effect of exercise on hemodynamic conditions in the

1077

BASIC RESEARCH PAPERS

Exercise has numerous overall health benefits.Exercise improves cardiorespiratory fitness levels andlowers all-cause and cardiovascular mortality rates.1-5

The fitness benefits of exercise include increased car-diovascular functional capacity, increased maximal car-

diac output, increased extraction of oxygen from theblood, and decreased myocardial oxygen demand.5Recent studies have noted that increased fitness levels,as measured with maximal exercise treadmill tests, canresult in up to a three-fold decrease in mortality rate.3

In spite of the numerous studies on the overallbenefits of exercise, the mechanism by which exerciseimproves arterial health and the intensity and dura-tion of exercise needed to achieve benefit have notbeen determined. It is postulated that the mechanismby which exercise reduces vascular disease is a resultof direct and indirect causes. Direct causes are thosethat occur while exercise is being performed and endon the cessation of exercise. Hemodynamic factors,such as increased shear stresses and removal of lipid

Effect of exercise on hemodynamicconditions in the abdominal aortaCharles A. Taylor, PhD, Thomas J.R. Hughes, PhD, and Christopher K.Zarins, MD, Stanford, Calif

Purpose: The beneficial effect of exercise in the retardation of the progression of cardio-vascular disease is hypothesized to be caused, at least in part, by the elimination ofadverse hemodynamic conditions, including flow recirculation and low wall shear stress.In vitro and in vivo investigations have provided qualitative and limited quantitativeinformation on flow patterns in the abdominal aorta and on the effect of exercise on theelimination of adverse hemodynamic conditions. We used computational fluid mechan-ics methods to examine the effects of simulated exercise on hemodynamic conditions inan idealized model of the human abdominal aorta.Methods: A three-dimensional computer model of a healthy human abdominal aorta wascreated to simulate pulsatile aortic blood flow under conditions of rest and graded exer-cise. Flow velocity patterns and wall shear stress were computed in the lesion-proneinfrarenal aorta, and the effects of exercise were determined.Results: A recirculation zone was observed to form along the posterior wall of the aortaimmediately distal to the renal vessels under resting conditions. Low time-averaged wallshear stress was present in this location, along the posterior wall opposite the superiormesenteric artery and along the anterior wall between the superior and inferior mesen-teric arteries. Shear stress temporal oscillations, as measured with an oscillatory shearindex, were elevated in these regions. Under simulated light exercise conditions, a regionof low wall shear stress and high oscillatory shear index remained along the posterior wallimmediately distal to the renal arteries. Under simulated moderate exercise conditions, allthe regions of low wall shear stress and high oscillatory shear index were eliminated.Conclusion: This numeric investigation provided detailed quantitative data on the effectof exercise on hemodynamic conditions in the abdominal aorta. Our results indicatedthat moderate levels of lower limb exercise are necessary to eliminate the flow reversaland regions of low wall shear stress in the abdominal aorta that exist under resting con-ditions. The lack of flow reversal and increased wall shear stress during exercise suggesta mechanism by which exercise may promote arterial health, namely with the elimina-tion of adverse hemodynamic conditions. (J Vasc Surg 1999;29:1077-89.)

From the Division of Vascular Surgery (Drs Taylor and Zarins),Department of Surgery, and the Division of Mechanics andComputation (Drs Taylor and Hughes), Department ofMechanical Engineering, Stanford University.

Reprint requests: Dr Charles A. Taylor, Assistant Professor,Division of Vascular Surgery, Stanford University MedicalCenter, Suite H3600, Stanford, CA 94305-5450.

Copyright © 1999 by the Society for Vascular Surgery andInternational Society for Cardiovascular Surgery, NorthAmerican Chapter.

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molecules from the vessel luminal surface, are exam-ples of potential direct mechanisms by which exercisereduces vascular disease. Increased shear stressincreases nitric oxide and prostacyclin release andinhibits atherosclerotic processes.6 Indirect causeswould be triggered by the onset of exercise andwould presumably continue on cessation of exercise.These causes would, in general, be systemic andunrelated to the local changes in the hemodynamicenvironment. The effect that exercise has on control-ling lipid abnormalities, diabetes, and obesity, onlowering blood pressure, on altering lipid and carbo-hydrate metabolism, and on increasing high-densitylipoproteins would be examples of indirect mecha-nisms by which exercise reduces vascular disease.

