附录B 外文原文
Rheological models for blood
Rheology is the science of the deformation and flow of materials. It deals with the theoretical concepts of kinematics, conservation laws and constitutive rela-tions, describing the interrelation between force, deformation and flow. The experimental determination of the rheological behaviour of materials is called rheometry. The object of haemorheology is the application of rheology to the study of flow properties of blood and its formed elements, and the coupling of blood and the blood vessels in living organisms. This field involves the investigation of the macroscopic behaviour of blood determined in rheometric experiments, its microscopic properties in vitro and in vivo and studies of the interactions among blood cellular components and between these components and the endothelial cells that line blood vessels.
Advances in the field of haemorheology have contributed in particular to the fundamental understanding of the changes in the rheological proper- ties of blood and its components due to pathological disturbances, and are based on the evidence that they might be the primary cause of many car- diovascular diseases. Haemorheological aberrations can easily be considered as a result (or an indicator) of insufficient circulatory function. Alternatively, deviations in haemorheological parameters may affect tissue perfusion and be manifested as circulatory problems. Basically, pathologies with haematological origin like leukemia, haemolytic anemia, thalassemia or pathologies associated with the risk factors of thrombosis and atherosclerosis like myocardial infarc- tion, hypertension, strokes or diabetes are mainly related to disturbances of local homeostasis. Therefore, the mathematical and numerical study of power- ful, yet simple, constitutive models that can capture the rheological response of blood over a range of flow conditions is ultimately recognised as an impor- tant tool for clinical diagnosis and therapeutic planning (see e.g. ).
The aim of this chapter is to present the rheological properties of blood, including its non-Newtonian characteristics, and review some of the macro-scopic mathematical models that have been proposed in the literature to model these features.
As already discussed whole blood is a concentrated suspension of formed cellular elements that includes red blood cells (RBCs) or erythrocytes, white blood cells (WBCs) or leukocytes and platelets or thrombocytes. These cellular elements are suspended in an aqueous polymer solution, the plasma, containing electrolytes and organic molecules such as metabolites, hormones, enzymes, antibodies and other proteins. Erythrocytes have been shown to exert the most significant influence on the mechanical properties of blood, mainly due to their presence in very high concentration compared to the other formed elements (approximately 4–6 106 RBCs/mm3), comprising about 40 to 45 % of its volume in healthy individuals (haematocrit, Ht).
While plasma is nearly Newtonian in behaviour, whole blood exhibits marked non-Newtonian characteristics, particularly at low shear rates. The non-Newtonian behaviour of blood is mainly explained by three phenomena: the erythrocytesrsquo; tendency to form a three-dimensional microstructure at low shear rates, their deformability and their tendency to align with the flow field at high shear rates.
As will be elaborated on below, the formation and breakup of this 3D microstructure, as well as the elongation and recovery of red blood cells, contribute to bloodrsquo;s shear thinning, viscoelastic and thixotropic behaviour1. Aggregation and deformation of erythrocytes are complex dynamic processes.
In which cellular and plasma components of blood contribute as essential factors. Experimental data under various flow conditions, particularly physi-ologically relevant flows, are required to develop meaningful models of these complex processes).
In this section we briefly discuss the physical behaviour of erythrocytes that have the strongest influence on the non-Newtonian behaviour of whole flowing blood at low shear rates.
In the presence of fibrinogen and globulins (two plasma proteins), erythro- cytes have the ability to form a primary aggregate structure of rod shaped stacks of individual cells called rouleaux. At very low shear rates the rouleaux align themselves in an end-to-side and side-to-side fashion and form a sec- ondary structure consisting of branched three-dimensional aggregates .While the definition of thixotropy varies greatly in the literature, here we refer to thixotropy as the dependence of the material properties on the time over which shear has been applied. This dependence is largely due to the finite time required for the three-dimensional structure of blood to form and break down.
Three-dimensional microstructure of RBC aggregates in human blood from a healthy donor. Rouleaux formed by rod shaped stacks of RBCs can be seen. The isolated darker circles on top of the rouleaux arise from rouleaux branching off these stacks, forming the three-dimensional microstructure of RBC aggregates. These branches are less transparent and therefore darker. The large light circles are white blood cells while the much smaller light circles are platelets. Magnification 100X, (courtesy of Prof. M.V. Kameneva, University of Pittsburgh, USA)(see Fig. 6.1). The biochemical process of rouleaux formation is still unclear. It has been experimentally observed that these stacks will not form if the ery- throcytes have been hardened or in the absence of fibrinogen and globulins.
