State of the art of the methods and techniques in modeling analysis and in vitro simulation of arterial endothelial hemodynamic microenvironment
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摘要: 动脉内皮微环境中的血压、壁面剪应力和牵张应力等血流动力学参量在维持内皮的正常生理功能中扮演着至关重要的角色。在体（in vivo）动脉内皮血流动力学微环境的建模分析与体外（in vitro）模拟研究不仅为心脑血管疾病早期诊断与预防、治疗与康复提供重要的生理指标，而且是深入理解心脑血管疾病发生发展机制不可或缺的基础，具有重要的科学意义和临床应用价值。本文综述了在体动脉内皮微环境的血流动力学建模分析、体外评估动脉内皮微环境血流动力学特性的模拟循环系统（Mock Circulatory System，MCS）以及用于细胞力学生物学研究的体外内皮细胞培养模型（Endothelial Cell Culture Model，ECCM）三方面的研究进展。通过对该领域的主要文献进行归纳和系统分析，指出了亟待解决的方法与技术问题，为进一步开展相关研究提供参考。Abstract: Hemodynamic variables in arterial endothelial microenvironment, such as blood pressure, wall shear stress and tensile stress, play critical roles in maintaining the normal physiological function of endothelium. Modeling analysis and in vitro simulation of in vivo arterial endothelial hemodynamic microenvironment may not only offer important physiological parameters for early diagnosis and prevention, treatment and rehabilitation of cardiovascular diseases but also establish a fundamental basis for further understanding the underlying mechanisms of disease initiation and progression, and therefore have important scientific significance and value of clinic application. This paper provides an overall review of research progresses in this area from three perspectives, i.e. modeling analysis of in vivo arterial endothelial hemodynamic microenvironment, in vitro mock circulatory system (MCS) for studying the characteristics of arterial endothelial hemodynamic microenvironment, and endothelial cell culture model (ECCM) for investigating cell mechanobiology under controlled in vitro conditions. We raise several methodological and technical problems of urgent need for better solution based on a summary and systematic analysis of major literatures in this field aiming to offer some references for relevant future studies.
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Keywords:
- arterial endothelium /
- microenvironment /
- hemodynamics /
- modeling analysis /
- in vitro simulation
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0 引言
FL-12风洞作为主力风洞承担着大量重要试验任务，其中包括进气道、吹气流动控制、引射短舱和TPS等多项试验，这些试验任务都需要供气控制系统输送稳定、可控的气流到试验模型，并要达到优于±3g/s的绝对控制精度，同时要求流量调节范围大、稳定时间短，因此实现流量宽范围快速精确控制是供气试验最为基础和关键的环节[1-3]。
目前模拟调节阀的高精度阀门定位器死区0.1%，综合误差0.5%[4]，达不到试验要求的流量控制精度，而且在实际工况中其工作流量特性随着试验模型的变化而变化，同时存在死区、调节滞后严重、调节范围不宽、密封件易磨损等问题，因此无法满足当前供气试验要求。
与模拟调节阀相比，数字阀具有可调范围宽、控制精度高、响应速度快、结构简单、鲁棒性强、可靠性高等特点[5-7]，目前数字阀主要分为PWM(脉冲宽度调制)数字阀和PCM(脉冲编码调制)数字阀[8-9]。PWM数字阀也称高速开关式数字阀，通过调节PWM信号的占空比来控制阀的平均流量，但是数字阀的流量和得失电时间存在一定的矛盾。PCM数字阀是将开关阀按照一定规律的排列组合(二进制、斐波那契数列等)实现对流量的控制，但是离散化的形式会导致流量输出的不连续性，同时小口径喷嘴的加工难度较高，进退阶时波动较大，频繁切换阀会造成冲击和噪声，缩短低位开关阀的寿命。
为解决PWM数字阀流量和得失电时间的矛盾和PCM数字阀的流量不连续性和低位开关阀的寿命问题，本文设计了PCM+PWM数字阀。该数字阀通过PCM数字阀提供基准流量，PWM数字阀在基准流量的基础上再进行调节，其中PCM数字阀采用多路文丘里喷嘴与开关阀按照二进制规律排列组合而成，PWM数字阀由单路小口径文丘里喷嘴与高频开关阀组成。
1 数字阀的设计指标和设计方案
1.1 设计指标
依据试验任务需求，FL-12风洞供气控制系统中数字阀设计的主要技术指标：(1) 阀前压力范围：6.0~8.0MPa；(2) 阀后压力范围：0.1~6.0MPa；(3) 流量控制范围：0.1~6.0kg/s；(4) 绝对控制精度：≤±3g/s；(5) 稳定控制时间：≤30s。
1.2 设计方案
本文中设计的数字阀由13位半PCM数字阀+ PWM数字阀，共计16路喷嘴和16路开关阀组成。图 1为数字阀支路示意图，气流依次通过喷嘴、高压金属软管、电磁阀后流出，系统先通过开关不同位的电磁阀来控制每路管道的通断以达到组合出不同流量的目的，当流量输出值与给定值的差值进入预先设定的误差带内，则停止动作PCM数字阀，由PWM数字阀通过脉宽调制控制。在实际流量控制中，PCM数字阀起到量程调节作用，PWM数字阀起到精细调节作用。
2 数字阀设计的关键技术
2.1 喷嘴的选择与设计
为使喷嘴流量特性不受后端试验模型状态变化及背压影响，采用了临界流喷嘴。临界流喷嘴主要包括临界流标准喷嘴和临界流文丘里喷嘴，其中临界流标准喷嘴结构如图 2所示。如果保持喷嘴入口压力p1和温度T1不变，使其出口压力p2逐渐减小，则通过喷嘴的气体流量qm将逐渐增加。当出口压力下降至pc时，通过喷嘴的流量将达到最大值，气体流速为当地声速，再继续降低出口压力，通过喷嘴的流量将不再增加，流速也保持声速不变。将喷嘴出口的流速达到声速的压力pc称为临界压力，pc/p1称为临界压力比，通过喷嘴的流量(qm)max称为临界流量[10]。
