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Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk

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Abstract

In this paper we perform shape optimization of a pediatric pulsatile ventricular assist device (PVAD). The device simulation is carried out using fluid–structure interaction (FSI) modeling techniques within a computational framework that combines FEM for fluid mechanics and isogeometric analysis for structural mechanics modeling. The PVAD FSI simulations are performed under realistic conditions (i.e., flow speeds, pressure levels, boundary conditions, etc.), and account for the interaction of air, blood, and a thin structural membrane separating the two fluid subdomains. The shape optimization study is designed to reduce thrombotic risk, a major clinical problem in PVADs. Thrombotic risk is quantified in terms of particle residence time in the device blood chamber. Methods to compute particle residence time in the context of moving spatial domains are presented in a companion paper published in the same issue (Comput Mech, doi:10.1007/s00466-013-0931-y, 2013). The surrogate management framework, a derivative-free pattern search optimization method that relies on surrogates for increased efficiency, is employed in this work. For the optimization study shown here, particle residence time is used to define a suitable cost or objective function, while four adjustable design optimization parameters are used to define the device geometry. The FSI-based optimization framework is implemented in a parallel computing environment, and deployed with minimal user intervention. Using five SEARCH/POLL steps the optimization scheme identifies a PVAD design with significantly better throughput efficiency than the original device.

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References

  1. Abraham F, Behr M, Heinkenschloss M (2005) Shape optimization in steady blood flow: a numerical study of non-newtonian effects. Comput Methods Biomech Biomed Eng 8:127–137

    Article  Google Scholar 

  2. Abraham F, Behr M, Heinkenschloss M (2005) Shape optimization in unsteady blood flow: a numerical study of non-newtonian effects. Comput Methods Biomech Biomed Eng 8:201–212

    Article  Google Scholar 

  3. Antaki JF, Ghattas O, Burgreen GW, He B (1995) Computational flow optimization of rotary blood pump components. Artif Organs 19:608–615

    Article  Google Scholar 

  4. Audet C (2004) Convergence results for pattern search algorithms are tight. Optim Eng 5(2):101–122

    Article  MATH  MathSciNet  Google Scholar 

  5. Audet C, Dennis JE Jr (2003) Analysis of generalized pattern searches. SIAM J Optim 13(3):889–903

    Article  MATH  MathSciNet  Google Scholar 

  6. Audet C, Dennis JE Jr (2004) A pattern search filter method for nonlinear programming without derivatives. SIAM J Optim 14(4):980–1010

    Article  MATH  MathSciNet  Google Scholar 

  7. Audet C, Dennis JE Jr (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17(1):2–11

    Article  MathSciNet  Google Scholar 

  8. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MATH  MathSciNet  Google Scholar 

  9. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322

    Article  MATH  MathSciNet  Google Scholar 

  10. Bazilevs Y, Ming-Chen H, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II. Int J Numer Methods Fluids 65:236–253

    Article  MATH  Google Scholar 

  11. Bazilevs Y, Ming-Chen H, Scott MA (2012) Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41

    Article  Google Scholar 

  12. Bazilevs Y, Ming-Chen H, Takizawa K, Tezduyar TE (2012) ALE–VMS and ST–VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid–structure interaction. Math Models Methods Appl Sci 22(supp02):1230002

    Article  Google Scholar 

  13. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, New York

    Google Scholar 

  14. Benson DJ, Bazilevs Y, De Luycker E, Hsu M-C, Scott M, Hughes TJR, Belytschko T (2010) A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM. Int J Numer Math Eng 83:765–785

    MATH  Google Scholar 

  15. Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2011) A large deformation, rotation-free, isogeometric shell. Comput Methods Appl Mech Eng 200:1367–1378

    Article  MATH  MathSciNet  Google Scholar 

  16. Bluestein D, Niu L, Schoephoerster R, Dewanjee M (1997) Fluid mechanics of arterial stenosis: relationship to the development of mural thrombus. Ann Biomed Eng 25:344–356

    Article  Google Scholar 

  17. Booker AJ, Dennis JE Jr, Frank PD, Serafini DB, Torczon V, Trosset MW (1999) A rigorous framework for optimization of expensive functions by surrogates. Struct Optim 17(1):1–13

    Article  Google Scholar 

  18. Burgreen GW, Antaki JF, Wu ZJ, Holmes AJ (2001) Computational fluid dynamics as a development tool for rotary blood pumps. Artif Organs 25:336–340

    Article  Google Scholar 

  19. Clark JB, Pauliks LB, Myers JL, Undar A (2011) Mechanical circulatory support for end-stage heart failure in repaired and palliated congenital heart disease. Curr Cardiol Rev 7(2):102–109

    Article  Google Scholar 

  20. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis. Toward integration of CAD and FEA. Wiley, Chichester

    Book  Google Scholar 

  21. Davis C (1954) Theory of positive linear dependence. Am J Math 1:448–474

    Google Scholar 

  22. Esmaily-Moghadam M, Hsia TY, Marsden AL (2013) A non-discrete method for computation of residence time in fluid mechanics simulations. Phys Fluids. doi:10.1063/1.4819142