For blood at rest, the three-dimensional structure formed by the RBCs appears solid-like, appearing to resist flow until a finite level of force is applied. The applied stress needed to initiate flow, e.g. in simple shear, is often referred to as the yi
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附录A 外文翻译
血流流变仪模型
流变学是研究材料的变形和性质的科学。它涉及运动学、守恒定律和本构关系的理论概念，描述了力、变形和势之间的相互关系。材料流变行为的实验测定称为流变仪。血液流变学的研究对象是流变学在研究血液及其形成元素的性质、活体中血液和血管的耦合等方面的应用。本研究涉及在血液流变学实验中测定血液的宏观行为、体外和体内的微观特性以及血液细胞组分和这些组分与血液系V的内皮细胞之间相互作用的研究。血液流变学的研究进展，特别是对血液和血液成分的流变学特性的病理变化的基本认识，并基于这些证据可能是许多汽车的主要原因。双血管疾病血液流变学的异常可以很容易地被认为是一个结果（或指标）的内循环功能。或者，血液流变学参数的偏差可能是一种组织灌注，并表现为循环问题。基本上，血液学起源的病症如白血病、溶血性贫血、地中海贫血或与血栓形成和动脉粥样硬化的危险因素相关的病理，如心肌梗塞、高血压、中风或糖尿病，主要与局部稳态紊乱有关。因此，能够在一系列范围内捕捉血液流变响应的幂函数的简单的本构模型的数学和数值研究最终被认为是临床诊断和治疗计划的重要工具。
本章的目的是介绍血液流变学特性，包括其非牛顿特性，并回顾文献中已经提出的一些宏观数学模型来模拟这些特征。
1.1血液力学性质的物理机制 1 . 1 xuegrave;血 yegrave;液 ligrave;力 xueacute;学 xigrave;ng性 zhigrave;质 de的 wugrave;物 lǐ理 jī机 zhigrave;制
As already discussed in Chapter 1 whole blood is a concentrated suspension of formed cellular elements that includes red blood cells (RBCs) or erythrocytes, white blood cells (WBCs) or leukocytes and platelets or thrombocytes. These cellular elements are suspended in an aqueous polymer solution, the plasma, containing electrolytes and organic molecules such as metabolites, hormones, enzymes, antibodies and other proteins. Erythrocytes have been shown to exert the most significant influence on the mechanical properties of blood,
如所讨论的，全血是形成的细胞成分的浓缩悬浮液，其包括红细胞（RBC）或红细胞、白血细胞（WBCs）或白细胞和血小板或血小板。这些细胞元素悬浮在水性聚合物溶液中，血浆中含有电解质和有机分子，如代谢物、激素、酶、抗体和其他蛋白质。红细胞对血液力学性能的影响最大，主要是因为它们与其他形成的元素（大约4～6 106个RBCS/MM3）在非常高的浓度下存在，在健康个体中包含约40至45%的体积（血细胞比容，HT）。
虽然血浆几乎是牛顿的行为，全血表现出明显的非牛顿特性，特别是在低剪切速率。血液的非牛顿行为主要由三种现象来解释：红细胞在低剪切速率下形成三维微观结构的倾向，它们的变形能力，以及它们在高剪切速率下与奥氏体的取向。
如下文所述，这种3D微结构的形成和破裂，以及红细胞的伸长和恢复，有助于血液的剪切变稀、粘弹性和触变行为。红细胞聚集和变形是复杂的动态过程 其中血液的细胞和血浆成分作为重要因素。在各种条件下，特别是与物理相关的实验数据，需要开发这些复杂过程的有意义的模型。
qiacute;其 zhōng中 xuegrave;血 yegrave;液 de的 xigrave;细 bāo胞 heacute;和 xuegrave;血 jiāng浆 cheacute;ng成 fegrave;n分 zuograve;作 weacute;i为 zhograve;ng重 yagrave;o要 yīn因 sugrave;素 。 zagrave;i在 gegrave;各 zhǒng种 tiaacute;o条 jiagrave;n件 xiagrave;下 ， tegrave;特 bieacute;别 shigrave;是 yǔ与 wugrave;物 lǐ理 xiāng相 guān关 de的 shiacute;实 yagrave;n验 shugrave;数 jugrave;据 ， xū需 yagrave;o要 kāi开 fā发 zhegrave;这 xiē些 fugrave;复 zaacute;杂 guograve;过 cheacute;ng程 de的 yǒu有 yigrave;意 yigrave;义 de的 moacute;模 xiacute;ng型 （ jiagrave;n见 〔 4 6 6 , 4 6 8 〕 ） 。
In this section we briefly discuss the physical behaviour of erythrocytes that have the strongest influence on the non-Newtonian behaviour of whole flowing blood at low shear rates.
