二维脉动流场中内皮细胞表面切应力分布的数值模拟

本文对三种生理相关的正弦入口速度波形的脉动流场内,VEC表面的切应力分布进行了有限差分方法的数值模拟.结果表明(1)脉动流场与稳态流场中内皮细胞表面的流场分布完全不同,脉动流场中内皮细胞表面的切应力变化幅值远大于稳态流场中的值.(2)同一时刻,每个VEC上的切应力分布是不均匀的,细胞形状影响其表面的切应力分布.(3)在脉动周期的不同时刻,细胞表面的切应力分布也是不均匀的,切应力分布随时间的变化波形与入口波形相类似,但相位有所超前.(4)细胞的伸长主要取决于EC表面的最大平均切应力大小.(5)本章的计算结果可以用于对Helmilinger实验现象的解释.     

二维脉动流场中内皮细胞表面切应力分布的数值模拟

本文对三种生理相关的正弦入口速度波形的脉动流场内,VEC表面的切应力分布进行了有限差分方法的数值模拟。结果表明：（1）脉动流场与稳态流场中内皮细胞表面的流场分布完全不同,脉动流场中内皮细胞表面的切应力变化幅度远大于稳态流场中的值。（2）同一时刻,每个VEC上的切应力分布是不均匀的,细胞形状影响其表面的切应力分布。（3）在脉动周期的不同时刻,细胞表面的切应力分布也是不均匀的,切应力分布随时间的变化波形与入口波形相类似,但相位有所超前,（4）细胞的伸长主要取决于EC表面的最大平均应力大小。（5）本章的计算结果可以用于Helmilinger实验现象的解释。     

切应力对内皮细胞膜微粘度的影响

目的:研究切应力对内皮细胞(EC)膜微粘度的影响.材料和方法:将EC置于脉动循环装置中,分别施加15dyne/cm2、50dyne/cm2、30 Odyne/cm2切应力,作用Oh、1h|2h、4h、6h、10h后,利用带偏振器的荧光分光光度计测量膜微粘度.结果:切应力使膜微粘度增加,且切应力越高,膜微粘度增加幅度越大.切应力作用4h,EC膜微粘度升至最高;4h～10h,膜微粘度开始缓慢恢复,但仍比静态对照显著升高.结论:在切应力作用下,EC膜微粘度增加,切应力是AS的致病因素.动脉狭窄处和大中动脉分叉处是AS好发的危险部位,也是防治的重点.     

流体切应力下血管内皮单核细胞趋化蛋白-1的表达

目的研究流体切应力对人血管内皮细胞的单核细胞趋化蛋白-1(MCP-1)表达的影响,探讨血流动力在动脉粥样硬化(AS)发生早期中的作用.方法利用平行板流动腔对血管内皮细胞施加不同切应力,分别采用夹心酶联免疫吸附测定(EL,ISA)及逆转录-聚合酶链反应(RT-PCR)法检测MCP-1蛋白及mRNA水平.结果以0.72Pa切应力进行不同时间作用,0.5h后MCP-1mRNA即达到静态时(0.160±0.037)的4倍(0.684±0.033),5h时略有升高,达0.707±0.089,12h后下降到低于对照组的水平(0.036±0.006,P＜0.001).灌流液中MCP-1蛋白时间依赖性增加,但5h后增长趋缓;而在不同切应力(0.30、0.72、2.40Pa)相同时间(5h)下,0.72Pa的作用最显著,MCP-1蛋白比静态对照增加了2倍多,mRNA水平则升高达4倍.结论MCP-1的表达对切应力的变化反应强烈,持续稳定的切应力则下调MCP-1的表达,此研究结果表明血流紊乱可促进AS病变的发生发展.     

