Table 1. Impedance measured from phantoms samples (n = 10) and s values (estimated from computer simulations) of the agar-gel cylinder and of sphere.
Phantom sample
|
|
Z (Ω)
|
|
σagar-gel (S/m)
|
σsphere (S/m)
|
Agar
|
|
322.4 ± 2.7
|
|
0.067
|
0.067
|
Agar + NaCl (1 wt%)
|
|
213.6 ± 2.4
|
|
0.067
|
0.113
|
Agar + NaCl (1.5 wt%)
|
|
177.5 ± 4.1
|
|
0.067
|
0.145
|
Agar + AuNPs (1 wt%)
|
|
185.9 ± 6.2
|
|
0.067
|
0.138
|
Table 2. Results of the RFA for different values of applied voltage on a 2-cm spherical zone in case of non doped tissue (ND) and two types of dopants: saline solution (0.9% NaCl) and AuNPs (0.01 wt%).
Dopant
|
Zi (W)
|
50 V
|
70 V
|
90 V
|
t100-W
|
B
|
A
|
t100-W
|
B
|
A
|
t100-W
|
B
|
A
|
ND
|
87.7
|
457
|
2.7
|
4.4
|
94.5
|
1.6
|
3.8
|
31.5
|
1.0
|
3.7
|
NaCl
|
1%
|
84.6
|
454
|
2.8
|
4.3
|
95
|
1.7
|
4.0
|
35
|
1.2
|
3.7
|
2%
|
82
|
452
|
2.8
|
4.3
|
97.5
|
1.7
|
4.0
|
35.5
|
1.2
|
3.7
|
5%
|
75.5
|
457
|
3.1
|
4.6
|
103
|
1.9
|
4.0
|
36
|
1.3
|
3.8
|
10%
|
67.8
|
450
|
3.5
|
5.0
|
109.5
|
2.2
|
4.2
|
37.5
|
1.3
|
3.9
|
AuNPs
|
1%
|
78
|
456
|
3.0
|
4.5
|
101
|
1.8
|
4.0
|
35.5
|
1.2
|
3.6
|
2%
|
71.5
|
451
|
3.2
|
4.7
|
106.5
|
2.0
|
4.1
|
36.5
|
1.3
|
3.8
|
5%
|
60
|
448
|
3.7
|
4.8
|
120.5
|
2.6
|
4.2
|
41
|
1.5
|
4.0
|
10%
|
51.6
|
479
|
4.4
|
5.0
|
144
|
3.2
|
4.4
|
49.5
|
2.3
|
4.0
|
Zi: initial impedance; t100-W: time until roll-off (in s); B and A: transverse and axial diameters (in cm) of the coagulation zone, respectively. The different values of concentration (from 1 to 10% are volume fraction).
Table 3. Results of the RFA for different values of applied voltage on a 3-cm spherical zone in case of non doped tissue (ND) and two types of dopants: saline solution (0.9% NaCl) and AuNPs (0.01 wt%).
Dopant
|
Zi (W)
|
50 V
|
70 V
|
90 V
|
t100-W
|
B
|
A
|
t100-W
|
B
|
A
|
t100-W
|
B
|
A
|
ND
|
87.7
|
465.5
|
2.7
|
4.4
|
94.5
|
1.6
|
3.8
|
31.5
|
1.0
|
3.7
|
NaCl
|
1%
|
82.5
|
438
|
2.6
|
4.4
|
92
|
1.8
|
3.9
|
32
|
1.2
|
3.8
|
2%
|
78
|
421.5
|
2.7
|
4.5
|
90
|
1.8
|
4.0
|
31.5
|
1.2
|
3.8
|
5%
|
67.7
|
392
|
2.7
|
4.6
|
86.5
|
1.8
|
4.2
|
30
|
1.2
|
3.8
|
10%
|
57
|
382
|
3.1
|
4.8
|
87
|
1.8
|
4.2
|
30.5
|
1.3
|
3.9
|
AuNPs
|
1%
|
71.7
|
402
|
2.7
|
4.5
|
88
|
1.8
|
4.1
|
30.5
|
1.3
|
3.7
|
2%
|
62
|
385
|
3.0
|
4.8
|
86.5
|
1.8
|
4.2
|
30
|
1.3
|
3.8
|
5%
|
47.6
|
399.5
|
3.0
|
4.8
|
97.8
|
1.9
|
4.3
|
34
|
1.3
|
4.0
|
10%
|
38
|
468
|
4.5
|
5.5
|
126.5
|
2.5
|
4.8
|
43.5
|
1.7
|
4.2
|
Zi: initial impedance; t100-W: time until roll-off (in s); B and A: transverse and axial diameters (in cm) of the coagulation zone, respectively. The different values of concentration (from 1 to 10% are volume fraction).