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图 2 临界流标准喷嘴的结构和流量特性Fig. 2 Structure and flow characteristic of the critical flow standard nozzle对于空气(γ=1.4)，可以通过公式1计算得到临界压力比为0.528。由于数字阀前压力一般稳定在8MPa，因此要保证“恒流”特性不变，出口压力p2必须低于临界压力4.224MPa，显然无法满足最大出口压力为6MPa的设计要求，而且压力损耗太大。
(1) 为使出口压力得到恢复，采用喉道后面带扩压管的临界流文丘里喷嘴，其出口压力高低与其扩散段尺寸有关[11]。根据JJG620-2008《临界流文丘里喷嘴》，可以计算出最大背压比p2/p1与扩散段面积比A2/A*的对应参数表(见表 1)，其中p1为入口压力，p2为出口压力，A*为喉道面积，A2为扩散段出口面积。
表 1 临界流文丘里喷嘴的最大允许背压比表(γ=1.4)Table 1 Maximum allowable back pressure ratio of the critical flow Venturi-type nozzleA2/A* p2/p1 A2/A* p2/p1 1.1 0.6863 1.9 0.8495 1.2 0.7376 2.0 0.8554 1.3 0.7701 2.5 0.8743 1.4 0.7930 3.0 0.8842 1.5 0.8101 3.5 0.8900 1.6 0.8233 4.0 0.8937 1.7 0.8339 5.0 0.8981 1.8 0.8424 10.0 0.9038 依据表 1，选择喷嘴扩散段面积比为4.0，在理想条件下，当出口压力低于0.8937倍入口压力，即可达到临界状态，喷嘴喉道流速为声速，流量由入口压力、入口温度与喉道面积唯一确定。依据圆环形喉道临界流文丘里喷嘴设计准则[12]，喷嘴的结构设计如图 3所示。
2.2 喉道面积的分配
PCM数字阀的喷嘴喉道面积按照二进制规律排列，通过这些不同的喉道可以组合不同喉道面积，组合喉道面积范围在所有喉道面积之和与最小喉道面积之间，最小分辨率是最小喉道面积，因此设计足够小的喉道面积就可以解决定位精度的问题，设计足够多的位数就可以解决流量调节范围的问题。
PCM数字阀的设计工况是入口压力为8.0MPa，入口温度为20℃，流量为6.0kg/s，在最大允许背压比范围内，根据公式(2) 可得PCM数字阀需要的喉道总面积为3.176cm2。
(2) 式中：p1为喷嘴入口压力(Pa)；T1为喷嘴入口温度(K)；A*为喉道面积(m2)。
经计算，将喉道总面积按照13位半二进制分配，各喷嘴喉道面积分配值及工作流量分配值如表 2所示。
表 2 PCM数字阀各喷嘴喉道面积及对应流量计算表Table 2 Nozzle throat area and calculated flow value of the PCM digital valveBit位 临界流量/(kg·s-1) 喷嘴喉道面积/cm2 喉道通径/mm 1 0.00059332 0.00031416 0.2000 2 0.0011866 0.00062832 0.2828 3 0.0023733 0.0012566 0.4000 4 0.0047466 0.0025133 0.5657 5 0.0094932 0.0050265 0.8000 6 0.018986 0.010053 1.1314 7 0.037973 0.020106 1.6000 8 0.075945 0.040212 2.2627 9 0.15189 0.080425 3.2000 10 0.30378 0.16085 4.5255 11 0.60756 0.3217 6.4000 12 1.2151 0.6434 9.0510 13 2.4303 1.2868 12.8000 13半 1.2151 0.6434 9.0510 合计 6.075 3.2170 实际设计PCM数字阀总喉道面积为3.217cm2，在不考虑喷嘴加工误差的情况下，其喉道面积分辨率(定位精度)为1/10239，在设计工况下对应的最小流量为0.6g/s。
PWM喷嘴喉道面积的选取需依据试验流量精度要求(±3g/s)，并充分考虑裕量，预设误差带为±6g/s，可在表 2中选取喉道口径0.8mm的喷嘴作为PWM数字阀的喷嘴。
2.3 电磁阀参数计算与型号选择
流量系数CV是电磁阀主要的计算参数，表征为阀门流通能力大小，根据设计工况，并按照公式(3) 进行计算，结果如表 3所示。
(3) 表 3 电磁阀流量系数计算与型号选择Table 3 Magnetic valve flow coefficient calculation and model selectionBit位 计算流量系数/(m3·h-1) 电磁阀流量系数/(m3·h-1) 电磁阀阀座口径/mm 电磁阀型号 PWM 0.02892 0.05 8.0 2/943 1 0.00195 0.13 2.0 A5232 2 0.00390 0.13 2.0 A5232 3 0.00781 0.13 2.0 A5232 4 0.01563 0.13 2.0 A5232 5 0.03125 2.0 8.0 B4623 6 0.0625 2.0 8.0 B4623 7 0.12501 2.0 8.0 B4623 8 0.25003 2.0 8.0 B4623 9 0.50005 2.0 8.0 B4623 10 1.00010 2.0 8.0 B4623 11 2.00021 8.0 25.0 A4625 12 4.00042 8.0 25.0 A4625 13 7.99895 20.0 32.0 A4827 13半 4.00042 8.0 25.0 A4625 式中：Q为标准状态下最大流量，Nm3/h；G为空气比重，为1.1kg/Nm3; T为气体温度, ℃; p1为入口压力, kg/cm2; p2为出口压力, kg/cm2; Δp=p1-p2, kg/cm2。
PCM数字阀的开关阀采用德国GSR二位二通系列的电磁阀, PWM数字阀的高频开关阀采用德国GSR 2/943，该阀动作频率可达1kHz，具有脉宽调制功能，线性流量控制。为使各喷嘴入口压力、温度等条件一致，入口压力稳定，出口压力满足喷嘴喉道气流为声速流要求，电磁阀的流量系数尽量选大，以减小工作压力降，同时需要一定容积的阀体/管道作为稳定段，增加喷嘴入口压力的稳定性[13]。
由于电磁阀不同口径的开关时间存在一定差异，其口径不大于25mm时阀门开关时间约为0.1s，而口径为32mm时阀门开关时间长达0.44s。为了减少各阀门在时间上的差异，增加阀门切换过程中的稳定性，电磁阀的口径都选用25mm以内的。口径32mm的电磁阀则由2个口径25mm的电磁阀组合替代，因此13位半的PCM数字阀具有15个支路，再加上PWM数字阀，共计16个支路。
3 流量控制策略
3.1 供气控制系统
供气控制系统的高压气源来自12~22MPa的高压储气罐，经减压阀降低至稳定的8MPa，再通过数字阀输出试验需要的流量值。在数字阀后端有高精度的文丘里流量计实时监测和反馈输出的流量值，从而组成闭环控制系统，如图 4所示。
3.2 流量调节运算方法
供气控制系统采用了微分前置非线性PID流量调节运算方法，其控制量通过数字阀完成，实现主管路流量的控制。该运算方法首先根据主管路流量给定与流量反馈完成PID运算，然后通过PID运算结果和数字阀气流入口总压总温，计算数字阀阀位偏差，将此偏差作为数字阀阀位补偿值重新调整阀位，从而调整主管路流量输出值，当流量输出值与给定值的差值进入预先设定的误差带内(±6g/s)，则停止动作PCM数字阀，由PWM数字阀通过脉宽调制控制。该运算的微分前置环节可对供气管道及管道设备(数字阀后的供气管道、空气换热器、空气过滤器等)容积造成的流量滞后进行补偿，缩短调节过渡过程时间，增加系统稳定性；比例和积分环节的运算律按照大误差小比例、小积分增益，以及小误差大比例、大积分增益的控制策略构建。
