×

zbMATH — the first resource for mathematics

A one-dimensional model for blood flow in prestressed vessels. (English) Zbl 1063.74072
Summary: We are interested in developing a simple model to investigate blood-vessel interactions in a finite arterial segment of the cardiovascular tree. For this purpose, we developed a continuum model for a vascular segment, and we coupled it with a discrete model for the remaining systemic circulation. In working out the modeling, we addressed some main issues, such as the nonlinearity of blood flow, the compliance of the vessel and the prestress state of the artery walls, that is always present aside from the filling of blood. Moreover, we set a discrete model capable of providing appropriate boundary conditions to the continuum model, by reproducing the proper waveforms entering the vessel and avoiding spurious reflections.
MSC:
74L15 Biomechanical solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
92C10 Biomechanics
76Z05 Physiological flows
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Atabek, H.B.; Lew, H.S., Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube, Biophysical J., 6, 481-503, (1966)
[2] Avanzolini, G.; Barbini, P.; Cappello, A.; Cevenini, G., CADCS simulation of the closed-loop cardiovascular system, Int. J. biomed. comput., 22, 39-49, (1988)
[3] Di Carlo, A.; Nardinocchi, P.; Teresi, L., How to model blood flow in distensible vessels, (), 141-145
[4] Formaggia, L.; Nobile, F.; Quarteroni, A.; Veneziani, A., Multiscale modelling of the circulatory system: a preliminary analysis, Comput. visual sci., 2, 75-83, (1999) · Zbl 1067.76624
[5] Fung, Y.C., Biomechanics. mechanical properties of living tissues, (1993), Springer
[6] 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, 1-48, (2000) · Zbl 1023.74033
[7] ()
[8] Khir, A.W.; Parker, K.H., Measurements of wave speed and reflected waves in elastic tubes and bifurcations, J. biomech., 35, 775-783, (2002)
[9] Kuiken, G.D.C., Wave propagation in a thin-walled liquid-filled, initially stressed tube, J. fluid mech., 141, 289-308, (1984) · Zbl 0573.76128
[10] Nardinocchi, P.; Teresi, L., The influence of initial stresses on blood vessel mechanics, J. mech. mech. biol., 3, 2, 215-229, (2003)
[11] Ottesen, J.T.; Olufsen, M.S.; Larsen, J.K., Applied mathematical models in human physiology, SIAM monograph on math. model & comput, (2004) · Zbl 1097.92016
[12] Pontrelli, G., Blood flow through a circular pipe with an impulsive pressure gradient, Math. models methods appl. sci., 10, 187-202, (2000) · Zbl 1023.76060
[13] Pontrelli, G., A multiscale approach for modelling wave propagation in an arterial segment, Comput. methods biomech. biomed. engrg., 7, 79-89, (2004)
[14] Quarteroni, A., Fluid – structure interaction for blood flow problems, ()
[15] Quarteroni, A.; Formaggia, L., Mathematical modelling and numerical simulation of the cardiovascular system, ()
[16] Sherwin, S.J.; Formaggia, L.; Peiro, J.; Franke, V., Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system, Int. J. numer. meth. fluids, 43, 6/7, 673-700, (2003) · Zbl 1032.76729
[17] Zhou, J.; Fung, Y.C., The degree of nonlinearity and anisotropy of blood vessel elasticity, Proc. natl. acad. sci. USA, 94, 14255-14260, (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.