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Computer modeling of cardiovascular fluid-structure interactions with the deforming-spatial-domain/stabilized space-time formulation. (English) Zbl 1178.76241

Summary: Hemodynamic factors such as the wall shear stress are believed to affect a number of cardiovascular diseases including atherosclerosis and aneurysm. Since resolving phenomena in a living human body is currently beyond the capabilities of in vivo measurement techniques, computer modeling is expected to play an important role in gaining a better understanding of the relationship between the cardiovascular diseases and the hemodynamic factors. We have developed a computer modeling technique for cardiovascular hemodynamic simulations. With this modeling technique, patient-specific 3D geometry of an artery can be analyzed. We take into account some of the important factors in human body for the purpose of demonstrating in vivo situations in a virtual world. The interaction between the blood flow and the deformation of the arterial walls is a factor that we are specifically focusing on. For such fluid-structure interactions, we have developed a computer modeling tool based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation. This simulation tool is applied to a patient-specific model under pulsatile blood flow conditions. The simulations show that the flow behavior with compliant arterial walls is different from what we see with rigid arterial walls. Consequently, the distribution of the wall shear stress on the compliant arterial walls is significantly different from that on the rigid arterial walls. We deduce that the compliance of the arterial walls needs to be taken into account in cardiovascular hemodynamic simulations, and the computer modeling tool we have developed can be effective in investigation of cardiovascular diseases.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76Z05 Physiological flows
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
92C10 Biomechanics
92-08 Computational methods for problems pertaining to biology
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[1] Komatsu, Y.; Yasuda, S.; Shibata, T.; Ono, Y.; Hyodo, A.; Nose, T., Management for subarachnoid hemorrhage with negative initial angiography, Neurolog. surg., 22, 43-49, (1994), (in Japanese)
[2] The International Study of Unruptured Intracranial Aneurysms Investigators. Unruptured intracranial aneurysms—risk of rupture and risks of surgical intervention, New Engl J Med 339 (24) (1998) 1725-1733.
[3] Nakagawa, T.; Hayashi, K., The incidence and treatment of asymptomatic, unruptured cerebral aneurysms, J. neurosurg., 80, 217-223, (1994)
[4] Karino, T.; Takeuchi, S.; Kobayashi, N.; Motomiya, M.; Mabuchi, S., Fluid dynamics of cerebrovascular disease, Neurosurgeons, 12, 15-24, (1993), (in Japanese)
[5] Malek, A.M.; Alper, S.L.; Izumo, S., Hemodynamic shear stress and its role in atherosclerosis, J. amer. med. assoc., 282, 2035-2042, (1999)
[6] Torii, R.; Oshima, M.; Kobayashi, T.; Takagi, K., The hemodynamic study of the cerebral artery using numerical simulations based on medical imaging data, J. visual., 4, 3, 277-284, (2001)
[7] Tezduyar, T.E., Stabilized finite element formulations for incompressible flow computations, Adv. appl. mech., 28, 1-44, (1992) · Zbl 0747.76069
[8] Tezduyar, T.E.; Behr, M.; Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I. the concept and the preliminary numerical tests, Comput. methods appl. mech. engrg., 94, 3, 339-351, (1992) · Zbl 0745.76044
[9] Tezduyar, T.E.; Behr, M.; Mittal, S.; Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: II. computation of free-surface flows, two-liquid flows, and flows with drifting cylinders, Comput. methods appl. mech. engrg., 94, 3, 353-371, (1992) · Zbl 0745.76045
[10] McDonald, D.A., Blood flow in arteries, (1974), Edward Arnold
[11] Tezduyar, T.E., Finite element methods for flow problems with moving boundaries and interfaces, Arch. comput. methods engrg., 8, 83-130, (2001) · Zbl 1039.76037
[12] Tezduyar, T.E., Finite element methods for fluid dynamics with moving boundaries and interfaces, (), (Chapter 17) · Zbl 0848.76036
[13] Stein, K.; Benney, R.; Kalro, V.; Tezduyar, T.E.; Leonard, J.; Accorsi, M., Parachute fluid-structure interactions: 3-D computation, Comput. methods appl. mech. engrg., 190, 373-386, (2000) · Zbl 0973.76055
[14] Stein, K.; Benney, R.; Tezduyar, T.; Potvin, J., Fluid-structure interactions of a cross parachute: numerical simulation, Comput. methods appl. mech. engrg., 191, 673-687, (2001) · Zbl 0999.76085
[15] Stein, K.R.; Benney, R.J.; Tezduyar, T.E.; Leonard, J.W.; Accorsi, M.L., Fluid-structure interactions of a round parachute: modeling and simulation techniques, J. aircraft, 38, 800-808, (2001)
[16] Tezduyar, T.E., Computation of moving boundaries and interfaces and stabilization parameters, Int. J. numer. methods fluids, 43, 555-575, (2003) · Zbl 1032.76605
[17] Hughes, T.J.R.; Brooks, A.N., A multi-dimensional upwind scheme with no crosswind diffusion, (), 19-35 · Zbl 0423.76067
[18] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[19] Tezduyar, T.E.; Mittal, S.; Ray, S.E.; Shih, R., Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements, Comput. methods appl. mech. engrg., 95, 221-242, (1992) · Zbl 0756.76048
[20] Newmark, N.M., A method of computation for structural dynamics, ASCE J. engrg. mech., 85, 67-94, (1959)
[21] Tezduyar, T.E.; Behr, M.; Mittal, S.; Johnson, A.A., Computation of unsteady incompressible flows with the finite element methods—space-time formulations, iterative strategies and massively parallel implementations, (), 7-24
[22] Nomura, T., ALE finite element computations of fluid-structure interaction problems, Comput. methods appl. mech. engrg., 112, 291-308, (1994) · Zbl 0845.76049
[23] 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)
[24] Otto, F., Die grundform des arteriellen pulses, Z. biol., 37, 483-586, (1899)
[25] Hayashi, K.; Handa, H.; Nagasawa, S.; Okumura, A.; Moritake, K., Stiffness and elastic behavior of human intracranial and extracranial arteries, J. biomech., 13, 175-184, (1980)
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