Review Determinants of Tumor Blood Flow: A Review1 · TUMOR BLOOD FLOW tumor blood flow. Therefore, in this article I will critically review the three determinants of blood flow (Z,

(CANCER RESEARCH 48, 2641-2658, May 15, 1988]

Review

Determinants of Tumor Blood Flow: A Review1

Rakesh K. JainDepartment of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

Abstract

Blood flow rate in a vascular network is proportional to the pressuredifference between the arterial and venous sides and inversely proportional to the viscous and geometric resistances. Despite rapid progress inrecent years, there is a paucity of quantitative data on these threedeterminants of blood flow in tumors and several questions remainunanswered. This paper reviews our current knowledge of these threeparameters for normal and neoplasia- tissues, the methods of their

measurements, and the implications of the results in the growth andmetastasis formation as well as in the detection and treatment of tumors.

Microvascular pressures in the arterial side are nearly equal in tumorand nonrumorous vessels. Pressures in venular vessels, which are numerically dominant in tumors, are significantly lower in a tumor than thosein a nonrumorous tissue. Decreased intravascular pressure and increasedinterstitial pressure in tumors are partly responsible for the vesselcollapse as well as the flow stasis and reversal in tumors.

The apparent viscosity (viscous resistance) of blood is governed by theviscosity of plasma and the number, size, and rigidity of blood cells.Plasma viscosity can be increased by adding certain solutes. The concentration of cells can be increased by adding cells to blood or by reducingplasma volume. The rigidity of RBC, which are numerically dominant inblood, can be increased by lowering pH, elevating temperature, increasingextracellular glucose concentration, or making the suspending mediumhypo- or Hypertonie. Effective size of blood cells can be increased by

forming RBC aggregates (also referred to as rouleaux). RBC aggregationcan be facilitated by lowering the shear rate (i.e., decreasing velocitygradients) or by adding macromolecules (e.g., fibrinogeni, globulins, dex-

trans). Since cancer cells and WBC are significantly more rigid thanRBC, their presence in a vessel may also increase blood viscosity andmay even cause transient stasis. Finally, due to the relatively largediameters of tumor microvessels the Fahraeus effect (i.e., reduction inhematocrit in small vessels) and the Fahraeus-Lindqvist effect (i.e.,

reduction in blood viscosity in small vessels) may be less pronounced intumors than in normal tissues.

Geometric resistance for a network of vessels is a complex function ofthe vascular morphology, i.e., the number of vessels of various types,their branching pattern, and their length and diameter. Geometric resistance to flow in a single vessel is proportional to the vessel length andinversely proportional to vessel diameter to the fourth power. Hence,vessel diameter is the dominant parameter in flow regulation. In normaltissues, changes in vessel diameter are mediated primarily via smoothmuscle cells. A tumor has two types of vessels: those recruited from thepreexisting network of the host vasculature; and those resulting from theangiogenic response to cancer cells. Since a tumor rarely invades thearteries and arterioles of the host vasculature, the smooth muscle cells,with their contractile and nervous apparatus, surrounding these vesselsmay respond to physical or chemical stimuli. Since the newly formedvessels lack smooth muscle cells, they may not respond to these stimuli.As a result, the overall response of tumors will depend on the ratio ofhost vessels to newly formed vessels. This ratio would vary from onelocation to another and from one day to the next in the same tumor andfrom one tumor to another.

Recent studies suggest that endothelial cells and pericytes also possess

Received 8/31/87; revised 2/1/88; accepted 2/23/88.The costs of publication of this article were defrayed in part by the payment

of page charges. This article must therefore be hereby marked advertisement inaccordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1This article is based on research supported by grants from the NationalCancer Institute, the National Science Foundation, and the Richard K. MellonFoundation; by a NIH Research Career Development Award; and by a Guggenheim Fellowship.

contractile elements capable of causing changes in vessel diameter. Theextent to which these cells control blood flow is not known. Other factorswhich may contribute to changes in effective diameter of tumor vesselsinclude: swelling or destruction of endothelial cells; adhesion of platelets,WBC, or cancer cells to the vascular endothelium; and partial or totalcollapse of a vessel due to increased interstitial and decreased microvas-cular pressures. Due to micro- and macroscopic heterogeneities in the

tumor microcirculation, care must be exercised in extrapolating from onetumor to another.

I. Introduction

Microcirculation plays an important role in the growth, metastasis, detection, and treatment of tumors. For example,angiogenesis and the resulting microcirculation are essentialfor supplying nutrients and for removing waste products duringtumor growth. Similarly, blood and lymph vessels provide thevehicle for cancer cells to metastasize to distant organs/tissues.In radiotherapy, the efficacy of treatment depends upon thelocal oxygen concentration which is governed by the local bloodflow. In chemotherapy and immunotherapy, blood flow playsan important role in the delivery of appropriate pharmacological agents. Finally, in hyperthermia, the temperature distribution and interstitial microenvironment in tumors are influencedby the local perfusion rates.

Flow rate of blood, Q, in any tissue, whether normal orneoplastic, is given by

FR(A)

where the pressure drop, Ap, is the pressure difference betweenthe arterial and venous ends of the tissue circulation. The flowresistance, FR, is a complex function of the vascular morphology (i.e., the number of blood vessels of various types; theirbranching pattern; and their diameter, length, and volume) andthe blood rheology (i.e., their viscosity). For the most simplecase of laminar flow through a circular rigid vessel of radius Rand length L, the flow resistance is given by the Hagen-Po-iseuille equation (1-3):

8r,L(B)

Thus, flow resistance is proportional to the blood viscosity, 77,and vessel length and inversely proportional to the fourth powerof the vessel radius. For a network of blood vessels, it isconvenient to express flow resistance as a product of j; andwhere Z is referred to as a geometrical resistance (hindrance).Therefore, blood flow through a tissue is given by

(Q

There are several comprehensive reviews on the vascular-extravascular exchange in tumors (4, 5) and the tumor bloodflow and its modifications (e.g., Refs. 6-9); however, there areno reviews in the literature on the parameters which govern

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tumor blood flow. Therefore, in this article I will criticallyreview the three determinants of blood flow (Z, rj, Ap), themethods of their measurement, and their values in tumors underdefined conditions. I will also attempt to identify the keyunanswered questions for each of these parameters and suggestpossible approaches for resolving these issues.

II. Vascular Morphology of Tumors: Structure, Organization,and Volume of Tumor Vascular Compartment

The literature on the vascular morphology of human andanimal tumors has been reviewed recently by Warren (10) andShubik (11). The structure, geometry, and arrangement oftumor vessels have been studied by many investigators since thework of Virchow (12). The motivations of these works haveranged from understanding pathophysiology (e.g., angiogenesis,growth, invasion, metastasis) to improving diagnosis and treatment of tumors. In what follows, I will briefly discuss themethods used, and then present qualitative and quantitativeresults.

A. Methods

The methodologies used to obtain tumor vascular parametershave included: (a) standard histological examination of tumorsusing light or electron microscopy (e.g., Refs. 10 and 13); (b)examination of tumor tissue injected with agents (e.g., Indiaink, benzidine, macromolecules, labeled RBC, colloidal carbon)which are retained by blood vessels (e.g., Refs. 14 and 15); (c)examination of the cast of the tumor vasculature made using apolymer (e.g., silicone rubber, vinyl acetate) or other substances(e.g., gallium) (e.g., Refs. 16-19); (d) gross or microscopicradiography and angioradiography (i.e., radiography with ra-diopaque contrast media) with or without the use of vasoactiveagents (e.g., Ref. 20); and (<â€¢)intravital observation of tumor

microcirculation with or without contrast agents (e.g., Ref. 21).The results have been analyzed either qualitatively to discernmacro- and microscopic organization of the vasculature orquantitatively using stereological principles to obtain morphological parameters (e.g., vessel length, diameter, surface area,and volume).

B. Macroscopic Organization

Unlike most normal tissues, the tumor vasculature is highlyheterogeneous and does not conform to the standard "normal"

morphology (i.e., artery to capillary bed to vein). The vascularmorphology of one tumor differs from another and to someextent is determined by the growth pattern of cancer cells.Macroscopically, the tumor vasculature can be studied in termsof two idealized categories (22).

In tumors with peripheral vascularization, the vessels arelocalized primarily at the periphery. The centers of these tumorsare usually poorly perfused; hence penetration of blood-bornesubstances is difficult. As the tumor grows and invades thesurrounding tissue, the vessels proliferate at the periphery. Intumors with central vascularization, vessels proliferate from thecenter like branches from a tree. One would expect a highvascular volume in the center of these tumors and a low vascularvolume in the periphery.

In reality, the tumors may have many modules, each moduleexhibiting one of these two types of idealized vascular patterns.The macroscopic architecture is different among various tumortypes and even between a spontaneous tumor and its transplants

(23-25). As expected, the response of a tumor to therapydepends on both the macroscopic and microscopic vascularmorphology (see, e.g., Refs. 23 and 26).

C. Microscopic Organization

Before I discuss the organization of vessels in the tumormicrocirculation, it is worthwhile to review the most commonlyaccepted terminology of blood vessels in an "ideal" normal

tissue with a simple route between arterial and venous sides(27-29). In such a tissue, blood flows successively through largearteries, small arteries, arterioles, terminal arterioles, capillaries, postcapillary venules, venules, small veins, and large veins.

The large and small arteries and arterioles are invested insmooth muscle cells and are capable of vasomotor adjustments.The terminal arterioles, the next branching order of arterialvessels, are invested proximally in vascular smooth muscle thatgradually decreases until a single smooth muscle cell, spirallywrapped, marks the end of the muscular investment. This finalsmooth muscle cell is referred to as the precapillary sphincterand serves as the final control site for blood flow into thecapillary bed.

Capillaries are vessels made of endothelial cells surroundedby a basement membrane. These vessels are devoid of smoothmuscle cells and hence are incapable of active vasoconstriction/vasodilation. (The capability of endothelial cells and pÃ©rimesto cause vasomotion cannot be excluded.) Their large surfaceareas and structure make them the ideal site for the exchangeof material between the blood and tissues. Normal capillariescan be divided into three categories based on their wall structure: (a) nonfenestrated (continuous); (b) fenestrated; and (c)discontinuous (sinusoids). Nonfenestrated capillaries are themost common type and are located in skin, connective tissue,skeletal and cardiac muscle, alveolar capillaries of the lung, andthe brain. In fenestrated capillaries there are fenestrae or trans-endothelial circular openings of about 400-800 A between thelumen and interstitium across the endothelial cells. These fenestrae may be open (e.g., in glomerular capillaries) or coveredby a thin ~60-80-A layered diaphragm similar to the diaphragmof vesicles. These capillaries are located in the intestinal mucosa, pancreas, giomerulus, peritubular capillaries, endocrineglands, the choroid plexus of the brain, and the ciliary body ofthe eye. Discontinuous capillaries have large diameters andwide openings between endothelial cells. Basal lamina is eitherdiscontinuous or absent. Examples of these capillaries includesinusoids of the liver, the spleen, and the bone marrow. (SeeRef. 5 for relationship of structure with transport properties.)

