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脉冲电场是心房颤动及肿瘤消融的一种新型物理能量源. 相比于传统热消融, 其具有非热、不损伤周边组织等优势. 物理消融过程中产生的扩散气泡可能导致气体栓塞, 对人体有潜在的危害. 然而当前尚未有针对消融脉冲参数对扩散气泡的影响研究. 因此, 本实验搭建了脉冲产生和气泡观察平台, 具体研究了溶液电导率, 脉冲电压、脉宽、输入能量等参数与扩散气泡之间的关系, 统计了不同条件下扩散气泡的尺寸分布范围, 并探究了扩散气泡的可能产生原因. 实验结果表明: 液体中产生的扩散气泡量与脉冲电压、输入能量正相关; 高电导率、长脉宽可以增强热效应, 并增加扩散气泡量, 且更易产生尺寸大于100 μm的扩散气泡; 通过对结果推测, 针电极为阴极时, 电解反应可能是扩散气泡的主要来源. 本研究有望指导未来脉冲电场消融参数的优化.Pulsed electric field is a novel physical energy source for treating atrial fibrillation and tumor ablation, which has advantages over traditional thermal ablation, such as being non-thermal, short treatment time, tissue selectivity, and low contact pressure requirements. The diffusion bubbles generated during physical ablation may lead to gas embolism and silent cerebral events, with potential hazards such as tissue damage and cerebral ischemia. Previous studies have shown that the number of bubbles generated is correlated with the electrical properties of the treated object, pulse parameters (pulse waveform, treatment time and input energy), and electrodes. The number of bubbles are more significant at the cathode than at the anode, and the number of bubbles positively correlates with the input energy. However, to the best of our knowledge, no studies have been conducted to investigate the effects of ablation pulse parameters on diffusion bubbles. Therefore, in our experiment, a platform for producing pulses and observing diffusion bubble is built, and the needle-ring electrode we made realizes the capture and measurement of diffusion bubbles. Since pulses with a voltage of 3 kV and a pulse width of 100 μs are commonly used as ablation parameters for atrial fibrillation and tumor in pulsed field ablation (PFA), the pulse width of unipolar pulse is selected as 5, 10, 50, and 100 μs, and the number of pulses applied is 1. The pulse voltage is determined according to the parameters commonly used in PFA and the simulation calculation of the field strength distribution of the needle-ring electrode. After determining the parameters, this experiment explicitly investigates the relationships among diffusion bubbles and solution conductivity, pulse voltage, pulse width, input energy, and other parameters. Meanwhile, the size distributions of diffusion bubbles under different operating conditions are statistically investigated. Besides, the possible causes of diffuse bubbles are also explored. We evaluate the number of bubbles by measuring the cross-sectional area of the diffusion bubbles from a top-down perspective. The experimental results show that the area of diffusion bubbles generated in the liquid is positively correlated with pulse voltage and input energy; high conductivity and long pulse width can enhance the thermal effect and increase the area of diffusion bubbles; diffusion bubbles with a diameter larger than 100 μm are easily generated under high conductivity and high pulse width conditions. By speculating on the results, the electrolytic reaction may be the main source of diffusion bubbles when the needle electrode is the cathode. This study is expected to optimize future pulsed electric field ablation parameters.
