GİRİŞ HIZ PROFİLİ VE GİRİŞ UZUNLUĞUNUN ABDOMİNAL AORT ANEVRİZMASI HEMODİNAMİĞİ SİMÜLASYONLARINA ETKİSİ

Abstract

Hesaplamalı Abdominal Aort Anevrizması (AAA) hemodinamiği çalışmalarında problem geometrisi, ağ, taşıma, türbülans ve reoloji modellerinin ayarlanması ile birlikte; sınır koşullarının (BC) belirlenmesi de hemodinamik değerlendirmenin güvenilirliğini ve doğruluğunu etkileyen çok önemli bir adımdır. Fizyolojik akışın geçici etkileri, Womersley profili tarafından iyi bir şekilde tarif edilir, ancak ilgili fonksiyonların karmaşık doğası nedeniyle bu profilin uygulanması zor olabilir. Öte yandan, giriş sınır koşulu olarak Plug veya Parabolik hız profilleri kullanan çalışmalar, Womersley profilinin tam özelliklerini elde etmek için genellikle büyük giriş uzunlukları kullanırlar. Bu çalışmada, Womersley, Parabolik ve Plug hız profilleri ve üç ayrı giriş uzunluğu kullanılarak (L_(ent )=D,3D and 11D) anevrizma içerisinde hemodinamik parametreler elde edilmiş ve sonuçlar Base koşul ile karşılaştırılarak incelenmiştir. Base koşulu, ortalama Reynolds sayıları 〖Re〗_m=340 ve 1160 olan iki fizyolojik akış koşulunda, anevrizma içine girmeden önce sağlanan tam gelişmiş akışla elde edilen bir çözümdür. Sonuçlar, ortalama debi arttıkça, karmaşık Womersley denkleminin uygulanmasının gerekli olmayabileceğini ortaya koymaktadır. 〖Re〗_m=1160 olan giriş debi profili için, en az L_(ent )= 3D olan bir giriş uzunluğu sağlanarak Womersley profili yerine Parabolik profil kullanılabilir. Öte yandan, 〖Re〗_m=340 olan debi profil için, Plug profilinin Womersley profili yerine kullanılması için en az L_(ent )= 11D olan bir giriş uzunluğu gereklidir.

Keywords

• Abdominal aort anevrizması hemodinamiği
• Womersley profili
• Duvar kayma gerilmesi parametreleri
• Girdap tanımlama yöntemleri

EFFECT OF INLET VELOCITY PROFILE AND ENTRANCE LENGTH ON ABDOMINAL AORTIC ANEURYSM HEMODYNAMICS SIMULATIONS

Abstract

In computational Abdominal Aortic Aneurysm (AAA) hemodynamics studies, along with adjusting the problem geometry, mesh, transport, turbulence and rheology models; setting up boundary conditions (BC) is also a very important step which affect the reliability and accuracy of the hemodynamic assessment. The transient effects of physiological flow are well described by the Womersley profile, though its application might be difficult due to the complex nature of functions involved. Conversely, in literature, studies utilizing Plug or Parabolic profiles as inlet boundary conditions generally requires large entrance lengths to obtain the exact characteristics of the Womersley profile. In the current study, the differences arising between those boundary conditions, Womersley, Parabolic and Plug, with different entrance lengths, L_(ent )=D,3D and 11D, are examined by comparing the results with a Base condition, which is a solution obtained with ensured fully-developed flow before entering the aneurysm sac at two physiological flow conditions with mean Reynolds numbers, 〖Re〗_m=340 and 1160. The results reveal that with increasing mean flow rate, applying the complex Womersley equation might not be necessary. For the inlet flow waveform with 〖Re〗_m=1160, the Parabolic profile can be used instead of the Womersley profile by supplying an entrance length L_(ent )= 3D. On the other hand, the Plug profile requires an entrance length at least L_(ent )= 11D to replicate the Base condition for waveform with 〖Re〗_m=340.

Keywords

• Abdominal aortic aneurysm hemodynamics
• Womersley profile
• Wall shear stress parameters