When vessels converge toward the exit of the capillary network, the resulting vessel is referred to as a postcapillary venule.These vessels are larger in diameter than capillaries, are composed of a single layer of endothelial cells and a basementmembrane, and are usually devoid of smooth muscle cells.These vessels have the weakest inlerendo thelial junctions. Theirsensitivity to prostaglandins, histamine, serotonin, and brady-kinin makes them preferential sites for plasma extravasationand diapedesis in inflammation (30). These vessels join to formvenules where the smooth muscle cells reappear.

In regions where the blood flow varies significantly over time,arteries may be directly connected to venules by arteriovenousanastomoses. The arterial side of arteriovenous anastomoses isinvested in smooth muscle cells. These vessels are found infingertips, toes, skin, nailfolds, lips, intestinal mucosa, thyroid,erectile tissue, etc.

In a normal tissue, these idealized vascular beds may be2642



TUMOR BLOOD FLOW

connected in parallel or series depending upon the organ. Forexample, in the kidney, the glomerular capillaries are in serieswith the tubular capillaries. In the enterohepatic circulation,the capillary beds of the spleen are in parallel with those of themesentery and in series with the liver microcirculation. Fordetails of the vascular morphology of various organs and tissues,the reader is referred to the Handbook of Physiology (31).

When a group of cancer cells is placed in a host tissue, tumorangiogenesis leads to the formation of capillary sprouts witheventual development of a tumor microcirculatory network.Therefore there are two sources for blood vessels in a tumor:(a) those recruited from the preexisting network of the hosttissue; and (h) those resulting from the angiogenic response oftumors. (For details on tumor angiogenesis, see Ref. 32.) Although the tumor microcirculation originates from the hostvasculature, its organization may be completely different depending upon the tumor type, its growth rate, and its locationin the tumor mass. As a result, the classification of blood vesselsdeveloped for normal tissues based on structure (anatomy) andfunction (physiology) may not be applicable to tumors. Warren(10) classified the blood vessels found in tumors into ninecategories based on their ultrastructure. I have modified hisnomenclature so that it corresponds as closely as possible tothat discussed earlier for a normal tissue: Class 1, arteries andarterioles; Class 2, nonfenestrated capillaries; Class 3, fenes-trated capillaries; Class 4, discontinuous capillaries (sinusoids);Class 5, blood channels without endothelial lining; Class 6,capillary sprouts; Class 7, postcapillary venules (giant capillaries); Class 8, venules and veins; and Class 9, arteriovenousanastomoses. Note that except for the capillary sprouts (Class5) and the blood channels (Class 6), the remaining vessel typesare structurally analogous to those found in a normal tissue. Akey difference is that the tumor vessels may contain tumor cellswithin the internal lining of endothelial cells (33). The vesselsof Classes 5 and 6 are found in a healing (granulation) tissue(34, 35). In the following, I will discuss characteristics of thesevessels with examples of tumors where they are found.

Arteries and Arterioles. Algire and Chalkley (36) and Cullinoand Grantham (16) using a transparent mouse chamber and anisolated rat tumor preparation, respectively, showed that various sarcomas and carcinomas increased the caliber of thearteries of the host tissue. Willis (37), on the basis of his ownwork and that in the literature, asserted that even in the mostinvasive tumors, the structure of arterial wall does not change,and malignant invasion of arterioles is extremely rare. Perhapsthe incorporation of "intact" arterial vessels in a tumor is partly

responsible for vasomotion and blood flow fluctuations observed in sandwiched tumors (38, 39) and for blood flow modifications due to heat and vasoactive agents (for a review, seeRefs. 8 and 9).

Nonfenestrated Capillaries. Warren (40), on the basis of hisstudy of hemangiopericytoma (a tumor derived from bloodvessels) grown in a hamster cheek pouch chamber, concludedthat nonfenestrated capillaries are found in the milieu of ahighly differentiated tumor. These vessels possess intact endothelial walls and a distinct basement membrane supported byfine strands of collagen fibers.

Fenestrated Capillaries. These capillaries with openings inthe endothelium have been found in the W256 carcinoma (41),in human renal carcinoma transplanted in nude mouse (42),and in various brain tumors (43). These fenestrations may bepartially responsible for the large permeability of tumor vessels(5).

Discontinuous Capillaries. These vessels, which resemble the

sinusoids in the liver and the spleen, are present in poorlydifferentiated mammary (44) and human renal carcinomas (45)and may be responsible for fibrin deposit in the extravascularspace. Plasma fibrinogen may extravasate through these inter-endothelial openings, clot, and become cross-linked in the tissuespace (5, 46).

Blood Channels. In melanomas and some sarcomas, bloodchannels are present which are not lined with endothelial cells(10). In these tumors, blood percolates between and aroundtumor cells; hence RBC come in contact with tumor cells. Thesechannels are connected to sinusoids or other types of vessels.

Capillary Sprouts. Similar to neovascularization in a granulation tissue, tumor angiogenesis leads to capillary sprouts.These sprouts may be of the tapering type or saccular dependingupon the caliber of the lumen. Endothelial cells of these sproutsdiffer from those of normal mature vessels (35). These newlyformed vessels are extremely fragile and are surrounded byRBC and fibrin deposits due to petechial (pinpoint) hemorrhage. The lumen of the sprouts contains a static column ofRBC which begin to flow when a capillary network is formed.

Postcapillary Venules. These vessels are highly tortuous andlarge in diameter. Unlike the postcapillary venules in normaltissues, these vessels are mostly devoid of basement membrane,and partly surrounded by fibrous tissue. These vessels are alsoreferred to as giant capillaries (10) or as venous capsules. Thesevessels have also been identified as a site for cancer cell intra-vasation (47, 48).

Venules and Veins. Similar to postcapillary venules thesevessels are highly tortuous, saccular, and dilated. The bloodflow and oxygen content in these vessels change with time.

Arteriovenous Anastomoses. A tumor may contain a largenumber of arteriovenous anastomoses. This direct shunting ofblood from the arterial to the venous side creates problems fordelivery of materials (e.g., anticancer agents) into a tumor.

Using the above vessel classification it should be possible, atleast in principle, to describe the organization of vessels in atumor. At a given location, blood may be routed from thearterial (Class 1) to the venous side (Class 8) via vessels ofClasses 2 through 7, or directly via arteriovenous shunts. Dueto the transient nature of tumor microcirculation, it is alsopossible that blood may flow from a venule (Class 8) via bloodvessels of Classes 2 through 7 and return to a venule (Class 8),similar to the "portal" system. Therefore, combinations of these

vessel types may lead to a nearly infinite number of vesselorganizations. Furthermore, due to the inherent heterogeneityin a tumor, the organization of vessels may be different fromone location to another and from one day to the next day. As aresult, one would expect different routes for blood flow in thewell-perfused advancing zone, in the intermediate seminecroticzone, and in the necrotic zone. A detailed study of vascularbranching patterns in a tumor has not been done to date.

/>. Quantitative Studies on Vascular Morphology

The spatial and temporal distributions of vascular volume,length, diameter, and vascular surface are defined as the vascular morphology of tumors. While there have been severalstudies in the literature since 1893 (10) on the vascular morphology of tumors, most of these are qualitative. The firstquantitative study on tumor vascular morphology was conducted by Algire and Chalkley (36) in two-dimensional tumorsusing the method of Chalkley (49). They examined the vascularvolume of several rapidly growing tumors (e.g., sarcomas, malignant melanomas) and slowly growing tumors (e.g., pig-

2643



TUMOR BLOOD FLOW

mcnted and amelanotic melanomas) in a mouse transparentchamber. The rapidly growing tumors elicited new capillarysprouts from the host vasculature in 2-3 days post-tumorimplant, and the vascular space increased to 40-50% within 5-8 days. The slowly growing tumors took at least 8 days for theinitial sprout formation and the vascular space never exceeded25% during the entire observation period. The capillaries inrapidly growing tumors were about 5 times the diameter ofthose in normal tissue, appeared like sinusoids, and rarelydifferentiated into arterioles and venules. Whereas in slowlygrowing tumors, the capillaries had the same diameter as normal capillaries and showed considerable differentiation intoarterioles and venules.

Following Algire's pioneering work, several investigators

have analyzed growth of vessels in two-dimensional tumors intransparent windows using intravital microscopy. Yamaura andSato (50) have carried out perhaps the most extensive quantitative study of the vasculature developed in ascites hepatomaAH 109A transplanted in the dorsal skin chamber in Donryurats. These authors divided the growth period of 25 days intofour stages according to changes in vascular morphology: Stage1, slight capillary alterations; Stage 2, formation of fine capillary network; Stage 3, modifications in arteries; and Stage 4,necrosis. These authors used Chalkley's method to measurevascular volume and Vogel's approach (44) to measure length

and surface area. The diameters of 200 vessels were measuredat random and represented in a histogram, where vessels ineach diameter class were recorded. The vessel length (cm/m3tissue), surface area (mm2/mm3 tissue), and volume (%) in

creased from 36, 20, and 20, respectively, in the s.c. tissue(control) to 160, 70, and 50 in the second stage of growth andthen decayed to nearly zero in Stage 4. In the second stage oftumor growth, the speed of neovascularization was 40-50 timeshigher than that in a granulation tissue (51). The number ofsmall vessels (<10 Â¿Â¿m)increased from 40% in Stage 1 to 70%in Stage 2. In Stages 3 and 4 the frequency of small diametervessels decreased, and the frequency of larger diameter vesselsincreased. Vessels with diameters of up to 200 urn have beenreported by Eddy and Casaren (52) in a malignant neurilem-moma grown in a hamster cheek pouch and by Peters et al. (53)in a I>MBA inoliiceli mammary adenocarcinoma grown in adorsal chamber in rats.

Using photomicroscopy, Endrich et al. (39) and Asaishi etal. (54) have measured the frequency distribution of the capillary diameter and length as a function of days postimplant inBAI 112 sarcoma in dorsal skin chambers in Wistar (WAG/Rij) rats and in A-Mel-3 amelanotic melanoma in dorsal skinchambers in hamsters, respectively. Both of these studies showan increase in capillary diameter and length with tumor growth.

Recently, using photomicroscopy and the stereological methods of Underwood (55), we have measured the vessel diameterdistribution, vessel length, surface area, and volume in granulation tissue (51) and in VX2 carcinoma grown in a rabbit earchamber (56). The similarity in the growth characteristics ofthe granulation tissue and the tumor is noteworthy. Our tumordata show increases in length, volume, and surface area similarto those reported in other two-dimensional tumors.

While tumors grown in transparent chambers provide theluxury of intravital observation, the results obtained must beinterpreted with caution. A major criticism of this approach isthe elevation of tissue pressure due to the proliferation of tumorcells and blood vessels in a rigid enclosure. This increase in

â€¢"IIn' abbreviation used is: DMBA, 7,12-dimethyl-benz(a)anthracene.

tissue pressure may lead to vascular stasis by crushing the bloodvessels and ultimately to pressure necrosis. This was confirmedby Younger and Algire (57) who reported return of blood flowin several vessels after the chamber was loosened. Therefore,the development of necrosis, although an inherent property oftumors, may be partly due to the technique itself in sandwichtumors. A second related problem with the chamber techniqueis that once the vessel density increases beyond a certain value,it is hard to observe the microcirculation. Therefore, reliabledata can be obtained only in the early stages of tumor growth.Finally, the tumors must be transplanted in s.c. tissues, andtheir growth is restricted in the lateral direction.

