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Article(id=1244321227804885370, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, articleNumber=null, orderNo=null, doi=10.16156/j.1004-7220.2025.05.023, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1736784000000, receivedDateStr=2025-01-14, revisedDate=1742400000000, revisedDateStr=2025-03-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1774598899078, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774598899078, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774598899078, creator=13701087609, updateTime=1774598899078, updator=13701087609, issue=Issue{id=1244321215637209904, tenantId=1146029695717560320, journalId=1244284848500682798, year='2025', volume='40', issue='5', pageStart='1079', pageEnd='1366', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774598896178, creator=13701087609, updateTime=1774599509568, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244323788452639476, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244323788452639477, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1256, endPage=1264, ext={EN=ArticleExt(id=1244321229675545025, articleId=1244321227804885370, tenantId=1146029695717560320, journalId=1244284848500682798, language=EN, title=Characterization of a Physiological Mock Circulation System Based on Capillary-Bundle Resistance Element, columnId=1244321216404767539, journalTitle=Journal of Medical Biomechanics, columnName=Original Articles, runingTitle=null, highlight=null, articleAbstract=
Objective

To investigate the feasibility of parallel capillary bundle arrays for physiomimetic impedance modeling and establish a parametric quantification framework, thereby providing a customizable impedance characterization methodology for diverse in-vitro mock circulation researches.

Methods

Based on the parallel flow resistance and Poiseuille equation, a tube resistance element with multiple parallel-aligned capillary glass tubes was designed and fabricated. The resistance values of the capillary-bundle and a ball valve were measured through constant flow experiments analogous to electrical resistance measurement method. Moreover, a simple lumped-parameter mock circulation loop was constructed and the pressure and flow rate for each node of the loop were measured under different input flow waveforms. An 0D-Windkessel model corresponding to the experiment was developed. The impedance and compliance were adjusted to match the simulated and experimental pressure and flow waveforms. The accuracy of the capillary bundle impedance in pulsatile experiments was verified by using the computational resistance values.

Results

The constant-flow impedance calibration experiments revealed that the capillary bundle impedance remained unaffected by flow rate variations over a wide flow range. When the capillary bundle impedance was integrated into the pulsatile circulatory system and the same impedance value obtained from the constant-flow calibration was applied in the computational model, the resulting pressure and flow waveforms showed good agreement with those measured in the pulsatile experiments. However, when the ball valves with nominally identical impedance values were inserted in the pulsatile system, the calculated impedance exhibited a two-fold difference, and significant discrepancies were observed between the simulated and experimental terminal flow waveforms.

Conclusions

The capillary bundle impedance maintains a constant value regardless of flow rate variations. Once the calibrated resistance value is determined through constant flow experiments, it can be directly applied to pulsatile systems. This approach can provide quantitative pulsatile flow conditions for testing various medical devices.

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目的

探究并联毛细管束仿生理阻抗的可行性及其定量表征方法，为各类体外循环研究提供个性化阻抗模拟方案。

方法

基于并联流阻及管内流动方程，设计制作毛细玻璃管束阻抗模块。类比电阻测试法，通过恒定流动实验分别对毛细管束以及球阀阻抗进行标定。搭建单支路体外循环系统，测试不同输入流量波形下循环各节点压力和流量参数，并构建与实验相对应的0D-Windkessel计算模型。通过调节阻抗及顺应性参数，使计算压力和流量波形与实验中的压力、流量波形相匹配，并利用模型反馈阻抗值验证毛细管束阻抗在脉动实验中的准确性。

结果

恒流标定实验结果表明，毛细管束阻抗在较大流量的区间内能够保持阻抗不随流量改变。进一步将毛细管束阻抗接入脉动循环中，计算模型采用与阻抗恒流实验相同的毛细管束阻抗时，所得压力、流量波形与脉动实验测定结果吻合较好；而相同阻值的球阀布置到脉动实验中时，计算模型所获近端和远端值却相差1倍，且末端计算流量波形与实测波形有较大差异。

结论

毛细管束阻抗具有阻抗不随流量改变的特性，标定方法简单；经恒流实验标定后可直接用于脉动流实验，可为各类医疗设备测试提供定量化的脉动循环工况。

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贺缨，教授，博士生导师，E-mail：
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作者贡献声明：

刘登吉负责脉动泵、循环元件、数据采集系统和实验方案的设计及测试，撰写论文；陈鑫科负责计算模型的参数匹配；韩丽莎负责实验测试和数据整理；曹禛负责泵头结构的设计；尹凯负责循环台设计及参数验证；迟青卓负责论文校对及修改；贺缨负责论文内容设计及修改，项目统筹。

