiple testing was considered, and again height is nominally sig-
nificant. Thus, these analyses corroborate that BMI and other parameters were not correlated with liver fat infil-
trate in our overweight subjects.
Table 1.
BMI (Kg·m
−2
), MRI PDFF (%), EIT liver conductivity (S·m
−1
) and injection current of all subjects.
(Subject 4: electrode malfunction, Subject 14: renal failure, Subject 18: leukemia, * asterisk).
Subjects
BMI(Kg·m
−2
)
EIT (S·m
−1
)
MRI PDFF (%)
Injection current (mA)
1
34.4
0.3518 ± 0.0192
2.14
1
2
49.7
0.3290 ± 0.0122
4.05
1
3
39.0
0.3296 ± 0.0130
3.82
2
4*
33.0
0.3819 ± 0.0224
27.89
3
5
30.6
0.3377 ± 0.0211
10.51
2
6
36.3
0.3444 ± 0.0322
4.14
2
7
29.3
0.3280 ± 0.0288
2.41
3
8
37.8
0.3405 ± 0.0134
2.25
2
9
32.0
0.3381 ± 0.0170
6.53
2
10
34.3
0.3007 ± 0.0167
16.44
2
11
27.9
0.3473 ± 0.0168
3.62
2
12
46.8
0.3307 ± 0.0113
5.14
2
13
38.9
0.3305 ± 0.0160
3.31
3
14*
25.5
0.3010 ± 0.0160
2.11
2
15
33.7
0.3306 ± 0.0127
10.78
2
16
27.4
0.3407 ± 0.0267
1.08
3
17
27.1
0.3243 ± 0.0125
6.20
3
18*
46.9
0.3455 ± 0.0149
18.56
2
19
29.8
0.3507 ± 0.0189
2.29
2
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Discussion
Non-invasive and cost-effective monitoring of fatty liver disease remains an unmet clinical need for the early
identification of cardiometabolic disorders. While liver biopsy has been performed to demonstrate non-alcoholic
fatty liver disease (NAFLD), the risk of bleeding and sampling errors limit its broad application to the general
population. While liver MRI is considered the non-invasive reference standard, it is costly and particularly inac
-
cessible for underserved populations. We hereby demonstrated liver EIT as a non-invasive and portable detection
method for operator-independent and cost-effective detection of liver content. Our pilot study recruited 19 adults
with BMI > 25 kg·m
−2
to undergo liver MRI scans. We performed the individual liver EIT measurements with the
portable multi-electrode array, and we used the MRI-acquired a priori knowledge of the liver anatomy to solve
the inverse problem for EIT reconstruction. We performed correlation analyses on liver EIT vs. MRI PDFF in
relation to the individual
demographics
24
. To our best knowledge, we have established a statistically significant
correlation between liver EIT and MRI PDFF.
EIT has been applied to clinical medicine over the past two decades. Diagnostic EIT was developed for pulmo-
nary function and lung
capacity
22
. For instance, transthoracic impedance pneumography has been demonstrated
to assess lung
capacity
17
,
25
, and EIT was used to measure myocardial motion and blood volume for cardiac output
(CO)
26
,
27
. EIT has also been applied for assessing conductivity in breast and brain
tissues
16
. Using the multi-
electrode configuration, we obtained voltage from the abdominal surface following by injection of AC current
to reconstruct the EIT conductivity distribution of the liver. However, solving the nonlinear forward and inverse
models for reconstructing EIT remains a computational
challenge
28
–
34
as they are often ill-posed problems with
solution existence, uniqueness, and instability
issues
33
. The non-linear inverse model for EIT reconstruction
requires a priori knowledge of the anatomic boundaries to enhance the spatial resolution for establishing the
absolute conductivity
value
35
. To improve the EIT reconstruction, investigators have integrated EIT with other
Figure 2.
Representative MRI multi-echo and EIT images. Four representative subjects with different BMI
values (Kg· m
−2
) were compared with MRI PDFF (%) and EIT conductivity (S·m
−1
), respectively. The transverse
MRI views demarcate the liver anatomy, the fat fractions provide the corresponding MRI PDFF, annotation
reveals the liver boundary condition following image segmentation, and 2-D EIT images unveil the abdomen
conductivity distribution and average liver conductivity. The subject 17 with a BMI of 27.1 kg·m
−2
developed
a relatively high MRI PDFF (6.2%) and a low EIT liver conductivity (0.3243 S·m
−1
); whereas the subject 3 with
BMI of 39 kg·m
−2
developed a relatively low MRI PDFF (3.82%) and high EIT liver conductivity (0.3296 S·m
−1
).