4 调试与应用
4.1 调试
FL-12风洞供气控制系统的数字阀安装示意图如图 5所示。
在调试中，需要在不同流量、不同试验模型状态的情况下，多次调整PID运算的比例增益、积分增益和调节微分增益等参数，使流量控制达到最佳状态。表 4给出了流量闭环控制的测试结果，当给定流量1.2、2.4、3.55和4.67kg/s时，系统流量控制的最大绝对误差分别为1.9、2.2、2.5和2.6g/s，最大相对误差分别为0.15%、0.09%、0.07%、和0.06%。调试数据表明，该套数字阀的流量控制精度能够满足设计指标±3g/s，同时能够实现宽范围的流量调节，且效果平稳，重复性好，可靠性高。
表 4 流量闭环控制的测试结果(单位:kg/s)Table 4 Test results of the flow closed loop control给定流量 1.2 2.4 3.55 4.67 均值流量 1.2012 2.3984 3.5518 4.6688 最大流量 1.2019 2.4022 3.5525 4.6720 最小流量 1.1996 2.3979 3.5480 4.6674 极差 0.0023 0.0043 0.0045 0.0046 最大绝对误差 0.0019 0.0022 0.0025 0.0026 最大相对误差 0.15% 0.09% 0.07% 0.05% 4.2 应用
数字阀在供气控制系统中调试完成后，开展了数十项供气试验。其中以某型飞机进气道试验为例，本次试验的供气流量为1.0和3.2kg/s，流量控制调节过程曲线和稳态过程曲线分别如图 6和7所示。
当供气流量为1.0kg/s时，流量稳定时间为15s，最大绝对误差为1.8g/s，最大相对误差为0.15%；当供气流量为3.2kg/s时，流量稳定时间为16s，最大绝对误差为2.7g/s，最大相对误差为0.08%。
5 结论
大量的供气试验结果表明，采用13位半PCM数字阀和PWM数字阀组合的数字阀在FL-12风洞供气控制系统中的应用是成功的，全面达到了设计指标。其控制精度高、响应时间短、调节范围宽和可靠稳定等特点，为风洞供气试验提供了强有力的支撑。
致谢: 感谢大连理工大学王宇副教授与博士研究生于苗、杨雨浓为本文插图制作提供的帮助。 -
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图 1 动脉内皮微环境中血压、壁面剪应力和周向牵张应力(或应变)作用于血管壁示意图
Fig. 1 Schematic diagram of blood pressure, wall shear stress, and circumferential tensile stress (or strain) applied on blood vessel's wall in vascular endothelial microenvironment
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图 4 考虑局部动脉解剖结构的MCS实物图
Fig. 4 An actual setup of the MCS with consideration of local arterial anatomic structure
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[1] PENG Z K, SHU B Y, ZHANG Y R, et al. Endothelial response to pathophysiological stress[J]. Arteriosclerosis Thrombosis and Vascular Biology, 2019, 39(11):e233-e243. http://d.old.wanfangdata.com.cn/OAPaper/oai_pubmedcentral.nih.gov_1157015
[2] JAMES B D, ALLEN J B. Vascular endothelial cell behavior in complex mechanical microenvironments[J]. ACS Biomaterials Science & Engineering, 2018, 4(11):3818-3842. DOI: 10.1007/s00018-012-1115-1
[3] CHIEN S. Mechanotransduction and endothelial cell homeostasis:the wisdom of the cell[J]. American Journal of Physiology-Heart and Circulatory Physiology, 2006, 292(3):H1209-H1224. DOI: 10.1152-ajpheart.01047.2006/
[4] ZHOU J, LI Y S, CHIEN S. Shear stress-initiated signaling and its regulation of endothelial function[J]. Arteriosclerosis, Thrombosis, and Vascular biology, 2014, 34(10):2191-2198. DOI: 10.1161/ATVBAHA.114.303422
[5] HAN Y, HUANG K, YAO Q P, et al. Mechanobiology in vascular remodeling[J]. National Science Review, 2018, 5(6):933-946. DOI: 10.1093/nsr/nwx153
[6] KANG H Y, FAN Y B, DENG X Y. Vascular smooth muscle cell glycocalyx modulates shear-induced proliferation, migration, and NO production responses[J]. American Journal of Physiology-Heart and Circulatory Physiology, 2010, 300(1):H76-H83. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0220504592/
[7] HSIEH H J, LIU C A, HUANG B, et al. Shear-induced endothelial mechanotransduction:the interplay between reactive oxygen species (ROS) and nitric oxide (NO) and the pathophysiological implications[J]. Journal of Biomedical Science, 2014, 21(1):3. DOI: 10.1186/1423-0127-21-3
[8] CHAO Y L, YE P, ZHU L L, et al. Low shear stress induces endothelial reactive oxygen species via the AT1R/eNOS/NO pathway[J]. Journal of Cellular Physiology, 2018, 233(2):1384-1395. DOI: 10.1002/jcp.26016
[9] 曲乐丰.颈动脉内膜斑块切除术:手术技巧及围术期处理[M].第一版.北京:人民军医出版社, 2015. QU L F. Carotid endarterectomy:surgical skills and perioderative treatment[M]. 1st ed. Beijing:People's Military Medical Press, 2015.
