1887
banner image
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.
f
The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow
Rent:
Rent this article for
Access full text Article
/content/aip/journal/pof2/22/12/10.1063/1.3529444
1.
1.A. J. Bryan and G. D. Angelini, “The biology of saphenous vein graft occlusion: Etiology and strategies for prevention,” Curr. Opin. Cardiol. 9, 641 (1994).
http://dx.doi.org/10.1097/00001573-199411000-00002
2.
2.S. D. Nikkari and A. W. Clowes, “Restenosis after vascular reconstruction,” Ann. Med. 26, 95 (1994).
http://dx.doi.org/10.3109/07853899409147335
3.
3.D. Mehta, M. B. Izzat, A. J. Bryan, and G. D. Angelini, “Towards the prevention of vein graft failure,” Int. J. Cardiol. 62, S55 (1997).
http://dx.doi.org/10.1016/S0167-5273(97)00214-3
4.
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).
http://dx.doi.org/10.1152/ajpheart.01347.2005
5.
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).
http://dx.doi.org/10.1114/1.1477445
6.
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).
http://dx.doi.org/10.1016/S0021-9290(01)00194-4
7.
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).
http://dx.doi.org/10.1115/1.1428554
8.
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).
http://dx.doi.org/10.1067/mva.1989.13652
9.
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).
10.
10.D. N. Ku, “Blood flow in arteries,” Annu. Rev. Fluid Mech. 29, 399 (1997).
http://dx.doi.org/10.1146/annurev.fluid.29.1.399
11.
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).
http://dx.doi.org/10.1067/mva.1987.avs0050413
12.
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).
http://dx.doi.org/10.1115/1.2895545
13.
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).
http://dx.doi.org/10.1115/1.2798319
14.
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).
http://dx.doi.org/10.1115/1.2795956
15.
15.F. Loth, P. F. Fischer, and H. S. Bassiouny, “Blood flow in end-to-side anastomosis,” Annu. Rev. Fluid Mech. 40, 367 (2008).
http://dx.doi.org/10.1146/annurev.fluid.40.111406.102119
16.
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).
http://dx.doi.org/10.1007/s00466-009-0421-4
17.
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).
http://dx.doi.org/10.1016/j.cma.2005.04.014
18.
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).
http://dx.doi.org/10.1016/j.jbiomech.2005.02.021
19.
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).
http://dx.doi.org/10.1007/s10439-006-9224-3
20.
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).
http://dx.doi.org/10.1161/CIRCULATIONAHA.107.689935
21.
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).
http://dx.doi.org/10.1007/s10439-010-9949-x
22.
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).
http://dx.doi.org/10.1016/j.cma.2009.11.013
23.
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).
http://dx.doi.org/10.1017/S0022112006003235
24.
24.A. L. Marsden, M. Wang, J. E. Dennis, Jr., and P. Moin, “Optimal aeroacoustic shape design using the surrogate management framework,” Optim. Eng. 5, 235 (2004).
http://dx.doi.org/10.1023/B:OPTE.0000033376.89159.65
25.
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).
http://dx.doi.org/10.1063/1.1786551
26.
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).
http://dx.doi.org/10.1016/j.cma.2007.12.009
27.
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).
http://dx.doi.org/10.1016/j.cma.2010.03.012
28.
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).
http://dx.doi.org/10.1007/BF01197708
29.
29.C. Audet and J. E. Dennis, Jr., “Mesh adaptive direct search algorithms for constrained optimization,” SIAM J. Optim. 17, 188 (2006).
http://dx.doi.org/10.1137/040603371
30.
30.S. Sankaran, “Stochastic optimization using a sparse grid collocation scheme,” Probab. Eng. Mech. 24, 382 (2009).
http://dx.doi.org/10.1016/j.probengmech.2008.11.002
31.
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).
http://dx.doi.org/10.1016/j.jcp.2008.01.019
32.