However, subject 11 with a BMI of 27.9 kg·m
−2
developed a relatively low MRI PDFF (3.62%) in association
with a relatively high EIT liver conductivity (0.3473 S·m
−1
), and the subject 10 with a BMI of 34.3 kg·m
−2
also developed a relatively high MRI PDFF (16.44%) in association with a low EIT liver conductivity (0.3007
S·m
−1
). These initial comparisons suggest inconsistent correlations between BMI and MRI PDFF and EIT liver
conductivity. Scale bar: 8 cm.
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imaging modalities, including co-registration with
MRI
36
–
38
and introduction of ultrasonic vibration to the target
tissue in the presence of the magnetic field. This integration could generate inductive currents within the liver
to enhance spatial resolution, thus, obviating the need for a priori knowledge of the liver geometry and position
in the abdomen for EIT
reconstruction
39
.
Figure 3.
Statistical analyses of BMI vs. MRI PDFF and vs. EIT liver conductivity. (
A
) BMI values are not
significantly correlated with MRI PDFF (Pearson correlation coefficient
R
= − 0.037,
p
= 0.89, n = 16). (
B
). BMI
values were also not significantly correlated with EIT liver conductivity values (
R
=−0.19,
p
= 0.47, n = 16). (
C
)
EIT liver conductivity values were negatively correlated with MRI PDFF (R
= −0.69,
p
= 0,003, n = 16). The
shaded areas reflect the 95% confidence intervals of the linear slope.
Table 2.
Demographics of overweight subjects. The demographics of 19 subjects, including sex, BMI, age,
waist circumference, height, and weight, are demonstrated. (Subject 4: electrode malfunction, Subject 14: renal
failure, Subject 18: leukemia, * asterisk).
Subjects
Sex
BMI(Kg·m
−2
)
Age (year)
Waist Circumference (cm)
Height (cm)
Weight (kg)
1
M
34.4
41
116
175
105.2
2
F
49.7
67
131
158.5
124.7
3
F
39.0
63
123.5
160
99.8
4*
F
33.0
35
116.5
168.9
94.1
5
F
30.6
61
92.5
155.5
73.9
6
F
36.3
27
103.5
163.5
97.2
7
F
29.3
42
91
155
70.3
8
F
37.8
60
115.5
174
114.5
9
F
32.0
36
113
170
92.5
10
F
34.3
36
101.5
152
79.2
11
M
27.9
47
95
178
88.5
12
F
46.8
39
130
160
119.8
13
F
38.9
48
114
168
109.9
14*
F
25.5
74
96
163.5
68.2
15
F
33.7
26
95
153
78.9
16
F
27.4
33
93.5
170.5
79.8
17
M
27.1
47
103
178
85.7
18*
M
46.9
57
141.5
177.5
147.7
19
F
29.8
30
102
180.3
96.9
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Alternative approaches have been applied to solve the ill-posed inverse problem for EIT reconstruction.
For instance, particle swarm optimization (PSO) was applied to solve EIT as a paradigm shift from the con-
ventional Gauss–Newton methods for rapid convergence with high spatial
resolution
40
,
41
. Recently, convolu-
tional neural networks (CNN) have also been applied to solve the non-linearity of the inverse problem for EIT
reconstruction
42
,
43
. Hamilton et al. obtained the absolute EIT images by combining the D-bar method with
subsequent processing using the CNN technique for sharpening the EIT
reconstruction
42
. Li et al. utilized deep
neural networks (DNN) to directly obtain a nonlinear relationship between the one-dimensional boundary volt
-
age and the internal conductivity
43
. The accuracy of EIT reconstruction may be improved by employing multiple
levels of the electrode arrays to circumferentially wrap around the upper abdomen. This multi-level electrode
array would enable current injection and voltage recording from the entire liver for 3-D EIT reconstruction.
As a corollary, we compared the liver anatomy with MRI PDFF from a representative 3-D rendering (Fig
S1A-B). The 3-D EIT conductivity distribution was reconstructed with the aid of the MRI multi-echo sequence
acquired a priori knowledge (Fig S1C). The high-fat region in the MRI PDFF (red dashed box) was also detected
by the EIT with the reduced conductivity. The 3-D EIT conductivity distribution reveals the inhomogeneous
fat distribution as supported by the MRI 3-D rendering images (Fig S1C). With additional scanning along the
z-direction, a precise conductivity distribution could be achieved to reveal the details of the heterogeneous fat
distribution.