  23. Moghadam ME, Migliavacca F, Vignon-Clementel IE, Hsia TY, Marsden AL, Modeling of Congenital Hearts Alliance (MOCHA) Investigators (2012) Optimization of shunt placement for the Norwood surgery using multi-domain modeling. J Biomech Eng 134(5):051002

    Article  Google Scholar 

  24. Gandhi SK, Huddleston CB, Balzer DT, Epstein DJ, Boschert TA, Canter CE (2008) Biventricular assist devices as a bridge to heart transplantation in small children. Circulation 118(14 Suppl):S89–93

    Article  Google Scholar 

  25. Ho KK, Anderson KM, Kannel WB, Grossman W, Levy D (1993) Survival after the onset of congestive heart failure in framingham heart study subjects. Circulation 88:107115

    Article  Google Scholar 

  26. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    Article  MATH  MathSciNet  Google Scholar 

  27. Humpl T, Furness S, Gruenwald C, Hyslop C, Van G (2010) The Berlin heart EXCOR pediatrics: the sick kids experience 2004–2008. Int J Artif Organs 34(12):1082–1086

    Article  Google Scholar 

  28. Jozsa J, Kramer T (2000) Modeling residence time as advection-diffusion with zero-order reaction kinetics. In Proceedings of the Hydrodynamics 2000 Conference. International Association of Hydraulic Engineering and Research

  29. Jozsa J, Kramer T, Peltoniemi H (2001) Assessing water exchange mechanisms in complex lake and coastal flows by modeling the spatial distribution of mean residence time. In CD-ROM Proceedings of the XXIX IAHR Congress, Beijing, pp 73–79

  30. Kiendl J, Bazilevs Y, Ming-Chen H, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199:2403–2416

    Article  MATH  Google Scholar 

  31. Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914

    Article  MATH  Google Scholar 

  32. Lehnhäuser T, Shäfer M (2005) A numerical approach for shape optimization of fluid flow domains. CMAME 194:5221–5241

    MATH  Google Scholar 

  33. Lewis RM, Torczon V (1996) Rank ordering and positive bases in pattern search algorithms. Technical Report 96–71, Institute for Computer Applications in Science and Engineering, Mail Stop 132C, NASA Langley Research Center, Hampton, 23681–2199

  34. Lewis RM, Torczon V (2002) A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM J Optim 12:1075–1089

    Article  MATH  MathSciNet  Google Scholar 

  35. Lloyd-Jones D, Adams RJ, Brown TM, Carnethon M, Dai S, De Simone G, Ferguson TB, Ford E, Furie K, Gillespie C, Go A, Greenlund K, Haase N, Hailper S, Ho PM, Howard V, Kissela B, Kittner S, Lackland D, Lisabeth L, Marelli A, McDermott MM, Meigs J, Mozaffarian D, Mussolino M, Nichol G, Roger VL, Rosamond W, Sacco R, Sorlie P, Stafford R, Thom T, Wasserthiel-Smoller S, Wong ND, Wylie-Rosett J (2010) American heart association statistics committee and stroke statistics subcommittee. executive summary: heart disease and stroke statistics, (2010) update: a report from the american heart association. Circulation 121:948954

    Google Scholar 

  36. Long CC, Moghadam ME, Marsden AL, Bazilevs Y (2013) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech. doi:10.1007/s00466-013-0931-y

  37. Long CC, Marsden AL, Bazilevs Y (2013) Fluid–structure interaction simulation of pulsatile ventricular assist devices. Comput Mech 52:971–981

    Article  MATH  Google Scholar 

  38. Lophaven SN, Nielsen HB, Søndergaard J (2002) DACE: a MATLAB Kriging toolbox version 2.0. Technical Report IMM-TR-2002-12, Technical University of Denmark, Copenhagen

  39. Malaisrie SC, Pelletier MP, Yun JJ, Sharma K, Timek TA, Rosenthal DN, Wright GE, Robbins RC, Reitz BA (2008) Pneumatic paracorporeal ventricular assist device in infants and children: initial stanford experience. J Heart Lung Transplant 27(2):173–177

    Article  Google Scholar 

  40. Marsden AL, Feinstein JA, Taylor CA (2008) A computational framework for derivative-free optimization of cardiovascular geometries. Comput Meth Appl Mech Eng 197(21–24):1890–1905

    Article  MATH  MathSciNet  Google Scholar 

  41. Marsden AL, Wang M, Jr Dennis JE, Moin P (2004) Optimal aeroacoustic shape design using the surrogate management framework. Optim Eng 5(2):235–262 Special issue: surrogate optimization

    Article  MATH  MathSciNet  Google Scholar 

  42. Marsden AL, Wang M, Dennis JE Jr, Moin P (2004) Suppression of airfoil vortex-shedding noise via derivative-free optimization. Phys Fluids 16(10):L83–L86