在这一节中，我们讨论了在低剪切速率下，红细胞在整个血液中的非牛顿行为具有最强的物理行为。
1.1.1低剪切速率行为：红细胞的聚集和解聚
1 . 1 . 1 dī低 jiǎn剪 qiē切 sugrave;速 lǜ率 xiacute;ng行 weacute;i为 ： hoacute;ng红 xigrave;细 bāo胞 de的 jugrave;聚 jiacute;集 heacute;和 jiě解 jugrave;聚
在存在纤维蛋白原和球蛋白（两种血浆蛋白）的情况下，红细胞具有形成棒状成堆的个体细胞的主要聚集结构的能力，称为RouLuux。在非常低的剪切速率下，RouLeAX在端到侧和侧到侧的方式对齐，形成由分支的三维聚集体构成的秒级结构。虽然触变性的定义在文献中有很大的不同，但在这里我们把触变性看作是材料性质对剪切施加时间的依赖性。这种依赖性很大程度上是由于血液三维结构所需的时间所形成和破坏。
图6.1。健康献血者红细胞聚集的三维微结构可以看到杆状杆状红细胞形成的棒状体。在RouLeAX顶部的孤立的深色圆产生于RouLux分支O O这些堆栈，形成RBC聚集体的三维微结构。这些枝条较不透明，因此较暗。大的光圆是白血细胞，而更小的光圈是血小板。M.V. Kameneva先生（美国匹兹堡大学教授）
见图6.1）。RouLux形成的生化过程尚不清楚。实验已经观察到，如果细胞硬化或不存在纤维蛋白原和球蛋白，这些堆不会形成。对于静止的血液，由RBCs形成的三维结构表现为固体状，表现为抵抗力，直到施加力的强度。所需的启动应力，例如在简单剪切中，通常被称为屈服应力，并且在正常条件下，主要是血细胞比容和血浆的纤维蛋白原浓度的函数。
附加因素，如红细胞形状、变形性和聚集倾向也取决于屈服应力参数的值。如下面所讨论的，在一般情况下，屈服应力的存在和处理屈服应力作为材料参数是一个有争议的问题。
当血液开始流动时，固体状的结构会分解成三种不同尺寸的三维网络，它们以单个单元的形式移动，达到一个平衡的剪切速率。剪切速率的增加导致平衡尺寸减小，E粘度降低。在Schmid Scho NbEin（450）的研究中，剪切速率在5.8和46 s - 1之间，剪切速率的每一倍导致平均聚集体尺寸减小约50%。
dāng当 xuegrave;血 yegrave;液 kāi开 shǐ始 liuacute;流 dograve;ng动 shiacute;时 ， gugrave;固 tǐ体 zhuagrave;ng状 de的 jieacute;结 gograve;u构 huigrave;会 fēn分 jiě解 cheacute;ng成 sān三 zhǒng种 bugrave;不 toacute;ng同 chǐ尺 cugrave;n寸 de的 sān三 weacute;i维 wǎng网 luograve;络 ， tā它 men们 yǐ以 dān单 gegrave;个 dān单 yuaacute;n元 de的 xiacute;ng形 shigrave;式 yiacute;移 dograve;ng动 ， daacute;达 dagrave;o到 yī一 gegrave;个 piacute;ng平 heacute;ng衡 de的 jiǎn剪 qiē切 sugrave;速 lǜ率 。 jiǎn剪 qiē切 sugrave;速 lǜ率 de的 zēng增 jiā加 dǎo导 zhigrave;致 piacute;ng平 heacute;ng衡 chǐ尺 cugrave;n寸 jiǎn减 xiǎo小 ， E niaacute;n粘 dugrave;度 jiagrave;ng降 dī低 。 zagrave;i在 S c h m i d S c h o N b E i n （ 4 5 0 ） de的 yaacute;n研 jiū究 zhōng中 ， jiǎn剪 qiē切 sugrave;速 lǜ率 zagrave;i在 5 . 8 heacute;和 4 6 s - 1 zhī之 jiān间 ， jiǎn剪 qiē切 sugrave;速 lǜ率 de的 měi每 yī一 begrave;i倍 dǎo导 zhigrave;致 piacute;ng平 jūn均 jugrave;聚 jiacute;集 tǐ体 chǐ尺 cugrave;n寸 jiǎn减 xiǎo小 yuē约 5 0 % 。
Once the chains are broken down to 4–10 cells, they are resistant to further shearing and, at high shear rates they roll, rotate and tumble as units along with individual cells. A critical shear rate gamma;˙max is defined as a constant shear rate at which, effectively there are no more aggregates (larger than 15 m). In