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Keywords:
- pulsed electric field /
- diffusion bubble /
- ablation parameter /
- electrolysis reaction /
- risk of embolism
[1] Kornej J, Börschel C S, Benjamin E J, Schnabel R B 2020 Circ. Res. 127 4Google Scholar
[2] Chen W, Zheng R, Baade P D, Zhang S, Zeng H, Bray F, Jemal A, Yu X Q, He J 2016 CA Cancer J. Clin. 66 115Google Scholar
[3] Koruth J S, Kuroki K, Kawamura I, Brose R, Viswanathan R, Buck E D, Donskoy E, Neuzil P, Dukkipati S R, Reddy V Y 2020 Circ. Arrhythm. Electrophysiol. 13 e008303Google Scholar
[4] Kuroki K, Whang W, Eggert C, Lam J, Leavitt J, Kawamura I, Reddy A, Morrow B, Schneider C, Petru J, Turagam M K, Koruth J S, Miller M A, Choudry S, Ellsworth B, Dukkipati S R, Neuzil P, Reddy V Y 2020 HeartRhythm 17 1528Google Scholar
[5] Neven K, van Es R, van Driel V, van Wessel H, Fidder H, Vink A, Doevendans P, Wittkampf F 2017 Circ. Arrhythm. Electrophysiol. 10 e004672Google Scholar
[6] van Driel V J H M, Neven K, van Wessel H, Vink A, Doevendans P A F M, Wittkampf F H M 2015 HeartRhythm 12 1838Google Scholar
[7] Calkins H, Hindricks G, Cappato R, et al. 2018 EP Europace. 20 157Google Scholar
[8] Li C Y, Li S N, Jiang C Y, Fu H, Liang M, Wang Z L, Zhong J Q, Zhou X H, Wu Q, Chang D, Wang Y, Zhou G Q, Liu W S, Song W, Sang C H, Long D Y, Du X, Dong J Z, Ma C S 2020 Pacing Clin Electrophysiol. 43 627Google Scholar
[9] Tolga A, Kivanc Y, Tumer Erdem G, Serdar B, Christian-H H, Roland R T 2019 J. Atr. Fibrillation 12 2208Google Scholar
[10] Chen X H, Ren Z G, Zhu T Y, Zhang X X, Peng Z Y, Xie H Y, Zhou L, Yin S Y, Sun J Y, Zheng S S 2015 Sci. Rep. 5 16233Google Scholar
[11] Gómez-Barea M, García-Sánchez T, Ivorra A 2022 Sci. Rep. 12 16144Google Scholar
[12] du Pré B C, van Driel V J, van Wessel H, Loh P, Doevendans P A, Goldschmeding R, Wittkampf F H, Vink A 2013 EP Europace 15 144Google Scholar
[13] Lavee J, Onik G, Mikus P, Rubinsky B 2007 Heart Surg. Forum. 10 E162Google Scholar
[14] Neven K, van Driel V, van Wessel H, van Es R, Doevendans P A, Wittkampf F 2014 HeartRhythm 11 1465Google Scholar
[15] Wittkampf F H, Van Driel V J, Van Wessel H, Vink A, Hof I E, Gründeman P F, Hauer R N, Loh P 2011 J. Cardiovasc. Electrophysiol. 22 302Google Scholar
[16] Wittkampf F H M, van Driel V J, van Wessel H, Neven K G E J, Gründeman P F, Vink A, Loh P, Doevendans P A 2012 Circ. Arrhythm. Electrophysiol. 5 581Google Scholar
[17] Koruth J S, Kuroki K, Iwasawa J, Viswanathan R, Brose R, Buck E D, Donskoy E, Dukkipati S R, Reddy V Y 2020 EP Europace 22 434Google Scholar
[18] Maan A, Koruth J 2022 Curr. Cardiol. Rep. 24 103Google Scholar
[19] Reddy V Y, Koruth J, Jais P, Petru J, Timko F, Skalsky I, Hebeler R, Labrousse L, Barandon L, Kralovec S, Funosako M, Mannuva B B, Sediva L, Neuzil P 2018 JACC Clin Electrophysiol. 4 987Google Scholar
