Wall Shear Stress Differences Between Arterial and Venous Coronary Artery Bypass Grafts One Month After Surgery

Although coronary artery bypass graft (CABG) surgery is a well-established intervention, graft failure can occur, and the underlying mechanisms remain incompletely understood. The purpose of this prospective study is to utilize computational fluid dynamics (CFD) to investigate how graft hemodynamics one month post surgery may vary among graft types, which have different long-term patency rates. Twenty-four grafts from 10 participants (64.6 ± 8.5 years, 9 men) were scanned with coronary CT angiography and 4D flow MRI one month after CABG surgery. Grafts included 10 left internal mammary arteries (LIMA), 3 radial arteries (RA), and 11 saphenous vein grafts (SVG). Image-guided CFD was used to quantify blood flow rate and wall area exposed to abnormal wall shear stress (WSS). Arterial grafts had a lower abnormal WSS area than venous grafts (17.9% vs. 70.1%; p = 0.001), and a similar trend was observed for LIMA vs. SVG (13.8% vs. 70.1%; p = 0.001). Abnormal WSS area correlated positively to lumen diameter (p < 0.001) and negatively to flow rate (p = 0.001). This CFD study is the first of its kind to prospectively reveal differences in abnormal WSS area 1 month post surgery among CABG types, suggesting that WSS may influence the differential long-term graft failure rates observed among these groups.


INTRODUCTION
Coronary artery disease is the leading cause of mortality worldwide. 18 In severe cases, coronary artery bypass graft (CABG) surgery may be performed, in which a harvested vessel is grafted to bypass coronary artery stenosis and improve myocardial perfusion. 34 However, despite advancements in surgical techniques, approximately 50% of saphenous vein grafts (SVG) and 10% of left internal mammary artery (LIMA) grafts fail within 10 years of surgery, 30 and the underlying mechanisms behind graft remodeling and failure have yet to be fully elucidated. 11 Altered hemodynamics are postulated to play a role in graft remodeling, as they are already known to influence pathophysiological processes in other cardiovascular diseases. One notable hemodynamic measure is wall shear stress (WSS), the tangential force per unit area exerted by blood on vessel walls. In the context of atherosclerosis, low WSS is known to be associated with endothelial dysfunction, leading to vascular remodeling and the initiation of atherogenic processes. 3 Previous studies have also pointed to the potential role of WSS in graft failure. 26 However, a direct and non-invasive measurement of WSS in coronary arteries and grafts is currently not feasible, since the vessel caliber is below the resolution of standard MRI techniques and modalities used to measure blood velocity, such as phase contrast and 4D flow MRI. 23 An emerging approach to obtain WSS non-invasively relies on computational fluid dynamics (CFD) and coronary CT angiography, which has higher spatial resolution than MRI. 35 Three-dimensional models of coronary arteries and grafts can be obtained through CT segmentation, which can be used to perform a CFD simulation. 1 By solving the Navier-Stokes equations that describe the behavior of any fluid, including blood, CFD simulations yield blood pressure, velocity, and WSS resolved over space and time. Blood velocity at the boundaries of the simulation, acquired with phase contrast or 4D flow MRI, can also be incorporated into the model to better account for patient-specific flow conditions. 25 Image-guided CFD can thus provide an approach to garner a better understanding of CABG hemodynamics that imaging alone cannot provide.
While there have already been some patient-specific CFD studies performed to quantify WSS in coronary artery bypass grafts, many were retrospectively performed and included only five or fewer patients. 29,40 In a retrospective CFD study with 5 CABG patients ranging from 1 to 17 years after surgery, Ramachandra et al. showed that time-averaged WSS was lower in venous grafts than in arterial grafts, and abnormal WSS area was higher in venous grafts. 29 However, this study is limited by its sample size and the irregular time between surgery and follow-up CT imaging on which the CFD simulations are based. As grafts were imaged at different post-operative time points, the degree of vessel remodeling and atherosclerotic progression may have significantly varied among patients. 11 On the other hand, a recent retrospective CFD study by Khan et al. performed in 15 patients (40 grafts) with a mean follow-up time of 10 ± 6 years post-surgery, each with at least one healthy and at least one diseased venous graft, showed that WSS, normalized by that in a cylindrical vessel with equivalent flow rate and diameter, was lower in digitally reconstructed pre-diseased graft segments than in patent grafts; however, the authors found no differences in the abnormal WSS area. 19 While this study is currently the largest of its kind with respect to CABG surgery, it lacked prospective data to compare how the graft remodeled over time and instead digitally reconstructed the prediseased condition in the analysis. More significantly, although these retrospective studies have shown differences in shear stress exposure between arterial and venous grafts that could result in their differential long-term failure rates, they reached different conclusions regarding whether abnormal WSS area plays a significant role or not, possibly due to their retrospective nature and the large variations in the time interval between surgery and imaging. 19,29 The objective of this prospective study is to use CFD to investigate graft hemodynamics in 10 participants (24 grafts) at a consistent follow-up time of one month after CABG surgery. Prior clinical studies have revealed significant differences in patency rate depending on the graft tissue (arterial vs. venous), source vessel, and implantation territory. 11,12,14,27 We hypothesize that, one month after CABG surgery, analogous differences exist in the graft wall area exposed to abnormally-low WSS, as determined by image-guided CFD.

