Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T22:42:17.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Vessel Wall Models for Simulation of Atherosclerotic VascularNetworks

Published online by Cambridge University Press:  15 June 2011

Yu. Vassilevski ,
S. Simakov ,
V. Salamatova ,
Yu. Ivanov  and
T. Dobroserdova
Yu. Vassilevski*
Affiliation:
Institute of Numerical Mathematics RAS, Gubkina st. 8, Moscow 119333, Russia
S. Simakov
Affiliation:
Moscow Institute of Physics and Technology, Institutskyi Lane 9, Dolgoprudny 141700, Russia
V. Salamatova
Affiliation:
Scientific Educational Center of Institute of Numerical Mathematics RAS, Gubkina st. 8, Moscow 119333, Russia
Yu. Ivanov
Affiliation:
Scientific Educational Center of Institute of Numerical Mathematics RAS, Gubkina st. 8, Moscow 119333, Russia
T. Dobroserdova
Affiliation:
Moscow State University, Leninskie Gory, Moscow 119991, Russia
*
* Corresponding author. E-mail: [email protected]
Get access

Abstract

There are two mathematical models of elastic walls of healthy and atherosclerotic bloodvessels developed and studied. The models are included in a numerical model of globalblood circulation via recovery of the vessel wall state equation. The joint model allowsus to study the impact of arteries atherosclerotic disease of a set of arteries onregional haemodynamics.

Keywords

atherosclerosismathematical modellingblood flowarterial wallwall state equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 7: Mathematical modeling in biomedical applications , 2011 , pp. 82 - 99
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

G., Cheng, H., Loree, R., Kamm, M., Fishbein, R., Lee. Distribution of circumferential stress in ruptured and stable atherosclerotic lesions: a structural analysis with histopathological correlation. Circulation, 87 (1993), 1179–1187. Google Scholar
L. Formaggia, A. Quarteroni, A. Veneziani. Cardiovascular mathematics, Vol. 1. Heidelberg, Springer, 2009.
A. Green, J. Adkins. Large Elastic Deformation. Clarendon Press, Oxford, 1970.
G. Holzapfel, R. Ogden (Eds.). Mechanics of Biological Tissue, Vol. XII. 2006.
G., Holzapfel, R., Ogden. Constitutive modelling of arteries. Proc. R. Soc. A, 466 (2010), No. 2118, 1551–1597. Google Scholar
J., Humphrey. Continuum biomechanics of soft biological tissues. Proc. R. Soc. Lond. A 459, (2003), 3–46. Google Scholar
V., Koshelev, S., Mukhin, T., Sokolova, N., Sosnin, A., Favorski. Mathematical modelling of cardio-vascular hemodynamics with account of neuroregulation. Matem. Mod., 19 (2007), No. 3, 15–28 (in Russian). Google Scholar
R., Lee, A., Grodzinsky, E., Frank, R., Kamm, F., Schoen. Structuredependent dynamic mechanical behavior of fibrous caps from human atherosclerotic plaques. Circulation, 83 (1991), 1764–1770. Google Scholar
J., Ohayon et al. Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: Potential impact for evaluating the risk of plaque rupture. Am. J. Physiol. Heart Circ. Physiol. 293 (2007), 1987–1996. Google Scholar
T.J., Pedley, X.Y., Luo. Modelling flow and oscillations in collapsible tubes. Theor. Comp. Fluid Dyn., 10 (1998), No. 1–4, f–294. Google Scholar
A. Quarteroni, L. Formaggia. Mathematical modelling and numerical simulation of the cardiovascular system. In: Handbook of numerical analysis, Vol.XII, Amsterdam, Elsevier, 2004, 3–127.
W., Riley, R., Barnes, et al. Ultrasonic measurement of the elastic modulus of the common carotid. The Atherosclerosis Risk in Communities (ARIC) Study. Stroke, 23 (1992), 952–956. Google Scholar
M., Rosar, C., Peskin. Fluid flow in collapsible elastic tubes: a three-dimensional numerical model. New York J. Math., 7 (2001), 281–302. Google Scholar
S.S., Simakov, A.S., Kholodov. Computational study of oxygen concentration in human blood under low frequency disturbances. Mat. Mod. Comp. Sim., 1 (2009), 283–295. Google Scholar
C., Tu, C., Peskin. Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods. SIAM J. Sci. Stat. Comp., 6 (1992), No. 13, 1361–1376. Google Scholar
Y.V., Vassilevski, S.S., Simakov, S.A., Kapranov. A multi-model approach to intravenous filter optimization. Int. J. Num. Meth. Biomed. Engrg., 26 (2010), No. 7, 915–925. Google Scholar
Y. Vassilevski, S. Simakov, V. Salamatova, Y. Ivanov, T. Dobroserdova. Blood flow simulation in atherosclerotic vascular network using fiber-spring representation of diseased wall. Math. Model. Nat. Phen. (in press), 2011.
Vito, R., Dixon, S.. Blood vessel constitutive models, 1995-2002. Annu. Rev. Biomed. Engrg., 5 (2003), 413–439. CrossRefGoogle Scholar
R. Wulandana. A nonlinear and inelastic constitutive equation for human cerebral arterial and aneurysm walls. Dissertation, University of Pittsburgh, Pittsburgh, 2003.