Recommendations on exercise intensity andduration have traditionally been made on the basis ofimproving cardiorespiratory fitness. In the AmericanCollege of Sports Medicine’s (ACSM) 1990 positionstand on exercise, it was recommended that, todevelop and maintain cardiorespiratory fitness, adultsshould train 3 to 5 days per week at 60% to 90% ofmaximum heart rate (HRmax) or at 50% to 85% ofmaximum oxygen uptake for 20 to 60 minutes withlarge muscle groups (eg, lower limb exercise, such asrunning and bicycling).1 The levels of exercise werecategorized after Pollack and Wilmore7 in the fol-lowing manner: very light exercise was defined as lessthan 35% of HRmax, light exercise was defined as 35%to 59% of HRmax, moderate exercise was defined as60% to 79% of HRmax, heavy exercise was defined as80% to 89% of HRmax, and very heavy exercise wasdefined as more than 90% of HRmax. Clearly, the rec-ommendations of the ACSM 1990 position standreflect moderate to heavy exercise conditions.

The ACSM recommendation distinguishedbetween exercise for fitness (the ability to performmoderate to vigorous levels of physical activity with-out undue fatigue and the capability of maintainingsuch activity throughout life) and the effect of exer-cise on the reduction of cardiovascular disease. It wasnoted that “…lower levels of physical activity thanrecommended by this position statement may reducethe risk for certain chronic degenerative diseases andyet may not be of sufficient quantity or quality toimprove maximum oxygen uptake.”1 Recent publichealth recommendations have reinforced this viewthat, for overall health benefits, individuals shouldengage in, at the least, moderate levels of physicalactivity in lieu of a regular exercise program.2

In addition to causing systemic changes in thecardiovascular system, exercise conditions have alocal effect on blood flow in the major arteries. For

example, in vivo and in vitro models have shown thatthe hemodynamics of the infrarenal abdominal aortaare characterized by regions of complex recirculatingflow under resting conditions8-15 and further thatthese regions of flow recirculation are not observedunder lower limb exercise conditions.16-18 Clearly, toexamine the effect of graded exercise on hemody-namic conditions in the abdominal aorta, detailedquantitative data on flow conditions are necessary.

In recent years, computational techniques havebeen used increasingly by researchers who seek tounderstand vascular hemodynamics.19-24 These meth-ods can augment the data provided by in vitro and invivo methods by enabling a complete characterizationof hemodynamic conditions under precisely con-trolled conditions. In contrast to the relatively largenumber of studies of pulsatile flow in models of thecarotid bifurcation and end-to-side anastomosis,there have been few numeric studies of flow in theabdominal aorta. Taylor et al25 described the flow inan abdominal aorta model under simulated restingand exercise steady flow conditions. It was noted thata region of flow recirculation and low wall shear stressdevelops along the posterior wall of the infrarenalabdominal aorta under simulated resting conditionsand disappears under simulated exercise conditions.Taylor et al26,27 described, qualitatively, the pulsatileflow in a model of an abdominal aorta under simulat-ed resting and exercise conditions. As in the steadyflow case, a flow recirculation region was noted atmid diastole in the infrarenal abdominal aorta undersimulated resting conditions and disappeared underexercise conditions. Taylor et al28 detailed, quantita-tively, the hemodynamic conditions under simulatedresting pulsatile flow conditions in an idealized modelof an abdominal aorta. The flow velocity patterns andspatial variations of mean wall shear stress and oscilla-tory shear index were reported.

