Finite element modeling of blood in arteries. (English) Zbl 0953.76058

Summary: We describe a finite element framework for computational vascular research. The software system developed provides an integrated set of tools to solve clinically relevant blood flow problems and test hypotheses regarding hemodynamic (blood flow) factors in vascular adaptation and disease. The validity of the computational method was established by comparing numerical results to an analytic solution for pulsatile flow as well as to published experimental flow data. We also describe the applications of the finite element method to qualitative and quantitative assessment of blood flow fields in a number of clinically relevant models.


76M10 Finite element methods applied to problems in fluid mechanics
76Z05 Physiological flows
92C10 Biomechanics
Full Text: DOI


[1] Aluru, N.R., Parallel and stabilized finite element methods for the hydrodynamic transport model of semiconductor devices, () · Zbl 0949.74077
[2] Bassiouny, H.S.; White, S.; Glagov, S.; Choi, E.; Giddens, D.P.; Zarins, C.K., Anastomotic intimal hyperplasia: mechanical injury or flow induced, J. vascular surgery, 15, 708-717, (1992)
[3] Bayliss, W.M., On the local reactions of the arterial wall to changes of internal pressure, J. physiol., 28, 220-231, (1902)
[4] Beere, P.A.; Glagov, S.; Zarins, C.K., Experimental atherosclerosis at the carotid bifurcation of the cynomolgus monkey. localization, compensatory enlargement, and the sparing effect of lowered heart rate, Arteriosclerosis and thrombosis, 12, 1245-1253, (1992)
[5] Booch, G., Object oriented analysis and design, (1994), Benjamin Cummings
[6] Brooks, A.N.; Hughes, T.J.R., Steamline upwind Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1981)
[7] Carter, D.R., Mechanical loading history and skeletal biology, J. biomech., 20, 1095-1109, (1987)
[8] Carter, D.R.; Wong, M.; Orr, T.E., Musculoskeletal ontogeny, phylogeny and functional adaptation, J. biomech., 24, 3-16, (1991)
[9] Conca, C.; Pares, C.; Pironneau, O.; Thiriet, M., Navier-Stokes equations with imposed pressure and velocity fluxes, Int. J. numer. methods engrg., 20, 267-287, (1995) · Zbl 0831.76011
[10] Courtois, P., On time and space decomposition of complex structures, Comm. ACM, 28, 6, (1985)
[11] Dalton, J.C., Doctrines of the circulation, (1884), Henry C. Lea’s Son & Co Philadelphia
[12] Dixon, J.R., Knowledge-based systems for design, J. mech. des., 117B, 11-16, (1995)
[13] Dym, C.L.; Levitt, R.E., Knowledge-based systems in engineering, (1991), McGraw-Hill NY
[14] Dzau, V.J.; Gibbons, G.H., Vascular remodeling: mechanisms and implications, J. cadiovascular pharmacol., 21, Suppl 1, S1-S5, (1993)
[15] Finnigan, P.; Hathaway, A.; Lorensen, W., Merging CAT and FEM, Mech. engrg., 112, 7, 32-38, (1990)
[16] Fung, Y.C., Biomechanics: motion, flow, stress, growth, (1990), Springer New York · Zbl 0743.92007
[17] Galt, S.W.; Zwolak, R.M.; Wagner, R.J.; Gilbertson, J.J., Differential response of arteries and vein grafts to blood flow reduction, J. vascular surgery, 17, 3, 563-570, (1993)
[18] Hughes, T.J.R.; Liu, W.K.; Zimmermann, T.K., Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. methods appl. mech. engrg., 29, 329-349, (1981) · Zbl 0482.76039
[19] Hughes, T.J.R.; Franca, L.P.; Balestra, M., A new finite element method for computational fluid dynamics: V. circumventing the babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolations, Comput. methods appl. mech. engrg., 59, 85-99, (1986) · Zbl 0622.76077
[20] Hughes, T.J.R., The finite element method, (1987), Prentice-Hall Englewood Cliffs, NJ
[21] Hughes, T.J.R.; Franca, L.P.; Hulbert, G.M., A new finite element method for computational fluid dynamics: VIII. the Galerkin/least squares method for advective-diffusive equations, Comput. methods appl. mech. engrg., 73, 173-189, (1989) · Zbl 0697.76100
