Patient-Specific Simulations Reveal Significant Differences in Mechanical Stimuli in Venous and Arterial Coronary Grafts

Abstract

Mechanical stimuli are key to understanding disease progression and clinically observed differences in failure rates between arterial and venous grafts following coronary artery bypass graft surgery. We quantify biologically relevant mechanical stimuli, not available from standard imaging, in patient-specific simulations incorporating non-invasive clinical data. We couple CFD with closed-loop circulatory physiology models to quantify biologically relevant indices, including wall shear, oscillatory shear, and wall strain. We account for vessel-specific material properties in simulating vessel wall deformation. Wall shear was significantly lower (p = 0.014*) and atheroprone area significantly higher (p = 0.040*) in venous compared to arterial grafts. Wall strain in venous grafts was significantly lower (p = 0.003*) than in arterial grafts while no significant difference was observed in oscillatory shear index. Simulations demonstrate significant differences in mechanical stimuli acting on venous vs. arterial grafts, in line with clinically observed graft failure rates, offering a promising avenue for stratifying patients at risk for graft failure.

Appendix

The following paragraphs elaborate the computation of mechanical stimuli indices from primary mechanics quantities such as velocity and displacements.

Time averaged wall shear stress (TAWSS) is computed as,

$$ \mathrm{TAWSS}=\frac{\mathrm{mag}\left({\displaystyle {\int}_0^{T_{\mathrm{CC}}}\left(\overrightarrow{\mathrm{WSS}}\right)dt}\right)}{T_{\kern0.1em \mathrm{C}\mathrm{C}}} $$

where $\left(\overrightarrow{\mathrm{WSS}}\right)$ is the wall shear stress vector, the tangential traction force produced by blood moving across the endothelial surface, T  _CC is the duration of one cardiac cycle, and mag indicates magnitude. For statistical analysis, TAWSS in each graft was normalized by the aortic value of TAWSS in the same patient to normalize for patient variability.

Oscillatory shear index, a measure of oscillatory component of the flow, is computed as,

$$ \mathrm{O}\mathrm{S}\mathrm{I}=\frac{1}{2}\left(1-\frac{\left|{\displaystyle {\int}_0^{T_{\mathrm{CC}}}\left(\overrightarrow{\mathrm{WSS}}\right)\kern0.1em }dt\right|}{{\displaystyle {\int}_0^{T_{\mathrm{CC}}}\left|\left(\overrightarrow{\mathrm{WSS}}\right)\right|dt}}\right). $$

Atheroprone area (A _athero), a measure of the area of the graft prone to atherosclerosis, is computed as,

$$ {A}_{\mathrm{athero}}=\left(\frac{{\displaystyle {\int}_{A_{\kern0.1em \mathrm{graft}}}fdA}}{{\displaystyle {\int}_{A_{\kern0.1em \mathrm{graft}}}dA}}\right),f=\left\{\begin{array}{l}1,\left|\overrightarrow{\mathrm{WSS}}\right|<4\frac{\mathrm{dyn}}{{\mathrm{cm}}^2,}\hfill \\ {}0,\mathrm{otherwise}\hfill \end{array}\right. $$

with the threshold for low WSS set to 4 dyn/cm² based on literature data [47].

Amongst several potential measures of vessel wall strain, we chose to quantify Green Strain Invariant 1 (GSI1), a scalar measure of strain that is insensitive to rigid body motions, measured with respect to diastolic configuration [48]. This is calculated as

$$ \mathrm{G}\mathrm{S}\mathrm{I}1=tr\left(\frac{1}{2}\left(\overline{\overline{F}}{\overline{\overline{F}}}^T-\overline{\overline{I}}\right)\right), $$

Where $\overline{\overline{F}}$ is a tensor defined as the gradient of displacement vector, $\overline{\overline{I}}$ is an identity tensor and tr is the matrix trace operator.

Diameter was computed from lumen area by approximating the lumen area to be a circle. Lumen area was measured perpendicular to the vessel centerline and averaged across the length of the vessel. Tortuosity was defined as distance between points along the length of centerline divided by the distance between first and last point on the centerline and is a measure of deviation of centerline from a straight line.