References

1. Armour C. H., Guo B., Pirola, S., Saitta S., Liu Y., Dong Z. and Xu X. Y, 2021, The influence of inlet velocity profile on predicted flow in type B aortic dissection, Biomech. Model. Mechanobiol., 20(2), pp. 481–490, doi: 10.1007/s10237-020-01395-4.
2. Arzani A., and Shadden S. C., 2015, Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow, J. Biomech. Eng., 138(1), 014503-014503-014510, doi: 10.1115/1.4032056.
3. Arzani A., Suh G. Y., Dalman R. L., and Shadden S. C., 2014, A longitudinal comparison of hemodynamics and intraluminal thrombus deposition in abdominal aortic aneurysms, American Journal of Physiology-Heart and Circulatory Physiology, 307(12), H1786-H1795, doi: 10.1152/ajpheart.00461.2014.
4. Biasetti J., Hussain F., and Gasser T. C., 2011, Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluid dynamical approach to intra-luminal thrombus formation, J. R. Soc. Interface., 8(63), 1449-61, doi: 10.1098/rsif.2011.0041.
5. Biasetti J., Spazzini P. G., Swedenborg J. and Christian Gasser T., 2012, An integrated fluid-chemical model toward modeling the formation of intra-luminal thrombus in abdominal aortic aneurysms, Front. Physiol., 3, no. July, pp. 1–16, doi: 10.3389/fphys.2012.00266.
6. Bilgi C. and Atalık K., 2020, Effects of blood viscoelasticity on pulsatile hemodynamics in arterial aneurysms, J. Nonnewton. Fluid Mech., 279, no. July 2019, doi: 10.1016/j.jnnfm.2020.104263.
7. Bit A., Alblawi A., Chattopadhyay H., Quais Q. A., Benim A. C., Rahimi-Gorji M., and Do H. T, 2020, Three dimensional numerical analysis of hemodynamic of stenosed artery considering realistic outlet boundary conditions, Comput. Methods Programs Biomed., 185, p. 105163, doi: 10.1016/j.cmpb.2019.105163.
8. Boyd A. J., Kuhn D. C. S., Lozowy R. J. and Kulbisky G. P., 2016, Low wall shear stress predominates at sites of abdominal aortic aneurysm rupture, J. Vasc. Surg., 63(6), pp. 1613–1619, doi: 10.1016/j.jvs.2015.01.040.

