Multi-Parameter Analysis in Single-cell
Electroporation Based on the Finite Element Model
1
2
3
Hongmei Liu, Chenguo Yao, Member, IEEE, Yan Mi, Chengxiang Li, Yajun Zhao, Yanpeng Lv
4
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing
University, Chongqing 400030, China
[email protected]
5
6
7
8
9
Abstract—Pulsed electric fields have recently been the focus
considerable attention because of their potential application in
12 biomedicine. However, their practical clinical applications are
13 limited by poor understanding of the interaction mechanism
14 between pulsed electric fields and cells, particularly in different
15 effect of electroporation exposed in different parameters, and the
16 optimal pulsed parameter is still vague. A multi-shelled dielectric
17 model considering the inner membrane was established by the
18 finite element software COMSOL in this paper. Different shock
19 protocols (different pulsed duration/strength/frequency/polarity)
20 was exposed to the cell model respectively to simulate and
21 analyze the influence of pulse parameters on varying degrees of
22 electroporation by comparing the dynamic development of the
23 pore radius and electroporation region. Results showed that the
24 conventional pulses have better efficiency in electroporation than
25 high frequency pulses; The monopolar pulses with cumulative
26 effect have much better electroporation effect than the bipolar
27 pulses which have weakening effect when duration of single pulse
28 reduced to nanosecond; and electric field strength was the major
29 factor
that induced electroporation, particularly in the
30 recoverable pore, but it had minimal effect on pore expansion.
31 However, pulse duration affects the non-recoverable pore, such
32 that the high-intensity wide pulse is more useful in the field of
33 irreversible electroporation. The high-intensity short pulse can
34 increase permeability and maintain cell viability. This work done
35 by this paper maybe can provide theoretical basis for further
36 research on complicated cell systems and promote the clinical
37 application of pulsed electric field.
either be reversible (which is used in electrochemotherapy [2]
or gene transfection [3]) or irreversible (which is used in other
54 applications for tissue ablation [4]). Despite significant interest
55 in this technique, but its practical clinical applications or
56 development are limited by the poor understanding of the
57 interaction mechanism between pulsed electric field and cells;
58 in particular, electroporation and its effect on parameter
59 selection are poorly understood.
10
52
11 of
53
Numerous studies have used experimental techniques to
provide insight into cell electroporation, such as uptake of
62 fluorescent molecules[5], measuring cell impedance[6], and
63 imaging cell transmembrane voltage[7]. And also many
64 different pulse parameters were selected in experimental
65 studies to investigate the effects of pulsed electric fields. Boris
66 Rubinsky et al.[8] shown that there is killing effect on human
67 liver cancer cell (HepG2) which exposed in 10 pulse with the
68 amplitude of 1.5kV/cm, duration of 300us, repetition frequency
69 of 1Hz, and the killing effect increase with the number of
70 pulse.
Rafael V Davalos et al.[9] selected 80 pulses with the
71 amplitude
of 2500V/cm, duration of 100us, repetition
72 frequency of 0.3Hz to treat nude mice solid tumor and it also
73 get a good ablation effect. And Yao et al.[10] conducted
74 preclinical animal studies by exposing liver in 90 pulses with
75 1500V/cm, duration of 100us, repetition frequency of 1Hz.
76 Result showed that the ablation boundary was clear. And so on.
77 We can see that these parameters are different, different pulse
78 parameters have different killing effect, but we just know a
38
Keywords—Dielectric model; electroporation; electroporation 79 vague answers about how much parameters influence on
39 region; finite elements; non-recoverable; optimal parameter;
80 treatment. Though many pulse parameters(90 pulses with
40 pulsing protocols; radii; recoverable;
81 100us, 1kV/cm~3kV/cm for irreversible electroporation(IRE),
82 8 pulses with 100us, 1kV/cm for reversible electroporation)
83 were studied and proposed in clinical application. In fact, it
41
I.
INTRODUCTION
42
Pulsed electric fields have recently been the focus of 84 were judged just depend on quantitative analysis of the
85 experiments or based on the ability to produce the pulse
43 considerable attention because of their potential application in
86 generator. Moreover, corresponding parameter should be
44 biomedicine because of their broad potential applications in
45 biomedicine;
pulsed electric fields induce cancer cell 87 selected pointedly because of organization is inhomogeneity,
88 but now, The optimal pulsed parameter is still not clear, the
46 electroporation, making them promising technologies for tumor
89 root cause is that the mechanism between pulsed electric field
47 therapy[1]. Electroporation occurs when a biological cell is
90 and cells, its interpretive competence is poor for the
48 exposed to electric pulses, resulting in the increase in cell
91 relationship between parameters and elecctroporated effects.
