Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T18:28:48.407Z Has data issue: false hasContentIssue false
  • English
  • Français

3D Simulations of Blood Flow Dynamics in Compliant Vessels: Normal, Aneurysmal, and Stenotic Arteries

Part of: Incompressible viscous fluids Physiological, cellular and medical topics

Published online by Cambridge University Press:  17 May 2016

Yongsam Kim ,
Yunyoung Park  and
Sookkyung Lim
Yongsam Kim*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Yunyoung Park*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Sookkyung Lim*
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, 45242, USA
*
*Corresponding author. Email addresses:[email protected] (Y. Kim), [email protected] (Y. Park), [email protected] (S. Lim)
*Corresponding author. Email addresses:[email protected] (Y. Kim), [email protected] (Y. Park), [email protected] (S. Lim)
*Corresponding author. Email addresses:[email protected] (Y. Kim), [email protected] (Y. Park), [email protected] (S. Lim)
Get access

Abstract

Arterial diseases such as aneurysm and stenosis may result from the mechanical and/or morphological change of an arterial wall structure and correspondingly altered hemodynamics. The development of a 3D computational model of blood flow can be useful to study the hemodynamics in major blood vessels and may provide an insight into the noninvasive technique to detect arterial diseases in early stage. In this paper, we present a three-dimensional model of blood flow in the aorta, which is based on the immersed boundary method to describe the interaction of blood flow with the aortic wall. Our simulation results show that the hysteresis loop is evident in the pressure-diameter relationship of the normal aorta when the arterial wall is considered to be viscoelastic. In addition, it is shown that flow patterns and pressure distributions are altered in response to the change of aortic morphology.