流体切应力对内皮细胞IL-8基因表达的影响及信号转导

目的流体切应力对于维持血管的稳定有着重要的作用.另外在一些病理情况下,例如动脉粥样硬化、高血压等心血管疾病的发病过程中,流体切应力也扮演着关键角色.我们以往的实验结果证实:以低流体切应力(4.2dyne/cm2)处理培养的人脐静脉内皮细胞1 h,其IL-8mRNA的表达上调;处理2 h其表达量上调更为明显.在本实验中我们将进一步阐明流体切应力对培养的人脐静脉内皮细胞IL-8基因表达、蛋白生成的影响及其信号转导途径.方法分别用实时定量RT-PCR及定量三明治ELISA检测IL-8基因表达及蛋白生成;通过基因转染及流式细胞数检测IL-8报告基因pEGFP1-IL8USCS经流体切应力作用后的激活情况;用免疫荧光化学染色观测对照和层流切应力处理以后NF-κB核转移情况;将对照和层流切应力处理后的内皮细胞裂解物进行I-κB和磷酸化的I-κB的免疫印迹实验,以检测切应力诱导的I-κB磷酸化和降解的情况;RT-PCR、Northern杂交和免疫荧光细胞化学染色观察TLR-4和TLR-2在人脐静脉内皮细胞上的表达;用RT-PCR技术从血管内皮细胞扩增胞内区段缺失突变TLR-4 cDNA克隆于真核表达质粒pcDNA3,构建重组TLR-4胞内缺失突变基因真核表达质粒pcDNA3-mTLR4,与pEGFP1-IL8USCS共转染内皮细胞,流式细胞术观察mTLR4对切应力诱导IL-8报告基因表达的影响.结果和讨论(1)未用切应力处理的内皮细胞没有IL-8基因的表达;切应力处理内皮细胞后,1 h IL-8 mRNA表达增加,2 h IL-8 mRNA表达量至最高值,3 h IL-8 mRNA表达量开始下降,4 h后IL-8 mRNA持续相对高表达;各实验组(2.23、4.20、6.08 dyne/cm2)均表现出相同的IL-8 mRNA随时间的变化规律,即IL-8的表达对切应力有时间依赖性.(2)未用切应力处理的内皮细胞没有IL-8基因的表达;切应力处理内皮细胞后,低切应力时IL-8 mRNA表达量明显增加,高切应力时IL-8 mRNA表达量较低.IL-8 mRNA的表达量与内皮细胞所施加的切应力强度呈反变关系;不同的切应力作用时间(1、2 h)均表现出相同的IL-8 mRNA随切应力强度的变化规律.提示流体切应力诱导内皮细胞表达IL-8,不仅与切应力的作用时间有关,而且IL-8的表达量与切应力作用强度有关,两者之间具有明显的直线负相关.直线回归方程:1 h时为y=7.57-0.11x,相关系数r=-0.97;2 h时为y=7.92-0.10 x,相关系数r=-0.96.(3)未用切应力处理的内皮细胞只有极少量的IL-8蛋白质生成;切应力处理内皮细胞1 h后,IL-8蛋白质生成量增加,处理5 h后IL-8蛋白质生成量增加至最高值,处理8 h后IL-8蛋白质生成量下降,10 h后IL-8蛋白质生成量维持在一个较高的水平.各实验组(2.23、4.20、6.08 dyne/cm2)均表现出相同的IL-8蛋白质生成量随切应力作用时间的变化规律.提示流体切应力确实可以诱导内皮细胞生成IL-8,并且IL-8的生成量与切应力的作用时间有关,呈双相性变化.(4)未用切应力处理的内皮细胞只有极少量的IL-8蛋白质生成;切应力处理内皮细胞后,低切应力(2.23 dyne/cm2)时IL-8蛋白质生成量明显增加,为高切应力(19.29 dyne/cm2)时IL-8蛋白质生成量的约6(作用5h)或7倍(作用6h).IL-8蛋白质生成量与内皮细胞所施加的切应力强度呈反变关系;直线回归方程:5 h时为y=760.12-36.06x,相关系数r=-0.978;6 h时为y=781.87-36.66x,相关系数r=-0.980.(5)pEGFP1-IL8USCS转染细胞,层流切应力刺激3 h后IL-8报告基因绿色荧光蛋白表达增强.(6)NF-κB p65免疫荧光细胞化学染色显示,切应力刺激0.5 h,胞核即出现阳性反应,刺激1.5 h后,胞核呈强阳性染色.(7)细胞裂解物免疫印迹显示,刺激10 min时磷酸化IκB即显著增强,1 h后磷酸化IκB印迹强度降到无,而IκB随刺激时间延长而逐渐降低,0.5和1 h后降至测不到IκB.(8)免疫荧光细胞化学染色显示脐静脉血管内皮细胞膜表达TLR-4.RT-PCR和Northern杂交显示,人脐静脉血管内皮细胞表达TLR-2和TLR-4 mRNAs;当切应力刺激1 h后,TLR-4 mRNA表达明显增强.pcDNA3-mTLR4和pEGFP 1-IL8USCS共转染细胞,层流切应力刺激3 h后荧光蛋白表达未明显增强.本实验中我们采用的切应力为2.23、4.20、6.08 dyne/cm2,这些切应力与动脉血管分叉处等低切应力区生理切应力大小相似,在这些低切应力区,血管内皮细胞可分泌IL-8,IL-8转而激活中性粒细胞和单核细胞,调控它们和内皮细胞的黏附,这将触发一系列的病理变化,例如:动脉粥样硬化等.结论流体切应力诱导内皮细胞IL-8 mRNA的表达及IL-8蛋白的生成,在感染及动脉粥样硬化等病理过程中扮演着重要角色.     

