Effect of Infrarenal Flow Waveform on Hemodynamics of Abdominal Aortic Aneurysms and Selection of Rheology Models

Öz

The infrarenal flow waveform (IFW) demonstrates distinct patterns in response to varying cardiac conditions, raising questions regarding the applicability of the Newtonian model due to variations of the shear rate (|γ ̇ |) distribution across different IFW patterns. This study aims to investigate the hemodynamic conditions generated by different IFW patterns within an Abdominal Aortic Aneurysm (AAA) model, and their impact on the predictions of various rheological models. Numerical simulations are conducted using a simplified, axisymmetric AAA geometry. Three IFW patterns, with varying peak systolic, diastolic, and mean flow rates are applied to the Newtonian, several shear-thinning and viscoelastic (Oldroyd-B) models. The hemodynamic conditions are compared by monitoring important wall shear stress (WSS) descriptors including time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), endothelial cell activation potential (ECAP); with |γ ̇ | distributions and the evolution of vortex patterns. The results demonstrate that even small changes of IFW influence the vortex transport mechanism (VTM) considerably. The transportation time of the vortices from proximal to distal regions within the bulge decreases by up to 50% with an increase in the mean flow rate. These alterations in the VTM affect |γ ̇ | distribution, causing significant variations in the predictions of the rheological models. Even at high mean flow rates, the Newtonian predicts an OSI_(max ) twice as large as that predicted by the Carreau and Power models, along with an ECAP_(max ) that is 5 times greater. However, the differences obtained by the Oldroyd-B model are relatively minor when compared to the viscous shear-thinning models. Therefore, the Newtonian model is not appropriate for the AAA simulations, even in cases characterized by high mean flow rates. Employing the Carreau and Power models, by integrating the patient-specific constants, might exhibit a potential in providing more accurate hemodynamic predictions. Moreover, together with |γ ̇ |, a comprehensive assessment of IFW pattern and resulting VTM prior to the rheological model selection is critical and recommended.

Anahtar Kelimeler

• Abdominal aortic aneurysm hemodynamics
• wall shear stress (WSS) descriptors
• vortex transport
• swirling strength
• blood rheology
• Oldroyd-B model
• OpenFOAM

İnfrarenal Akış Dalga Formunun Abdominal Aort Anevrizmalarının Hemodinamiği ve Reoloji Modellerinin Seçimi Üzerindeki Etkisi

Öz

İnfrarenal akış dalga formu (IFW), farklı kardiyak koşullara yanıt olarak belirgin desenler sergilemekte olup, Newtonyen modelin uygulanabilirliği konusunda, farklı IFW paternleri arasında kayma hızı (|γ̇|) dağılımındaki değişiklikler nedeniyle soru işaretleri doğurmaktadır. Bu çalışma, Abdominal Aort Anevrizması (AAA) modeli içinde farklı IFW paternleri tarafından oluşturulan hemodinamik koşulları ve çeşitli reolojik modellerin tahminlerine olan etkilerini araştırmayı amaçlamaktadır. Sayısal simülasyonlar, basitleştirilmiş, eksen simetrik AAA geometrisi kullanılarak gerçekleştirilmiştir. Değişen tepe sistolik, diyastolik ve ortalama akış hızlarına sahip üç IFW paterni, Newtonyen, birkaç vizkoz kayma-incelmesi modeli ve viskoelastik (Oldroyd-B) modellerine uygulanmıştır. Hemodinamik koşullar, zaman ortalamalı duvar kayma gerilimi (TAWSS), osilatuar kayma indeksi (OSI), endotelyal hücre aktivasyon potansiyeli (ECAP) gibi önemli duvar kayma gerilimi (WSS) tanımlayıcıları ile |γ̇| dağılımları ve girdap paternlerinin evrimi izlenerek karşılaştırılmıştır. Sonuçlar, küçük IFW değişikliklerinin bile girdap taşıma mekanizmasını (VTM) önemli ölçüde etkilediğini göstermektedir. Anevrizma içinde proksimalden distal bölgelere doğru girdapların taşıma süresi, ortalama akış hızındaki artışla birlikte %50'ye kadar azalabilir. VTM'deki bu değişiklikler, |γ̇| dağılımını etkileyerek reolojik modellerin tahminlerinde önemli değişikliklere yol açar. Yüksek ortalama akış hızlarında bile Newtonyen model, Carreau ve Power modellerinin tahmin ettiğinden iki kat daha büyük bir OSI_(max) ve beş kat daha büyük bir ECAP_(max) öngörmektedir. Bununla birlikte, Oldroyd-B modelinin elde ettiği farklar, viskoz kayma-incelmesi gösteren modellerle karşılaştırıldığında nispeten daha küçüktür. Bu nedenle, Newtonyen model, yüksek ortalama akış hızlarıyla karakterize edilen durumlarda bile AAA simülasyonları için uygun değildir. Carreau ve Power modellerinin, hasta özelindeki sabitlerle entegre edilerek kullanılması, daha doğru hemodinamik tahminler sağlamada potansiyel taşıyabilir. Ayrıca, |γ̇| ile birlikte, reolojik model seçimi öncesinde IFW paterni ve buna bağlı VTM'nin kapsamlı bir değerlendirilmesi kritik ve önerilmektedir.