The injection of dyes (microangiography), polymers, macro-molecules (dextrans), labeled erythrocytes, or other stain permits quantification of vascular morphology of three-dimensional tumors in a variety of sites. Due to unrestricted growthof tumors, the development of necrosis is less artifactual. Themain disadvantage of this approach is the inability to followthe growth of the same tumor. As a result, these techniques areinvasive in that they require the sacrifice of animals and removalof tissue and require a large number of experimental techniquesto relate structure with function.

Following the pioneering work of Cullino and Grantham(58), several investigators have used these injection techniquesto measure vascular volume of tumors at various stages ofgrowth (Table 1). Note that the vascular space in tumors variesfrom 1% in transplanted fibrosarcoma 4956 (58) to 27.5% in aspontaneous canine lymphosarcoma (69). The measured valueof vascular space of a given tumor depended upon the markerused. For example, the vascular space of W256 carcinoma wasfound to be 10.6 Â±0.5% (SD) using dextran 500 (M, 375,000;Mn 180,000) (58) and to be 0.79 Â±0.06% using 51Cr-labeled

erythrocytes (65). The reasons for this profound discrepancyare not completely clear. Possible reasons for overestimationusing dextran may be the extravasation and binding of dextrans(5, 70) and reasons for underestimation using erythrocytes maybe the significantly lower microvessel hematocrit compared tosystemic hematocrit (Refs. 3 and 68; also see Table 2 andSection III).

The results on the changes in vascular volume as a functionof tumor growth also depend on the tumor type. For example,Gullino and Grantham (58) found that the vascular spaceincreased linearly with tumor size for W256 when the tumorswere small (4-12 g), but no correlation was possible for largetumors. On the contrary, Song and Levitt (65) reported adecrease in vascular space as W256 tumors grew from 1 to 25g. Similarly, Vaupel (66) reported a decrease in vascular spaceand an increase in intercapillary distance in the growing DScarcinosarcoma in rats, especially in the initial phase of tumorgrowth. Song et al. (62) found no significant changes duringgrowth in the vascular volume of a mouse neuroblastoma. Liottaet al. (77) measured the vessel diameter distribution in T241fibrosarcoma grown in C57BL mouse and found that the fraction of vessels with diameters of >5 urn decreases exponentially.The size distribution and the mean diameter of vessels did notchange significantly during tumor growth (7-15 days), exceptfor an increase in the number of large vessels (>100 tan diameter) at later time periods. Recently, Karlsson et al. (67) measured the intratumor distribution of RBC volume and plasmavolume in a rat sarcoma at 14 and 20 days. Similar to Gullinoand Grantham (58), these authors found no significant difference in distribution of spaces in the peripheral and central(necrotic) regions of these tumors, whereas they found a wideheterogeneity of spaces in each region. Both RBC volume and

2644



TUMOR BLOOD FLOW

Table 1 Typical values of vascular space in solid tumors

HostMouseNude

mouseRatHamsterDogTumor72j

mammarycarcinomaMammaryadenocarcinoma

SCK mammarycarcinomaSLCcarcinomaNeuroblastomaGardner

lymphosarcomaClouser

human breastcarcinomaSL2murinelymphomaHuman

melanomasWalker

256carcinomaWalker256carcinomaFibrosarcoma

4956Hepatoma5123Hepatoma3683NovikofThepatomaHepatomaLCÂ°Hepatoma

HCHepatomaAHepatomaSLiverDS

carcinosarcomaMCAsarcomaFibrosarcomasA-MCC-MCBP-llHemangiopericytomaSpontaneous

lymphosarcomaWt

range(g)0.1-2.40.1-2.40-0.90.05-13(14

days)0-10-10.23.5-13.00.06-245.6-14.81.0-12.91.4-10.51.8-6.97.0-32.15.0-9.42.7-4.12.3-4.97.8-8.53-110.5?MethodMorphometryMorphometry

RBC*RBC*RBC*RBC*RBC*RBC*MorphometryDextranRBC*DextranDextranDextranDextranDextranDextranDextranDextranDextranMorphometryRBC

andalbuminRBCandIgGMorphometryAntipyrineVascular

space(%)15-1817

91.74.9~2~4~50.9-2.210.60.81.04.55.04.58.012.45.88.118.60.4-4.07-141.00.81.22114-27.5Ref.44596061626364641558655858585858585858586667684069

" LC, low catatase; HC. high catatase; A, ascites form; S, solid s.c. form.* Assumed //â€ž.= //w.

Table 2 Average microvascular hematocrits of normal and neoplastic tissuesobtained using labeled RBC andplasma"Species/tissueRatBoneCardiac

muscleLungSkinSpleenThyroidMuscleLungKidneySkinA-MC

fibrosarcomaC-MCfibrosarcomaHI'l

1 fibrosarcomaf}^/H,â€ž"

Ref.0.33

*0.650.830.911.221.27

-0.65f'0.930.520.430.640.750.78

J7168

Rabbit placenta

CatKidneyTongue

Dog lung

HumanCraniumCerebrum

0.68

0.180.840.84-0.95

0.840.92

72

73

74

7576

* Most of the normal tissue data were taken from Ref. 3.* Ratio of average microvessel hematocrit to systemic hematocrit.' Assuming H,â€ž= 45%.

plasma volume decreased during tumor growth in the rat sarcoma.

Despite the importance of knowing morphological parameters, there are limited number of studies in the literature wherethe vascular length, surface area, volume, and diameter distribution in three-dimensional tumors have been reported. Vogel(44, 78) quantified the vascular morphology of s.c. 72j mammary adenocarcinoma using microangiography during growth(6, 17, and 23 days) and following chemotherapy. He found a

marked widening of diameter with growth, accompanied by amarked drop in vessel length (134 to 19 cm/mm3 tissue) andsurface area (46 to 14 mm2/mm3). Vascular volume of 16% did

not change with growth. He referred to vessels with diameter<12 MUÃ•as capillaries and those with diameter >12 /im assinusoids. Vogel attributed the decrease in the surface area ofvessels with growth to the increase in the ratio of sinusoids tocapillaries.

Hilmas and Gillette (59) repeated similar studies in anothermammary adenocarcinoma grown in the gastrocnemius muscleof the right rear leg of C3H/BL mouse. They reported theirfindings in terms of viable (nonnecrotic) tissue which decreasedfrom >95% in 35 mm3 to <60% in tumors over 1500 mm3 (Fig.

1). The vascular volume remained constant around 17% duringgrowth (Fig. 2). The vessel length decreased dramatically in the

Ul UJ50-

O O

O 3g Â¿30

sit (- 2C -

Â§5UH*:

â€¢VASCULAR VOL<v NECROTIC VOLo VESSEL LENGTH IOOO

eooO

Q600

400 u<J0Â»

zoo >

2OO 4OO 6OO 800 WOO I2OO 1400

TUMOR VOLUME mm3

Fig. 1. Changes in vascular volume (%), necrotic volume (%), and vessel length(mm/mm3 of viable tumor tissue) as a function of size of a mouse mammary

carcinoma. From Ref. 59, with permission.

2645



TUMOR BLOOD FLOW

v VESSEL DIAMETER

o VASCULAR SURFACE AREA

2OO 40O 6OO 800 IOOO 1200 I4OO

TUMOR VOLUME mm9Fig. 2. Changes in mean diameter (;/m) and vascular surface area (mm ' 'mm '

of viable tumor tissue) as a function of tumor size. From Ref. 59, with permission.

beginning and then more gradually (Fig. 1). As seen in Fig. 2,the vessel surface area also decreased rapidly during the earlyphase of growth, and vessel diameter increased as more sinusoids appeared in a growing tumor. Interestingly, despite thedifferences in the methods of analysis, Hilmas and Gillette's

results are in excellent agreement with those of Vogel (44).These authors also studied the effect of radiation therapy onthe vascular morphology of tumors.

Recently, the vascular morphology of human tumor xeno-grafts in nude mice has been characterized by Solesvik et al.(15) and Kraus et al. (79). Using stereological principles, Solesvik et al. studied five melanoma xenografts with volume-doubling times ranging from 4.2 to 21.6 days and found that eachtumor had its own characteristic vascular structure. On a permm3 histologically intact tissue basis, the total vessel length

ranged from 32 Â±2 to 80 Â±4 mm, the total vessel surface arearanged from 1.6 Â±0.1 to 3.8 Â±0.2 mm2, and the total vesselvolume ranged from 0.009 Â±0.001 to 0.022 Â±0.002 mm3. The

necrotic fractions ranged from 30 Â±1 to 49 Â±4%; they wereinversely proportional to vessel volumes and directly proportional to doubling times. The vascular system of xenograftsoriginates from the host animal, and hence the vascular structure may not be totally representative of human tumors in situ.Nevertheless these studies provide a bridge between experimental animal tumors and human tumors.

One aspect of vascular morphology where very little quantitative data are available is the distribution of intercapillarydistance in tumors. Thomlinson and Gray (80) found histologically a band of viable tumor cells about 100 /Â¿mwide betweenthe blood vessel and necrosis in human lung cancers. Tannock(81) found viable tumor cords with a radius of 60-120 /Â¿msurrounding capillaries in a highly necrotic mouse mammarycarcinoma. These authors referred to this viable zone as thediffusion length of oxygen and nutrients in tumors. Tannockand Steel (82) showed that in this mouse mammary tumor, theintercapillary distance increased as the tumor grew. Similarresults were reported by Vaupel (66) in rat tumors. The decreasein vascular surface area and capillary density in tumors withincreasing weight was explained by Tannock (83) on the basisof difference in "turnover" times of endothelial and neoplastic

cells. Tannock and Hayashi (84) found the average turnovertime of endothelial cells to be about 50-60 h as compared tothe turnover time of 22 h for neoplastic cells. Interestingly,Denekamp (85) and coworkers have found that endothelial cellsof animal and human tumor multiply at least an order of

magnitude faster than those of normal vessels. Hammersen etal. (33) propose that the increased turnover of tumor endothelialcells reported by Denekamp may be a result of integration oftumor cells into the lining of newly formed and growing vessels.Interestingly, Tannock et al. found several blood vessels withinnecrotic tissue with stagnant blood in them. These results pointout the problems in relating structure with function.

E. Summary

The tumor vasculature is highly heterogeneous and does notconform to the "standard" normal vascular organization. The

vascular morphology of one tumor differs from another and isdetermined to some extent by the growth pattern of cancercells. Macroscopic-ally, the gross architecture of a tumor vas

culature falls into two categories, peripheral and central. Microscopically, the tumor vessels can be classified into ninecategories: arteries and arterioles; nonfenestrated, fenestrated,and discontinuous capillaries; blood channels; capillary sprouts;postcapillary venules; venules and veins; and arteriovenousanastomoses. There are no quantitative data on the detailedbranching pattern of these vessels in a tumor.