The computational method described herein wasused to quantitatively characterize the hemodynamicconditions under simulated resting, light exercise, andmoderate exercise pulsatile flow conditions in an ide-alized model of an abdominal aorta. The changes inthe flow velocity field, the spatial variations of wallshear stress, and the temporal oscillations of wall shearstress were described in detail, and the effect of exer-cise on abdominal aorta hemodynamics was deter-mined. We tested the hypothesis that simulated lowerlimb exercise eliminates hemodynamic conditions,such as flow recirculation, low mean wall shear stress,and temporal oscillations in shear stress, that arethought to be responsible for the localization of vas-cular disease in the infrarenal abdominal aorta.15,28

JOURNAL OF VASCULAR SURGERY1078 Taylor, Hughes, and Zarins June 1999

Further, we tested the hypothesis that light exerciseconditions are sufficient to eliminate regions of lowmean shear stress and high oscillatory shear index inthe infrarenal abdominal aorta.

METHODSA geometric solid model of an idealized abdom-

inal aorta, shown in Fig 1, was constructed with acustom software system, “The Stanford VirtualVascular Laboratory,” which was developed to aid inthe solution of blood flow problems.26,27 This sys-tem was developed with a knowledge-based, object-oriented programming language and combines geo-metric solid modeling, automatic finite elementmesh generation, multiphysics finite element meth-ods, and scientific visualization capabilities.29-33 Theanatomic dimensions of the idealized abdominalaorta model were obtained from Moore et al.10 Themodel constructed is not symmetric about the mid-sagittal plane but rather includes the feature that theleft renal artery is located inferior to the right renalartery. A finite element mesh with 268,563 tetrahe-dral elements and 58,151 nodes was generated withan automatic mesh generator.29

Approximately 70% of the blood that enters theabdominal aorta under resting conditions is extractedby the celiac, superior mesenteric, and renal arteries.Most of the remaining 30% flows down the infrarenalsegment through the bifurcation into the legs. Underlower limb exercise conditions, the total abdominal

aorta flow increases and, in addition, the amount ofblood extracted by the celiac, superior mesenteric,and renal arteries decreases, which further increasesthe infrarenal blood flow.34 The flow conditions aresummarized in Table I, and the mean flow distribu-tion is given in Table II. The values for resting andmoderate exercise conditions were obtained fromMoore et al,10 and light exercise conditions weretaken to be midway between these two states.

In contrast to steady flow studies, in vitro andcomputational studies of pulsatile blood flow neces-sitate the specification of flow waveforms and ofmean flow rates. The flow rates as a function of timeused in the present study for the inflow and branchvessels are shown in Fig 2. The flow rate waveformsshown in Fig 2 for the renal artery and iliac arteryare those for each of the right and left renal and iliacarteries, respectively. The suprarenal and infrarenalflow rate time functions and the celiac, superiormesenteric, renal, and inferior mesenteric mean flowrates were obtained from Moore and Ku.14,16 The

JOURNAL OF VASCULAR SURGERYVolume 29, Number 6 Taylor, Hughes, and Zarins 1079

Fig 1. Abdominal aorta model with branches identified.

Table I. Flow conditions

Light ModerateResting exercise exercise

Cardiac output (L/min) 4.5 6.0 7.5Heart rate (bpm) 66 100 133Abdominal aorta flow (L/min) 2.7 4.1 5.6

flow rate waveforms in the celiac, superior mesen-teric, renal, and inferior mesenteric arteries werecomputed to conserve mass and yield the mean flowrates given in Table II. Note that, under resting and

exercise conditions, the abdominal aorta inflow andrenal artery outflows are always positive, whereasunder resting conditions, the iliac flow waveformexhibits the triphasic character of in vivo measure-ments of infrarenal aortic flow. On the basis of thevolume flow waveforms shown in Fig 2, pulsatileflow velocity boundary conditions, derived fromWomersley theory, were prescribed for the inflowboundary and all outflow boundaries, excluding theleft and right iliac outflow boundaries, where zeropressure boundary conditions were prescribed.35 Itshould be noted that the Womersley boundary con-ditions are time-dependent, axisymmetric velocityprofiles at the inlet and outlet boundaries.