9. Brewster D. C., Cronenwett J. L., Hallett J. W., Johnston K. W., Krupski W. C. and 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, J. Vasc. Surg., 37(5), pp. 1106–1117, doi: 10.1067/mva.2003.363.
10. Campbell I. C., Ries J., Dhawan S. S., Quyyumi A. A., Taylor W. R. and Oshinski J. N., 2012, Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation, J. Biomech. Eng., 134(5), pp. 1–8, doi: 10.1115/1.4006681.
11. Chandra S., Raut S. S., Jana A., Biederman R. W., Doyle M., Muluk S. C., et al., 2013, Fluid-Structure Interaction Modeling of Abdominal Aortic Aneurysms: The Impact of Patient-Specific Inflow Conditions and Fluid/Solid Coupling, J. Biomech. Eng., 135(8), 081001-081001-081014, doi: 10.1115/1.4024275.
12. Chen X., Zhuang J., and Wu Y., 2020, The effect of Womersley number and particle radius on the accumulation of lipoproteins in the human aorta, Comput. Methods Biomech. Biomed. Engin., 23(10), pp. 571–584, doi: 10.1080/10255842.2020.1752681.
13. Chen Q., Zhong Q., Qi M. and Wang X. 2015. Comparison of vortex identification criteria for planar velocity fields in wall turbulence, Phys. Fluids, 27(8), doi: 10.1063/1.4927647.
14. Di Achille P., Tellides G., Figueroa C. A., Humphrey J. D., A haemodynamic predictor of intraluminal thrombus formation in abdominal aortic aneurysms, Proc. R. Soc. A Math. Phys. Eng. Sci., 470(2172), 2014, doi: 10.1098/rspa.2014.0163.
15. Drewe C. J., Parker L. P., Kelsey L. J., Norman P. E., Powell J. T., and Doyle B. J., 2017, Haemodynamics and stresses in abdominal aortic aneurysms: A fluid-structure interaction study into the effect of proximal neck and iliac bifurcation angle, J. Biomech., 60, 150-156, doi: https://doi.org/10.1016/j.jbiomech.2017.06.029.
16. Durst F., Ray S., Ünsal B., Bayoumi O. A., 2005, The Development Lengths of Laminar Pipe and Channel, J. Fluids Eng., 127, November 2005, 1154–1160, doi: 10.1115/1.2063088.
17. Finol E. A. and Amon C. H., 2001, Blood flow in abdominal aortic aneurysms: Pulsatile flow hemodynamics, J. Biomech. Eng., 123(5), pp. 474–484, doi: 10.1115/1.1395573.
18. Hoi Y., Wasserman B. A., Lakatta E. G. and Steinman D. A., 2010, Effect of common carotid artery inlet length on normal carotid bifurcation hemodynamics, J. Biomech. Eng., 132(12), pp. 1–14, doi: 10.1115/1.4002800.
19. Impiombato A. N., La Civita G., Orlandi F., Franceschini Zinani F. S., Oliveira Rocha L. A. and Biserni, C., 2021, A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow, Dynamics, 1(1), pp. 9–17, doi: 10.3390/dynamics1010002.
20. Janiga G., Berg P., Sugiyama S., Kono K., and Steinman D. A., 2015, The computational fluid dynamics rupture challenge 2013 - Phase I: Prediction of rupture status in intracranial aneurysms, Am. J. Neuroradiol., 36(3), pp. 530–536, doi: 10.3174/ajnr.A4157.
21. Li Z. and Kleinstreuer C., 2005, Blood flow and structure interactions in a stented abdominal aortic aneurysm model, Med. Eng. Phys., 27(5), pp. 369–382, doi: 10.1016/j.medengphy.2004.12.003.
22. Lodi Rizzini M., Gallo D., De Nisco G., D’ascenzo F., Chiastra C., Bocchino P. P., Piroli F., De Ferrari G. and Morbiducci U., 2020, Does the inflow velocity profile influence physiologically relevant flow patterns in computational hemodynamic models of left anterior descending coronary artery?, Med. Eng. Phys., 82, pp. 58–69, doi: 10.1016/j.medengphy.2020.07.001.
23. Madhavan S. and Kemmerling E. M. C., 2018, The effect of inlet and outlet boundary conditions in image-based CFD modeling of aortic flow, Biomed. Eng. Online, 17(1), pp. 1–20, doi: 10.1186/s12938-018-0497-1.
24. Markl M., Schnell S., Wu C., Bollache E., Jarvis K., Barker A. J., Robinson J. D., Rigsby C. K., 2016, Advanced flow MRI: emerging techniques and applications, Clin Radiol., 71(8):779-95, doi: 10.1016/j.crad.2016.01.011.
25. Morris L., Delassus P., Grace P., Wallis F., Walsh M. and McGloughlin T., 2006, Effects of flat, parabolic and realistic steady flow inlet profiles on idealised and realistic stent graft fits through Abdominal Aortic Aneurysms (AAA), Med. Eng. Phys., 28(1), SPEC. ISS., pp. 19–26, doi: 10.1016/j.medengphy.2005.04.012.
26. Ohtaroglu O., 2020, Experimental investigation of physiological flow in abdominal aortic aneurysm. METU.
27. “OpenFOAM 8,” OpenFOAM, 01-Sep-2020. [Online]. Available: https://openfoam.org/version/8/. [Accessed: 07-Jun-2022].
28. Pinto S. I. S. and Campos J. B. L. M., 2016, Numerical study of wall shear stress-based descriptors in the human left coronary artery, Comput. Methods Biomech. Biomed. Engin., 19(13), pp. 1443–1455, doi: 10.1080/10255842.2016.1149575.
29. Qiu Y., Yuan D., Wen J., Fan Y., and Zheng T., 2018, Numerical identification of the rupture locations in patient-specific abdominal aortic aneurysmsusing hemodynamic parameters, Comput. Methods Biomech. Biomed. Engin., 21(1), 1-12. doi: 10.1080/10255842.2017.1410796.
30. Reza M. M. S. and Arzani A., 2019, A critical comparison of different residence time measures in aneurysms, J. Biomech., 88:122–9.
31. Salman H. E., Ramazanli B., Yavuz M. M. and Yalcin H. C., 2019, Biomechanical Investigation of Disturbed Hemodynamics-Induced Tissue Degeneration in Abdominal Aortic Aneurysms Using Computational and Experimental Techniques, Front. in Biotech and Bioeng., 7, no. May, pp. 1–27, doi: 10.3389/fbioe.2019.00111.
32. San O. and Staples A. E., 2012, An improved model for reduced-order physiological fluid flows, J. Mech. Med. Biol., vol. 12(3), doi: 10.1142/S0219519411004666.
33. Scotti C. M., Jimenez J., Muluk S. C., and Finol E. A., 2008, Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction, Comput. Methods Biomech. Biomed. Engin., 11(3), 301-322. doi: 10.1080/10255840701827412.
34. Stamatopoulos C., Papaharilaou Y., Mathioulakis D. S., and Katsamouris A., 2010, Steady and unsteady flow within an axisymmetric tube dilatation. Experimental Thermal and Fluid Science, 34(7), 915-927. doi: https://doi.org/10.1016/j.expthermflusci.2010.02.008.
35. Wei Z.A., Huddleston C., Trusty P.M., Singh-Gryzbon S., Fogel M.A., Veneziani A. and Yoganathan A. P., 2019, Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics, Ann. Biomed. Eng., 47(11), pp. 2258–2270, doi: 10.1007/s10439-019-02307-z.
36. 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. doi: 10.1113/jphysiol.1955.sp005276.
37. Youssefi P., Gomez A., Arthurs C., Sharma R., Jahangiri, M. and Figueroa C. A., 2018, Impact of patient-specific inflow velocity profile on hemodynamics of the thoracic aorta, J. Biomech. Eng., 140(1), doi: 10.1115/1.4037857.