[20] Arshad R N, Abdul-Malek Z, Munir A, Ahmad M H, Sidik M A B, Nawawi Z 2021 2021 IEEE International Conference on the Properties and Applications of Dielectric Materials (ICPADM) Johor Bahru, Malaysia, July 11–15 July, 2021 p250
[21] Bardy G H, Coltorti F, Ivey T D, Alferness C, Rackson M, Hansen K, Stewart R, Greene H L 1986 Circulation 73 525Google Scholar
[22] Kandušer M, Belič A, Čorović S, Škrjanc I 2017 Sci. Rep. 7 8115Google Scholar
[23] Barak M, Katz Y 2005 CHEST 128 2918Google Scholar
[24] Holt P M, Boyd E G 1986 Circulation 73 1029Google Scholar
[25] Rowland E, Foale R, Nihoyannopoulos P, Perelman M, Krikler D M 1985 Heart 53 240Google Scholar
[26] Deneke T, Jais P, Scaglione M, Schmitt R, Di Biase L, Christopoulos G, Schade A, Mügge A, Bansmann M, Nentwich K, Müller P, Krug J, Roos M, Halbfass P, Natale A, Gaita F, Haines D 2015 J. Cardiovasc. Electrophysiol. 26 455Google Scholar
[27] Miyazaki S, Kajiyama T, Yamao K, Hada M, Yamaguchi M, Nakamura H, Hachiya H, Tada H, Hirao K, Iesaka Y 2019 Heart Rhythm 16 41Google Scholar
[28] Miyazaki S, Watanabe T, Kajiyama T, Iwasawa J, Ichijo S, Nakamura H, Taniguchi H, Hirao K, Iesaka Y 2017 Circ. Arrhythm. Electrophysiol. 10 e005612Google Scholar
[29] Warton J M 2012 Yearbook of Cardiology 2012 440Google Scholar
[30] van Es R, Groen M H A, Stehouwer M, Doevendans P A, Wittkampf F H M, Neven K 2019 J. Cardiovasc. Electrophysiol. 30 2071Google Scholar
[31] Osuna I A R, Cobelli P, Olaiz N 2022 Micromachines 13 1234Google Scholar
[32] Zhang R B, Zheng N C, Liu H Y, Wang L M 2015 IEEE Trans. Plasma Sci. 43 610Google Scholar
[33] Zhang R B, Li X, Wang Z Y 2019 IEEE Trans. Dielectr. Electr. Insul. 26 353Google Scholar
[34] Bradley C J, Haines D E 2020 J. Cardiovasc. Electrophysiol. 31 2136Google Scholar
[35] Zhang R B, Li X, Wang Z Y, Chen Z H, Du G 2018 Appl. Phys. Lett. 113 063701Google Scholar
[36] Jinback H, Stewart M T, Cheek D S, Francischelli D E, Kirchhof N 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society Minneapolis, MN, September 3–6, 2009 p3381
[37] Livia C, Sugrue A, Witt T, Polkinghorne M D, Maor E, Kapa S, Lehmann H I, DeSimone C V, Behfar A, Asirvatham S J, McLeod C J 2018 J. Am. Heart Assoc. 7 e009070Google Scholar
[38] Niessen C, Igl J, Pregler B, Beyer L, Noeva E, Dollinger M, Schreyer A G, Jung E M, Stroszczynski C, Wiggermann P 2015 J. Vasc. Interv. Radiol. 26 694Google Scholar
[39] Zager Y, Kain D, Landa N, Leor J, Maor E 2016 PLoS One 11 e0165475Google Scholar
[40] Zimmerman A, Grand D, Charpentier K 2017 J. Hepatocell. Carcinoma 4 49Google Scholar
[41] 王力, 陈林, 丰明俊, 马青 2009 北京生物医学工程 28 143Google Scholar
Wang L, Chen L, Feng M J, Ma Q 2009 Beijing Biomedical Engineering 28 143Google Scholar
[42] Rubinsky L, Guenther E, Mikus P, Stehling M, Rubinsky B 2016 Technol. Cancer Res. Treat. 15 NP95Google Scholar
