3
-
Dimensional Electrical Impedance Spectroscopy for
in situ
Endoluminal Mapping of
Metabolically Active Plaques
Parinaz Abiri*
1,2
, Yuan Luo*
3,4,
, Zi
-
Yu Huang*
4
, Qing
yu Cui*
2
, Sandra
Duarte
-
Vogel
5
, Mehrdad
Roustaei
1
, Chih
-
Chiang Chang
1
, Xiao
Xiao
1
, Rene packard
2
, Susana Cavallero
2
, Ramin
Ebrahimi
2
, Peyman Benharash
6
, Jun Chen
1
, Yu
-
Chong Tai
4
, Tzung K. Hsiai
1,2,4†
Affiliations:
1
Department of Bioengineering, University of California, Los Angeles, Los Angeles, CA 90095
2
Division of Cardiology, Department of Medicine, David Geffen School of Medicine,
University of California, Los Angeles, Los Angeles, CA 90095
3
State Key Laborato
ry of Transducer Technology, Shanghai Institute of Microsystem and
Information Technology, Chinese Academy of Sciences, Shanghai, 200050, China; and Center
of Materials Science and Optoelectronics Engineering, University of Chinese Academy of
Sciences, Bei
jing, 100049 China
4
Department of Medical Engineering, California Institute of Technology, Pasadena, CA 91125
5
Division of Laboratory Animal Medicine, University of California, Los Angeles, Los Angeles,
CA 90095
6
Division of Cardiac Surgery, Department
of Surgery, David Geffen School of Medicine,
University of California, Los Angeles, Los Angeles, CA 90095
*
These authors contributed equally to this work.
†
Corresponding Author: THsiai@mednet.ucla.edu.
Supplementary Materials:
List of
contents:
S
I
-
1. Partial ligation of carotid arteries in Yucatan mini
-
pigs
SI
-
2
. Deviation between the computational and experimental impedance
SI
-
3
. Comparison of impedance measurement with the computational model
SI
-
4
. Comparison of impedance measurement
before and after electroplating
SI
-
5
. Reconstruction of conductivity mapping from the impedance data
SI
-
6
. Histology
-
based 3
-
D FEM modeling
SI
-
1.
Partial ligation of carotid arteries in Yucatan mini
-
pigs
All animals were fed on a high
-
fat diet containing 4% cholesterol, 20% saturated fat, and 1.5%
supplemental choline (Test Diet; Purina, St. Louis, MO) for 2 weeks before surgical ligation of the
right carotid arteries. The pigs were anesthetized with intra
muscular Tiletamine and Zolazepam,
and Isoflurane was given to maintain general anesthesia during the procedure. A 6F introducer
sheath was inserted percutaneously via the Seldinger procedure into the right or left femoral artery
to monitor blood pressure
and to provide access for angiography. Bupivacaine was subcutaneously
injected in the ventral neck along the path of the incision site. A midline skin incision was placed
at the neck. Both right and left common carotid arteries were dissected approximately
5 cm in
length, but the right common carotid artery was tied off with a suture (Ethicon, Cornelia, Ga)
around a spacer (approximately 1.3 mm in diameter) positioned on the external surface of the
artery. The spacer was subsequently pulled out, leaving a 5
0
-
70% stenosis. Postoperative CT
angiography was performed to monitor the degree of surgical stenosis.
To deploy the microelectrode array for 3
-
D EIS measurement, the animals were
anesthetized as described above (
SI
-
1
). Bupivacaine was subcutaneously inje
cted in the ventral
neck along the path of the incision site. A midline skin incision was placed at the neck. The
common carotid arteries were dissected and a surgical cut
-
down was performed to directly
introduce the sheath and device into the carotid
arte
ry at the site of stenosis in the right carotid artery
and at the approximate mirror location in the left
carotid artery.
Supplementary Figure for
Movat staining.
Fig.
SI
-
1
.
Histological Mapping of Carotid Arteries
.
(A)
The 3
-
D histological reconstruction recapitulates the
endoluminal topology from 11 cross
-
sections of a
segment (4 mm) of carotid arteries. (B) The
representative Movat staining for connective tissue was
compared between the left and right carotid arteries.
I:
tunica intima; M: tunica media; E: tunica externa.
SI
-
2
. Deviation between the computational and experimental impedance
From each electrode position
(z, θ)
, we
calculated the summation of the square of the differences
between the experimental and sim
ulated EIS from the same pair of electrodes. The electrode
position resulting the largest reciprocal of the deviation, which is the square root of the summation,
is defined as the best fit scenario. The best fit electrode positions are circled in green in
the 3
-
D
deviation plots
(
Fig. SI
-
2
)
.
Fig. SI
-
2
: Deviation plots
. Total 36 electrode placements were tested in the simulation models. The
deviations between the simulated impedance and experimental impedance at 10 kHz were calculated and
the best fit
scenario of electrode position is highlighted in the green circle.
SI
-
3
. Comparison
between EIS
impedance measurement with the
finite element
model
From each carotid artery sample, we created a 3
-
D model and scanned through possible electrode
positions with a different combination of
푧
and
휃
. 15
-
permutation impedance values were
calculated for each combination, and computational EIS profiles were co
mpared with the measured
EIS to identify the best fit scenarios. Scatter plots of the 15
-
permutation impedance from the
measured EIS and representative computation model (simulation) are presented with the best fit
combination of
푧
and
휃
as highlighted i
n light blue (
Fig. SI
-
3
)
.
