Localization ofAtheroma:A Theory Based Boundary …As boundary-layer separation is a fric-tional...

Brit. Heart J., 1966, 28, 388.

Localization ofAtheroma: A Theory Based on BoundaryLayer Separation

J. A. FOX AND A. E. HUGH*From the Department of Civil Engineering, University of Leeds, and The North Staffordshire Royal Infirmary,

Stoke-on-Trent

Current reports of research into the problem ofatheroma deal largely with abnormalities and peculi-arities of lipid metabolism. As atheromatousplaques are rich in lipids, and can be produced inmost experimental animals by a high cholesteroldiet, it is reasonable to suppose that atheroma andlipid metabolism are related. There will, however,be some disagreement with Hess (1964) who statedthat " atherosclerosis is now rather generally acceptedto be a disorder of lipid metabolism", becausethere are several features of the disease that are notexplained in terms of lipid disturbance.The main alternative theory is that atheroma is

the result of intravascular clotting or thrombosis.This was originally expounded by Rokitansky in apaper in 1844, and it has been supported by severalauthors since, in particular by Duguid (1955) andOsborn (1963) in this country. The two theoriesmentioned have appeared to compete with oneanother for acceptance, and it has not hitherto beenpossible to suggest a way in which they might berelated.The development of atheroma is undoubtedly

related to hypertension as well as to lipid disturbance(Corcoran et al., 1956; Schettler, 1961). Twoexplanations of this relationship have been offered:Masson et al. (1958) believed that hypertensionproduced widespread vascular damage which facili-tated lipid deposition, while Page (1954) suggestedthat hypertension would lead to an increasedtransarterial filtration of some of the contents of thecirculating fluid, either plasma lipids (Page) orprotein (Duncan, Cornfield, and Buck, 1962),which would initiate the local formation ofatheroma.Any explanation of atheroma must account for

Received June 23, 1965.

*Formerly at the Department of Radiodiagnosis, Universityof Leeds.

388

the focal nature of the lesions and their predilectionfor certain areas of the arterial system, notablycurved segments and the mouths of branch vessels.Though local mechanical strain was for long believedto account for this, the alternative view, that flowdisturbances would affect these areas, has receivedmore recent support (Texon, 1960; Mitchell andSchwartz, 1965). Whereas Texon believed thatthe intima might become "sucked off" the mediadue to the generation of low pressures within thelumen by local velocity alterations, the latter supportthe concept that atheroma is due to thrombosis,precipitated by local turbulence, which woulddamage either the wall itself or the constituents ofthe blood.The use of the term "turbulence" implies that

extra motion is being generated; it is conventional tobelieve, however, that thrombosis or clotting isfacilitated by stasis rather than by excessive move-ment, and it is doubted whether turbulence itselfis the cause of intra-arterial thrombus formation.

It has not been widely believed that zones ofstasis might occur in the arterial system. In a fluidsystem, however, it is possible for well-definedstatic zones to form despite quite high velocitiesnear-by, due to a process known as "boundarylayer separation". There is a striking similaritybetween the regions where this occurs and the sitesof predilection of atheroma. We believe that staticzones occur in the arterial system, which might allowthe interaction of platelets and fibrin to form a meshin which lipid particles become trapped, and thatthis becomes organized to form a plaque ofatheromaas envisaged by Duguid.The process of boundary layer separation and the

factors that influence it are described, and it will besuggested how a number of the factors that areknown to be related to atherogenesis might affectthis process. This enables a link to be suggested

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Localization of Atheroma

between the "lipid" and the "thrombotic"theories previously mentioned, and it may well forma basis for a rational approach to the preventionif not the treatment of the disease.