Computational modeling of blood flow necessi-


Table II. Mean flow distribution (L/min)

Light Moderate Artery Resting exercise exercise

Celiac 0.53 0.41 0.28Superior mesenteric 0.4 0.31 0.22Left renal 0.4 0.34 0.28Right renal 0.4 0.34 0.28Inferior mesenteric 0.13 0.09 0.06Left iliac 0.4 1.32 2.25Right iliac 0.4 1.32 2.25

Fig 2. Flow rate time functions. Note ordinate scales for each plot.

tates solving, in the general case, three-dimensional,transient flow equations in deforming blood vessels.The appropriate framework for problems of this typeis the arbitrary Lagrangian-Eulerian (ALE) descrip-tion of continuous media in which the fluid andsolid domains are allowed to move to follow the dis-tensible vessels and deforming fluid domain.36

The vessel diameter change during the cardiaccycle is observed to be approximately 5% to 10% inmost of the major arteries, and, as a first approxima-tion, the vessel walls are often treated as being rigid.In addition, in diseased vessels, which are often thesubject of interest, the arteries are even less compli-ant and wall motion is further reduced. The assump-tion of zero wall motion was used for the computa-tions presented herein. Under this assumption, theLagrangian-Eulerian description of incompressibleflow in a deforming fluid domain reduced to theEulerian description of a fixed spatial domain.

The strong form of the problem governingincompressible, Newtonian fluid flow in a fixeddomain consists of the Navier-Stokes equations andsuitable initial and boundary conditions. Direct,analytic solutions of these equations are not availablefor complex domains, and numeric methods must beused. The finite element method has been the mostwidely used numeric method for solving the equa-tions governing blood flow.37

The finite element method used in the presentinvestigation is based on the theory of stabilized finiteelement methods developed by Brooks and Hughes38

and Hughes et al.39 The method is described in detailby Taylor et al27,28 as it is implemented in the com-mercial finite element program, Spectrum.32. Thebasic idea is to augment the Galerkin finite elementformulation with a least-squares form of the residual,including appropriate stabilization parameters. Thesestabilization parameters are designed so that themethod achieves exact solutions in the case of one-dimensional model problems that involve, for exam-ple, the steady advection-diffusion equation. A semi-discrete formulation with a second-order accuratetime-stepping algorithm is used, which results in anonlinear algebraic problem in each time step. Thisnonlinear problem is linearized, and the resulting linear systems of equations are iteratively solved withconjugate gradient and matrix-free GeneralizedMinimal Residual solvers to reduce memory require-ments.40 Because the flow computations were per-formed on a parallel computer, the computationaldomain was divided into 16 subdomains with a graphpartitioning method.41 The nonlinear evolutionequations were solved for the velocity and pressure

fields over three cardiac cycles with 200 time steps percardiac cycle on an IBM SP-2 parallel computer(Somers, NY). The method used has been shown viaanalytic and experimental validation studies to yieldaccurate solutions for pulsatile flow problems.27

In addition to the velocity field, quantitative valuesof the magnitude of the surface tractions are also ofinterest. The traction vector (t) can be computed fromthe stress tensor (δ) and surface normal vector (n) bythe equation, t = δn, and then the surface traction vec-tor (ts), defined as the tangential component of thetraction vector, can be computed from ts = t – (t · n)n.

We can define the mean shear stress (τmean), ascalar quantity, as the magnitude of the time-aver-aged surface traction vector as

τmean = }T1

} E1

0tsdt

and define the absolute shear stress (τabs), anotherscalar quantity, as the time-averaged magnitude ofthe surface traction vector as

τabs = }T1

} ∫1

0 ts dt

After He and Ku,42 we define the oscillatoryshear index (OSI) as

OSI = }12

} 11 – }ττm

a

e

b

a

s

n}2Note that the surface traction is a vector quanti-

ty and thus includes the direction of the surfaceforce and its magnitude. The magnitude of the sur-face traction reduces to the wall shear stress, τw =4µQ/πr3, where µ is the viscosity, Q is the flowrate, and r is the lumen radius, in the special case ofthe steady, uniaxial flow of a Newtonian fluid in acircular cylinder. However, for complex, recirculat-ing, and time-dependent flow fields, such as thosethat occur in the abdominal aorta, the surface trac-tion is a more general and useful measure of surfaceforces than the relation for wall shear stress, τw,given previously.