[43] 张若兵, 杜钢, 傅贤, 梁大鹏 2014 高电压技术 40 1889Google Scholar
Zhang R B, Du G, Fu X, Liang D P 2014 High Voltage Eng. 40 1889Google Scholar
[44] Shneider M N, Pekker M 2013 J. Appl. Phys. 114 214906Google Scholar
[45] 李元, 李林波, 温嘉烨, 倪正全, 张冠军 2021 物理学报 70 024701Google Scholar
Li Y, Li L B, Wen J Y, Ni Z Q, Zhang G J 2021 Acta Phys. Sin. 70 024701Google Scholar
[46] Shneider M N, Pekker M 2013 Phys. Rev. E 87 043004Google Scholar
[47] 姚陈果, 郑爽, 赵亚军, 刘红梅, 王艺麟, 董守龙 2020 高电压技术 46 1830Google Scholar
Yao C G, Zheng S, Zhao Y J, Liu H M, Wang Y L, Dong S L 2020 High Voltage Eng. 46 1830Google Scholar
[48] Chung E M L, Banahan C, Patel N, Janus J, Marshall D, Horsfield M A, Rousseau C, Keelan J, Evans D H, Hague J P 2015 PLoS One 10 e0122166Google Scholar
[49] Haines D E, Stewart M T, Ahlberg S, Barka N D, Condie C, Fiedler G R, Kirchhof N A, Halimi F, Deneke T 2013 Circ. Arrhythm. Electrophysiol. 6 16Google Scholar
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图 1 (a)实验系统的简易图, 包含扩散气泡观察系统、针-环电极、示波器、脉冲发生装置; (b)针-环电极装置模型图; (c)针电极实物图; (d) 电导率14.08 mS/cm, 脉宽100 μs, 脉冲输出电压250 V时, 拍摄的扩散气泡图像
Fig. 1. (a) A simple diagram of the experimental system, including the diffusion bubble observation system, needle-ring electrode, oscilloscope, and pulse generation device; (b) a model of the needle-ring electrode device; (c) the actual diagram of the needle electrode; (d) the image of the diffusion bubble generated by theconductivity of 14.08 mS/cm, pulse width of 100 μs, pulse output voltage of 250 V.
图 3 不同电压时的电流波形图(电导率-脉宽-电压) (a) 140.8 mS/cm-100 μs-20/80 V; (b) 140.8 mS/cm-50 μs-20/80 V; (c) 140.8 mS/cm-100 μs-90 V
Fig. 3. Current waveform plot at different voltages (electrical conductivity-pulse width-voltage): (a) 140.8 mS/cm-100 μs-20/80 V; (b) 140.8 mS/cm-50 μs-20/80 V; (c) 140.8 mS/cm-100 μs-90 V.
图 7 气泡直径尺寸分布图 (电导率-脉宽) (a) 140.8 mS/cm-5 μs; (b) 140.8 mS/cm-10 μs; (c) 140.8 mS/cm-50 μs; (d) 140.8 mS/cm-100 μs; (e) 14.08 mS/cm-5 μs; (f) 14.08 mS/cm-10 μs; (g) 14.08 mS/cm-50 μs; (h) 14.08 mS/cm-100 μs; (i) 1.408 mS/cm-50 μs; (j) 1.408 mS/cm-100 μs
Fig. 7. Distribution of bubble diameter size (electrical conductivity-pulse width): (a) 140.8 mS/cm-5 μs; (b) 140.8 mS/cm-10 μs; (c) 140.8 mS/cm-50 μs; (d) 140.8 mS/cm-100 μs; (e) 14.08 mS/cm-5 μs; (f) 14.08 mS/cm-10 μs; (g) 14.08 mS/cm-50 μs; (h) 14.08 mS/cm-100 μs; (i) 1.408 mS/cm-50 μs; (j) 1.408 mS/cm-100 μs.
表 1 脉冲参数表
Table 1. Pulse parameter table.
电导率/
(mS·cm–1)脉宽/μs 电压/V 140.8 5 100 120 140 160 180 200 10 60 80 100 120 140 160 50 20 30 40 50 60 70 100 10 20 30 40 50 60 14.08 5 650 700 750 800 850 900 10 400 450 500 550 600 650 50 200 225 250 275 300 325 100 125 150 175 200 225 250 1.408 50 800 820 840 860 880 900 100 600 650 700 750 800 850 表 2 扩散气泡面积随电压变化的拟合方程
Table 2. Fitting equation for the area of diffusion bubble with voltage.
