液体中高压脉冲电场产生扩散气泡的规律

武晓东; 陈沿州; 韩瑞; 郭雨怡; 庄杰; 石富坤

doi:10.7498/aps.72.20230443

摘要

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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
中国科学技术大学生物医学工程学院(苏州), 生命科学与医学部, 苏州　215163

2.
中国科学院苏州生物医学工程技术研究所, 苏州　215163

3.
济南国科医工科技发展有限公司, 济南　250101

通信作者: 石富坤, fukunshi@sibet.ac.cn

基金项目: 苏州市基础研究试点项目(批准号: SJC2021025)、山东省自然科学基金 (批准号: ZR2022QE168) 和泉城5150引才倍增计划资助的课题.

Authors and contacts

1.
Division of Life Sciences and Medicine, School of Biomedical Engineering (Suzhou), University of Science and Technology of China, Suzhou 215163, China

2.
Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou 215163, China

3.
Jinan Guoke Medical Technology Development Co., Ltd, Jinan 250101, China

Corresponding author: Shi Fu-Kun, fukunshi@sibet.ac.cn

Funds: Project supported by the Basic Research Pilot Project of Suzhou, China (Grant No. SJC2021025), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2022QE168), and the Quancheng 5150 Project, China.

文章全文 : translate this paragraph

参考文献

[1]	Kornej J, Börschel C S, Benjamin E J, Schnabel R B 2020 Circ. Res. 127 4 Google 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. 66 115 Google 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 e008303 Google 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 1528 Google 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 e004672 Google 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 1838 Google Scholar
[7]	Calkins H, Hindricks G, Cappato R, et al. 2018 EP Europace. 20 157 Google 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. 43 627 Google Scholar
[9]	Tolga A, Kivanc Y, Tumer Erdem G, Serdar B, Christian-H H, Roland R T 2019 J. Atr. Fibrillation 12 2208 Google 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 16233 Google Scholar
[11]	Gómez-Barea M, García-Sánchez T, Ivorra A 2022 Sci. Rep. 12 16144 Google 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 15 144 Google Scholar
[13]	Lavee J, Onik G, Mikus P, Rubinsky B 2007 Heart Surg. Forum. 10 E162 Google Scholar
[14]	Neven K, van Driel V, van Wessel H, van Es R, Doevendans P A, Wittkampf F 2014 HeartRhythm 11 1465 Google 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. 22 302 Google 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. 5 581 Google 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 22 434 Google Scholar
[18]	Maan A, Koruth J 2022 Curr. Cardiol. Rep. 24 103 Google 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. 4 987 Google 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 73 525 Google Scholar
[22]	Kandušer M, Belič A, Čorović S, Škrjanc I 2017 Sci. Rep. 7 8115 Google Scholar
[23]	Barak M, Katz Y 2005 CHEST 128 2918 Google Scholar
[24]	Holt P M, Boyd E G 1986 Circulation 73 1029 Google Scholar
[25]	Rowland E, Foale R, Nihoyannopoulos P, Perelman M, Krikler D M 1985 Heart 53 240 Google 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. 26 455 Google 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 41 Google 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 e005612 Google Scholar
[29]	Warton J M 2012 Yearbook of Cardiology 2012 440 Google 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 2071 Google Scholar
[31]	Osuna I A R, Cobelli P, Olaiz N 2022 Micromachines 13 1234 Google Scholar
[32]	Zhang R B, Zheng N C, Liu H Y, Wang L M 2015 IEEE Trans. Plasma Sci. 43 610 Google Scholar
[33]	Zhang R B, Li X, Wang Z Y 2019 IEEE Trans. Dielectr. Electr. Insul. 26 353 Google Scholar
[34]	Bradley C J, Haines D E 2020 J. Cardiovasc. Electrophysiol. 31 2136 Google Scholar
[35]	Zhang R B, Li X, Wang Z Y, Chen Z H, Du G 2018 Appl. Phys. Lett. 113 063701 Google 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 e009070 Google 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. 26 694 Google Scholar
[39]	Zager Y, Kain D, Landa N, Leor J, Maor E 2016 PLoS One 11 e0165475 Google Scholar
[40]	Zimmerman A, Grand D, Charpentier K 2017 J. Hepatocell. Carcinoma 4 49 Google Scholar
[41]	王力, 陈林, 丰明俊, 马青 2009 北京生物医学工程 28 143 Google Scholar Wang L, Chen L, Feng M J, Ma Q 2009 Beijing Biomedical Engineering 28 143 Google Scholar
[42]	Rubinsky L, Guenther E, Mikus P, Stehling M, Rubinsky B 2016 Technol. Cancer Res. Treat. 15 NP95 Google Scholar
[43]	张若兵, 杜钢, 傅贤, 梁大鹏 2014 高电压技术 40 1889 Google Scholar Zhang R B, Du G, Fu X, Liang D P 2014 High Voltage Eng. 40 1889 Google Scholar
[44]	Shneider M N, Pekker M 2013 J. Appl. Phys. 114 214906 Google Scholar
[45]	李元, 李林波, 温嘉烨, 倪正全, 张冠军 2021 物理学报 70 024701 Google Scholar Li Y, Li L B, Wen J Y, Ni Z Q, Zhang G J 2021 Acta Phys. Sin. 70 024701 Google Scholar
[46]	Shneider M N, Pekker M 2013 Phys. Rev. E 87 043004 Google 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 1830 Google Scholar Yao C G, Zheng S, Zhao Y J, Liu H M, Wang Y L, Dong S L 2020 High Voltage Eng. 46 1830 Google 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 e0122166 Google 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 16 Google Scholar

