On the impact of fluid structure interaction in blood flow simulations. Stenotic coronary artery benchmark. (English) Zbl 1464.76221
Summary: We study the impact of using fluid-structure interactions (FSI) to simulate blood flow in a stenosed artery. We compare typical flow configurations using Navier-Stokes in a rigid geometry setting to a fully coupled FSI model. The relevance of vascular elasticity is investigated with respect to several questions of clinical importance. Namely, we study the effect of using FSI on the wall shear stress distribution, on the Fractional Flow Reserve and on the damping effect of a stenosis on the pressure amplitude during the pulsatile cycle. The coupled problem is described in a monolithic variational formulation based on Arbitrary Lagrangian Eulerian (ALE) coordinates. For comparison, we perform pure Navier-Stokes simulations on a pre-stressed geometry to give a good matching of both configurations. A series of numerical simulations that cover important hemodynamical factors are presented and discussed.
MSC:
| 76Z05 | Physiological flows |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 92C10 | Biomechanics |
Software:
GASCOIGNEReferences:
| [1] | ADAN WEB: http://hemolab.lncc.br/adan-web/. Accessed: 30 Jan 2020 (2020) |
| [2] | Aulisa, E.; Bnà, S.; Bornia, G., A monolithic ALE Newton-Krylov solver with multigrid-Richardson-Schwarz preconditioning for incompressible fluid-structure interaction, Comput. Fluids, 174, 213-228 (2018) · Zbl 1410.76147 · doi:10.1016/j.compfluid.2018.08.003 |
| [3] | Balzani, D.; Deparis, S.; Fausten, S.; Forti, D.; Heinlein, A.; Klawonn, A.; Quarteroni, A.; Rheinbach, O.; Schröder, J., Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains, Int. J. Numer. Methods Biomed. Eng., 32, e02756 (2016) · doi:10.1002/cnm.2756 |
| [4] | Bazilevs, Y.; Calo, VM; Hughes, TJ; Zhang, Y., Isogeometric fluid-structure interaction: theory, algorithms, and computations, Comput. Mech., 43, 3-37 (2008) · Zbl 1169.74015 · doi:10.1007/s00466-008-0315-x |
| [5] | Bazilevs, Y.; Hsu, M-C; Zhang, Y.; Wang, W.; Kvamsdal, T.; Hentschel, S.; Isaksen, JG, Computational vascular fluid-structure interaction: methodology and application to cerebral aneurysms, Biomech. Model. Mechanobiol., 9, 481-498 (2010) · doi:10.1007/s10237-010-0189-7 |
| [6] | Becker, R.; Braack, M., A finite element pressure gradient stabilization for the Stokes equations based on local projections, Calcolo, 38, 173-199 (2001) · Zbl 1008.76036 · doi:10.1007/s10092-001-8180-4 |
| [7] | Becker, R., Braack, M., Meidner, D., Richter, T., Vexler, B.: The finite element toolkit Gascoigne 3d. https://www.gascoigne.de |
| [8] | Blanco, PJ; Bulant, CA; Müller, LO; Talou, GDM; Bezerra, CG; Lemos, PA; Feijóo, RA, Comparison of 1d and 3d models for the estimation of fractional flow reserve, Sci. Rep., 8, 17275 (2018) · doi:10.1038/s41598-018-35344-0 |
| [9] | Bluestein, D., Utilizing computational fluid dynamics in cardiovascular engineering and medicine—what you need to know. Its translation to the clinic/bedside, Artif. Organs, 41, 117-121 (2017) · doi:10.1111/aor.12914 |
| [10] | Carew, TE; Vaishnav, RN; Patel, DJ, Compressibility of the arterial wall, Circ. Res., 23, 61-68 (1968) · doi:10.1161/01.RES.23.1.61 |
| [11] | Carson, JM; Pant, S.; Roobottom, C.; Alcock, R.; Blanco, PJ; Bulant, CA; Vassilevski, Y.; Simakov, S.; Gamilov, T.; Pryamonosov, R.; Liang, F.; Ge, X.; Liu, Y.; Nithiarasu, P., Non-invasive coronary CT angiography-derived fractional flow reserve: a benchmark study comparing the diagnostic performance of four different computational methodologies, Int. J. Numer. Methods Biomed. Eng., 35, e3235 (2019) |
