Hemodynamic Analysis of a Compliant Femoral Artery Bifurcation Model

using a Fluid Structure Interaction Framework

YOUNG-HO KIM,1 JONG-EUN KIM,1 YASUSHI ITO,1 ALAN M. SHIH,1 BRIGITTA BROTT,2

and ANDREAS ANAYIOTOS3,4

1Department of Mechanical Engineering, University of Alabama at Birmingham, Birmingham, AL, USA; 2Division ofCardiovascular Disease, University of Alabama at Birmingham, Birmingham, AL, USA; 3Department of Biomedical

Engineering, University of Alabama at Birmingham, 1075 13th Street South, Hoehn 368, Birmingham, AL 35294-4440, USA;and 4Department of Mechanical and Materials Engineering, Cyprus University of Technology, Limassol 3036, Cyprus

(Received 25 May 2007; accepted 26 August 2008; published online 16 September 2008)

Abstract—The influence of wall motion on the hemodynamiccharacteristics of the human femoral bifurcation and itseffects on the development of peripheral artery disease hasnot been previously investigated. This study aimed ininvestigating the hemodynamics of a compliant patient-specific femoral artery bifurcation model by a fluid structureinteraction (FSI) scheme. The complex physiological geom-etry of the femoral artery bifurcation was reproduced fromsequentially obtained transverse CT scan images. Velocitywaveforms derived from phase contrast MR images wereextracted and mapped to define boundary conditions. Equa-tions governing blood flow and wall motion were solvedusing an FSI framework that utilizes commercial codes:FLUENT for computational fluid dynamics and ANSYS forcomputational structural dynamics. The results showed thatwall compliance decreased flow velocities at the relativelyhigh curvature geometries including common and superficialfemoral artery (SFA), and it created strong recirculation inthe profunda femoris artery close to the bifurcation. In theSFA region near the apex, time averaged wall shear stress(TAWSS) differences up to 25% between compliant and rigidmodels were observed. The compliant model also exhibitedlower TAWSS and oscillatory shear at the superior section ofthe common femoral artery close to the bifurcation. Thepresence of wall motion, however, created minor differencesin the general flow-field characteristics. We conclude thatwall motion does not have significant influence on the globalfluid dynamic characteristics of the femoral artery bifurca-tion. Longer arterial segments need to be simulated to see theeffect of wall motion on tortuousity which was previouslycited as an important factor in the development of athero-sclerosis at the femoral artery.

Keywords—Computational fluid dynamics, Fluid structure

interaction, Blood flow, Wall shear stress, CT image-based

model.

INTRODUCTION

Lower limb peripheral arterial disease (PAD) affectsapproximately 8 million Americans.19 It is particularlyprevalent in elderly persons, affecting 12–20% thoseover 65 years of age.38,43 Even in those who areasymptomatic, it is associated with impaired functionand quality of life.34 Atherosclerosis is widely acceptedas the main causative factor in the development oflower limb PAD. The atherosclerosis in PAD patientsis frequently observed on the site at the femoral arterybifurcation at the division of the Common FemoralArtery (CFA) into the Superficial Femoral Artery(SFA) and the Profunda Femoris Artery (PFA).14,15

The PFA provides blood to the thigh muscle, whilethe SFA provides blood to the lower limb and extendsto the popliteal artery. The lateral circumflex artery(LCA), branches out from the PFA, the location ofwhich may vary in each patient. The development ofatherosclerotic plaque in the femoral artery restrictsblood supply to the lower extremities, leading toischemia and lower limb disability. The distensibility ofthe arterial wall has usually been neglected in arterialhemodynamic studies. Wall motion, however, mayinfluence the distribution of wall shear stress (WSS),oscillatory shear index (OSI), wall shear stress tem-poral gradient (WSSTG), curvature, and wall rough-ness, which have previously been cited as havingan important role in the initiating mechanisms ofatherosclerosis.3,7,44–46,48,52

Experimental studies on arterial segments includingfemoral artery bifurcations,7 femoral graft-arteryjunctions,27 carotid artery bifurcations,6,30,36 andarteriovenous anastomoses31 using idealized or sim-plified arterial geometries have shown that hemody-namic characteristics are influenced by anatomicgeometry, pulsatile flow, arterial curvature, arterial

Address correspondence to Andreas Anayiotos, Department of

Biomedical Engineering, University of Alabama at Birmingham,

1075 13th Street South, Hoehn 368, Birmingham, AL 35294-4440,

USA. Electronic mail: aanayiot@eng.uab.edu

Annals of Biomedical Engineering, Vol. 36, No. 11, November 2008 (� 2008) pp. 1753–1763