Keywords

Blood flowimmersed boundary methodcompliant vesselaortic aneurysmaortic stenosis

MSC classification

Secondary: 76D05: Navier-Stokes equations 92C35: Physiological flow
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1167 - 1190
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Armentano, R. L., Barra, J. G., Levenson, J., Simon, A., and Pichel, R. H.. Arterial wall mechanics in conscious dogs: Assessment of viscous, inertial, and elastic moduli to characterize aortic wall behavior. Circ. Res. 76:468–478, 1995.Google Scholar
[2]Armentano, R. L., Megnien, J. L., Simon, A., Bellenfant, F., Barra, J., and Levenson, J.. Effects of hypertension on viscoelasticity of carotid and femoral arteries in humans. Hypertension 26:48–54, 1995.CrossRefGoogle ScholarPubMed
[3]Arthurs, K. M., Moore, L. C., Peskin, C. S., Pitman, E. B., and Layton, H. E.. Modeling arteriolar flow and mass transport using the immersed boundary method. J. Comput. Phys. 147(2):402–440, 1998.CrossRefGoogle Scholar
[4]Bauer, R. D., Busse, R., Schabert, A., Summa, Y., and Wetterer, E.. Separate determination of the pulsatile elastic and viscous forces developed in the arterial wall in vivo. Pflugers Arch. 380(3):221–226, 1979.Google Scholar
[5]Bazilevs, Y., Calo, V. M., Hughes, T. J. R., and Zhang, Y.. Isogeometric fluid-structure interaction: Theory, algorithms, and computations. Comput. Mech., 43(1):3–37, 2008.Google Scholar
[6]Berger, S. A. and Jou, L-D.. Flows in stenotic vessels. Annu. Rev. Fluid Mech. 32:347–382, 2000.Google Scholar
[7]Blanco, P. J., Leiva, J. S., Feijoo, R. A., and Buscaglia, G. C.. Black-box decomposition approach for computational hemodynamics: One-dimensional models. Comput. Methods Appl. Mech. Eng., 200(13-16);1389–1405, 2011.Google Scholar
[8]Bonnemain, J., Malossi, A. C. I., Lesinigo, M., Deparis, S., Quarteroni, A., and von Segesser, L. K.. Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations. Med. Eng. Phys., 35(10):1465–1475, 2013.Google Scholar
[9]Boudoulas, H., Toutouzas, P. K., and Wooley, C. F.. Functional Abnormalities of the Aorta. Futura Publishing Company, New York, 1996.Google Scholar
[10]Canic, S., Hartley, C. J., Rosenstrauch, D., Tambaca, J., Guidoboni, G., and Mikelic, A.. Blood flow in compliant arteries: An effective viscoelastic reduced model, numerics and experimental validation. Ann. Biomed. Eng., 34(4):575–592, 2006.Google Scholar
[11]Canic, S., Muha, B., and Bukac, M.. Stability of the Kinematically Coupled Beta-Scheme for fluid-structure interaction problems in hemodynamics. Int. J. Numer. Analysis & Modeling., 12(1):54–80, 2015.Google Scholar
[12]Crosetto, , Reymond, P. P., Deparis, S., Kontaxakis, D., Stergiopulos, N., and Quarteroni, A.. Fluid-structure interaction simulation of aortic blood flow. Computers & Fluids, 43(1):46–57, 2011.Google Scholar
[13]Deparis, S., Discacciati, M., Fourestey, G., and Quarteroni, A.. Fluid-structure algorithm based on Steklov-Poincare operators. Comput. Methods Appl. Mech. Eng., 195(41-43):5797–5812, 2006.Google Scholar
[14]Duraiswamy, N., Schoephoerster, R. T., Moreno, M. R., and Moore, J. E. Jr.Stented artery flow patterns and their effects on the artery wall. Annu. Rev. Fluid. Mech., 39:357–382, 2007.Google Scholar
[15]Egelhoff, C. J., Budwig, R. S., Elger, D. F., Khraishi, T. A., and Johansen, K. H.. Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions. J. Biomech., 32(12):1319–1329, 1999.Google Scholar
[16]FinolE, A. E, A., Keyhani, K., and Amon, C. H.The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions. J. Biomech. Eng., 125(2):207–217, 2003.Google Scholar
[17]Formaggia, L., Gerbeau, J. F., Nobile, F., and Quarteroni, A.. On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng., 191(6-7):561–582, 2001.CrossRefGoogle Scholar
[18]Formaggia, L., Lamponi, D., and Quarteroni, A.. One-dimensional models for blood flow in arteries. J. Eng. Math., 47(3-4):251–276, 2003.Google Scholar
[19]Formaggia, L., Quarteroni, A., and Vergara, C.. On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. J. Comput. Phys., 244:97–112, 2013.Google Scholar
[20]Ganten, M-K., Krautter, U., Tengg-Kobligk, H. V., Bockler, D., Schumacher, H., Stiller, W., Delorme, S., Kauczor, H., Kauffmann, G. W., and Bock, M.. Quantification of aortic distensibility in abnormal aortic aneurysm using ECG-gated multi-detector computed tomography. Eur. Radiol., 18(5):966–973, 2008.Google Scholar
[21]Giannattasio, C., Failla, M., Emanuelli, G., Grappiolo, A., Boffi, L., Corsi, D., and Mancia, G.. Local effects of atherosclerotic plaque on arterial distensibility. Hypertension, 38(5):1177–1180, 2001.Google Scholar
[22]Griffith, B. E. and Peskin, C. S.. On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems. J. Comput. Phys., 208(1):75–105, 2005.CrossRefGoogle Scholar
[23]Guidoboni, G., Glowinski, R., Cavallini, N., and Canic, S.. Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow. J. Comput. Phys., 228(18):6916–6937, 2009.Google Scholar
[24]Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. R.. Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys., 71(2):231–303, 1987.Google Scholar
[25]Hung, T. and Tsai, T.. Pulsatile blood flows in stenotic artery. J. Eng. Mech., 122(9):890–896, 1996.Google Scholar
