Ebook: Handbook of Hemorheology and Hemodynamics
This publication primarily focuses on the macro- and micro-rheological behavior of blood and its formed elements, on interactions between the formed elements and blood vessel walls, and on the microvascular aspects of hemodynamics. Since many aspects of hemorheology and hemodynamics are affected by disease or clinical states, these effects are discussed as are hyperviscosity syndromes, therapy for disturbed blood rheology, and methods in hemorheology and hemodynamics. Sections of the Handbook include History of Hemorheology; Hemorheology, covering basic aspects, blood composition, blood rheology, cell mechanics, pathophysiology, methods and comparative studies; Hemodynamics, covering basic principles, microcirculation, in vivo effects, endothelium and methods; and Clinical Aspects of Hemorheology, covering hyperviscosity, clinical significance and treatment. The goal is to foster greater interchange between workers in the fields so as to promote collaborative efforts and, hopefully, improved health. In selecting topics for this handbook the editors have attempted to provide a general overview of both basic science and clinical hemorheology and hemodynamics. Hemorheology and hemodynamics are closely related, the former dealing with all aspects of the flow and interactions of the individual blood cells mostly studied in vitro, the latter with the in vivo relationships among vessel architecture, driving pressure, flow rate and shear stress. The linkage between the in vitro and in vivo research described in the book will be of interest to both basic science and clinical investigators. The editors of the handbook have each been active in the fields of bio- and hemorheology for many years, and have published extensively. They have successfully achieved their objective to publish a well-written and well-edited handbook that will be valuable for researchers and students in the field.
The appearance of this Handbook is a timely event, as it is 20 years since the publication of the “Handbook of Bioengineering”  that dealt mainly with basic aspects of hemodynamics and hemorheology. Also, in the 1980s and 1990s a number of books were published that focused on clinical aspects of blood rheology [2–5]. In selecting topics for the present handbook the editors have attempted to provide a general overview of both basic science and clinical hemorheology and hemodynamics. Hemorheology and hemodynamics are closely related, the former dealing with all aspects of the flow and interactions of the individual blood cells mostly studied in vitro, the latter with the in vivo relationships among vessel architecture, driving pressure, flow rate and shear stress. The linkage between the in vitro and in vivo research described in the book will be of interest to both basic science and clinical investigators.
With respect to hemorheology, the new book successfully updates developments and advances in the flow properties of human blood cells (microrheology). Furthermore, in the chapters on cell mechanics, these flow properties are related to events occurring at the level of the bonds between the interacting corpuscles (platelets and white cells as well as red cells), and between the corpuscles and the vessel wall (molecular rheology). A welcome feature of the handbook is that it includes a chapter on comparative hemorheology, showing that the rheological properties of red cells vary widely among the animal species, thus shedding light on the process of adaptation to a specific environment or lifestyle, and a chapter on neonatal and fetal blood rheology showing the considerable adaptation processes in play at birth and in infancy and childhood. Also dealt with in some depth are the effects of diseases on the mechanical and adhesive properties of red cells and the underlying molecular mechanisms, particularly those found in malaria. A related subject, the damage sustained by red cells due to flow-induced mechanical trauma, is also presented.
With respect to hemodynamics, it is evident in the chapters of section III of the handbook that the field has advanced significantly in the last 30 years, particularly with respect to our understanding of microcirculatory blood flow using novel experimental techniques, the latter being the subject of a separate chapter.
The handbook closes with chapters on clinical states associated with abnormal blood rheology, including a chapter on the yet controversial subject of rheological therapy.
The editors of the handbook have each been active in the fields of bio- and hemorheology for many years, and have published extensively. They have successfully achieved their objective to publish a well-written and well-edited handbook that will be valuable for researchers and students in the field.
Shu Chien, MD, PhD
Harry L. Goldsmith, PhD
 R. Skalak and S. Chien, Eds., Handbook of Bioengineering, McGraw-Hill, New York, 1987.
 S. Chien, J. Dormandy, E. Ernst and A. Matrai, Eds., Clinical Hemorheology, Martinus Nijhoff Publ., Dordrecht, 1987.
 G.D.O. Lowe, Ed. Clinical Blood Rheology, CRC Press, Boca Raton, FL, 1988.