49 membrane permeability and the appearance of hydrophilic
92 Nevertheless, for different tissue, the optimal pulsed parameter
50 pores. Depending on the field intensity and duration or number
93 is still to be further studied, a theoretical model should be
51 of pulses applied, permeabilization of the hydrophilic pore can
94 established to supplement experimental knowledge and analyze
Project supported by Fund for Innovative Research Groups of China (51321063); 95 the effect electroporation on parameter selection. In this study,
96 a finite element model of cells under the pulsed electric field
National Natural Science Foundation of China (51477022); Natural Science
Foundation Project of CQ CSTC (cstc2014jcyjjq90001); Fundamental Research
Funds for the Central Universities (106112015CDJZR158804).
60
61
1
TABLE 1 PARAMETERS OF THE CELL ELECTROPORATION MODEL
E
B
P
rc
dmem A
N
θ θnp
C
O
dne
Fig. 1 Multi-shelled dielectric model of the
spherical cell
A5
A4
A3
A2
A1
A6 A7
α=15°
O
B1
C1
E
Fig. 2 Schematic diagram of sampling points on the
cell membrane boundary
Symbol
rc
rn
dmem
dne
λm
λmem
λc
λne
λnp
λp
ε0
εm
εmem
εc
εne
εnp
α
rp
N0
VEP
Vrest
q
n
ω0
F
R
T
r*
D
β
γ
σ0
σ′
Fmax
rh
rt
Value
10 µm
5 µm
5 × 10−9 m
40 × 10−9 m
0.2 sm−1
3 × 10−7 sm−1
0.3 sm−1
6 × 10−3 sm−1
1.35 sm−1
0.22 sm−1
8.85 × 10−12 m−3 kg−1 s−4 A−2
80 ε0
8.57 ε0
154.4 ε0
28 ε0
52 ε0
1 × 109 m−2 s−1
0.8 × 109 m
1.5 × 109 m−2
170 mV
−80 mV
2.46
0.15
2.65
9.65 × 10−4 Cmol−1
8,314 J K−1 mol−1
295 K
0.51 × 10−9 m
5 × 10−14 m−2 s−1
1.4 × 10−19 J
1.8 × 10−11 J m−1
1 × 10−6 J m−2
2 × 10−2 J m−2
0.70 × 10−9 N V−2
0.97 × 10−9 m
0.31 × 10−9 m
Definition and source
Cell radius [13]
Nucleus radius
Membrane thickness [14]
Nuclear envelope thickness [14]
Extracellular conductivity [15]
Membrane conductivity [16]
Cytoplasm conductivity [17]
Nuclear envelope conductivity [18]
Nucleoplasm conductivity [18]
Conductivity of the solution filling the pore
Dielectric permittivity of the vacuum
Media permittivity [15]
Cell membrane permittivity [19]
Cytoplasm permittivity [20]
Nuclear envelope permittivity [18]
Nucleoplasm permittivity [18]
Creation rate coefficient [13]
Minimum radius of hydrophilic pores [11]
Equilibrium pore density at Vm = 0 [11]
Characteristic voltage of electroporation [13]
Rest potential [11]
Pore creation rate [11]
Relative entrance length of pores [13]
Energy barrier within pore [13]
Faraday’s constant
Gas constant
Absolute temperature
Minimum radius of hydrophilic pores [12]
Diffusion coefficient for pore radius [12]
Steric repulsion energy [12]
Edge energy [12]
Tension of the bilayer without pores [12]
Tension of hydrocarbon–water interface [12]
Maximum electric force for Vm = 1 V [12]
Constant for advection velocity [12]
Constant for advection velocity [12]
2
was established to investigate cell electroporation and the
influence of pulse parameters on varying degrees of
5 electroporation. This work done by this paper maybe can
6 provide theoretical basis for further research on complicated
7 cell systems and promote the clinical application of pulsed
8 electric field.