[26]Jung, H., Choi, J., and Park, C.. Asymmetric flows of non-Newtonian fluids in symmetric stenosed artery. Korea-Australia Rheology J., 16(2):101–108, 2004.Google Scholar
[27]Kim, Y. and Peskin, C. S.. 2-D parachute simulation by the immersed boundary method. SIAM J. Sci. Comput., 28(6):2294–2312, 2006.Google Scholar
[28]Kim, Y. and Peskin, C. S.. Penalty immersed boundary method with an elastic boundary with mass. Phys. Fluids, 19(5), 2007.Google Scholar
[29]Kim, Y., Lim, S., Raman, S. V., Simonetti, O. P., and Friedman, A.. Blood flow in a compliant vessel by the immersed boundary method. Ann. Biomed. Eng., 37(5):927–942, 2009.Google Scholar
[30]Kim, Y., Lee, W., and Jung, E.. An immersed boundary method heart model coupled with a multicomponent lumped model of the circulatory system. SIAM J. Sci. Comput., 32(4):1809–1831, 2010.Google Scholar
[31]Kim, H. J., Vignon-Clementel, I. E., Figueroa, C. A., LaDisa, J. F., Jansen, K. E., Feinstein, J. A., and Taylor, C. A.. On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Ann. Biomed. Eng., 37(11):2153–2169, 2009.Google Scholar
[32]Kleinstreuer, C., Li, Z., and Farber, M. A.. Fluid-structure interaction analyses ofstented abdominal aortic aneurysms. Annu. Rev. Biomed. Eng., 9:169–204, 2007.Google Scholar
[33]Kuttler, U., Gee, M., Forster, D., Comerford, A., and Wall, W. A.. Coupling strategies for biomedical fluid-structure interaction problems. Int. J. Numer. Methods Biomed. Eng., 26(3-4):305–321, 2010.CrossRefGoogle Scholar
[34]Lai, M. C. and Peskin, C. S.. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys., 160(2):705–719, 2000.Google Scholar
[35]Lanne, T., Stale, H., Bengtsson, H., Gustafsson, D., Bergvist, D., Sonesson, B., Lecerof, H., and Dahl, P.. Noninvasive measurement of diameter changes in the distal abdominal aorta in man. Ultrasound Med. Biol., 18(5):451–457, 1992.Google Scholar
[36]Lasheras, J. C.The biomechanics of arterial aneurysms. Annu. Rev. Fluid. Mech., 39:293–319, 2007.Google Scholar
[37]Malek, A. M., Alper, S. L., and Izumo, S.. Hemodynamics shear stress and its role in atherosclerosis. JAMA, 282(21):2035–2042, 1999.CrossRefGoogle ScholarPubMed
[38]Malossi, A. C. I., Blanco, P. J., Crosetto, P., Deparis, S., and Quarteroni, A.. Implicit coupling of one-dimensional and three-dimensional blood-flow models with compliant vessels. SIAM J. Multi-scale Model. Simul., 11(2):474–506, 2013.CrossRefGoogle Scholar
[39]Nichols, W. and O'Rourke, M.. McDonald's Blood Flow in Arteries. Edward Arnold Ltd., London, 2005.Google Scholar
[40]Nobile, F. and Vergara, C.. An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J. Sci. Comput., 30(2):731–763, 2008.Google Scholar
[41]Pearson, A. C., Guo, R., Orsinelli, D. A., Binkley, P. F., and Pasierski, T. J.. Transesophageal echocardiographic assessment of the effects of age, gender, and hypertension on thoracic aortic wall size, thickness, and stiffness. American Heart J., 128(2):344–351, 1994.Google Scholar
[42]Peskin, C. S.Numerical analysis of blood flow in the heart. J. Comput. Phys., 25(3):220–252, 1977.Google Scholar
[43]Peskin, C. S. and McQueen, D. M.. Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity. In Mechanics for a New Millennium: Proceedings of the 20th International Conference on Theoretical and Applied Mechanics, 2000, edited by Aref, H. and Phillips, J. W., Kluwer Academic Publishers, 2001.Google Scholar
[44]Peskin, C. S.The immersed boundary method. Acta Numerica 11:479–517, 2002.Google Scholar
[45]Reymond, P., Merenda, F., Perren, F., Rufenacht, D., and Stergiopulos, N.. Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol., 297(1):208–222, 2009.Google Scholar
[46]Rosar, M. E. and Peskin, C. S.. Fluid flow in collapsible elastic tubes: A three-dimensional numerical model. New York J. Math., 7:281–302, 2001.Google Scholar
[47]Scotti, C. M., Shkolnik, A. D., Muluk, S. C., and Finol, E. A.. Fluid-structure interaction in abdominal aortic aneurysms: Effects of asymmetry and wall thickness. Biomed. Eng., 4:64, 2005.Google Scholar
[48]Sherwin, S. J., Franke, V., Peiró, J., and Parker, K.. One-dimensional modelling of a vascular network in space-time variables. J. Eng. Math., 47(3-4):217–250, 2003.Google Scholar
[49]Shu, C. W. and Osher, S.. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys., 77(2):439–471, 1988.Google Scholar
[50]Shu, C. W. and Osher, S.. Efficient implementation of essentially non-oscillatory shock-capturing schemes II. J. Comput. Phys., 83(1):32–78, 1989.Google Scholar
[51]Stary, H. C.Atlas of Atherosclerosis: Progression and Regression. 2nd edn. Parthenon Publishing, London, 2003.Google Scholar
[52]Varghese, S. S., and Frankel, S. H.. Numerical modeling of pulsatile turbulent flow in stenotic vessels. J. Biomech. Eng., 125(4):445–460, 2003.Google Scholar
[53]Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E., and Taylor, C. A.. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng., 195:3776–3796, 2006.Google Scholar
[54]Wilson, K. A., Lee, A. J., Hoskins, P. R., Fowkes, F. G. R., Ruckley, C. V., and Bradbury, A. W.. The relationship between aortic wall distensibility and rupture of infrarenal abdominal aortic aneurysm. J. Vasc. Surg., 37(1):112–117, 2003.Google Scholar
[55]Wolinsky, H. and Glagov, S.. A lamellar unit of aortic medial structure and function in mammals. Circ. Res., 20(1):99–111, 1967.Google Scholar