 A.M. Ehrly, Therapeutic Hemorheology, Springer-Verlag, New York, 1991.
 J.F. Stoltz, M. Singh and P. Riha, Hemorheology in Practice, IOS Press, Amsterdam, 1999.
If the rate of appearance of publications in the field can be taken as a criterion, hemorheology can be considered as coming of age in the fairly recent past - perhaps forty or so years ago. This relative lateness is due largely to the previous lack of measuring equipment with the required sophistication; a particular problem being the complex nature of blood viscosity and the need for adequate viscometers capable of measuring it. Nevertheless the ease of availability of blood, its dramatic color and its obvious connection to well being have made it a subject of study since ancient times. What is more, many of those ancient studies were of physical properties of blood that have direct hemorheological relevance. So it could be said that hemorheology is one of the oldest of clinical research areas.
In analyzing blood flows, one is generally interested in how the blood responds to forces (e.g., pressure gradients, shear stresses). The general fluid mechanical procedure used to predict how a fluid flows in response to forces involves three steps:
(1) Consideration of all the forces being exerted on an infinitesimally small volume of fluid. This is done by use of the physical principle known as the conservation of momentum, and results in equations which relate the forces to velocity gradients.
(2) Introduction of rheological (“constitutive”) equations which are specific to the fluid being analyzed. These equations indicate how the fluid responds to forces, and relate the forces to the resulting velocity gradients. The rheological equations contain fluid specific characteristics (e.g., apparent viscosity as a function of shear rate).
(3) Substitution of the rheological equations into the conservation of momentum equations, and integration of the resultant differential equations to obtain macroscopic relationships, such as between flow rates and pressure gradients.
In this chapter, this procedure will be illustrated for specific applications to blood.
The function of blood is to feed all the tissues of the body with vital materials and to remove waste. To do this in the human adult it has to traverse the complicated vascular network, which varies in diameter from some 3 cm down to about 5 μm. Furthermore, the blood must circulate above a limiting rate if it is to do its work effectively enough to keep the organism healthy. This rate of circulation is determined by the driving pressure generated by the heart, by the geometrical resistance offered by the vasculature and by the flow properties of the blood. These flow properties are the concern of the hemorheologist and they are dependent on the composition of the blood and the properties of its constituents; hence, knowledge of them is vital to any understanding of hemorheology. This chapter gives an overview of the composition of normal adult human blood and some indication of the ways in which it can be altered in diseased states. There is also discussion of the normal changes in blood composition that take place as the fetus develops through to the neonatal period. Finally, there is a brief review of the variations that occur in other mammals, emphasizing the similarities and the great differences that exist compared with the human adult.
In order to quantitatively understand the conditions of blood flow through various in vitro and in vivo geometries, the flow properties of blood must be experimentally determined. In this chapter, we initially consider the rheological behavior of blood under conditions where the blood is treated as a homogenous fluid and thus where the formed elements (e.g., red blood cells, white blood cells) are tacitly ignored. This approach is then modified in order to consider flows where the blood cell characteristic dimensions approach those of the geometries in which the flow takes place. The former approach yields the macro-rheological properties of blood while the latter yields micro-rheological characteristics; in general, data obtained in geometries of 200 μm or less are considered micro-rheological. It is of interest to note that the study of blood rheology dates, at least, to the work of Poiseuille who attempted to derive an equation for blood flow in tubes. However, due to experimental difficulties associated with blood coagulation he was unsuccessful with these attempts, and thereafter turned to simpler fluids such as water and oil to develop his well-known equation .
Time-Varying Flow of Blood in Vivo
The most obvious feature of the circulation is the pulse. Pulsatile flow can be analyzed as containing steady plus harmonic components. The heartbeat of 60-120 beats per minute gives a fundamental Fourier component of 1 to 2 Hz. Because the flow is time varying, pressure-flow relations are a function of both the shear viscosity and the shear elasticity of the blood. The viscoelasticity of blood has a direct effect on the propagation of the pulse throughout the arterial system . Blood flow in vivo covers a wide range of shear rates and varied vascular geometry (smooth wall of uniform diameter, tapered vessels, bifurcations, side branches, stenoses).