THE BoUNDARY LAYERWhen flow occurs over any surface, the fluid

adjacent to it is brought to rest because of thefrictional stresses exerted upon the fluid by thesurface. Layers further from the surface alsohave their velocity reduced by these stresses, thereduction being less the further the layer is situatedfrom the boundary. A typical velocity distributionproduced in this manner is shown in Fig. 1.The boundary layer thickness is usually assumed

to be equal to that distance from the boundary atwhich the local velocity 'u' equals 0 99U, where 'U'is the undisturbed stream velocity.

In a pipe (i.e. a flat boundary rolled into acylinder), the boundary layers formed at dia-metrically opposite walls meet at the centre line, andthe entire flow is a type of boundary layer flow(except at the entrance of the pipe). In boundarylayers, flow may be either laminar or turbulent innature. If laminar, the velocity distribution isparaboloidal, but if turbulent, the velocity distribu-tion is of an approximately exponential form (moreaccurately, logarithmic).Due to these variations in velocity, the fluid near

the boundary has low momentum, but the fluid

a

FIG. 1.-Velocity distribution in a boundary layer.

momentum increases rapidly towards the centreof the pipe.

Boundary Layer Separation. Due to its momen-tum, it is possible for fluid to pass from a region oflow pressure into a region of higher pressure (i.e.against a positive pressure gradient). The fluidnear a boundary, having low momentum, mayrapidly be brought to rest under the action of such agradient; beyond this stagnation point, its flow willbe reversed (Fig. 2).

Because of this reversal near the boundary, asurface forms over which there is no fluid velocity.This is the surface of separation, on one side ofwhich the reversal effects result in the formation of

BOUNDARY

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LAYER FLOW

SEPARATION

SEPARATION ZONE

POINT

b Px

x 2FIG. 2.-(a) Shows the surface of separation and stagnation point of a separated boundary layer and (b) shows

the positive pressure gradient that caused the separation.

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FIG. 3.-Boundary layer separations at divergent duct.

vortices adjacent to the boundary. On the otherside, the boundary layer, now separate from thewall, continues its forward motion. Near the walljust beyond the stagnation point the fluid velocitiesare extremely low, and this allows prolonged con-tact between the fluid (and its constituents) and theboundary. (This is not a steady process; the sur-face of separation oscillates due to a type of feed-back mechanism.)

Positive pressuregradients can occur (1) in a diver-gent channel; (2) in a bend; and (3) at a junction.

(1) Divergent Channels. To maintain continuityof flow, average flow velocities must decrease in the

direction of flow (Fig. 3). The energy lost asvelocity energy is partly converted into pressureenergy (some is lost in turbulent friction). Pro-vided that frictional losses are not excessive, thisprocess can produce a positive pressure gradient,and if this is sufficiently large the boundary layerwill separate as illustrated (Fig. 3). If the positivepressure gradient is not large enough, the boundarylayer will not separate, but the velocity profile willbe distorted (Fig. 4).

(2) Curves and Bends (Fig. 5). For flow in acurved path, a force must act in a direction towardsthe centre of curvature of the flow. Neglectingfriction, the pressure in the straight entry section

SURFACE OF

FIG. 4.-Boundary layer just not separating as positivepressure gradient is not large enough. FIG. 5.-Boundary layer separations at bends.

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and in the straight exit section will be the same,i.e. PO, and uniform across the vessel cross-section.At point B the pressure PB will be greater than

PO, and at C it will be less than PO, so that thecentrally directed force necessary to cause curvi-linear motion can be produced.The pressure gradients from A to B and C to D

must thus be positive, and boundary layer separa-tions will, therefore, occur at these sections asillustrated in Fig. 5.

