# Aorta Ascending Aneurysm Analysis Using CFD Models towards Possible Anomalies

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Patient Data

#### 2.2. Model Geometry and Mesh

#### 2.3. Boundary Conditions

## 3. Results

#### 3.1. Blood Velocity

#### 3.2. Wall Shear Stress

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Informed Consent

## References

- Biasetti, J.; Hussain, F.; Gasser, T. Blood flow and coherent vortices in the normal and aneurysmatic aortas: A fluid dynamical approach to intra-luminal thrombus formation. J. R. Soc. Interface
**2011**. [Google Scholar] [CrossRef] [PubMed] - Soudah, E.; Loong, T.; Bordone, M.; Pua, U.; Narayanan, S. CFD modelling of abdominal aortic aneurysm on hemodynamic loads using a realistic geometry with CT. Comput. Math. Methods Med.
**2013**. [Google Scholar] [CrossRef] [PubMed] - Bonow, R.; Mann, D.; Zipes, D.; Libby, P. Braunwald’s Heart Disease. In A Textbook of Cardiovascular Medicine; Elsevier Health Sciences: Amsterdam, The Netherlands, 2011; Volume 2. [Google Scholar]
- Vorp, D. Biomechanics of abdominal aortic aneurysm. J. Biomech.
**2007**, 40, 1887–1902. [Google Scholar] [CrossRef] [PubMed] - Humphrey, J. Cardiovascular Solid Mechanics. In Cells, Tissues and Organs; Springer: New York, NY, USA, 2002. [Google Scholar]
- Powell, J.; Brown, L.; Forbes, J. Final 12-year follow-up of surgery versus surveillance in the UK small aneurysm trial. Br. J. Surg.
**2007**, 94, 702–708. [Google Scholar] [CrossRef] [PubMed] - Filardi, V. CFD analysis to evaluate hemodynamic parameters in a growing abdominal aortic aneurysm. Vasc. Dis. Manag.
**2015**, 12, E84–E95. [Google Scholar] - Biglino, G.; Cosentino, D.; Steeden, J.; De Nova, L.; Castelli, M.; Ntsinjana, H.; Pennati, G.; Taylor, A.; Schievano, S. Using 4D cardiovascular magnetic resonance imaging to validate computational fluid dynamics: A case study. Front. Pediatr.
**2015**, 3. [Google Scholar] [CrossRef] [PubMed] - Valverde, I.; Nordmeyer, S.; Uribe, S.; Greil, G.; Berger, F.; Kuehne, T. Systemic-to-pulmonary collateral flow in patients with palliated univentricular heart physiology: Measurement using cardiovascular magnetic resonance 4D velocity acquisition. J. Cardiovasc. Magn. Reson.
**2012**, 14. [Google Scholar] [CrossRef] [PubMed] - Francois, C.; Srinivasan, S.; Schiebler, M.; Reeder, S.; Niespodzany, E.; Landgraf, B. 4D cardiovascular magnetic resonance velocity mapping of alterations of right heart flow patterns and main pulmonary artery hemodynamics in tetralogy of Fallot. J. Cardiovasc. Magn. Reson.
**2012**, 14. [Google Scholar] [CrossRef] [PubMed] - Geiger, J.; Markl, M.; Jung, B.; Grohmann, J.; Stiller, B.; Langer, M. 4D-MR flow analysis in patients after repair of tetralogy of Fallot. Eur. Radiol.
**2011**, 21, 1651–1657. [Google Scholar] [CrossRef] [PubMed] - Carlsson, M.; Toger, J.; Kanski, M.; Bloch, K.; Stahlberg, F.; Heiber, E. Quanification and visualization of cardiovascular 4D velocity mapping accelerated with parallel imaging or k-t BLAST: Head to head comparison and validation at 1.5T and 3T. J. Cardiovasc. Magn. Reson.
**2011**, 13. [Google Scholar] [CrossRef] [PubMed] - De Vecchi, A.; Nordsletten, D.; Razavi, R.; Greil, G.; Smith, N. Patient specific fluid/structure ventricular modelling for integrated cardiac care. Med. Biol. Eng. Compt.
**2013**, 51, 1261–1270. [Google Scholar] [CrossRef] [PubMed] - COMSOL. Multiphysics User’s Guide; COMSOL Inc.: Burlington, MA, USA, 2012; p. 1372. [Google Scholar]
- De Santis, G.; De Beule, M.; Van Canneyt, K.; Segers, P.; Verdonck, P.; Verhegghe, B. Full-hexahedral structured meshing for image-based computational vascular modeling. Med. Eng. Phys.
**2011**, 33, 1318–1325. [Google Scholar] [CrossRef] [PubMed] - Baker, T.; Pebay, P.; Pousin, J. Dynamic meshing for finite element based segmentation of cardiac imagery. In Proceedings of the WCCM V-Fifth World Congress on Computational Mechanics, Vienna, Austria, 2002. [Google Scholar]
- Sochi, T. Non-Newtonian Rheology in Blood Circulation. In Fluid Dynamics; Department of Physics and Astronomy, University College London: London, UK, 2014; Volume 1. [Google Scholar] [CrossRef]
- Herzog, C.; Zwrner, P.; Doll, J.; Nielsen, C.; Nguyen, S.; Savino, G.; Vogl, T.; Costello, P.; Schoepf, U. Significant coronary artery stenosis: comparison on per-patient and per-vessel or per-segment basis at 64-section CT angiography. Radiology
