Numerical Analysis of Haemodynamic of Blood Flow in the Carotid Sinus with OpenFOAM

Öz

Investigation of blood flow in the carotid artery is an important issue in haemodynamic studies. In this research, the behaviour of the flow is investigated by focusing on critical points such as the place where the bifurcation begins, and the sinus region at ICA, with using an open source code program for analysis. The parametric 3-D geometry of the carotid artery was created with open source code software, based on real angiogram data in the literature. In this study, OpenFOAM which is also an open source CFD software package, was used in the analysis of computational fluid dynamics. Continuity and momentum equations are discretized with Semi-Implicit Method for pressure linked equations (SIMPLE) for steady flow, and with Pressure Implicit with splitting of operators (PISO) for pulsatile flow. Pulsatile flow at the inlet of the common carotid artery (CCA) is used as a inlet boundary condition, referring to a similar model in the literature. The shear stresses at the carotid sinus, as well as at the carotid bifurcation, was examined. The results are obtained for wall shear stresses, streamlines and velocity contours, and are compared with the published previous literature.

Anahtar Kelimeler

• Carotid sinus
• Hemodynamics
• OpenFOAM

Karotis Sinüsteki Kan Akışının Hemodinamisinin OpenFOAM ile Sayısal Analizi

Öz

Karotis arterdeki kan akımının araştırılması hemodinamik çalışmalarda önemli bir konudur. Bu araştırmada, çatallanmanın başladığı yer ve iç karotis arter (ICA)'deki sinüs bölgesi gibi kritik noktalara odaklanılarak akışın davranışı açık kaynak kodlu bir program kullanılarak analiz edilmiştir. Karotis arterin parametrik 3 Boyutlu geometrisi, literatürdeki gerçek anjiyogram verilerine dayalı olarak açık kaynak kodlu bir yazılım ile oluşturulmuştur. Bu çalışmada, hesaplamalı akışkanlar dinamiği (HAD) analizinde aynı zamanda açık kaynak kodlu bir HAD yazılım paketi olan OpenFOAM kullanılmıştır. Süreklilik ve momentum denklemleri, daimi akış koşulunda Basınca bağlı denklemler için Yarı-Kapalı Yöntem (SIMPLE) ile, ve pulsatil akış için ise Operatörlerin bölünmesi ile Kapalı Basınç yöntemi (PISO) ile ayrıklaştırılır. Ortak karotis arterin (CCA) girişindeki pulsatil akış, literatürdeki benzer bir modele atıfta bulunularak giriş sınır koşulu olarak kullanılmıştır. Karotis sinüsdeki ve çatallanma noktasındaki kayma gerilmeleri incelenmiştir. Sonuçlar duvar kayma gerilmeleri, akım çizgileri ve hız konturları için elde edilmiş ve yayınlanmış önceki literatürle karşılaştırılmıştır.

