Computational Evaluation of Venous Graft Geometries in Coronary Artery Bypass Surgery

Abstract

Cardiothoracic surgeons are faced with a choice of different revascularization techniques and diameters for saphenous vein grafts (SVG) in coronary artery bypass graft surgery . Using computational simulations, we virtually investigate the effect of SVG geometry on hemodynamics of both venous grafts and the target coronary arteries. We generated patient-specific 3-dimensional anatomic models of coronary artery bypass graft surgery patients and quantified mechanical stimuli. We performed virtual surgery on 3 patient-specific models by modifying the geometry vein grafts to reflect single, Y, and sequential surgical configurations with SVG diameters ranging from 2 mm to 5 mm. Our study demonstrates that the coronary artery runoffs are relatively insensitive to the choice of SVG revascularization geometry. We observe a 10% increase in runoff when the SVG diameter is changed from 2 mm to 5 mm. The wall shear stress of SVG increases dramatically when the diameter drops, following an inverse power scaling with diameter. For a fixed diameter, the average wall shear stress on the vein graft varies in ascending order as single, Y, and sequential graft in the patient cohort. The runoff to the target coronary arteries changes marginally due to the choice of graft configuration or diameter. The shear stress on the vein graft depends on both flow rate and diameter and follows an inverse power scaling consistent with a Poiseuille flow assumption. Given the similarity in runoff with different surgical configurations, choices of SVG geometries can be informed by propensity for graft failure using shear stress evaluations.

Keywords: Blood flow simulation; Coronary artery bypass graft surgery (CABG); Shear stress; Vein graft; Virtual surgery.

Figure 1:

Patient-specific models from CT scan of three patients who had undergone CABG surgery with the corresponding virtual modification on venous grafts to single, Y, and sequential configurations. Vessels are colored by their modulus values, E (Pa). DIAG – diagonal branch of left coronary artery, PDA – posterior descending artery, OM – obtuse marginal, LCx – left circumflex artery. Arrows indicate the proximal and distal anastomoses in the sequential graft. Baseline clinical geometry is marked by the gray box.

Figure 2:

Summary of mean flow rates (a,d,g) and pressures (b,e,h) at target coronary arteries connected to SVG, and time and spatially averaged wall shear stress (WSS_avg, (c,f,i)) on the vein graft with different configurations. Notice that the flow to the distal coronary and pressure in the graft is independent of the choice of revascularization geometry. The wall shear stress is variable across patients and surgical geometries, however. DIAG – diagonal branch of left coronary artery, PDA – posterior descending artery, OM – obtuse marginal, LCx – left circumflex artery. Baseline clinical geometry is marked by the gray box.

Figure 3:

Flow rates and time-averaged wall shear stress (TAWSS) distributions along the centerline of vein grafts in each patient. x is the location along the centerline, and L_SVG is the length of the respective graft. Solid and dotted lines are the cross-section averaged TAWSS and dashed-dotted lines are the location of first anastomosis in the sequential graft (green), or bifurcation in the y-graft (red). In (a), (e), (i), the solid lines and the dotted lines are plotted to show the flow rates in the two branches in the single and Y-graft, while the solid lines in the Y-graft include the trunk. Flow rate is constant along the length of the graft until it reaches an anastomotic point, due to mass conservation. The TAWSS is highly variable along the length of the graft, due to diameter variations.

Figure 4:

Summary of mean flow rate (a,e,h) and pressure (b,f,i) at target coronary arteries connected to single saphenous vein grafts (SVG), time and spatially averaged wall shear stress (WSS_avg) (c,g,j), vascular resistance of the vein graft with varying diameter from 2 mm to 5 mm (d,h,l) from 3D CFD simulations. DIAG – diagonal branch of the left coronary artery, PDA – posterior descending artery, OM – obtuse marginal, LCx – left circumflex artery.

Figure 5:

Time-averaged wall shear stress distributions along the centerline of a vein graft in SVG connected to OM in Patient 2. x is the location along the centerline, and L_SVG is the length of the saphenous vein graft. Solid lines are data from 3-D CFD simulation, and dashed lines are estimated from Poiseuille flow relationship. (b) The scaling of WSS_avg on the grafts to the diameter, D_SVG. The dashed line is ${\text{WSS}}_{\text{avg}}\sim {{\text{D}}_{\text{SVG}}}^{-3}$.

Figure 6:

Virtually evaluated time-averaged wall shear stress (TAWSS) vein grafts in each patient with D_SVG = 2 mm (a,d,g), D_SVG = 3 mm (b,e,h), D_SVG = 4 mm (c,f,i) computed with Poiseuille assumptions. The TAWSS in Figure 4 is rescaled by the factor of D³_SVG/D³_SVG-Original. x is the location along the centerline, and L_SVG is the length of each graft. Solid and dotted lines are the extrapolated TAWSS and dashed-dotted lines are the location of first anastomosis in the sequential graft (green), or bifurcation in the y-graft (red). The dashed lines are 25 dynes/cm². Note that the TAWSS can be modulated to reach physiological, or pathologically low or high values by only changing the diameter of the graft.

Figure 7.

Graphical summary of workflow and representative results for one patient. Cardiac CT data are used to construct a three-dimensional anatomic model of aorta, coronary arteries and bypass grafts. Modifications to the vein graft geometry are made. Computational fluid dynamic simulation are performed using the resultant model coupled with lumped parameter zero-dimensional circuit models of cardiac, coronary, and systemic circulations to compute vessel flow rates and wall shear stress for different geometries.