(3) Junctions. Referrring to Fig. 6, if section 2 isof the same cross-sectional area as section 1, theaverage velocity at section 2 will be less than atsection 1, because of the outflow through the branchvessel. By a similar argument to that used in con-sidering the divergent vessel problem, the lowervelocity at section 2 implies a higher pressure therethan at section 1. Slowly-moving fluid near theboundary will tend to have its forward motionreversed if this pressure rise is sufficiently great.The boundary layer on the branch side of the mainvessel will be carried off through the branch, buton the opposite wall the boundary layer will befully exposed to the reversing effect of the pressurerise, which may result in its separation from thewall (see separation A in Fig. 6).At the mouth of the branch vessel, the fluid has

to travel in a curved path; the pressure at the up-stream edge of the mouth falls to provide the neces-sary centrally-directed force required to maintainthis curved path. Further along the branch, wherethe flow is not curvilinear, there will be no transversepressure gradient. This reversion to a uniformpressure distribution creates a positive-pressuregradient along the upstream wall of the branch, andthis is a potent cause of boundary layer separationin this region.

It is thus seen that where a branch vessel isgiven off, there are two possible sites for boundarylayer separation, i.e. in the main vessel oppositeand slightly downstream of the axis of the branch,and at the proximal portion of the branch itself.The forces that cause separation aremuch stronger inthe latter.The above principles apply not only to the case of

the right-angled branch but also to junctions ofdifferent geometry, including the case of a majorvessel dividing into two branches of equal size,provided that the total area of flow increases at suchjunctions.

Motion within Separation Zone; Effect of ReynoldsNumber. As boundary-layer separation is a fric-tional phenomenon, it must be controlled by the

Reynolds number of the flow. If the frictionalstresses in the fluid are great in relation to itsmomentum, then the reverse velocities will be low,i.e. vortex formation will be weak, and the fluid inthe separation zone will tend to stagnate. Con-versely, if momentum effects dominate the motion,the separated zone will be in a strongly turbulentstate.This ratio of momentum effects to frictional

effects is in fact Reynolds number,

Re = vd v = velocityv d= diam. vessel.

v = coeff. kinematic viscosity.

STAGNATION POINTS

N 1\ SECTION

I IE

FIG. 6.-Boundary layer separations at junctions.

Flows with low Reynolds numbers have verystagnant separation zones, and flows with highReynolds numbers have very turbulent separationzones. The factors that cause low Reynoldsnumbers are low velocity, small diameter, and highviscosity (see expression).

EXPERIMENTAL DEMONSTRATION OF PHENOMENAIt was decided to demonstrate the phenomena

described above by using free surface flows inwhich separations can be demonstrated with greaterease than in bounded flows.An Ahlborn tank was used in these experiments.

This consists of a glass sheet over which sheet flowsof water can be produced of any depth and velocityrequired. Various channel configurations wereproduced by using strips of aluminium sheet bentto suitable shapes (see Fig. 7-11).

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Localization of Atheroma 393

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FIG. 11.-At a curved segment, static zones form on opposite walls as shown.

Fine aluminium powder scattered over the watersurface was used to reveal the flow patterns,and tofacilitate the photography of these patterns.A wide range of flow velocities was investigated

and the theoretical points made in this paper wereverified and demonstrated (Fig. 7-11).

It may be felt that an investigation of thephenomena using open channel flows instead ofbounded flows renders the experimental workinvalid when applied to bounded flows. As surfacewaves were avoided this possible criticism would notbe applicable. The photographs give a picturerepresenting a longitudinal section through thebounded flow problem, i.e. they give a two-dimensional section through a three-dimensionalflow.

DISCUSSIONThe striking similarity between the areas at

which atheroma is commonly found, and thosewhere the occurrence of boundary layer separationis predicted, leads to strong suspicions that thereis a causal relation between the two processes. Thestagnant or low velocity areas due to the separa-tion of the boundary layer permit intravascularaggregation, leading to a variety of clotting (Dinten-fass, 1964b); organization of the solid material orthrombus would follow, resulting in the formationof an atheromatous plaque.As boundary layer separation, and therefore

stasis, occurs regularly at junctions, even in health,it is possible that deposition begins for two