**2007**, 244, 112–120. [Google Scholar] [CrossRef] [PubMed] - Bluestein, D.; Dumont, K.; de Beule, M. Intraluminal thrombus and risk of rupture in patient specific abdominal aortic aneurysm—FSI modelling. Comput. Methods Biomechan. Biomed. Eng.
**2009**, 12, 73–81. [Google Scholar] [CrossRef] - Vorp, D.; Raghavan, M.; Webster, M. Mechanical wall stress in abdominal aortic aneurysm: Influence of diameter and asymmetry. J. Vasc. Surg.
**1998**, 27, 632–639. [Google Scholar] [CrossRef] - Ouriel, K.; Green, R.; Donayre, C.; Shortell, C.; Elliott, J.; DeWeese, J. An evaluation of new methods of expressing aortic aneurysm size: Relationship to rupture. J. Vasc. Surg.
**1992**, 15, 12–20. [Google Scholar] [CrossRef] - Shipkowitz, T.; Rodgers, V.G.; Frazin, L.J.; Chandran, K.B. Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches. J. Biomech.
**2000**, 33, 717–728. [Google Scholar] [CrossRef] - Alastruey, J.; Xiao, N.; Fok, H.; Schaeffter, T.; Figueroa, C. On the impact of modelling assumptions in multi-sacle, subject-specific models of aortic heamodynamics. J. R. Soc. Interface
**2016**, 13. [Google Scholar] [CrossRef] [PubMed] - Jung, H.; Choi, J.; Park, C. Asymmetric flows of non-newtonian fluids in a symmetric stenosed artery. Korea-Aust. Rheol. J.
**2004**, 1, 101–108. [Google Scholar] - Migliavacca, F.; Petrini, L.; Montanari, V.; Quagliana, I.; Auricchio, F.; Dubini, G. A predictive study of the mechanical behaviour of coronary stents by computer modelling. Med. Eng. Phys.
**2005**, 27, 13–18. [Google Scholar] [CrossRef] [PubMed] - Kajzer, W.; Kackmarek, M.; Marciniak, J. Biomechanical analysis of stent-oesophagus system. J. Mater. Process. Technol.
**2005**, 162–163, 196–202. [Google Scholar] [CrossRef] - Gundert, T. Improving Cardiovascular Stent Design Using Patient-Specific Models and Shape Optimization. Master’s Thesis, Marquette University, Milwaukee, WI, USA, 2011; p. 104. [Google Scholar]
- Kleinstreuer, C.; Li, Z. Analysis and computer program for rupture-risk prediction of abdominal aortic aneurysms. Biomed. Eng. Online
**2006**, 5. [Google Scholar] [CrossRef] [PubMed] - Vorp, D.; Lee, P.; Wang, D. Association of intraluminal thrombus in abdominal aortic aneurysm with local hypoxia and wall weakening. J. Vasc. Surg.
**2001**, 34, 291–299. [Google Scholar] [CrossRef] [PubMed] - Nicholls, S.; Gardner, J.; Meissner, M.; Johans, K. Rupture in small abdominal aortic aneurysms. J. Vasc. Surg.
**1998**, 28, 884–888. [Google Scholar] [CrossRef] - Bauer, M.; Siniawski, H.; Pasic, M.; Schaumann, B.; Hetzer, R. Different hemodynamic stress of the ascending aorta wall in patients with bicuspid and tricuspid aortic valve. J. Card. Surg.
**2006**, 21, 21820. [Google Scholar] [CrossRef] [PubMed] - Morbiducci, U.; Ponzini, R.; Rizzo, G.; Cadioli, M.; Esposito, A.; Montevecchi, F.M.; Redaelli, A. Mechanistic insight into the physiological relevance of helical blood flow in the human aorta an in vivo study. Biomech. Model. Mechanobiol.
**2010**, 10, 339–355. [Google Scholar] [CrossRef] [PubMed] - Hsu, M.C.; Kamensky, D.; Bazilevs, Y.; Sacks, M.S.; Hughes, T.J. Fluid-structure interaction analysis of bioprosthetic heart valves: Significance of arterial wall deformation. Comput. Mech.
**2014**, 54, 10551071. [Google Scholar] [CrossRef] [PubMed] - Lee, C.-H.; Liu, K.S.; Jhong, G.H.; Liu, S.J.; Hsu, M.Y.; Wang, C.J.; Hung, K.C. Finite element analysis of helical flows in human aortic arch: A novel index. Biomicrofluidics
**2014**, 8, 024111. [Google Scholar] - Bonomi, D.; Vergara, C.; Faggiano, E.; Stevanella, M.; Conti, C.; Redaelli, A.; Puppini, G.; Faggian, G.; Formaggia, L.; Luciani, G.B. Influence of the aortic valve leaflets on the fluid-dynamics in aorta in presence of a normally functioning bicuspid valve. Biomechan. Model. Mechanobiol.
**2015**, 14, 1349–1361. [Google Scholar] [CrossRef] [PubMed] - Morbiducci, U.; Ponzini, R.; Rizzo, G.; Cadioli, M.; Esposito, A.; De Cobelli, F.; Del Maschio, A.; Montevecchi, F.M.; Redaelli, A. In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging. Ann. Biomed. Eng.
**2009**, 37, 516–531. [Google Scholar] [CrossRef] [PubMed] - Guzzetti, S.; Passerini, T.; Slawinski, J.; Villa, U.; Veneziani, A.; Sunderam, V. Platform and algorithm effects on computational fluid dynamics applications in life sciences. Future Gener. Comput. Syst.
**2017**, 67, 382–396. [Google Scholar] [CrossRef] - Suh, G.Y.; Les, A.S.; Tenforde, A.S.; Shadden, S.C.; Spilker, R.L.; Yeung, J.J.; Cheng, C.P.; Herfkens, R.J.; Dalman, R.L.; Taylor, C.A. Hemodynamic changes quantified in abdominal aortic aneurysms with increasing exercise intensity using MR exercise imaging and image-based computational fluid dynamics. Ann. Biomed. Eng.
**2011**, 39, 2186–2202. [Google Scholar] [CrossRef] [PubMed] - Bird, R.B.; Armstrong, R.C.; Hassager, O. Dynamics of Polymeric Liquids, Vol 1: Fluid Mechanics, 2nd ed.; Wiley: Hoboken, NJ, USA, 1987; ISBN 978-0-471-80245-7. [Google Scholar]
- Carreau, P.J.; De Kee, D.C.R.; Chhabra, R.P. Rheology of Polymeric Systems, Principles and Applications; Hanser/Gardner Publications: Cincinnati, OH, USA, 1997; p. 520. [Google Scholar]