电导率/(mS·cm–1) 脉宽/μs Y=AX+B A B 横截距 140.8 5 300 –34533 115 10 655 –52863 80 50 1452 –17757 12 100 2597 –20567 8 14.08 5 35 –23288 665 10 60 –24444 407 50 498 –108883 218 100 712 –104663 146 1.408 50 9.5 –7541 793 100 35 –23448 669 表 3 不同脉冲参数的输入能量表
Table 3. Input energy table for different pulse parameters.
电导率/(mS·cm–1) 脉宽/μs 输入能量/mJ 140.8 5 1.25 1.80 2.45 3.20 4.05 5.00 10 0.90 1.60 2.50 3.60 4.90 6.40 50 0.50 1.12 2.00 3.12 4.50 6.12 100 0.25 1.00 2.25 4.00 6.25 9.00 14.08 5 6.03 7.00 8.03 9.14 10.32 11.57 10 4.57 5.78 7.14 8.64 10.28 12.07 50 5.70 7.23 8.93 10.80 12.85 15.10 100 4.46 6.43 8.75 11.43 14.46 17.86 1.408 50 10.65 11.2 11.76 12.32 13.00 13.50 100 12.00 14.08 16.33 18.75 21.33 24.08 表 4 各脉冲参数下产生的最大气泡直径尺寸及平均气泡尺寸
Table 4. The maximum bubble diameter size and average bubble size generated under each pulse parameter.
电导率/(mS·cm–1) 脉宽/μs 最大气泡尺寸/平均气泡尺寸/ μm 140.8 5 0/0 60/23 85/27 130/28 145/31 160/32 10 0/0 100/21 135/27 155/25 190/28 220/29 50 33/16 80/26 90/32 130/39 160/38 220/37 100 24/14 100/27 130/37 190/36 200/44 225/42 14.08 5 25/14 40/23 55/24 70/24 75/25 90/23 10 35/19 55/23 65/25 80/25 95/28 115/25 50 20/18 40/22 115/25 135/28 145/29 200/31 100 35/17 80/25 90/28 110/29 175/33 190/35 1.408 50 15/13 18/14 20/15 22/14 25/16 30/16 100 35/20 42/19 42/21 52/23 55/24 62/22 -
[1] Kornej J, Börschel C S, Benjamin E J, Schnabel R B 2020 Circ. Res. 127 4Google Scholar
[2] Chen W, Zheng R, Baade P D, Zhang S, Zeng H, Bray F, Jemal A, Yu X Q, He J 2016 CA Cancer J. Clin. 66 115Google Scholar
[3] Koruth J S, Kuroki K, Kawamura I, Brose R, Viswanathan R, Buck E D, Donskoy E, Neuzil P, Dukkipati S R, Reddy V Y 2020 Circ. Arrhythm. Electrophysiol. 13 e008303Google Scholar
[4] Kuroki K, Whang W, Eggert C, Lam J, Leavitt J, Kawamura I, Reddy A, Morrow B, Schneider C, Petru J, Turagam M K, Koruth J S, Miller M A, Choudry S, Ellsworth B, Dukkipati S R, Neuzil P, Reddy V Y 2020 HeartRhythm 17 1528Google Scholar
[5] Neven K, van Es R, van Driel V, van Wessel H, Fidder H, Vink A, Doevendans P, Wittkampf F 2017 Circ. Arrhythm. Electrophysiol. 10 e004672Google Scholar
[6] van Driel V J H M, Neven K, van Wessel H, Vink A, Doevendans P A F M, Wittkampf F H M 2015 HeartRhythm 12 1838Google Scholar
[7] Calkins H, Hindricks G, Cappato R, et al. 2018 EP Europace. 20 157Google Scholar
[8] Li C Y, Li S N, Jiang C Y, Fu H, Liang M, Wang Z L, Zhong J Q, Zhou X H, Wu Q, Chang D, Wang Y, Zhou G Q, Liu W S, Song W, Sang C H, Long D Y, Du X, Dong J Z, Ma C S 2020 Pacing Clin Electrophysiol. 43 627Google Scholar