[10] SCHWARZMAIER-D'ASSIE A, NYOLCZAS N, HEMETSBER-GER R, et al. Comparison of short-and long-term results of drug-eluting vs. bare metal stenting in the porcine internal carotid artery[J]. Journal of Endovascular Therapy, 2011, 18(4):547-558. DOI: 10.1583/10-3347.1
[11] Marcheix B, Eynden F V, Demers P, et al. Influence of diabetes mellitus on long-term survival in systematic off-pump coronary artery bypass surgery[J]. Annals of Thoracic Sur-gery, 2008, 86(4):1181-1188. DOI: 10.1016/j.athoracsur.2008.06.063
[12] NAITO N, NISHIMURA T, LIZUKA K, et al. Rotational speed modulation used with continuous-flow left ventricular assist device provides good pulsatility[J]. Interactive CardioVascular and Thoracic Surgery, 2018, 26(1):119-123. DOI: 10.1093/icvts/ivx236
[13] LIN W, XIONG L, HAN J, et al. Hemodynamic effects of external counterpulsation is a different measure of impaired cerebral autoregulation from vasoreactivity to breath-holding[J]. European Journal of Neurology, 2014, 21(2):326-331. DOI: 10.1111/ene.12314
[14] XIONG L, LIN W H, HAN J H, et al. Enhancing cerebral perfusion with external counterpulsation after ischaemic stroke:how long does it last?[J]. Journal of Neurology, Neurosur-gery, and Psychiatry, 2016, 87(5):531-536. DOI: 10.1136/jnnp-2014-309842
[15] BUSCHMANN E E, HILLMEISTER P, PERSSON A B, et al. Short-term external counterpulsation augments cerebral blood flow and tissue oxygenation in chronic cerebrovascular occlusive disease[J]. European Journal of Neurology, 2018, 25(11):1326-1332. DOI: 10.1111/ene.13725
[16] GOTO C, HIGASHI Y, KIMURA M, et al. Effect of different intensities of exercise on endothelium-dependent vasodilation in humans-role of endothelium-dependent nitric oxide and oxidative stress[J]. Circulation, 2003, 108(5):530-535. DOI: 10.1161/01.CIR.0000080893.55729.28
[17] SPENCE A L, CARTER H H, NAYLOR L H, et al. A prospective randomized longitudinal study involving 6 months of endurance or resistance exercise. Conduit artery adaptation in humans[J]. The Journal of Physiology, 2013, 591(5):1265-1275. DOI: 10.1113/jphysiol.2012.247387
[18] GREEN D J. Exercise training as vascular medicine:direct impacts on the vasculature in humans[J]. Exercise and Sport Sciences Reviews, 2009, 37(4):196-202. DOI: 10.1097/JES.0b013e3181b7b6e3
[19] GREEN D J, HOPMAN M T E, PADILLA J, et al. Vascular adaptation to exercise in humans:role of hemodynamic stimuli[J]. Physiological Reviews, 2017, 97(2):495-528. DOI: 10.1152/physrev.00014.2016
[20] HUANG C Y, HOLFELD J, SCHADEN W, et al. Mechanotherapy:revisiting physical therapy and recruiting mechanobiology for a new era in medicine[J]. Trends in Molecular Medicine, 2013, 19(9):555-564. DOI: 10.1016/j.molmed.2013.05.005
[21] 王艳霞, 刘海斌, 刘波, 等.运动对动脉内皮功能的调控及血流剪切力的介导作用[J].北京生物医学工程, 2017, 36(6):639-647. DOI: 10.3969/j.issn.1002-3208.2017.06.015 WANG Y X, LIU H B, LIU B, et al. Regulation of artery endothelial function by exercise training and the role of wall shear stress[J]. Beijing Biomedical Engineering, 2017, 36(6):639-647. DOI: 10.3969/j.issn.1002-3208.2017.06.015
[22] WANG Y X, WANG Y, LI S Q, et al. The analysis of wall shear stress modulated by acute exercise in the human common carotid artery with an elastic tube model[J]. Computer Modeling in Engineering and Sciences, 2018, 116(2):127-147. DOI: 10.31614/cmes.2018.03985
[23] LIU H B, YUAN W X, WANG Q Y, et al. Carotid arterial stiffness and hemodynamic responses to acute cycling intervention at different times during 12-week supervised exercise training period[J]. BioMed Research International, 2018(5):2907548. http://downloads.hindawi.com/journals/bmri/2018/2907548.pdf
[24] BIGLINO G, COSENTINO D, STEEDEN J A, et al. Using 4D cardiovascular magnetic resonance imaging to validate computational fluid dynamics:a case study[J]. Frontier in Pediatrics, 2015, 3:107. https://www.ncbi.nlm.nih.gov/pubmed/26697416
[25] ONG C W, XIONG F, KABINEJADIAN F, et al. Hemodynamic analysis of a novel stent graft design with slit perforations in thoracic aortic aneurysm[J]. Journal of Biomechanics, 2019, 85:210-217. DOI: 10.1016/j.jbiomech.2019.01.019
[26] VAN ROSENDAEL A R, SHAW L J, XIE J X, et al. Superior risk stratification with coronary computed tomography angiography using a comprehensive atherosclerotic risk score[J]. JACC:Cardiovascular Imaging, 2019, 12(10):1987-1997. DOI: 10.1016/j.jcmg.2018.10.024
[27] MET R, BIPAT S, LEGEMATE D A, et al. Diagnostic performance of computed tomography angiography in peripheral arterial disease:a systematic review and meta-analysis[J]. Journal of the American Medical Association, 2009, 301(4):415-424. DOI: 10.1001/jama.301.4.415
[28] MOTOYAMA S, ITO H, SARAI M, et al. Plaque characterization by coronary computed tomography angiography and the likelihood of acute coronary events in mid-term follow-up[J]. Journal of the American College of Cardiology, 2015, 66(4):337-346. DOI: 10.1016/j.jacc.2015.05.069
[29] CHOI E K, CHOI S I, RIVERA J J, et al. Coronary computed tomography angiography as a screening tool for the detection of occult coronary artery disease in asymptomatic individuals[J]. Journal of the American College of Cardiology, 2008, 52(5):357-365. DOI: 10.1016/j.jacc.2008.02.086
[30] KIM W Y, DANIAS P G, STUBER M, et al. Coronary magnetic resonance angiography for the detection of coronary stenoses[J]. The New England Journal of Medicine, 2001, 345(26):1863-1869. DOI: 10.1056/NEJMoa010866
[31] HAGSPIEL K D, NORTON P T. Computed Tomography Angiography (CTA)[M]//Kramer C M. Imaging in peripheral arterial disease.: Springer Nature Switzerland AG, 2020: 45-61.
