Improving Blood Flow Simulations by Incorporating Measured

Subject-Specific Wall Motion

JONAS LANTZ,1,4 PETTER DYVERFELDT,2,3 and TINO EBBERS1,2,3,4

1Department of Science and Technology, Linkoping University, Linkoping, Sweden; 2Department of Medical and HealthSciences, Linkoping University, Linkoping, Sweden; 3Center for Medical Image Science and Visualization (CMIV), Linkoping

University, Linkoping, Sweden; and 4Swedish e-Science Research Centre (SeRC), Linkoping, Sweden

(Received 10 March 2014; accepted 31 May 2014)

Associate Editor Ajit P. Yoganathan oversaw the review of this article.

Abstract—Physiologically relevant simulations of blood flowrequire models that allow for wall deformation. Normally afluid–structure interaction (FSI) approach is used; however,this method relies on several assumptions and patient-specificmaterial parameters that are difficult or impossible tomeasure in vivo. In order to circumvent the assumptionsinherent in FSI models, aortic wall motion was measuredwith MRI and prescribed directly in a numerical solver. Inthis way is not only the displacement of the vessel accountedfor, but also the interaction with the beating heart andsurrounding organs. In order to highlight the effect of wallmotion, comparisons with standard rigid wall models wasperformed in a healthy human aorta. The additional com-putational cost associated with prescribing the wall motionwas low (17%). Standard hemodynamic parameters such astime-averaged wall shear stress and oscillatory shear indexseemed largely unaffected by the wall motion, as a conse-quence of the smoothing effect inherent in time-averaging.Conversely, instantaneous wall shear stress was greatlyaffected by the wall motion; the wall dynamics seemed toproduce a lower wall shear stress magnitude compared to arigid wall model. In addition, it was found that if wall motionwas taken into account the computed flow field agreed betterwith in vivo measurements. This article shows that it isfeasible to include measured subject-specific wall motion intonumerical simulations, and that the wall motion greatlyaffects the flow field. This approach to incorporate measuredmotion should be considered in future studies of arterialblood flow simulations.

Keywords—Computational fluid dynamics, Magnetic reso-

nance imaging, Fluid–structure interaction, Aorta, Time

averaged wall shear stress, Prescribed wall motion.

INTRODUCTION

There is a close relationship between blood flow andmany terms of cardiovascular diseases.16 In order tounderstand the genesis and progression of these dis-eases, accurate description and assessment of bloodflow features are crucial. With numerical modeling it ispossible to compute hemodynamic parameters that areotherwise not possible to obtain in vivo. For example, itappears that the patchy distribution of atheroscleroticlesions is caused by local features in the blood flow;disturbed or even turbulent flows seem to have differ-ent effects compared to steady laminar flows1,11,15). Inorder to quantify the effect of the flow on arterialendothelial cells, a number of hemodynamic indiceshas been put forward, the most common reported inthe literature being the time-averaged wall shear stress(TAWSS) and the oscillatory shear index (OSI). In vivomeasurements of arterial WSS using current clinicalimaging modalities suffer from accuracy issues,13,14

therefore modeling is the main approach to WSSestimation. In addition, individual variability makes itdifficult to use imaging and experiences from largergroups to provide information on a single individualpatient.17 Arterial geometry is probably the single mostimportant determinant of local blood flow patterns,and modeling the interaction between the blood flowand the arterial wall represents one of the majorchallenges in the field of computational hemodynam-ics.3 As noted by Barakat,2 there is a critical need forsystematic investigations on how vessel geometry innumerical models affects arterial flow fields. The sim-ulations used for WSS assessment typically assumethat the arterial walls are rigid, which greatly simplifiesthe simulation process. The effect of wall motionon velocity and WSS fields is often assumed to be

Address correspondence to Jonas Lantz, Department of Science

and Technology, Linkoping University, Linkoping, Sweden. Elec-

tronic mail: jonas.lantz@liu.se

Cardiovascular Engineering and Technology (� 2014)

DOI: 10.1007/s13239-014-0187-5

� 2014 Biomedical Engineering Society

negligible. This may be reasonable in older subjectsand certain patient groups with increased vascularstiffness.16,19 However, vessel walls are typically notrigid and such an assumption will introduce a mis-match between inlet and outlet flow rates, making adirect comparison with in vivo measurements difficult.The limitation introduced by this mismatch in flow canonly be overcome with a model that accounts for walldistensibility.

