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Am J Physiol Heart Circ Physiol 291: H668-H676, 2006. First published April 7, 2006; doi:10.1152/ajpheart.01301.2005
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Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling

Beverly T. Tang,1 Christopher P. Cheng,1 Mary T. Draney,2 Nathan M. Wilson,2 Philip S. Tsao,3 Robert J. Herfkens,4 and Charles A. Taylor1,2,5

Departments of 1Mechanical Engineering, 2Surgery, 3Medicine, 4Radiology, and 5Bioengineering, Stanford University, Stanford, California

Submitted 8 December 2005 ; accepted in final form 8 March 2006


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Localization of atherosclerotic lesions in the abdominal aorta has been previously correlated to areas of adverse hemodynamic conditions, such as flow recirculation, low mean wall shear stress, and high temporal oscillations in shear. Along with its many systemic benefits, exercise is also proposed to have local benefits in the vasculature via the alteration of these regional flow patterns. In this work, subject-specific models of the human abdominal aorta were constructed from magnetic resonance angiograms of five young, healthy subjects, and computer simulations were performed under resting and exercise (50% increase in resting heart rate) pulsatile flow conditions. Velocity fields and spatial variations in mean wall shear stress (WSS) and oscillatory shear index (OSI) are presented. When averaged over all subjects, WSS increased from 4.8 ± 0.6 to 31.6 ± 5.7 dyn/cm2 and OSI decreased from 0.22 ± 0.03 to 0.03 ± 0.02 in the infrarenal aorta between rest and exercise. WSS significantly increased, whereas OSI decreased between rest and exercise at the supraceliac, infrarenal, and suprabifurcation levels, and significant differences in WSS were found between anterior and posterior sections. These results support the hypothesis that exercise provides localized benefits to the cardiovascular system through acute mechanical stimuli that trigger longer-term biological processes leading to protection against the development or progression of atherosclerosis.

atherosclerosis; shear stress; magnetic resonance imaging; finite element analysis

ADVERSE HEMODYNAMIC conditions, such as complex, recirculating flow, low mean wall shear stress, high spatial gradients in shear stress, and high particle residence times, are hypothesized to contribute to the localization of atherosclerotic plaque throughout the vasculature. In the abdominal aorta, a correlation between atherosclerosis and areas of low wall shear stress has been elucidated with prior autopsy (2, 7, 27, 31, 39) and experimental studies (5, 16, 19, 20, 22, 32). Specifically, Cornhill et al. (2) observed a high probability of occurrence of sudanophilic lesions along the posterior and lateral walls of autopsy specimens obtained from young, healthy males, whereas Roberts et al. (27) and Glagov et al. (7) reported atherosclerosis to be more common in the abdominal aorta than in the thoracic aorta. Furthermore, previous investigations completed by Friedman et al. (5), Moore et al. (16), and Pedersen et al. (22) correlated regions of low wall shear stress and/or high temporal oscillations in shear to locations of increased intimal thickening using in vitro flow models and autopsy specimens. Recent in vivo studies have shown that endothelial cells located in disturbed flow regions of the porcine aorta express a proinflammatory transcription profile (21), and in vitro cell culture work has shown that oscillating shear can induce an inflammatory response, including an increase in reactive oxygen species (3, 9, 29).

Conversely, elevated blood flow associated with exercise has been hypothesized to result in hemodynamic conditions that inhibit atherosclerosis, such as unidirectional laminar flow, increased wall shear stress, and enhanced transport of cholesterol from the vessel wall (11, 18, 32, 33). It has been shown in vitro that the vascular endothelium can sense and respond to high shear environments by alignment in the direction of flow, upregulation of vasodilators and antioxidants, and downregulation of vasocontrictors, inflammatory molecules, and adhesion proteins (6, 12, 36, 37), along with a variety of other responses that mediate the initiation and proliferation of disease. Although it is known that high shear forces are able to induce an atheroprotective phenotype on endothelial cells in culture, the lack of spatial and temporal quantification of physiological flow and shear stress patterns has hampered the use of more realistic flow conditions in biological experiments in vitro.