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Biomechanical characterization of ventricular-arterial coupling during aging: A multi-scale model study[J]. 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注：可调式球阀的内部最大流通直径10 mm，通过调整旋转角度调节阻抗；嵌套硅胶管内直径为12 mm。

, figureFileSmall=ck1QN7TnLbUqJ3mloMpXKQ==, figureFileBig=QXUA8BYrdvKjqB+lJf1hoA==, tableContent=null), ArticleFig(id=1244321239628628952, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Fig. 2, caption=The constant-current loop used for impedance calibration　(a) Layout of calibration loop, (b) Pressure sensors and flow meters used in the experiment, figureFileSmall=eYoRFfKQmydRNMdlxRooNQ==, figureFileBig=jKBWjgAuEhfFVOqJKyAlLQ==, tableContent=null), ArticleFig(id=1244321239750263772, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=图2, caption=用于阻抗标定的恒流循环

注：图2（a）中p1、p2分别为测试段节点前、后压力；Q为通过测试段阻抗的流量。

, figureFileSmall=eYoRFfKQmydRNMdlxRooNQ==, figureFileBig=jKBWjgAuEhfFVOqJKyAlLQ==, tableContent=null), ArticleFig(id=1244321239855121374, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Fig. 3, caption=Schematic diagrams of single-branch RCR loop　(a) Experimental loop, (b) Computational loop, figureFileSmall=Uvi60/X1uR9Gs0LntEwAjg==, figureFileBig=rK7Q6eg35u+tNLYmZmdKTQ==, tableContent=null), ArticleFig(id=1244321239964173281, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=图3, caption=单支路RCR循环示意图, figureFileSmall=Uvi60/X1uR9Gs0LntEwAjg==, figureFileBig=rK7Q6eg35u+tNLYmZmdKTQ==, tableContent=null), ArticleFig(id=1244321240048059366, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Fig. 4, caption=Trend of impedance measurement values for the capillary bundle resistance and adjustable ball valve with flow rate variation, figureFileSmall=V2zU1DgNm65CpaDwdEwaoA==, figureFileBig=z/ksCtrYHSSJZNwI9204BA==, tableContent=null), ArticleFig(id=1244321240165499876, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=图4, caption=毛细管束阻抗与可调球阀阻抗测定值随流量变化趋势, figureFileSmall=V2zU1DgNm65CpaDwdEwaoA==, figureFileBig=z/ksCtrYHSSJZNwI9204BA==, tableContent=null), ArticleFig(id=1244321240287134697, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Fig. 5, caption=Comparison of impedance calculation and experimental waveform fitting for ball valves and capillary bundle impedance　(a) Pressure waveform fitting results of ball valves (Curve_sinx), (b) Flow rate waveform fitting results of ball valve (Curve_sinx), (c) Pressure waveform fitting results of capillary Bundle impedance (Curve_sinx), (d) Flow rate waveform fitting results of capillary bundle impedance (Curve_sinx), (e) Pressure Waveform fitting results of capillary bundle impedance (Curve_35%), (f) Flow rate waveform fitting results of capillary bundle (Curve_35%), figureFileSmall=9p2wOS44WjEilHUiiWQshQ==, figureFileBig=tcSKgRJpO9bkOjQbTPkV2Q==, tableContent=null), ArticleFig(id=1244321240425546730, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=图5, caption=球阀与毛细管束阻抗计算与实验波形拟合情况对比, figureFileSmall=9p2wOS44WjEilHUiiWQshQ==, figureFileBig=tcSKgRJpO9bkOjQbTPkV2Q==, tableContent=null), ArticleFig(id=1244321240542987246, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Fig. 6, caption=Calculation and experimental waveform fitting results of capillary bundle impedance under high-impedance conditions　(a) Comparison of model input flow waveforms under high and low-impedance conditions, (b) Pressure waveform fitting results under high-impedance conditions, (c) Flow rate waveform fitting results under high-impedance conditions, figureFileSmall=uM1jKYON2OfMdh8UCzLtsw==, figureFileBig=gmoDo6TXIdk0awCTD9+5RQ==, tableContent=null), ArticleFig(id=1244321240652039156, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=图6, caption=高阻抗下毛细管束阻抗计算与实验波形拟合情况, figureFileSmall=uM1jKYON2OfMdh8UCzLtsw==, figureFileBig=gmoDo6TXIdk0awCTD9+5RQ==, tableContent=null), ArticleFig(id=1244321240748508151, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Tab. 1, caption=