RESULTSA contour slice of axial velocity and a vector slice

of the velocity field are displayed in Fig 3 under sim-ulated resting, light exercise, and moderate exerciseconditions at four times in the cardiac cycle alongthe midsagittal plane of the aorta. Note that underresting conditions a vortex developed along the pos-terior wall of the aorta. Under light exercise condi-tions, this flow recirculation region, while still appar-ent, had been reduced substantially in size. Under


moderate exercise conditions, this flow recirculationregion was absent.

Contour plots of time-averaged (mean) wallshear stress are displayed in Fig 4 along the posteri-or wall. Note that under resting conditions, regionsof low (<1 dyne/cm2) mean wall shear stress wereapparent along the posterior wall opposite the celiacand superior mesenteric arteries and below the renalartery branches along the lateral and posterior walls.Under light exercise conditions, a single region oflow mean wall shear stress was observed along the

posterior wall at the level of the renal arteries. Noregions of low mean wall shear stress were apparentunder moderate exercise conditions.

Mean wall shear stress is plotted as a function ofarc length in Figs 5 and 6 along the anterior andposterior walls, respectively. It was noted that, alongthe anterior wall, gaps in the plots of shear stress cor-responded to the location of the branch vessels. Itwas also observed that mean shear stress increasedsignificantly in the neighborhood of the celiac, supe-rior mesenteric, and inferior mesenteric vessels.


Fig 3. Midplane slice of abdominal aorta model that displays contours of axial velocity andvelocity vector field for (a) resting conditions, (b) light exercise conditions, and (c) moderateexercise conditions.

Under resting, light exercise, and moderate exerciseconditions, the mean shear stress along the anteriorwall in the distal infrarenal aorta exceeded the shearstress at the level of the diaphragm. It was observedthat under resting conditions the mean shear stressapproached zero along the posterior wall oppositethe celiac and superior mesenteric vessels andapproximately 2 cm distal to the left renal artery.Under light exercise conditions, a single region oflow mean wall shear stress appeared immediately dis-tal to the left renal artery. Under moderate exerciseconditions, no regions of low mean wall shear stresswere observed along the posterior wall of theabdominal aorta. It was also observed that under allflow conditions the mean shear stresses increased inthe distal infrarenal abdominal aorta to a level thatexceeded that at the level of the diaphragm.

The OSI is plotted as a function of arc length inFigs 7 and 8 along the anterior and posterior walls,respectively. Examination of the OSI along the ante-rior wall under resting conditions revealed a sharpincrease of the OSI from zero in the suprarenal aortato approximately 0.3 immediately distal to the leftrenal artery and then a gradual decline to a value ofapproximately 0.05 at the level of the aortic bifurca-tion. Under light exercise conditions, the OSI waszero along the anterior wall except for immediatelydistal to the left renal artery where it increased fromzero to approximately 0.05. Under moderate exerciseconditions, the OSI was zero along the anterior wallof the abdominal aorta. The OSI along the posteriorwall under resting conditions increased from zero inthe suprarenal aorta to approximately 0.4 oppositethe superior mesenteric artery, decreased to less than


Fig 4. Mean shear stresses for abdominal aorta model under (a) resting conditions, (b) lightexercise conditions, and (c) moderate exercise conditions.


Fig 5. Mean shear stress along anterior wall from diaphragm to aortic bifurcation.

Fig 6. Mean shear stress along posterior wall from diaphram to aortic bifurcation.


Fig 8. Oscillatory shear index along posterior wall from diaphragm to aortic bifurcation.

Fig 7. Oscillatory shear index along anterior wall from diaphragm to aortic bifurcation.

0.1 at the level of the renal arteries, increased to amaximum value of 0.47 distal to the renal arteries,and then decreased to a value of approximately 0.1 atthe level of the aortic bifurcation. Under light exer-cise conditions, the OSI along the posterior wallincreased from zero in the suprarenal aorta to approx-imately 0.45 at the level of the the left renal artery andthen decreased to less than 0.1 for the remainder ofthe infrarenal abdominal aorta. Under moderate exer-cise conditions, the OSI was zero along the posteriorwall of the abdominal aorta except for immediatelydistal to the renal arteries where it attained a value ofapproximately 0.05.

