# Numerical Investigation of the Relationship between Anastomosis Angle and Hemodynamics in Ridged Spiral Flow Bypass Grafts

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometry

^{2}) that revolved once around the length of the entire graft. At the inlet, the ridge is oriented 180° from the standard axis. The cross-sectional profile of the graft, as in Figure 2a, was taken entirely from the reference study [24]. The bypass graft was attached to the host artery at angles of 15° increments from 30° to 75°. To ensure that the flows into and out of the grafts were fully developed, sufficient entry and exit lengths were added upstream and downstream of the grafts, respectively, as seen in Figure 2b.

#### 2.2. Mesh Generation

#### 2.3. Determination of the Optimal Anastomosis Angle

^{3}, and its shear-thinning properties were considered by describing the viscosity using the Carreau model (time constant = 3.313 s; power-law index = 0.3568; zero-shear viscosity = 0.056 kg m

^{−1}s

^{−1}; infinite shear viscosity = 0.0035 kg m

^{−1}s

^{−1}). The flow was set to be laminar, and heat transfer effects were ignored. A constant, uniform velocity of 0.317 m/s and zero pressure were imposed on the inlet and outlet, respectively. Rigid wall and non-slip assumptions were used for the walls [24].

^{−6}, monitoring the overall mass balance, and waiting for the outlet velocity value to approach a constant value with further iterations.

#### 2.4. Comparison of Performance between a Conventional Graft and Spiral-Flow-Inducing Graft

^{−6}. To avoid instabilities, the simulation was run for five periods, and results were extracted from the final cycle.

## 3. Results

#### 3.1. Optimization of Anastomosis Angle

#### 3.1.1. Pressure Drop

#### 3.1.2. Axial Velocity and Secondary Velocity

#### 3.1.3. Wall Shear Stress

^{2}= 0.9923). This relationship may be explained by both the bulk motion and the secondary flow components of the fluid. As observed in the axial velocity contour maps (Figure 6), higher axial velocities near the walls and higher velocity gradients were observed for larger anastomosis angles which translate to increased shear stress [42]. Furthermore, the swirl motion represented by the secondary velocity also generated higher shear stress in the artery walls due to the tangential velocity vector [39]. This seemed to suggest that increasing the anastomosis angle between the graft and artery may have the beneficial effect of reducing the tendency of the graft to induce intimal thickening by increasing the WSS. However, this presented a problem wherein an increased anastomosis angle resulted in the development of pathologically high WSS.

#### 3.1.4. Recirculation

#### 3.2. Data Validation

## 4. Discussion

#### 4.1. Optimal Anastomosis Angle

#### 4.2. Comparison of Spiral-Flow-Inducing Graft Design vs. Conventional Graft Design

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Geometric model used for CFD simulation. (

**a**) The cross-sectional profile of the ridged bypass graft; (

**b**) model dimensions based on anastomosis angle.

**Figure 9.**Areas on the host artery (unrolled) affected by abnormal WSS. Only pertinent regions where abnormal WSS was observed were shown instead of the whole arterial length.

**Figure 10.**Extent of the area affected by abnormal WSS. The 30-degree anastomosis angle resulted in the total elimination of abnormally high WSS, so it is not present in the chart on the right.

**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° ridged graft. (

**a**) CFD result; (

**b**) Doppler imaging result from Kokkalis et al. [50].

**Figure 13.**Comparison of hemodynamic performance resulting from bypass grafts of varying anastomosis angles.

**Figure 14.**Time-averaged wall shear stress contours of the artery (unrolled) using a 30° anastomosis angle with non-spiral and spiral graft configurations.

Angle (Degrees) | Total Pressure Drop (Pa) |
---|---|

30 | 474.8 |

45 | 498.39 |

60 | 526.22 |

75 | 554.61 |

**Table 2.**Quantitative validation of simulation results by comparison of different variables from CFD simulation against data from the literature.

Variable | Data from Literature (One Circular Ridge, Oriented at 180°) | CFD Result (One Elliptical Ridge, Oriented at 180°) | Percentage Difference (%) |
---|---|---|---|

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 |

Configuration | Maximum (Pa) | Area Average (Pa) |
---|---|---|

Non-spiral | 4.679 | 0.944 |

Spiral | 4.663 | 1.067 |

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**MDPI and ACS Style**

Apan, J.J.; Tayo, L.; Honra, J.
Numerical Investigation of the Relationship between Anastomosis Angle and Hemodynamics in Ridged Spiral Flow Bypass Grafts. *Appl. Sci.* **2023**, *13*, 4046.
https://doi.org/10.3390/app13064046

**AMA Style**

Apan JJ, Tayo L, Honra J.
Numerical Investigation of the Relationship between Anastomosis Angle and Hemodynamics in Ridged Spiral Flow Bypass Grafts. *Applied Sciences*. 2023; 13(6):4046.
https://doi.org/10.3390/app13064046

**Chicago/Turabian Style**

Apan, Jhon Jasper, Lemmuel Tayo, and Jaime Honra.
2023. "Numerical Investigation of the Relationship between Anastomosis Angle and Hemodynamics in Ridged Spiral Flow Bypass Grafts" *Applied Sciences* 13, no. 6: 4046.
https://doi.org/10.3390/app13064046