Study Population
This study was approved by the research ethics board of the Sunnybrook Health Sciences Centre and by the institutional review board at the University of Toronto. All procedures followed were in accordance with the Helsinki Declaration of 1975. A flow diagram of the study is presented in Fig. 1. In this single-center prospective study, 13 consecutive participants presenting to the Sunnybrook Health Sciences Centre for CABG surgery from November 2017 to August 2018 were identified and enrolled into the present study. Informed consent was obtained from all individual participants included in the study. The inclusion criteria included the following: age > 18 years, able to provide informed consent, no prior CABG surgery, left ventricular ejection fraction > 20%, and planned to have at least one venous and one arterial graft implanted. The exclusion criteria included any contraindication to cardiac CT or MRI, such as allergy to contrast media, estimated glomerular filtration rate < 30 mL/min, uncontrolled atrial fibrillation precluding proper gating of the study, pregnant or breastfeeding women, women of child-bearing age, claustrophobia, and metallic implants capable of interfering with MRI.

Imaging Acquisition
Cardiac CT angiography and 4D flow MRI were performed 3-6 weeks after CABG surgery. This 1month time point is chosen to be as close to the initial surgery as possible to reflect graft conditions prior to remodeling or failure. Earlier imaging is not feasible due to patient recovery time. Cardiac CT studies were performed on a 320-detector row CT scanner (Aquilion One; Canon Medical Systems, Markham, Ontario, Canada). Patient preparation for heart rate control, intravenous contrast protocol, and choice of scan parameters were performed following prior studies. 5,17 Four-dimensional (4D) flow MRI was performed shortly after with a 3 Tesla MRI system (Magneton PRISMA, Siemens, Erlangen, Germany) using a 4D flow imaging sequence with retro-gating and adaptive navigator respiratory gating. Imaging parameters were as follows: velocity encoding = 150 cm/s, field of view = 200-420 mm 9 248-368 mm, spatial resolution = 1.9-3.5 9 2.0-3.2 9 1.8-3.5 mm, temporal resolution = 39.9-47.2 ms, flip angle = 8°. No gadolinium contrast agent was administered. Figure 2 provides a visual summary of the methodology used in this study. From the CT images, a three-dimensional anatomical model of the aorta and the supra-aortic branches, coronary arteries, and bypass grafts was generated using SimVascular (Stanford University, Stanford, California), an open-source software for cardiovascular modeling. 38 The generated reconstructions were vetted by a cardiothoracic radiologist with ten years of experience in cardiovascular imaging (L.J.J.). For this purpose, the generated reconstructions were superimposed to the original CT images using 3D Slicer (Harvard University, Cambridge, Massachusetts).

