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Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. (English) Zbl 1398.92056

Summary: The Fontan procedure is a surgery that is performed on single-ventricle heart patients, and, due to the wide range of anatomies and variations among patients, lends itself nicely to study by advanced numerical methods. We focus on a patient-specific Fontan configuration, and perform a fully coupled fluid-structure interaction (FSI) analysis of hemodynamics and vessel wall motion. To enable physiologically realistic simulations, a simple approach to constructing a variable-thickness blood vessel wall description is proposed. Rest and exercise conditions are simulated and rigid versus flexible vessel wall simulation results are compared. We conclude that flexible wall modeling plays an important role in predicting quantities of hemodynamic interest in the Fontan connection. To the best of our knowledge, this paper presents the first three-dimensional patient-specific fully coupled FSI analysis of a total cavopulmonary connection that also includes large portions of the pulmonary circulation.

MSC:

92C35 Physiological flow
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Z05 Physiological flows
76M10 Finite element methods applied to problems in fluid mechanics
74L15 Biomechanical solid mechanics
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[1] Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: 173–201 · Zbl 1169.76352 · doi:10.1016/j.cma.2007.07.016
[2] Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37 · Zbl 1169.74015 · doi:10.1007/s00466-008-0315-x
[3] 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 · Zbl 1161.74020 · doi:10.1007/s00466-006-0084-3
[4] Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng. doi: 10.1016/j.cma.2009.04.015 · Zbl 1229.74096
[5] Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen JG (2009) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech, In the same issue · Zbl 1301.92014
[6] Bischoff M, Wall WA, Bletzinger K-U, Ramm E (2004) Models and finite elements for thin-walled structures. In: Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, vol 2, Solids, structures and coupled problems, chap 3. Wiley
[7] Bove EL, de Leval MR, Migliavacca F, Guadagni G, Dubini G (2003) Computational fluid dynamics in the evaluation of hemodynamic performance of cavopulmonary connections after the Norwood procedure for hypoplastic left heart syndrome. J Thorac Cardiovasc Surg 126: 1040–1047 · doi:10.1016/S0022-5223(03)00698-6
[8] Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-{\(\alpha\)} method. J Appl Mech 60: 371–375 · Zbl 0775.73337 · doi:10.1115/1.2900803
[9] de Leval MR, Dubini G, Migliavacca F, Jalali H, camporini G, Redington A, Pietrabissa R (1996) Use of computational fluid dynamics in the design of surgical procedures: application to the study of competitive flows in cavo-pulmonary connections. J Thorac Cardiovasc Surg 111(3): 502–513 · doi:10.1016/S0022-5223(96)70302-1
[10] Dubini G, de Leval MR, Pietrabissa R, Montevecchi FM, Fumero R (1996) A numerical fluid mechanical study of repaired congenital heart defects: application to the total cavopulmonary connection. J Biomech 29(1): 111–121 · doi:10.1016/0021-9290(95)00021-6
[11] Ensley AE, Ramuzat A, Healy TM, Chatzimavroudis GP, Lucas C, Sharma S, Pettigrew R, Yoganathan AP (2000) Fluid mechanic assessment of the total cavopulmonary connection using magnetic resonance phase velocity mapping and digital particle image velocimetry. Ann Biomed Eng 28: 1172–1183 · doi:10.1114/1.1317533
[12] Farhat C, Geuzaine P, Grandmont C (2001) The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. J Comput Phys 174(2): 669–694 · Zbl 1157.76372 · doi:10.1006/jcph.2001.6932
[13] Fontan F, Baudet E (1971) Surgical repair of tricuspid atresia. Thorax 26: 240–248 · doi:10.1136/thx.26.3.240
[14] Giardini A, Balducci A, Specchia S, Gaetano G, Bonvicini M, Picchio FM (2008) Effect of sildenafil on haemodynamic response to exercise capacity in fontan patients. Eur Heart J 29: 1681–1687 · doi:10.1093/eurheartj/ehn215
[15] Hjortdal VE, Emmertsen K, Stenbog E, Frund T, Rahbek Schmidt M, Kromann O, Sorensen K, Pedersen EM (2003) Effects of exercise and respiration on blood flow in total cavopulmonary connection: a real-time magnetic resonance flow study. Circulation 108: 1227–1231 · doi:10.1161/01.CIR.0000087406.27922.6B
[16] Holzapfel GA (2000) Nonlinear solid mechanics, a continuum approach for engineering. Wiley, Chichester · Zbl 0980.74001
[17] Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications, Mineola
[18] Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian- Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29: 329–349 · Zbl 0482.76039 · doi:10.1016/0045-7825(81)90049-9
[19] Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39: 3172–3178 · doi:10.1161/STROKEAHA.107.503698
[20] Jansen KE, Whiting CH, Hulbert GM (1999) A generalized-{\(\alpha\)} method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: 305–319 · Zbl 0973.76048 · doi:10.1016/S0045-7825(00)00203-6
[21] Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119: 73–94 · Zbl 0848.76036 · doi:10.1016/0045-7825(94)00077-8
[22] Khunatorn Y, Mahalingam S, DeGroff CG, Shandas R (2002) Influence of connection geometry and SVC-IVC flow rate ratio on flow structures within the total cavopulmonary connection: a numerical study. J Biomech Eng Trans ASME 124: 364–377 · doi:10.1115/1.1487880
[23] Kulik TJ, Bass JL, Fuhrman BP, Moller JH, Lock JE (1983) Exercise induced pulmonary vasoconstriction. Br Heart J 50: 59–64 · doi:10.1136/hrt.50.1.59