DISCUSSIONThe numeric method used to characterize

abdominal aorta hemodynamics enables the extrac-tion of complete spatial and temporal variations infield quantities, including velocity and shear stress,to quantitatively test hypotheses related to the effectof exercise on hemodynamic conditions. The signif-icance of the findings regarding the effect of exerciseon the velocity field and shear stresses is describedsubsequently, followed by an examination of theassumptions used in the present investigation.

Under resting conditions, a flow recirculationregion appeared along the posterior wall of theabdominal aorta in late systole and was presentthroughout diastole. This recirculation regionextended from the level of the renal arteries to theinferior mesenteric artery. This finding is consistentwith prior in vitro9,10,14 and in vivo8,11,18 studies offlow in the abdominal aorta. It should be noted,however, that the extent of the flow recirculationregion under resting conditions has not been report-ed previously because velocity measurements in theinfrarenal aorta have been restricted to, at most, afew cross sections.

The plots of shear stress and oscillatory shearindex along the anterior and posterior walls providequantitative data on the spatial variation of sheardown the length of the abdominal aorta. Under rest-ing conditions, the mean shear stress in the abdomi-nal aorta at the level of the diaphragm was calculatedto be approximately 1.2 dynes/cm2. Moore et al15

measured the shear stress at this location to be 1.3 ±0.6 dynes/cm2 in an in vitro study with approxi-mately the same flow conditions and model dimen-sions as those used in this study. Along the anteriorwall, the ostia of the celiac, superior mesenteric, andinferior mesenteric arteries are sites of relatively highmean shear stress and low oscillatory shear index forall flow conditions. As discussed subsequently, this isbelieved to be the result of an inadequate modeling

assumption, incorporated into the idealized model,whereby the junctures between the branch vesselsand the aorta are not smoothly tapered. Under rest-ing conditions, the anterior wall of the infrarenalaorta between the superior mesenteric and inferiormesenteric arteries was a site of low shear stress andhigh oscillatory shear index. Under light and moder-ate exercise conditions, the anterior wall of theabdominal aorta experienced mean shear stresses inexcess of that found at the level of the diaphragm.Along the posterior wall, under resting conditions,the mean shear stress was low and oscillatory shearindex high opposite of the superior mesenteric arteryand at approximately 2 cm distal to the left renalartery in the region noted for flow recirculation. Thedistal abdominal aorta below the inferior mesentericartery and proximal to the bifurcation is a site of rel-atively high mean shear stress and moderate values ofthe oscillatory shear index. Under light exercise con-ditions, a region of low mean wall shear stressremained, yet disappeared under moderate exerciseconditions. Although shear stresses were reported byMoore et al15 for two locations in the infrarenalabdominal aorta under resting conditions, the spatialdistribution of shear stress magnitude had not beenquantified previously.

As noted previously, vascular disease is moreprominent in the abdominal aorta as compared withthe thoracic aorta. The localization of early athero-sclerotic lesions was examined by Cornhill et al43 bystaining with Sudan IV and using image processingtechniques to identify sudanophilic lesions in thecadaveric aortas of young accident victims. It wasnoted that the highest probability of occurrence ofsudanophilia was associated with the inflow tracts ofthe celiac, superior mesenteric, renal, and inferiormesenteric ostia. In the present study, along the aor-tic wall, these ostia were not observed to be sites oflow mean shear stress under resting or exercise flowconditions, yet regions of low mean shear stress werenoted within the branch vessels. Again, note that themodel does not incorporate the tapering of thebranch vessels in the immediate vicinity of the ostia.