DOI: 10.1007/s10439-008-9558-0

0090-6964/08/1100-1753/0 � 2008 Biomedical Engineering Society

1753

wall motion and arterial stenosis.1–3,6–8,16,22,26,27,31,32

Recent improvements in medical imaging techniques,and three-dimensional geometric reconstruction ofarteries, allow computational fluid dynamic CFDmethods to investigate complex vascular flows throughpatient-specific artery models.17,49,57

CFD studies, however, do not usually consider thecompliance of arterial wall due to the complexity of thenumerical modeling and the requirement for a fluidstructure interaction (FSI) environment to solve for thecoupled fluid/structure problem. The assumption of arigid wall in CFD analysis of arterial models mayunderestimate the temporal and spatial magnitudeof slow moving zones.58 To assess the effect of wallcompliance on the near wall hemodynamic characteris-tics of arteries such as WSS, OSI, and WSSTG, FSIalgorithms have been employed to take into accountthe effect of arterial wall compliance in the fluiddynamic analysis.10,13,29,33,56 Various arterial sites havebeen analyzed by FSI such as the carotid arterialbifurcation,54 an abdominal aortic aneurysm model,39

and a stented aortic aneurysm model.28

In this study, we aimed in assessing WSS, OSI, andWSSTG in the femoral artery bifurcation by a newlydeveloped fluid structure interaction framework thatsimultaneously computes both hemodynamic andmechanical characteristics by taking into account theinteraction between blood flow and arterial wallmotion.

MATERIAL AND METHODS

Model Reconstruction and Mesh Generation

A 6 cm-long biofidelic femoral bifurcation modelwas reconstructed from CT data which provides abetter contrast of the arterial wall and lumen crosssection than MR, but does not have the capability ofrendering the velocity measurements. A 992 CT scanimage set was obtained from a 55-year-old femalevolunteer suffering from paraplegia. This datasetranges from the abdomen to the toes, using a GELightSpeed Proscanner with 1.25 mm slice thicknessand 0.25 mm overlap. An informed written consentfrom the patient was received, and the protocol wasapproved by the local institutional review board. The60 slices of the images were used to reconstruct thefemoral model. The image resolution was 512 9 512pixels per slice, and each pixel represented a 0.79 9

0.79 mm2 area. Image segmentation and geometryextraction from the images were performed to obtainthe inner surface of the femoral artery. Two surfacetriangulation methods, a direct advancing frontmethod and a modified decimation method,21 were

used to create high-quality surface meshes. A tetra-hedral mesh for CFD simulations was created bysubdividing non-simplicial elements in a hybrid meshto estimate WSS precisely.20

The wall thickness of the CFA was set to 0.74 mmby assuming a radius-to-thickness ratio of 4.122 usingthe reconstructed geometry. This was adopted from aprevious reported study.48 The wall thickness couldnot be obtained from the CT information due to therelatively large pixel size and low signal to noise ratio(SNR) that did not allow clear distinction betweenarterial wall and adjacent tissue structure. The sameradius-to-thickness ratio was used to determine thethicknesses of the SFA, PFA and LCA. Figure 1illustrates structural and fluid meshes of the patient-specific femoral artery used in this study. A commoninterface was defined at the inner wall of the femoralartery. The finer mesh with 367,315 tetrahedra coversthe inside of the femoral artery and is used for flowfield analyses. There are 18,695 triangles on the com-mon interface. The coarse tetrahedral mesh repre-senting the wall of the femoral artery is used forstructural analyses. It has 43,774 tetrahedra and 4761triangles on the common interface.

Fluid Structure Interaction Framework

An in-house loosely coupled fluid structure inter-action (FSI) framework was developed and employedfor this study. This framework enables to select

FIGURE 1. Structural (coarse) and fluid (fine) mesh of thefemoral artery bifurcation (A: Anterior, P: Posterior, L: Left, R:Right views).

KIM et al.1754

any well-proven CFD and computational structuraldynamic (CSD) codes. An accurate and efficient datatransfer between fluid and structure using interpolationtechniques is essential in space due to naturallyunmatched meshes between fluid and structure. Theframework consists of: a conservative point-wiseinterpolation12 module for blood pressure transfer towall, a curvature-gradient index local fitting method24

for wall motion transfer to fluid domain, a semi-torsional spring analogy55 for fluid volume meshmovement, and a serial staggered method11 with sub-cycling for synchronizing time levels between CFD andCSD solvers. The entire FSI process is automaticallyexecuted using Bash/Perl script files for data extrac-tion, manipulation, file handling, and code execution.The details of the FSI framework are described in theliterature.23 Two commercial codes, FLUENT forCFD and ANSYS for CSD, were used in this study. Inorder to take into account arterial dynamic wall mo-tion, a time integration option in ANSYS was switchedon to include the inertial effect of the wall in the FSIsimulation.