[24] Marsden AL, Vignon-Clementel IE, Chan F, Feinstein JA, Taylor CA (2007) Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection. Ann Biomed Eng 35(2): 250–263 · doi:10.1007/s10439-006-9224-3
[25] Marsden AL, Bernstein AD, Reddy VM, Shadden S, Spilker R, Chan FP, Taylor CA, Feinstein JA (2009) Evaluation of a novel Y-shaped extracardiac fontan baffle using computational fluid dynamics. J Thorac Cardiovasc Surg, To appear
[26] Marsden AL, Vignon-Clementel IE, Chan F, Feinstein JA, Taylor CA (2007) Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection. Ann Biomed Eng 35: 250–263 · doi:10.1007/s10439-006-9224-3
[27] Masters JC, Ketner M, Bleiweis MS, Mill M, Yoganathan A, Lucas CL (2004) The effect of incorporating vessel compliance in a computational model of blood flow in a total cavopulmonary connection (tcpc) with caval centerline offset. J Biomech Eng 126: 709–713 · doi:10.1115/1.1824126
[28] Migliavacca F, Dubini G, Bove EL, de Leval MR (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: 805–813 · doi:10.1115/1.1632523
[29] Migliavacca F, Dubini G, Pietrabissa R, de Leval MR (1997) Computational transient simulations with varying degree and shape of pulmonic stenosis in models of the bidirectional cavopulmonary anastomosis. Med Eng Phys 19: 394–403 · doi:10.1016/S1350-4533(96)00070-7
[30] Pedersen EM, Stenbog EV, Frund T, Houlind K, Kromann O, Sorensen KE, Emmertsen K, Hjortdal VE (2002) Flow during exercise in the total cavopulmonary connection measured by magnetic resonance velocity mapping. Heart 87: 554–558 · doi:10.1136/heart.87.6.554
[31] Petrossian E, Reddy VM, Collins KK, Culbertson CB, MacDonald MJ, Lamberti JJ, Reinhartz O, Mainwaring RD, Francis PD, Malhotra SP, Gremmels DB, Suleman S, Hanley FL (2006) The extracardiac conduit Fontan operation using minimal approach extracorporeal circulation: early and midterm outcomes. J Thorac Cardiovasc Surg 132(5): 1054–1063 · doi:10.1016/j.jtcvs.2006.05.066
[32] Sahni O, Muller J, Jansen KE, Shephard MS, Taylor CA (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comput Methods Appl Mech Eng 195: 5634–5655 · Zbl 1125.76046 · doi:10.1016/j.cma.2005.10.018
[33] Shachar GB, Fuhrman BP, Wang Y, Lucas RV Jr, Lock JE (1982) Rest and exercise hemodynamics after the fontan procedure. Circulation 65: 1043–1048
[34] Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63 · Zbl 1110.74689 · doi:10.1115/1.1530635
[35] Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193: 2019–2032 · Zbl 1067.74587 · doi:10.1016/j.cma.2003.12.046
[36] Takizawa K, Christopher J, Moorman C, Martin J, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2009) Space-time finite element computation of arterial FSI with patient-specific data. In: Schrefler B, Onate E, Papadrakakis M (eds) Computational methods for coupled problems in science and engineering, coupled problems 2009
[37] Takizawa K, Christopher J, Tezduyar TE, Sathe S (2009) Space-time finite element computation of arterial fluid–structure interactions with patient-specific data. Commun Numer Methods Eng, published online. doi: 10.1002/cnm.1241 · Zbl 1180.92023
[38] Tezduyar TE, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite element computation of 3D flows. Computer 26: 27–36 · Zbl 05090697 · doi:10.1109/2.237441
[39] Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575 · Zbl 1032.76605 · doi:10.1002/fld.505
[40] Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the stabilized finite element methods–space-time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol. 246/ AMD-Vol. 143, pp 7–24. ASME, New York
[41] Tezduyar TE, Sathe S (2007) Modelling of fluid–structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54: 855–900 · Zbl 1144.74044 · doi:10.1002/fld.1430
[42] Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modelling of fluid–structure interactions with the space-time finite elements: arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922 · Zbl 1276.76043 · doi:10.1002/fld.1443
[43] Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space-time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027 · Zbl 1118.74052 · doi:10.1016/j.cma.2004.09.014
[44] Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space-time fluid–structure interaction technique. Int J Numer Methods Fluids 57: 601–629 · Zbl 1230.76054 · doi:10.1002/fld.1633
[45] Tezduyar TE, Schwaab M, Sathe S (2008) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng, published online. doi: 10.1016/j.cma.2008.05.024 · Zbl 1229.74100
[46] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the deforming-spatial-domain/stabilized space-time formulation. Comput Methods Appl Mech Eng 195: 1885–1895 · Zbl 1178.76241 · doi:10.1016/j.cma.2005.05.050
[47] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490 · Zbl 1160.76061 · doi:10.1007/s00466-006-0065-6
[48] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43: 151–159 · Zbl 1169.74032 · doi:10.1007/s00466-008-0325-8
[49] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Commun Numer Methods Eng, published online. doi: 10.1002/cnm.1289 · Zbl 1183.92050
[50] Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195: 3776–3796 · Zbl 1175.76098 · doi:10.1016/j.cma.2005.04.014
[51] Zhang Y, Wang W, Liang X, Bazilevs Y, Hsu M-C, Kvamsdal T, Brekken R, Isaksen JG (2009) High-fidelity tetrahedral mesh generation from medical imaging data for fluid–structure interaction analysis of cerebral aneurysms. Comput Model Eng Sci 42: 131–149
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