Fabrication and measured impedance of capillary bundle impedances

, figureFileSmall=null, figureFileBig=null, tableContent=
模型 r1/mm r2/mm l/cm N Qmax/（mL·s-1） R/[（mmHg·s）·mL-1]
空管路     0.053
R11.32101977.5570.528
R21.3251977.5571.680
R324107119.320.240
R412104887.925.284
), ArticleFig(id=1244321240912086009, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=表1, caption=

不同毛细管束阻抗制作及其测定值

, figureFileSmall=null, figureFileBig=null, tableContent=
模型 r1/mm r2/mm l/cm N Qmax/（mL·s-1） R/[（mmHg·s）·mL-1]
空管路     0.053
R11.32101977.5570.528
R21.3251977.5571.680
R324107119.320.240
R412104887.925.284
), ArticleFig(id=1244321241042109439, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=EN, label=Tab. 2, caption=

Comparison of computed feedback impedance and experimental measurements for ball valves and capillary bundles

, figureFileSmall=null, figureFileBig=null, tableContent=
模型情况 Rp Rd Ca Rz
球阀实验  0.580 
计算0.8500.4300.5500.115
毛细管束实验0.2400.5280.610 
阻抗计算0.3800.5900.6000.115
), ArticleFig(id=1244321241167937538, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321227804885370, language=CN, label=表2, caption=

球阀与毛细管束阻抗计算反馈值与实验测定值对比

, figureFileSmall=null, figureFileBig=null, tableContent=
模型情况 Rp Rd Ca Rz
球阀实验  0.580 
计算0.8500.4300.5500.115
毛细管束实验0.2400.5280.610 
阻抗计算0.3800.5900.6000.115
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基于毛细管束阻抗元件的仿生理脉动循环台参数定量化研究
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刘登吉 , 陈鑫科 , 韩丽莎 , 曹禛 , 迟青卓 , 尹凯 , 贺缨
医用生物力学 | 论著 2025,40(5): 1256-1264
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医用生物力学 | 论著 2025, 40(5): 1256-1264
基于毛细管束阻抗元件的仿生理脉动循环台参数定量化研究
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刘登吉, 陈鑫科, 韩丽莎, 曹禛, 迟青卓, 尹凯, 贺缨
作者信息
  • 大连理工大学　能源与动力学院，海洋能源利用与节能教育部重点实验室，辽宁　大连　116024

通讯作者:

贺缨，教授，博士生导师，E-mail：
Characterization of a Physiological Mock Circulation System Based on Capillary-Bundle Resistance Element
Dengji LIU, Xinke CHEN, Lisha HAN, Zhen CAO, Qingzhuo CHI, Kai YIN, Ying HE
Affiliations
  • Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China
出版时间: 2025-10-01 doi: 10.16156/j.1004-7220.2025.05.023
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摘要
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目的

探究并联毛细管束仿生理阻抗的可行性及其定量表征方法，为各类体外循环研究提供个性化阻抗模拟方案。

方法

基于并联流阻及管内流动方程，设计制作毛细玻璃管束阻抗模块。类比电阻测试法，通过恒定流动实验分别对毛细管束以及球阀阻抗进行标定。搭建单支路体外循环系统，测试不同输入流量波形下循环各节点压力和流量参数，并构建与实验相对应的0D-Windkessel计算模型。通过调节阻抗及顺应性参数，使计算压力和流量波形与实验中的压力、流量波形相匹配，并利用模型反馈阻抗值验证毛细管束阻抗在脉动实验中的准确性。

结果

恒流标定实验结果表明，毛细管束阻抗在较大流量的区间内能够保持阻抗不随流量改变。进一步将毛细管束阻抗接入脉动循环中，计算模型采用与阻抗恒流实验相同的毛细管束阻抗时，所得压力、流量波形与脉动实验测定结果吻合较好；而相同阻值的球阀布置到脉动实验中时，计算模型所获近端和远端值却相差1倍，且末端计算流量波形与实测波形有较大差异。

结论

毛细管束阻抗具有阻抗不随流量改变的特性，标定方法简单；经恒流实验标定后可直接用于脉动流实验，可为各类医疗设备测试提供定量化的脉动循环工况。

体外循环实验系统  /  毛细管束阻抗  /  压力波形  /  集总参数模型  /  脉动式容积泵
Objective

To investigate the feasibility of parallel capillary bundle arrays for physiomimetic impedance modeling and establish a parametric quantification framework, thereby providing a customizable impedance characterization methodology for diverse in-vitro mock circulation researches.