MRI Velocity Mapping and Boundary Conditions

Phase contrast MRI data were acquired to measureblood flow velocity at four different sections shown inFig. 2 (39.2 mm, 19.2 mm above branch and 11 mm,21 mm below branch) by a GE MR scanner (1.5 T,Signa). The scan parameters were 4 mm slice thickness,40 ms TR, 6 ms TE, 32 cardiac phases, 20� FA,113 9 150 cm FOV, and a 512 9 512 matrix. The

encoding velocity was 150 cm/s corresponding to 180�phase shift. Only axial velocity was measured under theassumption that in-plane velocity components are rel-atively trivial. The image has 0.59 mm in-plane reso-lution. To obtain velocity map from MRI during thecardiac cycles, a region of interest was determinedmanually around the vessel lumen detected age. Thephase angle value in each pixel was converted tovelocity by18:

V ¼ VENC � Uv=180�; Uv ¼ ½�180�; �180�� ð1Þ

where, VENC is encoding velocity, and Fv is the phaseangle obtained by phase image. The calculated velocitythen was mapped by an interpolation method based ona radial basis function. The thin plate spline method9

was used for the interpolation. Time-dependentvelocity profiles were mapped through 32 cardiacphases. Around 40 pixels for the SFA and PFA, and20 pixels for the LCA were used to quantify thevelocity.

The mapped and interpolated flow rates used incalculating velocity at the SFA, PFA and LCA outletswere consistent with MRI data through the entirecardiac cycle as shown in Fig. 3. These time-varyingmapped flow rate were used for three outlet boundaryconditions in FLUENT via user defined function(UDF).

CFD analysis in rigid wall vessel simulationsmay use only flow rate boundary conditions. Howeverin compliant wall vessel FSI simulations, a time-dependent pressure profile, is necessary to apply forceson the wall. The time dependent pressure profile atSection 2 in Fig. 2 was used as the inlet boundarycondition. To calculate the pressure profile at Section 2,

FIGURE 2. The four sections where the velocity profileswere measured by MRI-PCA.

FIGURE 3. Flow rate comparison between MRI-PCA calcu-lated measurements and CFD simulated measurements at theSFA, PFA and LCA outlets.

Hemodynamic Analysis of Femoral Artery Bifurcation 1755

two physiological flow rates at Sections 1 and 2 werecalculated based on the velocity profiles. The Navier–Stokes equations for one dimensional flow in an elastictube can be reduced to5

QiðtÞ �QoðtÞDz

¼ 3pr3

2hE

dPoðtÞdt

ð2Þ

PoðtÞ � PiðtÞDz

¼ qpr2

dQiðtÞdtþ 8l

pr4QiðtÞ ð3Þ

where Qi and Qo are the flow rates at the Sections 1 and2, respectively, Dz is the distance between Sections 1and 2, Pi and Po are the pressure at the Sections 1 and2, respectively, r is the inside radius of tube, h is thewall thickness, q is the density of blood, l is dynamicviscosity of blood and E is the elastic modulus set to1.61e06 Pa.37 The pressure waveform estimated byintegrating Eq. (2) is illustrated in Fig. 4. This pressurewaveform was used as an inlet boundary condition atthe Section 2 by UDF in FLUENT. The mapped MRIvelocities at Section 4 (of the PFA, SFA, and LCA),were used as the outlet boundary conditions.

Vessel Material Properties

The blood vessel was assumed as a homogenous,hyperelastic, nonlinear, and nearly incompressiblematerial. Poisson’s ratio was set to 0.4999 to depictincompressible material. The density of the vessel wasset to 1100 kg/m3. The in vivo material properties ofthe CFA were identified through inverse finite element(FE) analysis. An ideal cylinder FE model that surro-gates the vessel from Section 1 to 2 in Fig. 2 wasgenerated. Mooney–Rivlin hyperelastic model35 wasused for the constitutive model of compliant arteries.

The strain energy potential W is expressed by fiveparameters Cij ‘s in incompressible Mooney–Rivlinmodel:

W ¼X2

iþj¼1CijðI1 � 3ÞiðI2 � 3Þj i; j ¼ 0; 1; 2 ð4Þ

where I1 and I2 are strain invariants. In this study, thefive parameters in Eq. (4) were based on the results ofin vitro tensile test from literature.41 The value of C10,however, was modified to consider in vitro property ofthe PAD patients, in which the blood vessel is pre-pressurized at the diastolic phase. For this, the pres-sure difference between systolic and diastolic phasefrom Eq. (2) was applied to the ideal cylinder. Thevalue of C10 was determined until the diameter changereached to the 6.2% diameter change of the CFA forthe PAD patient at a systolic phase.50 The fiveparameters used in Mooney–Rivlin model are shownin Table 1.