Quantitative morphometric studies in two-dimensional tumors show that vascular volume, length, and surface area increase during the early stages of tumor growth, and then decrease after the onset of necrosis. Frequency of large diametervessels increases in the later stages of growth. Most quantitativestudies in three-dimensional tumors miss the early growthperiod of increase in vascular volume, length, and surface area.While studies of later stages of growth show a decrease in vesselsurface area and length, the results on vascular volume aremixed. Some studies show that the fractional vascular volumeof tumors remains fairly constant during growth, suggesting anincrease in the number of blood vessels with low blood flow,while others show that the fractional vascular volume decreasesas a tumor grows, in agreement with the observation that tumorblood flow rate per unit tumor weight decreases as a tumorgrows.

There are no quantitative data on the vascular morphologyof human tumors. These data should be obtained by studyinghuman tumors in situ using a variety of noninvasive techniquesor by perfusing human tumors ex vivo (17, 86).

III. Rheological Properties of Blood and Cells in Normal andTumor Circulation

A major resistance to fluid flow in a tube or vessel is the fluidviscosity. For simple shear flows, the viscosity y3 is defined asthe ratio of the shear stress r3 to the shear rate 73

77 = T/ÃŒ (D)

where shear stress on a surface is the force per unit area actingon the surface in a direction tangential to the surface and shearrate is the velocity gradient in the fluid. When T varies linearlywith 7 and rÂ¡is constant, the fluid is referred to as Newtonian.Examples of such fluid are water, saline, plasma, and honey.When r is a nonlinear function of 7, the fluid is referred to asnon-Newtonian, e.g., blood. For non-Newtonian fluids, theratio of r/7 is referred to as the apparent viscosity, T;,,,and is afunction of 7. For example, the rheological behavior of bloodcan be described by the nonlinear equation developed by Casson

3 Units: Viscosity: poise (P) = 100. P =Pa = N/m2 = 10 dyn/cm2. Shear rate = s~'.

dyn. s/cm2 = dPa.s. Shear stress :

2646



TUMOR BLOOD FLOW

(87)

\T = -J-Ty + \1Â¡c vy

where rÂ¡cis the Casson viscosity and ry is the yield stress (i.e.,such a fluid will not flow if r < ry). In this equation, ry and T/Care functions of the hematocrit, H, and the plasma proteinconcentrations. (For details, see Ref. 88.)

In Poiseuille flow through a tube of radius, R, the velocityprofile is parabolic with maximum velocity in the center andzero at the walls, and the shear rate (i.e.. velocity gradient)increases linearly with radial distance from the center (where itis zero) and reaches it maximum value at the wall, 7Â»..For suchprofiles, the maximum velocity, VmaÂ»,is equal to twice the meanvelocity, r. It can be also shown that for Newtonian fluid, thewall (maximum) shear rate, â€¢>â€ž,,is equal to 4V/R, and the meanshear rate (7) is equal to two-thirds of the maximum shear rate:

natively with Ringer's solution and whole blood, and the flow

resistances are computed using Equation C. If the geometric'' ' resistance is assumed to remain unchanged during alternate

perfusions, and if the viscosity of Ringer's solution is known,

the in vivo apparent viscosity of blood, ija, is

2P (F)

(G)

(H)

For non-Newtonian fluids, the velocity profile resembles ablunted parabola, and the wall shear rat e is usually higher thanfor a Newtonian fluid. For such fluids, 4P/Ã„ may be used as anapparent wall shear rate (â€¢>â€ž.).

Under normal conditions, blood can be divided by volumeinto about 55-60% plasma and about 45-40% cells, or "formedelements." The plasma is essentially a dilute electrolyte solution

containing total solutes equal to 9.55 weight %, most of whichare proteins (~8 weight %). Plasma behaves in a Newtonianfashion with a viscosity, qp, of 1.2-1.3 cP at 37Â°C.Plasma

viscosity is a function of protein concentration, primarily tibrinogen and some of the globular proteins (2). The cells consistof-95% RBC, -0.13% WBC, and -4.9% platelets, by number.In cancer patients, cancer cells are also present in blood. Thedeformability and interaction of these various types of cellswith one another and the vessel wall affect the flow behavior ofblood.

The Theological behavior of blood, therefore, depends notonly on shear rate but also on cell concentration, cell deformability, cell aggregation, plasma viscosity, protein concentration, and temperature. In what follows, I will first outline themethods of measurement of blood viscosity and its key determinants, cell concentration and cell deformability, both in vitroand in vivo; then I will present pertinent in vitro and in vivoTheological data for normal blood and finally discuss the rheol-ogy of blood in cancer patients and in tumor microcirculation.

A. Methods

I. Apparent Viscosity. Apparent viscosity measurements ofblood are made in vitro in either rotational viscometers (e.g.,two concentric cylinders or a cone and plate geometry) orcapillary tube viscometers. The former type provide well-defined shear rates; the latter types are cheaper, are easier to use,and require much smaller fluid volume. The problem with tubeviscometers, however, is that r;,,is a function of tube diameterfor blood (see the Fahraeus-Lindqvist effect in Section 111B).

Information on in vivo blood viscosity in the microcirculationhas come from pressure-flow (AP-ÃŸ) relationship obtainedusing macroscopic or microscopic approaches. In the macroscopic approach, an isolated organ or tissue is perfused alter-

By varying the hematocrit and other constituents of blood, theeffect of various parameters on ij.,can be obtained.

In the microscopic approach, AP, Q. L, and K are measuredin a microcirculatory preparation in vivo using intravital microscopy and modern optoelectronic instrumentation. The apparent viscosity of blood is then calculated assuming thatHagen-Poiseuille equation (A and B) holds for all segments ofthe vasculature. (The methods of measurement of L and R werediscussed in Section II, and those of AP and Q are discussed inSection IV and Ref. 48, respectively.) Since it is possible tooptically measure the hematocrit, H, this approach also permitsevaluation of the relationship between Â«â€žand //. The majorproblem with both macro- and microscopic methods is theinability to determine the shear rates precisely.

2. Cell Concentration and Hematocrit. Concentration of RBC(hematocrit) can be easily measured in vitro by centrifugingwhole blood and evaluating fractional volume occupied bypacked RBC. Measuring concentrations of WBC, platelets, andcancer cells requires separating or staining these cells andcounting their number in a known volume of sample eithermanually or optoelectronically.

Since microvascular hematocrit is an important determinantof blood viscosity and of oxygen transport, several measurements have been made of in vivo hematocrit using macroscopicand microscopic approaches. In the macroscopic (or wholeorgan/tissue) approach, an average (lumped) hematocrit of allvessels in a tissue is made by indirectly measuring the fractionalvolume of RBC by radiolabeling RBC and plasma. The keyproblem with this method is the extravasation of plasma markers (e.g., albumin), which must be accounted for in estimatingthe volume (5).

In the microscopic approach, hematocrit in individual bloodvessels is measured in various microcirculatory preparationsusing various optical and electronic techniques (3). These techniques include: (a) direct cell counting using still photographyin a blood vessel after flow has been occluded by a bluntinstrument, referred to as flow occlusion method; (h) direct cellcounting using high speed cinephotomicrography or stroboscopie lighting; (c) electronic cell counting by monitoring thechanges in light intensity caused by the single-file passage ofRBC through a capillary; (ti) measurement of the time-averagedintensity of light transmitted through a vessel, referred to asopacity; and (e) correlation between hematocrit and absorbance(= log (/o//); where /Â»and / are intensities of incident andtransmitted light, respectively.) According to Zweifach andLipowsky (3), the first four methods are generally limited tosmall capillaries and/or vessels with low hematocrits, while thefifth method is useful for larger vessels (>20 Â¿tmdiameter).

While any of the above methods can be used to measureconcentrations of other blood cells or cancer cells in microves-sels, recent developments in intravital fluorescence microscopyfacilitate their visualization and, hence, quantitative measurements.

3. Cell Deformability. Deformability of various types of cellscan be studied qualitatively by observing/photographing cells

2647



TUMOR BLOOD FLOW

as they pass through narrow glass tubes in vitro or capillariesin vivo. Quantitative measurements of cell deformability havecome from two methods: (a) nitration experiments, in whichpressure required to filter a cell suspension through a membraneof known pore size is used as a measure of cell rigidity; and (h)micropipet aspiration experiments, in which the rate and extentof deformation of a cell of radius Rc aspirated by a micropipetof radius Rp (<Re) are used to calculate the rheological properties of the cell. The latter method has been used to quantifyrigidity of RBC, WBC, and cancer cells. A less commonly usedmethod to measure deformability is based on the analysis ofcell deformation in a well-defined flow field in a rheoscope (89).

4. Cell Aggregation and Adhesion. At low shear rates, thebridging of adjacent RBC by fibrinogen, globulins, or othermacromolecules (e.g., dextrans) causes these cells to aggregateand form rouleaux. Stresses greater than >0.1 dyne/cm2 cause

rouleaux disaggregation. The net aggregation energy can beestimated from the shear stress required to disaggregate therouleaux or from changes in RBC membrane strain energy dueto elastic deformation of cells in rouleaux (2, 90). Similarly, theshear stress required to detach WBC, platelets, or cancer cellsfrom a surface (e.g., glass coverslip, vascular endothelium,another cell) can provide a measure of cellular adhesion.

B. Rheological Behavior of Normal Blood in Vitro and in Vivo

The importance of blood rheology in blood flow in normalmicrocirculation has prompted numerous studies on this subject. (For reviews, see, e.g. Refs. 2 and 3.) In the following, Iwill present and discuss typical data to provide a backgroundfor understanding alterations in blood rheology during theneoplastic disease.

1. Effect of Shear Rate. Shown in Fig. 3 is the in vitrorelationship between apparent viscosity, >;,â€žand shear rate, â€¢>,

in normal human blood with a hematocrit of 45%. Note that atlow shear rates RBC aggregate and form rouleaux leading toan increase in rÂ¡a.As shear rate (or stress) is increased, theserouleaux break up and Â»;â€žreaches an asymptotic value at shearrates >100 s"1. An increase in shear stress also causes defor

mation of the dispersed RBC and the alignment of their majoraxes with the direction of flow. Thus, disaggregation and deformation both contribute to the reduction in rÂ¡a.