Anahtar Kelimeler

• Abdominal aort anevrizması hemodinamiği
• Duvar kayma gerilimi (WSS) tanımlayıcıları
• Girdap taşınımı
• Döngüsel kuvvet
• Kan reolojisi
• Oldroyd-B modeli
• OpenFOAM

Kaynakça

1. Arzani, A. (2016). Hemodynamics and transport in patient-specific abdominal aortic aneurysms (Doctoral dissertation, University of California, Berkeley).
2. Arzani, A. (2018). Accounting for residence-time in blood rheology models: Do we really need non-Newtonian blood flow modelling in large arteries? Journal of the Royal Society Interface, 15(146). https://doi.org/10.1098/rsif.2018.0486
3. Arzani, A., & Shadden, S. C. (2016). Characterizations and correlations of wall shear stress in aneurysmal flow. Journal of Biomechanical Engineering, 138(1). https://doi.org/10.1115/1.4032056
4. Bessonov, N., Simakov, A. S. S., Vassilevskii, Y., & Volpert, V. (2016). Methods of blood flow modelling. Mathematical Modelling of Natural Phenomena, 11(1), 1–25. https://doi.org/10.1051/mmnp/201611101
5. Biasetti, J., Hussain, F., & Gasser, T. C. (2011). Blood flow and coherent vortices in the normal and aneurysmatic aortas: A fluid dynamical approach to intraluminal thrombus formation. Journal of the Royal Society Interface, 8(63), 1449–1461. https://doi.org/10.1098/rsif.2011.0041
6. Bilgi, C., & Atalik, K. (2019). Numerical investigation of the effects of blood rheology and wall elasticity in abdominal aortic aneurysm under pulsatile flow conditions. Biorheology, 56(1), 51–71. https://doi.org/10.3233/BIR-180202
7. Bilgi, C., & Atalık, K. (2020). Effects of blood viscoelasticity on pulsatile hemodynamics in arterial aneurysms. Journal of Non-Newtonian Fluid Mechanics, 279, Article 104263. https://doi.org/10.1016/j.jnnfm.2020.104263
8. Bodnár, T., Sequeira, A., & Prosi, M. (2011). On the shear-thinning and viscoelastic effects of blood flow under various flow rates. Applied Mathematics and Computation, 217(11), 5055–5067. https://doi.org/10.1016/j.amc.2010.07.054