While MRI images provided the a priori knowledge to solve the ill-posed inverse problem for EIT reconstruc-
tion, alternative methods to provide the boundary conditions would allow for low-cost liver EIT screening for the
underserved populations. The previous studies have proposed the sensors to integrate the detection of the EIT
signals with stretch or acceleration to reconstruct the anatomical contour of the upper
abdomen
44
–
47
. Khor et al
.
have demonstrated the wearable sensors integrating with strain gauge and EIT electrodes for measuring ana-
tomical contour needed to monitor the neonatal lung
function
45
. de Gelidi et al
.
integrated the accelerometer to
detect the dorsal shape with EIT sensors for improving lung function
monitoring
46
. Moreover, Darma et al
.
have
combined EIT sensors with flexible stretch sensors to measure the contour of the arm for EIT
reconstruction
47
.
These proposed sensors have the capacity to acquire the change in resistance and to extract the curvature from
Figure 4.
MRI PDFF vs. age, waist, height, and weight. The Pearson correlation coefficients (
R
) and
p
values
were analyzed for (A) age, (B) waist circumference, (C) height, and (D) weight. The circles denote female
subjects and triangles denote male subjects. The 95% confidence intervals of the linear slopes are illustrated as
shaded area.
R
values are −0.13 for age (
p
= 0.64, n
= 16), −0.23 for waist circumference (
p
= 0.4, n = 16), −0.59 for
height (
p
= 0.016, n
= 16)., and −0.41 for weight (
p
= 0.12, n
= 16), demonstrating low to intermediate correlation
with MRI PDFF.
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each sensor based on the pre-established curvature-resistance relation. Thus, these studies provided the poten
-
tial solutions for simultaneously acquiring both abdominal contours and voltage signals for EIT constructions.
A potential alternative method which is still under investigation to acquire the peripheral boundary is fre
-
quency-differential electrical impedance tomography (fdEIT). fdEIT has been proposed to address technical
difficulties encountered by unknown boundary geometry and uncertainty in electrode positions from a con-
ventional EIT imaging
method
48
. fdEIT allows for reconstructing various tissue conductivity by injecting cur
-
rent at two distinct frequencies to the abdomen, followed by acquiring the resulting surface-voltage. Sun et al
.
have applied fdEIT to reconstruct the conductivity distribution of calf muscle in response to stimulation. Their
reconstruction images illustrated the potential feasibility of distinguishing the boundary between the muscle and
subcutaneous fat in human
calf
49
. In addition, Menden et al
.
have recently proposed a reconstruction algorithm
for frequency-differential EIT using absolute
values
50
. The preliminary result demonstrated the potential for
differentiating organ and spine boundaries. Moreover, Yao et al
.
have demonstrated the detection of multicom
-
ponent distribution through
fdEIT
51
. Hence, accurately selecting the two frequencies would have potential to
acquire the peripheral boundary and differentiate the fatty from the non-fatty tissues by virtue of tissue-specific
electrical properties (Table S1)
48
–
50
. As a result, the peripheral layer can be used as the a priori knowledge to solve
the inverse problem for EIT reconstruction, thus, obviating the need for MRI. Furthermore, establishing an atlas
of external liver MRI images and an anthropometric database would help calibrate the boundary conditions of
the liver to improve EIT reconstruction.
Our liver EIT results further reveal the effect of fluid accumulation on the liver EIT conductivity. If we
included two subjects with electrolytes abnormities (leukemia and renal failure), the correlation value between
EIT and MRI PDFF was decreased from R
= −0.69 (p
= 0.003, n
= 16) to R
= −0.21 (p
= 0.4, n
= 18) (Fig S2A). If
we further excluded the two subjects with anemia, the correlation improved from R
= −0.69 (p
= 0,003, n
= 16)
to R
= −0.70 (p
= 0.0049, n
= 14) (Fig S2B). In this case, the pre-existing medical conditions, including leukemia,
renal failure, and anemia, disrupted the impedimetric property of liver, resulting in altered EIT conductivity.
In summary, we enrolled overweight subjects to undergo MRI scans and liver EIT measurements to recon-
struct the EIT conductivity distribution. We demonstrated that the increase in liver EIT conductivity is correlated
with a decrease in MRI PDFF. As a corollary, the 3-D EIT conductivity map revealed the heterogeneous distribu-
tion of fatty gradient as evidenced by the 3-D MRI PDFF. Our correlation analyses supported that subject-specific
Figure 5.