Cornhill et al43 also noted a region of high prob-ability of occurrence of sudanophilia along the pos-terolateral wall of the infrarenal aorta and along theanterior wall between the superior and inferiormesenteric arteries and concluded that these loca-tions were not “expected to experience unusualhemodynamic stresses.” The results presented here-in clearly show otherwise. Namely, under restingconditions, these regions experience low mean wallshear stress and high oscillatory shear index. Finally,Cornhill et al43 showed areas of high probability of


occurrence of sudanophilia along the posterior wallat the level of the celiac and superior mesentericarteries. As noted previously, under resting condi-tions, this is also a region of low mean wall shearstress and high oscillatory shear index. Clearly, directcorrelative studies need to be performed betweenhemodynamic conditions and plaque localization inthe abdominal aorta, but the results presented here-in show that under resting conditions, low meanwall shear stress and high oscillatory shear indexoccur in regions noted to have a high probability ofoccurrence of sudanophilic lesions.

The effect of exercise on the reduction of flowrecirculation, the increase of wall shear stress, andthe reduction of shear stress oscillations suggests onepossible direct benefit of exercise—namely, the elim-ination of hemodynamic conditions known to corre-late with the location of atherosclerotic plaques.45-47

Further, this study shows that light exercise does noteliminate all of the regions of low wall shear stressand high oscillatory shear index. An obvious ques-tion arises as to how a relatively short duration ofexercise could have a long-term effect on cardiovas-cular health through a direct mechanism becausethis mechanism would only be active for a small frac-tion of the entire day. It should be noted that therelationship between increased shear stress and inhi-bition of disease need not be a linear relationship—namely, a doubling of shear stress for a short dura-tion could have a substantial effect. Further, thedirect action of hemodynamic forces on the vesselwalls could trigger biochemical phenomena, whichwould act even beyond the cessation of exercise.This could be a result of the relationship betweenincreased shear stress on the endothelium andincreased nitric oxide and prostacyclin release notedby Niebauer and Cooke.6

The major assumptions used in this investigationinvolve the anatomic dimensions of the model, theflow conditions, a rigid wall approximation, andNewtonian viscosity. The use of these assumptions,as for prior in vitro investigations, is believed to con-stitute a reasonable first approximation to the actualhemodynamic conditions in the abdominal aortas ofhealthy humans.

The anatomic dimensions used in the presentstudy were on the basis of those reported by Mooreet al10 and include a tapering of the abdominal aortaand lumbar curvature. Potential limitations of thisrepresentation include a relatively abrupt change indimensions at the branch ostia and the lack of cur-vature of the branch vessels. These anatomic approx-imations, made on the basis of a lack of availableanatomic data, would likely alter local flow condi-

tions in the neighborhood of the ostia. The impor-tance of including branch vessel taper and curvaturein aortic flow studies merits further investigation.44

The physiologic conditions used in the presentstudy were on the basis of those reported by Mooreet al10 and Moore and Ku,14,16 but they differ in thatthe numeric method used herein necessitates thespecification of the time-varying outflow for the celi-ac, superior mesenteric, renal, and inferior mesentericvessels. In contrast, only mean flow was determinedand reported by Moore et al10 and Moore andKu14,16 for these branch vessels. Three features ofabdominal aortic flow waveforms, consistentlyobserved in normal subjects under resting condi-tions, were used in the present study. First, the flowrate is observed to be positive throughout the cardiaccycle at the entrance to the abdominal aorta at thelevel of the diaphragm.12,13,48 The second feature ofabdominal aortic flow observed in normal subjectsunder resting conditions is the triphasic flow wave-form in the infrarenal aorta.12,13,48 The third featureis a positive net renal artery flow.12,13,48,49

The determination of appropriate boundary con-ditions and flow waveforms for investigations ofabdominal aorta hemodynamic conditions merits fur-ther attention, especially for exercise flow conditionsin which direct measurements are problematic. In themethod used in the present study, assumptions arenecessary for the variation in velocity at the bound-aries where flow is specified. The velocity profiles atthe inlet to the abdominal aorta at the level of thediaphragm and the celiac, superior mesenteric, renal,and inferior mesenteric artery outflows were specifiedwith Womersley theory for pulsatile flow, whichresults in an axisymmetric velocity profile. Moore etal13 confirmed the validity of the assumption ofaxisymmetric flow in the supraceliac abdominal aorta.This condition was also used in the model flow stud-ies reported by Pedersen et al9 and Moore andKu.14,16 Regarding the outflow velocity profiles, thelength of the branch vessels was chosen to minimizethe effect of the outlet boundary condition on theflow in the aorta. It is likely that the assumption ofplanar branch vessels in the vicinity of the ostia on theaorta has a greater effect on the flow conditions in theaorta than the axisymmetric outlet velocity profile,but this was not examined in the present study.