9. Brewster, D. C., Cronenwett, J. L., Hallett, J. W., Johnston, K. W., Krupski, W. C., & Matsumura, J. S. (2003). Guidelines for the treatment of abdominal aortic aneurysms: Report of a subcommittee of the Joint Council of the American Association for Vascular Surgery and Society for Vascular Surgery. Journal of Vascular Surgery, 37(5), 1106–1117. https://doi.org/10.1067/mva.2003.363
10. Chen, Q., Zhong, Q., Qi, M., & Wang, X. (2015). Comparison of vortex identification criteria for planar velocity fields in wall turbulence. Physics of Fluids, 27(8). https://doi.org/10.1063/1.4927647
11. Cho, Y. I., & Kensey, K. R. (1991). Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows. Biorheology, 28(3–4), 241–262. https://doi.org/10.3233/BIR-1991-283-415
12. Deplano, V., Guivier-Curien, C., & Bertrand, E. (2016). 3D analysis of vortical structures in an abdominal aortic aneurysm by stereoscopic PIV. Experiments in Fluids, 57(11), 167. https://doi.org/10.1007/s00348-016-2263-0
13. Egelhoff, C. J., Budwig, R. S., Elger, D. F., Khraishi, T. A., & Johansen, K. H. (1999). Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions. Journal of Biomechanics, 32(12), 1319–1329. https://doi.org/10.1016/S0021-9290(99)00134-7
14. Elhanafy, A., Guaily, A., & Elsaid, A. (2019). Numerical simulation of Oldroyd-B fluid with application to hemodynamics. Advances in Mechanical Engineering, 11(5), 1–7. https://doi.org/10.1177/1687814019852844 Epps, B. P. (2017). Review of vortex identification methods. AIAA SciTech Forum - 55th AIAA Aerospace Sciences Meeting, 1–22. https://doi.org/10.2514/6.2017-0989
15. Faraji, A., Sahebi, M., & Salavati Dezfouli, S. (2022). Numerical investigation of different viscosity models on pulsatile blood flow of thoracic aortic aneurysm (TAA) in a patient-specific model. Computer Methods in Biomechanics and Biomedical Engineering, 0(0), 1–13. https://doi.org/10.1080/10255842.2022.2102423
16. Favero, J. L., Secchi, A. R., Cardozo, N. S. M., & Jasak, H. (2010). Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations. Journal of Non-Newtonian Fluid Mechanics, 165(23–24), 1625–1636. https://doi.org/10.1016/j.jnnfm.2010.08.010
17. Finol, E. A., & Amon, C. H. (2001). Blood flow in abdominal aortic aneurysms: Pulsatile flow hemodynamics. Journal of Biomechanical Engineering, 123(5), 474–484. https://doi.org/10.1115/1.1395573
18. Fisher, C., & Rossmann, J. S. (2009). Effect of non-Newtonian behavior on hemodynamics of cerebral aneurysms. Journal of Biomechanical Engineering, 131(9), 1–9. https://doi.org/10.1115/1.3148470
19. Fuchs, A., Berg, N., & Prahl Wittberg, L. (2021). Pulsatile aortic blood flow—A critical assessment of boundary conditions. ASME Journal of Medical Diagnostics, 4(1), 011002. https://doi.org/10.1115/1.4048978
20. Guranov, I., Ćoćić, A., & Lečić, M. (2013). Numerical studies of viscoelastic flow using the software OpenFOAM. Proceedings in Applied Mathematics and Mechanics, 13(1), 591–592. https://doi.org/10.1002/pamm.201310276
21. Habla, F., Tan, M. W., Haßlberger, J., & Hinrichsen, O. (2014). Numerical simulation of the viscoelastic flow in a three-dimensional lid-driven cavity using the log-conformation reformulation in OpenFOAM. Journal of Non-Newtonian Fluid Mechanics, 212, 47–62. https://doi.org/10.1016/j.jnnfm.2014.08.005
22. Javidi, M., & Hrymak, A. N. (2015). Numerical simulation of the dip-coating process with wall effects on the coating film thickness. Journal of Coatings Technology and Research, 12(5), 843–853. https://doi.org/10.1007/s11998-015-9699-7
23. Juster, H. R., Distlbacher, T., & Steinbichler, G. (2014). Viscosity analysis of a polymer-based drug delivery system using open-source CFD methods and high-pressure capillary rheometry. International Polymer Processing, 29(5), 570–578. https://doi.org/10.3139/217.2892
24. Karimi, S., Dabagh, M., Vasava, P., Dadvar, M., Dabir, B., & Jalali, P. (2014). Effect of rheological models on the hemodynamics within human aorta: CFD study on CT image-based geometry. Journal of Non-Newtonian Fluid Mechanics, 207, 42–52. https://doi.org/10.1016/j.jnnfm.2014.03.007