Fluid–structure interaction (FSI) models computethe aortic wall deformation due to changes in aorticpressure, and can yield physiological pulse waveforms and pressures.3 However, these models arebased on several assumptions including the wallthickness, the stress-strain relationship of the arterialwall, homogeneous material properties, the impact ofsurrounding tissue and organs, and pressure and masswave reflections from arterial bifurcations and bran-ches outside the computational domain. Dependingon desired model complexity and available data onthe subject/patient, the wall can be modeled usingeither a linear10 or non-linear4,8 material model.However, to obtain an accurate wall deformation fornon-linear material models, the residual stresses, thatare present even in a non-pressurized aortic wall, mustbe accounted for. Furthermore, the descending aortais longitudinally tethered by the spine, while theascending aorta is less constrained by external tissuesand structures,12 which will also affect the wall mo-tion. In addition, the translation of the wall resultingfrom the motion of the beating heart is often ne-glected, even though it can have a significant impacton the flow field.7

The uncertainties included in FSI models pose agreat obstacle when performing patient-specific simu-lations. However, as noted by Taylor and Figueroa,18

new imaging techniques permit the direct character-ization the motion of the vessel wall. Consequently, thelimitations of current FSI models may be overcome bydirectly prescribing measured wall motion in thenumerical model. Magnetic resonance imaging (MRI)has earlier been used to measure arterial wall motion:Jin et al.7 prescribed the wall motion from twothrough-plane MRI measurements in the ascendingaorta, and performed interpolation in between the twoplanes while keeping the aortic arch and descendingaorta rigid. Their conclusion was that the computedflow field only agreed with the measured flow fieldwhen the full wall motion (displacement due to pres-sure changes and translation due to the beating heart)was included, suggesting that the flow field is not onlydependent on the geometry but also on the motion ofthe aorta. In a study by Torii et al.,20 the motion of theright coronary artery over 14 time points in the cardiaccycle was measured and implemented in a numerical

solver. The MRI data acquisition in their studyrequired seven separate scanning sessions, each lasting75–90 min, over a period of a month. Their conclu-sions were that the wall motion affected the instanta-neous wall shear stress and that vessel motionmeasured by MRI could be incorporated in numericalsolvers.

The goal of this study was to measure the full three-dimensional wall motion of a healthy human aortaover the entire cardiac cycle using a single MRI mea-surement, and incorporate this information into anumerical model. This allows us to investigate theimpact of wall motion on hemodynamics, as well as theimportance of including wall motion in image-basedCFD models. Incorporating the three-dimensional wallmotion in the model does not only address subject-specific wall displacement, but does also include theeffects of translational vessel motion caused by inter-action with surrounding organs and tissues. To dem-onstrate the effect of the wall dynamics, a comparisonwith rigid wall models was performed.

METHOD

MRI Acquisition

Time resolved-wall motion and flow were acquiredwith a three-dimensional cine balanced steady-state freeprecession (bSSFP) sequence on a 1.5 T Philips AchievaMRI scanner (Philips Healthcare, Best, the Nether-lands). A sagittal slab orientation in the ‘‘candy-caneview’’ was prescribed to cover the thoracic aorta.Imaging parameters included flip angle = 80�, pixelbandwidth = 1325 Hz, TR/TE = 4.0/2.0 ms, and k-space segmentation factor = 11 (temporal resolu-tion = 44 ms). The scanned subject had a heart rate of56 bpmand 25 frames evenly distributed throughout thecomplete cardiac cycle were reconstructed. Additionalimaging parameters included amatrix size of 176 9 176,30 slices and a three-dimensional field-of-view of300 9 300 9 60 mm (voxel size = 1.7 9 1.7 9 2 mm).The scan time was 480 heartbeats, or about 8 min and30 s. In addition, through-plane velocity profiles weremeasured in the ascending and descending aorta, as wellas in a plane through the three branching vessels of theaortic arch. Imaging parameters were as follows.Ascending and descending aorta: Pixel size =

1.56 9 1.56 mm, slice thickness = 7 mm, temporalresolution = 30 ms, VENC = 200 cm/s, TR/TE =

4.98/2.96 ms, pixel bandwidth = 498 Hz, k-space seg-mentation factor = 3. Neck: Pixel size = 1.56 9

1.56 mm, slice thickness = 6 mm, temporal resolu-tion = 27 ms, VENC = 150 cm/s, TR/TE = 6.63/3.94 ms, pixel bandwidth = 342 Hz, k-space segmen-tation factor = 2.