[32] CAVALLO A U, KOKTZOGLOU I, EDELMAN R R, et al. Noncontrast magnetic resonance angiography for the diagnosis of peripheral vascular disease[J]. Circulation:Cardiovascular Imaging, 2019, 12(5):e008844. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=4f8514485f0cae20a36d9a6dece1ba70
[33] CHO S J, JUNG S C, SUH C H, et al. High-resolution magnetic resonance imaging of intracranial vessel walls:Comparison of 3D T1-weighted turbo spin echo with or without DANTE or iMSDE[J]. PloS One, 2019, 14(8):0220603.
[34] VRANIC J E, HUYNH T J, FATA P, et al. The ability of magnetic resonance black blood vessel wall imaging to evaluate blunt cerebrovascular injury following acute trauma[J]. Journal of Neuroradiology, 2019(in press). doi: 10.1016/J.NEURAD.2019.01.091.
[35] TENG Z Z, SADAT U, BROWN A J, et al. Plaque hemorrhage in carotid artery disease:pathogenesis, clinical and biomechanical considerations[J]. Journal of Biomechanics, 2014, 47(4):847-858. DOI: 10.1016/j.jbiomech.2014.01.013
[36] VASBINDER G B C, NELEMANS P J, KESSELS A G H, et al. Accuracy of computed tomographic angiography and magnetic resonance angiography for diagnosing renal artery stenosis[J]. Annals of Internal Medicine, 2004, 141(9):674-682. DOI: 10.7326/0003-4819-141-9-200411020-00007
[37] VAN ROOIJ W J, SPRENGERS M E, DE GAST A N, et al. 3D rotational angiography:the new gold standard in the detection of additional intracranial aneurysms[J]. American Journal of Neuroradiology, 2008, 29(5):976-979. DOI: 10.3174/ajnr.A0964
[38] LANG S, HOELTER P, BIRKHOLD A I, et al. Quantitative and qualitative comparison of 4D-DSA with 3D-DSA using computational fluid dynamics simulations in cerebral aneurysms[J]. American Journal of Neuroradiology, 2019, 40(9):1505-1510. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=4183f348b9175eff0bbb908d3a39bd9e
[39] LANG S, HOELTER P, SCHMIDT M, et al. Evaluation of an artificial intelligence-based 3D-angiography for visualization of cerebral vasculature[J]. Clinical Neuroradiology, 2019. doi: 10.1007/s00062-019-00836-7.
[40] LANDRY A, SPENCE J D, FENSTER A. Measurement of carotid plaque volume by 3-dimensional ultrasound[J]. Stroke, 2004, 35(4):864-869. DOI: 10.1161/01.STR.0000121161.61324.ab
[41] TURK M, PRETNAR-OBLAK J, ZUPAN M, et al. Ultrasound diagnosis of carotid artery stiffness in patients with ischemic leukoaraiosis[J]. Ultrasound in Medicine and Biology, 2015, 41(1):64-71. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=21cec0365b08a8cfa7860c5ac919825a
[42] BOTS M L, WESTERINK J, RABELINK T J, et al. Assessment of flow-mediated vasodilatation (FMD) of the brachial artery:effects of technical aspects of the FMD measurement on the FMD response[J]. European Heart Journal, 2005, 26(4):363-368. DOI: 10.1093/eurheartj/ehi017
[43] SCHINKEL A F L, BOSCH J G, STAUB D, et al. Contrast-enhanced ultrasound to assess carotid intraplaque neovasculari-zation[J]. Ultrasound in Medicine and Biology, 2020, 46(3):466-478. DOI: 10.1016/j.ultrasmedbio.2019.10.020
[44] CHENG J M, GARCIA-GARCIA H M, DE BOER S P M, et al. In vivo detection of high-risk coronary plaques by radiofrequency intravascular ultrasound and cardiovascular outcome:results of the ATHEROREMO-IVUS study[J]. European Heart Journal, 2014, 35(10):639-647. DOI: 10.1093/eurheartj/eht484
[45] MYNARD J P, STEINMAN D A, Effect of velocity profile skewing on blood velocity and volume flow waveforms derived from maximum Doppler spectral velocity[J]. Ultrasound in Medicine and Biology, 2013, 39(5):870-881. DOI: 10.1016/j.ultrasmedbio.2012.11.006
[46] KHAN M A, LIU J, TARUMI T, et al. Measurement of cerebral blood flow using phase contrast magnetic resonance imaging and duplex ultrasonography[J]. Journal of Cerebral Blood Flow and Metabolism, 2017, 37(2):541-549. DOI: 10.1177/0271678X16631149
[47] MORBIDUCCI U, PONZINI R, RIZZO G, et al.In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging[J]. Annals of Biomedical Engineering, 2009, 37(3):516-531. DOI: 10.1007/s10439-008-9609-6
[48] MARKL M, FRYDRYCHOWICZ A, KOZERKE S, et al. 4D flow MRI[J]. Journal of Magnetic Resonance Imaging, 2012, 36(5):1015-1036. DOI: 10.1002/jmri.23632
[49] GATEHOUSE P D, KEEGAN J, CROWE L A, et al. Applications of phase-contrast flow and velocity imaging in cardiovascular MRI[J]. European Radiology, 2005, 15(10):2172-2184. DOI: 10.1007/s00330-005-2829-3
[50] BARKER A J, LANNING C, SHANDAS R. Quantification of hemodynamic wall shear stress in patients with bicuspid aortic valve using phase-contrast MRI[J]. Annals of Biomedical Engineering, 2010, 38(3):788-800. DOI: 10.1007/s10439-009-9854-3
[51] XU L J, LIANG F Y, GU L X, et al. Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery[J]. Journal of Biomechanics, 2018, 72:187-199. DOI: 10.1016/j.jbiomech.2018.03.014
[52] STEINMAN D A. Image-based computational fluid dynamics modeling in realistic arterial geometries[J]. Annals of Biomedical Engineering, 2002, 30(4):483-497. DOI: 10.1114/1.1467679
[53] TAYLOR C A, STEINMAN D A. Image-based modeling of blood flow and vessel wall dynamics:applications, methods and future directions[J]. Annals of Biomedical Engineering, 2010, 38(3):1188-1203. DOI: 10.1007/s10439-010-9901-0