Methods

Based on the parallel flow resistance and Poiseuille equation, a tube resistance element with multiple parallel-aligned capillary glass tubes was designed and fabricated. The resistance values of the capillary-bundle and a ball valve were measured through constant flow experiments analogous to electrical resistance measurement method. Moreover, a simple lumped-parameter mock circulation loop was constructed and the pressure and flow rate for each node of the loop were measured under different input flow waveforms. An 0D-Windkessel model corresponding to the experiment was developed. The impedance and compliance were adjusted to match the simulated and experimental pressure and flow waveforms. The accuracy of the capillary bundle impedance in pulsatile experiments was verified by using the computational resistance values.

Results

The constant-flow impedance calibration experiments revealed that the capillary bundle impedance remained unaffected by flow rate variations over a wide flow range. When the capillary bundle impedance was integrated into the pulsatile circulatory system and the same impedance value obtained from the constant-flow calibration was applied in the computational model, the resulting pressure and flow waveforms showed good agreement with those measured in the pulsatile experiments. However, when the ball valves with nominally identical impedance values were inserted in the pulsatile system, the calculated impedance exhibited a two-fold difference, and significant discrepancies were observed between the simulated and experimental terminal flow waveforms.

Conclusions

The capillary bundle impedance maintains a constant value regardless of flow rate variations. Once the calibrated resistance value is determined through constant flow experiments, it can be directly applied to pulsatile systems. This approach can provide quantitative pulsatile flow conditions for testing various medical devices.

