No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow
4.M. Sankaranarayanan, D. N. Ghista, C. L. Poh, T. Y. Seng, and G. S. Kassab, “Analysis of blood flow in an out-of-plane CABG model,” Am. J. Physiol. Heart Circ. Physiol. 291, H283 (2006).
5.K. Perktold, A. Leuprecht, M. Prosi, T. Berk, M. Czerny, W. Trubel, and H. Schima, “Fluid dynamics, wall mechanics, and oxygen transfer in peripheral bypass anastomoses,” Ann. Biomed. Eng. 30, 447 (2002).
6.A. Leuprecht, K. Perktold, M. Prosi, T. Berk, M. Czerny, W. Trubel, and H. Schima, “Numerical study of hemodynamics and wall mechanics in distal end-to-side anastomoses of bypass grafts,” J. Biomech. 35, 225 (2002).
7.F. Loth, S. A. Jones, C. K. Zarins, D. P. Giddens, R. F. Nassar, S. Glagov, and H. S. Bassiouny, “Relative contribution of wall shear stress and injury in experimental intimal thickening at PTFE end-to-side arterial anastomoses,” J. Biomech. Eng. 124, 44 (2002).
8.H. S. Bassiouny, S. White, S. Glagov, E. Choi, D. P. Giddens, and C. K. Zarins, “Anastomotic intimal hyperplasia: Mechanical injury or flow induced,” J. Vasc. Surg. 10, 326 (1989).
9.T. R. Kohler, T. R. Kirkman, L. W. Kraiss, B. K. Zierler, and A. W. Clowes, “Increased blood flow inhibits neointimal hyperplasia in endothelialized vascular grafts,” Circ. Res. 69, 1557 (1991).
11.C. K. Zarins, M. A. Zatina, D. P. Giddens, D. N. Ku, and S. Glagov, “Shear stress regulation of artery lumen diameter in experimental atherogenesis,” J. Vasc. Surg. 5, 413 (1987).
12.D. P. Giddens, C. K. Zarins, and S. Glagov, “The role of fluid mechanics in localization and detection of atherosclerosis,” J. Biomech. Eng. 115, 588 (1993).
13.J. A. Moore, D. A. Steinman, S. Prakash, K. W. Johnson, and C. R. Ethier, “A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses,” J. Biomech. Eng. 121, 265 (1999).
14.F. Inzoli, F. Migliavacca, and G. Pennati, “Numerical analysis of steady flow in aorto-coronary bypass 3-D model,” J. Biomech. Eng. 118, 172 (1996).
16.Y. Bazilevs, M. -C. Hsu, Y. Zhang, W. Wang, X. Liang, T. Kvamsdal, R. Brekken, and J. G. Isaksen, “A fully-coupled fluid-structure interaction simulation of cerebral aneurysms,” Comput. Mech. 46, 3 (2010).
17.I. E. Vignon-Clementel, C. A. Figueroa, K. E. Jansen, and C. A. Taylor, “Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries,” Comput. Methods Appl. Mech. Eng. 195, 3776 (2006).
18.F. Migliavacca, R. Balossino, G. Pennati, G. Dubini, T. -Y. Hsia, M. R. de Leval, and E. L. Bove, “Multiscale modelling in biofluidynamics: Application to reconstructive paediatric cardiac surgery,” J. Biomech. 39, 1010 (2006).
19.A. L. Marsden, I. E. Vignon-Clementel, F. P. Chan, J. A. Feinstein, and C. A. Taylor, “Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection,” Ann. Biomed. Eng. 35, 250 (2007).
20.A. L. Marsden, A. J. Bernstein, R. L. Spilker, F. P. Chan, C. A. Taylor, and J. A. Feinstein, “Large differences in efficiency among Fontan patients demonstrated in patient specific models of blood flow simulations,” Circulation 116, 480 (2007).
21.A. S. Les, S. C. Shadden, C. A. Figueroa, J. M. Park, M. M. Tedesco, R. J. Herfkens, R. L. Dalman, and C. A. Taylor, “Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics,” Ann. Biomed. Eng. 38, 1288 (2010).
22.M. Probst, M. Lulfesmann, M. Nicolai, H. M. Bucker, M. Behr, and C. H. Bischof, “Sensitivity of optimal shapes of artificial grafts with respect to flow parameters,” Comput. Methods Appl. Mech. Eng. 199, 997 (2010).
23.A. L. Marsden, M. Wang, J. E. Dennis, Jr., and P. Moin, “Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation,” J. Fluid Mech. 572, 13 (2007).
25.A. L. Marsden, M. Wang, J. E. Dennis, Jr., and P. Moin, “Suppression of vortex-shedding noise via derivative-free shape optimization,” Phys. Fluids 16, L83 (2004).
26.A. L. Marsden, J. A. Feinstein, and C. A. Taylor, “A computational framework for derivative-free optimization of cardiovascular geometries,” Comput. Methods Appl. Mech. Eng. 197, 1890 (2008).
27.W. Yang, J. A. Feinstein, and A. L. Marsden, “Constrained optimization of an idealized y-shaped baffle for the Fontan surgery at rest and exercise,” Comput. Methods Appl. Mech. Eng. 199, 2135 (2010).
28.A. J. Booker, J. E. Dennis, Jr., P. D. Frank, D. B. Serafini, V. Torczon, and M. W. Trosset, “A rigorous framework for optimization of expensive functions by surrogates,” Struct. Optim. 17, 1 (1999).