Time Averaged WSS, OSI, and WSSTG

Time averaged wall shear stress (TAWSS) wasmeasured by calculating temporal mean of WSS duringan entire cardiac cycle. OSI was obtained using theform26:

R T0~s�j jdt

R T0~sxj jdt

ð5Þ

where T is the time for a cardiac cycle, ~sx is theinstantaneous WSS vector and ~s� is the WSS compo-nent acting in the direction opposite to the temporalmean WSS vector. The WSSTG is defined as a maxi-mum among the gradients of WSS in two consecutivetime steps during the cycle.54

RESULTS

Wall Displacement

Time-varying lumen diameters of the CFA and SFAare measured at Sections 2 and 3 as shown in Fig. 2,respectively. The maximum anterior-to-posteriorlumen diameters of CFA and SFA at peak systole are6.35 and 4.67 mm, respectively. This corresponds to5.7% and 3.7% expansion of the lumen diameter at

FIGURE 4. Calculated pressure at Section 2 using theNavier–Stokes equations for one dimensional flow in anelastic tube with flow rates based on MRI-PCA.

TABLE 1. Modified coefficients of five-coefficient Mooney-Rivlin model for patient-specific arterial properties.

Parameters C10 C01 C20 C11 C02

Values (kPa) 4.10 2.75 590.42 857.18 0

KIM et al.1756

peak systole as shown in Fig. 5. The increase of ante-rior-to-posterior lumen diameters of CFA and SFA islarger than that of right-to-left ones.

Flow Pattern Comparison

The validity of the CFD and FSI models in com-parison to the raw MRI data in the model, are dem-onstrated in the time histories of Figs. 6a and 6b,where good agreement is seen. The hemodynamiccharacteristics of the compliant model through the FSIanalysis are compared to those of the rigid wall modelusing CFD analysis. Figures 7a and 7b show theinstantaneous streamlines during the decelerationphase of the cycle at phases 0.23/0.78 s and 0.54/0.78 s,respectively. More recirculation in the PFA sectionclose to the bifurcation in the compliant model is

observed. The recirculation is more accentuated laterin diastole for phase 0.54/0.78 s. The velocity contoursin Fig. 8 show that wall compliance decreases flowvelocities at the posterior CFA at Section 2 and theanterior SFA at Section 3 where the radius of curva-ture is relatively high.

Wall Shear Stress

Comparison of the instantaneous peak systolic WSSdistributions between the compliant and rigid cases isshown in Fig. 9. A maximum difference between thetwo models is shown at the left anterior view close tothe branch of PFA. The plots demonstrating the dif-ference in TAWSS, WSSTG, and OSI between the twocases are illustrated in Figs. 10–12, respectively. Asseen in Fig. 9, high WSS is shown at the branch ofPFA and bifurcation. Low WSS regions appeararound the outer wall of the posterior view upstreamof the bifurcation and on anterior to left aspect close to

FIGURE 5. Time-dependent lumen diameter changes: (a)CFA at Sections 2; (b) SFA at Sections 3.

FIGURE 6. Time-dependent velocity at Section 3: (a) Nearright wall; (b) Near posterior wall.

Hemodynamic Analysis of Femoral Artery Bifurcation 1757

the branch of PFA where the geometry has a mildcurvature along the distal direction. In these regions,the TAWSS for the compliant model appears to beonly 10% lower than the rigid model, and there aresome patchy regions that illustrate OSI differences upto 25%. In contrast, the WSSTG difference contourplots in Figs. 11a and 11b show the highest (25%)difference on the posterior right side of the SFA nearthe bifurcation along the distal direction.

DISCUSSION

Correct modeling of fluid dynamics and the char-acterization of the near wall phenomena is importantin understanding the initializing mechanisms and thedevelopment of atherosclerotic plaque as well as pre-dicting changes that may occur with treatments such asstent placement or surgical repair. Our results indicate

that there are significant differences up to 25% in wallshear stress temporal gradient (WSSTG) between arigid and a compliant model of the femoral artery. The10–25% difference regions (Fig. 11) cover a wideextent in the superficial femoral artery near the bifur-cation. There is also a significant region of differencesfrom 5 to 20% at a region of the common femoralartery near the bifurcation (Fig. 11). Our results alsoshow that there are some regions of differences inoscillatory shear index (OSI) that reach up to 25% atthe common femoral artery close to the bifurcation.