Image Segmentation and Mesh Generation
Then, a three-dimensional mesh suitable for CFD analysis was generated with SimVascular. Local mesh element size was determined through spatial resolution studies to find the coarsest mesh required for convergence of average flow rate within 2% in each vessel. The aorta and supra-aortic branches had an element size set to 1.00 mm, while the coronary arteries and bypass grafts had target element sizes ranging from

Computational Fluid Dynamics Simulations and Post-Processing
For each participant, two CFD simulations were performed with SimVascular. An initial CFD simulation on the full model of the aortic arch and the coronary territories was performed with rigid vessel walls to determine the blood flow rate at the origin of the left and right coronary trees. For this full model simulation, a pulsatile blood flow rate in the ascending aorta, derived from 4D flow MRI data using Segment (Medviso, Lund, Sweden) and FourFlow (Lund University, Lund, Sweden), was imposed as an inlet boundary condition with a parabolic flow profile. While the inlet flow profile at the ascending aorta has been shown to affect distal intravascular hemodynamics in the aorta, this initial CFD simulation is only used to obtain inlet blood flow rate waveforms in the coronary arteries and bypass grafts for further coupled momentum method simulations, and a 1D flow profile in the ascending aorta is sufficient to capture this information. 24 For outlets at the ascending aorta and supra-aortic branches, a Windkessel resistance-capacitance-resistance model was used as in most studies of this type, and in the coronary outlets, a modified lumped parameter model was used as in similar studies that model the coronary arteries. 20 Cardiac output was derived by multiplying the patient 4D flow MRImeasured stroke volume by the patient heart rate measured after MRI acquisition. Mean arterial pressure was then calculated from the cuff blood pressure measured after MRI acquisition using the following formula 4 : where P mean is the mean arterial pressure, P dia is the diastolic blood pressure, and P sys is the systolic blood pressure. As an initial guess, the systemic vascular resistance seen from the ascending aorta was computed for each participant by dividing the mean arterial pressure by the cardiac output. The total distal coronary resistance was assumed to be 24 times the systemic vascular resistance, corre-FIGURE 2. Visual summary of the methodology used in this study, which consists of six steps. In step 1, cardiac CT and 4D flow MRI images are acquired 1 month after surgery. A 3D reconstruction of the vessels of interest is performed (step 2) and used to generate a computational mesh (step 3). A CFD simulation of the aorta, coronary arteries, and grafts is performed assuming fixed vessel walls (step 4), followed by a more precise CFD simulation of the left and right coronary territories alone with compliant vessel walls (step 5). Flow rates and WSS are finally calculated (step 6).
sponding to 4% of the cardiac output going to the coronary arteries. 31 In theory, this assumption could be verified through mass conservation by using 4D flow MRI to measure flow rates at all aortic outlets and subtract them from the inlet flow rate at the ascending aorta. However, the 4D flow acquisition is limited by various factors, including acquisition noise, spatio-temporal resolution, and encoding velocity, which can lead to a violation of mass conservation measured from 4D flow MRI. 6 Previous works have estimated that a 10-20% discrepancy in mass conservation can be observed in 4D flow-measured aortic flow rates. 7,33 While the 4% assumption is not patientspecific and will impact graft flow rate, this assumption is commonly used in other works that model the coronary arteries due to the lack of non-invasive methods to obtain coronary artery flow rates. 19,29 The total systemic capacitance was initially set to be 0.001 cm 5 /dyne, while the total coronary capacitance was initially set to be 3.6 9 10 -5 cm 5 /dyne and 2.5 9 10 -5 cm 5 /dyne for the left and right coronary territories, respectively, based on a previous study. 31 Total systemic resistance and capacitance were then split among individual vessel outlets according to a generalized form of Murray's law based on each vessel's relative cross-sectional area. 41 These values were then manually tuned for each participant until the simulated systolic and diastolic pressures were consistent with cuff blood pressure measured after MRI imaging.
A second CFD simulation employing the coupled momentum method for compliant vessel walls 9 was performed for the left and right coronary territories using the flow rates calculated by the first simulation as inlet boundary conditions. Simulations using compliant vessel walls are considered to provide more accurate results compared to rigid wall simulations, and since previous studies have reported mixed differences in WSS-related quantities between the two simulation methodologies, 2, 37 coupled momentum method simulations were performed in this study to err on the side of caution. This two-step approach was necessary, since a compliant-wall simulation of the whole domain had prohibitive computational cost. As previous works have demonstrated that the inlet velocity profile imposed in the left anterior descending coronary artery does not impact hemodynamics past the theoretical entrance length, 22 a Womersley flow profile at the inlets of the coronary territories was used. For the compliant wall simulations, the elastic moduli were set as follows based on the literature: 1.15 MPa for coronary arteries, 1.4 MPa for LIMA, 5 MPa for SVG, and 2.68 MPa for radial arteries (RA). 29,32 The wall thickness of each vessel was estimated using a previously-established relation between coronary artery radius and wall thickness. 28 From the results of the coupled momentum method simulation, the flow rate and distribution of time-averaged WSS on the walls of each graft were computed with SimVascular. The percent area of the graft walls exposed to WSS below 1 Pa, henceforth referred to as abnormal WSS area, was computed with ParaView (Kitware, Clifton Park, New York) and MATLAB (MathWorks, Natick, Massachusetts). There is currently no consensus on a threshold for abnormally-low WSS, as previous in vitro vascular biology studies have utilized WSS values ranging anywhere from 0 to 1.2 Pa in order to stimulate vascular remodeling responses in endothelial cells. 13,39 In this study, a 1 Pa threshold was chosen, as WSS under 1 Pa has been clinically shown to predict plaque burden in coronary arteries. 3,36 Relation Between WSS, Graft Diameter, and Flow Rate To explore potential factors that contribute to observed differences in abnormal WSS area, graft diameter and flow rate were also quantified. Average graft diameter was calculated from the reconstructed 3D model using VMTK 16 and MATLAB. In a cylindrical vessel subject to steady laminar flow, WSS is where l is the dynamic viscosity of blood, Q is the flow rate, and D is the diameter of the vessel. 21 From this relation, we can see that larger vessel diameters and smaller flow rates lead to lower WSS.

