Fast and Accurate Computation of the Displacement Force of Stent Grafts after Endovascular Aneurysm Repair
Abstract
:1. Introduction
2. Materials and Methods
2.1. Geometry
2.2. CFD Computation
2.2.1. Governing Equations
2.2.2. Boundary Conditions
2.2.3. Meshing and Computing
2.2.4. Calculation of Displacement Force
2.3. The Proposed Approach to Computing DF
2.3.1. Governing Equations
2.3.2. Measurement of the Cross-Sectional Area and Angles of SG Ends
2.4. Statistical Analysis
3. Results
4. Discussions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Heading | CFD Method (N) | Simplified Momentum Quantitative (N) | Relative Error (%) | ||||||
---|---|---|---|---|---|---|---|---|---|
Fx | Fy | Fz | F | Fx | Fy | Fz | F | ||
SG1 | 4.49 | −2.12 | −2.51 | 5.56 | 4.67 | −2.15 | −2.58 | 5.75 | 3.42 |
SG2 | –0.37 | −2.39 | −1.74 | 2.98 | −0.38 | −2.44 | −1.76 | 3.03 | 1.67 |
SG3 | 0.87 | −2.72 | –1.25 | 3.11 | 0.9 | −2.73 | −1.24 | 3.13 | 0.55 |
SG4 | −5.62 | −3.34 | 2.56 | 7.02 | −5.62 | −3.35 | 2.62 | 7.05 | 0.45 |
SG5 | 3.14 | −1.80 | 0.73 | 3.69 | 3.12 | −1.81 | 0.78 | 3.7 | 0.16 |
SG6 | −0.31 | −0.71 | 0.07 | 0.78 | −0.11 | −0.76 | 0.31 | 0.83 | 6.91 |
SG7 | 0.59 | −1.83 | 3.07 | 3.62 | 0.55 | −1.74 | 3.07 | 3.57 | 1.39 |
SG8 | −0.13 | −1.61 | −1.95 | 2.53 | −0.14 | −1.64 | −1.92 | 2.53 | 0.36 |
SG9 | 0.01 | −0.24 | −2.40 | 2.42 | 0.02 | −0.24 | −2.39 | 2.41 | 0.45 |
SG10 | −0.48 | −0.73 | −3.25 | 3.37 | −0.46 | −0.71 | −3.16 | 3.27 | 3 |
SG11 | 3.13 | −1.80 | 0.72 | 3.68 | 3.1 | −1.78 | 0.73 | 3.65 | 1.02 |
SG12 | 0.16 | −1.83 | −1.75 | 2.54 | 0.18 | −1.81 | −1.75 | 2.52 | 0.56 |
SG13 | −0.20 | −0.53 | −1.95 | 2.03 | −0.20 | −0.52 | −1.93 | 2.01 | 0.92 |
SG14 | −0.27 | −5.96 | −1.59 | 6.18 | −0.30 | −5.98 | −1.58 | 6.19 | 0.25 |
SG15 | −0.73 | −5.07 | −4.37 | 6.73 | −0.77 | −5.00 | −4.31 | 6.65 | 1.14 |
SG16 | −2.12 | −3.30 | −2.49 | 4.64 | −2.11 | −3.30 | −2.48 | 4.63 | 0.23 |
SG17 | −1.00 | −0.81 | −2.37 | 2.69 | −0.98 | −0.78 | −2.32 | 2.64 | 2.08 |
SG18 | −3.03 | −5.82 | −4.86 | 8.17 | −3.06 | −5.72 | −4.83 | 8.09 | 0.94 |
SG19 | −0.48 | −2.03 | −1.65 | 2.66 | −0.47 | −2.01 | −1.65 | 2.64 | 0.59 |
SG20 | 0.09 | −4.73 | −4.35 | 6.43 | 0.09 | −4.67 | −4.28 | 6.34 | 1.41 |
Heading | CFD Method (°) | Simplified Momentum Quantitative (°) | Relative Error (%) | ||||||
---|---|---|---|---|---|---|---|---|---|