Table 4. Results of the RFA for different values of applied voltage on a 4-cm spherical zone in case of non doped tissue (ND) and two types of dopants: saline solution (0.9% NaCl) and AuNPs (0.01 wt%).
Dopant
|
Zi (W)
|
50 V
|
70 V
|
90 V
|
t100-W
|
B
|
A
|
t100-W
|
B
|
A
|
t100-W
|
B
|
A
|
ND
|
87.7
|
440
|
2.7
|
4.4
|
94.5
|
1.6
|
3.8
|
31.5
|
1.0
|
3.7
|
NaCl
|
1%
|
81.4
|
400
|
2.7
|
4.4
|
87
|
1.6
|
3.9
|
30
|
1.2
|
3.6
|
2%
|
76
|
367
|
2.6
|
4.4
|
80
|
1.7
|
3.9
|
29
|
1.2
|
3.6
|
5%
|
64
|
306
|
2.5
|
4.3
|
66
|
1.7
|
3.9
|
25.5
|
1.2
|
3.6
|
10%
|
52
|
269
|
2.5
|
4.4
|
55
|
1.7
|
3.8
|
22.5
|
1.2
|
3.4
|
AuNPs
|
1%
|
69
|
327
|
2.5
|
4.4
|
71
|
1.7
|
3.9
|
27
|
1.2
|
3.6
|
2%
|
58
|
287
|
2.5
|
4.4
|
60
|
1.7
|
3.9
|
23.5
|
1.2
|
3.6
|
5%
|
42
|
245
|
2.5
|
4.4
|
50.5
|
1.6
|
3.8
|
20.5
|
1.2
|
3.6
|
10%
|
31.9
|
265
|
2.6
|
4.9
|
54.5
|
1.7
|
3.9
|
21.5
|
1.2
|
3.6
|
Zi: initial impedance; t100-W: time until roll-off (in s); B and A: transverse and axial diameters (in cm) of the coagulation zone, respectively. The different values of concentration (from 1 to 10% are volume fraction).
Table 5. Results of the ex vivo experiments for the three considered groups (n=4, mean ± standard deviation).
Group
|
Coagulation diameters
|
troll-off (s)
|
Transverse (cm)
|
Axial (cm)
|
ND
|
2.4 ± 0.2
|
3.4 ± 0.5
|
281 ± 31
|
NaCl
|
3.0 ± 0.4
|
3.7 ± 0.4
|
379 ± 12
|
AuNPs
|
3.7 ± 0.3
|
4.1 ± 0.2
|
432 ± 36
|
troll-off: time until roll-off (at which point the ablation ceased). ND Group: non doped tissue; NaCl Group: infusion of 2 mL of 0.9% NaCl; AuNPs Group: infusion of 2 mL of 0.1 wt%. AuNPs.
Table 6. Estimation of the characteristics of the tissue doped with different concentration (C, volume fraction) of a solution of 0.01% (wt) AuNPs and a solution 0.9% NaCl
Dopant
|
C (%)
|
FD (´10-9)
|
s (S/m)
|
c (J/kg·K)
|
k (W/m·K)
|
|
0 (non doped)
|
0
|
0.2
|
3455
|
0.502
|
0.9% NaCl
|
1
|
-
|
0.219
|
3455
|
0.502
|
2
|
-
|
0.238
|
3455
|
0.502
|
5
|
-
|
0.297
|
3455
|
0.502
|
10
|
-
|
0.394
|
3455
|
0.502
|
0.01 wt% AuNPs
|
1
|
54.15
|
0.271
|
3455
|
0.502
|
2
|
108.30
|
0.342
|
3455
|
0.502
|
5
|
270.75
|
0.555
|
3455
|
0.502
|
10
|
541.50
|
0.910
|
3455
|
0.502
|
σ : electrical conductivity, c: specific heat, k: thermal conductivity, Tissue properties estimated at 37 °C. In the case of AuNPs s was estimated using the FD value (volume fraction of solid AuNPs within the doped tissue); while that in the case of NaCl s was estimated using Eq. (1) proposed in [9].
Table 7. Characteristics of the materials used in the computational model [20].
Material
|
r (kg/m3)
|
s (S/m)
|
c (J/kg·K)
|
k (W/m·K)
|
Healthy tissue
|
1080
|
0.2
|
3455
|
0.502
|
Metal (electrode)
|
8000
|
7.4·106
|
480
|
18
|
Plastic (insulated trocar)
|
70
|
10-5
|
1045
|
0.026
|
ρ: density, σ: electrical conductivity, c: specific heat, k: thermal conductivity. Tissue properties assessed at 37 °C.