LANTZ et al.

Numerical Model

The three-dimensional aortic wall was delineated inall 25 time frames of the MR data, yielding time-re-solved aortic geometry at 44 ms temporal resolution.The vessel wall delineation was performed using afreely available software (Segment Heiberg et al.6), andwas improved using manual corrections at a fewlocations. A high quality mesh was constructed inANSYS ICEM 14.5 for the first geometry, with3 million anisotropic hexahedral cells. A fine near-wallresolution was obtained by gradually letting the firstlayer thickness grow with a expansion factor of 1.1until the cell size matched the bulk mesh. A sensitivitystudy on meshes with 3 and 5 million cells was per-formed, and the difference in velocity and wall shearstress was less than 4%, at it was determined that themesh with 3 million cells was sufficient for this study.

In order to minimize the additional computationalcost of including wall motion, the topology of theinitial mesh was kept constant and stretched to matchthe subsequent geometries. In this way re-meshing wasnot needed, and the cost of interpolating flow variablesbetween different topologies could be avoided. Themesh quality was monitored to ensure that no negativeor low-quality cells were obtained.

The pulsatile flow inside the aorta was simulatedusing ANSYS CFX 14.5. The fluid was assumed to beNewtonian with a viscosity of 3.5e�3 Pa s andincompressible with a density of 1060 kg/m3. The timestep in the simulation was 0.0044 s (1/10 of the timeresolution of the MRI wall motion measurement), andpiecewise cubic hermite spline interpolation was per-formed in time to obtain intermediate geometries foreach time step in the flow simulation. The mesh motionwas incorporated through a user defined FORTRANsubroutine in CFX, and called at the beginning of eachtime step. For details on the mesh interpolation, see thesupplementary materials. The numerical schemes forthe advection and temporal terms were second orderaccurate and convergence was obtained when theresiduals had decreased 5 orders of magnitude andglobal imbalances of mass and momentum were lessthan 0.1%. Typically 5–6 iterations per time step wererequired. Four cardiac cycles were simulated, but re-sults were only taken from the last cycle to ensure thatinitial transient effects had disappeared.

The measured in-plane velocity profile in theascending aorta and branching vessels were used asboundary conditions in the model, see Fig. 1. As thetemporal resolution of the simulation was higher thanthe measurement, piecewise cubic hermite splineinterpolation was performed in the temporal domainto obtain values for the boundary condition for alltime steps. In the descending aorta a constant static

pressure boundary condition was set. Besides the pre-scribed motion, the aortic wall was considered non-deformable and to obey the no-slip condition. In orderto investigate the influence of wall motion, five differ-ent cases were simulated: three cases with wall motionand two rigid wall cases. A simulation with all 25measured geometries was considered as the baselinecase since it used all information available. A secondcase used every third measured geometry, resulting innine geometries in total, while a third case used onlytwo measurements: the first geometry (minimum vol-ume) and the sixth geometry (maximum volume), seeFig. 2. Finally, two rigid wall simulations were per-formed: one simulation with the smallest aortic volumeand one simulation with the largest volume. In thisway the influence of the size of the vessel could bededucted, as well as how the dynamics of the wallmotion affected the flow field.

Post-processing

The CFD-results were post-processed in Matlab,and TAWSS and OSI were computed. The TAWSSvariable is simply the average WSS magnitude (sw)over one cardiac cycle, defined as:

TAWSS ¼ 1

T

ZT

0

swdt ð1Þ

while the OSI variable is defined as:

OSI ¼ 0:5 1�1T

R T0 swdt

������

1T

R T0 swj jdt

0@

1A ð2Þ

FIGURE 1. MRI-measured velocity profiles were prescribedas boundary conditions in the ascending aorta and in thebranching vessels leaving the aortic arch; the resulting flowrates are here presented for each vessel.