下颌切牙牙槽骨骨吸收前后三维有限元应力分析

主要利用三维有限元应力分析的方法研究观察下颌切牙牙槽骨骨吸收前后在垂直载荷、15°斜向载荷、30°斜向载荷分别作用下牙槽骨骨组织表面的vonMises应力分布特点及牙齿的舌向位移值。在垂直载荷、15°斜向载荷作用下,牙周健康的下颌切牙牙槽骨骨组织表面vonMises应力最大值分别是13.171和14.315MPa,均位于根尖处牙槽骨,舌向位移值分别是0.056和0.197mm;在30°斜向载荷作用下vonMises应力最大值是15.262MPa,分布于根尖处牙槽骨和牙槽嵴顶,舌向位移值为0.324mm。而牙槽骨骨吸收达根长1/2时,在垂直载荷作用下vonMises应力明显增加,最大值位于根尖处牙槽骨;在不同的斜向载荷作用下,所产生应力继续显著增加,vonMises应力最大值可达牙周健康的下颌切牙的3～5倍,分布部位完全由根尖处牙槽骨转移到牙槽嵴顶,分布的面积也越来越小,发生了由面分布到点分布的转变,应力越来越集中于某一点。且牙齿已发生明显的舌向位移,可高达2.850mm。提示当牙槽骨骨吸收接近根长1/2或以上时,在牙周基础治疗过程中,应考虑进行调牙合、松牙固定术等治疗,分散牙合力以避免过大应力的产生和应力分布的改变,减轻对牙周组织的损伤。     

外周血内皮祖细胞种植小径聚氨酯人工血管及流体切应力处理的实验研究

本研究收集健康成人骨髓单个核细胞,用血管内皮生长因子等加以诱导分化,通过荧光显微镜和荧光免疫标记等方法观察和鉴定诱导后的细胞。之后将诱导分化的内皮祖细胞种植到聚氨酯小径人工血管表面,予以15 dyn／cm2的流体切应力处理,并用扫描电镜观察。结果发现外周血单个核细胞诱导分化成为内皮祖细胞,ac- LDL及lectin抗体荧光标记阳性。扫描电镜下,未种植细胞的聚氨酯小径人工血管表面孔径大小比较适合内皮祖细胞爬行;静态种植细胞后,人工血管表面内皮祖细胞排列不整齐;切应力条件下种植细胞后,人工血管表面内皮祖细胞排列较为整齐。因此,在体外能将外周血单个核细胞诱导分化成为内皮祖细胞,内皮祖细胞是小径人工血管内皮化的理想种子细胞。流体切应力对小径聚氨酯人工血管表面内皮祖细胞的生长排列有着良好的机械塑形作用。     

切应力对与血管平滑肌细胞联合培养的内皮细胞微管骨架重构的影响

目的探讨切应力对与血管平滑肌细胞(VSMCs)联合培养的内皮细胞(ECs)中微管的聚集重构的影响,为阐明应力诱导血管重建的分子机制提供一些实验证据。方法应用ECs与VSMCs联合培养的平行平板流动腔系统,给ECs面施加15dyne/cm2的层流切应力,以静态条件下联合培养的ECs为对照组,用WesternBlot、免疫荧光细胞化学和图像分析等技术,研究切应力作用下与VSMCs联合培养的ECs的微管聚集的变化。结果静态联合培养组,ECs微管骨架的排列是稀疏、发散和无规律的。切应力诱导了ECs的微管的重构,,微管骨架变得有序,朝切应力的方向规律的排列。切应力能够促进ECs的微管聚集,与对照组相比,切应力作用下的ECs内多聚微管的数量增加,切应力作用3h,ECs内多聚微管的数量达到峰值,之后开始下降。结论切应力诱导和促进了EC的微管骨架发生重构(聚集)。结果提示:微管可能是机械应力刺激作用的靶标,应力可能通过它改变ECs的形态,影响细胞的黏附与迁移等功能。     

