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

庄杰; 韩瑞; 季振宇; 石富坤

doi:10.7498/aps.72.20230203

摘要

脉冲电场消融(pulsed field ablation, PFA)以其非热、消融边界清晰等优势成为肿瘤和组织消融的关注重点. 然而, 组织生物物理特性和脉冲参数的多样性导致PFA效果难以预测. 本研究考虑PFA消融阈值和两个常用电导率模型参数的不确定性, 评估其对消融深度的影响. 从模型复杂度、参数敏感度分布、模型鲁棒性给出了模型选择的指标. 结果表明单因素决定的模型具有更强的鲁棒性. 消融阈值和组织初始电导率依次是影响消融深度评估的两个最敏感参数. 该策略可用于多种数学物理和仿真模型, 以增强模型可信度和简化模型.

关键词:

Abstract

Pulsed field ablation (PFA) is a new type of physical energy source in the fields of tumor and atrial fibrillation ablation, which is based on irreversible electroporation with non-thermal, clear ablation boundaries, selective killing, and rapid advantages. The PFA triggers off the changes in the electrical conductivity of ablation zone, which can be described by a step function and used to predict the ablation zone. However, current research does not compare the advantages and disadvantages of different conductivity models, nor does it consider the effects of model parameter change caused by individual differences and errors on the efficacy of PFA. This work is devoted to comparing two commonly used conductivity models (Heaviside model and Gompertz model), and quantifying the influence of model input uncertainty on model output and PFA ablation zone.In this work, we carry out uncertainty quantification and sensitivity analysis to quantify the influence of model parameter uncertainty on model output, clarify the parameter sensitivity distribution, and provide model selection criteria from the perspectives of model complexity, parameter sensitivity distribution, and model robustness. Combined with finite element simulation, the study quantifies the effects of uncertainty in the most sensitive parameters of the conductivity model and ablation threshold on the PFA ablation zone. The results show that different conductivity models exhibit different robustness under the same proportion of variation in parameters. The Heaviside model, which is determined by a single factor, has strong robustness. The uncertainty output of the Gompertz model is jointly determined by multiple sensitivity parameters, making it susceptible to various conditions. The ablation threshold and pre-treatment tissue conductivity are the two most sensitive parameters affecting the assessment of ablation depth. Changes in the ablation threshold result in a Gaussian distribution of ablation depth. The greater the change in pre-treatment tissue conductivity, the greater the change in ablation depth is, which, however, follows a nonlinear proportional relationship. This approach can improve the accuracy and reliability of PFA ablation prediction, and provide a visual and global way to show the influence of input uncertainties on model output and parameter sensitivity ranking, thus effectively improving the accuracy of model prediction, reducing computational costs, and optimizing the selection of candidate models. This strategy can be applied to a variety of mathematical physics and simulation models to enhance model credibility and simplify the models.

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　215000

2.
中国科学院苏州生物医学工程技术研究所, 苏州　215163

3.
空军军医大学军事生物医学工程学系, 西安　710032

4.
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)和科技部重点研发计划(批准号: 2019YFC0119102)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 215000, China

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

3.
Faculty of Biomedical Engineering, Air Force Military Medical University, Xi’an 710032, China

4.
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 National Key R&D Program of China (Grant No. 2019YFC0119102).