[22] Johan, Z.; Hughes, T.J.R.; Shakib, F., A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids, Comput. methods appl. mech. engrg., 87, 281-304, (1991) · Zbl 0760.76070
[23] Kamiya, A.; Togawa, T., Adaptive regulation of wall shear stress to flow change in the canine carotid artery, Am. J. physiol., 239, H14-H21, (1980)
[24] Ku, D.N.; Giddens, D.P.; Zarins, C.K.; Glagov, S., Pulsatile flow and atherosclerosis in the human carotid bifurcation. positive correlation between plaque location and low oscillating shear stress, Arteriosclerosis, 5, 293-302, (1985)
[25] Ku, D.N.; Giddens, D.P., Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation, J. biomech., 20, 4, 407-421, (1987)
[26] Langille, B.L., Remodeling of developing and mature arteries: endothelium, smooth muscle, and matrix, J. cardiovascular pharmacol., 21, Suppl 1, S11-S17, (1993)
[27] Liu, S.Q.; Fung, Y.C., Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction, J. biomech. engrg., 111, 4, 325-335, (1989)
[28] W. Lorensen, Personal communication.
[29] Loth, F., Velocity and wall shear stress measurements inside a vascular graft model under steady and pulsatile flow conditions, ()
[30] Moore, J.E., Magnetic resonance imaging of pulsatile hemodynamics in a model of the human abdominal aorta, ()
[31] Moore, J.E.; Ku, D.N.; Zarins, C.K.; Glagov, S., Pulsatile flow visualization in the abdominal aorta under differing physiologic conditions: implications for increased susceptibility to atherosclerosis, J. biomech. engrg., 114, 391-397, (1992)
[32] Nielsen, E.H.; Dixon, J.R.; Zinsmeister, G.E., Capturing and using designer intent in a design-with-features system, (), 95-102
[33] Pelc, N.J.; Sommer, F.G.; Li, K.C.P.; Brosnan, T.J.; Herfkens, R.J.; Enzmann, D.R., Quantitative magnetic resonance flow imaging, Magnetic resonance qtly., 10, 3, 125-147, (1994)
[34] Perktold, K.; Resch, M.; Peter, R., Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation, J. biomech., 24, 6, 409-420, (1991)
[35] Perktold, K.; Peter, R.O.; Resch, M.; Langs, G., Pulsatile non-Newtonian flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles, J. biomedical engrg., 13, 507-515, (1991)
[36] Saad, Y.; Shultz, M.H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. scientif. statist. comput., 7, 856-869, (1986) · Zbl 0599.65018
[37] Sani, R.L.; Gresho, P.M., (), 983-1008
[38] Shephard, M.S.; Georges, M.K., Automatic three-dimensional mesh generation by the finite octree technique, Int. J. numer. methods engrg., 32, 709-749, (1991) · Zbl 0755.65116
[39] Steinman, D.A.; Ethier, C.Ross; Zhang, X.; Karpik, S.R., The effect of flow waveform on anastomotic wall shear stress patterns, ASME adv. bioengrg., 173-176, (1995)
[40] Simon, H., The sciences of the artificial, (1982), MIT Press Cambridge, MA
[41] Welch, R.V.; Dixon, J.R., Representing function, behavior and structure during conceptual design, (), 11-18
[42] Womersley, J.R., Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. physiol., 127, 553-563, (1955)
[43] Zarins, C.K.; Giddens, D.P.; Bharadvaj, B.K.; Sottiurai, V.S.; Mabon, R.F.; Glagov, S., Carotid bifurcation atherosclerosis: quantitative correlation of plaque localization with flow velocity profiles and wall shear stress, Circulation res., 53, 502-514, (1983)
[44] Zarins, C.K.; Zatina, M.A.; Giddens, D.P.; Ku, D.N.; Glagov, S., Shear stress regulation of artery lumen diameter in experimental atherogenesis, J. vascular surgery, 5, 413-420, (1987)
[45] Zarins, C.K.; Glagov, S.; Vesselinovitch, D.; Wissler, R.W., Aneurysm formation in experimental atherosclerosis: relationship to plaque evolution, J. vascular surgery, 12, 246-256, (1990)
[46] Zarins, C.K., Hemodynamic factors in atherosclerosis, (), 96-107
[47] ()
[48] ()
[49] ()
[50] ()
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.