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separate reasons. Either abnormal constituentsappear in the circulating fluid, such as excessivelyadhesive platelets which permit formation of anidus on the vessel wall, which encourages a fibrinmeshwork to develop even in the presence ofnormalamounts of fluid stasis; or, excessive intravascularstasis, due to more marked boundary separation,allows even normal blood constituents to adhere tothe vessel wall. In either case the precise nature ofthe deposit would be determined both by the localshear rate, and by the composition of the circulatingfluid. It would be expected that a considerableamount of cholesterol would become enmeshed inthe fibrin network if the circulating blood werecholesterol rich, but in neither of the circumstancespostulated would an excess of cholesterol be neces-sary to initiate the process of deposition.Although well-defined static zones would be likely

at arterial mouths at all times, it is thought that inthe healthy state the zone would be small and that itwould oscillate, both as a natural consequence ofthe instability of the separation process, and be-cause of physiological fluctuations in flow rates fromtime to time. These would counteract anytendency to deposition of normal blood contents.Reversal of flow, due to pulsatility, causes boundarylayers to form on opposite walls of branch mouthsin turn; this might result in the formation of twoareas of deposition, or alternatively, could have acleansing effect on the major site of stasis, so reduc-ing the tendency to deposition and the chance oforganization.From the factors known to control the process of

boundary layer separation, it can be predicted thatconditions that would give rise to a larger morestably-located area of stasis would be locally reducedvelocity and increased blood viscosity. Each ofthese might become of pathological significance.

In the absence of abnormally-adhesive circulat-ing particles it is possible that variations in viscositymight be the key to atheromatous development.There are considerable practical difficulties in the

accurate measurement of blood viscosity, whichprevent this being done as a routine. Severalviscometers are available (Harkness, 1963) but noin vivo technique has been devised. Dintenfass hasdescribed (1964b) a technique for the fairly rapidestimation of viscosity of blood removed from thecirculation, which enables the estimation to becarried out without the need for anticoagulants,but this has yet to be widely adopted. It is foundthat the thixotropic nature of blood necessitates theemployment of a constant rate of shear before com-parisons can be made; even this does not provide astandard for comparison with intravascular condi-tions where shear rates alter constantly.

The evidence available suggests that widevariations in blood viscosity are possible, in variouspathological states, such as congestive failure andcoronary disease (Dintenfass, 1964a). One of themost potent causes of an alteration in viscosity isthe haematocrit value, especially at high shear rates.High hsemoglobin values will be associated withhigher viscosity ranges; possibly related to the re-duced viscosity of anaemia is the low incidence ofocclusive vascular disease in premenopausal women(after the menopause the incidence is similar to thatin men). Whether the cholesterol (and other fat)level of serum has any influence on viscosity isuncertain (Shinagawa, 1964). It is possible thathigh levels of cholesterol initiate excessive boundarylayer separation by increasing blood viscosity, andthat its excessive local deposition is only a secondaryphenomenon.The recent finding that a high sugar consumption

may increase the atheromatous tendency (Yudkinand Roddy, 1964) may have its basis in an alterationof plasma viscosity following a high sugar intake.The alteration in viscosity of water when sugar isadded is well known, but the effect on plasma vis-cosity of comparatively small alterations in bloodsugar has not, to our knowledge, been investigated.This theory offers a simple alternative to the previousone postulating a defect of the whole metabolicstate of the organism.

If this theory is correct, then the effect of otherfactors that alter viscosity may be predicted, re-garding their atherogenic potency. An increase inviscosity will give rise to an increase in the stabilityof the stagnant zone, and will tend to increase itssize.From the effect of Reynolds number on boundary

layer separation it would be expected that alterationsin flow velocities would have similarly predictableconsequences. Factors that are thought to have animportant bearing on the development of atheromaare stress and exercise. The effect of exercise onthe circulation is to increase flow volumes; in effect,this is an increase in flow velocity. The structuresmost likely to be affected by exercise are the heartand the legs (considering "exercise" in its usuallyaccepted meaning). Even if there was an increasedtendency to stagnant deposition in arteries becauseof viscosity alterations, regular and fairly frequentincreases of flow rates as a result of exercise wouldintroduce violent turbulence into the static areas,resulting in clearing of any recently accumulatedloosely-attached debris.One of the regions where this would be less likely

is in the cerebral circulation, where the peripheralresistance is thought to be constant, and flow ratesless variable than elsewhere in the body. Cerebral