[9] Tolga A, Kivanc Y, Tumer Erdem G, Serdar B, Christian-H H, Roland R T 2019 J. Atr. Fibrillation 12 2208Google Scholar
[10] Chen X H, Ren Z G, Zhu T Y, Zhang X X, Peng Z Y, Xie H Y, Zhou L, Yin S Y, Sun J Y, Zheng S S 2015 Sci. Rep. 5 16233Google Scholar
[11] Gómez-Barea M, García-Sánchez T, Ivorra A 2022 Sci. Rep. 12 16144Google Scholar
[12] du Pré B C, van Driel V J, van Wessel H, Loh P, Doevendans P A, Goldschmeding R, Wittkampf F H, Vink A 2013 EP Europace 15 144Google Scholar
[13] Lavee J, Onik G, Mikus P, Rubinsky B 2007 Heart Surg. Forum. 10 E162Google Scholar
[14] Neven K, van Driel V, van Wessel H, van Es R, Doevendans P A, Wittkampf F 2014 HeartRhythm 11 1465Google Scholar
[15] Wittkampf F H, Van Driel V J, Van Wessel H, Vink A, Hof I E, Gründeman P F, Hauer R N, Loh P 2011 J. Cardiovasc. Electrophysiol. 22 302Google Scholar
[16] Wittkampf F H M, van Driel V J, van Wessel H, Neven K G E J, Gründeman P F, Vink A, Loh P, Doevendans P A 2012 Circ. Arrhythm. Electrophysiol. 5 581Google Scholar
[17] Koruth J S, Kuroki K, Iwasawa J, Viswanathan R, Brose R, Buck E D, Donskoy E, Dukkipati S R, Reddy V Y 2020 EP Europace 22 434Google Scholar
[18] Maan A, Koruth J 2022 Curr. Cardiol. Rep. 24 103Google Scholar
[19] Reddy V Y, Koruth J, Jais P, Petru J, Timko F, Skalsky I, Hebeler R, Labrousse L, Barandon L, Kralovec S, Funosako M, Mannuva B B, Sediva L, Neuzil P 2018 JACC Clin Electrophysiol. 4 987Google Scholar
[20] Arshad R N, Abdul-Malek Z, Munir A, Ahmad M H, Sidik M A B, Nawawi Z 2021 2021 IEEE International Conference on the Properties and Applications of Dielectric Materials (ICPADM) Johor Bahru, Malaysia, July 11–15 July, 2021 p250
[21] Bardy G H, Coltorti F, Ivey T D, Alferness C, Rackson M, Hansen K, Stewart R, Greene H L 1986 Circulation 73 525Google Scholar
[22] Kandušer M, Belič A, Čorović S, Škrjanc I 2017 Sci. Rep. 7 8115Google Scholar
[23] Barak M, Katz Y 2005 CHEST 128 2918Google Scholar
[24] Holt P M, Boyd E G 1986 Circulation 73 1029Google Scholar
[25] Rowland E, Foale R, Nihoyannopoulos P, Perelman M, Krikler D M 1985 Heart 53 240Google Scholar
[26] Deneke T, Jais P, Scaglione M, Schmitt R, Di Biase L, Christopoulos G, Schade A, Mügge A, Bansmann M, Nentwich K, Müller P, Krug J, Roos M, Halbfass P, Natale A, Gaita F, Haines D 2015 J. Cardiovasc. Electrophysiol. 26 455Google Scholar
[27] Miyazaki S, Kajiyama T, Yamao K, Hada M, Yamaguchi M, Nakamura H, Hachiya H, Tada H, Hirao K, Iesaka Y 2019 Heart Rhythm 16 41Google Scholar
[28] Miyazaki S, Watanabe T, Kajiyama T, Iwasawa J, Ichijo S, Nakamura H, Taniguchi H, Hirao K, Iesaka Y 2017 Circ. Arrhythm. Electrophysiol. 10 e005612Google Scholar