Statistical Analysis
All analyses were performed using JASP (version 0.13, University of Amsterdam, Amsterdam, Netherlands). Comparisons were made for graft tissue type (arterial vs. venous), source vessel (LIMA vs. SVG, LIMA vs. non-LIMA), and implantation territory (left vs. right). Linear mixed models were used for significance testing and correlation analyses with patient as a random effects variable. 8 A p-value of < 0.05 was considered significant. A multiple linear regression was performed to investigate the contribution of flow rate and graft diameter to abnormal WSS area.

Patient Characteristics
Thirteen participants were enrolled in the study and three were excluded: one due to withdrawn consent prior to the 1-month follow-up and two due to nondiagnostic CT image quality. The final cohort consisted of 10 participants with 24 grafts. A flow diagram of the study is shown in Fig. 1. Baseline patient characteristics are summarized in Table 1.

Validation of CFD Results Against 4D Flow MRI
To validate the CFD simulation methodology and boundary conditions, blood flow velocity was sampled from the full model rigid wall CFD simulation and 4D flow MRI at three different planes along the aorta for five representative study participants. A diagram showing the location of the sampling planes as well as the velocity profiles for a representative study participant is provided in Fig. 3. Relative error in average blood flow velocity was computed for each plane in all 5 cases, as reported in Table 2. The average relative error for all planes ranged from 3.12 to 6.58%, indicating good agreement between numerical results and 4D flow MRI data. While possible in the aorta, this validation could not be performed in coronary arteries and grafts, due to their small caliber compared to the resolution of 4D flow MRI.

Distribution of Abnormal WSS Area on Graft Walls
The graft wall area exposed to abnormal WSS (< 1 Pa) 13 is illustrated in Fig. 4. Remarkable qualitative differences in the extent of the abnormal WSS area can be observed among different grafts. The following sections compare WSS distributions between grafts of different tissue (arterial or venous), source vessel (LIMA, RA, SVG), and implantation territory.

Comparison of Abnormal WSS Area between Arterial and Venous Grafts
Grafts were categorized based on whether they were arterial (LIMA, RA) or venous (SVG). Table 3 reports the percent area exposed to abnormal WSS, average graft diameter, and flow rate for arterial and venous grafts. Results from statistical comparisons between arterial and venous grafts are reported in Table 4. Venous grafts had a higher mean percent area exposed to abnormal WSS than that of arterial grafts (p = 0.001). This difference is visible in Fig. 5, where scatterplots show the relation between percent area with abnormal WSS and either graft lumen diameter (Fig. 5a) or flow rate (Fig. 5b).
Potential factors that could contribute to these differences in WSS distribution include graft lumen diameter and graft flow rate. Venous grafts had a larger mean average graft diameter than that of arterial grafts (p = 0.003). For mean graft flow rate, no statistically significant differences were found between arterial and venous grafts (p = 0.053).