流体切应力作用强度对内皮细胞IL一8生成的影响

血管内皮细胞衬于血管腔的表面,是血流机械应力的主要感受者.切应力可以直接调节内皮细胞生物活性物质的合成和分泌,其中包括诱导内皮细胞生成IL一8,而且IL一8的生成量与切应力作用时间有关.为阐明内皮细胞IL一8的生成除了与切应力的作用时间有关外还与切应力的强度有关,我们用不同强度的流体切应力(2.09、4.61、6.1 9、8.51、10.50、12.59、14.41、17.22、18.32 dyne/cm2)处理培养的人脐静脉内皮细胞,然后采用双抗体夹心ABC-ELISA技术检测内皮细胞IL一8蛋白质的生成.结果显示未用切应力处理的内皮细胞只有极少量的IL一8蛋白质生成;切应力处理内皮细胞后,低切应力(2.09dyne/cm2)时IL一8蛋白质生成量明显增加,约为高切应力(18.32 dyne/cm2)时IL-8蛋白质生成量的6(作用5 h)或7倍(作用6 h).IL一8蛋白质生成量与内皮细胞所施加的切应力强度呈反变关系;直线回归方程5 h时为y=760.12-36.06x,相关系数γ=-0.978;6 h时为y=781.87-36.66x,相关系数γ=-0.980.式中y为切应力作用下内皮细胞IL-8的生成量;x为施加于内皮细胞的切应力强度(dyne/cm2).不同的切应力作用时间(5 h、6 h)均表现出相同的IL-8蛋白质生成量随切应力强度的变化规律.提示流体切应力诱导内皮细胞生成IL一8的量,不仅与切应力的作用时间有关,而且IL-8的生成量与切应力强度有关.流体低切应力诱导内皮细胞IL-8的生成量急剧增高,可能在急性炎症和动脉粥样硬化的发生、发展过程中具有重要作用.     

切应力条件下与血管平滑肌细胞联合培养的内皮细胞整合素β1和F-actin的变化

目的 探讨与血管平滑肌细胞联合培养的内皮细胞力学信号转导的机制，研究切应力对联合培养的内皮细胞表面整合素和F-actin的影响。方法 应用免疫荧光双重标记、激光共聚焦扫描显微镜和计算机图象分析等技术，观察了在2Pa层流切应力的作用下，与血管平滑肌细胞联合培养的内皮细胞表面整合素β1的含量及细胞骨架F-actin的变化，时相点分别取lh、6h、12h和24h。同时，以静态条件下联合培养的内皮细胞为对照组。结果 静态条件下联合培养的内皮细胞表面整合素β1含量少，F-actin含量亦少；在2Pa层流切应力的作用下，随着时间延长，整合素β1表达逐渐增多，并且有沿F-actin分布的趋势，在12h达到峰值，后又下降；F-actin含量持续增加直至24h。结论 结果提示整合素β1作为重要的粘附分子，与细胞骨架F-actin的相互协作，在联合培养的内皮细胞的力学信号转导中起重要作用。     

流体切应力梯度对血管内皮细胞排列和形状的影响

目的研究不同梯度切应力作用下,血管内皮细胞(endothelial cells,ECs)排列和形状变化,旨在了解流体切应力梯度对ECs形态的影响,为进一步探讨其功能变化提供实验基础。方法建立可对体外培养ECs施加梯度切应力的流动腔装置,并应用该装置对人脐静脉ECs加载了大小在15dyn/cm2～6.6dyn/cm2(1dyn=10-5N)范围、梯度分别为1.5dyn/cm2和3dyn/cm2的切应力,加载时间均为6h。比较这两种不同切应力梯度对ECs的细胞方向角、细胞宽长比和细胞形态指数的影响。结果在不同切应力梯度作用下,ECs的细胞方向角分布散乱,细胞无排列规律。与3dyn/cm2相比,1.5dyn/cm2切应力梯度下ECs的宽长比和细胞形态指数明显减少,趋向于拉伸状态。结论在不同切应力梯度作用下,ECs均排列紊乱,无规律可循。然而,在相对较小的切应力梯度作用下,细胞容易被拉伸,细胞形状趋向于伸长,而较大切应力梯度作用下,细胞形状则趋向于圆形。     