25. Lee, S. W., & Steinman, D. A. (2007). On the relative importance of rheology for image-based CFD models of the carotid bifurcation. Journal of Biomechanical Engineering, 129(2), 273–278. https://doi.org/10.1115/1.2540836
26. Les, A. S., Shadden, S. C., Figueroa, C. A., Park, J. M., Tedesco, M. M., Herfkens, R. J., Dalman, R. L., & Taylor, C. A. (2010). Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Annals of Biomedical Engineering, 38(4), 1288–1313. https://doi.org/10.1007/s10439-010-9949-x
27. Leuprecht, A., & Perktold, K. (2001). Computer simulation of non-Newtonian effects on blood flow in large arteries. Computer Methods in Biomechanics and Biomedical Engineering, 4(2), 149–163. https://doi.org/10.1080/10255840008908002
28. Maazioui, S., Kissami, I., Benkhaldoun, F., Maazouz, A., & Ouazar, D. (2021). Concentrated phosphate slurry flow simulations using OpenFOAM. Proceedings of the International Conference on Industrial Engineering and Operations Management, 1843–1852.
29. Madhavan, S., & Kemmerling, E. M. C. (2018). The effect of inlet and outlet boundary conditions in image-based CFD modeling of aortic flow. Biomedical Engineering Online, 17(1), 1–21. https://doi.org/10.1186/s12938-018-0497-1
30. McGloughlin, T. M., & Doyle, B. J. (2010). New approaches to abdominal aortic aneurysm rupture risk assessment. Arteriosclerosis, Thrombosis, and Vascular Biology, 30(9), 1687–1694. https://doi.org/10.1161/ATVBAHA.110.204529
31. Mendieta, J. B., Fontanarosa, D., Wang, J., Paritala, P. K., McGahan, T., Lloyd, T., & Li, Z. (2020). The importance of blood rheology in patient-specific computational fluid dynamics simulation of stenotic carotid arteries. Biomechanics and Modeling in Mechanobiology, 19(5), 1477–1490. https://doi.org/10.1007/s10237-019-01282-7
32. Morbiducci, U., Gallo, D., Massai, D., Ponzini, R., Deriu, M. A., Antiga, L., Redaelli, A., & Montevecchi, F. M. (2011). On the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation. Journal of Biomechanics, 44(13), 2427–2438. https://doi.org/10.1016/j.jbiomech.2011.06.028
33. Moyle, K. R., Antaki, J. F., Greenwald, L., Hariharan, P., & Reddy, V. M. (2006). Comparison of inflow boundary conditions for hemodynamic simulations in idealized and anatomically realistic models of the aorta. Journal of Biomechanical Engineering, 128(5), 745–749. https://doi.org/10.1115/1.2187035
34. Mutlu, O., Salman, H. E., Al-Thani, H., El-Menyar, A., Qidwai, U. A., & Yalcin, H. C. (2023). How does hemodynamics affect rupture tissue mechanics in abdominal aortic aneurysm: Focus on wall shear stress derived parameters, time-averaged wall shear stress, oscillatory shear index, endothelial cell activation potential, and relative residence time. Computers in Biology and Medicine, 154. https://doi.org/10.1016/j.compbiomed.2023.106609
35. Ohtaroglu, O. (2020). Experimental investigation of physiological flow in abdominal aortic aneurysm (Master’s thesis, Middle East Technical University, Ankara, Turkey).
36. Pinto, S. I. S., & Campos, J. B. L. M. (2016). Numerical study of wall shear stress-based descriptors in the human left coronary artery. Computer Methods in Biomechanics and Biomedical Engineering, 19(13), 1443–1455. https://doi.org/10.1080/10255842.2016.1149575
37. Qiu, Y., Yuan, D., Wen, J., Fan, Y., & Zheng, T. (2018). Numerical identification of the rupture locations in patient-specific abdominal aortic aneurysms using hemodynamic parameters. Computer Methods in Biomechanics and Biomedical Engineering, 21(1), 1–12. https://doi.org/10.1080/10255842.2017.1410796
38. Quemada, D. (1978). Rheology of concentrated disperse systems. Rheologica Acta, 653, 643–653.
39. Ramazanli, B., Yavuz, M. M., & Sert, C. (2023). Effect of inlet velocity profile and entrance length on abdominal aortic aneurysm hemodynamics simulations. Journal of Thermal Science and Technology, 43(2), 159–174. https://doi.org/10.47480/isibted.1391391