[29] Warton J M 2012 Yearbook of Cardiology 2012 440Google Scholar
[30] van Es R, Groen M H A, Stehouwer M, Doevendans P A, Wittkampf F H M, Neven K 2019 J. Cardiovasc. Electrophysiol. 30 2071Google Scholar
[31] Osuna I A R, Cobelli P, Olaiz N 2022 Micromachines 13 1234Google Scholar
[32] Zhang R B, Zheng N C, Liu H Y, Wang L M 2015 IEEE Trans. Plasma Sci. 43 610Google Scholar
[33] Zhang R B, Li X, Wang Z Y 2019 IEEE Trans. Dielectr. Electr. Insul. 26 353Google Scholar
[34] Bradley C J, Haines D E 2020 J. Cardiovasc. Electrophysiol. 31 2136Google Scholar
[35] Zhang R B, Li X, Wang Z Y, Chen Z H, Du G 2018 Appl. Phys. Lett. 113 063701Google Scholar
[36] Jinback H, Stewart M T, Cheek D S, Francischelli D E, Kirchhof N 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society Minneapolis, MN, September 3–6, 2009 p3381
[37] Livia C, Sugrue A, Witt T, Polkinghorne M D, Maor E, Kapa S, Lehmann H I, DeSimone C V, Behfar A, Asirvatham S J, McLeod C J 2018 J. Am. Heart Assoc. 7 e009070Google Scholar
[38] Niessen C, Igl J, Pregler B, Beyer L, Noeva E, Dollinger M, Schreyer A G, Jung E M, Stroszczynski C, Wiggermann P 2015 J. Vasc. Interv. Radiol. 26 694Google Scholar
[39] Zager Y, Kain D, Landa N, Leor J, Maor E 2016 PLoS One 11 e0165475Google Scholar
[40] Zimmerman A, Grand D, Charpentier K 2017 J. Hepatocell. Carcinoma 4 49Google Scholar
[41] 王力, 陈林, 丰明俊, 马青 2009 北京生物医学工程 28 143Google Scholar
Wang L, Chen L, Feng M J, Ma Q 2009 Beijing Biomedical Engineering 28 143Google Scholar
[42] Rubinsky L, Guenther E, Mikus P, Stehling M, Rubinsky B 2016 Technol. Cancer Res. Treat. 15 NP95Google Scholar
[43] 张若兵, 杜钢, 傅贤, 梁大鹏 2014 高电压技术 40 1889Google Scholar
Zhang R B, Du G, Fu X, Liang D P 2014 High Voltage Eng. 40 1889Google Scholar
[44] Shneider M N, Pekker M 2013 J. Appl. Phys. 114 214906Google Scholar
[45] 李元, 李林波, 温嘉烨, 倪正全, 张冠军 2021 物理学报 70 024701Google Scholar
Li Y, Li L B, Wen J Y, Ni Z Q, Zhang G J 2021 Acta Phys. Sin. 70 024701Google Scholar
[46] Shneider M N, Pekker M 2013 Phys. Rev. E 87 043004Google Scholar
[47] 姚陈果, 郑爽, 赵亚军, 刘红梅, 王艺麟, 董守龙 2020 高电压技术 46 1830Google Scholar
Yao C G, Zheng S, Zhao Y J, Liu H M, Wang Y L, Dong S L 2020 High Voltage Eng. 46 1830Google Scholar
[48] Chung E M L, Banahan C, Patel N, Janus J, Marshall D, Horsfield M A, Rousseau C, Keelan J, Evans D H, Hague J P 2015 PLoS One 10 e0122166Google Scholar
[49] Haines D E, Stewart M T, Ahlberg S, Barka N D, Condie C, Fiedler G R, Kirchhof N A, Halimi F, Deneke T 2013 Circ. Arrhythm. Electrophysiol. 6 16Google Scholar
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