3
20
4
21
voltage (∆Ψ) can be computed using electromagnetic field
theory by solving the following equation:
( )   0 r (
22

( ))  0,
t
  i (t )  0 (t ).
23
9
(1)
(2)
When electroporation happened, pores provide new
conductive pathways for the transmembrane current density J,
26 the additional term JEP, as follows:
24
10
II.
MODEL AND METHODS
A. Model of Electroporation
Here, we establish a multi-shelled dielectric model of the
13 cell and consider this cell with a radius of 10 µm exposed to an
14 electric field of strength E in an underground field with a
15 conductive medium. its electrical characteristics are described
16 by conductivity and permittivity based on the finite element ,
17 and every part of the cell was regarded as isotropic, linear, and
18 homogeneous media. As shown in Fig.1. The electric potential
19 Ψ inside and outside the cell ,and the induced transmembrane
25
11
12
27
J (t ) 
m0 (i  0 )
d

 0 mem  (i  0 )
d
t
 iEP (t ) N (t ),
(3)
where iEP is the current through a single pore, N is the
density of the pore, all of them can be characterized by the
30 following equation:
28
29
31
iEP (t )  ( i  0 )P rP2
A
,
d
(4)
evm  1
, (5)
 nvm ) / (0  nvm )  (0e0  nvm  nvm ) / (0  nvm )
A. Effects of Pulse Strength
42
Regardless of shock duration or shape, increasing the shock
e (0 e
43 strength increases the degree of electroporation, as shown by
44 the effect of electroporation exposed to the pulsed electric
2
dN (t )
N (t )  q (  (t )/VEP )2
  e(  (t )/VEP ) (1 
e
).
2
(6) 45 field. For the single cell under 500 V/cm, no electroporation
dt
N0
46 occurs; however, the effect of electroporation increases when
47 this value is exceeded. The increase in pore density of A1 is
3
where vm  (i  0 )( F / RT ) , then, we can get:
48 quasi-exponential with pulse strength, as shown in Fig. 3. As
49 the strength of the pulsed electric field increases, a larger area
( i  0 )
 0 mem  ( i  0 )
J (t ) 
m (t ) 
,
4
(7) 50 reaches the transmembrane potential threshold, resulting in the
d
d
t
51 expansion of the pore region. And also, The electric field
52 intensity also affects the distribution of the recoverable and
2
5
where m (t )  m0  N (t )P rP A is the variable
−8
53 non-recoverable pores. The maximum pore radius 4.18 × 10
6 conductivity of the electroporated membrane.
54 m occurs at 0.5 µs after the pulse with an electric field of 0.75
7
Also, pore radius should be considered, for a cell with a 55 kV/cm, which is located at 31.5°. When the electric field
56 intensity is 1 kV/cm, the maximum pore radius reaches 5.07 ×
8 total number of K pores, the rate of change of their radii rj is
−8
57 10 at the 40.68° position. With 5 kV/cm, the maximum value
9 determined by the following ordinary differential equation [12]:
−8
58 is 6.4 × 10
m and the location is 66.89°. Therefore, the cell
dr j
59 membrane exhibits electroporation from non-electroporation,
Vm2 Fmax
D
 U (rj , Vm ,  eff ) 
(

60 particularly recoverable electroporation, as the electric field
10
dt
kT 1  rh / (r  rt )
61 increases. Then, the cell membrane exhibits electroporation
(8)
r* 1
62 characterized by non-recoverable electroporation. The region
4  ( ) 4  2  2 eff r ) j  1, 2,3, , K .
r r
63 of non-recoverable electroporation, the maximum shift to the
64 pole, and the value of the maximum pore radius increase with
11
All parameters are defined in Table 1.
65 the increase in the electric field.
0  nvm
timulation protocols
13
The cell was exposed to different shock protocols.
14 Specifically, this study investigated the effects of the
15 following: 1) Shock duration, by keeping the shock strength
16 constant and varying its duration. The shock duration used in
17 this study was 5–15 µs, and pulses with different durations
18 were tested. 2) Shock strength, by employing the variable
19 aforementioned duration for several different shock strengths.
20 The cell was exposed to electric fields of 0.25–5.0 kV/cm. 3)
21 Shock frequency, by applying trains of high-frequency pulses
22 while keeping the total duration of the trains at 10 µs; the
23 frequency was 0.2 and 2 MHz. The monophasic and biphasic
24 pulse trains were tested. Monophasic pulses had equal on and
25 off phases, whereas biphasic pulses had equal positive and
26 negative phases and the same total duration as that of the
27 monophasic pulse.