pulsatile mock circulation loop  /  capillary-bundle resistance  /  pressure waveform  /  lumped parameter model  /  pulsatile piston pump
刘登吉, 陈鑫科, 韩丽莎, 曹禛, 迟青卓, 尹凯, 贺缨. 基于毛细管束阻抗元件的仿生理脉动循环台参数定量化研究. 医用生物力学, 2025 , 40 (5) : 1256 -1264 . DOI: 10.16156/j.1004-7220.2025.05.023
Dengji LIU, Xinke CHEN, Lisha HAN, Zhen CAO, Qingzhuo CHI, Kai YIN, Ying HE. Characterization of a Physiological Mock Circulation System Based on Capillary-Bundle Resistance Element[J]. Journal of Medical Biomechanics, 2025 , 40 (5) : 1256 -1264 . DOI: 10.16156/j.1004-7220.2025.05.023
正文
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随着人口老龄化进程加快，心血管疾病患病量逐年增加[1]。近20年间，心室辅助装置、人工心脏瓣膜和支架治疗技术已成为治疗心血管疾病的有效手段。而这些医疗器械的持续更新和改进需通过可靠有效的心血管循环系统进行评价。体外模拟循环系统（mock circulatory loop，MCL）作为模拟人体循环系统血流动力学状态的实验平台，因其参数可控、无需伦理认证等优点，已成为医疗器械进入在体测试之前的重要测试平台[2-3]。基本的MCL由四部分组成，包括模拟左心室的动力源、模拟血流流阻的节流阀、模拟血管顺应性的封闭顺应腔以及模拟心房及静脉回流的开放式水箱[4-5]。循环系统通过顺应腔、节流阀等元件的相互配合，将人体生理压力、流量等参数等效为液压管路中的液压参数，进而模拟出仿生理脉动压力和流量波形[6]。
为准确且稳定地复现生理流动，模拟循环系统需采用性能稳健且易于调节的元件匹配血液循环各部分阻抗及顺应性。以往研究通常采用离心泵或活塞泵等作为仿生理脉动循环平台的动力源[7-10]。Vivitro-SuperPump往复式脉动泵是仿生理动力源中代表性商业产品[11]。在体外循环中，表征流动阻力的节流阀则直接影响压力波形，其定量化和精细调节对模拟循环参数化分析至关重要。阻抗元件可控调节及定量化分析是体外循环平台研究的重要内容。
在一些体外循环研究中，通过工业级球阀模拟循环流阻进而复现循环各节点压力波形，并针对性开展各类医疗器械测试[12-15]。Yokoyama等[16]设计了不同气液压缩比脉动泵，结合外周旋动球阀获得不同腔室内气液压缩比下的心室收缩曲线，复现了不同人群心输出状态。球阀通过调节过流孔面积获得不同外周阻力，过流孔面积随阀门开度呈非线性变化[17]。刘宇[18]给出了体外实验常用的球阀开合角度与流阻之间的关系，指出球阀流阻会随流量非线性变化而不易于工况调节。Saha等[19]研究表明，球阀即便用于定常流动中阻抗也表现出与流量的相关性，阻抗值随流量增大而增加，稳定性差。Tao等[20]研究表明，球阀阻力系数随开合角度呈幂指数规律衰减，精细工况调整复杂，且球阀出口易出现明显湍流区域，易引入非生理性湍流扰动。有研究团队设计了电控阻抗-顺应性（R-C）混合腔室系统，通过控制算法精细控制电动球阀开合角度，实现了循环压力波形精细化调整，但还未解决球阀阻抗稳定性问题[21-22]。
多孔介质渗透特性在生物系统中普遍存在。McGuire等[23]揭示了水力传导率与组织变形之间的依赖关系，即多孔介质内部微结构会改变流体传输效率。同时，多孔介质结构与真实人体血管床相接近，采用多孔介质表征毛细管网阻力是可行方法。Scharfchwerdt等[24]设计了多孔介质阻抗，以期克服一般节流阀不易控制收缩期压力变化的缺陷。Coccarelli等[25]在一维动脉系统血流动力学的计算模拟中采用多孔介质管路模拟外周阻抗，计算与实验结果有很好的一致性。该研究团队还设计了填充微球的弹性管路模拟毛细管网，验证多孔介质模拟微循环流阻的可行性[26]。Jin等[27]通过可变多孔介质模型分析了压力对血管有效渗透率的影响。此外，基于多孔介质原理的管束/孔板式阻力阀也可用于体外实验研究。Franzetti等[28-29]在主动脉夹层特性研究的体外循环实验中采用孔板式阻抗结构，该结构可通过模块化方式增加流阻，且这种模块化孔板不会随流量变化产生非线性增加的流动阻力。Kung等[30]设计的毛细管束阻抗模型能够克服阻抗值随流量非线性变化的缺陷，但该研究仅给出几类用于特定节点分析的阻抗模块，难以实现常用节流阀大范围阻抗调节的功能。