Previous in vivo studies using noninvasive medical imaging techniques to quantify blood flow and wall shear stress during resting and exercise conditions in the human abdominal aorta have been limited to localized imaging planes (1, 19, 20, 24, 32) and have not fully described the three-dimensional distribution of hemodynamic conditions. Similarly, in vitro flow studies have traditionally been coupled with imaging techniques that only enable flow and shear stress quantification at specific sites (16, 22). Although these methods facilitate higher resolution and a greater number of images compared with in vivo studies due to lack of motion and longer allowable scanning times, they are still limited to quantification at a set number of axial imaging planes and were conducted for a single, idealized abdominal aorta model.

Computational flow simulations, using finite element methods to solve the Navier-Stokes equations, provide a means to quantify and visualize complex hemodynamic conditions along the entire abdominal aorta with excellent spatial and temporal resolution. Although this analysis has previously been described for idealized models under pulsatile resting and exercise conditions (33, 34), the present investigation has leveraged recent advances enabling the construction of more anatomically representative abdominal aortic models from three-dimensional magnetic resonance angiography (MRA) data. This technique has been successfully applied to other parts of the vasculature, such as the carotid artery, where hemodynamic conditions are also believed to have an effect on the localization of atherosclerotic plaque (13, 30). Furthermore, in vivo, pulsatile velocity profiles obtained from cine phase-contrast magnetic resonance imaging (PC-MRI) were used to specify inlet and outlet boundary conditions. These flow simulations result in a subject-specific, three-dimensional description of the flow patterns present in the human abdominal aorta. In particular, spatial variations in mean wall shear stress and oscillations in shear were quantified under resting and exercise conditions for five young, healthy adults and compared with previously obtained results from in vivo, in vitro, and computational studies.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Magnetic resonance imaging. Gadolinium-enhanced MRA scans of five healthy subjects (2 women and 3 men, aged 20–30 yr) in the supine position were obtained in a 1.5-T GE Signa (GE Medical Systems, Milwaukee, WI) MR scanner. These imaging studies were conducted under an Institutional Review Board-approved protocol, and informed consent was obtained from each of the five healthy subjects. A three-dimensional fast gradient echo MRA sequence was used to obtain a volume of coronal slices. Slice thickness ranged from 2.0 to 2.6 mm (reconstructed at 1.0 to 1.3 mm), with 72 to 96 slices per volume. A 512 x 192 acquisition matrix (reconstructed to 512 x 512) was used with an in-plane field of view of 30 x 30 to 40 x 40 cm2 to provide an in-plane reconstructed spatial resolution of 0.586 to 0.781 mm. Other scan parameters included repetition times (TR) of 3.8 to 4.6 ms, echo times (TE) of 0.852 to 0.980 ms, and flip angles of 20° or 25°.

During the same imaging study, cine PC-MRI were taken perpendicularly to the aorta at rest at the supraceliac and infrarenal levels in the 1.5-T GE Signa. The acquisitions were gated to the cardiac cycle using ECG leads, and 24 time points within the cardiac cycle were reconstructed. Three components of velocity were measured through 5-mm-thick slices with through-plane velocity encoding gradients of 150 cm/s and in-plane velocity encoding gradients between 25 and 50 cm/s. Other imaging parameters included 24 or 25 cm2 field of views, 256 x 256 or 512 x 512 acquisition matrices, 0.47- to 0.98-mm pixel sizes, 14- to 26-ms TRs, 5.2- to 9.1-ms TEs, and a 20° flip angle. True through-plane velocity resolution equaled four times the TR (56 to 104 ms).