Comparison of Abnormal WSS Area between Source Vessels
A similar analysis was performed to compare the WSS distribution between LIMA and non-LIMA grafts (RA and SVG), as well as between LIMA and SVG. Radial arteries were not considered as a category on their own and were instead grouped with SVGs, as the sample size is small (n = 3). Additionally, the comparison between LIMA and non-LIMA grafts is of particular interest, as LIMA grafts are clinically observed to have lower rates of repeat revascularization and mortality compared to other source vessels 15 . Table 3 reports the percent abnormal WSS area, average graft diameter, and flow rate for different graft vessel types. Table 4 reports the results from statistical significance testing for differences in these measures across different source vessel types. LIMA grafts had a lower mean percent area exposed to abnormal WSS compared to non-LIMA grafts (p = 0.004) and compared to SVGs (p = 0.001). These differences are visible in Fig. 6, where scatterplots show the relation between percent area with abnormal WSS and either average graft diameter [ Fig. 6a] or flow rate [ Fig. 6b].
Mean average LIMA graft diameter was smaller than the mean average non-LIMA graft diameter (p = 0.003) as well as the mean average SVG diameter (p = 0.002). No differences were found in the mean graft flow rate between LIMA grafts and either non-LIMA grafts (p = 0.39) or SVG (p = 0.13).

Comparison of Abnormal WSS Area between Left and Right Territory Grafts
All LIMA grafts were implanted to the left anterior descending artery, while SVG and RA grafts were implanted to both the left and right territories. Table 3 reports the percent area with abnormal WSS, average graft diameter, and flow rate for different implantation territories. Table 4 reports the results from statistical significance testing for differences in these measures across different implantation territories. Percent area exposed to abnormal WSS was not different between left territory grafts and right territory grafts (p = 0.69). Figure 7 depicts the area exposed to   Fig. 7(a)] or flow rate [ Fig. 7(b)]. No differences were found in mean average graft diameter between left territory and right territory grafts (p = 0.18). However, mean flow rate in grafts implanted to the left territory was lower than that in grafts implanted to the right territory (p = 0.03).

Relation of Abnormal WSS Area to Flow Rate and Diameter
For the entire cohort of grafts, abnormal WSS area was found to be positively correlated to average graft lumen diameter (p < 0.001) and negatively correlated to graft flow rate (p = 0.001). Graft flow rate and diameter were not correlated each other (p = 0.279), nor was the graft flow rate correlated to the inverse cube of diameter (p = 0.653). The fitted regression equation was of the following form: . Graphical illustration of the 24 grafts considered in this study, with the area of their walls exposed to abnormal WSS (< 1 Pa) highlighted in red. Grafts are grouped by type of source vessel and implantation territory. Grafts are not to scale. where A is the abnormal WSS area, Q. is the graft flow rate, and D is the average graft lumen diameter. The form of the regression equation was chosen based on the formula for WSS in a cylindrical vessel with steady, laminar flow given at the end of the Methods section. 21 Results of the multiple regression are reported in Table 5. Regression coefficients were significant (p < 0.001), indicating that graft flow rate and the inverse cube of graft diameter are linearly related to abnormal WSS area. The regression model resulted in an R 2 value of 0.888, indicating good agreement between model and data. Standardized regression coefficients were 2 0.69 for graft flow rate and 2 0.60 for the inverse cube of graft diameter, suggesting that flow may play a larger role than diameter in predicting graft abnormal WSS area. (a) (b) FIGURE 5. Scatterplots depicting the percent area of graft wall exposed to abnormal WSS (< 1 Pa) versus average graft diameter (a) and average flow rate (b), for arterial (red circles, n = 13) and venous (blue triangles, n = 11) grafts. The area exposed to abnormal WSS is lower in arterial grafts, as visible in both panels. The average diameter of venous grafts is higher than in arterial grafts (5a).
(a) (b) FIGURE 6. Scatterplots depicting the percent area of graft wall exposed to abnormal WSS (< 1 Pa) versus average graft diameter (a) and average flow rate (b), for grafts based on LIMA (red circles, n = 10), RA (orange squares, n = 3) and SVG (blue triangles, n = 11). The area exposed to abnormal WSS is lower in LIMA grafts than in SVG, as visible in (a). LIMA grafts also have lower average diameter (a).