There has not been a previous study on the com-pliance of the femoral bifurcation, however, Younisand colleagues54 used an FSI technique to study animage based model of the carotid bifurcation. Theyreported minor differences in TAWSS differencesbetween the rigid and compliant models. They found,however, significant differences in the WSSTG andOSI between the two models except at the apex. In our

FIGURE 7. Comparison of streamlines between rigid and compliant arteries: (a) at time 0.2926/0.78 s; (b) at time 0.5368/0.78 s.

KIM et al.1758

study, the wall compliance created minor TAWSSdifferences at most locations, but up to 25% differ-ences in WSSTG and OSI at some locations. We hadobserved 20% reduction in instantaneous WSS for thecompliant model around the branch at peak systolewhich is somewhat lower than in what is reported inprevious studies.2,40 However, this can be explained bythe lower distensibility of the muscular femoral arter-ies which was modeled as opposed to greater disten-sibility of large elastic arteries such as aortic andcarotid.25,42,53

It has been widely accepted that WSS and relatedparameters such as WSSTG and OSI are importantfactors in the development of atherosclerosis on thefemoral artery,22,46,47,51 and the carotid artery.1,2,16,26

Ku and colleagues26 reported low OSI in additionto low WSS enhanced the development of plaques.Bao and colleagues4 showed that WSSTG leads toenhanced endothelial proliferation.

Our data show that compliance increases the regionsof high OSI and WSSTG making thus specific regionsof the femoral artery bifurcation more prone to thedevelopment of disease. However, in addition to OSI

and WSSTG, curvature, wall roughness and wallmotion have also been indicated to have a role in theinitializing mechanisms of atherosclerosis at the fem-oral artery bifurcation.7,44–46,52 The current studycould not assess the effects of wall motion in changesin roughness, or curvature.

Earlier experimental studies have also revealed thatthe inherent tortuousity of the femoral artery increasesthe rate of atherosclerosis and that the inner curvaturewalls are more prone to atherosclerotic plaques thanthe outer curvature walls.45,46 These studies also sug-gested that the curvature of the SFA is more of a riskfactor for atherosclerosis than the presence and loca-tion of branches. Wood and colleagues52 showed astrong correlation between tortuousity and flow dis-turbance in computational reconstructed SFA’s. Theysuggested that the regions of low time averaged WSSmight be high-risk regions of atherogenesis and pro-gression of atheroma. A limitation of this present studyis that the arterial segment simulated had significantcurvature but no tortuousity. Longer sections ofthis artery may be able to incorporate the effect oftortuousity and need to be simulated in the future to

FIGURE 8. Comparison of velocity between rigid and compliant arteries at peak pressure loads: (a) Rigid CFA at Section 2;(b) Compliant CFA at Section 2; (c) Rigid SFA at Section 3; Compliant SFA at Section 3.

Hemodynamic Analysis of Femoral Artery Bifurcation 1759

evaluate the effect of wall compliance on tortuousityWSSTG and OSI.

CONCLUSIONS

Using an in house FSI system, the flow character-istics and WSS field of a compliant femoral arterybifurcation model was studied in comparison to a rigidmodel. Minor differences were found in TAWSS and

differences of 25% in WSSTG were observed at thebifurcation on the side of the SFA. The generalvelocity field was essentially insensitive to wall motion.We conclude that wall compliance at the femoralartery bifurcation does not significantly changeparameters previously reported as important in thedevelopment of arterial disease but longer arterialsegments need to be simulated to see the effect of wallmotion on tortuousity.

FIGURE 9. Instantaneous WSS contours of rigid and compliant artery and difference contour between them at peak systole and atdifferent angles: (a) WSS of rigid artery at right; (b) WSS of rigid artery at left; (c) WSS of compliant artery at right; (d) WSS ofcompliant artery at left; (e) WSS difference at right; (f) WSS difference at left.

KIM et al.1760

FIGURE 10. TAWSS difference contour between them at different angles: (a) TAWSS difference at right; (b) TAWSS difference atleft.

FIGURE 12. OSI difference contour between them at different angles: (a) OSI difference at right; (b) OSI difference at left.

FIGURE 11. WSSTG difference contour between them at different angles: (a) WSSTG difference at right; (b) WSSTG difference atleft.

Hemodynamic Analysis of Femoral Artery Bifurcation 1761

ACKNOWLEDGMENT

The authors would like to thank Mr. Corey Shum inthe Enabling Technology Laboratory, University ofAlabama at Birmingham for extracting geometry datafrom the CT scan.

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