Image processing, model construction, and boundary condition specification. Each volume of MRA data was corrected by using proprietary software (GE Medical Systems, Milwaukee, WI) for known gradient nonlinearities during acquisition that can cause distortion in the slice direction (4). Three-dimensional, subject-specific solid models of the aorta and its major branches (celiac, superior mesenteric, and renal arteries) were created from the MRA images using custom software (41) and discretized by using a commercially available, automatic mesh generation program (MeshSim, Simmetrix, Clifton Park, NY). Figure 1 summarizes the model construction procedure from MR data to creating a finite element mesh. The subject-specific meshes had an average size of 1.22 ± 0.26 million tetrahedral elements (241,000 ± 48,000 nodes), which corresponded to a maximum element edge length of 0.75 mm.


Figure 1
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  		Fig. 1. Schematic of solid model construction from magnetic resonance angiography data. a: Volume-rendered image of a contrast-enhanced magnetic resonance angiogram illustrating abdominal aortic anatomy. b: Centerline paths were created along the vessels of interest. c: Two-dimensional segmentations of vessel lumen were taken perpendicularly to the vessel path. Segmentations were found using a level set method (see Ref. 38). d: Two-dimensional segmentations were lofted to form solid models for each vessel which were then joined to form a complete three-dimensional solid model of the aorta and its branches. e: The solid model was discretized into a finite element mesh (gold) and is shown superimposed on the original volume-rendered magnetic resonance angiogram. Inset: surface mesh in greater detail.

 
The cine phase contrast images (PC-MRI) taken perpendicularly to the aorta at the supraceliac and infrarenal levels were used to calculate in vivo, time-resolved volumetric flow. For each of the 24 time points, the lumen of the aorta was determined from the intensity magnitude images using a level set method (38), and through-plane velocity values for each pixel were integrated over the bounded area to calculate a total volume flow rate (40). The flow waveforms at the supraceliac and infrarenal locations were peak-aligned and subtracted to determine the amount of flow entering the digestive and renal arteries, where the flow split was prescribed by using data previously compiled by Moore and Ku (31% to the celiac artery, 23% to the superior mesenteric artery, and 23% to each renal artery) (15). The periodic flow waveforms were then used to compute analytic velocity profiles using pulsatile flow theory (42), which served as inlet (supraceliac aorta) and outlet (celiac, superior mesenteric, renal, and one set of iliac arteries) boundary conditions. The remaining outlets (opposite side external and internal iliac arteries) were prescribed with zero-pressure boundary conditions, and a rigid wall assumption and a no-slip boundary condition at the wall were also prescribed.

To simulate exercise, the total volumetric flows under resting conditions at the supraceliac and infrarenal levels of the aorta were increased threefold and sixfold, respectively, and the cardiac cycle was shortened to represent a 50% increase in resting heart rate. These values were derived from average increases measured in vivo at the supraceliac and infrarenal levels in 11 young, healthy subjects pedaling on a custom-built MR-compatible exercise cycle (32). Average exercise flow waveforms were computed by using data from the same 11 subjects and scaled to represent the total increased volumetric flow at each anatomic level for each subject. Figure 2 illustrates boundary condition specification for one representative subject-specific flow simulation under resting and simulated exercise conditions.


Figure 2
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  		Fig. 2. Boundary condition specification for one representative subject-specific simulation. Flow rate through time was calculated from phase contrast magnetic resonance images taken at the supraceliac and infrarenal levels of the aorta at rest. These two flow-rate waveforms were then peak-aligned and subtracted to find the total amount of flow leaving the celiac (b), superior mesenteric (c), and renal (d and e) arteries. The distribution to these individual arteries was that previously compiled by Moore et al. (Ref. 15). Furthermore, half of the flow at the infrarenal level was prescribed to the right external (g) and right internal (f) iliac arteries. Exercise conditions were simulated by increasing the heart rate by 50%, increasing flow at the supraceliac level by three times, increasing flow at the infrarenal level by six times, and changing the flow rate waveform from a triphasic shape to a biphasic shape. All changes made to simulate exercise were consistent with changes found in vivo between rest and cycling exercise in young, healthy adults as previously reported by Taylor et al. (Ref. 32). A time-varying, analytic velocity profile, derived from the Womersley theory (Ref. 42), was prescribed at the inlet (a) and all outlets (b–g) where a flow boundary condition is specified.