综上所述，克服传统球阀流阻随流量非线性变化以尽可能再现各类生理波形是体外循环系统重要研究内容。采用多孔介质阻力阀是合理有效的设计，但还需要针对球阀及多孔介质阻力阀的稳定性进行更多定量分析。本文根据Kung等[30]阻抗标定方法，采用恒定流实验对球阀和多孔介质阻抗进行定量化测试，设计适于体外脉动实验台的稳定阻抗，进一步将阻抗布置在脉动循环台中，通过搭建与脉动循环相一致的0D集总参数模型，通过计算和实验相互验证阻抗稳定可用，为体外实验循环阻抗定量化设计提供新思路。
1　材料与方法
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1.1　毛细管束阻抗设计及测试方法
对于节流阀流动阻抗值标定，一般基于层流条件下Poseuille方程进行推导：
式中：Δp为圆管的压降；Q圆管所流经的体积流量；r为圆管半径；μ为工质动力黏度；l为圆管长度；R为流阻。
但在湍流流动中，额外的能量冲击导致圆管内压降与流速平方成正比[30]，这使得Poseuille定律阻抗计算失效。Tao等[20]研究认为，球阀开合角度减小导致其下游湍流作用增强，不确定度增加。刘宇[18]研究指出，体外循环实验中，在多数工况下球阀内部通过的液体流速超过其最大层流流速，无法简单通过计算流通面积计算流阻。Jin等[17]研究表明，阀门几何参数能够改变球阀阻抗特性，但无法从根本上解决湍流导致的非线性问题。Chern等[31]通过流动可视化实验证实，球阀在部分开度下因湍流分离导致了压降-流量关系显著偏离层流理论预测。因此，如何避免湍流与保持层流，以及保证流阻与流速无关，对体循环流阻的定量化分析十分关键。
根据流阻定义式，在长度一定直圆管通道中，减小流通截面半径即可获得较高流动阻力，同时也意味着圆管在保证层流的前提下只能容纳较低流速，需要满足层流流动条件雷诺数Re<2 000。基于此，本文参照Kung等[30]的方法，将单圆管通道内的流动替换为多条平行并联布置的毛细管路内的流动。每条毛细管内的流量分配为流通总流量与毛细管个数之比，毛细管束最大层流流量Qmax应满足如下层流关系：
总阻抗由各毛细管并联表达，即
式中：Rchannel为圆管内总流阻为单个毛细管内流阻；N为毛细管总个数。基于此原理，选用不同管径及长度的玻璃管进行管束阻抗制作。将不同管径、长度的毛细玻璃管按中心阵列排布，玻璃管外侧均匀涂抹工业玻璃胶，保证中心排列下各毛细管之间不存在缝隙。将毛细管束安装到一根内径12 mm硅胶管中[见图1（a）]。为验证所设计的阻抗具备可定量化分析的特性，采用体外循环中广泛应用的球阀[见图1（b）]作为对比参照。
搭建恒流实验循环系统[见图2（a）]，分别对毛细管束阻抗及球阀进行阻抗测试，改变恒流循环流量以分析两种阻抗在不同流量下的阻抗变化情况。恒流实验所用恒流泵可实现最高166.7 mL/s（10 L/min）流量输出。该循环设计了测试支路和分流支路，在测试支路前设置分流阀，调整分流阀开闭以调整测试支路流量。测试支路末端设置有节流阀用于稳压，以保证经过测试阻抗后的压力为正值，实验中末端阻抗初始调整完成后不做变动，确保对照实验准确。通过对恒流泵输出功率以及分流阻抗的调整，改变测试支路流量，探究不同流量下毛细管束阻抗以及球阀阻抗值变化情况。
研究采用基恩士GPM-001型压力传感器，量程为±300 mmHg（1 mmHg=0.133 kPa，下同），精度为满量程1%，为确保测试准确采用数字压差计对传感器进行校准。流量测量采用CG063N型夹持式超声流量计（上海迅音科技有限公司）。量程为-5~15 L/min，零点漂移±0.1 L/min[见图2（b）]。两款传感器输出电压信号至NI数据采集卡，并通过所构建的NI-LabVIEW上位机程序实现数据采集和存储等功能。
1.2　基于毛细管束阻抗的脉动实验验证
进一步基于Westerhof等[32]提出的三元集总参数阻抗-顺应性（R-C-R）Windkessel模型，分别构建物理模型以及与实验对应的0D参数模型。依托自主研发的脉动泵，将用于测试的阻抗分别布置到单支路实验循环中，构建与实验循环相对应的Windkessel计算模型。通过调整0D模型阻抗与顺应性参数值，使实验循环和计算模型各节点压力、流量波形互相匹配。对比0D模型参数值与该阻抗在恒流实验测定值是否一致，判断阻抗应用在脉动循环的合理性。
自主研发的脉动泵基于伺服电机配套伺服电缸驱动内部活塞进行往复运动，并通过模拟瓣膜控制活塞缸内液体流向，进而复现左心室的收缩舒张功能。泵体采用80 mm直径活塞缸，往复最大行程40 mm，可模拟最高200 mL每搏输出，经实验验证可实现缸内压力300 mmHg以上长时间运行。伺服电机控制采用周期同步位置控制（cyclic synchronous position，CSP）模式，可自主设定电机运行曲线用于复现多种流量输出波形。参照商业化产品Vivitro-Superpump公开运行曲线数据，本研究还原了标准正弦曲线（Curve_sinx）以及收缩期占比35%的拟合曲线（Curve_35%）以给定脉动泵不同的流量波形输出，两种输出曲线均能够复现真实生理流量波形[33]，用以探究不同流量下阻抗值的稳定性。