Whitmore (91) estimated the apparent shear rates in thecirculation of humans and found ->â€žto vary between 60 and 80s"1. Lipowsky et al. (92) recently measured the mean blood

velocity, V, in the microcirculation of cat mesentery and foundTV for 10- to 60-iim-diameter vessels to be 1200 s~' in the

i io2

> IOÂ°0 o -

Temperoture 37"C

IO"' IO'1 IO2 IO'I IOShear Rate (sec'1)

Fig. 3. Logarithmic relation between apparent viscosity and shear rate innormal human blood containing 45% RBC by volume. Inset, RBC aggregates atlow shear rates, and RBC disaggregation and deformation at high shear rates.From Ref. 2, with permission.

arterioles and 850 s ' in the venules, with an overall average of1330 s~'. More specifically, they found that 7Â».rose from ~1400s"1 in 50-fim arterioles to a maximum of ~ 1800 s"1 in 20-/im

terminal arterioles, and then it steadily declined to a minimumof 500 s~' in the 20-/tin postcapillary venules but rose to 800s~" in 50-/im venules. Based on the in vitro data in Fig. 3, rja in

the microcirculation should be constant. However, the in vivodata of Lipowsky and Zweifach (93) for the cat mesentery doesnot support this conclusion. In these experiments, the apparentviscosity was found to increase from ~3 cP during normal flowvelocity, V ~\ cm/s (7 ~2000 s~'), to -20 cP as flow wasreduced to P-0.03 cm/s (7Â»,~60 s"1). Zweifach and Lipowsky

(3) attribute this increase in <;â€žduring reduction in 7 to bothRBC aggregation, as suggested by in vitro studies, and leuko-cyte-endothelial adhesion, as evidenced by in vivo observation.

According to these authors, the role of RBC aggregation inincreasing Â»;â€žin vivo is still unresolved.

2. Effect of Hematocrit. The apparent viscosity of RBC suspension in vitro rises nearly exponentially with increasing hematocrit. The role RBC deformability plays in reducing rÂ¡abecomes apparent when one compares these viscosity results withthose for suspension of RBC hardened with aldehyde treatmentor rigid spheres.

Fig. 4 shows the in vivoapparent viscosity results as a functionof hematocrit in the blood perfusing the isolated dog hind limb(94). The in vivo results are compared with in vitro resultsobtained in a large diameter tube viscometer. Although the invivo and in vitro results show the same qualitative behavior, thein vivo TI,is about one-half of in vitro i\a. (Similar results havebeen obtained for the rabbit ear (95); rat tail artery (96); cat calfmuscle (97, 98); and dog lung (99).) The lower value of r,a invivo was attributed to lower hematocrit in the microvasculatureof the tissue (//mv) compared to the perfusate hematocrit, as aconsequence of the Fahraeus effect (see next section). As amatter of fact, the average hematocrit of blood in the microcirculation of several normal and neoplastic tissues (measuredusing radiolabeled RBC and plasma) has been found to beconsiderably lower than the systemic hematocrit (Table 2). Thelower microvessel hematocrit results in a lower apparent viscosity similar to the Fahraeus-Lindqvist effect (see SectionIIIB3).

3. Effect of Vessel (Tube) Diameter: The Fahraeus Effect andthe Fahraeus-Lindqvist Effect. Since the pioneering work ofFahraeus (1929) and Fahraeus and Lindqvist (1931) whichshowed that the hematocrit and apparent viscosity in a tube ofdiameter <~350 Â¡anare less than those in a larger tube, manyin vitro and in vivo studies have been performed on the effectof tube (vessel) diameter on these parameters. To understand

0 20 40 60 80

PERFUSION HEMATOCRIT (%)

Fig. 4. Effect of hematocrit on in vivo apparent blood viscosity in the circulation of isolated dog hind limb. The results are compared with in vitro apparentviscosity measured using glass tube viscometer with large diameter (I mm) athigh shear rates. The value of viscosity is lower in vivo due to the Fahraeus-Lindqvist effect in the tissue microcirculation. From Ref. 94, with permission.

2648



TUMOR BLOOD FLOW

Fig. 5. Definitions of systemic (feed), microvessel (tube), and efferent (discharge) hematocrits. Adapted from Ref. 2.

1000

Fig. 6. Effects of tube diameter on (A) tube hematocrit, H-, (Fahraeus effect)and (B) apparent blood viscosity (Fahraeus-Lindqvist effect). Note that //, isnormalized with respect to discharge hematocrit (//,,) and relative blood viscosity(v,) is normalized with respect to suspending fluid viscosity. Note also that theminimum in A/T///D occurs when tube diameter is ~ 15-20 pm, and in ij, whentube diameter is ~5-7 ^m. From Refs. 103 and 104 as adapted in Ref. 2, withpermission.

these results it is useful to del ine hematocrits measured in vitroand in vivo, respectively, at three different locations: (a) tube(#T) or microvessel (HmJ hematocrit; (b) feed (HF) or systemic(#syS); and (c) discharge (HD) or efferent (HE) hematocrit (Fig.5). The Fahraeus effect4 refers to decrease in Hr/HD (or //mv/HE) in narrow tubes, and the Fahraeus-Lindqvist effect refersto the concomitant decrease in the apparent viscosity in thetube or vessel.

The Fahraeus effect results from the migration of RBCtoward the center of the tube, leaving the fluid near the wallrelatively cell free. Since the velocity of plasma is highest in thecenter and lowest near the wall, the cells travel faster than theplasma (suspending media). From simple mass balance on cells,one can write

(J)

where K*u and K are the average velocities of cells and whole

4The Fahraeus effect (//T < HD) should not be confused with the possibility

of (a) HO < Hf or (b) H0 > HT. The former occurs due to (a) cell screening, i.e.,the cells are blocked at the tube (vessel) entrance due to stearic hindrance; and/or (b) "plasma skimming", i.e., a disproportionate amount of fluid enters thetube (vessel) from the cell-free layer at the wall of the feeding reservoir (vessel)(2, 100). The latter (//,, > //, ) occurs when there is considerable fluid loss fromthe vessels, e.g., in shock (101) or in tumors (Refs. 4, 5, and 102; also see SectionHIC).

blood. Since >",..â€žis greater than I. //, is less than //,, in small

tubes (Fig. 6.1). In large tubes, the ratio of cell-free layerthickness to the tube radius is small. As tube radius growssmaller (R < 250 /im), this effect becomes more pronounced(Fig. 6A).

As tube diameter decreases below 15-20 /Â¿m,the RBC occupya larger fraction of the lumen, and as a result, the difference inthe cell velocity and the plasma velocity decreases causing //, /HD to rise. This ratio reaches a value of 1.0 for a tube diameterof ~2.7 firn (minimum tube diameter through which a normalhuman RBC can pass) (Fig. 6.1 ).

As shown in Fig. 6B, the decrease in IIÂ¡ in tubes withdiameters between 15 and 20 Aimand 300 pm is accompaniedby a similar decrease in TJO.However, unlike the Fahraeus effect,the trend reversal in the Fahraeus-Lindqvist effect does notbegin until the diameter is lowered in the 5-7-/Â¿mrange. Below5-7 urn diameter, rÂ¡abegins to increase rapidly to infinity as dtends to ~2.7 urn for human cells. The fact that TJOis notdetermined by //T in the 5-20-Aim-diameter range needs furtherresearch.

Shown in Fig. 1A are the in vivo Hmv data as a function ofvessel diameter in the cat mesentery. These results are inqualitative agreement with the in vitro data shown in Fig. 6A.Note that the value of Hmv/Hsys is about 0.23 for -lO-fiincapillaries (105); whereas the lowest value of HT/HD in vitro is

H mi ero / M j

iâ€”iâ€”iâ€”iâ€”iâ€”iâ€”mâ€”iâ€”iâ€”iâ€”i1â€”\70 40 50 to 30 20 10 7 K> 20 30 40 50 60 70

VESSEL DIAMETER ((im)

58 50 42 34 26 18 IO 7 IO 18 26 ÃŒ4 42 50 58

VESSEL DIAMETER I/iÂ«")

Fig. 7. Effect of vessel diameter on (A) microvessel hematocrit (from Ref.105, with permission) and (B) apparent blood viscosity (from Ref. 92, withpermission) in the cat mesentery. The microvascular hematocrit was normalizedwith respect to systemic value (//.â€ž35%). Note that //â€ž.reached its minimum in~ 12 fitn-diameter postcapillary venules, while the viscosity was minimum in â€”12-(im precapillary vessels.

2649



TUMOR BLOOD FLOW

only ~0.5. This discrepancy between in vivo and in vitro results Aggregation of RBC caused by low shear stress and/or byis not totally understood. A possible explanation is the preferential shunting of RBC through some part of the vasculature(105). It is interesting to note that //m,///sys was higher invenules (0.53 Â±0.25) than in arterioles (0.46 Â±0.25) of comparable size range (10-60 urn diameter).

Shown in Fig. IB are the in vivo estimates of t]aas a functionof vessel diameter in the cat mesentery. Two conclusions canbe drawn from this work: (a) rÂ¡avalues are lower for arterioles(3.6 Â±1.9 cP) than for venules (5.2 Â±2.7 cP) (92). Zweifachand Lipowsky (3) attribute the elevated viscosities in the venulesto higher hematocrit (Fig. 7A) and lower shear rates in venulesas compared to arterioles of the same diameter. Note that lowshear rates can facilitate RBC aggregation and leukocyte-en-dothelium adhesion. In addition, in exteriorized preparations amild inflammatory response may increase WBC flux and adhesion leading to reduced lumen (functional) diameter. If theunobstructed lumen diameter is used in Equation B to calculatertâ€ž,the estimate of rÂ¡amay be higher by a factor of 2 or more(105). Since most vessels in tumors are venular, these resultssuggest a higher viscosity in the tumor microcirculation, (h)The average ?/â€žvalue obtained from the microscopic approachis higher than that from the macroscopic approach (~2 cP; Fig.4). Zweifach and Lipowsky (3) attribute the relatively high i\avalue to the inability to measure hemodynamic parameters invessels of zero //mv (i.e., plasma only) or very low //mv. Thisbias should be kept in mind when measuring i/,, in tumormicrocirculation which may contain a large number of plasmachannels.

4. Effect of Cell Deformability and Aggregation. Since thedeformability of the cellular elements of the blood contributessignificantly to the apparent viscosity of blood in large tubes(see, e.g., Fig. 4) and in small tubes (see, e.g., Figs. 6 and 7),considerable information has been gathered in the last decadeon the rheological properties of RBC, WBC, and cancer cells.Most of the quantitative data has come from micropipet aspiration experiments (90).

In these experiments a step negative pressure is applied to acell via glass micropipet. The projection length of the cell inthe pipet is measured as a function of time and applied pressure.The data for RBC are analyzed using a Kelvin model to obtainthe elastic modulus, E, and the membrane viscosity, Â»/,â€ž..,â€ž(90).The WBC and cancer cell data are analyzed using a standardviscoelastic model to obtain the elastic coefficients, A', and A:,

and the cell viscosity, jjÂ«u.The reason for using different modelsis that for RBC the membrane and its associated cytoskeletonprovide the principal resistance to cell deformation; whereasdue to the presence of granules and nucleus, the cytoplasmprovides the resistance to deformation of WBC and cancercells. (For more details on this subject, see Refs. 48, 90, and106.)

Under normal conditions, WBC are less deformable thanRBC (106). Cancer cells are even less deformable than WBC(48). Activation of T cells and large granular lymphocytes mayalso increase their rigidity (107). Low pH, elevated temperature,high extracellular glucose concentration, or changes in thetonicity of the suspending medium in either direction (hypo- orhypertonic) make RBC less deformable (2, 108). Reduced deformability of cells reduces their migration toward the tubecenter and hence causes a reduction in the Fahraeus effect.Seshadri et al. (109) found that heating of RBC led to anincrease in rÂ¡ain large tubes (~30 firn diameter). These resultshave interesting implications in the hyperthermic and hyperglycÃ©mietreatment of cancer (9, 110-112).

macromolecules increases the effective size of cells. This, inturn, facilitates their migration toward center (hence accentuates the Fahraeus effect) and increases cell screening at thetube entrance. Both lower the tube hematocrit. On the otherhand in large tubes RBC aggregates increase T\â€žand henceresistance to flow.