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vascular disease is much less a disease of thesedentary than is coronary disease, but appears tohave a relation to polycythaemia (J. A. Acheson,personal communication, 1965) where serum vis-cosity would be raised.The effect of "stress" on circulatory flow rates is

much less predictable. Presumably, stress resultsin increased liberation of adrenaline, which in turnproduces constriction of small vessels, with itstendency to increase blood pressure, etc. A similarvasoconstriction, produced as a result of a less clearlydefined stimulus, possibly of renal origin, is thoughtto be the cause of essential hypertension. Such avasoconstriction, especially if of unequal amount indiffering parts of the body, could have a markedeffect at the mouths of the larger vessels, due to thealteration of pressure gradient in these places.As boundary-layer separation is very closely

governed by the actual size and shape of vascularbranches, it is wondered whether a process similarto atheromatous development is responsible for theadjustment of arterial size to local flow demands.Osborn (1963) cited examples of apparent athero-matous change in the vessels of infants and smallchildren, and it was suggested (Hugh and Fox,1963) that this might be a physiological process ofadjustment rather than a pathological one. Oneof the ways of providing a system free of boundarylayer separation zones is to adjust the calibre ofbranches to suit the amount of flow within them.Even if this were done for any particular flow state,then an alteration in the amount of flow would alterthe conditions. In the body, in health, flow ratesvary constantly, because of pulsatility and variationsin physiological requirements (shunting of blood invarious areas because of exercise, taking food,sleep, etc.).

Attention has recently been drawn (Ross Russell,1963) to the occurrence of micro-emboli in relationto arterial stenoses, in particular to those found at theorigin of the internal carotid artery. The emboliformed may have a varying composition (David,et al., 1963). The phenomena related to theseemboli have for some time been thought to be simi-lar to those which can herald the onset of a majorcerebral catastrophe ("stuttering" onset of a hemi-plegia). Similarly, small areas of infarction areknown to occur distal to a renal artery stenosis.Once a stenosis forms in an artery, the velocity

of flow across it will increase and prevent a rapidbuild up of further deposits. Immediately beyondthe stenosis, however, where the flow profile expands,there will be areas of quite marked stagnation, andthe formation of deposits will be facilitated, if otherconditions are suitable (platelets, fibrin, andcholesterol, etc.). Once deposits reach a critical

size they produce their own effect on flow. Asboundary layer separation is an unsteady oscillatingphenomenon, the instability promotes detachmentof any loosely attached particles. If these areaggregates of blood constituents they may besufficiently integrated to pass on without breakingup to become lodged in the appropriate distalvessel.The absence of atheroma in the venous system

may also be explained by this hypothesis. Bound-ary layer separation, and stasis zones, occur wherearterial branching produces a net increase in thearea of flow. In the venous system, the junction ofveins results in a corresponding reduction in flowarea, so that velocities will tend to increase, thuspromoting the stability of the boundary layer andreducing the likelihood of zones of stasis.One of the major abnormalities arising from this

hypothesis as a possible cause of atheroma is altera-tion in blood viscosity, and it is suggested that moreattention be given to measuring this; the develop-ment of suitable techniques which give results thatindicate intravascular conditions will probablyrequire a large part of the effort. When suitabletechniques are available, they should be directednot only to the patients who already exhibit signs ofatheromatous development, but to those in whomsuch development is likely, together with a suitable"control" population. A study of the effect onblood viscosity of varying contents of cholesterol,sugar, etc., might be the most rapid means of con-firming this theory, which could lead to a re-orientation of thought and investigation into theproblem of atheroma.