S
III. RESULTS
The calculations were conducted in COMSOL
Multiphysics using the Electric Currents, Transient Analysis
32 application mode [21]. In this study, we built a multilayer
33 dielectric sphere model, and two opposing copper electrodes
34 were applied; one electrode was set as the pulsed signal,
35 whereas the other electrode was set to the ground to obtain the
36 electric field under a pulse signal. All outside boundaries were
37 considered insulated. To analyze the evolution of pore radii on
38 the surface of the cell membrane, seven sampling points were
39 selected, as shown in Fig. 2. The angle between two points was
40 15°.
30
31
83.08
40
82
82.85
41.66
76
20
74.7
74
10.32
73.33
72
10
N
S
L
23.62
67.6
5.90
0
68
80
78
30
66
67
84
1.5
68
66
3.45
0.751
70
3
5
E (kV)
Fig. 3. Effect of electric field intensity, E. N is the maximum pore density, B
is electroporation area, and L is the fitted curve.
69
28
29
41
N(×1015m-2)
12
B.
vm
S(0)
A
1
B. Effects of Pulse Duration
71
Regardless of shock strength, increasing the shock duration
72 increases the degree of non-recoverable electroporation; this
73 phenomenon is proven by the effect of electroporation exposed
74 to the pulsed electric field.
70
There are three types of pores: non-recoverable pores,
recoverable pore, and no-pores. And this study found that when
77 cell exposed in the pulse with strength of 1.5kV/cm, perforated
78 area on the cell membrane increase with the duration increase
79 when the duration of pulse under 3us( do not show the figure in
80 the paper), but when beyond 3us, minimal change was
81 observed in the total electroporation region and density, and
82 there still no non-recoverable pores appear until the width up to
83 9.5 µs, the degree of non-recoverable electroporation increases
84 with the duration.
75
76
1
2
Fig. 4 shows the temporal–spatial distribution of pore radii
under different duration. When the single-cell was exposed in
25
RE
RE
NO
20
3
the pulse with strength of 1.5kV/cm, width of 5 µs, the pores
120
2us
3us
6us
9us
10us
RE
Non-RE
RE
2us
8us
12us
16us
20us
30us
NO
100
80
rj (nm)
rj (nm)
15
10
40
20
5
0
0
60
20
40
60
80
100
arc (o)
120
140
160
0
0
180
20
40
60
80
100
arc (0)
120
(a) 1.5 kV/cm, 5us
(b) 1.5 kV/cm, 15 µs.
(c) 1.5 kV/cm, 5us
(d) 1.5 kV/cm, 15 µs.
140
160
180
Fig. 4. Effects of pulse duration on the temporal–spatial distribution of pore radii. (a)(c) is for the pulses with the strength of 1.5kV/cm, duration of 15us at
different time. (b)(d) is for the pulses with strength of 1.5kV/cm, duration of 5us at different time.
4
5
were created and evolution with time, but the pore radii
decrease after pulse treatment (Fig. 4 (a)(c)), which reveals that
8 all the pores are recoverable. When the pulse duration is 15 µs
9 (as shown in the Fig. 4 (b)(d)), the region of non-recoverable
10 pores expands significantly compared with that under the
11 duration of 10 µs. Moreover, minimal change is observed in
12 the total electroporation region and density. We can guess that
13 duration is a first kind important parameters for the pores
14 evolution, especially the creation of non-recoverable pore.
conventional pulse with 1,000 V/cm amplitude and 10 µs
width. However, under the monopolar and bipolar pulses with
27 1,000 V/cm amplitude, the pulse width was still 10 µs. After
28 the first pulse, recoverable electroporation occurred. The pore
29 radii became recoverable during the interval time (5 µs)
30 between the first and second pulses. With the occurrence of the
31 second pulse, the pore radii increased along with the
32 transmembrane
voltage. However, no non-recoverable
33 electroporation occurred even after two pulses. Thus, the
34 conventional pulse is better than the monopolar and bipolar
35 pulses when the total high-level time inner burst is fixed.
