Finite Element Modeling of Three-Dimensional Pulsatile Flow in the Abdominal Aorta: Relevance to Atherosclerosis

AbstractThe infrarenal abdominal aorta is particularly prone to atherosclerotic plaque formation while the thoracic aorta is relatively resistant. Localized differences in hemodynamic conditions, including differences in velocity profiles, wall shear stress, and recirculation zones have been implicated in the differential localization of disease in the infrarenal aorta. A comprehensive computational framework was developed, utilizing a stabilized, time accurate, finite element method, to solve the equations governing blood flow in a model of a normal human abdominal aorta under simulated rest, pulsatile, flow conditions. Flow patterns and wall shear stress were computed. A recirculation zone was observed to form along the posterior wall of the infrarenal aorta. Low time-averaged wall shear stress and high shear stress temporal oscillations, as measured by an oscillatory shear index, were present in this location, along the posterior wall opposite the superior mesenteric artery and along the anterior wall between the superior and inferior mesenteric arteries. These regions were noted to coincide with a high probability-of-occurrence of sudanophilic lesions as reported by Cornhill et al. (Monogr. Atheroscler. 15:13--19, 1990). This numerical investigation provides detailed quantitative data on hemodynamic conditions in the abdominal aorta heretofore lacking in the study of the localization of atherosclerotic disease. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 0270Dh, 8710+e

[1]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[2]  P Boesiger,et al.  Human abdominal aorta: comparative measurements of blood flow with MR imaging and multigated Doppler US. , 1989, Radiology.

[3]  D. Ku,et al.  Pulsatile flow visualization in the abdominal aorta under differing physiologic conditions: implications for increased susceptibility to atherosclerosis. , 1992, Journal of biomechanical engineering.

[4]  K. Perktold,et al.  Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. , 1995, Journal of biomechanics.

[5]  Mark S. Shephard,et al.  Automatic three‐dimensional mesh generation by the finite octree technique , 1984 .

[6]  D. Ku,et al.  Pulsatile velocity measurements in a model of the human abdominal aorta under simulated exercise and postprandial conditions. , 1994, Journal of biomechanical engineering.

[7]  M H Buonocore,et al.  Blood flow measurements in the aorta and major arteries with MR velocity mapping , 1994, Journal of magnetic resonance imaging : JMRI.

[8]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[9]  D. Steinman,et al.  The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. , 1994, Journal of biomechanical engineering.

[10]  Thomas J. R. Hughes,et al.  Computational investigations in vascular disease , 1996 .

[11]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[12]  Thomas J. R. Hughes,et al.  Finite element modeling of blood flow in arteries , 1998 .

[13]  Robert H. Wilkins,et al.  Autopsy Studies in Atherosclerosis: I. Distribution and Severity of Atherosclerosis in Patients Dying without Morphologic Evidence of Atherosclerotic Catastrophe , 1959 .

[14]  K Perktold,et al.  Pulsatile albumin transport in large arteries: a numerical simulation study. , 1996, Journal of biomechanical engineering.

[15]  C. Kleinstreuer,et al.  Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis. , 1997, Journal of vascular surgery.

[16]  D. Ku,et al.  Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation: Positive Correlation between Plaque Location and Low and Oscillating Shear Stress , 1985, Arteriosclerosis.

[17]  K. T. Scott,et al.  Non-planar curvature and branching of arteries and non-planar-type flow , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  C. Higgins,et al.  Flow pattern analysis in the abdominal aorta with velocity‐encoded cine MR imaging , 1993, Journal of magnetic resonance imaging : JMRI.

[19]  J F Cornhill,et al.  Topography of human aortic sudanophilic lesions. , 1990, Monographs on atherosclerosis.

[20]  Thomas J. R. Hughes,et al.  A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids , 1991 .

[21]  D. Ku,et al.  Pulsatile flow in the human left coronary artery bifurcation: average conditions. , 1996, Journal of biomechanical engineering.

[22]  Francis Loth,et al.  Velocity and wall shear measurements inside a vascular graft model under steady and pulsatile flow conditions , 1993 .

[23]  G. Hutchins,et al.  Correlation between intimal thickness and fluid shear in human arteries. , 1981, Atherosclerosis.

[24]  J. Womersley Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known , 1955, The Journal of physiology.

[25]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[26]  S. Glagov,et al.  Atherosclerosis of human aorta and its coronary and renal arteries. A consideration of some hemodynamic factors which may be related to the marked differences in atherosclerotic involvement of the coronary and renal arteries. , 1961, Archives of pathology.

[27]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[28]  D D Duncan,et al.  The effect of compliance on wall shear in casts of a human aortic bifurcation. , 1990, Journal of biomechanical engineering.

[29]  C. Zarins,et al.  Carotid Bifurcation Atherosclerosis: Quantitative Correlation of Plaque Localization with Flow Velocity Profiles and Wall Shear Stress , 1983, Circulation research.

[30]  A P Yoganathan,et al.  Two-dimensional velocity measurements in a pulsatile flow model of the normal abdominal aorta simulating different hemodynamic conditions. , 1993, Journal of biomechanics.

[31]  Michael M. Resch,et al.  Pulsatile non-Newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles. , 1991, Journal of biomedical engineering.

[32]  D N Ku,et al.  Reverse flow in the major infrarenal vessels--a capacitive phenomenon. , 1988, Biorheology.

[33]  S Glagov,et al.  Flow patterns in the abdominal aorta under simulated postprandial and exercise conditions: an experimental study. , 1989, Journal of vascular surgery.

[34]  S Glagov,et al.  Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. , 1994, Atherosclerosis.

[35]  C Kleinstreuer,et al.  Numerical investigation and prediction of atherogenic sites in branching arteries. , 1995, Journal of biomechanical engineering.

[36]  N J Pelc,et al.  Quantitative magnetic resonance flow imaging. , 1994, Magnetic resonance quarterly.

[37]  Michael M. Resch,et al.  Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation. , 1991, Journal of biomechanics.

[38]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[39]  Mark S. Shephard,et al.  Automatic three-dimensional mesh generation by the finite octree technique , 1984 .

[40]  D A Steinman,et al.  Particle volumetric residence time calculations in arterial geometries. , 1996, Journal of biomechanical engineering.

[41]  D. Ku,et al.  Pulsatile velocity measurements in a model of the human abdominal aorta under resting conditions. , 1994, Journal of biomechanical engineering.

[42]  P Boesiger,et al.  Hemodynamics in the abdominal aorta: a comparison of in vitro and in vivo measurements. , 1994, Journal of applied physiology.