 
Once the boundary conditions were applied at each inlet and outlet, the flow solution for each subject-specific mesh was obtained by using a stabilized finite element method to solve the incompressible Navier-Stokes equations (34).

Analysis of simulation results. From the simulation results, time-averaged wall shear stress ({tau}mean) was computed for each subject at rest and under simulated exercise conditions. {tau}mean is defined as the magnitude of the time-averaged surface traction vector ts, which is the tangential component of the traction vector t.

Formula 1(1)
where ts = t – (t·n)n and t = {sigma}n; {sigma} is the stress tensor, n is the surface normal vector, and T is the period of the cardiac cycle. A comparison between the two physiological states was made by subtracting the time-averaged wall shear stress map at rest from that of simulated exercise and normalizing this difference map to each subject’s resting condition.

Temporal oscillations in wall shear stress are described by the oscillatory shear index (OSI) (8):

Formula 2(2)
Note that the values of OSI range from 0 to 0.5, where a value of 0 corresponds to a unidirectional wall shear stress throughout the cardiac cycle, whereas a value of 0.5 corresponds to wall shear stress with a time-average of zero. Because the OSI is already a normalized quantity, the change in OSI between rest and exercise was found by subtracting the OSI map under exercise conditions from the OSI map under resting conditions.

To quantitatively analyze and compare the mean wall shear stress (WSS), WSS normalized difference, OSI, and OSI difference maps for all subjects, 5-mm strips were taken perpendicularly around the circumference of the aorta at the supraceliac, infrarenal, and suprabifurcation levels, and values were averaged over the surface area. Although these locations were chosen for their relevance to atherosclerosis and the slice thickness was chosen to be comparable to that of previous in vivo MRI rest/exercise studies (32), any location and slice thickness can be analyzed by using this technique. In addition, spatially averaged mean WSS and OSI were found for the entire infrarenal aorta (defined from the infrarenal slice to the suprabifurcation slice), as well as for the anterior and posterior portions of the infrarenal aorta.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
The flow solutions computed with resting conditions for each subject demonstrated low, recirculating flow in the infrarenal segment of the abdominal aorta during the diastolic portion of the cardiac cycle. Furthermore, reverse flow was observed along the posterior wall at the level of the celiac and superior mesenteric branches during diastole, and multiple vortices could be observed in each of these subject-specific simulations. The vortices were localized to the celiac branching, renal branching, and suprabifurcation levels.

Under simulated exercise conditions, higher velocity, more unidirectional flow was observed throughout the cardiac cycle. The retrograde flow observed under resting conditions in the infrarenal aorta during diastole was eliminated during simulated exercise conditions for three of the five subjects. Reverse flow along the posterior wall at the celiac and superior mesenteric branches was significantly reduced but still present. Figure 3 summarizes these results for one representative subject. Velocity magnitude is plotted on a midplane slice under resting and simulated exercise conditions at peak systole, end systole, and mid-diastole. Note that regions of low flow velocities and recirculation zones that exist along the posterior wall under resting conditions are replaced by higher flow velocities and less complex flow under simulated exercise conditions.


Figure 3
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  		Fig. 3. Velocity magnitude plotted on a midplane slice of the abdominal aorta for one representative subject under resting (left) and simulated exercise (right) conditions. Three time points during the cardiac cycle, corresponding to peak systole (a), end systole (b), and mid-diastole (c), are shown. Regions of low flow velocities and recirculation zones that exist along the posterior wall under resting conditions were replaced by higher flow velocities and more laminar flow under simulated exercise conditions.

 
Time-averaged WSS plots (Fig. 4) revealed areas of low WSS (<4 dyn/cm2) along the posterior wall in both the infrarenal section and the section opposite to the celiac and superior mesenteric arteries under resting conditions. These regions of low time-averaged WSS were mostly eliminated with exercise conditions. A more detailed illustration is given in Fig. 5, where WSS vectors are plotted along the posterior wall for one representative subject.