[54] XU L J, ZHAO B, LIU X S, et al. Computational methods applied to analyze the hemodynamic effects of flow-diverter devices in the treatment of cerebral aneurysms:Current status and future directions[J]. Medicine in Novel Technology and Devices, 2019, 3:100018. DOI: 10.1016/j.medntd.2019.100018
[55] VASSILEVSKI Y V, DANILOV A, SIMAKOV S, et al. Patient-specific anatomical models in human physiology[J]. Russian Journal of Numerical Analysis and Mathematical Modelling, 2015, 30(3):185-201. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1515/rnam-2015-0017
[56] SEN Y K, QIAN Y, AVOLIO A, et al. Image segmentation methods for intracranial aneurysm haemodynamic research[J]. Journal of Biomechanics, 2014, 47(5):1014-1019. DOI: 10.1016/j.jbiomech.2013.12.035
[57] MOYLE K R, ANTIGA L, STEINMAN D A. Inlet conditions for image-based CFD models of the carotid bifurcation:Is it reasonable to assume fully developed flow?[J]. Journal of Biomechanical Engineering-Transactions of the ASME, 2006, 128(3):371-379. DOI: 10.1115/1.2187035
[58] LIANG F Y, LIU X S, YAMAGUCHI R, et al. Sensitivity of flow patterns in aneurysms on the anterior communicating artery to anatomic variations of the cerebral arterial network[J]. Journal of Biomechanics, 2016, 49(15):3731-3740. DOI: 10.1016/j.jbiomech.2016.09.031
[59] JANSEN I G H, SCHNEIDERS J J, POTTERS W V, et al. Generalized versus patient-specific inflow boundary conditions in computational fluid dynamics simulations of cerebral aneurysmal hemodynamics[J]. American Journal of Neuroradiology, 2014, 35(8):1543-1548. DOI: 10.3174/ajnr.A3901
[60] CHENG Z, JULI C, WOOD N B, et al. Predicting flow in aortic dissection:comparison of computational model with PC-MRI velocity measurements[J]. Medical Engineering & Physics, 2014, 36(9):1176-1184. https://www.ncbi.nlm.nih.gov/pubmed/25070022
[61] XU L J, YIN L K, LIU Y J, et al. A computational study on the influence of aortic valve disease on hemodynamics in dilated aorta[J]. Mathematical Biosciences and Engineering, 2019, 17(1):606-626. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4728110/
[62] LIANG F, OSHIMA M, HUANG H, et al. Numerical study of cerebroarterial hemodynamic changes following carotid artery operation:a comparison between multiscale modeling and stand-alone three-dimensional modeling[J]. Journal of Biomechanical Engineering, 2015, 137(10):101011. DOI: 10.1115/1.4031457
[63] ZHOU X D, YIN L K, XU L J, et al. Non-periodicity of blood flow and its influence on wall shear stress in the carotid artery bifurcation:an in vivo measurement-based computational study[J]. Journal of Biomechanics, 2020, 101:109617. DOI: 10.1016/j.jbiomech.2020.109617
[64] DAWSON E A, GREEN D J, CABLE N T, et al. Effects of acute exercise on flow-mediated dilation (FMD) in healthy humans[J]. Journal of Applied Physiology, 2013, 115(11):1589-1598. DOI: 10.1152/japplphysiol.00450.2013
[65] HSIAO S T, SPENCER T, BOLDOCK L, et al. Endothelial repair in stented arteries is accelerated by inhibition of Rho-associated protein kinase[J]. Cardiovascular Research, 2016, 112(3):689-701. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d11db2424147228a65a72ff1dddf9375
[66] GEHRON J, ZIRBES J, BONGERT M, et al. Development and validation of a life-sized mock circulatory loop of the human circulation for fluid-mechanical studies[J]. ASAIO Journal, 2019, 65(8):788-797. DOI: 10.1097/MAT.0000000000000880
[67] D'SOUZA G A, TAYLOR M D, BANERJEE R K. Methodology for hemodynamic assessment of a three-dimensional printed patient-specific vascular test device[J]. Journal of Medical Devices-Transactions of the ASME, 2019, 13(3):031011. DOI: 10.1115/1.4043992
[68] LI M T, WALK R, ROKA-MOIIA Y, et al. Circulatory loop design and components introduce artifacts impacting in vitro evaluation of ventricular assist device thrombogenicity:a call for caution[J]. Artificial organs, 2019. doi: 10.1111/aor.13626.
[69] 刘赵淼, 南斯琦, 史艺.中等严重程度冠状动脉病变模型的血流动力学参数分析[J].力学学报, 2015, 47(6):1058-1064. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=lxxb201506018 LIU Z M, NAN S Q, SHI Y. Hemodynamic parameter analysis for coronary artery stenosis of intermediate severity model[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6):1058-1064. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=lxxb201506018
[70] 刘赵淼, 杨刚, 逄燕, 等.不同心排出量下主动脉瓣血流动力学的PIV实验研究[J].力学学报, 2019, 51(6):1918-1925. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=lxxb201906028 LIU Z M, YANG G, PANG Y, et al. Experimental study on hemodynamics of aortic valve under varied cardiac output using PIV[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6):1918-1925. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=lxxb201906028
[71] LIU Z M, ZHAO S W, LI Y J, et al. Influence of coronary bifurcation angle on atherosclerosis[J]. Acta Mechanica Sinica, 2019, 35(6):1269-1278. DOI: 10.1007/s10409-019-00878-7
[72] LIU Z M, YANG G, NAN S Q, et al. The effect of anastomotic angle and diameter ratio on flow field in the distal end-to-side anastomosis[J]. Proceedings of the Institution of Mechanical Engineers Part H-Journal of Engineering in Medicine, 2019. doi: 10.1177/0954411919894410.
[73] 黄鹏辉, 黄柊喻, 党维国, 等.用于心室辅助装置血流动力学性能评价的体外循环系统技术进展[J].医用生物力学, 2018, 33(4):365-371. HUANG P H, HUANG Z Y, DANG W G, et al. A review on mock circulatory systems for in vitro hemodynamics performance evaluation of ventricular assist devices[J]. Journal of Medical Biomechanics, 2018, 33(4):365-371.