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参考文献

[1]	Ivorra A, Al-Sakere B, Rubinsky B, Mir L M 2009 Phys. Med. Biol. 54 5949 Google Scholar
[2]	Sel D, Cukjati D, Batiuskaite D, Slivnik T, Mir L M, Miklavcic D 2005 IEEE T. Bio-Med. Eng. 52 816 Google Scholar
[3]	Garcia P A, Rossmeisl J H, Davalos R V 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society Guadalajara, Mexico, 30 Auguest–3 September, 2011 pp739–742
[4]	Perera-Bel E, Aycock K N, Salameh Z S, Gómez-Barea M, Davalos R V, Ivorra A, Ballester M A G 2022 IEEE T. Bio-Med. Eng. 70 1902
[5]	Neal R E, Garcia P A, Robertson J L, Davalos R V 2012 IEEE T. Bio-Med. Eng. 59 1076 Google Scholar
[6]	Zhao Y, Bhonsle S, Dong S, Lyu Y, Liu H, Safaai-Jazi A, Davalos R V, Yao C 2018 IEEE T. Bio-Med. Eng. 65 1810 Google Scholar
[7]	Shi F, Steuer A, Zhuang J, Kolb J F 2019 IEEE T. Bio-Med. Eng. 66 2010 Google Scholar
[8]	郭雨怡, 石富坤, 王群, 季振宇, 庄杰 2022 物理学报 71 068701 Google Scholar Guo Y Y, Shi F K, Wang Q, Ji Z Y, Zhuang J 2022 Acta Phys. Sin. 71 068701 Google Scholar
[9]	Shi F, Kolb J F 2020 Biosens. Bioelectron. 157 112149 Google Scholar
[10]	Bounik R, Cardes F, Ulusan H, Modena M M, Hierlemann A 2022 BMEF 2022 9857485
[11]	Corovic S, Lackovic I, Sustaric P, Sustar T, Rodic T, Miklavcic D 2013 BioMed. Eng. OnLine 12 16 Google Scholar
[12]	Zhao Y J, Davalos R V 2020 Appl. Phys. Lett. 117 143702 Google Scholar
[13]	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 Yao C G, Zhen S, Zhao Y Z, Liu H M, Wang Y L, Dong S L 2020 High Voltage Engineering 46 1830 (in Chinese)
[14]	Smith R C 2013 Uncertainty Quantification: Theory, Implementation, and Applications (Vol. 12) (Siam)
[15]	Lai X, Wang S, Ma S, Xie J, Zheng Y 2020 Electrochimica Acta 330 135239 Google Scholar
[16]	Vazquez-Arenas J, Gimenez L E, Fowler M, Han T, Chen S K 2014 Energ. Convers. Manage. 87 472 Google Scholar
[17]	Edouard C, Petit M, Forgez C, Bernard J, Revel R 2016 JOPS 325 482
[18]	Ye X, Liu S, Yin H, He Q, Xue Z, Lu C, Su S 2021 Front. Cardiovasc. Med. 8
[19]	张家明陈志坚 2022 临床心血管病杂志 38 851 Zhang J M, Chen Z J 2022 J Clin. Cardiol. 38 851
[20]	O’Brien T J, Lorenzo M F, Zhao Y, Neal Ii R E, Robertson J L, Goldberg S N, Davalos R V 2019 Int. J. Hyperther. 36 952 Google Scholar
[21]	Lemieux C 2009 Monte Carlo and Quasi-Monte Carlo Sampling (Springer, New York, NY)
[22]	Haemmerich D, Schutt D J, Wright A S, Webster J G, Mahvi D M 2009 Physiol. Meas. 30 459 Google Scholar
[23]	Sobol′ I M 2001 Math. Comput. Simulat. 55 271 Google Scholar
[24]	Oliveira J F, Jorge D C P, Veiga R V, Rodrigues M S, Torquato M F, da Silva N B, Fiaccone R L, Cardim L L, Pereira F A C, de Castro C P, Paiva A S S, Amad A A S, Lima E A B F, Souza D S, Pinho S T R, Ramos P I P, Andrade R F S 2021 Nat. Commun. 12 333 Google Scholar
[25]	Kaminska I, Kotulska M, Stecka A, Saczko J, Drag-Zalesinska M, Wysocka T, Choromanska A, Skolucka N, Nowicki R, Marczak J, Kulbacka J 2012 Gen. Physiol. Biophys. 31 19 Google Scholar
[26]	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. Electrophy. 4 987 Google Scholar
[27]	Belalcazar A 2021 Heart Rhythm 2 560 Google Scholar
[28]	Kos B, Zupanic A, Kotnik T, Snoj M, Sersa G, Miklavcic D 2010 J. Membrane Biol. 236 147 Google Scholar
[29]	Shi F, Zhuang J, Kolb J F 2019 J. Phys. D 52 495401 Google Scholar
[30]	Perera-Bel E, Mercadal B, Garcia-Sanchez T, Ballester M A G, Ivorra A 2021 IEEE T. Bio-Med. Eng. 68 1318

施引文献

图 1 1/6三维PVI脉冲电场消融模型

Fig. 1. One-sixth three-dimensional PVI pulsed electric field ablation model.

下载: 全尺寸图片幻灯片

图 2 H模型和G模型的电导率输出的平均值、标准差和90%预测空间

Fig. 2. Mean value, standard deviation, and 90% prediction space of conductivity output of H and G models.

下载: 全尺寸图片幻灯片

图 3 H模型和 G 模型的各参数一阶Sobol敏感度指数和平均Sobol指数

Fig. 3. First order Sobol sensitivity index and average Sobol index of each parameter of the H and G models.

下载: 全尺寸图片幻灯片

图 4 三维PVI消融模型的电场分布

Fig. 4. Electric field distribution of three-dimensional PVI ablation model.

下载: 全尺寸图片幻灯片

图 5 改变σ₀, 不确定度分别为10% ((a), (c))和20% ((b), (d))时, 消融深度的统计结果

Fig. 5. The statistical results of the ablation depth by changing σ₀ with uncertainty of 10% ((a), (c)) and 20%((b), (d)).

下载: 全尺寸图片幻灯片

图 6 消融阈值的均匀分布导致消融深度呈高斯分布

Fig. 6. The uniform distribution of the ablation threshold results in a Gaussian distribution of the ablation depth.

下载: 全尺寸图片幻灯片

图 7 用于多模型评估的UQ和SA示意图

Fig. 7. Schematic diagram for UQ and SA for multi-model evaluation.