Incorporating Wall Motion in Blood Flow Simulations

where T is the time for one cardiac cycle. OSI describesthe cyclic departure of the WSS vector from its pre-dominant axial alignment,5,9 and values can rangefrom 0 to 0.5, where zero means that the instantaneousWSS vector is aligned with the time-averaged WSSvector throughout the cardiac cycle. A value of 0.5implies that the instantaneous WSS vector never isaligned with the time-averaged vector, indicating avery oscillatory behavior. OSI is insensitive to shearmagnitude and must therefore be used with caution; alarge OSI value can indicate a disturbed flow regionwith high or low WSS magnitudes. In addition to WSSvariables, velocity profiles in the descending aorta werecompared with MRI measurements.

RESULTS

The translational motion of the ascending aorta canbe quite complex, as shown in Fig. 3. It can be seenthat the aorta first moves toward the right side of thebody and then anteriorly during systole, and thenreturning slowly back in a left-posterior direction tothe original position during diastole. At 0.75 s there isa sudden movement, which could be an effect of atrialcontraction. The total distance traveled by the centroidis over 20 mm, which is on the order of an aorticdiameter. The effect of only including two geometriesis apparent on the translation; the translation appearsstraight and does not account for the complex motionin the simulation with 25 measurements.

Even though only a single aorta has been studied,the modeling is subject-specific and the velocity profilesin the descending aorta can be validated by directcomparisons with measured in vivo data. Qualitatively,the simulations with prescribed wall motion results invelocity profiles that better match the MRI measure-ments, compared to the rigid wall simulations, seeFigs. 4 and 5. It can also be seen that the two rigid wallsimulations give different results, as a result of thedifference in volume. The case with rigid wall andmaximum volume (Rigid Max Vol.) has a lower meanvelocity compared to the case with rigid wall andminimum volume (Rigid Min Vol.). This is due to thelarger volume and that conservation of mass effectivelydecreases the mean velocity in the cross-section. Simi-larly, the Rigid Min Vol. case over predicts the velocitymagnitude compared to MRI measurements. In addi-tion, the shape of the velocity profile is different in therigid wall cases compared to the prescribed wall andMRI results; in general there is a better agreementbetween MRI measurements and numerical simula-tions with prescribed wall motion.

This is also highlighted in Fig. 6, where the flow ratethrough a plane in the descending aorta for each case isplotted. Table 1 summarizes the peak flow rate andwhen it occurs for each case. The wall motion seems tohave less effect on the TAWSS and OSI parameters,indicated by the close resemblance between the aortasin Fig. 7. Considering the TAWSS, the rigid-wall sim-ulation with the smallest volume experienced elevatedvalues compared to the other simulations, which couldbe an effect of the smaller volume creating higher

FIGURE 2. Volume of the aorta over one cardiac cycle,where circles indicate each measured geometry for the baseline case (25 measurements). The case with 9 measurementsused every third geometry while the case with 2 measure-ments used the first geometry (minimum volume), and thesixth geometry (maximum volume). For all cases PiecewiseCubic Hermite Spline interpolation was used between themeasurements.

FIGURE 3. Translation of the centroid in a cross-section inthe ascending aorta. The cardiac cycle starts at x, y 5 0, andthe centroid is then translated in a loop as a result of thebeating heart and flow forces. The effect from using all 25measurements compared to 9 or 2 measurements is apparent;most of the translation is lost if only 2 measurements areincluded in the simulation.

LANTZ et al.

velocities, and thus, also higher shear rates closer to thewall. On the other hand, for the OSI parameter the rigidsimulation with the largest volume experienced elevatedvalues compared to the other simulations. This could be

an effect of an overall lower velocity magnitude whichcould increase wall shear stress oscillation.

To assess whether wall motion affected instanta-neous WSS values, the WSS magnitude at peak flow

FIGURE 4. Comparison of velocity profiles from MRI measurements and CFD simulations in the descending aorta during systolicacceleration and peak flow rate. Body position is indicated in top left plot, with A: anterior, P: posterior, L: left and R: right.

FIGURE 5. Comparison of velocity profiles from MRI measurements and CFD simulations in the descending aorta during systolicdeceleration. Note the different color scale compared to Fig. 4. Negative values indicate backflow, towards the heart. Sameorientation as in Fig. 4.

Incorporating Wall Motion in Blood Flow Simulations

rate for all cases was studied, see Fig. 8. The cases withwall motion exhibits a different WSS pattern and lowermagnitude compared to the rigid wall cases. In addi-tion, locations with high WSS values in the cases withprescribed wall motion experiences even higher valueswhen the wall is considered rigid. In particular the casewith the smallest domain volume has the highest WSSvalues, again an effect of the smaller volume creatinghigher velocities and shear rates.