Figure 4
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  		Fig. 4. Wall shear stress (WSS) averaged over three cardiac cycles, plotted along the posterior wall of all five subjects under resting (left) and simulated exercise (middle) conditions. Normalized difference maps (right), defined by (WSSexercise – WSSrest)/WSSrest, illustrate locations of greatest change in WSS between rest and simulated exercise. Areas of low mean wall shear stress present at the level of the renal arteries and below under resting conditions were mostly eliminated under simulated exercise conditions for all subjects. Furthermore, differing anatomy and physiology played a large role in the distinct shear stress patterns that are observed in each subject.

 

Figure 5
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  		Fig. 5. WSS vectors plotted along the posterior wall of the infrarenal aorta for one representative subject under resting (left) and simulated exercise (right) conditions. Four evenly-spaced time points throughout the cardiac cycle are shown, and vectors are colored by magnitude. Vectors are mostly unidirectional during the systolic portion of each cycle but become highly varying in direction during diastole.

 
OSI, averaged over three cardiac cycles, is plotted along the posterior wall of all five subjects under resting and simulated exercise conditions in Fig. 6. Areas of high oscillations in shear stress were found to correspond to areas of low mean WSS, and although OSI is reduced under simulated exercise conditions, regions of high oscillations (OSI = 0.5) still exist in certain locations, such as at the level of the renal arteries. OSI difference maps show that the greatest change between resting and simulated exercise conditions occurs in the section between the renal arteries and the iliac bifurcation.


Figure 6
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  		Fig. 6. Oscillatory shear index (OSI) averaged over three cardiac cycles, plotted along the posterior wall of all five subjects under resting (left) and simulated exercise (middle) conditions. OSI difference maps (right), defined by OSIrest – OSIexercise, illustrate locations of greatest change in OSI between rest and simulated exercise. Areas of high OSI correlated to areas of low mean WSS (plotted in Fig. 4), and although oscillations in shear stress were reduced under simulated exercise conditions, high oscillations (OSI = 0.5) were still present in certain locations (i.e., level of the renal arteries).

 
Figure 7 summarizes the mean WSS and OSI results for all five subjects at the supraceliac, infrarenal, and suprabifurcation levels. Between resting and simulated exercise conditions, WSS increased from 8.4 ± 1.8 to 20.2 ± 3.7 dyn/cm2 at the supraceliac level (P = 0.0004), 5.1 ± 1.3 to 33.3 ± 12.6 dyn/cm2 at the infrarenal level (P = 0.0001), and 5.1 ± 0.8 to 33.2 ± 4.5 dyn/cm2 at the suprabifurcation level (P = 0.0050). Furthermore, the difference in WSS between rest and simulated exercise, normalized to each subject’s resting WSS values, was found to be 1.37 ± 0.32 at the supraceliac level, 5.97 ± 1.13 at the infrarenal level, and 5.56 ± 0.56 at the suprabifurcation level. This normalized difference between rest and simulated exercise was significantly higher (P ≤ 0.002) for the infrarenal and suprabifurcation levels compared with the supraceliac location.


Figure 7
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  		Fig. 7. Summary of mean WSS (in dyn/cm2) and OSI results for all five subjects at three specific locations of interest. A 5-mm strip was taken around the circumference of the vessel at each location, and values were averaged over the surface area. On the model (left), wall shear stress contours are shown together with locations where results were extracted for one representative subject. A statistically significant (P ≤ 0.005) increase in WSS was found at each location, and the greatest change between rest and simulated exercise conditions occurred at the infrarenal level. In addition, statistically significant decreases in OSI were found at the infrarenal and suprabifurcation levels, and the greatest change in OSI between rest and simulated exercise conditions occurred in the suprabifurcation region.