[74] 柳兆荣, 李惜惜.血液动力学原理和方法[M].上海:复旦大学出版社, 1997. [75] KRUEGER J W, YOUNG D F, CHOLVIN N R. An in vitro study of flow response by cells[J]. Journal of Biomechanics, 1971, 4(1):31-36. http://www.sciencedirect.com/science/article/pii/0021929071900133
[76] MEIKLE M C, REYNOLDS J J, SELLERS A, et al. Rabbit cranial sutures in vitro:a new experimental model for studying the response of fibrous joints to mechanical stress[J]. Calcified Tissue International, 1979, 28(2):137-144. DOI: 10.1007%2FBF02441232
[77] DAVIS C A, ZAMBRANO S, ANUMOLU P, et al. Device-based in vitro techniques for mechanical stimulation of vascular cells:a review[J]. Journal of Biomechanical Engineering-Transactions of the ASME, 2015, 137(4):040801. DOI: 10.1115/1.4029016
[78] MAVI M F, JI J Y. Endothelial wound recovery is influenced by treatment with shear stress, wound direction, and substrate[J]. Cellular and Molecular Bioengineering, 2013, 6(3):310-325. DOI: 10.1007/s12195-013-0277-8
[79] HUANG X L, SHEN Y, ZHANG Y, et al. Rac1 mediates laminar shear stress-induced vascular endothelial cell migration[J]. Cell Adhesion & Migration, 2013, 7(6):462-468. DOI: 10.4161/cam.27171
[80] MUN G I, PARK S, KREMERSKOTHEN J, et al. Expression of synaptopodin in endothelial cells exposed to laminar shear stress and its role in endothelial wound healing[J]. FEBS Letters, 2014, 588(6):1024-1030. DOI: 10.1016/j.febslet.2014.02.012
[81] ZHANG J, FRIEDMAN M H. Adaptive response of vascular endothelial cells to an acute increase in shear magnitude[J]. American Journal of Physiology-Heart and Circulatory Physio-logy, 2012, 302(4):H983-H991. DOI: 10.1152/ajpheart.00168.2011
[82] ZHANG J, FRIEDMAN M H. Adaptive response of vascular endothelial cells to an acute increase in shear stress frequency[J]. American Journal of Physiology-Heart and Circulatory Physiology, 2013, 305(6):H894-H902. DOI: 10.1152/ajpheart.00174.2013
[83] WANG Y X, LIU H B, LI P S, et al. ROS and NO dynamics in endothelial cells exposed to exercise-induced wall shear stress[J]. Cellular and Molecular Bioengineering, 2019, 12(1):107-120. DOI: 10.1007/s12195-018-00557-w
[84] YOSHINO D, SATO K, SATO M. Endothelial cell response under hydrostatic pressure condition mimicking pressure therapy[J]. Cellular and Molecular Bioengineering, 2015, 8(2):298-303. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0234700455/
[85] RUSSO T A, STOLL D, NADER H B, et al. Mechanical stretch implications for vascular endothelial cells:altered extracellular matrix synthesis and remodeling in pathological conditions[J]. Life Sciences, 2018, 213(15):214-225. https://www.sciencedirect.com/science/article/abs/pii/S0024320518306556
[86] LEE C H, SHIN H J, CHO I H, et al. Nanofiber alignment and direction of mechanical strain affect the ECM production of human ACL fibroblast[J]. Biomaterials, 2005, 26(11):1261-1270. DOI: 10.1016/j.biomaterials.2004.04.037
[87] ZHAO S M, SUCIU A, ZIEGLER T, et al. Synergistic effects of fluid shear stress and cyclic circumferential stretch on vascular endothelial cell morphology and cytoskeleton[J]. Arteriosclerosis, Thrombosis, and Vascular Biology, 1995, 15(10):1781-1786. DOI: 10.1161/01.ATV.15.10.1781
[88] PENG X Q, RECCHIA FA, BYRNE B J, et al. In vitro system to study realistic pulsatile flow and stretch signaling in cultured vascular cells[J]. American Journal of Physiology-Cell Physiology, 2000, 279(3):C797-C805. DOI: 10.1152/ajpcell.2000.279.3.C797
[89] QIU Y C, TARBELL J M. Interaction between wall shear stress and circumferential strain affects endothelial cell biochemical production[J]. Journal of Vascular Research, 2000, 37(3):147-157. DOI: 10.1159/000025726
[90] DANCU M B, TARBELL J M. Large negative stress phase angle (SPA) attenuates Nitric Oxide production in bovine aortic endothelial cells[J]. Journal of Biomechanical Engineering-Transactions of the ASME, 2006, 128(3):329-334. DOI: 10.1115/1.1824120
[91] GIRIDHARAN G A, NGUYEN M D, ESTRADA R, et al. Microfluidic cardiac cell culture model (μCCCM)[J]. Analytical Chemistry, 2010, 82(18):7581-7587. DOI: 10.1021/ac1012893
[92] ESTRADA R, GIRIDHARAN G A, NGUYEN M D, et al. Endothelial cell culture model for replication of physiological profiles of pressure, flow, stretch, and shear stress in vitro[J]. Analytical Chemistry, 2011, 83(8):3170-3177. DOI: 10.1021/ac2002998
[93] LIU Z R, JIANG W Y, HUO Y, et al. The analysis of the steady flow in the flow chamber[J]. Journal of Hydrodynamics:Series B, 1997(2):37-45. http://d.old.wanfangdata.com.cn/OAPaper/oai_pubmedcentral.nih.gov_2289785
[94] 徐刚, 覃开蓉, 柳兆荣.平行平板流动腔脉动流切应力的计算[J].力学季刊, 2000, 21(1):45-51. DOI: 10.3969/j.issn.0254-0053.2000.01.010 XU Gang, QIN K R, LIU Z R. Calculation of the shear stress in the parallel-plate flow chamber under pulsatile flow condition[J]. Chinese Quarterly of Mechanics, 2000, 21(1):45-51. DOI: 10.3969/j.issn.0254-0053.2000.01.010
[95] ANDREWS A M, JARON D, BUERK D G, et al. Direct, real-time measurement of shear stress-induced nitric oxide produced from endothelial cells in vitro[J]. Nitric Oxide, 2010, 23(4):335-342. DOI: 10.1016/j.niox.2010.08.003
[96] CHEN Y F, CHAN H N, MICHAEL S A, et al. A microfluidic circulatory system integrated with capillary-assisted pressure sensors[J]. Lab on a Chip, 2017, 17(4):653-662. DOI: 10.1039/C6LC01427E