Red Cell Concentration and Deformation
Normal human blood contains a high concentration of red blood cells (RBC), which are elastic elements. The maximum theoretical volume concentration of red cells without squeezing and deforming is 58%. Because normal cell concentration is in the range from 30 to 60%, flow cannot occur through the varied geometry of the circulation without elastic cell deformation and orientation and hence storage of elastic energy in the cells.
Blood flows only because the RBC are deformable and can be reoriented to slide on the low viscosity plasma. The elastic deformability of cells means that energy can be stored in and recovered from cell deformation. The elastic energy is measurable when flow changes with time. Oscillatory flow is particularly useful for measuring this energy and characterizing viscoelastic properties of blood.
For red blood cells (RBC) to survive in the harsh hemodynamic environment of the circulation in vivo, they must remain non-adhesive and maintain a set of unique stability. In healthy humans, RBC survive for about 120 days in the circulation, whereas in certain pathological conditions where membrane stability, cellular deformability or adhesiveness are compromised, the lifespan of the RBC can be dramatically reduced or its function severely compromised, often with severe clinical manifestations. Of a number of disorders affecting the mechanical and adhesive properties of human RBC, homozygous sickle cell disease and malaria are arguably the most important and certainly, in the case of malaria, the most studied. In this chapter, we review the structure-function relationships that determine the mechanical and adhesive properties of RBC and describe some techniques and methods, old and new, for quantifying these important rheological properties. In particular, we concentrate on RBC infected with malaria parasites as a specific example of how recent research on this human pathogen has not only advanced our knowledge of this important human disease and opened up new possible avenues for therapy, but has also increased our understanding of RBC structure-function relationships at the molecular level and the mechanisms that regulate and maintain their unique rheological properties.
The reversible aggregation of human red blood cells (RBC) continues to be of interest in the field of hemorheology [1-12], in that RBC aggregation is a major determinant of the in vitro rheological properties of blood. In addition, the in vivo flow dynamics and flow resistance of blood are influenced by RBC aggregation . Measures of RBC aggregation, such as the erythrocyte sedimentation rate (ESR), are commonly used as diagnostic tests and as one index to the efficacy of therapy (e.g., following drug therapy in rheumatoid arthritis); in diabetes mellitus RBC aggregation is normalized by improved glycemic control  There is now general agreement regarding the correlations between elevated levels of fibrinogen or other large plasma proteins and enhanced RBC aggregation, and the effects of molecular mass and concentration for neutral polymers such as dextran . However, the specific mechanisms involved in RBC aggregation have not yet been elucidated, and thus it is not yet possible to fully understand the relations between pathology and altered RBC aggregation.
RBC form multi-cell linear or branched aggregates in vitro when they are suspended in either plasma or solutions containing large polymers (e.g., dextran ≥ 40 kDa); the linear forms are often termed rouleaux since they resemble a stack of coins. In vivo RBC aggregation occurs at low shear forces or stasis and is a major determinant of low shear blood viscosity and thus in vivo flow dynamics . It is important to note that RBC aggregation is a reversible process, with aggregates dispersed by mechanical or fluid flow forces, and then reforming when the forces are removed. Conversely, RBC agglutination and blood coagulation are irreversible processes due to either protein polymerization or strong antigen-antibody attractive forces. Abnormal increases of RBC aggregation have been observed in several diseases associated with vascular disorders (e.g., diabetes mellitus or hypertension). RBC aggregation is primarily determined by RBC aggregability (i.e., the intrinsic cell characteristics affecting RBC aggregation) and by the concentration of the inducing macromolecule or the plasma level of large proteins . In blood, fibrinogen is one of the most important determinants of blood viscosity due to its strong tendency to increase both plasma viscosity and RBC aggregation . In the past, most reports dealt primarily with the ability of plasma proteins to promote aggregation; for example higher fibrinogen levels have been linked to elevated blood viscosities in hypertensive patients .