 
Between resting and simulated exercise conditions, OSI decreased from 0.14 ± 0.07 to 0.06 ± 0.03 at the supraceliac level (P = 0.0638), 0.23 ± 0.03 to 0.07 ± 0.03 at the infrarenal level (P = 0.0345), and 0.20 ± 0.03 to 0.02 ± 0.01 at the suprabifurcation level (P = 0.0006). The average decrease in OSI between resting and simulated exercise conditions was 0.08 ± 0.07 at the supraceliac level, 0.16 ± 0.04 at the infrarenal level, and 0.18 ± 0.04 at the suprabifurcation level.

In addition, under resting conditions, there was a significant (P ≤ 0.02) difference in mean WSS values between the supraceliac and infrarenal levels as well as between the supraceliac and suprabifurcation levels, and there was a significant (P ≤ 0.02) difference in OSI values between the supraceliac and infrarenal levels. Under simulated exercise conditions, a significant (P ≤ 0.001) difference in mean WSS was found between the supraceliac and suprabifurcation levels, and significant (P ≤ 0.05) differences were found in WSS between the supraceliac and infrarenal levels and in OSI between both the supraceliac and suprabifurcation as well as the infrarenal and suprabifurcation levels.

When the entire portion of the infrarenal aorta (from the infrarenal slice to the suprabifurcation slice) was taken into account, the mean WSS, averaged over all subjects, increased from 4.8 ± 0.6 to 31.6 ± 5.7 dyn/cm2 (P = 0.0003), and OSI decreased from 0.22 ± 0.03 to 0.03 ± 0.02 (P = 0.0010) between resting and simulated exercise conditions.

This portion of the infrarenal aorta was then divided into anterior and posterior sections, and the mean WSS was found to be 5.4 ± 0.6 (anterior) and 4.2 ± 0.6 (posterior) dyn/cm2 under resting conditions and 36.1 ± 8.6 (anterior) and 26.9 ± 3.5 (posterior) dyn/cm2 under simulated exercise conditions. Similarly, the averaged OSI was found to be 0.18 ± 0.04 (anterior) and 0.26 ± 0.03 (posterior) under resting conditions and 0.02 ± 0.01 (anterior) and 0.05 ± 0.04 (posterior) under simulated exercise conditions. The differences in mean WSS and OSI between anterior and posterior sections were statistically significant (P ≤ 0.0001) at rest but exhibited higher P values (P < 0.05 for mean WSS) or were not significant at all (P = 0.13 for OSI) under simulated exercise conditions.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
The results found from these computational flow simulations provide, for the first time, quantitative data on subject-specific spatial variations in shear stress at rest and exercise in the human abdominal aorta. Although results obtained with previous computational investigations offered spatial and temporal hemodynamic quantification on idealized models and those obtained with in vivo imaging techniques enabled subject-specific quantification at discrete locations, this study leveraged both methodologies to attain a three-dimensional, spatially varying description of hemodynamic conditions in five young, healthy adults.

The reverse-flow patterns that were observed along the posterior wall of the infrarenal aorta and opposite the celiac and superior mesenteric arteries at rest were consistent with previous computational (35), in vitro (15, 23), and in vivo (10, 17, 28, 32) studies and correlated to areas of localized sudanophilia (2). In computational simulations of blood flow in an idealized abdominal aortic geometry, Taylor et al. (35) noted that the velocity field in the infrarenal aorta was directed toward the anterior wall and that a recirculation region existed along the posterior wall at the level of the renal arteries. Similar features were also observed in these subject-specific simulations and were most likely due to the flow being diverted anteriorly by the celiac and superior mesenteric arteries, causing a vortex to form inferiorly, near or below the level of the renal arteries. Therefore, the anatomical positioning of the celiac and superior mesenteric bifurcations, relative to the renal bifurcations, necessarily affected the location of the recirculation zone in each subject. Furthermore, this vortex moved superiorly along the posterior wall in diastole due to the net flow reversal, and the extent to which the vortex traveled was largely determined by the heart rate of the individual. In subjects with faster heart rates, the unidirectional flow of systole arrived before the recirculation region was able to progress superiorly. However, in subjects with slower heart rates, longer diastoles allowed the vortex to become more developed and travel farther upstream. This observation may seem counterintuitive to the correlation between cardiovascular fitness and low heart rate, but any increase in vortex formation that may occur is likely counterbalanced by the overall vasoprotective effects of exercise, including increased coronary artery filling time with lengthened diastole and increased shear stress acting upon the endothelium during the exercise bout.