DISCUSSION
For the first time prospectively, image-guided CFD simulations were used to estimate abnormal WSS area in 24 bypass grafts of 10 study participants 1 month after bypass surgery. Arterial grafts were found to have a lower abnormal WSS area than venous grafts and a smaller graft lumen diameter. The source vessel also appears to relate to different hemodynamic conditions, with LIMA grafts having lower abnormal WSS area and smaller average lumen diameter than both non-LIMA grafts and SVGs alone. Implantation territory did not appear to play a role in the abnormal WSS area. For the whole cohort, both flow rate and diameter were correlated to abnormal WSS area, and a multiple regression analysis suggested that flow may play a larger role than diameter in predicting graft abnormal WSS area.
Our results are in relative agreement with previous CFD studies performed in the context of CABG surgery. A retrospective CFD study performed by Ramachandra et al. demonstrated that time-averaged WSS was lower in venous grafts than in arterial grafts, and abnormal WSS area with a threshold of < 0.4 Pa was higher in venous grafts. 29 However, another retrospective CFD study by Khan et al. showed that normalized WSS was lower in pre-diseased SVG segments than in patent SVGs, but they found no differences in the abnormal WSS area. 19 This discrepancy could in part be due to the differences in study design. In the Khan et al. study, the anatomy of the pre-diseased SVG was retrospectively and digitally generated (extrapolated) from images of fully stenosed grafts, while in this present prospective study, all simulations were directly based on participant images taken 1 month after surgery. Additionally, the threshold for abnormal WSS was defined on a graft-specific basis in the Khan et al. study. In our study, a common WSS threshold of 1 Pa was used for all grafts.
Our findings pertaining to abnormal WSS also align with clinically-observed graft failure rates. Specifically, LIMA grafts are observed to have higher long-term patency rates than SVGs. 11,14 Arterial grafts have also been observed to have better long-term patency than venous grafts. 11,27 When taken into consideration with our findings of significant differences in abnormal WSS area among the same graft groups, these results suggest that abnormal WSS area measured 1-month post-surgery may be a marker of graft remodeling beyond the 1-month time point.
One strength of our study is the use of 4D flow MRI to derive patient-specific boundary conditions, as opposed to formulating boundary conditions based on average patient data from literature. 10 Limitations include the uncertainties associated with the acquisition of CT images and the associated reconstruction of the 3D model, 4D flow MRI measurements, and vessel wall material properties used for all participants.
(a) (b) FIGURE 7. Scatterplots showing the relation between the percent area of graft wall exposed to an abnormal WSS of < 1 Pa and either average graft diameter (a) or graft flow rate (b). Marker color and shape correspond to implantation territory: left territory (red circles; n = 19) and right territory (green triangles; n = 5). Additionally, statistical comparisons made between the left and right implantation territories could be skewed by the LIMA grafts, which were all implanted to the left territory. Due to the limited number of grafts typically found in a CABG patient, statistical comparisons with linear mixed models based on implantation territory could not be made if all LIMA grafts were excluded, since LIMA grafts are the most common. Furthermore, while this study demonstrates differences in abnormal WSS area measured 1 month post surgery that appear to align with long-term failure rates, longitudinal data on our cohort would be required to assess correlations between hemodynamics and long-term failure. Taken as a whole, our CFD study is the first of its kind to prospectively show significant differences in the abnormal wall shear stress area 1 month post surgery among different graft types and source vessels, which suggests that wall shear stress could play a role in the differential graft failure rates observed among these groups. Some of the observed differences seem to be in part related to underlying differences in graft diameter and blood flow rate. A future study will look at longitudinal data at the 1-year post-operative time point from the same participants in this study to relate CFD-derived hemodynamics to coronary artery bypass graft remodeling, which can be a precursor to longer term failure. 11  Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.