Short pulsed microwave ablation: computer modeling and ex vivo experiments

Figures & data

Figure 1 (A) Geometry and dimensions of 14 G MW antenna. (B) Materials making up the antenna. C: Geometry of the computer model and a scheme of the CZ measures: A represents the axial diameter and B the middle of the transverse diameter. Dimensions in mm and schemes out of scale.

Table 1. Number and characteristics (power and time) of the ex vivo experiments.

	Continuous		Pulsed
Power (W) Time (s)	60 W	80 W	60 W	80 W	100 W	125 W
120	1	1	–	–	–	–
151	1	–	–	–	–	–
180	2	2	1	1	1	1
200	1	–	–	–	–	–
240	1	1	–	–	–	–
254	1	–	–	–	–	–
300	2	2	1	1	1	1
360	1	1	–	–	–	–
373	1	–	–	–	–	–
505	1	–	–	–	–	–
600	2	2	1	1	1	1

Table 2. Characteristics of materials used in the computer model [25,27,46,51].

Material	σ(S/m)	${\mathrm{\epsilon }}_{\mathrm{r}}$	k(W/m·K)	ρ(kg/m^3)	c(J/kg·K)
Liver	1.8^a	44.3^a	0.564	1050^b	3400^b
				370^c	2156^c
Copper	5.87 × 10^7	1	385	9000	384
Alumina	0	10	30	3970	875
PTFE	1.6 × 10^-5	1.8	0.24	1200	1050
Stainless steel	1.74 × 10^6	1	16.2	8000	500

σ: (effective) conductivity;${ \epsilon }_r:$ relative permittivity; k: thermal conductivity; ρ: density; c: specific heat.

^aMeasured at 37 °C, ^bfor temperatures between 37 to 99 °C, ^cfor temperatures higher than 100 °C.

Figure 2. Relation between the computed (FEM) and experimental (ex vivo) values obtained for the transverse (A) and axial (B) diameters of the coagulation zone for continuous and pulsed MWA. The regression line considered zero crossing.

Figure 3. (A and B) Coagulations zones created in an ex vivo model with pulsed MWA at 125 W for 5 min. The dashed lines represent the contours measured on the images: white line for the zone with only white coagulation, and orange for the zone with red hyperemia also. The solid lines represent the Ω = 4.6 isolines (white solid line) and Ω = 1 (orange solid line) computed by the Arrhenius function to represent the CZ boundary. C and D: Comparison of experimental and computational (FEM) results.

Figure 4. Axial and transverse diameters (A and B) and volumes of the coagulation zones (C and D) computed under ex vivo conditions for different duty cycle values with intensive and low cooling. Duty cycles of 100% are those of the continuous mode while values <100% are in the pulsed mode.

Table 3. Computer result of the simulations mimicking the ex vivo experiments reported by Tosoratti et al [40] (Phase 2).

							CZ
Cooling	ton(s)	toff(s)	DC(%)	Time(min)	P(W)	E(kJ)	A(cm)	B(cm)	S(%)	VCZ(cm^3)
Intensive	2	8	20%	10	140	16.8	4.11	3.73	91%	28.78
	3	12	20%	10	140	16.8	3.90	3.67	94%	26.15
	4	16	20%	10	140	16.8	3.91	3.66	94%	26.26
	2	3	40%	10	70	16.8	3.92	3.60	92%	25.85
	4	6	40%	10	70	16.8	3.95	3.64	92%	27.20
	8	12	40%	10	70	16.8	3.83	3.51	92%	24.51
	3	2	60%	10	46.75	16.8	3.81	3.49	92%	23.50
	6	4	60%	10	46.75	16.8	3.78	3.45	91%	22.55
	12	8	60%	10	46.75	16.8	3.93	3.65	93%	26.82
	2	0	100%	10	28	16.8	3.79	3.49	92%	23.59
Low	2	8	20%	10	140	16.8	4.03	3.80	94%	29.14
	3	12	20%	10	140	16.8	3.97	3.69	93%	28.70
	4	16	20%	10	140	16.8	4.06	3.64	90%	26.51
	2	3	40%	10	70	16.8	3.98	3.55	89%	25.12
	4	6	40%	10	70	16.8	4.05	3.51	87%	26.26
	8	12	40%	10	70	16.8	4.08	3.54	87%	27.13
	3	2	60%	10	46.75	16.8	4.00	3.52	88%	25.22
	6	4	60%	10	46.75	16.8	4.03	3.58	89%	25.30
	12	8	60%	10	46.75	16.8	4.11	3.62	88%	27.06
	2	0	100%	10	28	16.8	4.03	3.46	86%	25.15

t_ON: power activated interval; t_OFF: power inactivated interval; DC: Duty cycle (100·t_ON/(t_ON +t_OFF)): P: Power; E: Energy; A and B: Axial and transverse diameter of coagulation zone, respectively; S: Sphericity ratio (B/A); V_CZ: Volume of coagulation zone. Values of DC of 100% correspond with the continuous mode while values <100% are those of the pulsed mode.