Complex velocity patterns were also exhibited under exercise conditions, but the increase in flow produced a more unidirectional, laminar flow environment in the infrarenal portion of the aorta and a reduction in the size of the recirculation region at the level of the renal arteries, consistent with observations made with previous computational (33) and in vitro (14) experimental studies in idealized models. Elimination of flow reversal with exercise has also been described in prior in vivo studies (32).

Plots of spatial variations in shear stress and temporal oscillations in shear illustrated that much of the low wall shear stress that existed at rest was eliminated during exercise, yet pockets of high oscillations in shear were still present under exercise conditions. Most of the subjects had reduced oscillations in shear along the posterior infrarenal wall but retained a region of localized higher OSI at the level of the renal branching points, where the previously mentioned flow recirculation persisted. Previous work (5, 16, 22) has suggested a correlation between localization of atherosclerosis and areas of low mean WSS and/or high OSI. This investigation demonstrated that the increase in flow and heart rate associated with exercise was sufficient to eliminate low mean WSS but not temporal oscillations in shear stress and suggests that a higher level of exercise may be needed to counter the deleterious effects of high OSI. Furthermore, difference maps between rest and exercise illustrated that areas with the greatest increases in WSS were not necessarily the same locations with the greatest decreases in OSI.

Mean WSS, averaged over 5-mm-thick circumferential bands for all subjects, was found to be higher than previously reported values at similar locations with in vivo (32) and in vitro (16) imaging techniques. The average flow rates obtained or used in the aforementioned studies were comparable to those used in this current subject-specific investigation; however, the average aortic diameter at the supraceliac level in this analysis was found to be considerably smaller than those in other studies, thus explaining, in part, the higher mean WSS values found in this present investigation. The lower average diameter might be due to underestimation of the lumen boundary by the image segmentation method used or the diastolic-weighted nature of time-averaged MRA data.

Another explanation for the higher mean WSS and OSI values obtained in the present study might be the lower spatial resolution and temporal averaging of MRI techniques used in previous studies compared with the current computational simulations. Because the reported values were found by averaging around the circumference of the aorta, a more spatially well-defined low WSS recirculation zone, such as what was observed in these computational simulations, would necessarily lead to higher averaged WSS. Furthermore, the higher spatial and temporal resolution of the current simulations were able to reveal small oscillations in flow direction, thus leading to higher OSI values compared with previous in vivo imaging studies (32). It should also be noted that a number of slice thicknesses (1, 2, 3, 4, 5, and 10 mm) were used to analyze mean WSS and OSI in this work with little effect on the final results.

Preliminary mesh-dependence studies showed that mean WSS values averaged around circumferential sections increased between solutions run with 260,000, 1.2 million, and 3.7 million elements. Although these results imply that mesh independence has not yet been achieved, the flow features and quantitative data elucidated in this study are still believed to be informative, demonstrative of in vivo conditions, and representative of what can be feasibly accomplished with current computing technology. Furthermore, although the absolute values of shear stress and OSI may have differed between mesh sizes, the ultimate trends between rest and exercise did not, thus suggesting that the conclusions reached in this work would be similar at higher mesh densities.