EIT liver conductivity vs. age, waist, height, and weight. The
R
values for age (R
=−0.1,
p
= 0.71,
n = 16), waist circumference (R =−0.05,
p
= 0.85, n = 16), height (R =0.63,
p
= 0.0092, n = 16) and weight (R = 0.19,
p
= 0.47, n
= 16) demonstrate low to intermediate correlation with EIT conductivity.
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EIT offers a non-invasive and portable method for the operator-independent and cost-effective detection of
hepatic fat infiltrate in the overweight populations.
Methods
Study design.
The recruitment of human subjects was conducted at the UCLA Center for Human Nutrition
in compliance with the UCLA Human Subjects Protection Committee. The study protocol (#15–001,756) was
approved by the UCLA Internal Review Board. All subjects provided written informed consent before participat-
ing in research procedures. All experiments were performed in accordance with relevant named guidelines and
regulations. We enrolled a total of 19 volunteers including, 15 females and 4 males, from 27 to 74 years old with
a waist circumference from 91 cm to 141.5 cm and body mass index (BMI) defined as body mass divided by the
square of the body height from 25.5 to 46.8 kg/m
2
(Fig.
1
). Inclusion criteria for all subjects included the ability
to travel for phlebotomy for whole blood collection, no prescription or over-the-counter medications for weight
loss, and absence of alcohol consumption, no weight change
> 5 pounds in the previous 3 months, overweight
with BMI > 25, and waist circumference > 40
′′
for men or
> 35
′′
for women. All subjects must be able to follow
instructions and to consent. Exclusion criteria for all subjects included coronary artery disease on medications,
claustrophobia, previous liver cancer, liver surgery, alcoholism (DSM-5 criteria: alcohol abuse or dependence),
metallic implants or other factors hazardous to the MRI scanner as per the MRI safety guidelines, and body
weight
> 300 pounds (weight and size restrictions for undergoing MRI). Note that an MRI scan was performed
to establish PDFF for quantifying fatty infiltrates in the liver. Clinical demographic and physical characteristics
of human subjects were collected in terms of gender, BMI (kg·m
−2
), age (years), waist circumference (cm), height
(cm), and weight (kg) (Table
2
). Following enrollment and consent, the subjects underwent a 30-min liver MRI
scan, including multi-echo imaging for mapping the proton density fat fraction (PDFF) (Fig.
6
). Next, EIT
measurement was acquired by placing 32 electrodes to the upper abdominal region, as indicated by the fiduciary
markers immediately following the MRI scan (Fig.
6
A). A pair of electrodes was used to inject the AC current
to the abdomen, and the electrode array was used to record voltage by the pairwise algorithm (Fig.
6
B). Liver
MRI provided the a priori knowledge of the boundary conditions needed for the EIT conductivity map recon-
struction and PDFF (Fig.
6
C-D). EIT conductivity map was reconstructed to distinguish the liver conductivity
Figure 6.
Schematic of EIT measurement, reconstruction, and 2-D representation. (
A
) Schematic illustrates
circumferential electrode placement around the abdomen for pairwise voltage measurements. The fiducial
markers indicate the anatomic level at which the multi-electrode array was circumferentially positioned for
liver EIT measurements. (
B
) Thirty-two electrodes were adhered to the abdomen, as indicated by the fiducial
markers. The recorded voltage signals were input to a signal adaptor and the data acquisition channels for
EIT measurements. (
C
) A representative MRI multi-echo image demarcates the boundary conditions for the
abdomen, liver, stomach, and spleen. S1: Stomach, S2: Spleen, S3: Spine. (
D
) A representative PDFF map is
compared with the corresponding EIT image. (
E
) A representative 2-D EIT image reveals the conductivity
distribution. Scale bar: 8 cm.
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gradient from other tissues or organs (Fig.
6
E). Finally, subject-specific EIT (conductivity map) was compared
with the corresponding MRI PDFF (Fig.
6
E).
Determination of Liver MRI proton‑density fat fraction PDFF.
Non-contrast-enhanced abdominal
MRI scans were performed on a 3-Tesla system (Skyra or Prisma, Siemens, Erlangen, Germany) using a body
array and a spine array coils. The protocol included breath-held anatomical scouts, a breath-held
T
2
-weighted
2-D multi-slice half-Fourier single-shot turbo spin-echo (HASTE) sequence, and a breath-held 3-D multi-
echo gradient-echo sequence (TE
= 1.23, 2.46, 3.69, 4.92, 6.15, 7.38 ms; TR
= 8.94 ms, flip angle
= 4 deg, typi-
cal field of view = 400 × 350 × 256
mm
3
, typical matrix size = 192 × 168 × 64, parallel imaging factor = 4, typical
scan time
= 19 s) to quantify PDFF. Scanner software (LiverLab, Siemens, Erlangen, Germany), which utilized a
multi-peak fat spectral model with single
R
2
* for multi-step signal fitting, was used to calculate
PDFF
52
. The MRI
images and PDFF maps were saved in DICOM format and downloaded from the scanner for analysis.