施引文献

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.

下载: 全尺寸图片幻灯片

图 2 (a) YZ截面场强分布图; (b) XY截面场强分布图

Fig. 2. (a) Field intensity distribution of the YZ cross-section; (b) field intensity distribution of the XY cross-section.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

图 4 不同电导率下, 扩散气泡面积随电压变化的线性拟合图　(a) 140.8 mS/cm; (b) 14.08 mS/cm; (c) 1.408 mS/cm

Fig. 4. Linear fit of diffusion bubble area with voltage under different electrical conductivity: (a) 140.8 mS/cm; (b) 14.08 mS/cm; (c) 1.408 mS/cm.

下载: 全尺寸图片幻灯片

图 5 不同电导率下, 针电极为阳极时的扩散气泡面积统计　(a) 140.8 mS/cm; (b) 14.08 mS/cm

Fig. 5. Statistical analysis of the diffusion bubble area when the needle electrode acts as an anode under different electrical conductivity: (a) 140.8 mS/cm; (b) 14.08 mS/cm.

下载: 全尺寸图片幻灯片

图 6 不同电导率下, 扩散气泡面积随输入能量变化的拟合图　(a) 140.8 mS/cm; (b) 14.08 mS/cm; (c) 1.408 mS/cm

Fig. 6. Fitted plot of diffusion bubbles area as a function of input energy under different electrical conductivity: (a) 140.8 mS/cm; (b) 14.08 mS/cm; (c) 1.408 mS/cm.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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
1.408	100	600	650	700	750	800	850

下载: 导出CSV

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
电导率/(mS·cm^–1)	脉宽/μs	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
1.408	100	35	–23448	669

下载: 导出CSV

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
1.408	100	12.00	14.08	16.33	18.75	21.33	24.08

下载: 导出CSV

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
1.408	100	35/20	42/19	42/21	52/23	55/24	62/22