At present, there are two co-existing models for RBC aggregation: bridging and depletion. In the bridging model, red cell aggregation is proposed to occur when the bridging forces due to the adsorption of macromolecules onto adjacent cell surfaces exceed disaggregating forces due to electrostatic repulsion, membrane strain and mechanical shearing [15, 19-23]. This model seems to be similar to other cell interactions like agglutination, with the only difference being that the proposed adsorption energy of the macromolecules is much smaller in order to be consistent with the relative weakness of these forces. In contrast, the depletion model proposes quite the opposite. In this model RBC aggregation occurs as a result of a lower localized protein or polymer concentration near the cell surface compared to the suspending medium (i.e., relative depletion near the cell surface). This exclusion of macromolecules near the cell surface leads to an osmotic gradient and thus depletion interaction . As with the bridging model, disaggregation forces are electrostatic repulsion, membrane strain and mechanical shearing. Several previous reports have dealt with the experimental and theoretical aspects of depletion aggregation, often termed depletion flocculation, as applied to the general field of colloid chemistry [25-28]. However, polymer depletion as a mechanism for red blood cell aggregation has received much less attention, with only a few literature reports relevant to this approach [24, 29-33].
Leukocytes circulate in small numbers compared to red cells and have little effect on bulk blood viscosity except in some leukemias where the ‘leukocrit’ approaches hematocrit. Their main functions are carried out in tissue, and they have evolved specialized adhesive and migratory capabilities to allow recruitment from the blood across vascular endothelium. However, although the cardiovascular system essentially acts as a dispersal system for leukocytes, this does not mean that their mechanical properties are unimportant, or that they cannot influence blood flow. Their slow motion through blood capillaries was recognized early and modern interest in their rheological behavior was spurred by the observations of deformation in human microvessels and glass capillaries made by Bagge, Branemark, Skalak and colleagues [1-3]. It has become evident that these ‘normal’ slow flowing leukocytes can hold up and modify the capillary transit of red cells and influence perfusion and resistance in the microcirculation [4-6]. If perfusion pressures are reduced (e.g., in shock) this slow transit may be reduced to leukostasis . In addition, leukocytes, and especially the most numerous neutrophilic granulocytes, can dramatically change their mechanical properties when ‘activated’ by a variety of agents . Activation at the vessel wall is a necessary part of their physiological migratory response, but if it occurs inappropriately, circulating cells have the potential to cause pathogenic microvascular occlusion .
Because of the importance of the mechanical properties of resting and activated leukocytes in the physiology and pathology of the microcirculation, they have been widely studied using rheological techniques. Here we review the theoretical and experimental analyses of leukocyte deformation, and the structural elements that influence the cellular rheology. Physico-chemical factors that influence leukocyte deformation are then described, and the impact of flow resistance on normal and pathological microcirculation is considered.
Circulating leukocytes and platelets must adhere to the wall of blood vessels in order to carry out the protective function of immunity for leukocytes and hemostasis for platelets: failure or lack of control in recruitment can be pathogenic. Given the importance of these adhesive processes, it is not surprising that they have been widely studied both in vivo using intravital microscopy and in vitro using flow-based models. It has become increasingly recognized that adhesion is constrained by the local hemodynamic environment and modulated by the rheological properties of the blood. The rate of motion of the cells before capture and the shear forces acting on them during adhesion critically control the efficiency of attachment. The rheology of the blood influences these hemodynamic parameters. It also affects the efficiency with which cells are brought into contact with the wall because margination in the flow depends on the concentration of the red cells and their flow-dependent tendency to aggregate . Thus, physiological and pathological mechanisms of leukocyte and platelet adhesion represent important rheological phenomena requiring understanding at the biomechanical as well as molecular-biological levels.
Flow-based studies have revealed that in each case, leukocytes and platelets use a multi-step process to achieve controlled recruitment [2, 3]. Broadly, specialized receptors support capture of fast-moving cells, separate receptors support stable attachment, and activating signals are required for transition between the states. The actual substrates and receptors differ; leukocytes usually adhere to intact endothelium while platelets typically adhere to sub-endothelial matrix exposed in damaged vessels. In the case of leukocytes, attachment is followed by migration through the endothelium, while platelets undergo spreading and an aggregation phase, and act as a surface for coagulation and fibrin deposition. Leukocyte adhesion is mainly restricted to post capillary venules where shear rates and stresses are relatively low. However, platelet adhesion is possible in all vessels in order to inhibit blood loss, and can occur in arteries at much higher shear rates and stresses. Clearly, there are interesting parallels but important distinctions between the behaviors of the two cell types.