**Figure 6.**Ascending aorta aneurysm (Patient 1): (

**a**) computed tomography (CT) data and segmentation; and (

**b**) mesh.

**Figure 18.**Formation of vortical structures (at peak systole): (

**a**) Patient-pilot; (

**b**) Patient 1; (

**c**) Patient 2.

Patient | ${\mathit{d}}_{\mathrm{anterior}}$ (cm) | $\mathit{r}$ (cm) | $\mathit{R}$ (cm) | ${\mathit{D}}_{\mathrm{TAA}}$ (cm) | ${\mathit{L}}_{\mathrm{TAA}}$ (cm) | χ | β | γ | Type |
---|---|---|---|---|---|---|---|---|---|

Pilot | 2.80 | 1.40 | 1.40 | 2.80 | - | 1.00 | 1.00 | - | - |

1 | 3.54 | 2.06 | 2.70 | 4.76 | 6.92 | 1.35 | 0.76 | 0.69 | saccular with azimuthal symmetry (35% of deformation) |

2 | 2.69 | 0.56 | 3.33 | 3.88 | 11.53 | 1.44 | 0.17 | 0.34 | fusiform with only anterior wall dilated (44% of deformation) |

Patients | Velocity Magnitude Range (m/s) | WSS Range (Pa) |
---|---|---|

Patient—pilot | 0.1–0.55 | 2–14 |

4 < 50% area < 6 (LWSS) | ||

8 < 50% area < 12 (HWSS) | ||

Patient 1—TAA | 0.1–0.35 | 1–7 |

85% area < 5 (LWSS) | ||

Patient 2—TAA | 0.1–0.60 | 0–14 |

0 < 60% area < 3 (LWSS) | ||

8 < 40% < 11 (HWSS) |

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**MDPI and ACS Style**

Simão, M.; Ferreira, J.; Tomás, A.C.; Fragata, J.; Ramos, H.
Aorta Ascending Aneurysm Analysis Using CFD Models towards Possible Anomalies. *Fluids* **2017**, *2*, 31.
https://doi.org/10.3390/fluids2020031

**AMA Style**

Simão M, Ferreira J, Tomás AC, Fragata J, Ramos H.
Aorta Ascending Aneurysm Analysis Using CFD Models towards Possible Anomalies. *Fluids*. 2017; 2(2):31.
https://doi.org/10.3390/fluids2020031

**Chicago/Turabian Style**

Simão, Mariana, Jorge Ferreira, António C. Tomás, José Fragata, and Helena Ramos.
2017. "Aorta Ascending Aneurysm Analysis Using CFD Models towards Possible Anomalies" *Fluids* 2, no. 2: 31.
https://doi.org/10.3390/fluids2020031