用流动双折射法研究动脉分叉处血液流场的剪应力分布

用流动双折射法，对三种动脉分叉模型所模拟的血液流场剪应力分布进行了研究，发现流场中零应力点的位置、最大剪应力沿壁面的分布及相应极值点的位置均随分流比的变化而改变，与总流量无关，且应力集中点与动脉分叉几何形状有关。     

端点条件对平行平板流动腔底部切应力的影响

高度远小于横向和纵向几何尺寸的平行平板流动腔是当前用以体外研究细胞在切应力场作用下的力学行为,特别是粘附特性的主要工具之一。本文对实际使用的具有不同入口和出口边界条件的流动腔内流体定常流动的流场进行了详细分析,计算出几种常用的不同人口和出口流量分布所对应平行平板流动腔底部的切应力场分布。详细讨论端点条件对腔室底部切应力的影响情况。指出端点条件的影响只局限在离开腔室差不多为腔室宽度的区域之内,本文结果对于分析流动腔内细胞的力学行为和讨论切应力对细胞的影响有重要实际意义。     

应力培养对血管内皮细胞形态结构的影响

为在体外形成一个抗流动切应力作用能力强的单层内皮细胞，在１５ｄｙｎｅｓ／ｃｍ＾２切应力的条件下，培养内皮细胞２４ｈ。细胞内皮细胞中央出现应力纤维，Ｇ０／Ｇ１期细胞增加，这一现象提示，在切应力条件下培养内皮细胞，可增强细胞抗血流冲击的能力。     

Steady unidirectional laminar flow inhibits monolayer formation by human and rat microvascular endothelial cells.

Endothelialization of artificial vascular grafts is rapid and complete in numerous animal models, including dogs and rats, but not in human patients. One possible explanation for this well-known, yet puzzling observation might be that monolayer formation of human endothelial cells (ECs), and of canine or rodent ECs, is affected differently by flow-induced shear stress. To begin testing this hypothesis, the authors wounded confluent monolayers of cultured rat and human ECs and exposed these cultures for 20 h to unidirectional steady laminar shear stress of 10 dyn/cm(2) induced by fluid flow perpendicular to the wound boundaries. In comparison to experimental control cultures simultaneously maintained under static (no-flow) conditions, flow-induced shear stress attenuated the monolayer formation (sheet migration) in both human and rat ECs. In brief, compared to control, the average human EC monolayer formation under shear was reduced by 33% whereas the average rat EC monolayer formation was reduced by 34%. Furthermore, the cell responses showed a dependence on fluid flow direction that differed per species. When exposed to shear stress, human EC monolayer formation was reduced by 16% in the upstream direction (opposing the direction of flow) and reduced by 50% in the downstream direction (with the direction of flow), whereas rat EC monolayer formation was reduced by 64% upstream and showed no change downstream. These findings suggest that although overall monolayer formation is inhibited by fluid-induced shear stress to the same extent in both species, there are cell type- and/or species-dependent migration responses to fluid-induced shear stress, and that different flow conditions possibly contribute to species-specific patterns of endothelialization.     

Hemodynamic simulation study of a novel intra-aorta left ventricular assist device

The intra-aorta pump proposed here is a novel left ventricular assist device (LVAD). The mathematic model and the in vitro experiment demonstrate that the pump can satisfy the demand of human blood perfusion. However, the implantation of LVAD will change the fluid distribution or even generate a far-reaching influence on the aorta. At present, the characteristics of endaortic hemodynamics under the support of intra-aorta pump are still unclear. In this article, a computational fluid dynamics study based on a finite-element method was performed for the aorta under the support of intra-aorta pump. To explore the hemodynamic influence of intra-aorta pump on aorta, fully coupled fluid-solid interaction simulation was used in this study. From the flow profiles, we observed that the maximum disturbed flow and nonuniform flow existed within the aortic arch and the branches of the aortic arch. Flow waveforms at the inlets of aortas were derived from the lumped parameter model that we proposed in our previous study. The results demonstrated that the intra-aorta pump increased the blood flow in the aorta to normal physiologic conditions, but decreased the pulsatility of the flow and pressure. The pulsatility index changed from 2,540 to 1,370. The pressure gradient (PG) for heart failure conditions was 18.88 mm Hg/m vs. 25.51 mm Hg/m for normal physiologic conditions; for intra-aorta pump assist conditions, normal PG value could not be regained. Furthermore, our experimental results showed that the wall shear stress (WSS) of aorta under heart failure and normal physiologic conditions were 1.5 and 6.3 dynes/cm, respectively. The intra-aorta pump increased the WSS value from 1.5 to 4.1 dynes/cm.     