To ensure alignment of the subsequent EIT slice position to a corresponding mid-liver MRI slice, we affixed
two to three MRI-visible fiducial markers (MR-SPOT 122, Beekley Medical, Bristol, CT) to the skin above the
expected mid-liver region prior to performing the MRI scan (Fig.
6
A). The positioning of the fiducial markers
was examined on the anatomical scouts. If needed, the MRI technologist would re-position the fiducial markers
on the subject’s abdomen and re-acquire the scouts. At least one adjustment would be required, and this entire
alignment required less than 3 min.
The echo 1 (TE
= 1.23) magnitude images from the 3-D multi-echo gradient-echo sequence were used for
contouring the body and the liver to create a 3-D anatomy model. An axial slice in the MRI PDFF maps that
contained MRI-visible fiducial markers was selected for analysis. Five circular regions of interest (ROIs) with an
area of 5
mm
2
were delineated in the slice with fiducial markers by a trained researcher to avoid blood vessels,
bile ducts, and imaging artifacts, and at least 1–2 cm away from the liver capsule. The mean PDFF from the ROIs
(0–100%) was reported for each subject.
Theoretical Framework for EIT reconstruction (EIDORS).
The EIT imaging reconstruction was
implemented as previously
described
11
. Following the injection of a known current to the abdomen, an EIT
conductivity map across the abdomen was reconstructed with a set of voltages recorded by an electrode array
placed on the surface of the upper abdomen (see Fig S3)
7
. With a priori knowledge of the target object (liver), the
geometric boundary conditions were established with a high degree of precision to mitigate instability inherent
from the ill-posed EIT inverse
problem
53
(Fig.
6
D), and the solution was obtained by using a regularized Gauss–
Newton (GN) type solver(Fig. S3).
The Gauss–Newton (GN) type solver calculates the conductivity by minimizing
∅
, the L2 norm (the square
root of the sum of the squares of the values) of the difference between the measured voltage
V
o
,
and a function
of the conductivity
f
(σ)
:
where
f
(σ)
is considered to be the "forward problem" derived from the Laplace equations:
By taking the first-order Taylor series expansion of
∅
:
where
σ
0
is a reference conductivity value, and
J
is the Jacobian matrix of our inverse problem.
By setting
∂
∅
∂
σ
=
0
, we minimized
∅
and obtained
σ
as follows:
Equation (
4
) is an unconstrained GN form of the inverse problem. Due to the ill-posed nature of the EIT
inverse problem, achieving a converged solution from this unconstrained GN form is challenging. The solu-
tion
σ
is highly sensitive to perturbations in voltage (
V
) measurement, which means a small noise in
V
leads
to instability in the final solution. A general method to mitigate the issue is to introduce a constraint term that
sways the solution towards the preferred solution:
To balance the tradeoff between fitting the error and constraining the solution from the undesired proper
-
ties, we incorporated a constraint term,
‖
Ŵσ
‖
2
,
to the objective function and the resulted form is commonly
known as the Tikhonov Regularization. The coefficient,
, is the regularization parameter that suppresses the
conductivity spikes in the solution space.
With a priori conductivity within a similar area, the term,
Ŵ
, was introduced as a “weighted” Laplacian opera-
tor that enables us to adjust more properties of the conductivity and suppress the non-smooth regions. Akin to
the present work, this strategy is useful in medical imaging, where a priori anatomic information of individual
organs was obtained from MRI multi-echo sequence and integrated with the EIT solutions. By applying the
regulation term to Eq. (
2
), we generated the solution as follows:
(1)
∅=�
V
o
−
f
(σ)
�
(2)
∇·
(
−
σ
∇
V
)
=
0
(3)
∅=�
V
o
−
f
(σ)
�
∼
=
�
(
V
o
−
f
(
σ
0
)
)
−
J
(σ
−
σ
0
)
�
(4)
σ
=
σ
0
+
(
J
T
J
)
−
1
J
T
(
V
o
−
f
(
σ
0
)
)
(5)
∅
2
=�
ε
�
2
+
�
Ŵσ
�
2