# Numerical Investigation of the Relationship between
## 3 Results
### Data Validation  
To validate the results of the simulation, we compared the results obtained with the simulation to data available in the literature. A qualitative comparison was performed by comparing the result of the steady-state, 60\({}^{\circ}\) graft simulation in Figure 12a against the measurements of [PERSON] et al. in an in vitro study characterizing the secondary flow characteristics of a ridged graft design using vector Doppler imaging, as seen in Figure 12b [50]. The secondary velocity profile of the present study was quite similar to that observed in an actual experiment. Regions of high and low secondary velocity magnitudes from the imaging procedure were successfully replicated in the present study.  
To further confirm the validity of the results, a quantitative comparison was also performed. The pressure drop, secondary velocity, WSS, and recirculation values calculated from the steady-state simulation of the 60\({}^{\circ}\) ridged graft were compared to the results obtained in the reference study [24]. Table 2 summarizes these data.  
In four out of five variables observed, the percentage difference between the reference and calculated data was reasonably low. However, of note is the percentage difference between the area affected by recirculation at Plane 2 of the previous and present studies. The data from the literature are significantly higher than the calculated value which may seem to invalidate the results of the present study. However, it must be noted that these two data sets did not come from the same, exact geometry. The reference study did not  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Data from Literature** & **CFD Result** & **Percentage** \\
**Variable** & **(One Circular Ridge,** & **(One Elliptical Ridge,** & **Difference (\%)** \\  & **Oriented at 180\({}^{\circ}\))** & **Oriented at 180\({}^{\circ}\))** & \\ \hline Pressure drop (Pa) & 545.86 & 526.22 & 3.66 \\ Secondary velocity (m/s) & 0.022 & 0.024 & 8.70 \\ WSS (Pa) & 2.432 & 2.09 & 15.13 \\ Recirculation Plane 1 (\%) & 5.31 & 5.21 & 1.90 \\ Recirculation Plane 2 (\%) & 3.52 & 1.00 & 111.50 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Quantitative validation of simulation results by comparison of different variables from CFD simulation against data from the literature.  
Figure 12: Qualitative validation of the simulation results by comparison of secondary velocity contours on the cross-section of the artery 5 mm from the distal anastomosis toe of a 60\({}^{\circ}\) ridged graft. (**a**) CFD result; (**b**) Doppler imaging result from [PERSON] et al. [50].  
present the result for the steady-state simulation for their optimal design (one elliptical ridge, oriented at 180\({}^{\circ}\)). Only the simulation result for a graft with one circular ridge oriented at 180\({}^{\circ}\) was available for comparison. Their data showed that while keeping other variables fairly equal, the use of a tall, elliptical ridge significantly reduced the extent of recirculation at the second monitoring plane located 5 mm from the anastomosis toe compared with the use of a circular ridge [24]. This could be explained by the increased secondary velocity caused by the elliptical ridge. [PERSON] et al. had shown that swirling flow creates a sweeping washout effect that effectively reduces wall collisions and, in turn, both stasis and retrograde flow [15]. The increased secondary velocity of the elliptical ridge must have enhanced the washout characteristics in the outflow, thereby reducing the area affected by recirculation. This, with its possible synergistic effect with other optimized design parameters, may explain the huge difference between the recirculation percentage in the second monitoring plane despite close values for other variables.