Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-14T11:24:12.989Z Has data issue: false hasContentIssue false
  • English
  • Français

Blood Flow Simulation in Atherosclerotic Vascular Network Using Fiber-Spring Representation of Diseased Wall

Published online by Cambridge University Press:  10 August 2011

Yu. Vassilevski ,
S. Simakov ,
V. Salamatova ,
Yu. Ivanov  and
T. Dobroserdova
Yu. Vassilevski*
Affiliation:
Institute of Numerical Mathematics RAS, 119333, Moscow, 8 Gubkina St., Russia
S. Simakov
Affiliation:
Moscow Institute of Physics and Technology, 141700, Dolgoprudny, 9 Instituskii Lane, Russia
V. Salamatova
Affiliation:
Scientific Educational Center of Institute of Numerical Mathematics RAS 119333, Moscow, 8 Gubkina St., Russia
Yu. Ivanov
Affiliation:
Scientific Educational Center of Institute of Numerical Mathematics RAS 119333, Moscow, 8 Gubkina St., Russia
T. Dobroserdova
Affiliation:
Moscow State University, 119991, Moscow, Leninskie Gory, Russia
*
⋆ Corresponding author. E-mail: vasilevs@dodo.inm.ras.ru
Get access

Abstract

We present the fiber-spring elastic model of the arterial wall with atherosclerotic plaque composed of a lipid pool and a fibrous cap. This model allows us to reproduce pressure to cross-sectional area relationship along the diseased vessel which is used in the network model of global blood circulation. Atherosclerosis attacks a region of systemic arterial network. Our approach allows us to examine the impact of the diseased region onto global haemodynamics.

Keywords

atherosclerosismathematical modelingblood flowarterial wall
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 333 - 349
Copyright
© EDP Sciences, 2011

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

Cheng, G. C., Loree, H. M., Kamm, R. D., Fishbein, M. C., Lee, R. T.. Distribution of circumferential stress in ruptured and stable atherosclerotic lesions. A structural analysis with histopathological correlation. Circ. Res., 4 (1993), No. 87, 1179–1187. CrossRefGoogle Scholar
L. Formaggia, A. Quarteroni, A. Veneziani. Cardiovascular mathematics. Heidelberg, DE: Springer, 2009.
Gasser, T. C., Holzapfel, G. A.. A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation. Comp. Mech., 29 (2002), No. 4–5, 340–360. CrossRefGoogle Scholar
Holzapfel, G. A., Gasser, T. C., Ogden, R. W.. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity, 61 (2000), No. 1, 1–48. CrossRefGoogle Scholar
Holzapfel, G. A., Stadler, M., Schulze-Bauer, C. A.. A layer-specific three-dimensional model for the simulation of balloon angioplasty using magnetic resonance imaging and mechanical testing. Ann. Biomed. Eng., 30 (2002), No. 6, 753–767. CrossRefGoogle ScholarPubMed
El Khatib, N., Génieys, S., Volpert, V.. Atherosclerosis initiation modeled as an inflammatory process. Math. Model. Nat. Phen., 2 (2007), No. 2, 126–141. CrossRefGoogle Scholar
El Khatib, N., Génieys, S., Zine, A. M., Volpert, V.. Non-Newtonian effects in a fluid-structure interaction model for atherosclerosis. J. Tech. Phys., 1 (2009), No. 50, 55–64. Google Scholar
Loree, H. M., Kamm, R. D., Stringfellow, R. G., Lee, R. T.. Effects of fibrous cap thickness on peak circumferential stress in model atherosclerotic vessels. Circ. Res., 4 (1992), No. 71, 850–858. CrossRefGoogle Scholar
Mori, Y., Peskin, C. S.. A universal programmable fiber architecture for the representation of a general incompressible linearly elastic material as a fiber-reinforced fluid. Adv. Appl. Math., 43 (2009), No. 1, 75–100. CrossRefGoogle Scholar
Pedley, T. J., Luo, X. Y.. Modelling flow and oscillations in collapsible tubes. Theor. Comp. Dluid Dyn., 10 (1998), No. 1–4, 277–294. CrossRefGoogle Scholar
Rosar, M., Peskin, C.. Fluid flow in collapsible elastic tubes: a three-dimensional numerical model. New York J. Math., 7 (2001), 281–302. Google Scholar
Simakov, S. S., Kholodov, A. S.. Computational study of oxygen concentration in human blood under low frequency disturbances. Mat. Mod. Comp. Sim., 1 (2009), No. 283–295. CrossRefGoogle Scholar
Taylor, C. A., Draney, M. T.. Experimental and computational methods in cardiovascular fluid mechanics. Ann. Rev. Fluid Mech., (2004), No. 36, 197–231. CrossRefGoogle Scholar
Tu, C., Peskin, C.. Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods. SIAM J. Scientific and Statistical Computing, 6 (1992), No. 13, 1361–1376. CrossRefGoogle Scholar
Van de Vosse, F. N.. Mathematical modelling of the cardiovascular system. J. Eng. Math., (2003), No. 47, 175–183. CrossRefGoogle Scholar
Vassilevski, Y. V., Simakov, S. S., Kapranov, S. A.. A multi-model approach to intravenous filter optimization. Int. J. Num. Meth. Biomed. Eng., 26 (2010), No. 7, 915–925. Google Scholar