The additional computational resources requiredfor reading, interpolating and writing new meshes wereconsidered, and it was found that incorporating all 25measured geometries in the simulation increased thetime for simulating one cardiac cycle by 17% com-pared to a standard rigid wall simulation, see Table 2.For nine geometries the additional time was 13%,while for only two geometries it was 7%.

DISCUSSION

This study introduced blood flow simulations withprescribed subject-specific in vivo wall motion mea-sured by 4D-MRI. Traditional simulations of aortic

flows normally assume rigid walls or compute the walldisplacement through a FSI simulation. The assump-tion of rigid walls neglects the dynamics that is intro-duced by the moving wall, while FSI simulationsrequire knowledge of material parameters and in vivoboundary conditions that are often unknown. Thetranslation of the aorta is rarely accounted for, and asthe number of uncertainties increase, the accuracy ofthe simulation result may become degraded. A FSIsimulation of the model was not performed, as subject-specific wall material properties were not available andusing standard values from literature would only adduncertainty to the results. A range of different wallparameters and different values of the wall thicknesswould therefore have to be simulated and compared tothe measured wall motion, but this was not the scopeof the study. Instead, the method and results presentedin this study shows that these hurdles can be overcomeby measuring the wall motion using MRI and directlyprescribe it in the numerical simulation. However, itshould be noted that the MRI measurements of time-resolved 3D vascular geometry provides informationthat enables inverse modeling for determination of wallproperties. In this way local wall stiffness can becomputed, which would increase the accuracy of anFSI simulation.

The additional computational cost involved in pre-scribing the wall motion comes from reading newmeshes and interpolating coordinates for each timestep in the numerical simulation. However, with asingle cardiac cycle only taking 3 h for a rigid wallsimulation, the additional cost of involving a pre-scribed wall motion was only 30 min. This can cer-tainly be considered affordable, as the physiologicalrelevance increases considerably. In fact, MRI acqui-sition, segmentation, meshing, and setup of the CFD-model takes longer time, making the additional timerequired for including wall motion negligible. Notethat the extra effort of meshing 25 geometries did nottake 25 times longer compared to when meshing only asingle geometry; much of the initial work could bescripted and reused. The mesh motion subroutine usedin the simulation software can probably be optimizedeven further, decreasing the additional computationaleffort even more.

The translation of the ascending aorta is complex,as a result of the motion from the beating heart. Themeasured motion agreed very well with the resultsfrom the study of Jin et al.,7 both in shape and dis-tance. They also measured a sudden change in thetranslation at the end of diastole, which probablyoriginates from atrial contraction as it occurs at the P-wave in the electrocardiogram. Flow forces may alsointroduce a translating motion, but this effect is mostlikely small compared to the effect from the heart

FIGURE 6. Comparison of the flow rate in a plane in thedescending aorta for the different simulations. Notice how therigid wall assumption affects the flow rate as there is noWindkessel effect in the model. For the cases with prescribedwall motion the flow rate agrees better with the MRI mea-surements.

TABLE 1. Peak flow rate and when peak flow rate occurs foreach case.

Case Peak flow rate (mL/s) Time (s)

MRI measurement 454 0.16

Rigid wall 567 0.07

2 Measurements 433 0.07

9 Measurements 436 0.14

25 Measurements 430 0.20

LANTZ et al.

motion. Conservation of mass together with a rigidwall assumption implies that the amount of mass thatenters the domain in the ascending aorta must at thesame time leave it in the branching vessels in the aorticarch and in the abdominal aorta. This is not the case

in vivo where the aortic volume changes. Instead, theaorta acts as an elastic reservoir, when the aortic walldistends due to increased aortic pressure. This Wind-kessel effect will affect the local flow field as mass isstored and removed at different locations and times,

FIGURE 7. (a, b) Upper row, left to right: TAWSS for the cases with prescribed wall motion using 25 geometries, 9 geometries, 2geometries, and rigid wall assumption at minimum volume and at maximum volume, respectively. Lower row, Left to right: OSI forthe cases with prescribed wall motion using 25 geometries, 9 geometries, 2 geometries, and rigid wall assumption at minimumvolume and at maximum volume, respectively.