Fig. SI
-
3
: Computation Models
. Comparisons with the simplified 3
-
D schematic indicate the position of
the electrodes in the endolumen
where the computational impedance values are overlapping with the
experimental EIS. Experimental impedance at 10 kHz is plotted alongside the modeling results at the given
z and θ values, and the combination with the best fit was highlighted. Computationa
l EIS are compared
among (A)
LCA
, (B) RC
A
1, (C) RC
A
2 position A, and (D) RC
A
2 position B.
SI
-
4
. Comparison of impedance measurement before and after electroplating
The flexible electrodes (either b
efore or after electroplating) we
re submerged in a large
container
of saline solution (0
.9% wt NaCl).
The g
eometric effect wa
s considered negligible
under these
settings. The impedance spectra were measured using Gamry G 300 with 50 mV
,
and
the
frequency
range
d from
100 Hz
to
300
kHz. The electroplating of Pt Black
resulted in a
low c
ontac
t impedance
for the electrodes, as evidenced by the
significantly flattening
in the EIS curve beyond 1
kHz.
T
herefore,
we
validat
ed the
selection
of
10 kHz
for
the
EIS analyse
s
and computational m
odeling.
Fig
.
SI
-
4
:
E
lectrochemical impedance spectra
.
A comparison
between before and after electroplating
demonstrated
a significant
decrease
in
contact impedance.
SI
-
5
. Reconstruction of conductivity mapping from the impedance data
Our
computational
model was composed of
t
h
e arterial wall
that
was
represented by 576 elements
(
Figure SI
-
5Bi
)
,
and the annular collagen layer by
288 elements
(
Figure SI
-
5Bii
). The initial
conductivities of arterial wall elements were derived from the EIS measurements. The
collagen
layer was assigned
with
a large element size
and
a uniform conductivity
.
We
var
i
ed
t
he
conductivity distribution to a direction that
optimally
reproduce
d
the
15 permutations for the
impedance measurement
s
. To this end, we used
the “
genetic
algorithm
”
so that
all elements
“evolve
d
” to reach the final mapping results. The implementation was as follows: the conductivity
value from each of the 864 elements was considered as an 864×1 vector. We generated a solution
candidate pool (100) by adding
a Gaussian
-
distributed noise to this initial 864×1 vector,
퐶
⃑
1
,
퐶
⃑
2
,
...
퐶
⃑
100
. For each candidate, we calculated the 15 impedance values by solving the Laplace
equation:
푍
12
,
sim
,
푍
13
,
sim
,
푍
14
,
sim
,
...
푍
56
,
sim
(1)
We defined our fitness function as
follows:
푓
=
√
(
푍
12
,
measured
−
푍
12
,
sim
)
2
+
(
푍
13
,
measured
−
푍
13
,
sim
)
2
+
⋯
(
푍
56
,
measured
−
푍
56
,
sim
)
2
(2)
The
“
genetic algorithm
”
was implemented by the following steps:
i.
Calculate the fitness function for all of the solution candidates in the pool
.
ii.
Rank the
candidates according to their fitness function from small to large values
.
iii.
Identify the top
-
10 candidates from the pool:
퐶
⃑
1
∗
,
퐶
⃑
2
∗
,
...
퐶
⃑
10
∗
.
iv.
Generate a new pool of 90 candidates as follows:
퐶
⃑
푖
∗
=
∑
(
휎
휆
푘
퐶
⃑
푘
∗
+
(
1
−
휎
)
10
푘
=
1
휆
푘
∑
퐶
⃑
푘
∗
10
1
10
)
,
푖
=
11
,
12
,
...
100
,
(3)
where
휎
=
1
.
3
is a factor to moderate the boundaries of the candidate space obtained from the
above equation, and
∑
휆
푘
10
1
=
1
(
50
)
.
Steps i
-
iv were repeated until the minimum fitness function reaches the predefined target,
and the solution candidate
퐶
⃑
1
푓푖푛푎푙
was used to assign
to
the conductivity dist
ribution to generate
the final
EIT mapping
(see
Figure
4
).
We excluded the outmost layer as the calculated conductivity
distribution was fairly homogeneous
since
the major heterogeneity resided in the inner layer (576
elements).
Fig
.
SI
-
5
: Finite element model for reconstructing
the
conductivity maps.
(A) The configuration of the
6
-
point electrodes (EIS sensor) generates 15 permutations. (B
-
i) 576
-
element mapping scheme represents
the inner smooth muscle layer. (B
-
ii) 864
-
element mapping s
cheme
includes
the collagen layer
(yellow)
.
SI
-
6
. Histology
-
based 3
-
D FEM modeling
Fig
.
SI
-
6
:
Finite Element Model for 3
-
D
histology and computational
modeling
.
(A)
Representative
histological cross
-
sections
from the right carotid artery (RC2
)
were demarcated by the
Movat staining
for
connective tissue
, the boundaries
for
collagen, smooth muscle
,
and the
lipid
component. (B)
These
demarcations from the histological slices allowed for reconstructing a
3
-
D model. The positions of the
electrodes
(r
ed)
were
defined by the
푧
and
휃
coordinates.
Table I. Tissue properties used
for the computational model
(
57)
Collagen layer
Smooth muscle cell layer
Fat tissue
흈
(
푺
/
풎
)
0.174
0.307
0.042
휺
32000
149000
193000