[97] SEI Y J, AHN S I, VIRTUE T, et al. Detection of frequency-dependent endothelial response to oscillatory shear stress using a microfluidic transcellular monitor[J]. Scientific Reports, 2017, 7(1):10019. DOI: 10.1038/s41598-017-10636-z
[98] SATO K, SATO K. Recent progress in the development of microfluidic vascular models[J]. Analytical Sciences, 2018, 34(7):755-764. DOI: 10.2116/analsci.17R006
[99] SEBASTIAN B, DITTRICH P S. Microfluidics to mimic blood flow in health and disease[J]. Annual Review of Fluid Mechanics, 2018, 50(1):483-504. DOI: 10.1146/annurev-fluid-010816-060246
[100] ZHENG C H, YU Z L, ZHOU Y, et al. Live cell imaging analysis of the epigenetic regulation of the human endothelial cell migration at single-cell resolution[J]. Lab on a Chip, 2012, 12(17):3063-3072. DOI: 10.1039/c2lc40192d
[101] PRIM D A, POTTS J D, EBERTH J F. Pulsatile perfusion bioreactor for biomimetic vascular impedances[J]. Journal of Biomechanical Engineering-Transactions of the ASME, 2018, 12(4):041002. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=9f55ad1df2dd7f2b3e558070f7d4ffe0
[102] CHEN Z Z, GAO Z M, ZENG D P, et al. A Y-shaped microfluidic device to study the combined effect of wall shear stress and ATP signals on intracellular calcium dynamics in vascular endothelial cells[J]. Micromachines, 2016, 7(11), 213. DOI: 10.3390/mi7110213
[103] CHEN Z Z, YUAN W M, XIANG C, et al. A microfluidic device with spatiotemporal wall shear stress and ATP signals to investigate the intracellular calcium dynamics in vascular endothelial cells[J]. Biomechanics and Modeling in Mechano-biology, 2019, 18(1):189-202. DOI: 10.1007/s10237-018-1076-x
[104] ZHANG Z Q, XU L J, LIU R, et al. Importance of incorporating systemic cerebroarterial hemodynamics into computational modeling of blood flow in intracranial aneurysm[J]. Journal of Hydrodynamics, 2019. doi: 10.1007/s42241-019-0038-9.
[105] QIN K R, JIANG Z L, SUN H, et al. A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries[J]. Acta Mechanica Sinica, 2006, 22(1):76-83. DOI: 10.1007/s10409-005-0082-2
[106] ZHU Y, LI Y Z, QIN K R, et al. Transportation of dynamic biochemical signals in non-reversing oscillatory flows in blood vessels[J]. Science China-Physics Mechanics & Astronomy, 2013, 56(2):322-327. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgkx-eg201302011
[107] LI X Y, LIU X S, LI X, et al. Tortuosity of the superficial femoral artery and its influence on blood flow patterns and risk of atherosclerosis[J]. Biomechanics and Modeling in Mechano-biology, 2019, 18(4):883-896. DOI: 10.1007/s10237-019-01118-4
[108] WANG Y X, XIANG C, LIU B, et al. A multi-component parallel-plate flow chamber system for studying the effect of exercise-induced wall shear stress on endothelial cells[J]. Biomedical Engineering Online, 2016, 15(Suppl 2):154. DOI: 10.1186/s12938-016-0273-z
[109] LIU B, QU M J, QIN K R, et al. Role of cyclic strain frequency in regulating the alignment of vascular smooth muscle cells in vitro[J]. Biophysical Journal, 2008, 94(4):1497-1507. DOI: 10.1529/biophysj.106.098574
[110] QIN K R, HU X Q, LIU Z R. Analysis of pulsatile flow in the parallel-plate flow chamber with spatial shear stress gradient[J]. Journal of Hydrodynamics:Series B, 2007, 19(1):113-120. DOI: 10.1016/S1001-6058(07)60036-5
[111] QIN K R, XIANG C, GE S Z. Generation of dynamic biochemical signals with a tube mixer:effect of dispersion in an oscillatory flow[J]. Heat and Mass Transfer, 2010, 46(6):675-686. DOI: 10.1007/s00231-010-0602-x
[112] LI Y J, LI Y Z, CAO T, et al. Transport of dynamic biochemical signals in steady flow in a shallow Y-shaped microfluidic channel:effect of transverse diffusion and longitudinal dispersion[J]. Journal of Biomechanical Engineering-Transactions of the ASME, 2013, 135(12):121011. DOI: 10.1115/1.4025774
[113] LI Y J, CAO T, QIN K R. Transmission of dynamic biochemical signals in the shallow microfluidic channel:nonlinear modulation of the pulsatile flow[J]. Microfluidics and Nanofluidics, 2018, 22(8):1-13. https://www.researchgate.net/publication/326540266_Transmission_of_dynamic_biochemical_signals_in_the_shallow_microfluidic_channel_nonlinear_modulation_of_the_pulsatile_flow
[114] QIN K R, XIANG C, XU Z, et al. Dynamic modeling for shear stress induced ATP release from vascular endothelial cells[J]. Biomechanics and Modeling in Mechanobiology, 2008, 7(5):345-353. DOI: 10.1007/s10237-007-0088-8
[115] QIN K R, XIANG C, CAO L L. Dynamic modeling for flow-activated Chloride-selective membrane current in vascular endothelial cells[J]. Biomechanics and Modeling in Mechano-biology, 2011, 10(5):743-754. DOI: 10.1007/s10237-010-0270-2
[116] LI L F, XIANG C, QIN K R. Modeling of TRPV4-C1-mediated calcium signaling in vascular endothelial cells induced by fluid shear stress and ATP[J]. Biomechanics and Modeling in Mechanobiology, 2015, 14(5):979-993. DOI: 10.1007/s10237-015-0647-3
[117] XIANG C, CAO L L, QIN K R, et al. Dynamic modeling and control of extracellular ATP concentration on vascular endothelial cells via shear stress modulation[J]. Journal of Control Theory and Applications, 2010, 8(3):326-332. DOI: 10.1007/s11768-010-0030-y
[118] NA J T, XUE C D, LI Y J, et al. Precise generation of dynamic biochemical signals by controlling the programmable pump in a Y-shaped microfluidic chip with a 'christmas tree' inlet[J]. Electrophoresis, 2020. doi: 10.1002/elps.201900400.
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