36 Meanwhile, the evolution of pore radii was associated with the
37 square of the transmembrane voltage; thus, the evolution of the
38 pore radii exposed to the monopolar pulse was the same as that
39 exposed to the bipolar pulse. And then, we set the pulse width
40 to nanoseconds (500 ns), repetition frequency to 1 MHz, and
41 duty cycle to 50%. As shown in Fig.5 (c)(d). electroporation
42 exhibited a cumulative effect on the monopolar pulse, whereas
43 a weakening effect was observed on the bipolar pulse; the next
44 pulse exhibited an opposite polarity, resulting in the rapid
45 decrease and subsequent increase in the transmembrane
6
25
7
26
C. Effects of Shock Frequency and Polarity
16
The on time of different pulse types was fixed to 10 µs to
17 observe the principle of energy equivalence. The condition of a
15
single pulse, multiple monopolar pulses, and bipolar pulses
were simulated in this study. The simulation results showed
20 that the membrane electroporated more easily under the
21 traditional single pulse, leading to cell death. The calculations
22 presented in Fig. 5 (a)(b) show the evolution of pore radii
23 exposed to different pulses. This finding implies that non24 recoverable electroporation occurred upon exposure to the
18
19
A1
A2
A3
A4
A5
A6
E
70
60
4
So monopolar pulses were more efficient at electroporation
than bipolar electric pulses.
60
1.0
50
0.8
50
rj (nm)
3
40
0.6
30
0.4
20
10
40
0.2
0
0
2
4
6
8
10
12
T (us)
14
16
1.0
E
0.8
30
0.6
20
0.4
10
0.2
0
0
0.0
20
18
A1
A2
A3
A4
A5
A6
2
4
6
8
10
12
14
16
E (kV/cm)
voltage, but was insufficient to reach the transmembrane
voltage threshold and for electroporation to occur (Fig. 15(b)).
rj (nm)
2
E (kV/cm)
1
0.0
20
18
T (us)
(a)
(b)
ec.dV
E
1.2
ec.dV
E
1.0
0.6
1.0
0.8
0.4
ec.dV (V)
0.6
0.0
0.0
E (kV/cm)
0.5
0.3
0.6
E (kV/cm)
ec.dV (V)
0.9
0.3
0.2
-0.3
-0.5
0.0
0.0
-0.6
-1.0
0
1
2
T (us)
3
4
5
0
1
2
T (us)
3
4
5
(d)
(c)
Fig. 5 (a)(b) : Temporal–spatial distribution of pore radii in different pulse frequencies. (a) Conventional pulse with pulse width of 10 µs; (b) Monopolar pulse
with pulse width of 5 µs; (c)(d): Temporal distribution of the transmembrane voltage at different polarities. (c) Monopolar pulse with 500 ns × 4; (d) Bipolar
pulse with 500 ns × 4.
5
cannot enter the cell even through the largest pore when the
electric field is 0.6 kV/cm. However, when the electric field
28 exceeded 0.75 kV/cm, 70 kDa molecules can transmit into the
29 cell,
but no significant increase in macromolecular
30 transmittance was observed. All these findings reveal that, with
31 the increase in the electric field, the number of pores increased
32 significantly, whereas the number of large pores changed
33 slightly. This conclusion is consistent with the findings on the
34 relationship of the electroporation region with electric field
35 strength. As the electric field increases, the number of pores
36 increases considerably (Fig. 11). When the strength of the
37 electric field exceeded 0.75 kV/cm, the number of recoverable
38 pores significantly increased, whereas the non-recoverable
39 pores changed only slightly (Fig. 12). From our simulation, we
40 conclude that the strength of the electric field is the major
41 factor that induces electroporation but has minimal effect on
42 pore expansion. For several applications that require reversible
43 electroporation, such as drug delivery, the high-intensity short
44 pulse can be used to increase permeability and maintain cell
45 viability.
26
6
I.
DISCUSSION
The model presented in this study allows us to investigate
the temporal and spatial distributions of cell electroporation.
9 We evaluate how well the results of the simulation match those
10 of the experiments. During the evaluation of this simulation,
11 we noted that this study is unable to find in the literature all of
12 the parameters required by the simulation for a single cell. The
13 parameters listed in Table 1, such as cell radius, intracellular
14 and extracellular conductivities, and membrane thickness, were
15 obtained from external sources, other theoretical models, or
16 experiments. Thus, differences between experimental and
17 simulation results are to be expected.