实验循环采用三元件布置。将用以验证稳定性的阻抗布置为实验回路中的近端阻抗Rp以及远端阻抗Rd，中心节点布置有一个容积815 mL顺应腔表征循环系统顺应性Ca。自研脉动泵装置采用工业级升降式单向阀模拟房室瓣，在单向阀关闭时机械撞击导致了出口流量波形的波动，为避免导入计算模型中的流量波动引起计算发散，在泵出口处布置有顺应腔用以减轻流量振荡。同时，为确保脉动流量峰值不超过毛细管束阻抗最大层流流量限制，脉动泵设置50 mL搏出量下Curve_sinx、Curve_35%两种生理波形输出，为阻抗验证提供生理环境。将泵出口处顺应腔后的流量Q1（Qin）作为实验循环输入流量，分别测定循环中近端阻抗前压力p1、顺应腔压力p2、远端阻抗后压力p3以及末端流量Q2共4个压力、流量波形作为实验测定数据[见图3（a）]。
所构建的0D计算模型如图3（b）所示，其中输入流量Qin为实验测定Q1流量波形，为实现计算闭环，计算模型末端采用实验测定的p3节点压力波形数据的1/3代替水箱的脉动压差，并增加阻抗Rz表征远端阻抗到水箱之间的管路流阻，以期更准确复现实验循环。导入各实验数据共10个周期，将实验Qin、p3波形数据作为计算模型的边界条件输入。采用四阶Runge-Kutta方法列出并求解模型中p2节点方程得到p2压力波形，进一步反推得到p1、p3以及Q2的波形。对计算模型中Rp、Rd、Ca、Rz进行调整，使计算模型各节点压力、流量波形与实验波形相互拟合，以计算模型中的Rp、Rd值对比恒流实验阻抗测定值。以此探究阻抗在脉动循环下的稳定性。
2　实验测试结果
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共设计制作了4种不同阻抗的毛细管束阻抗。应用雷诺数层流判定准则[见式（3）]，计算每个毛细管束模块所能容纳的最高层流流量阈值（Qmax）。各管束阻抗模块应用的毛细管内径、外径、长度、个数以及每个模块所允许的最高层流流量阈值如表1所示。恒流实验分别测定了每个阻抗模块在4种不同流量下的压差与流量。为减小测量误差，压差与流量数据分别取1 min均值并得到压差Δp与流量Q散点关系，进行线性插值拟合，以插值曲线斜率表征该毛细管束阻抗值。以毛细管束阻抗R3、R1为例：R3内径2 mm、管个数7根；R1内径1.3 mm、管个数19根，单根毛细管阻抗计算值差别约为半径4次方成反比，再由式（2）考虑管个数，R1阻抗理论值约为R3的两倍，与实验测定阻抗值相吻合。
由毛细管束阻抗R1以及球阀在不同流量下阻抗变化情况可见，在流量28~38 mL/s范围内，R1阻抗基本维持在0.51 mmHg·s/mL。而球阀在10~20 mL/s流量范围内，阻抗在0.35~0.55 mmHg·s/mL之间呈现相关性增长（见图4）。基于流动判定准则，毛细管束阻抗在高流量范围内能够保证阻值恒定，则在与球阀相同流量范围内同样可以保证阻值恒定。因此，本文所设计的毛细管束阻抗能够区别于球阀实现阻抗不随流量变化这一特性。
为进一步验证毛细管束阻抗以及球阀在脉动循环下的稳定程度，将阻抗布置在单支路脉动循环中进行稳定性验证。首先，将两个可调球阀分别布置为脉动循环中的近、远端阻抗，调整两个球阀刻度（内部开合面积）一致，泵设置50 mL搏出量Curve_sinx曲线，测定各节点压力、流量波形。进一步将毛细管束阻抗R3和R1分别布置为近、远端阻抗，泵设置50 mL搏出量Curve_sinx以及Curve_35%两种波形输出，同样测定各节点压力、流量波形。调整计算模型参数值，使计算循环与实验循环各波形互相匹配，以计算模型参数值检验实验阻抗值。图5所示为球阀以及毛细管束阻抗计算与实验波形拟合情况，表2给出了球阀与毛细管束阻抗的计算反馈值与实验测定值。可以看到，当布置的两个球阀在开合面积一致的前提下，近端和远端阻抗计算反馈值却相差1倍，且末端流量计算与实验波形匹配较差。
而毛细管束阻抗计算反馈值与实验测定值一致，且末端流量波形匹配效果好。球阀实验结果进一步证明了球阀难以在脉动实验中进行定量的局限，而毛细管束阻抗实验结果表明其在不超过最大层流流量限制时可在脉动实验中稳定表征阻力，阻力值与恒流实验测定值相一致（见表2）。
进一步探究阻抗增加时毛细管束阻抗应用在脉动循环下的可靠性。分别将毛细管阻抗R1、R2布置为近、远端阻抗，泵设置50 mL搏出量Curve_sinx曲线输出。比较高阻抗工况（R1/R2）循环输入流量波形与低阻抗工况（R3/R1）波形发现，当后端为较高阻抗时，峰值流量相较于低阻抗时降低，而舒张末期流量有所增加[见图6（a）]，这一变化趋势与Liang等[34]人体心血管系统阻抗影响的计算模型结果吻合。Franzetti等[28]研究表明，人体的特征阻抗范围为0.098~1.51 mmHg·s/mL，外周阻抗范围为1.666~14.59 mmHg·s/mL。本文所使用的两套阻抗在人体阻抗范围，所对应的流量近似主动脉上三分支或腹主动脉流量。本文结果表明，较高阻抗毛细管束阻抗下，Rp、Rd、Rz和Ca计算反馈值分别为0.760、1.785、0.115 mmHg·s/mL和0.600 mL/mmHg；Rp、Rd和Ca的实验测定值分别为0.522、1.680 mmHg·s/mL和0.610 mL/mmHg。由高阻抗工况计算与实验波形拟合情况可见，该工况阻抗计算值较实验测定值偏高，计算模型末端流量Q2整体较实验流量低约5 mL/s[见图6（c）、（d）]，推测产生该现象的原因是后端阻抗较高，在流经阻抗时，液体可能积聚在阻抗前端而产生了一定的流量损失。但从反馈的阻抗计算值分析，计算值与实验测定值基本吻合，验证了高阻值毛细管束阻抗也可在脉动循环中稳定表征阻力。