Table 4. Computer result of the simulations mimicking in vivo conditions (Phase 3).

							CZ
Cooling	ton(s)	toff(s)	DC(%)	Time(min)	P(W)	E(kJ)	A(cm)	B(cm)	S(%)	VCZ(cm^3)
Intensive	2	8	20%	10	140	16.8	3.50	3.01	86%	14.85
	3	12	20%	10	140	16.8	3.48	3.03	87%	14.43
	4	16	20%	10	140	16.8	3.45	3.03	88%	13.56
	2	3	40%	10	70	16.8	3.42	3.05	89%	13.76
	4	6	40%	10	70	16.8	3.48	3.19	92%	14.31
	8	12	40%	10	70	16.8	3.39	3.07	91%	12.24
	3	2	60%	10	46.75	16.8	3.28	2.98	91%	11.01
	6	4	60%	10	46.75	16.8	3.36	3.03	90%	12.55
	12	8	60%	10	46.75	16.8	3.33	3.00	90%	12.84
	2	0	100%	10	28	16.8	3.20	2.93	92%	10.14
Low	2	8	20%	10	140	16.8	3.61	3.03	84%	13.05
	3	12	20%	10	140	16.8	3.58	3.02	84%	12.45
	4	16	20%	10	140	16.8	3.57	3.03	85%	12.36
	2	3	40%	10	70	16.8	3.48	3.03	87%	12.85
	4	6	40%	10	70	16.8	3.46	2.99	86%	12.87
	8	12	40%	10	70	16.8	3.30	2.95	89%	12.03
	3	2	60%	10	46.75	16.8	3.50	3.01	86%	13.55
	6	4	60%	10	46.75	16.8	3.35	2.96	88%	12.05
	12	8	60%	10	46.75	16.8	3.56	3.03	85%	12.56
	2	0	100%	10	28	16.8	3.44	2.93	85%	12.19

t_ON: power activated interval; t_OFF: power inactivated interval; DC: Duty cycle (100·t_ON/(t_ON +t_OFF)): P: Power; E: Energy; A and B: Axial and transverse diameter of coagulation zone, respectively; S: Sphericity ratio (B/A); V_CZ: Volume of coagulation zone. Values of DC of 100% correspond with the continuous mode while values <100% are those of the pulsed mode.

Table 5. Computer result of the simulations using long pulses.

							CZ
	ton(s)	toff(s)	DC(%)	Time(min)	P(W)	E(kJ)	A(cm)	B(cm)	S(%)	VCZ(cm^3)
Ex vivo	30	90	25%	11.2	100	16.8	4.04	3.40	84%	22.51
	50	50	50%	5.6	100	16.8	4.07	3.61	88%	24.84
In vivo	30	90	25%	11.2	100	16.8	3.14	2.7	86%	8.59
	75	75	50%	5.6	100	16.8	3.6	2.98	83%	12.85

Figure 5. CZ contour at the end of the application of the first pulse (gray line) and at the end of power application (black line) for 1000 W (A-B) and 46.75 W (C-D) under ex vivo (A-C) and in vivo (B-D) conditions. All cases were with a 60% protocol (6 s on - 4 s off).

Table 6. Computer result of the simulations using short pulses with very high power utlined in orange.

Condition	ton (s)	toff (s)	DC (%)	Time (s)	P (W)	E (kJ)	A (cm)	B (cm)	S (%)	VCZ (cm^3)
Ex vivo	6	4	60%	28	1000	16.8	4.74	3.28	69%	24.07
	6	4	60%	600	46.75	16.8	3.78	3.45	91%	22.55
	4	6	40%	42	1000	16.8	4.95	3.57	72%	28.03
	4	6	40%	600	70	16.8	3.95	3.64	92%	27.20
In vivo	6	4	60%	28	1000	16.8	4.61	3.40	74%	24.38
	6	4	60%	600	46.75	16.8	3.36	3.03	90%	12.55
	4	6	40%	42	1000	16.8	4.85	3.39	70%	26.67
	4	6	40%	600	70	16.8	3.48	3.19	92%	14.31

The rest of the cases were extracted from Tables 3 and 4.

Figure 6. Evolution of CZ volume during the MWA, including the 10 min cooling phase in which CZ can increase due to thermal latency. Dashed colored lines show the end of the power application in the different cases.

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