In the absence of RBC aggregation, WBC migrate to thecenter of the vessel due to their effectively larger size, whereasin the presence of RBC aggregates (due to slow flow) the largerrouleaux occupy the central position and push WBC to the wallwhich raises their concentration in the vessel. Such lateraldisplacement of WBC by RBC also occurs in a tube withincreasing diameter. In addition, in convergent flows, WBCentering from one capillary tend to be pushed to the wall byRBC entering from the second capillary. It is of interest to notehere that postcapillary venules have nearly the lowest shear ratein the circulation, are formed by converging capillaries and havea gradually increasing diameter. All these conditions favorWBC migration to the wall, so that -95% of WBC roll alongthe wall in the postcapillary venules. The location near the walland slow rolling speed facilitate extravasation of WBC whenneeded to fight inflammation and/or help them respond toextravascular signal. At the same time, WBC marginationincreases resistance to blood flow during inflammation, shock,and other low-flow states (105, 113). The implications of thesefindings to the movement of cancer cells, single or in clumps,have not been explored completely.

C. Blood Rheology in Cancer Patients

The presence of cancer may alter the factors governing therheological properties of blood. These factors include bloodand plasma viscosity; concentration, deformability, and aggregation of RBC; and concentration of plasma proteins. Thesechanges affect not only the flow of blood through normal andtumor microcirculation but also the onset of metastasis and theeffectiveness of cancer treatment.

The effect of the long-term growth of a tumor, whethertransplanted or spontaneous, in producing anemia in the hosthas been known for a long time (114). The effect of anemia onthe fraction of hypoxic tumor cells was studied by Hill et al.(115). The systemic hematocrit drops as tumors grow larger.Interestingly enough, the average hematocrit in the tumorjni-crocirculation (//mv) is lowered proportionately so that the //mv///sys ratio remains fairly constant. Using a tissue isolated tumorpreparation, Butler et al. (102) and Sevick and Jain (112) foundthat due to fluid loss from the vasculature, the hematocrit inthe efferent blood of W256 mammary carcinoma was about 5%higher than in the systemic blood (Table 3). Similar resultswere obtained by Vaupel et al. (116) for human breast cancer

Table 3 Ratio of efferent (discharge) hematocrit to afferent (systemic) hematocritin mammary carcinomas in rats

Tumortype7,

12-Dimethylbenz(a)anthraceneW-NitrosomethylureaW256MTW9W256

Human medullary cell carcinoma'Human squamous cellcarcinoma'â€¢

Mean Â±SE; />< 0.01.6 Xenographs in nude rats.Wt(g)2.3

Â±0.43.9 Â±0.63.8 Â±1.04.3 Â±0.9

GrowingRegressing

0.5-1.82.35 Â±0.282.23 Â±0.27//O///ly,.051

Â±0.013.029 Â±0.007.068 Â±0.011.042 Â±0.006.038 Â±0.007.048 Â±0.0111.05 Â±0.05

1.081.09Ref102112

116

2650



TUMOR BLOOD FLOW

xenografts in nude rats. The effect of this hemoconcentrationon tumor blood flow is not understood.

In one of the most extensive studies of the blood rheology ofcancer patients, Dintenfass (117) found a decrease in hematocritwhich was statistically significant (Table 4). Note that thehematocrit drop in malignant melanoma patients, both survivors and deceased, over 10 years was not as pronounced as inmice bearing a transplanted tumor.

Dintenfass (117) also reported a significant increase in theaggregation and rigidity of RBC (P < 0.001), fibrinogen andglobulin concentrations, and plasma and blood viscosity (afteradjusting to normal hematocrit) in melanoma patients (Table4). The increase in RBC aggregation has been reported in lungand bowel cancers (118, 119), in breast cancer (120), and invarious carcinomas (121). Associated with the aggregation ofRBC are increased fibrinogen and globulin concentrations anddecreased albumin/fibrinogen ratio. The increased fibrinogenand albumin concentrations may also explain the increasedplasma viscosity. Similarly, the increased RBC aggregation mayexplain increased blood viscosity (corrected to standard hematocrit) (117, 121). The increase in RBC rigidity is difficult toexplain, especially in light of the relationship between rigidityand aggregation (117).

On the basis of a 10-year follow-up of ~ 130 patients, Dintenfass (117) proposed the use of viscosity tests as diagnostic andprognostic tools. He correlated the sum of standard deviationsfrom the mean of plasma viscosity and RBC aggregation withsurvival time. The greater the departure from the norm, asexpressed by the sum of SD, the shorter was the survival time.He also tried to predict survivors (i.e., metastasis-free patients)from the patients who died of mÃ©tastases,on the basis of hislong-term data (-1971, 1973, 1975, 1977, 1980), and foundthat the discriminating power of viscosity tests (i.e., increasedplasma viscosity and RBC aggregation in decreased subjects ascompared to survivors) holds for a period of less than 2 years.

In the absence of RBC aggregation, the cancer cells similarto WBC may occupy the more central position in the post-

capillary venules due to their larger size. However, when RBCaggregation occurs due to low shear rates and/or high plasmaprotein concentration, the cancer cells are pushed to the wall.Near vessel walls, cancer cells may be coated by platelets andfibrin, making them inaccessible to immunological attack (117),as well as extravasate to form metastatic foci. (For more detailson metastasis, see Ref. 48.)

D. Summary

The apparent viscosity of blood in large blood vessels (>500firn) is governed primarily by hematocrit and shear rate. Bloodviscosity increases with increasing hematocrit. At low shearrates, RBC aggregate to form rouleaux which cause an increasein viscosity. RBC aggregation is also facilitated by macromol-ecules (e.g., fibrinogen, some fraction of globulins, dextrans).

Due to their deformability, cells migrate toward the centerleaving a cell-free marginal layer at the vessel periphery. Themigration toward center is increased with increasing effectivesize and deformability of cells or cell aggregates. Since the cellsin the center travel faster than the plasma, hematocrit in smalltubes (<500 urn diameter) is lowered (the Fahraeus effect). Astube diameter becomes comparable to cell diameter, both vesselhematocrit and apparent viscosity begin to increase (trendreversal in the Fahraeus and the Fahraeus-Lindqvist effects).

In vivo microvessel hematocrit also exhibits the Fahraeuseffect; however, the drop in //â€ž,Â»in vivo is more than in vitrovalues for vessels of comparable diameter. On the contrary, thedrop in apparent viscosity in vivo is not as pronounced as thein vivo hematocrit would suggest. These discrepancies betweenin vitro and in vivo results could be partly due to the limitationsof measurement techniques.

The presence of neoplastic disease may alter factors governing apparent viscosity of blood, which may affect blood circulation through normal and tumor tissues, and the onset ofmÃ©tastases.Decrease in the systemic hematocrit with tumorgrowth has been reported for both humans and animals. The

Table 4 Rheological parameters of systemic blood in normal subjects and in patients who survived and who died of malignant melanoma*

Survivors Deceased

Parameters

Normalvalues

(mean Â±SD)

1977 evaluation

if Mean Â±SD

1980 evaluation

n Mean Â±SD

1977 evaluation

I Mean Â±SD

1980 evaluation

I Mean Â±SDBlood viscosity (cP) at 180 s"1

MenWomenAll

Hematocrit, %MenWomenAll

Rigidity of RBCMenWomenAll

Aggregation of RBC; erythrocytesedimentation rate (mm/h)(37-C)

5.44 Â±0.754.70 Â±0.30

46.8 Â±3.741.2 Â±1.5

0.956 Â±0.059 66

109 Â±74 66

1.02Â±0.10

162Â±83

61

61

1.02Â±0.11

169 Â±99

2612

2612

231134

34

5.21 Â±1.064.57 Â±0.95

42.6 Â±7.037.0 Â±5.4

1.031 Â±0.1531.067 Â±0.1721.043 Â±0.156

192 Â±98

44

56

45

45

7.42 Â±4.96

41.3 Â±6.1

1.035 Â±0.138

183 Â±92

Albumin/fibrinogenratioAlbumin/globulin

ratioPlasma

viscosity16.3

Â±3.7 66 11.3 Â±4.4 58 11.2 Â±3.5 35 9.9 Â±4.4 54 10.9Â±5.11.65

Â±0.28 68 1.30 Â±0.25 63 1.28 Â±0.25 36 1.19 Â±0.29 58 1.20Â±0.271.23

Â±0.09 70* 1.23 Â±0.10 65* 1.24 Â±0.10 36 1.34 Â±0.16 56' 1.28 Â±0.16

' Data are from Ref. 117.* Note that differences between parameters in patients and in normal subjects are significant at P < 0.001 or better, except for values marked b and c.c Not significant.'/Â»Â«eO.OS.

2651



TUMOR BLOOD FLOW

//,â€ž>///,,,,ratio remains unchanged despite the drop in // v.Simultaneous rise in fibrinogen and/or globulin level increasesthe plasma viscosity and RBC aggregation. As a result, apparentblood viscosity goes up after adjusting to normal hematocrit.RBC aggregates, due to their effectively large size, push WBCand cancer cells toward vessel walls, facilitating their extravasation and ultimately metastasis formation.

Although one can speculate about the Theological behaviorof blood in the tumor microcirculation based on the aboveinformation, distributions of //,â€ž>and Â»/â€žin individual vessels oftumors need to be measured directly. More specifically thequestions that should be answered include: (a) How do abnormalities in the vascular morphology of tumors (e.g., presenceof dilated and tortuous vessels, plasma channels, sinusoids) andlow shear rates affect //mv and rÂ¡al(b) What is the role of shape,size, and rigidity of cancer cells with respect to RBC and WBCon their radial distribution in vessels? (c) What is the effect oflowered hematocrit on flow resistance versus oxygen transportfrom the point of view of tumor growth and treatment (e.g.,radiotherapy)? Recent developments in various optoelectronicmethods to measure microcirculatory parameters as well as thepossibility of perfusing isolated tumor tissue, ex vivo, shouldmake it possible to answer these questions. (122-124).

IV. Microvascular Pressures in Normal and Tumor Tissues

Pressure, /', in a fluid is defined as the mean compressive

force per unit area acting on fluid surfaces in directions normalto the surface at any point. Stephen Hales (125) was probablythe first person to measure mean arterial pressure (by insertinga tube in the artery of the neck of an unanesthetized horse).Since that time, many direct and indirect techniques have beendeveloped to measure pressure in macro- and microcirculation(for historical perspective, see, e.g., Refs. 3, 27, 126, and 127).The motivation for these studies has been 2-fold: (a) the bloodflow in a vessel is governed by the pressure difference betweenits arterial and venous end (see Equation A); and (b) thetranscapillary exchange of various solutes is associated with theexchange of fluid between the vascular and the interstitial spaceswhich, in turn, is governed by the hydraulic and osmotic (on-cotic) pressure differences between these two spaces (5).