The effect of aortic compliance was not consid-ered in the present investigation. Prior investigationsof flow in deformable models have shown that, ingeneral, the incorporation of the effect of compliancealters the magnitude of shear stress but does notchange the locations of low and high shear regions.In an investigation of the effect of wall compliance


on pulsatile flow in the carotid artery bifurcation,Perktold and Rappitsch21 described a weakly coupledfluid-structure interaction finite element method forsolving for blood flow and vessel deformation. Theyconcluded that the wall shear stress magnitudedecreased by approximately 25% in the distensiblemodel as compared with the rigid model yet that theoverall effect on the velocity field was relativelyminor. It should be noted that although neglectingwall distensibility may not have a major effect on theprimary flow field, the incorporation of wall mechan-ics in these studies is important for other reasons,including the description of the stress environmentwithin the vessel walls and the interaction betweendeformability and mass transport phenomena. Insummary, the use of rigid models for flow studies inidealized models of the human abdominal aortashould be viewed as a first approximation.

A Newtonian constitutive model for viscosity wasused in the present investigation. It is generally accept-ed that this is a reasonable first approximation to thebehavior of blood flow in large arteries. Perktold etal20 examined non-Newtonian viscosity models forsimulating pulsatile flow in carotid artery bifurcationmodels. They concluded that the shear stress magni-tudes predicted with non-Newtonian viscosity modelsresulted in differences on the order of 10% as com-pared with Newtonian models. Future studies ofabdominal aorta hemodynamic conditions shouldassess the effects of non-Newtonian rheologic models.

The accuracy of the finite element method forsolving the governing equations was not examinedquantitatively in the present study because of a lackof published data. In other models, Taylor et al27

examined the accuracy of this method used forblood flow computations. Numeric results werefound to be in excellent agreement with Womersleytheory and with laser Doppler anemometry velocitydata obtained by Loth50 for steady and pulsatile flowin a model of an end-to-side anastomosis.27 It wasnot possible to examine further refinements in thefinite element mesh used as a result of the limitationof computational resources. However, the stabilizedfinite element method used has been shown toexhibit excellent coarse grid accuracy.27 It is notexpected that further refinements in the mesh willresult in substantial qualitative or quantitative differ-ences in the computed solution.

CONCLUSIONThe characterization of the temporal and spatial

variations of the velocity field in an idealized model ofthe abdominal aorta enables new insights into thewall shear stresses acting on the luminal surface under

resting and exercise conditions. Under resting condi-tions, regions of low mean wall shear stress and highoscillatory shear index were noted along the anteriorwall between the superior mesenteric and inferiormesenteric arteries and along the posterior wall oppo-site the superior mesenteric artery and approximately2 cm distal to the renal arteries. Moderate exerciseconditions were necessary to eliminate all regions oflow mean wall shear stress and high oscillatory shearindex. The numeric studies described herein providefurther impetus to examine abdominal aorta hemody-namics in vivo with magnetic resonance imaging tech-niques and to assess the validity of the assumptionsmade regarding vascular anatomy and physiologicconditions, blood theology, and vessel mechanics.

We thank Jeff Buell, Mary Draney, Alok Mathur,David Parker, and Arthur Raefsky for their assistance.Software was provided by Centric Engineering Systems,Inc, TechnoSoft, Inc, XOX Inc, and RensselaerPolytechnic Institute’s Scientific Computing ResearchCenter. Hewlett-Packard provided a model 755/125workstation used in this research.

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Submitted Sep 16, 1998; accepted Dec 11, 1998.


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