SUMMARY

The coincidence between the sites where atheromacommonly forms and the zones where in a flowsystem local stasis is produced due to boundarylayer separation appears to support the view thatatheroma is due to a process of deposition, or throm-bosis, from the circulating blood.

This paper considers the factors controllingboundary layer separation, and presents pictures offlow experiments carried out to confirm the locationof the zones of stasis produced by the separation.Some of the factors known to be related to athero-

genesis are considered from the way in which theymight affect the process ofboundary layer separation.The viscosity of the circulating fluid is suggestedto be the probable main factor controlling thedeposition of atheroma; and further investigation ofthe effect on viscosity of various blood constituentsappears desirable.

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We wish to thank Professor R. H. Evans, Departmentof Civil Engineering and Professor A. S. Johnstone,Department of Radiodiagnosis, both of the Universityof Leeds, for their encouragement of the collaborationwhich led to this paper.

Dr. R. Y. Keers kindly read the original manuscript,and we are indebted to him for his helpful criticism andadvice.

REFERENCESCorcoran, A. C., Lewis, L. A., Dustan, H. P., and Page, I. H.

(1956). Atherosclerotic complications in hypertensivedisease. Ann N.Y. Acad. Sci., 64, 620.

David, N. J., Klintworth, G. K., Friedberg, S. J., and Dillon,M. (1963). Fatal atheromatous cerebral embolismassociated with bright plaques in the retinal arterioles.Neurology (Minneap.), 13, 708.

Dintenfass, L. (1964a). Rheologic approach to thrombosisand atherosclerosis. Angiology, 15, 333.

- (1964b). A trolley viscometer for estimating viscosityand clotting of blood in hospital wards. Lancet, 2,567.

Duguid, J. B. (1955). Mural thrombosis in arteries. Brit.med. Bull., 11, 36.

Duncan, L. E., Cornfield, J., and Buck, K. (1962). Theeffect of blood pressure in the passage of labeled plasmaalbumin into canine aortic wall. J. clin. Invest., 41,1537.

Harkness, J. (1963). A new instrument for the measurementof plasma-viscosity. Lancet, 2, 280.

Hess, R. (1964). Evaluation of drugs active against experi-mental atherosclerosis. In Advances in Lipid Research,ed. R. Paoletti and D. Kritchewsky, Vol. 2, p. 295.Academic Press, New York.

Hugh, A. E., and Fox, J. A. (1963). Hypotensive anes-thesia. Lancet, 2, 247.

Masson, G. M. C., McCormack, L. J., Dustan, H. P., andCorcoran, A. C. (1958). Hypertensive vascular diseaseas a consequence of increased arterial pressure. Amer.J. Path., 34, 817.

Mitchell, J. R. A., and Schwartz, C. J. (1965). ArterialDisease. Blackwell Scientific Publications, Oxford.

Osborn, G. R. (1963). The Incubation Period of CoronaryThrombosis. Butterworth, London.

Page, I. H. (1954). Atherosclerosis (Lewis A. ConnorMemorial Lecture.) Circulation, 10, 1.

Rokitansky, C. (1844). Handbuch der pathologischen Ana-tomie. Braumuller, Vienna. See A Manual of Patho-logical Anatomy transl. Geo. E. Day,.(1852), Vol. 4,pp. 261-272. Sydenham Society, London.

Ross Russell, R. W. (1963). Atheromatous retinal embol-ism. Lancet, 2, 1354.

Schettler, G. (1961). Arteriosklerose. Thieme, Stuttgart.Shinagawa, T. (1964). Studies on atherosclerosis, mainly

about its relationship with serum viscosity. Jap. Circu-lat. J., 28, 324.

Texon, M. (1960). The hemodynamic concept of athero-sclerosis. Bull. N.Y. Acad. Med., 36, 263.

Yudkin, J., and Roddy, J. (1964). Levels of dietary sucrosein patients with occlusive atherosclerotic disease.Lancet, 2, 6.

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