FIGURE 8. Left to right: wall shear stress magnitude at peak flow rate with prescribed wall motion using 25 geometries, 9geometries, 2 geometries, and rigid wall assumption at minimum volume and at maximum volume, respectively.

Incorporating Wall Motion in Blood Flow Simulations

compared to when the aortic walls are considered rigid.This effect can be seen in the velocity profiles found inFigs. 4 and 5, and is more pronounced in Fig. 6 wherethe flow rates for each case are plotted. The effect ofthe wall motion is obvious, as the rigid wall assump-tion results in a totally different flow rate curve com-pared to the measurement. The lack of distensibility ina rigid wall model forces more blood through themodel during systole, while the models that accountfor wall motion will store parts of the blood volumeand release it later in the cardiac cycle. It is also seen inFig. 6 that the models that use all 25 measurementsand 9 measurements agrees better with MRI data,compared to the case which only used 2 measurements.Incorporating only 2 geometries was apparentlyinsufficient to accurately capture the Windkessel-effect.This is because the local wall displacement was notcaptured accurately enough in the interpolation,compared to when including more geometries. Boththe shape and magnitude of the velocity profile in thedescending aorta changed when incorporating wallmotion and the agreement with in vivo measurementsimproved considerably. Clearly, the interactionbetween the wall and the flow will affect the hemody-namics. There are small differences in the shape of thevelocity profile between the baseline case and the twocases with fewer geometries. This indicates that themethod works for 4D morphological data with rela-tively low temporal resolution, which in turn wouldshorten scan time. The small differences between theMRI velocity profiles and the baseline CFD case couldbe to uncertainties in boundary condition specification,MRI measurement and segmentation of the wall.

The time-averaged WSS and OSI are both time-integrated quantities—as such, time dependent effectsmay be filtered out and diminished in the results. Thiscan be seen in the results for TAWSS and OSI, wherethe prescribed wall motion simulations yield verysimilar results. This is in line with a previous study10

where it was concluded that the time-averaging theWSS parameters effectively filters out any temporaleffects. On the other hand, the instantaneous WSSmagnitude is affected by the wall motion: at peak flowrate both rigid wall cases result in higher WSS valuescompared to the three cases with prescribed wall

motion. Instantaneous WSS, as well as time-averagedWSS and OSI have been suggested to play a role in thedevelopment of atherosclerosis.1,11,15,16 If rigid-wallCFD is used to find thresholds for when atheroscle-rosis can develop, then those thresholds values mightbe inaccurate. This study shows that a rigid wallassumption might be questionable if one is interestedin instantaneous WSS values.

CONCLUSIONS

Incorporating subject-specific wall motion in bloodflow simulations results in considerable improvementof the computed flow field compared to in vivo mea-surements. The proposed approach is straight forwardto implement, and the additional computational costscompared to usage of a rigid wall model is relativelysmall. With the inclusion of measured subject-specificwall motion, the physiological relevance of simulationsof arterial blood flow increases, and can lead to novelinsights in vascular blood flow dynamics.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s13239-014-0187-5) contains supplementary material, which isavailable to authorized users.

ACKNOWLEDGMENTS

This study was funded by the Swedish e-ScienceResearch Centre, the Centre for Industrial InformationTechnology, the Swedish Research Council, and theEuropean Research Council. The Swedish NationalInfrastructure for Computing is acknowledged forcomputational resources provided by the NationalSupercomputer Centre.

CONFLICT OF INTEREST

The authors declared that they have no conflict ofinterest.

STATEMENT OF ANIMAL STUDIES

No animal studies were carried out by the authorsfor this article.

STATEMENT OF HUMAN STUDIES

All procedures followed were in accordance with theethical standards of the responsible committee on

TABLE 2. Wall clock time for one cardiac cycle for each caseusing 40 CPU cores.

Simulation case No. of meshes Time (h) Additional time

Rigid wall min volume 1 3.0 –

Rigid wall max volume 1 3.0 –

Prescribed wall motion 2 3.2 7%

Prescribed wall motion 9 3.4 13%

Prescribed wall motion 25 3.5 17%

LANTZ et al.

human experimentation (institutional and national)and with the Helsinki Declaration of 1975, as revisedin 2000 (5). Informed consent was obtained from thesubject for being included in the study.