Here we review basic concepts of dynamic cellular adhesion and experimental approaches to their investigation that are largely common between the platelets and leukocytes. The specific mechanisms underlying adhesion in the vascular system are then described for the different cells, and the major physico-chemical modulators of adhesion are outlined. Finally, ways in which abnormal adhesive responses can contribute to pathology are considered with particular attention to how these might influence blood circulation.
The factors that determine the rheological behavior of blood, a two-phase fluid, include the relative volume of each phase as reflected by the hematocrit value, plasma composition and the properties of cellular elements. The contribution of these factors to blood rheology has been detailed in previous chapters (Chapters II.2 and II.3.a). Thus it is not surprising that the mechanisms of blood rheology alterations are also related to these factors.
In a classification published by P.F. Leblond in an early, 1987 textbook of hemorheology, hyperviscosity syndromes were discussed from a pathophysiological point of view : a) Polycythemic disorders to include erythrocytosis and leukocytosis. b) Sclerocythemic disorders to include conditions with impaired red blood cell (RBC) deformability. c) Plasmatic disorders to include alterations in plasma viscosity and red cell aggregation. Similar approaches have been used by others . J-F. Stoltz classified hyperviscosity syndromes into five groups : a) Increase in number of blood cells; b) Altered plasma protein levels; c) Increased RBC internal rigidity; d) Changes in RBC viscoelastic properties; e) Enhanced RBC aggregation.
These classifications, based on the mechanisms of hemorheological alterations, need to be revised in light of developments in the past twenty years. There has been a significant change in our understanding of the factors that determine the degree of RBC aggregation: in addition to plasma factors and local shear forces, RBC properties are now well established as an additional factor affecting the intensity of aggregation. Thus, enhanced RBC aggregation may not always be related to plasma composition changes, but can co-exist with plasma viscosity alterations. RBC properties therefore influence both cell deformability and aggregation.
Table 1 presents a classification of hemorheological alterations based upon the considerations described above.
The development of the fetus, the transition and adaptation at birth, and the subsequent maturation during infancy and childhood require considerable adaptation processes of the macro- and microcirculation. The fetus lives in a severely hypoxic atmosphere with an oxygen saturation of 65 to 70% in blood flowing to vital organs such as the brain. This borderline oxygen supply makes the fetus extremely vulnerable to hypoxicischemic events. At birth, the cardiovascular system undergoes eminent changes such as the sudden interruption of placental blood flow and the redistribution of cardiac output to the pulmonary arteries. Moreover, the neonate is at high risk to acquire disorders with strong impact on blood circulation (e.g., septicemia). The circulation continues to show marked changes with growth and further organ differentiation during infancy and childhood.
Peculiar rheologic properties of blood appear to play an important role in the maintenance of high blood flow conditions in spite of very low blood pressure in the fetus and neonate . On the other hand, sudden changes of rheologic properties may develop in the perinatal period with marked effects on circulation such as polycythemia resulting from placental transfusion .
This overview is designed to describe the physiology and pathophysiology of hemorheological parameters during the fetal and neonatal period. In addition, some information on developmental hemorheology during infancy and childhood will also be presented.
Prosthetic heart valves, heart-assist devices, oxygenators, dialyzers and other biomedical devices that repair, replace or support various organ systems of the human body are in wide clinical use. These devices are responsible for saving, extending, and enhancing the lives of patients with otherwise hopeless medical conditions. The safety and efficacy of these blood-contacting biomedical devices strongly depends on the extent to which they damage blood. Unfortunately, in many cases these devices cause dangerous complications triggered by non-physiological factors within the blood flow.
