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Microcirculation, 12: 515, 2005Copyright c 2005 Taylor & Francis Inc.ISSN: 1073-9688 print / 1549-8719 onlineDOI: 10.1080/10739680590894966

Microvascular Rheology and HemodynamicsHERBERT H. LIPOWSKY

Department of Bioengineering, The Pennsylvania State University, University Park,Pennsylvania, USA

ABSTRACT

The goal of elucidating the biophysical and physiological basis of pressureflow relations in the mi-crocirculation has been a recurring theme since the first observations of capillary blood flow in livingtissues. At the birth of the Microcirculatory Society, seminal observations on the heterogeneous distri-bution of blood cells in the microvasculature and the rheological properties of blood in small bore tubesraised many questions on the viscous properties of blood flow in the microcirculation that capturedthe attention of the Societys membership. It is now recognized that blood viscosity in small bore tubesmay fall dramatically as shear rates are increased, and increase dramatically with elevations in hema-tocrit. These relationships are strongly affected by blood cell deformability and concentration, red cellaggregation, and white cell interactions with the red cells and endothelium. Increasing strength of redcell aggregation may result in sequestration of clumps of red cells with either reductions or increasesin microvascular hematocrit dependent upon network topography. During red cell aggregation, resis-tance to flow may thus decrease with hematocrit reduction or increase due to redistribution of red cells.Blood cell adhesion to the microvessel wall may initiate flow reductions, as, for example, in the caseof red cell adhesion to the endothelium in sickle cell disease, or leukocyte adhesion in inflammation.The endothelial glycocalyx has been shown to result from a balance of the biosynthesis of new glycans,and the enzymatic or shear-dependent alterations in its composition. Flow-dependent reductions inthe endothelial surface layer may thus affect the resistance to flow and/or the adhesion of red cellsand/or leukocytes to the endothelium. Thus, future studies aimed at the molecular rheology of theendothelial surface layer may provide new insights into determinants of the resistance to flow.Microcirculation (2005) 12, 515. doi:10.1080/10739680590894966

KEY WORDS: blood viscosity, flow, intravascular pressure, rheology, shear rates, wall shear stress

INTRODUCTION

At the birth of the Microcirculatory Society in 1954,relatively little was known of the rheological behaviorof blood in the microcirculation. The seminal stud-ies of Poiseuille (54), Landis (39), Fahraeus (20),Vejlens (68), and Krogh (38) provided a conceptualframework for understanding the basis for the resis-tance to flow. Although best known for his experi-mental studies of the flow of fluids through tubes,Poiseuilles earlier observations on the separation ofcells and plasma in arterioles and venules led to thediscovery of plasma skimming and the need fora greater understanding of the mechanics of bloodflow (67). The pioneering intravital studies of Landis,

Supported in part by NIH research grant R01 HL-39286.Address correspondence to Herbert H. Lipowsky, PhD, Depart-ment of Bioengineering, Penn State University, 205 HallowellBldg., University Park, PA 16802, USA. E-mail: [email protected] 7 September 2004; accepted 28 September 2004.

using a forerunner of the modern servo-null tech-nique to measure capillary pressure, attempted to ex-plore the applicability of Poiseuilles law to describemicrovascular resistance. Fahraeus discovery of re-ductions in tube hematocrit as blood flows throughsmall bore tubes, and subsequent studies on the at-tendant reduction in blood viscosity (21), defined theapproach to elucidating the rheological basis of mi-crovascular blood flow. The comprehensive experi-mental studies on leukocyte behavior in the microvas-culature by Vejlens delineated many features of theirdistribution and sequestration in the microcirculationthat affect blood flow. The pioneering observationsby Krogh delineated many facets of flow distributionthrough networks of capillaries and sequestration ofred cells under normal and pathological conditions.

However, it would take the subsequent five decadesto develop a comprehensive understanding of the rolefor the intrinsic properties of blood and microvascu-lar topography as determinants of the resistance toflow. Due to the advent of new quantitative methodsfor intravital microscopy, it is now well understoodthat in addition to blood cell concentration, red cell

Microvascular rheology and hemodynamics6 HH Lipowsky

deformability and aggregation and white blood celldeformability and adhesion to the endothelium arethe principal intrinsic factors that affect resistanceto flow. The extent to which they affect resistance isdetermined by topographical branching patterns andmicrovessel diameters. During the last five decades,numerous contributions by members of the Micro-circulatory Society have explored the details of theseinteractions in health and disease. A brief overviewof some of these studies that have set the stage forfuture studies of interactions between blood rheol-ogy and microvascular function is presented in thefollowing.