29.C. Audet and J. E. Dennis, Jr., “Mesh adaptive direct search algorithms for constrained optimization,” SIAM J. Optim. 17, 188 (2006).
31.N. Zabaras and B. Ganapathysubramanian, “A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach,” J. Comput. Phys. 227, 4697 (2008).
32.P. G. Constantine, M. S. Eldred, and C. G. Webster, “Design under uncertainty employing stochastic expansion methods,” AIAA Paper No. 2008-6001, 2008.
34.P. Koumoutsakos, D. Buche, and N. N. Schraudolph, “Accelerating evolutionary algorithms with Gaussian process fitness function models,” IEEE Trans. Syst. Man Cybern., Part C Appl. Rev. 35, 183 (2005).
35.S. Sankaran, C. Audet, and A. L. Marsden, “A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation,” J. Comput. Phys. 229, 4664 (2010).
36.D. Xiu and J. S. Hesthaven, “High order collocation methods for the differential equation with random inputs,” J. Sci. Comput. 27, 1118 (2005).
37.I. Babuška, F. Nobile, and R. Tempone, “A stochastic collocation method for elliptic partial differential equations with random input data,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 45, 1005 (2007).
38.S. Sankaran and A. L. Marsden, “A stochastic collocation method for uncertainty quantification in cardiovascular simulations,” J. Biomech. Eng. (in press).
39.A. Jameson, L. Martinelli, and N. A. Pierce, “Optimum aerodynamic design using the Navier Stokes equations,” Theor. Comput. Fluid Dyn. 10, 213 (1998).
42.A. Klimke, “Uncertainty modeling using fuzzy arithmetic and sparse grids,” Ph.D. thesis, Universität Stuttgart, 2006.
44.G. Iaccarino and P. Constantine, “Large eddy simulations of flow around a cylinder with uncertain wall heating,” 47th AIAA Aerospace Sciences Meeting, Orlando, Florida;
44.AIAA Paper No. 2009-975, 2009.
45.N. Zabaras and X. Ma, “An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations,” J. Comput. Phys. 228, 3084 (2009).
46.A. Klimke, “Sparse grid interpolation toolbox users guide,” IANS Report No. 2006/001, University of Stuttgart, 2006.
47.J. P. Schmidt, S. L. Delp, M. A. Sherman, C. A. Taylor, V. S. Pande, and R. B. Altman, “The Simbios National Center: Systems biology in motion,” in Computational System Biology, special issue of Proc. IEEE 96, 1266 (2008).
49.K. E. Jansen, C. H. Whiting, and G. M. Hulbert, “A generalized-alpha method for integrating the filtered Navier Stokes equations with a stabilized finite element method,” Comput. Methods Appl. Mech. Eng. 190, 305 (2000).
50.J. P. Ku, M. R. Draney, F. R. Arko, W. A. Lee, F. Chan, N. J. Pelc, C. K. Zarins, and C. A. Taylor, “In vivo validation of numerical predictions of blood flow in arterial bypass grafts,” Ann. Biomed. Eng. 30, 743 (2002).
51.M. Lei, J. P. Archie, and C. Kleinstreuer, “Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis,” J. Vasc. Surg. 25, 637 (1997).
53.L. Badimon and J. J. Badimon, “Changes in vascular geometry in atherosclerotic plaque rupture and its relationship to thrombosis in acute vascular events,” Advanced Cardiovascular Engineering (Plenum, New York, 1992), pp. 175–187.
54.Y. Bazilevs, M. -C. Hsu, D. J. Benson, S. Sankaran, and A. L. Marsden, “Computational fluid structure interaction: Methods and application to a total cavopulmonary connection,” Comput. Mech. 45, 77 (2009).
55.C. Audet and J. E. Dennis, Jr., “A progressive barrier approach to derivative-free nonlinear programming,” SIAM J. Optim. 20, 445 (2009).
Article metrics loading...
It is well known that the fluid mechanics of bypass grafts impacts biomechanical responses and is linked to intimal thickening and plaque deposition on the vessel wall. In spite of this, quantitative information about the fluid mechanics is not currently incorporated into surgical planning and bypass graft design. In this work, we use a derivative-free optimization technique for performing systematic design of bypass grafts. The optimization method is coupled to a three-dimensional pulsatile Navier–Stokes solver. We systematically account for inevitable uncertainties that arise in cardiovascular simulations, owing to noise in medical image data, variable physiologic conditions, and surgical implementation. Uncertainties in the simulation input parameters as well as shape design variables are accounted for using the adaptive stochastic collocation technique. The derivative-free optimization framework is coupled with a stochastic response surface technique to make the problem computationally tractable. Two idealized numerical examples, an end-to-side anastomosis, and a bypass graft around a stenosis, demonstrate that accounting for uncertainty significantly changes the optimal graft design. Results show that small changes in the design variables from their optimal values should be accounted for in surgical planning. Changes in the downstream (distal) graft angle resulted in greater sensitivity of the wall-shear stress compared to changes in the upstream (proximal) angle. The impact of cost function choice on the optimal solution was explored. Additionally, this work represents the first use of the stochastic surrogate management framework method for robust shape optimization in a fully three-dimensional unsteady Navier–Stokes design problem.
Full text loading...
Most read this month