下载: 全尺寸图片幻灯片

表 1 不同模型的参数

Table 1. Parameters for different models

参数	模型
参数	Heaviside	Gompertz
σ₀/(S·m^–1)	0.23	0.23
α	0.02	0.02
T₀/℃	37	37
T/℃	40	40
E₀/(V·cm^–1)	850	—
E₁/(V·cm^–1）	1550	—
W	0.90	—
σ_m/(S·m^–1)	—	0.44
E_i/(V·cm^–1）	—	870
E_m/(V·cm^–1)	—	1038
D	—	18

下载: 导出CSV

[1]	Ivorra A, Al-Sakere B, Rubinsky B, Mir L M 2009 Phys. Med. Biol. 54 5949 Google Scholar
[2]	Sel D, Cukjati D, Batiuskaite D, Slivnik T, Mir L M, Miklavcic D 2005 IEEE T. Bio-Med. Eng. 52 816 Google Scholar
[3]	Garcia P A, Rossmeisl J H, Davalos R V 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society Guadalajara, Mexico, 30 Auguest–3 September, 2011 pp739–742
[4]	Perera-Bel E, Aycock K N, Salameh Z S, Gómez-Barea M, Davalos R V, Ivorra A, Ballester M A G 2022 IEEE T. Bio-Med. Eng. 70 1902
[5]	Neal R E, Garcia P A, Robertson J L, Davalos R V 2012 IEEE T. Bio-Med. Eng. 59 1076 Google Scholar
[6]	Zhao Y, Bhonsle S, Dong S, Lyu Y, Liu H, Safaai-Jazi A, Davalos R V, Yao C 2018 IEEE T. Bio-Med. Eng. 65 1810 Google Scholar
[7]	Shi F, Steuer A, Zhuang J, Kolb J F 2019 IEEE T. Bio-Med. Eng. 66 2010 Google Scholar
[8]	郭雨怡, 石富坤, 王群, 季振宇, 庄杰 2022 物理学报 71 068701 Google Scholar Guo Y Y, Shi F K, Wang Q, Ji Z Y, Zhuang J 2022 Acta Phys. Sin. 71 068701 Google Scholar
[9]	Shi F, Kolb J F 2020 Biosens. Bioelectron. 157 112149 Google Scholar
[10]	Bounik R, Cardes F, Ulusan H, Modena M M, Hierlemann A 2022 BMEF 2022 9857485
[11]	Corovic S, Lackovic I, Sustaric P, Sustar T, Rodic T, Miklavcic D 2013 BioMed. Eng. OnLine 12 16 Google Scholar
[12]	Zhao Y J, Davalos R V 2020 Appl. Phys. Lett. 117 143702 Google Scholar
[13]	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 Yao C G, Zhen S, Zhao Y Z, Liu H M, Wang Y L, Dong S L 2020 High Voltage Engineering 46 1830 (in Chinese)
[14]	Smith R C 2013 Uncertainty Quantification: Theory, Implementation, and Applications (Vol. 12) (Siam)
[15]	Lai X, Wang S, Ma S, Xie J, Zheng Y 2020 Electrochimica Acta 330 135239 Google Scholar
[16]	Vazquez-Arenas J, Gimenez L E, Fowler M, Han T, Chen S K 2014 Energ. Convers. Manage. 87 472 Google Scholar
[17]	Edouard C, Petit M, Forgez C, Bernard J, Revel R 2016 JOPS 325 482
[18]	Ye X, Liu S, Yin H, He Q, Xue Z, Lu C, Su S 2021 Front. Cardiovasc. Med. 8
[19]	张家明陈志坚 2022 临床心血管病杂志 38 851 Zhang J M, Chen Z J 2022 J Clin. Cardiol. 38 851
[20]	O’Brien T J, Lorenzo M F, Zhao Y, Neal Ii R E, Robertson J L, Goldberg S N, Davalos R V 2019 Int. J. Hyperther. 36 952 Google Scholar
[21]	Lemieux C 2009 Monte Carlo and Quasi-Monte Carlo Sampling (Springer, New York, NY)
[22]	Haemmerich D, Schutt D J, Wright A S, Webster J G, Mahvi D M 2009 Physiol. Meas. 30 459 Google Scholar
[23]	Sobol′ I M 2001 Math. Comput. Simulat. 55 271 Google Scholar
[24]	Oliveira J F, Jorge D C P, Veiga R V, Rodrigues M S, Torquato M F, da Silva N B, Fiaccone R L, Cardim L L, Pereira F A C, de Castro C P, Paiva A S S, Amad A A S, Lima E A B F, Souza D S, Pinho S T R, Ramos P I P, Andrade R F S 2021 Nat. Commun. 12 333 Google Scholar
[25]	Kaminska I, Kotulska M, Stecka A, Saczko J, Drag-Zalesinska M, Wysocka T, Choromanska A, Skolucka N, Nowicki R, Marczak J, Kulbacka J 2012 Gen. Physiol. Biophys. 31 19 Google Scholar
[26]	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. Electrophy. 4 987 Google Scholar
[27]	Belalcazar A 2021 Heart Rhythm 2 560 Google Scholar
[28]	Kos B, Zupanic A, Kotnik T, Snoj M, Sersa G, Miklavcic D 2010 J. Membrane Biol. 236 147 Google Scholar
[29]	Shi F, Zhuang J, Kolb J F 2019 J. Phys. D 52 495401 Google Scholar
[30]	Perera-Bel E, Mercadal B, Garcia-Sanchez T, Ballester M A G, Ivorra A 2021 IEEE T. Bio-Med. Eng. 68 1318

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