In what follows I will first outline various methods of bloodpressure measurements in vessels, then present a brief summaryof results on normal tissues, and discuss in detail the microvas-cular pressure measurements in tumor tissues, and finally pointout the issues that need to be explored further.

A. Methods

The methods to measure blood pressure can be divided intotwo categories: (a) macroscopic, limited to larger blood vessels(diameter > 1 mm); and (b) microscopic, developed for smallervessels (127). In each category, when the pressure sensor is incontact with the blood directly or hydraulically via a fluid, themethod of pressure determination is referred to as a directmethod; otherwise it is referred to as an indirect method. Whilewe are interested here in the microscopic pressure measurements, a brief discussion of macroscopic methods is in order tounderstand the constraints of the former methods.

Macroscopic Methods. Sphygmomanometry is the mostwidely used indirect method to measure systolic (maximum)and diastolic (minimum) arterial pressure in humans. Thismethod, first developed in 1905 by Korotkoff, is based onbalancing the pressure in an air-filled cuff against the vascular

pressure. In this method the arterial blood flow is stopped byincreasing the cuff pressure. The pressure is then slowly lowereduntil arterial pressure exceeds the cuff pressure and a sound isheard (Korotkoff sound), which indicates the onset of bloodflow. This is assumed to be the systolic pressure, and thepressure when the blood flow becomes continuous is diastolicpressure. Korotkoff sounds can be detected by a stethoscope orby acoustic, optical, or electronic means (for details, see Refs.126 and 127).

Direct pressure measurements are made using pressure transducers which convert hydraulic pressure into mechanical displacement of a thin elastic body. This displacement is convertedinto an electrical signal using electrical (e.g., strain gauge) oroptical (e.g., fiber optics) means. Due to recent developmentsin solid state electronics (i.e., semiconductors) the miniaturizedtransducers can be placed on the catheter tip, which can thenbe directly placed in a blood vessel. However, due to cost,sterilization, and some technical problems (e.g., temperaturesensitivity, fragility) the pressure transducer is connected to theblood stream hydraulically, e.g., via a fluid-filled catheter. Thedynamic response of the catheter-transducer system is governedby the overall compliance C, the change in volume per unitchange in pressure. Units: cms/dyn = 1333 cm3/mm Hg) of the

system (i.e., the sum of catheter, fluid and transducer compliances) and the flow resistance (defined by Equation A. Units:dyn-s/cm5) through the catheter (126, 127). In addition to the

inherent catheter compliance, the presence of an air bubble mayincrease the overall compliance in an unpredictable way. Fordetails of ways of handling these problems, the reader is referredto the review by 1maglieli a (127).

Microscopic Methods. Indirect estimates of microvascularpressure have come from two approaches: (a) monitoring pressure during mechanical obstruction until flow stasis and subsequent release of a vessel until flow reappears; and (b) monitoring exchange of fluid following vessel occlusion. The firstmethod was probably used by Kreis (128) to estimate thecapillary pressure in the human finger (see Ref. 27 for details).Roy and Brown (129), Hill (130), and Algire (131, 132) used amuch improved system for mechanical occlusion and release ofmicrovessels to measure microvascular pressures in the web ofthe frog, the bat wing, and the transparent dorsal skin chamberin the mouse, respectively. This technique was also applied tomeasure capillary pressures in the digits of the upper and lowerextremities in humans (133-135). While these data generallyagree with the direct pressure measurements, the error introduced due to mechanical properties of the vessel wall and theperivascular tissue cannot be ascertained.

The second indirect method is based on the technique developed by Landis (136) for measuring fluid exchange and wasused by Intaglietta and Zweifach (cited in Ref. 127) to measurepressure in capillaries. According to the Starling hypothesis,the net exchange of fluid across a vessel is zero if the differencebetween the intra- and extravascular hydrostatic pressure iscounterbalanced by the difference in the osmotic pressures. Ifthe osmotic pressures and the interstitial pressures can bemeasured or estimated independently, this method permitsestimation of the microvascular pressure from the microocclu-sion experiments.

All methods for direct pressure measurement in microvesselsrequire penetration of the vessel itself or its side branch bysome type of microannulae (e.g., glass micropipet, polyethylenecatheter). The microannulae may be connected to a low compliance pressure transducer either directly (passively) or via anactive interface-nulling system. The passive systems are limited

2652



TUMOR BLOOD FLOW

by both the small amount of fluid that can be transferred fromthe vessel to overcome the compliance (C) of the system andthe mechanical energy available to overcome the flow resistance(FR). Since the time constant of response of these systems isapproximately (C x FR) and FR is proportional to (I/A4)

(Equation B), the minimum tip diameter for the passive systemis ~15 urn (for details of analysis see Refs. 137 and 138).Rappaport et al. (139) and Levasseur et al. (140) developedthese systems with tip diameters ~20 urn and obtained a frequency response of ~20-45 Hz.

Lundis (136, 141, 142) developed the first active system inwhich he inserted a dye-tilled micropipet into microvessels andmanually adjusted the pressure in the pipette to obtain a stationary dye-plasma interface. Eichna and Bordley (135) andLevick and Michel (143) improved this method for use inhumans. Wiederhielm et al. (144) improved this technique intwo ways, (a) Instead of using a dye to visually track dye-plasmainterface, the micropipet was filled with 2 M NaCl solution, theelectrical resistance of which is much less than that of plasma.Movement of fluid into and out of the pipet would change theelectrical resistance which can be monitored using a Wheatstonebridge, (b) Instead of adjusting counter pressure in the pipetmanually, a servocontrol system was used. This system gave afrequency response of ~20 Hz for pipets with tip diameters of0.5-5.4 um. lmaglietta et al. (145, 146) further refined thissystem to the point that it is now available commercially (e.g.,IPM, Inc., San Diego, CA) and is being used routinely inlaboratories all over the world for pressure measurements inanimals and humans (see Sections IVB and IVC).

A major problem in the use of these techniques is the fabrication of the micropipet itself. For details, see the work ofMuheim (147) and Misiewicz (148).

B. Microvascular Pressures in Normal Tissues

Although the first microvascular pressure measurements innormal tissues were made more than 100 years ago (128, 129),most investigations have been made in the past 20 years duelargely to the availability of the servo-null pressure system. Thismethod has been used to map pressures in the microvasculatureof the mesentery, interstitial muscle, various skeletal muscles,pial surface of the brain, lung, and heart of various animals; batwing; and the nailfold of human fingers. (For detailed discussionof these results, see Refs. 3 and 148.)

Shown in Table 5 are typical pressure profiles in the micro-vascular networks of various two-dimensional tissues and skel

etal muscles. The cat mesentery network data of Zweifach andLipowsky (156) are shown in more detail in Fig. 8A. Note thatmost pressure drop occurs in the arterial side, with the sharpestfall occurring in the narrowest arterioles (~ 15-35 urn diameter).This pressure drop must be differentiated from the pressuredrop per unit length occurring in vessels of various types asshown in Fig. SB. The pressure drops in the latter case weremeasured by using a dual servo-null system in each vessel. Notethat unlike the network pressure gradients (Fig. 8/1) (A/>//)

along the length of single unbranched microvessels in the network reaches its maximum at the true capillary level (92). Sincethe capillary length is very small, the pressure drop across agiven capillary is small (~1 mm Hg). Due to these smallpressure differences, even small changes in blood rheologicalfactors may alter blood flow distribution. For instance, atbifurcations the entrance of one RBC into one branch raisesthe apparent viscosity and reduces the flow into that branch,favoring the entrance of the next cell into the next branch. Sucheffects are even stronger when the less deformatale WBC entersa branch, and the resulting transient plugging (-5-10 s toseveral minutes) leads to preferential redistribution of blood toother vessel(s)( 157).

Micropressures undergo periodic fluctuations synchronouswith the action of the heart, spontaneous vasomotion at thelevel of arterioles, and the respiratory cycle. Shown in Fig. 9are pressure recordings of various vessels in the cat mesentery(149). Note that frictional resistance encountered in the successive branchings of the arterial tree dampens the pulsatile waveform but does not completely abolish it even in the capillaries.The amplitude of pulse is ~ 1-2 cm H2O in capillaries and ~4-5 cm H2O in venules where the mean pressure is as low as ~10-

15 cm H2O. These periodic as well as irregular pressure fluctuations in capillaries and postcapillary venules may affect thefluid exchange between the vascular and extravascular spaces(3-5).

A limited number of studies have been reported in the literature on changes in microvascular pressure due to variousphysical and physiological changes in the host. Zweifach (149,158) found a positive correlation between systemic pressureand pressure in microvessels >40-50 ^m, whereas micropressure in smaller vessels (<20 /tm) became relatively independentof systemic pressures. Bohlen et al. (153) on the other handreported a linear relationship between systemic pressure andmicrovascular pressure even for capillaries. Further work isrequired in this area to resolve this controversy.

Several investigators have shown an increase in capillary

Table 5 Typical microvessel pressure" distribution in various normal tissues

A. Two-dimensional arrays

Arterial diameter Venous diameter

RabbitomentumCatmesenteryCat

brain (piamater)BatwingMouse

skin40-50

urn5167726970-9530Mm3850554660-7020MUÃ•3338453635-5010Mm28331920-2515//m27301610-1720>im24281416-1830Â«im222610-1440-50tira20248-10Ref.93149150151131,

132

B. Skeletal muscle

Rat spinotrapeziusRat cremasterRat anterior gracilisCat tenuissimusAlc66

909093A243

3955

84A330

284368A424

242639V416

2224V313 1718V210 1210

15VI5

912152 153154155

" Values are mean pressures in mm Hg. From Ref. 3, with permission.4 Region of active venous vasomotion.' Arterial (A) and venous (V) dichotomous branchings numbered beginning with sector that feeds the arteries.

2653



TUMOR BLOOD FLOW

VELOCITY -mm/nc PRESSURE -minMg

80 MESENTERYCAT

32 24 16 8 16

VESSEL OIAMETER-micro

24 32 40 48

E

SA*

3.2

2.8

24

2.0

1.6

1.2

0.8

0.4

ARTERIAL VENOUS g

48 32 16 8 48

VESSEL DIAMETER (|jm)

Fig. 8. .I, arteriovenous distribution of microvascular pressures as a functionof vessel diameter in the cat mesentery. From Ref. 156, with permission. B,arteriovenous distribution of microvascular pressure gradients along the lengthof single unbranched microvessels in the network. From Ref. 92, with permission.

