Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise

Quarteroni, 2003, Optimal control and shape optimization in aorto-coronaric bypass anastomoses, Math. Models Methods Appl. Sci., 13, 1801, 10.1142/S0218202503003124 Abraham, 2005, Shape optimization in steady blood flow: a numerical study of non-newtonian effects, Comput. Methods Biomech. Biomed. Eng., 8, 127, 10.1080/10255840500180799 Probst, 2010, Sensitivity of optimal shapes of artificial grafts with respect to flow parameters, Comput. Methods Appl. Mech. Engrg., 199, 997, 10.1016/j.cma.2009.11.013 Marsden, 2008, A computational framework for derivative-free optimization of cardiovascular geometries, Comput. Methods Appl. Mech. Engrg., 197, 1890, 10.1016/j.cma.2007.12.009 Booker, 1999, A rigorous framework for optimization of expensive functions by surrogates, Struct. Optim., 17, 1, 10.1007/BF01197708 D.B. Serafini. A Framework for Managing Models in Nonlinear Optimization of Computationally Expensive Functions. PhD thesis, Rice University, Houston, TX, 1998. Audet, 2006, Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim., 17, 2, 10.1137/040603371 Marsden, 2004, Optimal aeroacoustic shape design using the surrogate management framework, SIAM J. Optim., 5, 235 Marsden, 2004, Suppression of airfoil vortex-shedding noise via derivative-free optimization, Phys. Fluids, 16, L83, 10.1063/1.1786551 Marsden, 2007, Large differences in efficiency among Fontan patients demonstrated in patient specific models of blood flow simulations, Circ. Suppl. II, 116 Fletcher, 2002, Nonlinear programming without a penalty function, Math. Program., 91, 239, 10.1007/s101070100244 Marino, 2002, Outcomes after the Fontan procedure, Curr. Opin. Pediatr., 14, 620, 10.1097/00008480-200210000-00010 Reddy, 1997, Extracardiac conduit total cavopulmonary anastomosis, Oper. Techniques Cardiac Thorac. Surg., 2, 221, 10.1016/S1085-5637(07)70061-X Walker, 2000, Distribution of hepatic venous blood in the total cavopulmonary connection: an in vitro study, Eur. J. Cardiothorac. Surg., 17, 658, 10.1016/S1010-7940(00)00425-5 Whitehead, 2007, Nonlinear power loss during exercise in single-ventricle patients after the Fontan: insights from computational fluid dynamics, Circulation, 116, I-165, 10.1161/CIRCULATIONAHA.106.680827 Marsden, 2010, A new multi-parameter approach to computational simulation for fontan assessment and redesign, Congenital Heart disease, 5, 104, 10.1111/j.1747-0803.2010.00383.x Dubini, 1996, A numerical fluid mechanical study of repaired congenital heart defects: application to the total cavopulmonary connection, J. Biomech., 29, 111, 10.1016/0021-9290(95)00021-6 Migliavacca, 2003, Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis, J. Biomech. Eng., 125, 805, 10.1115/1.1632523 Katajima, 2008, Functional analysis of fontan energy dissipation, J. Biomech., 4, 2246 Marsden, 2007, Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection, Ann. Biomed. Eng., 35, 250, 10.1007/s10439-006-9224-3 Marsden, 2009, Evaluation of a novel Y-shaped extracardiac Fontan baffle using computational fluid dynamics, J. Thocac. Cardio. Surg., 137, 394, 10.1016/j.jtcvs.2008.06.043 Ensley, 2000, Toward designing the optimal total cavopulmonary connection: an in vitro study, Ann. Thorac. Surg., 68, 1384, 10.1016/S0003-4975(99)00560-3 Okano, 2002, Extracardiac total cavopulmonary connection using a y-shaped graft, Ann. Thorac. Surg., 74, 2195, 10.1016/S0003-4975(02)03978-4 Soerensen, 2007, Introduction of a new optimized total cavopulmonary connection, Ann. Thorac. Surg., 83, 2182, 10.1016/j.athoracsur.2006.12.079 Fontan, 1971, Surgical repair of tricuspid atresia, Thorax, 26, 240, 10.1136/thx.26.3.240 Wilson, 2001, A software framework for creating patient specific geometric models from medical imaging data for simulation based medical planning of vascular surgery, Lect. Notes Comput. Sc., 2208, 449, 10.1007/3-540-45468-3_54 Schmidt, 2008, The simbios national center: systems biology in motion, 1266 Taylor, 1998, Finite element modeling of blood flow in arteries, Comput. Method. Appl. Mech. Engrg., 158, 155, 10.1016/S0045-7825(98)80008-X Whiting, 2001, A stabilized finite element method for the incompressible Navier-Stokes equations using a hierarchical basis, Int. J. Numer. Methods Fluids, 35, 93, 10.1002/1097-0363(20010115)35:1<93::AID-FLD85>3.0.CO;2-G Brooks, 1981, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-stokes equations, Comput. Meth. Appl. Mech. Engrg., 