7
8
Similarly, the permeability of the molecule was used to
assess electroporation in different electric field strengths
20 [22][23]. The results revealed that, when the pulse duration and
21 the treatment time are same, the permeability is closely related
22 to the electric field strength. Gabriel [24] reported that
23 fluorescence intensity increases with electric field strength with
24 the use of propidium iodide. Demiryurek revealed that 10 kDa
25 molecules can transmit to cells, whereas 70 kDa molecules
18
19
27
1
Although electroporation is associated with the electric
field, pulse duration is also an important factor. Saulis and
3 Saulė [22] revealed that, with the increase in pulse duration, the
4 pore radii also increased. We obtained a similar conclusion in
5 our simulation. When the electric field is 1.5 kV/cm and the
6 pulse duration is low, all the pores on the cell membrane are
7 recoverable after electroporation. However, when the pulse
8 duration reaches a critical value, the non-recoverable pore
9 appears on the membrane and its region increases along with
10 pulse duration and maximum cell radius. The pore density and
11 the entire electroporation area did not change significantly. The
12 pulse duration is the main factor that affected the development
13 of the pore radii under the appropriate electric field intensity.
14 Therefore, the pulse duration should be longer in a reasonable
15 range in the field of irreversible electroporation.
59
2
60
For high-frequency pulses, the influence of frequency and
polarity is still unclear. Several researchers agree with the
18 energy equivalence principle; therefore, the conventional single
19 pulses and high-frequency monopolar and bipolar pulses would
20 have similar results upon treatment with cell suspension
21 [26][27]. Bilska [25] established a numerical model. Neumann
22 [28] built a resistance–capacitance cell circuit model, which
23 revealed that the degree of electroporation decreased with the
24 increase in pulse frequency by theoretical analysis. Kotnik et
25 al. [29][30] revealed that the influence of high-frequency
26 bipolar pulse perforation was significantly weaker than that of
27 monopolar pulses from electrophoresis, electrolysis, and other
28 points of view. Based on previous studies, Zimmerman [31]
29 proposed a weakening effect by bipolar pulses through an
30 experiment on calcium ion absorption. Bennett L.Ibey, Olga
31 N.Pakhomova, et.al [32] investigated whether the same
32 advantage existed for bipolar nanosecond-pulsed electric field
33 as compared to monopolar pulse. It show that bipolar
34 nanosecond
electric pulses are less efficient at
35 electropermeabilization and killing cells than monopolar
36 pulses. In this study, we proposed the cumulative effect of the
37 high-frequency monopolar pulses and the weakening effect of
38 the bipolar pulses from the change of the transmembrane. From
39 the developing trends of the pore radii, we can conclude that a
40 high frequency is not conducive for the development of the
41 pore radii or non-recoverable electroporation, which benefits
42 reversible electroporation. The low frequency or the wide pulse
43 duration is beneficial to irreversible electroporation. All these
44 findings are summarized in our simulation, which requires
45 further experimental verification.
72
16
17
46
II.
CONCLUSION
In this study, a finite element model of cells under the
pulsed electric field was established to investigate cell
49 electroporation and the influence of pulse parameters on
50 varying degrees of electroporation. The strength of the electric
51 field was the major factor that induced electroporation,
52 particularly the recoverable pore, but minimal effect was
53 exhibited on pore expansion. Pulse duration was observed on
54 non-recoverable pores. Thus, the high-intensity wide pulse is
55 more useful in the field of irreversible electroporation, whereas
56 the high-intensity short pulse can increase permeability and
57 maintain cell viability because of the cumulative effect of
58 monopolar nanosecond electric pulses and the weakening
47
48
effect of bipolar nanosecond electric pulses. Monopolar pulses
are more efficient in electroporation than bipolar electric
61 pulses.
The results explained the effect of electroporation on the
selectivity of pulse parameters. However, further experiments
64 are needed to validate the theoretical basis for the related
65 experimental research and clinical treatment. To a certain
66 extent, the model can be exploited further to investigate the
67 behavior of more complicated cell systems and to promote the
68 clinical application of pulsed electric fields.
62
63
69
70
ACKNOWLEDGMENT
71
The authors thanks Rui Shaoqing for her help in the
simulation technology and analysis of the data.
73
74
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75
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