The precise mechanisms of blood damage in blood-contacting devices are heterogeneous and are not well understood in spite of numerous investigations of blood trauma conducted over several decades by investigators worldwide. This body of research has revealed that blood trauma is related to non-physiological flow conditions such as elevated shear forces, turbulence, cavitation, prolonged contact and collision between blood cells and foreign surfaces. These factors may induce a variety of damage mechanisms: overstretching or fragmentation of a subpopulation of erythrocytes causing free hemoglobin to be released into plasma (i.e., hemolysis); activation or dysfunction of platelets and leukocytes; increased concentrations of inflammatory mediators; complement activation; and sub-lethal blood trauma such as alterations in mechanical properties of erythrocytes as manifested by an increase in RBC aggregation and decrease in their deformability (see Figure 1). This latter sublethal RBC mechanical damage causes a shortening of RBC life span, a decrease in density of functioning capillaries and area of contact surface of RBC with capillary walls, and may lead to anemia, tissue hypoxia and other complications. Even moderate hemolysis, which is not an immediate threat to renal function, is an important warning sign of other potential blood cell damage such as platelet activation, white blood cell (WBC) dysfunction, and other serious complications such as scavenging of nitric oxide , damage to glycocalyx and endothelial cells, and impairment of the vascular smooth muscle tone . Although damage to platelets and WBC is an extremely important topic, this chapter concentrates on the mechanical trauma to RBC and related changes in rheological properties of whole blood. In summary, in vitro experimental studies and clinical experience with artificial organs presented in this chapter substantiate the assertion that mechanical stress substantially impairs the mechanical properties of RBC and adversely affects whole blood rheology, and that this impairment may contribute to various medical complications in dialysis, prosthetic heart valve and circulation-assist device recipients.
In most of the world, the term “blood transfusion” usually means the infusion of stored red blood cell (RBC) concentrates, often termed “packed cells”, into the circulatory system. Such transfusions are given in response to severe anemia, significant blood loss, or as therapy (e.g., sickle cell disease). While intended to be beneficial, infusion of stored RBC can impact blood rheology in both large vessels and the levels, but additional factors related to storage are also involved. Thus, understanding the practice and problems of transfusion medicine is a necessary prerequisite for exploring hemorheological changes that occur subsequent to the transfusion of stored cells.
In 1678, ages before there was any concept of blood viscosity, it was appreciated by Anthony van Leeuwenhoek (Delft, the Netherlands) that red blood cells (RBC) have to deform in order to negotiate capillary passages . Using his home-made microscopes he also noticed the phenomenon of reversible red cell aggregation in relation to slow and stagnant in vivo blood flow . Van Leeuwenhoek was far ahead of his contemporary scientists, and although the existence and importance of blood circulation was recognized 175 years later (i.e., around 1850 by Harvey and Virchof), studies of the flow behavior of blood, hemorheology, were neglected for at least another 80 years. In 1931, Fåhraeus and Lindqvist published their classic study entitled “The Viscosity of Blood in Narrow Capillary Tubes”  that re-awakened scientific interest in hemorheology. However, until fairly recently, progress in this branch of science has been relatively slow, primarily due to the absence of reliable hemorheological laboratory instruments.
Because of the non-Newtonian flow behavior of whole blood, viscosity measurements were initially limited to studies of plasma and serum. In fact, the clinical condition known as “Hyperviscosity Syndrome” was originally defined solely by high plasma viscosity. However, special instruments developed in the last few decades and dedicated to the measurement of various hemorheological parameters (e.g., whole blood viscosity, RBC aggregation, RBC deformability) greatly improve our measurement abilities and thus are a welcome addition to the early plasma viscometers.
In this chapter no comprehensive treatment of all described methods and techniques has been attempted. Rather, instead of listing all home-made techniques and instruments that have appeared in the literature and sometimes used only once by a single group, a survey of generally accepted methods and/or techniques as well as some recent developments are presented. Relevant website addresses are provided in the hope that these will be updated regularly by the manufacturers and vendors. However, in order to increase the direct practical value of this chapter, more detailed descriptions of relevant, commercially available instruments are given. Comparative studies of these methods and/or instruments are briefly discussed. Note that the latest version of the “Guidelines for Measurement of Blood Viscosity and Erythrocyte Deformability”  dates back to 1986 and a more recent version, comparing the newer techniques and instruments and giving generally agreed upon recommendations, is urgently needed. Finally, some general practical hemorheological laboratory techniques are described.