32, 199, 10.1016/0045-7825(82)90071-8 Jansen, 2000, A generalized-α method for integrating the filtered navierstokes equations with a stabilized finite element method, Comput. Meth. Appl. Mech. Engrg., 190, 305, 10.1016/S0045-7825(00)00203-6 Vignon-Clementel, 2006, Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries, Comput. Meth. Appl. Mech. Engrg., 195, 3776, 10.1016/j.cma.2005.04.014 Figueroa, 2006, A coupled momentum method for modeling blood flow in three-dimensional deformable arteries, Comput. Meth. Appl. Mech. Engrg., 195, 5685, 10.1016/j.cma.2005.11.011 Ku, 2002, In vivo validation of numerical predictions of blood flow in arterial bypass grafts, Ann. Biomed. Eng., 30, 743, 10.1114/1.1496086 Ku, 2005, Comparison of CFD and MRI flow and velocities in an in vitro large artery bypass graft model, Ann. Biomed. Eng., 33, 257, 10.1007/s10439-005-1729-7 Hjortdal, 2003, Effects of exercise and respiration on blood flow in total cavopulmonary connection: A real-time magnetic resonance flow study, Circulation, 108, 1227, 10.1161/01.CIR.0000087406.27922.6B Kulik, 1983, Exercise induced pulmonary vasoconstriction, Brit. Heart J., 50, 59, 10.1136/hrt.50.1.59 Shephard, 1991, Automatic three-dimensional mesh generation by the finite octree technique, Int. J Numer. Meth. Eng., 32, 709, 10.1002/nme.1620320406 Isaaks, 1989 Lophaven, 2002 Beal, 2007, Optimal sensor placement for enhancing sensitivity to change in stiffness for structural health monitoring, Optim. Eng., 9, 119, 10.1007/s11081-007-9023-1 Zhao, 2006, Using pattern search methods for surface structure determination of nanomaterials, J. Phys.: Condens. Matter, 18, 8693 Torczon, 1997, On the convergence of pattern search algorithms, SIAM J. Optim., 7, 1, 10.1137/S1052623493250780 Audet, 2003, Analysis of generalized pattern searches, SIAM J.Optim., 13, 889, 10.1137/S1052623400378742 Audet, 2004, A pattern search filter method for nonlinear programming without derivatives, SIAM J.Optim., 14, 980, 10.1137/S105262340138983X Abramson, 2009, Orthomads: a deterministic mads instance with orthogonal directions, SIAM J. Optim., 20, 948, 10.1137/080716980 Marsden, 2007, Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation, J. Fluid Mech., 572, 13, 10.1017/S0022112006003235 Giardini, 2008, Natural history of exercise capacity after the Fontan operation: a longitudinal study, Ann. Thorac. Surg., 85, 818, 10.1016/j.athoracsur.2007.11.009 Hsia, 2004, Computational fluid dynamic study of flow optimization in realistic models of the total cavopulmonary connections, J. Surg. Res., 116, 305, 10.1016/j.jss.2003.08.004 Rosenthal, 1995, Thromboembolic complications after Fontan operations, Circulation, 92, 287, 10.1161/01.CIR.92.9.287 Coon, 2001, Thrombus formation after the Fontan operation, Ann. Thorac. Surg., 71, 1990, 10.1016/S0003-4975(01)02472-9 Chowdhury, 2005, Specific issues after extracardiac Fontan operation: ventricular function, growth potential, arrhythmia, and thromboembolism, Ann. Thorac. Surg., 80, 665, 10.1016/j.athoracsur.2005.02.024 Alexi-Meskishvili, 2000, Optimal conduit size for extracardiac Fontan operation, Eur. J. Cardiothorac. Surg., 18, 690, 10.1016/S1010-7940(00)00593-5 Grabowski, 1995, Thrombolysis, flow and vessel wall interactions, J. Vasc. Interv. Radiol., 6, 25s, 10.1016/S1051-0443(95)71245-3 Loscalzo, 2003 Lopez, 2009, Pathophysiology of venous thrombosis, Thromb. Res., 123, S30, 10.1016/S0049-3848(09)70140-9 Wessler, 1962, Thrombosis in the presence of vascular stasis, Am. J. Med., 33, 648, 10.1016/0002-9343(62)90244-9 Walker, 2005, Prophylactic anticoagulation following the fontan operation, Heart, 91, 854, 10.1136/hrt.2004.039073 Ikeda, 1991, The role of von willebrand factor and fibrinogen in platelet aggregation under varying shear stress, J. Clin. Invest., 87, 1234, 10.1172/JCI115124 Gijsen, 1999, The influence of the non-newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model, J. Biomechanics, 32, 601, 10.1016/S0021-9290(99)00015-9 Gijsen, 1999, The influence of the non-newtonian properties of blood on the fow in large arteries: unsteady flow in a 903 curved tube, J. Biomechanics, 32, 705, 10.1016/S0021-9290(99)00014-7 Sankaran, 2009, Stochastic optimization using a sparse grid collocation scheme, Probab. Eng. Mech., 24, 382, 10.1016/j.probengmech.2008.11.002 Sankaran, 2010, A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation, J. Comput. Phys., 229, 4664, 10.1016/j.jcp.2010.03.005