THE IN VITRO FRAMEWORK

Acquisition of the viscosity of blood by bulk viscom-etry has emphasized the importance of shear rate,hematocrit, and red cell aggregation and deformabil-ity as it pertains to flow in large blood vessels (11).With the use of tube, Couette, and cone-plate vis-cometers, under the assumption that blood is a ho-mogeneous fluid with an intrinsic viscosity, in vitrostudies have revealed that blood viscosity falls about75% as shear rates ( ) rise from on the order of 0.1to 1000 sec1. A comparison of this shear thinningof blood in the presence and absence of aggregatingagents suggests that about 75% of the decrease is a re-sult of the disruption of red cell aggregates, and 25%is due to red cell deformation in response to increasedshear stresses. At a given shear rate, blood viscos-ity rises exponentially with increasing red blood cell(RBC) concentration (hematocrit) to a degree depen-dent on prevailing . The viscosity of the suspendingmedium (plasma) has been shown to be invariantwith (Newtonian) and is dependent mainly on pro-tein content and temperature.

Within the circulation, in large diameter vessels rep-resentative of the macrocirculation (i.e., >100 m),blood may be treated as a homogeneous continuumwith intrinsic properties characterized by an appar-ent viscosity. The term apparent viscosity is usedsince viscosity of a homogeneous fluid (e.g., water,molasses) is a material property that may be depen-dent on shear rate and temperature and is invariantwith the size of the vessel through which it flows. Invivo, ever diminishing length scales and the particu-late nature of blood affect this relationship as bloodcourses its way through successive divisions of thecirculatory tree. The term effective viscosity ()is often used to represent the value of viscosity thatsatisfies Poiseuilles law, since it does not explicitly

reflect the shear dependency of viscosity along thetube radius.

According to Poiseuilles law, flow (Q) and pressuredrop (P) are related by

Q = 128

D4

lP (1)

where D is luminal diameter and l is vessel length.Hence, given measurements of Q and P, one maycalculate for a microvessel of specified length anddiameter. The dominance of noncontinuum effects inthe smallest microvessels (approaching red cell di-ameter) results in an effective blood viscosity that isstrongly dependent on microvessel diameter and adeparture from this relationship.

PRESSURE AND FLOW RELATIONS IN THEMICROVASCULAR NETWORK

Direct measurements of pressures and flows in ex-teriorized tissues have provided a wealth of dataon microvascular hemodynamics throughout succes-sive microvascular divisions (77). Relating these datato the architecture of the microvascular networkhas presented a challenging problem. The disparatetopography of arterioles, capillaries, and venulesamong numerous tissues (e.g., mesentery, omentum,intestine, striated muscle) has prompted a searchfor methods to discern commonalities in structureand function among various tissues. As typified inFigure 1 for the mesenteric circulation (cat) (75), thedistribution of intravascular pressures (determinedby the servo-null method (33; 73)) and red cell ve-locity (two-slit method (71)) is presented using vessellumen width (assumed equal to internal diameter) asan index of position within the hierarchy of microves-sels. The increasingly precipitous decline in arterialpressure with diminishing diameters reflects a steadyrise in resistance to flow for the entire throughput ofthe network. It is evident that the resistance to flowwithin each major architectural division (arterioles,precapillaries, capillaries, etc.) attains a maximumin the precapillary vessels; in contrast to the expecta-tion that the maximum resistance (R ) occurs in thesmallest vessels, based upon Poiseuilles law, whereR = P/Q = (128/)(/D4). The steady declinein red cell velocity in the arteriolar network, and itssubsequent rise in venular segments, represent con-servation of the total throughput of the network asthe number of vessels varies through sequential seg-ments. These trends have been shown to be indicativeof the unique branching patterns of many tissues, as

Microvascular rheology and hemodynamicsHH Lipowsky 7

Figure 1. Arteriovenous distribution of intravascularpressure and red cell velocity from arterioles to venulesin mesentery (cat) obtained in the laboratory of BenjaminW. Zweifach (75) (with permission). Microvessel diameter(abscissa) is taken as an index of position within the net-work. Pressure falls in accord with the resista

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