下载: 导出CSV

[1]	Kornej J, Börschel C S, Benjamin E J, Schnabel R B 2020 Circ. Res. 127 4 Google 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. 66 115 Google 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 e008303 Google 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 1528 Google 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 e004672 Google 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 1838 Google Scholar
[7]	Calkins H, Hindricks G, Cappato R, et al. 2018 EP Europace. 20 157 Google 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. 43 627 Google Scholar
[9]	Tolga A, Kivanc Y, Tumer Erdem G, Serdar B, Christian-H H, Roland R T 2019 J. Atr. Fibrillation 12 2208 Google 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 16233 Google Scholar
[11]	Gómez-Barea M, García-Sánchez T, Ivorra A 2022 Sci. Rep. 12 16144 Google 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 15 144 Google Scholar
[13]	Lavee J, Onik G, Mikus P, Rubinsky B 2007 Heart Surg. Forum. 10 E162 Google Scholar
[14]	Neven K, van Driel V, van Wessel H, van Es R, Doevendans P A, Wittkampf F 2014 HeartRhythm 11 1465 Google 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. 22 302 Google 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. 5 581 Google 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 22 434 Google Scholar
[18]	Maan A, Koruth J 2022 Curr. Cardiol. Rep. 24 103 Google 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. 4 987 Google 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 73 525 Google Scholar
[22]	Kandušer M, Belič A, Čorović S, Škrjanc I 2017 Sci. Rep. 7 8115 Google Scholar
[23]	Barak M, Katz Y 2005 CHEST 128 2918 Google Scholar
[24]	Holt P M, Boyd E G 1986 Circulation 73 1029 Google Scholar
[25]	Rowland E, Foale R, Nihoyannopoulos P, Perelman M, Krikler D M 1985 Heart 53 240 Google 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. 26 455 Google 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 41 Google 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 e005612 Google Scholar
[29]	Warton J M 2012 Yearbook of Cardiology 2012 440 Google 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 2071 Google Scholar
[31]	Osuna I A R, Cobelli P, Olaiz N 2022 Micromachines 13 1234 Google Scholar
[32]	Zhang R B, Zheng N C, Liu H Y, Wang L M 2015 IEEE Trans. Plasma Sci. 43 610 Google Scholar
[33]	Zhang R B, Li X, Wang Z Y 2019 IEEE Trans. Dielectr. Electr. Insul. 26 353 Google Scholar
[34]	Bradley C J, Haines D E 2020 J. Cardiovasc. Electrophysiol. 31 2136 Google Scholar
[35]	Zhang R B, Li X, Wang Z Y, Chen Z H, Du G 2018 Appl. Phys. Lett. 113 063701 Google 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 e009070 Google 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. 26 694 Google Scholar
[39]	Zager Y, Kain D, Landa N, Leor J, Maor E 2016 PLoS One 11 e0165475 Google Scholar
[40]	Zimmerman A, Grand D, Charpentier K 2017 J. Hepatocell. Carcinoma 4 49 Google Scholar
[41]	王力, 陈林, 丰明俊, 马青 2009 北京生物医学工程 28 143 Google Scholar Wang L, Chen L, Feng M J, Ma Q 2009 Beijing Biomedical Engineering 28 143 Google Scholar
[42]	Rubinsky L, Guenther E, Mikus P, Stehling M, Rubinsky B 2016 Technol. Cancer Res. Treat. 15 NP95 Google Scholar
[43]	张若兵, 杜钢, 傅贤, 梁大鹏 2014 高电压技术 40 1889 Google Scholar Zhang R B, Du G, Fu X, Liang D P 2014 High Voltage Eng. 40 1889 Google Scholar
[44]	Shneider M N, Pekker M 2013 J. Appl. Phys. 114 214906 Google Scholar
[45]	李元, 李林波, 温嘉烨, 倪正全, 张冠军 2021 物理学报 70 024701 Google Scholar Li Y, Li L B, Wen J Y, Ni Z Q, Zhang G J 2021 Acta Phys. Sin. 70 024701 Google Scholar
[46]	Shneider M N, Pekker M 2013 Phys. Rev. E 87 043004 Google 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 1830 Google Scholar Yao C G, Zheng S, Zhao Y J, Liu H M, Wang Y L, Dong S L 2020 High Voltage Eng. 46 1830 Google 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 e0122166 Google 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 16 Google Scholar