Hemorheological values vary widely among the animal species. To understand the structure-function relationships of red blood cells (RBC) together with associated physiological mechanisms, comparative studies are still a classical approach. Some animal species show extraordinary values of blood viscosity and RBC indices which would be pathologic for man. These differences can reflect an adaptation process to a specific environment or way of life. Different species also use different mechanisms to maintain blood flow, and in some cases these differences might indicate which variables limit the demand for oxygen delivery in a species or under certain circumstances. Nevertheless, when comparing values to man, it should be kept in mind that every hemorheologic “disturbance” in a healthy animal reflects a physiologic circumstance. It is necessary to know that the hemorheological profile of an animal cannot be judged by a single rheological value, but must be considered as part of the cardiovascular system in which the blood is flowing. That is, the hemorheological profile of an animal species is a conglomerate of properties which has to be considered in evaluating its cardiovascular relevance in a species-specific manner. These speciesspecific differences look chaotic at first sight, and no clear guiding principle has been found to combine these profiles to a universal “logic” at present. Therefore changes in parameters during disease, after interventions, or during environmental or associated changes need to be related to their species-specific reference values; describing an animal's clinical or physiological condition using comparisons to values from other species is most likely not a valid approach.
The circulatory system consists of a pump (the heart) and an extensive, highly branching system of tubes (blood vessels) containing a fluid (blood) with specialized capabilities for the transport of oxygen, nutrients, many other substances and heat. The rates of blood flow through the blood vessels depend on many physical factors, including the diameters, lengths and other geometric features of the vessels, their mechanical properties, the structures of networks that they form, the pressure generated by the heart to drive the flow, and the rheological properties of the blood. All of these factors are themselves subject to variation according to a number of short-term and long-term biological control mechanisms. In order to understand this system, it is helpful to start by considering the mechanics of fluid flow through a single tube with a uniform cylindrical cross-section. Under appropriate conditions, the relationship between driving pressure and flow rate can be described by the equation generally known as Poiseuille's law. In this chapter, a derivation of this equation is presented, and its restrictions and limitations are discussed. This provides a basis for consideration of a range of more complex fluid dynamical phenomena occurring in the circulatory system. More detailed discussions of many of the topics mentioned here can be found in the several books [1-5].
To elucidate the basis for the drop in pressure from large artery to vein, Jean Léonard Marie Poiseuille (1797-1869) undertook a series of seminal studies that defined the laws of fluid flow in tubes of uniform cross-section and that identified the microcirculation as the major site of the resistance to flow [1, 2]. While best known for his meticulous experimental studies of viscous flow in glass tubes , he also made numerous observations in the mesentery of the frog and other microvascular preparations; these observations served to highlight the dynamics of red cell distribution, the presence of the annular plasma layer and the “skimming” of plasma by capillaries, and the adhesion of white cells to the endothelium of post-capillary venules . Yet it wasn't until almost a century later that physiologists began to methodically explore the resistance to flow within the microcirculation proper using techniques of intravital microscopy. Landis  pioneered many quantitative methods for describing microvascular structure and function. Using finely drawn pipettes inserted into microvessels of frog mesentery, and calculating the velocity of bolus infusions of dyes through successive microvascular divisions, Landis attempted to calculate the resistance to flow within the capillary network and concluded that Poiseulle's law cannot be applied to the flow of blood through the capillary network except in a very limited sense. However, with the advent of sophisticated instruments for measurement of capillary pressure [5, 6] and red blood cell velocity , relatively precise quantitative measurements of pressure drops  and flow rates [9, 10] could be obtained; such measurements thus provided direct in situ flow resistance data for the hierarchy of microvessels from arteriole to venule .
As shown in Figure 1, measurements of pressure drops and flows in single unbranched microvessels  reveal that over the broad range of diameters (D) within the microcirculation proper, Poiseuille's fourth power relationship (i.e., resistance varies inversely with D4) far overshadows other determinants of resistance in the normal flow state. The significance of this relationship cannot be understated in light of the fact that control and regulation of microvascular blood flow is manifest by the ability of the vascular system to alter resistance in response to vasomotor adjustments. However, striking departures from Poiseuille's relationship may dictate the outcome of pathological flow states, with some examples including the low flow state, inflammation, and blood cell disorders. While the resistance to flow spans nearly five decades as blood courses its way from arteriole to venule, the large scatter in the experimental data may reflect significant departures from the flow of a Newtonian fluid through a smooth walled tube of circular cross-section. The effects of irregularities in geometry, broad variations in microvessel hematocrit and shear rates, blood cell deformability, red cell aggregation and blood cell adhesion to the endothelium are reviewed in the following.