Anahtar Kelimeler

• Carotid sinus
• Hemodynamics
• OpenFOAM

Kaynakça

1. [1] Ku, D.N.1997. Blood Flow in Arteries, Annual Review of Fluid Mechanics, Cilt. 29, s. 399-434. Doi.org/10.1146/annurev.fluid.29.1.399
2. [2] Caro, C.G., FitzGerald, J.M., Schroter, R.C. 1971. Atheroma and Arterial Wall Shear Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism for Arterogenesis, Proceedings of the Royal Society of London Series B. , Cilt. 1046 (177), s.109-133. Doi.org/10.1098/rspb.1971.0019
3. [3] Malek, A.M., Alper, S.I., Izumo, S. 1999.Hemodynamic Shear Stress and Its Role in Atherosclerosis, The Journal of the American Medical Association, Cilt. 282 (21), s.2035-2042. Doi.org/10.1001/jama.282.21.2035
4. [4] Perktold, K., Hilbert, D. 1986. Numerical Simulation of Pulsatile Flow in a Carotid Bifurcation Model, Journal of Biomedical Engineering, Cilt. 8, s.193-199. Doi.org/10.1016/0141-5425(86)90083-X
5. [5] Nazemi, M., Kleinstreuer, C., Archie, Jr. J.P. 1990. Pulsatile Two-Dimensional Flow and Plaque Formation in a Carotid Artery Bifurcation, Journal of Biomechanics, Cilt. 23 (10), s.1031-1037. Doi.org/10.1016/0021-9290(90)90318-W
6. [6] Rindth, C.C.M., Vosse v.d., F.N., Steenhoven, V. A.A., Janssen, J.D. 1987. A Numerical and Experimental Analysis of the Flow Field in a Two-Dimensional Model of the Human Carotid Artery Bifurcation, Journal of Biomechanics, Cilt. 20 (5), s. 499-509. Doi.org/10.1016/0021-9290(87)90250-8
7. [7] Bharadvaj, B.K., Mabon, R.F., Giddens, D.P. 1982. Steady Flow in a Model of the Human Carotid Bifurcation Part I- Flow Visualization, Journal of Biomechanics, Cilt. 15 (5), s.349-362. Doi.org/10.1016/0021-9290(82)90057-4
8. [8] Perktold, K., Resch, M., Florian, H., 1991. Pulsatile Non-Newtonian Flow Characteristics in a Three Dimensional Human Carotid Bifurcation Model, Journal of Biomechanical Engineering, Cilt. 113, s.464-475. Doi.org/10.1115/1.2895428

9. [9] Perktold, K., Peter, R.O., Resch, M., Langs, G. 1991. Pulsatile Non-Newtonian Blood Flow in Three Dimensional Carotid Bifurcation Models: a Numerical Study of Flow Phenomena Under Different Bifurcation Angles, Journal of Biomedical Engineering, Cilt.13, s.507-515. Doi.org/10.1016/0141-5425(91)90100-L
10. [10] Sinnot, M., Cleary, P.W., Prakash, M. 2006. An Investigation of Pulsatile Blood Flow in a Bifurcation Artery Using a Grid-Free Method. Fifth International Conference on CFD in the Process Industries, 13-15 Aralık, Melbourne, Australia.
11. [11] Nguyen, K.T., Clark, C.D., Chancellor, T.J., Papavassiliou, D.V. 2008. Carotid Geometry Effects on Blood Flow and on Risk for Vascular Disease, Journal of Biomechanics, Cilt. 41, s.11-19. Doi.org: 10.1016/j.jbiomech.2007.08.012
12. [12] Nagargoje, M., Gupta, R. 2020. Effect of Sinus Size and Position on Hemodynamics During Pulsatile Flow in a Carotid Artery Bifurcation, Computer Methods and Programs in Biomedicine, Cilt. 192, s.1-14. Doi.org: 10.1016/j.cmpb.2020.105440
13. [13] Bharadvaj, B.K., Mabon, R.F., Giddens, D.P. 1982. Steady Flow in a Model of the Human Carotid Bifurcation Part II- Laser Doppler Anemometer Measurements, Journal of Biomechanics, Cilt. 15 (5), s. 363-378. Doi.org/10.1016/0021-9290(82)90058-6
14. [14] Ku, D.N., Giddens, D.P. 1983. Pulsatile Flow in a Model Carotid Bifurcation, Arteriosclerosis. Cilt. 3 (1), s. 31-39. Doi.org/10.1161/01.ATV.3.1.31
15. [15] Ku, D.N., Giddens, D.P. 1987. Laser Doppler Anemometer Measurements of Pulsatile Flow in a Model Carotid Bifurcation, Journal of Biomechanics, Cilt. 20 (4), s.407-421. Doi.org/10.1016/0021-9290(87)90048-0
16. [16] Zarins, C.K., Giddens, D.P., Bharadvaj, B.K., Sottiurai, V.S., Mabon, R.F. 1983. Carotid Bifurcation Atherosclerosis Quantitative Correlation of Plaque Locazation with Flow Velocity Profiles and Wall Shear Stress. Circulation Research, Cilt. 53 (4), s.502-514. Doi.org/ 10.1161/01.res.53.4.502
17. [17] OpenFOAM açık kaynak kodlu programın resmi internet sitesi, www.openfoam.org