New J-3 flexible-leaflet polyurethane heart valve prosthesis with improved hydrodynamic performance.

The aim of this new three-leaflet valve development was to design a leaflet with minimum membrane stresses during performance. This is achieved by manufacturing the valve leaflets shaped almost flat in a medium opening position. Thus, the leaflets have two stable positions, one with maximum opening area and the other with favorable stress distribution in the closed position. The transition between the two end positions is achieved through a two-dimensional rolling motion without buckling and with minimum membrane stresses (bulge forces). The manufacturing technique is dip-coating in polyurethane. Hydrodynamic evaluation of the J-3 valve in steady and pulsatile flow showed minimum pressure drop compared to other commercially available valves. Laser-Doppler-anemometry studies indicated very low shear stresses in the flow field downstream of the valve. In durability tests prototypes have reached lifetimes of up to 17 years. In conclusion, the J-3 valve shows superior hydrodynamic performance thereby reducing potential thrombus formation. Minimization of stresses within the valve leaflets through design could reduce calcification.     

In vitro comparison of steady and pulsatile flow characteristics of jellyfish heart valve

In examining the hydrodynamic performance of artificial heart valves in vitro, experiments are carried out under either steady or pulsatile flow conditions. Steady flow experiments are simple to set up and analysis of the data is also simple; however, their validity and accuracy have been questioned. In this study, the flow characteristics of jellyfish valves are evaluated and analyzed for steady and pulsatile flow conditions. The analysis is given in terms of velocity and shear stress distributions for a cardiac flow rate of 4.5l/min, and the corresponding steady flow rate is measured at two locations, 0.5D and 1D downstream of the valve face (D being the diameter of the pipe). At the 0.5D location, the velocity profile results obtained for both flow conditions indicated that jetting flow occurred close to the wall, and flow reversal as well as stagnation zones occurred in the core of the valve chamber. These phenomena were also evident in the shear stress profiles for both pulsatile and steady flow conditions. At this location, the maximum difference between the steady and pulsatile values of peak velocity is about 18%. However, the maximum difference between the peak shear stresses was in the range of 5%–7%. At the 1D location, the flow characteristics observed under both the pulsatile and steady flow conditions were almost identical, with a maximum difference between the peak values of less than 4%. From the data presented here, it can be stated that, at least in the initial optimization of the valve hemodynamic performance, the steady hydrodynamic evaluation of the valve could be an effective tool for analyzing the flow characteristics.     

The Flow Field along the Entire Length of Mouse Aorta and Primary Branches

There is a spatial disposition to atherosclerosis along the aorta corresponding to regions of flow disturbances. The objective of the present study is to investigate the detailed distribution of hemodynamic parameters (wall shear stress (WSS), spatial gradient of wall shear stress (WSSG), and oscillatory shear index (OSI)) in the entire length of C57BL/6 mouse aorta with all primary branches (from ascending aorta to common iliac bifurcation). The detailed geometrical parameters (e.g., diameter and length of the vessels) were obtained from casts of entire aorta and primary branches of mice. The flow velocity was measured at the inlet of ascending aorta using Doppler flowprobe in mice. The outlet pressure boundary condition was estimated based on scaling law. The continuity and Navier–Stokes equations were solved using three-dimensional finite element method (FEM). The model prediction was tested by comparing the computed flow rate with the flow rate measured just before the common iliac bifurcation, and good agreement was found. It was also found that complex flow patterns occur at bifurcations between main trunk and branches. The major branches of terminal aorta, with the highest proportion of atherosclerosis, have the lowest WSS, and the relatively atherosclerotic-prone aortic arch has much more complex WSS distribution and higher OSI value than other sites. The low WSS coincides with the high OSI, which approximately obeys a power law relationship. Furthermore, the scaling law between flow and diameter holds in the entire aorta and primary branches of mice under pulsatile blood flow conditions. This model will eventually serve to elucidate the causal relation between hemodynamic patterns and atherogenesis in KO mice.