[1]	王孟莎, 徐强, 聂腾飞, 罗欣怡, 郭烈锦. 电解液浓度对光电极表面气泡演化及传质特性的影响. 物理学报, 2024, 73(18): 188201. doi: 10.7498/aps.73.20240533
[2]	张福平, 李玺钦, 杜金梅, 刘雨生, 叶福庆. 铁电陶瓷脉冲耐压失效分布及耐压可靠性. 物理学报, 2024, 73(10): 107701. doi: 10.7498/aps.73.20231354
[3]	乌日乐格, 那仁满都拉. 具有传质传热及扩散效应的双气泡的相互作用. 物理学报, 2023, 72(19): 194703. doi: 10.7498/aps.72.20230863
[4]	孟星柔, 刘若琪, 贺亚峰, 邓腾坤, 刘富成. 反应扩散系统中交叉扩散引发的图灵斑图之间的转变. 物理学报, 2023, 72(19): 198201. doi: 10.7498/aps.72.20230333
[5]	庄杰, 韩瑞, 季振宇, 石富坤. 量化电导率模型参数多样性导致的脉冲电场消融预测的不确定性. 物理学报, 2023, 72(14): 147701. doi: 10.7498/aps.72.20230203
[6]	鞠晓璐, 李可, 余福成, 许明伟, 邓彪, 李宾, 肖体乔. 电解池电化学反应过程的运动衬度X射线成像. 物理学报, 2022, 71(14): 144101. doi: 10.7498/aps.71.20220339
[7]	钟诚, 陈智全, 杨伟国, 夏辉. 电解质对浓悬浮液中胶体颗粒扩散特性的影响. 物理学报, 2013, 62(21): 214207. doi: 10.7498/aps.62.214207
[8]	沈礼, 野仕伟, 戴长建. 电场中Eu原子电离阈移动的实验研究. 物理学报, 2012, 61(6): 063301. doi: 10.7498/aps.61.063301
[9]	袁强, 胡东霞, 张鑫, 赵军普, 胡思得, 黄文会, 魏晓峰. 激光脉冲参数对冲击点火的影响. 物理学报, 2011, 60(4): 045207. doi: 10.7498/aps.60.045207
[10]	张福平, 杜金梅, 刘雨生, 刘艺, 刘高旻, 贺红亮. PZT 95/5陶瓷电致失效机理研究. 物理学报, 2011, 60(5): 057701. doi: 10.7498/aps.60.057701
[11]	陈怀军, 莫嘉琪. 双参数奇摄动非线性反应扩散问题. 物理学报, 2010, 59(7): 4409-4412. doi: 10.7498/aps.59.4409
[12]	吕耀平, 顾国锋, 陆华春, 戴瑜, 唐国宁. 在不同扩散系数下反应扩散平面波的折射. 物理学报, 2009, 58(5): 2996-3000. doi: 10.7498/aps.58.2996
[13]	胡艺, 葛云, 章东, 郑海荣, 龚秀芬. 调频超声脉冲驱动微气泡运动偏移的研究. 物理学报, 2009, 58(7): 4746-4751. doi: 10.7498/aps.58.4746
[14]	吴俊林, 黄新民. 非广延反应扩散系统的广义主方程. 物理学报, 2006, 55(12): 6234-6237. doi: 10.7498/aps.55.6234
[15]	何寿杰, 陈岐岱, 李雪辰, 艾希成, 张建平, 王龙. 圆锥气泡声致发光光脉冲和光谱. 物理学报, 2005, 54(2): 977-981. doi: 10.7498/aps.54.977
[16]	李子荣, 孟庆安, 管荻华, 王刚. PAN为基凝胶聚合物电解质自扩散系数的NMR研究. 物理学报, 1999, 48(6): 1175-1178. doi: 10.7498/aps.48.1175
[17]	陶悦群, 邱励俭. 弹丸消融过程的数值分析(Ⅰ). 物理学报, 1988, 37(10): 1672-1677. doi: 10.7498/aps.37.1672
[18]	陈式刚. 反应扩散系统中的涨落问题. 物理学报, 1982, 31(1): 50-57. doi: 10.7498/aps.31.50
[19]	张承福, 吴惟敏. 随机磁场中的双极电场与双极扩散. 物理学报, 1981, 30(3): 333-343. doi: 10.7498/aps.30.333
[20]	陈良恒. 不可逆化学反应扩散方程. 物理学报, 1981, 30(7): 857-865. doi: 10.7498/aps.30.857

计量

文章访问数: 3040
PDF下载量: 93
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板