SMALL ARTERIES

100-

40L

HjO 100

IMC(A) 40

IMC

I sec

(B)

lue

401-

100

(80i.) 1C)*V- (SM (D)

ARTERIOLESÃ•MC

80

50 (40p) (E) *"â€¢ (Â»VI <f)

PraupllUryC.IMC5025037CmH,O20118Â«)

(G) 0_EpiUÂ«rvIMCHH32i

j, n i irrâ€”~(10M)

IH)VmbIMCtâ€”

t

Wp'â€¢IO*-

I2BÂ«) (1)

Fig. 9. Pulsatile nature of the pressure waveform is attenuated as the bloodstream moves through arteriolar and precapillary branchings but is not completelyabolished in any of the microvessels, including the narrow true capillaries in thecat mesentery. From Ref. 149, with permission.

pressure due to hydrostatic load (134, 142, 143). Levick andMichel (1978) found that the capillary pressure on the toesincreased only to about two-thirds of that based on hydrostaticload as the subject moved from the horizontal to the upright

position. Zweifach and Lipowsky (3) attribute this discrepancyto modifications in pre- and postcapillary resistance.

Capillary pressure rises as the temperature of the skin and/or the room is raised, or the venous pressure is raised (143,159). Finally, the use of anesthetics may affect blood pressureby suppressing spontaneous vasomotion. Spontaneous vaso-motion is, presumably, responsible for the pressure fluctuationsin capillaries (159).

C. Microvascular Pressure in Tumors

Unlike normal tissues, the studies on the microvascular pressure in tumors are limited. Algire and Legallais (160) wereprobably the first to measure the microvascular pressure in twosarcomas and a mammary adenocarcinoma grown in the dorsalchambers in mice. Using an indirect vascular occlusion method,Algire (131, 132) measured the blood pressure in the skin.Without giving any numerical results, Algire and Legali is (160)state that "the blood pressure of tumor vessels approximatesthat of venous pressure." They also reported slower blood flow

in tumor vessels than in capillaries of striated muscle. Theseinvestigators decreased the peripheral vascular pressure of miceby histamine injections and found reductions in blood circulation in tumor and surrounding host tissues.

Decreased intravascular pressure and/or increased extravas-cular pressure in tumors has been demonstrated by severalinvestigators working with tumors grown in transparent chambers (e.g. Refs. 4, 41, 50, 52, 53, 160, and 161). By raisingvenous pressure in the chamber (161) or by loosening thechamber (52, 53) blood flow could be restored in previouslyischemic/necrotic tumor areas. Yamaura and Sato (50) attributed the flow instability (i.e., stasis and reversal) with theanimal's movement to lowered microvascular pressure in tu

mors. While studying the dissemination of malignant tumors,Young and Griffith (162) proposed that the pressure in tumorvessels is "disproportionately high in relation to the tonicity ofthe vascular wall."

Peters et al. (53) reported the first direct measurements ofmicrovascular pressures in a DMBA-induced mammary adenocarcinoma grown in the rat dorsal skin chamber. Theirnormal s.c. tissue and tumor data are shown in Table 6 andFig. 10. Note that on the arterial side the values did not differsignificantly between nontumorous and tumor vessels, whereasvenous pressures in the tumor were significantly lower thanthose in nontumorous tissue. Furthermore, although the arterialpressures were identical in both tissue types, the pressure gradient is significantly higher along the tumor capillaries (sinusoids) and relatively small along the tumor venules. (Theseresults suggest a higher flow resistance in tumor vasculature.)These investigators found the pulsatile nature of pressure in thearterioles; however, no pulsatility was detected in the venousside.

Wiig (164) measured microvascular pressures in the superficial layers (<!((() urn) of DMBA-induced mammary tumors inrats. By making silicone rubber castings of the tumor vasculature, Wiig showed that the surface arterioles seemed to supplyvascular branches going into the central tumor regions. However, pressure drop during passage of blood from surface todeeper areas makes it difficult to estimate microvascular pressure in deeper vessels. Nevertheless, his key finding is that themean interstitial fluid pressure in the center of these tumors(5.5 g) is ~16 mm Hg which exceeds the surface vascularpressure (Table 6) and hence may be responsible for reducedblood flow and pO2 in the center of these tumors.

2654



TUMOR BLOOD FLOW

Table 6 Microvascular pressures in tumors (mm Hg)

TumorMammary

adenocarci-nomaAH

109 Ahepatoma'DMBA-induced

mammary carcinoma'>60UHI44.5

Â±9.7(21)Arterial41-60

21-40/im /im23.0

Â±6.3(5)36-53

(1)38.9

Â±5.8(18)11-20Â»ini17.3

Â±2.523.8

Â±4.4(4)Â£10

<1011-209.1

Â±2.5Â°8.7 Â±1.9Â°(4) (12)Venous21-30pni8.2

Â±2.6Â°(17)-7.5-18.413.3

Â±3.0(16)31-50

51-100Â¿im/im7.9Â±3.1Â°8.8 Â±2.3

(12) (13)-7.5

(1)9.7

Â±2.4(31)>1008.1

Â±1.8(4)8.9

Â±2.6(25)Ref.53163164

A-Mel-3 amelanotic melanoma''

37.9 Â±1.5 36.8 Â±1.5 24.7 Â±1.2 12.8 Â±1.2 -11.0 Â±1.1 165

" Significantly lower (/' â€¢0.01) than nontumorous s.c. tissue (Fig. 10).* Indirect method of pressure measurement.e Measured in superficial layer (<100 urn) of tumor weighing 1-17 g. Mean interstitial fluid pressure in the center of tumor -16 mm Hg." 30'C.

30

Pressure(cm H20)

20

10-Ã TUMOR

50 30 10 10 30 50

ARTERIAL VENOUS

100 Internal Diameter ( // )

Fig. 10. Microvascular pressure profiles in the nontumorous subcutaneoustissue and mammary adenocarcinoma grown in the dorsal skin chamber in rats.Values are mean Â±SD (bars). Note that the pressure in 10-50urn venousmicrovessels is significantly less in tumors than in nontumorous tissue. FromRef. 53, with permission.

Hori c/ al. (163), using an indirect method similar to that ofAlgire (132), measured micro vascular pressure in normal s.c.tissue and in a hepatoma (AH 109A) grown in a dorsal skinchamber in rats. Similar to Peters et al. (53) they found thatthe microvascular pressure in the tumor was lower than in thenormal subcutis. There were many tumor vessels with pressureless than 4 mm Hg. When the mean arterial pressure waselevated from 100 to ISO mm Hg with a continuous infusionof angiotensin II, RBC velocity and diameter of tumor vesselsincreased without an increase in normal tissue. These resultsmay explain increased efficacy of cancer chemotherapy due toangiotensin II.

Endrich and Hammersen (165) have measured microvascularpressure in A-Mel-3 amelanotic melanoma grown in the dorsalskin chamber in hamsters at 30"C, 35Â°C,and 42.5'C. At 30Â°C

their microvascular pressures were significantly higher thanthose measured by Peters et al. (53) (Table 6). As temperaturewas increased precapillary pressures decreased while ventilarpressure increased. These reductions in arteriolar-venular pressure gradients are in agreement with simultaneous flow reduction in this tumor during hyperthermia.

D. Summary

Microvascular pressures in the arterial side are nearly equalin tumor and nontumorous vessels. Venous pressures on theother hand in tumors are significantly lower than those innontumorous tissue. Decreased pressure in venular vessels,

which are numerically dominant in a tumor, and increasedinterstitial fluid pressure may (a) reduce extravasation of fluidand solute molecules in tumors (see Ref. 5 for details); and (b)cause flow stasis and hypoxia in tumors. The reason(s) for lowtumor microvascular pressure is not completely understood.Possible causes include: (a) increased number of vessels intumors; (b) tortuous nature of tumor vessels; and (c) increasedviscous resistance in tumors. Understanding the precise role ofeach of these geometric and rheological factors would help inmodifying blood flow and transport of molecules in tumors.

V. Conclusions and Future Perspective

The tumor microcirculation is heterogeneous both temporally and spatially. The objective of this review article was tosummarize critically current understanding of the parameterswhich are responsible for the heterogeneity in blood flowthrough this circulatory network. Various experimental andtheoretical approaches to quantify these parameters were discussed. The unresolved problems were pointed out throughoutthe text in hopes of stimulating multidisciplinar}- research in

this area. The data available in the literature suggest that thereare significant differences in the perfusion pressures and viscousand geometric resistances between normal and neoplastic tissues, between two locations within the same tumor, and at thesame location at different times. Evidence that microvascularpressure is low in transplanted tumors is direct and convincing.Evidence that viscous and geometric resistances in tumors areincreased is indirect and must be proven quantitatively. Recentdevelopments in the microvascular technology as well as non-invasive imaging have the potential of allowing the assessmentof these parameters.

In the author's opinion, the key unanswered questions in this

area of research are: (a) What is the intratumor viscosity? Howdoes it change with tumor size, type, and location within thetumor. How does it differ from that in the host tissue? Can thedifference be explained on the basis of number, size, and rigidityof cells in blood; plasma viscosity; and vascular geometry? (b)What is the geometric resistance of a tumor? How does itchange with tumor size, type, and location? How is it relatedto the geometry of the vascular network? (c) How do the threeparameters (A/7. Z, and >;)respond to various physical (e.g.,radiation, heat, photodynamic therapy, hemodilution) andchemical (e.g., vasoactive drugs) stimuli? Are the mechanismsof tumor blood flow modification different from those of normal tissues? (</) How different are the three determinants ofblood flow in human tumors from those for transplanted tu-

2655



TUMOR BLOOD FLOW

mors? What key parameters are needed to predict the hemo-

dynamic response of human tumors?The need to answer these questions is urgent for improving

detection and treatment of tumors.

Acknowledgments

I wish to express my sincere gratitude to Dr. P. M. Cullino for hispioneering work in the pathophysiology of tumors and to my formerand current students who have contributed in many ways to the researchon blood flow in tumors. I also appreciate the helpful comments ofDrs. S. Chien, W. Dewey, H. Eddy, G. Hahn, M. Â¡maglietta, H.Lipowsky, H. Reinhold, and P. Vaupel. I would like to acknowledgethe skillful assistance of D. Bigos and D. Dlugokecki in typing thismanuscript.

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2. Chein, s.. Usami, S., and Skalak, R. Blood flow in small tubes. In: E. M.Renkin and C. C. Michel (eds.). Handbook of Physiology, Sect. 2, Vol. 4,Chap. 6, pp. 217-250. Bethesda, MD: American Physiological Society,1984.

3. Zweifach, B. W., and Lipowsky. H. H. Pressure-flow relations in blood andlymph microcirculation. In: E. M. Renkin and C. C. Michel (eds.), Handbook of Physiology, Sect. 2, Vol. 4, Chap. 7, pp. 251-308. Bethesda, MD:American Physiological Society, 1984.

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7. Vaupel, P., and Hammersen, F. (eds.). Mikrozirkulation in malignen Tumoren, In: Progress in Applied Microcirculation, Vol. 2. Basel: S. Karger,AG, 1983.

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1963.13. Hammersen, F., Osterkamp-Baust. V., and Endlich, B.: Ein Beitrag zum

Feinban terminaler Strombahnen und ihrer Entstehung of bÃ¶sartigenTumoren. Mikrozirk. Forsch. Klin., 2: 15-51, 1983.

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15. Solesvik, O. V., Rofstad, E. K., and Brustad, T. Vascular structure of fivehuman malignant melanomas grown in athymic nude mice. Br. J. Cancer,46:557-567, 1982.

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