3　讨论
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本文所设计的毛细管束阻抗基于阻抗并联思路，将来流分散成多根毛细管内的流动，保证毛细管内流动处于层流状态使其可定量化标定。这种阻抗结构简单，制作及标定方便。给定目标阻抗值即可设计相对应毛细管束阻抗，再通过恒流实验标定出实际阻抗，将其接入脉动循环实验台后可获得确定的脉动工况，无需像球阀一样进行反复调节适配才能找到目标工况。而且不同毛细管束阻抗RCR组合可以很好模拟人体流量特征，适合医疗设备各种定工况下模拟血压测试。
0D-Windkessel计算模型可以帮助设计和校验体外循环的RCR参数值。例如，可以首先通过计算模型匹配目标压力与流量波形以获得相应RCR参数值，进而设计出对应阻值的阻抗接入实验循环中，通过比较计算与实验循环中各节点压力、流量波形，调整相应计算与实验循环阻抗值直至两者具有较好的波形匹配度。但由于球阀在脉动循环中阻抗值产生改变，因此该方法难以匹配球阀阻抗。
在选取毛细管时需注意，若采用管径较细、毛细管数较多的管束时，其实验测定值会高于由公式得出的计算值。本文推测，导致这方面偏差的原因是毛细管管壁占据了过多的流通面积，使得阻抗值升高。为确保该类阻抗的准确性及可用性，后续设计时应尽量选取管壁较薄的毛细管，并控制管束数量以避免管壁过厚影响阻抗表征。
目前的毛细管阻抗采用石英玻璃毛细管，考虑其承压能力强、获取便携的特点将其制备为循环的外周阻抗元件，后续可采用承压效果更好的管路材料制备管束阻抗。也可将阻抗设计为多管束可调组合，进一步增加可调工况精细程度的同时，不必占用过多空间。
4　结论
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本文提出了一种体外循环阻抗定量化分析方法，设计并制作了4种毛细管束阻抗，结合恒流、脉动循环及0D集总参数模型，探究了毛细管束和球阀在不同流量下的阻抗特性。
首先，通过恒流循环直接标定出阻抗元件的参数值。进一步基于自主研发的脉动泵和单路集总参数实验循环，测试了毛细管束和球阀在脉动循环下的阻抗特性，并与相同布置的0D循环计算模型所反馈的阻抗值进行比较。结果表明，在计算模型中匹配与毛细管束阻抗实验相同的压力和流量波形时阻抗计算反馈值与实测值基本保持一致，验证了毛细管束阻抗在脉动循环下的稳定性。而通过计算模型匹配球阀阻抗实验中的波形时，计算阻抗值与实验值差异显著，表明球阀在脉动循环中其阻抗随流量动态变化，其参数难以定量化分析。
综上所述，毛细管束阻抗具备很好的阻抗稳定性，更接近人体毛细管床结构。这种融合恒流实验与0D集总参数模型的阻抗标定方法，可为人工心脏、人工瓣膜以及可穿戴设备等医疗产品性能测试时提供稳定可靠的个性化阻抗设计。
基金
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  • 中央高校基本科研业务费(DUT22YG206)
  • 国家自然科学基金项目(51976026; 12302399)
文献
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doi: 10.16156/j.1004-7220.2025.05.023
  • 接收时间：2025-01-14
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2025-01-14
  • 修回日期：2025-03-20
基金
中央高校基本科研业务费(DUT22YG206)
国家自然科学基金项目(51976026; 12302399)
作者信息
    大连理工大学　能源与动力学院，海洋能源利用与节能教育部重点实验室，辽宁　大连　116024

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贺缨，教授，博士生导师，E-mail：
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https://castjournals.cast.org.cn/joweb/yyswlx/CN/10.16156/j.1004-7220.2025.05.023
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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