40. Razavi, A., Shirani, E., & Sadeghi, M. R. (2011). Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models. Journal of Biomechanics, 44(11), 2021–2030. https://doi.org/10.1016/j.jbiomech.2011.04.023
41. Reza, M. M. S., & Arzani, A. (2019). A critical comparison of different residence time measures in aneurysms. Journal of Biomechanics, 88, 122–129. https://doi.org/10.1016/j.jbiomech.2019.03.028
42. Saha, S. C., Francis, I., Saha, G., Huang, X., & Molla, M. M. (2024). Hemodynamic Insights into Abdominal Aortic Aneurysms: Bridging the Knowledge Gap for Improved Patient Care. Fluids, 9(2), 50. https://doi.org/10.3390/fluids9020050
43. Salman, H. E., Ramazanli, B., Yavuz, M. M., & Yalcin, H. C. (2019). Biomechanical investigation of disturbed hemodynamics-induced tissue degeneration in abdominal aortic aneurysms using computational and experimental techniques. Frontiers in Bioengineering and Biotechnology, 7, Article 111. https://doi.org/10.3389/fbioe.2019.00111
44. Saqr, K. M., Rashad, S., Tupin, S., Niizuma, K., Hassan, T., Tominaga, T., & Ohta, M. (2020). What does computational fluid dynamics tell us about intracranial aneurysms? A meta-analysis and critical review. Journal of Cerebral Blood Flow & Metabolism, 40(5), 1021–1039. https://doi.org/10.1177/0271678X19854640
45. Scotti, C. M., Jimenez, J., Muluk, S. C., & Finol, E. A. (2008). Wall stress and flow dynamics in abdominal aortic aneurysms: Finite element analysis vs. fluid-structure interaction. Computer Methods in Biomechanics and Biomedical Engineering, 11(3), 301–322. https://doi.org/10.1080/10255840701827412
46. Soudah, E., Loong, E. Y. K., Bordone, T. H., Pua, M., & Narayanan, S. (2013). CFD modelling of abdominal aortic aneurysm on hemodynamic loads using a realistic geometry with CT. Computational and Mathematical Methods in Medicine, 2013, Article 472564. https://doi.org/10.1155/2013/472564
47. Soulis, J. V., Giannoglou, G. D., Chatzizisis, Y. S., Seralidou, K. V., Parcharidis, G. E., & Louridas, G. E. (2008). Non-Newtonian models for molecular viscosity and wall shear stress in a 3D reconstructed human left coronary artery. Medical Engineering & Physics, 30(1), 9–19. https://doi.org/10.1016/j.medengphy.2007.02.001
48. Stamatopoulos, C., Papaharilaou, Y., Mathioulakis, D. S., & Katsamouris, A. (2010). Steady and unsteady flow within an axisymmetric tube dilatation. Experimental Thermal and Fluid Science, 34(7), 915–927. https://doi.org/10.1016/j.expthermflusci.2010.02.008
49. Stergiou, Y. G., Athanasios, G. K., Aikaterini, A. M., & Spiros, V. P. (2019). Fluid-Structure Interaction in Abdominal Aortic Aneurysms: Effect of Haematocrit. Fluids, 4(1), 11. https://doi.org/10.3390/fluids4010011
50. 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. (2011). Hemodynamic Changes Quantified in Abdominal Aortic Aneurysms with Increasing Exercise Intensity Using MR Exercise Imaging and Image-Based Computational Fluid Dynamics. Annals of Biomedical Engineering, 39(2), 864–883. https://doi.org/10.1007/s10439-011-0313-6
51. Wei, Z. A., Huddleston, C., Trusty, P. M., Singh-Gryzbon, S., Fogel, M. A., Veneziani, A., & Yoganathan, A. P. (2019). Analysis of inlet velocity profiles in numerical assessment of Fontan hemodynamics. Annals of Biomedical Engineering, 47(11), 2258–2270. https://doi.org/10.1007/s10439-019-02307-z
52. Weller, H. G., Tabor, G., Jasak, H., & Fureby, C. (1998). A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in Physics, 12(6), 620. https://doi.org/10.1063/1.168744
53. Womersley, J. R. (1955). Method for the calculation of velocity, rate of flow, and viscous drag in arteries when the pressure gradient is known. The Journal of Physiology, 127(3), 553–563. https://doi.org/10.1113/jphysiol.1955.sp005276
54. Zheng, E. Z., Rudman, M., Singh, J., & Kuang, S. B. (2019). Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM. Applied Mathematical Modelling, 72, 50–67. https://doi.org/10.1016/j.apm.2019.03.003