    Article  Google Scholar 

  43. Marsden AL, Wang M, Dennis JE Jr, Moin P (2007) Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation. J Fluid Mech 572:13–36

    Article  MATH  MathSciNet  Google Scholar 

  44. Miller LW (2011) Left ventricular assist devices are underutilized. Circulation 123:15528

    Google Scholar 

  45. Narracott A, Smith S, Lawford P, Liu H, Himeno R, Wilkinson I, Griffiths P, Hose R (2005) Development and validation of models for the investigation of blood clotting in idealized stenoses and cerebral aneurysms. Int J Artif Organs 8:56–62

    Article  Google Scholar 

  46. Ortega JM, Hartman J, Rodriguez JN, Maitland DJ (2013) Virtual treatment of basilar aneurysms using shape memory polymer foam. Ann Biomed Eng 41:725–743

    Article  Google Scholar 

  47. Rayz V, Boussel L, Ge L, Leach J, Martin A, Lawton M, McCulloch C, Saloner D (2010) Flow residence time and regions of intraluminal thrombus deposition in intracranial aneurysms. Ann Biomed Eng 38:3058–3069

    Article  Google Scholar 

  48. Reininger A, Reininger C, Heinzmann U, Wurzinger L (1995) Residence time in niches of stagnant flow determines fibrin clot formation in arterial branching model-detailed flow analysis and experimental results. Thromb Haemost 74:916–922

    Google Scholar 

  49. Rockett SR, Bryant JC, Morrow WR, Frazier EA, Fiser WP, McKamie WA, Johnson CE, Chipman CW, Imamura M, Jaquiss RD (2008) Preliminary single center north american experience with the berlin heart pediatric excor device. ASAIO J 54(5):479–482

    Google Scholar 

  50. Serafini DB (1998) A framework for managing models in nonlinear optimization of computationally expensive functions. PhD thesis, Rice University, Houston

  51. Simpson TW, Korte JJ, Mauery TM, Mistree F (1998) Comparison of response surface and kriging models for multidisciplinary design optimization. AIAA Paper 98–4755

  52. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE–VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19:171–225

    Article  MathSciNet  Google Scholar 

  53. Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space-time finite element computation of arterial fluid–structure interactions with patient-specific data. Int J Numer Methods Biomed Eng 26:101–116

    Article  MATH  Google Scholar 

  54. Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012) Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854

    Article  MATH  Google Scholar 

  55. Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338

    Article  MATH  MathSciNet  Google Scholar 

  56. Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid–structure interaction modeling of cerebral aneurysms. Int J Numer Meth Fluids 65:308–323

    Article  MATH  Google Scholar 

  57. Takizawa K, Takagi H, Tezduyar TE, Torii R (2013) Estimation of element-based zero-stress state for arterial FSI computations. Comput Mech. doi:10.1007/s00466-013-0919-7

  58. Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid–structure interaction techniques. Comput Mech 48:247–267

    Article  MATH  MathSciNet  Google Scholar 

  59. Takizawa K, Tezduyar TE (2012) Space-time fluid–structure interaction methods. Math Models Methods Appl Sci 22(supp02):1230001

    Article  MathSciNet  Google Scholar 

  60. Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013) Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech. doi:10.1007/s00466-013-0880-5

  61. Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900

    Article  MATH  MathSciNet  Google Scholar 

  62. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech 43:39–49

    Article  MATH  Google Scholar 

  63. Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198:3524–3533

    Article  MATH  MathSciNet  Google Scholar 

  64. Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space-time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:1665–1710

    Article  MATH  MathSciNet  Google Scholar 

  65. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46:17–29

    Article  MATH  MathSciNet  Google Scholar 

  66. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space-time finite element computation of complex fluid–structure interactions. Int J Numer Methods Fluids 64:1201–1218

    Article  MATH  Google Scholar 

  67. Torczon V (1997) On the convergence of pattern search algorithms. SIAM J Optim 7:1–25

    Article  MATH  MathSciNet  Google Scholar 

  68. Yang W, Feinstein JA, Marsden AL (2010) Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise. Comput Methods Appl Mech Eng 199:2135–2149

    Article  MATH  Google Scholar 

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Acknowledgments

The support of the AFOSR Award No. FA9550-12-1-0005 and a Burroughs Wellcome Fund Career Award at the Scientific Interface is gratefully acknowledged. We also thank Oak Ridge National Laboratory (ORNL) and the University of Tennessee for providing the HPC resources that have contributed to the research results reported in this paper.

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Authors and Affiliations

  1. T-3 Fluid Dynamics and Solid Mechanics, Los Alamos National Laboratory, Los Alamos, NM, 87545-1663, USA

    C. C. Long

  2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0411, La Jolla, CA, 92093-0411, USA

    A. L. Marsden

  3. Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA, 92093-0085, USA

    Y. Bazilevs

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Long, C.C., Marsden, A.L. & Bazilevs, Y. Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech 54, 921–932 (2014). https://doi.org/10.1007/s00466-013-0967-z

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