一旦链被分解成4至10个细胞，它们就抵抗进一步剪切，并且在高剪切速率下，它们滚动、旋转和翻滚，作为单元与单个细胞一起。临界剪切速率alpha;max被认为是一个恒定的剪切速率，在这里，E不再有更多的聚集体（大于15mu;m）。在健康人的全血，临界值的临界值，主要在5—100 s - 1范围内。DTENFASS〔127〕将所报告的值的变化归因于原始样品的聚集度，如下文所讨论的，与触变性一致。 血液的性质。在疾病状态下，临界剪切速率可显著增加。例如，在急性心肌梗死患者的血液样本中，弥散的临界剪切速率被发现大于约250 s - 1，并且平均骨料粒径大于所有剪切速率的对照。
在增加剪切作用下的解聚过程是可逆的。当剪切速率准静态地下降到较低的值时，内生细胞形成较短的链，然后更长的RouLoux，最终形成3-D微观结构〔200〕。达到平衡的结构所必需的时间（在聚集和解聚过程中）都是血液在低剪切速率下的触变行为的原因。相关的时间常数是剪切速率的函数。发现在较高的剪切速率下，平衡更迅速地达到，并且在较低的剪切速率下逐渐趋于平衡。 例如，在锥板粘度计中，在0.01和1 s～1之间的剪切速率，发现在20～200秒的时间间隔之后达到平衡分布。
加速流对AGGE-GATE门的结构有显著的影响。在剪切速率之间的加速下，发生了RouLux的伸长率，当保持在剪切剪切速率时，这一现象是不可见的。伸长在RouLeAx中特别明显，桥大较大的二级结构，并且发现是由单个细胞的重新排列（从平行堆叠到剪切叠堆的细胞滑动）和单个细胞的变形（椭球变形和最终Pro）引起的。后期变形）。作为这些机制的结果，骨料长度可以增加到三倍[450 ]。在剪切的正弦变化下，观察到AGGRE门的弹性行为〔102, 449, 517〕。虽然从准静态剪切实验获得全血粘度的典型数据，小振幅振荡剪切实验被用来测量粘性和弹性性质的制度的小变形从其余的历史。
1.1.2全血高剪切速率行为：分散红细胞的剪切力
在Couette rheometer中，当血液经受恒定的剪切速率略高于alpha;max时，细胞可以旋转。随着剪切速率的增加，它们的旋转速度变小，剪切速率超过230 s～1时，它们停止旋转并保持与方向的对齐（450）。
当剪切速率超过400 s～1时，红细胞失去双凹形，变为完全伸长，并在伸长的椭球上转变为平行于方向的长轴。在这个阶段，只有红细胞的碰撞。当一个更快速移动的细胞接触较慢的细胞时，会出现细胞之间没有进一步的相互作用。密切观察表明，变化的细胞轮廓是一致的坦克踏板运动的细胞膜的内部，类似于一个UID滴变形。红细胞的高变形性是由于细胞核的缺乏、其膜的弹性和粘性性质以及几何形状、体积和膜表面积等几何因素引起的。
xigrave;细 bāo胞 zhī之 jiān间 meacute;i没 yǒu有 jigrave;n进 yī一 bugrave;步 de的 xiāng相 hugrave;互 zuograve;作 yograve;ng用 。 migrave;密 qiegrave;切 guān观 chaacute;察 biǎo表 miacute;ng明 ， biagrave;n变 huagrave;化 de的 xigrave;细 bāo胞 luacute;n轮 kuograve;廓 shigrave;是 yī一 zhigrave;致 de的 tǎn坦 kegrave;克 tagrave;踏 bǎn板 yugrave;n运 dograve;ng动 de的 xigrave;细 bāo胞 moacute;膜 de的 negrave;i内 bugrave;部 ， legrave;i类 sigrave;似 yuacute;于 yī一 gegrave;个 U I D dī滴 biagrave;n变 xiacute;ng形 ， [ 8 3 , 1 5 4 , 4 4 9 ] 。 hoacute;ng红 xigrave;细 bāo胞 de的 gāo高 biagrave;n变 xiacute;ng形 xigrave;ng性 shigrave;是 yoacute;u由 yuacute;于 xigrave;细 bāo胞 heacute;核 de的 quē缺 faacute;乏 、 qiacute;其 moacute;膜 de的 taacute;n弹 xigrave;ng性 heacute;和 niaacute;n粘 xigrave;ng性 xigrave;ng性 zhigrave;质 yǐ以 jiacute;及 jǐ几 heacute;何 xiacute;ng形 zhuagrave;ng状 、 tǐ体 jī积 heacute;和 moacute;膜 biǎo表 miagrave;n面 jigrave;积 děng等 jǐ几 heacute;何 yīn因 sugrave;素 yǐn引 qǐ起 de的 。 6.1.3Further comments on the role of erythrocyte deformability
1.1.3关于红细胞变形能力作用的进一步评述
1 . 1 . 3 guān关 yuacute;于 hoacute;ng红 xigrave;细 bāo胞 biagrave;n变 xiacute;ng形 neacute;ng能 ligrave;力 zuograve;作 yograve;ng用 de的 jigrave;n进 yī一 bugrave;步 piacute;ng评 shugrave;述
It has been shown experimentally that at a haematocrit above 30
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