32.P. G. Constantine, M. S. Eldred, and C. G. Webster, “Design under uncertainty employing stochastic expansion methods,” AIAA Paper No. 2008-6001, 2008.
33.
33.B. Faverjon and R. Ghanem, “Stochastic inversion in acoustic scattering,” J. Acoust. Soc. Am. 119, 3577 (2006).
http://dx.doi.org/10.1121/1.2200149
34.
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).
http://dx.doi.org/10.1109/TSMCC.2004.841917
35.
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).
http://dx.doi.org/10.1016/j.jcp.2010.03.005
36.
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.
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).
http://dx.doi.org/10.1137/050645142
38.
38.S. Sankaran and A. L. Marsden, “A stochastic collocation method for uncertainty quantification in cardiovascular simulations,” J. Biomech. Eng. (in press).
39.
39.A. Jameson, L. Martinelli, and N. A. Pierce, “Optimum aerodynamic design using the Navier Stokes equations,” Theor. Comput. Fluid Dyn. 10, 213 (1998).
http://dx.doi.org/10.1007/s001620050060
40.
40.N. V. Queipo, R. T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan, and P. Kevin Tucker, “Surrogate-based analysis and optimization,” Prog. Aerosp. Sci. 41, 1 (2005).
http://dx.doi.org/10.1016/j.paerosci.2005.02.001
41.
41.T. Gerstner and M. Griebel, “Numerical integration using sparse grids,” Numer. Algorithms 18, 209 (1998).
http://dx.doi.org/10.1023/A:1019129717644
42.
42.A. Klimke, “Uncertainty modeling using fuzzy arithmetic and sparse grids,” Ph.D. thesis, Universität Stuttgart, 2006.
43.
43.H. N. Najm, “Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics,” Annu. Rev. Fluid Mech. 41, 35 (2009).
http://dx.doi.org/10.1146/annurev.fluid.010908.165248
44.
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.
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).
http://dx.doi.org/10.1016/j.jcp.2009.01.006
46.
46.A. Klimke, “Sparse grid interpolation toolbox users guide,” IANS Report No. 2006/001, University of Stuttgart, 2006.
47.
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).
http://dx.doi.org/10.1109/JPROC.2008.925454
48.
48.C. A. Taylor, T. J. R. Hughes, and C. K. Zarins, “Finite element modeling of blood flow in arteries,” Comput. Methods Appl. Mech. Eng. 158, 155 (1998).
http://dx.doi.org/10.1016/S0045-7825(98)80008-X
49.
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).
http://dx.doi.org/10.1016/S0045-7825(00)00203-6
50.
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).
http://dx.doi.org/10.1114/1.1496086
51.
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).
http://dx.doi.org/10.1016/S0741-5214(97)70289-1
52.
52.S. Sankaran and N. Zabaras, “A maximum entropy approach for property prediction of random microstructures,” Acta Mater. 54, 2265 (2006).
http://dx.doi.org/10.1016/j.actamat.2006.01.015
53.
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. 175187.
54.
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).
http://dx.doi.org/10.1007/s00466-009-0419-y
55.
55.C. Audet and J. E. Dennis, Jr., “A progressive barrier approach to derivative-free nonlinear programming,” SIAM J. Optim. 20, 445 (2009).
http://dx.doi.org/10.1137/070692662
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/12/10.1063/1.3529444
Loading
/content/aip/journal/pof2/22/12/10.1063/1.3529444
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/pof2/22/12/10.1063/1.3529444
2010-12-22
2014-07-28

Abstract

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.

Loading

Full text loading...

/deliver/fulltext/aip/journal/pof2/22/12/1.3529444.html;jsessionid=749245eifp3gs.x-aip-live-03?itemId=/content/aip/journal/pof2/22/12/10.1063/1.3529444&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/pof2
true
true
This is a required field
Please enter a valid email address
This feature is disabled while Scitation upgrades its access control system.
This feature is disabled while Scitation upgrades its access control system.
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/12/10.1063/1.3529444
10.1063/1.3529444
SEARCH_EXPAND_ITEM