REFERENCES1Assemat, P., and K. Hourigan. Evolution and rupture ofvulnerable plaques: a review of mechanical effects. Chro-noPhysiol. Ther. 3:23–40, 2013.2Barakat, A. I. Blood flow and arterial endothelial dys-function: mechanisms and implications. C.R. Phys. 14:479–496, 2013.3Caballero, A., and S. Laın. A review on computationalfluid dynamics modelling in human thoracic aorta. Car-diovasc. Eng. Technol. 4(2):103–130, 2013.4Gao, F., Z. Guo, M. Sakamoto, and T. Matsuzawa. Fluid–structure interaction within a layered aortic arch model. J.Biol. Phys. 32:435–454, 2006.5He, X., and D. N. Ku. Pulsatile flow in the human leftcoronary artery bifurcation: average conditions. J. Bio-mech. Eng. 118:74–82, 1996.6Heiberg, E., J. Sjogren, M. Ugander, M. Carlsson, H.Engblom, and H. Arheden. Design and validation of seg-ment—freely available software for cardiovascular imageanalysis. BMC Med. Imaging 10:1, 2010.7Jin, S., J. Oshinski, and D. P. Giddens. Effects of wallmotion and compliance on flow patterns in the ascendingaorta. J. Biomech. Eng. 125:347–354, 2003.8Khanafer, K., J. Bull, and R. Berguer. Fluid–structureinteraction of turbulent pulsatile flow within a flexible wallaxisymmetric aortic aneurysm model. Eur. J. Mech. B28:88–102, 2009.9Ku, D. N., D. P. Giddens, C. K. Zarins, and S. Glagov.Pulsatile flow and atherosclerosis in the human carotidbifurcation. Positive correlation between plaque locationand low oscillating shear stress. Arteriosclerosis 5:293–302,1985.

10Lantz, J., J. Renner, and M. Karlsson. Wall shear stress ina subject specific human aorta—influence of fluid–structureinteraction. Int. J. Appl. Mech. 3:759–778, 2011.

11Malek, A. M., S. L. Alper, and S. Izumo. Hemodynamicshear stress and its role in atherosclerosis. JAMA 282:2035–2042, 1999.

12Moireau, P., N. Xiao, M. Astorino, C. A. Figueroa, D.Chapelle, C. A. Taylor, and J. F. Gerbeau. External tissuesupport and fluid–structure simulation in blood flows.Biomech. Model. Mechanobiol. 11:1–18, 2012.

13Mynard, J. P., B. A. Wasserman, and D. A. Steinman.Errors in the estimation of wall shear stress by maximumDoppler velocity. Atherosclerosis 227:259–266, 2013.

14Petersson, S., P.Dyverfeldt, and T. Ebbers. Assessment of theaccuracy ofMRI wall shear stress estimation using numericalsimulations. J. Magn. Reson. Imaging 36:128–138, 2012.

15Resnick, N., H. Yahav, A. Shay-Salit, M. Shushy, S.Schubert, L. C. M. Zilberman, and E. Wofovitz. Fluidshear stress and the vascular endothelium: for better andfor worse. Prog. Biophys. Mol. Biol. 81:177–199, 2003.

16Steinman, D. A. Image-based computational fluid dynam-ics modeling in realistic arterial geometries. Ann. Biomed.Eng. 30:483–497, 2002.

17Taylor, C. A., M. T. Draney, J. P. Ku, D. Parker, B. N.Steele, K. Wang, and C. K. Zarins. Predictive medicine:computational techniques in therapeutic decision-making.Comput Aided Surg. 4:231–247, 1999.

18Taylor, C. A., and C. Figueroa. Patient-specific modelingof cardiovascular mechanics. Annu. Rev. Biomed. Eng.11:109–134, 2009.

19Taylor, C. A., and D. A. Steinman. Image-based modeling ofblood flow and vessel wall dynamics: applications, methodsand future directions.Ann. Biomed. Eng. 38:1188–1203, 2010.

20Torii, R., J. Keegan, N. B. Wood, A. W. Dowsey, A. D.Hughes, G.-Z. Yang, D. N. Firmin, S. A. Thom, and X. Y.Xu. MR image-based geometric and hemodynamic inves-tigation of the right coronary artery with dynamic vesselmotion. Ann. Biomed. Eng. 38:2606–2620, 2010.

Incorporating Wall Motion in Blood Flow Simulations