Relations describing fluid flow in cylindrical tubes were formulated by Poiseuille approximately 150 years ago, resulting in the well-known Poiseuille Equation. The experiments underlying this formulation were conducted using simple fluids and the viscosity concept was introduced in the equation as a constant, being directly proportional to flow resistance. This was an oversimplification for blood flow and experimental work in the early 1900's revealed that blood viscosity could not be represented with a constant, but rather depended on flow conditions (i.e., tube diameter, flow rate). Blood viscosity expressed as apparent viscosity (i.e., the empirical ratio of the volumes of water and blood which would flow in a given time under the same specified conditions) was reported to take values between 5-100, depending on the velocity of flow and diameter of the tube . This early understanding of blood rheology that dominated the first several decades of 20th century was clearly described in the famous publication of Whittaker and Winton .
This publication is not primarily famous for this description of the shear rate dependence of blood viscosity, but rather because it pointed out that measurements of blood viscosity in cylindrical tubes could not be used to predict its effects on in vivo blood flow . Whittaker and Winton compared the apparent viscosity of blood under a constant pressure difference as determined by simultaneously measuring flow through a dog hind limb preparation and a glass viscometer arranged in parallel. The results clearly indicated that the apparent viscosity of blood determined using the flow rate through the hind limb was lower than the value obtained using the glass viscometer (Figure 1). The differences between apparent viscosity values measured in vivo and ex vivo were more prominent at higher hematocrit values .
This approach for calculating apparent viscosity using pressure drop and flow rate data measured in vivo has been used by other investigators under various conditions and in different experimental settings [2, 3]. These investigations were usually done using isolated organs  or specially designed arterio-venous shunts to allow the measurements of pressure and flow through a calibrated tube . Additionally, the role of hemorheological parameters in determining pressure-flow relationship in various organs [4-8] or under various pathophysiological conditions  have been investigated.
Vascular endothelium is a monocellular layer positioned between the muscular media, or the adventitia in capillaries, and the circulating blood . While it has long been recognized that this tissue acts as a selective sieve to facilitate bi-directional passage of macromolecules and blood gases between tissues and blood, the strategic importance of the endothelium in regulating vascular homeostasis, as well as its protective role, have been more recently described. The critical location of this tissue allows it to sense changes in hemodynamic forces and blood-borne signals. In turn, these stimuli trigger a response that is mediated by the release of a number of autocrine and paracrine substances. For example, myogenic or adrenergic tone are endothelium-independent, yet vascular homeostasis is controlled by a balanced release of endothelium-derived bioactive factors. The loss of the structural and/or functional integrity of the endothelium (i.e. endothelial dysfunction) disrupts this balance, thereby predisposing the vessel wall to vasoconstriction, leukocyte adhesion, platelet activation, mitogenesis, peroxidation, thrombosis, impaired coagulation, vascular inflammation, and ultimately, atherogenesis  (Figure 1). The following paragraphs describe how hemorheology interferes with the production of endothelial autacoids, how the endothelium functions, and how it influences vascular flow and hemorheology.
Over the last 30 years significant progress has been made in the fields of hemodynamics and hemorheology, spurred on by innovative developments in measurement techniques  and instrumentation [2-3]. Measurements obtained via these methods have been used for monitoring hemodynamic phenomena and diagnosing circulatory disorders, thus providing a deeper understanding of hemodynamic-related diseases in humans .
Understanding of hemodynamics was greatly enhanced by Poiseuille (1799-1869), who developed a relation between flow rate and pressure (Poiseuille's law). The most frequently measured parameters in hemodynamics are blood flow rate and blood pressure, and thus one can calculate resistance to flow as the ratio of pressure to flow. Of course, this resistance concept is a “black box” approach in which all of the parameters that affect resistance are lumped together. For in vitro studies of flow in single tubes or networks, it is rather straightforward to define and measure such parameters (e.g., diameter, viscosity, length) and to understand their interrelations. Conversely, it is difficult to measure the in-vivo hemodynamic parameters. Recently, however, developments in optics and electronics have resulted in various techniques for measuring these hemodynamic parameters, with some techniques commercially available. The objective of this chapter is to introduce the principles and application of conventional and new techniques for laboratory and clinical measurements of hemodynamic parameters.