θx | θy | θz | θx | θy | θz | ||||
SG1 | 35.71 | 111.92 | 116.66 | 36.18 | 112.41 | 116.79 | 1.29 | 0.43 | 0.11 |
SG2 | 97.26 | 143.59 | 125.45 | 97.04 | 143.4 | 125.7 | 0.22 | 0.13 | 0.2 |
SG3 | 73.37 | 150.82 | 113.25 | 73.77 | 150.7 | 113.68 | 0.54 | 0.08 | 0.38 |
SG4 | 142.94 | 118.35 | 68.21 | 143.17 | 118.42 | 68.62 | 0.16 | 0.06 | 0.6 |
SG5 | 32.28 | 119.37 | 77.82 | 31.81 | 119.27 | 78.64 | 1.46 | 0.09 | 1.04 |
SG6 | 97.72 | 156.59 | 68.04 | 113.1 | 156.29 | 84.96 | 13.6 | 0.19 | 19.91 |
SG7 | 81.18 | 119.09 | 30.65 | 80.67 | 120.35 | 32.05 | 0.64 | 1.04 | 4.36 |
SG8 | 93.08 | 130.47 | 139.36 | 92.96 | 129.56 | 140.28 | 0.13 | 0.7 | 0.66 |
SG9 | 89.57 | 95.65 | 174.34 | 89.81 | 95.8 | 174.2 | 0.26 | 0.16 | 0.08 |
SG10 | 98.15 | 102.58 | 164.94 | 98.15 | 102.56 | 164.96 | 0 | 0.02 | 0.01 |
SG11 | 31.78 | 119.14 | 78.42 | 31.76 | 119.24 | 78.68 | 0.07 | 0.08 | 0.34 |
SG12 | 85.98 | 135.83 | 133.89 | 86.33 | 136.01 | 133.75 | 0.4 | 0.14 | 0.1 |
SG13 | 95.77 | 104.86 | 164.01 | 95.77 | 105.1 | 163.78 | 0.01 | 0.23 | 0.14 |
SG14 | 92.74 | 164.98 | 104.76 | 92.46 | 164.86 | 104.93 | 0.3 | 0.07 | 0.16 |
SG15 | 96.69 | 138.78 | 130.43 | 96.25 | 138.83 | 130.48 | 0.46 | 0.04 | 0.04 |
SG16 | 117.11 | 135.35 | 122.34 | 117.21 | 135.22 | 122.4 | 0.08 | 0.1 | 0.05 |
SG17 | 111.7 | 107.28 | 151.68 | 111.75 | 107.49 | 151.5 | 0.04 | 0.19 | 0.12 |
SG18 | 112.26 | 135.01 | 126.65 | 111.78 | 135.45 | 126.54 | 0.42 | 0.32 | 0.09 |
SG19 | 100.19 | 139.54 | 128.63 | 100.35 | 139.74 | 128.37 | 0.16 | 0.15 | 0.2 |
SG20 | 89.18 | 137.48 | 132.51 | 89.19 | 137.44 | 132.55 | 0 | 0.03 | 0.03 |
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Qing, M.; Liu, Z.; Zheng, T. Fast and Accurate Computation of the Displacement Force of Stent Grafts after Endovascular Aneurysm Repair. Bioengineering 2022, 9, 447. https://doi.org/10.3390/bioengineering9090447
Qing M, Liu Z, Zheng T. Fast and Accurate Computation of the Displacement Force of Stent Grafts after Endovascular Aneurysm Repair. Bioengineering. 2022; 9(9):447. https://doi.org/10.3390/bioengineering9090447
Chicago/Turabian StyleQing, Ming, Zhan Liu, and Tinghui Zheng. 2022. "Fast and Accurate Computation of the Displacement Force of Stent Grafts after Endovascular Aneurysm Repair" Bioengineering 9, no. 9: 447. https://doi.org/10.3390/bioengineering9090447