Other limitations of this investigation included the use of a rigid wall model and assumptions of a Newtonian viscosity and those made for the inlet and outlet flow conditions. It is thought that incorporation of wall compliance would decrease the magnitude of shear stress, perhaps balancing the increase that would be found with more refined finite element meshes. In a weakly coupled fluid structure interaction finite element method, Perktold and Rappitsch (26) reported a 25% decrease in WSS when wall deformability was taken into account. However, they also noted that incorporating compliance only had a small effect on the flow field, thus suggesting that the locations of recirculation zones would remain relatively unchanged.

Using a Newtonian constitutive model for viscosity is a reasonable approximation for blood flow in large arteries, and Perktold et al. (25) reported shear stress magnitude differences only on the order of 10% between non-Newtonian and Newtonian viscosity models for simulating pulsatile flow in the carotid artery.

Inlet and outlet velocity profiles were derived from Womersley’s theory for pulsatile flow (42), which resulted in an axisymmetric, parabolic-shaped profile. Although PC-MRI taken at the supraceliac level revealed a more plug-shaped profile, little difference was found in downstream WSS and OSI patterns when the inlet was prescribed with the velocity profile obtained directly from PC-MRI. Furthermore, limitations in the temporal resolution of PC-MRI led to temporal smoothing of the inlet and outlet volumetric flow profiles.

Despite these limitations and discrepancies with previously reported work, the findings on the hemodynamic conditions that existed during resting and light exercise conditions were still compelling. At rest, a significantly higher mean WSS and lower OSI was found at the supraceliac level compared with the infrarenal level, as well as at the anterior wall of the infrarenal aorta compared with the posterior wall, and both the supraceliac portion and anterior wall of the infrarenal aorta are known to be less prone to atherosclerotic lesions than the infrarenal portion and posterior wall, respectively (2, 7, 31, 39). This confirms previous reports of correlation between hemodynamic conditions and localization of disease.

Under simulated exercise conditions, the differences in mean WSS and OSI between the supraceliac and infrarenal levels and the anterior and posterior walls became less significant, thus suggesting that exercise is able to create more uniform hemodynamic conditions throughout the entire aorta and expose lesion-prone areas to the flow environment experienced by lesion-resistant areas. Furthermore, the significant increases in mean WSS and decreases in OSI observed in almost all portions of the aorta analyzed in this study support the hypothesis that exercise is able to provide localized benefits to the cardiovascular system via acute mechanical stimuli that can trigger longer-term biological processes leading to protection against the development or progression of atherosclerosis in certain areas.

In conclusion, the combination of MRI and computational fluid dynamics used in this investigation enabled a more complete, subject-specific characterization of the hemodynamic conditions that exist in the abdominal aorta under resting and exercise conditions. The findings reported in this study support the hypothesis that even relatively light levels of exercise were sufficient to improve local unfavorable hemodynamic conditions, such as flow recirculation, low WSS, and high temporal oscillations in shear stress, that were present at rest and found in regions more susceptible to atherosclerotic development. Thus these simulations provide motivation for examining flow conditions at higher levels of exercise and incorporating more physiologically accurate attributes, such as vessel deformability, into future investigations. Furthermore, these whole vessel, subject-specific modeling techniques provide additional insight into the differences in flow features among individuals that was not possible with idealized models and offer spatial detail that cannot be achieved with localized imaging planes. The data gathered in this study can be used to guide future cell culture experiments, and the complexity of the flow features observed suggests that more refined experimental techniques may be required to emulate these phenomena in vitro to study the effect of physiologically relevant mechanical forces on the endothelium.


   GRANTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This research was supported by the National Science Foundation Grant No. 0205741, the Pacific Vascular Research Foundation, the National Institutes of Health Grant No. P41RR09784, the Lucas Foundation, and GE Medical Systems.


   ACKNOWLEDGMENTS
 
We gratefully acknowledge Anne Sawyer-Glover for assisting in the magnetic resonance imaging portions of this study.


   FOOTNOTES
 

Address for reprint requests and other correspondence: C. A. Taylor, Clark Center, E350, 318 Campus Dr., Stanford, CA 94305-5431 (e-mail: taylorca{at}stanford.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

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