| [12] | Cebral, JR; Mut, F.; Weir, J.; Putman, C., Quantitative characterization of the hemodynamic environment in ruptured and unruptured brain aneurysms, Amer. J. Neuroradiol., 32, 145-151 (2010) · doi:10.3174/ajnr.A2419 |
| [13] | Delfino, A.; Stergiopulos, N.; Moore, J. Jr; Meister, J-J, Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation, J. Biomech., 30, 777-786 (1997) · doi:10.1016/S0021-9290(97)00025-0 |
| [14] | Donea, J.; Giuliani, S.; Halleux, JP, An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions, Comput. Methods Appl. Mech. Eng., 33, 689-723 (1982) · Zbl 0508.73063 · doi:10.1016/0045-7825(82)90128-1 |
| [15] | Failer, L., Richter, T.: A Newton multigrid framework for optimal control of fluid-structure interactions. Optim. Eng. doi:10.1007/s11081-020-09498-8(2020) · Zbl 1514.76051 |
| [16] | Failer, L.; Richter, T., A parallel Newton multigrid framework for monolithic fluid-structure interactions, J. Sci. Comput., 82, 28 (2020) · Zbl 1514.76051 · doi:10.1007/s10915-019-01113-y |
| [17] | Fung, Y.C.: Biomechanics: Mechanical properties of living tissues. Springer (1993) |
| [18] | Gee, MW; Förster, Ch; Wall, WA, A computational strategy for prestressing patient-specific biomechanical problems under finite deformation, Int. J. Numer. Methods Biomed. Eng., 26, 52-72 (2010) · Zbl 1180.92009 · doi:10.1002/cnm.1236 |
| [19] | Gurtin, ME; Fried, E.; Anand, L., The Mechanics and Thermodynamics of Continua (2010), Cambridge: Cambridge University Press, Cambridge · doi:10.1017/CBO9780511762956 |
| [20] | Heywood, J.; Rannacher, R.; Turek, S., Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 22, 325-352 (1996) · Zbl 0863.76016 · doi:10.1002/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y |
| [21] | Holzapfel, GA; Gasser, TC; Ogden, RW, A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. Elast. Phys. Sci. Solids, 61, 1-48 (2000) · Zbl 1023.74033 · doi:10.1016/S0022-3697(99)00252-8 |
| [22] | Jin, S.; Oshinski, J.; Giddens, DP, Effects of wall motion and compliance on flow patterns in the ascending aorta, J. Biomech. Eng., 125, 347-354 (2003) · doi:10.1115/1.1574332 |
| [23] | Jodlbauer, D.; Langer, U.; Wick, T., Parallel block-preconditioned monolithic solvers for fluid-structure interaction problems, Int. J. Numer. Methods Eng., 117, 623-643 (2019) · Zbl 07865264 · doi:10.1002/nme.5970 |
| [24] | Liang, F.; Takagi, S.; Himeno, R.; Liu, H., Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenoses, Med. Biol. Eng. Comput., 47, 743-755 (2009) · doi:10.1007/s11517-009-0449-9 |
| [25] | Libby, P.; Buring, JE; Badimon, L.; Hansson, GK; Deanfield, J.; Bittencourt, MS; Tokgözoǧlu, L.; Lewis, EF, Atherosclerosis, Nat. Rev. Dis. Primers, 5, 56 (2019) · doi:10.1038/s41572-019-0106-z |
| [26] | Moireau, P.; Xiao, N.; Astorino, M.; Figueroa, CA; Chapelle, D.; Taylor, CA; Gerbeau, J-F, External tissue support and fluid-structure simulation in blood flows, Biomech. Model. Mech., 11, 1-18 (2012) · doi:10.1007/s10237-011-0289-z |
| [27] | Morris, PD; van de Vosse, FN; Lawford, PV; Hose, DR; Gunn, JP, ‘Virtual” (computed) fractional flow reserve: Current challenges and limitations, JACC: Cardiovasc. Interv., 8, 1009-1017 (2015) |
| [28] | Nobile, F.; Pozzoli, M.; Vergara, C., Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics, J. Comput. Phys., 273, 598-617 (2014) · Zbl 1351.76324 · doi:10.1016/j.jcp.2014.05.020 |
| [29] | Nobile, F.; Vergara, C., An effective fluid-structure interaction formulation for vascular dynamics by generalized robin conditions, SIAM J. Sci. Comput., 30, 731-763 (2008) · Zbl 1168.74038 · doi:10.1137/060678439 |
| [30] | Perktold, K.; Rappitsch, G., Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model, J. Biomech., 28, 845-856 (1995) · doi:10.1016/0021-9290(95)95273-8 |
| [31] | Pichler, G.; Martinez, F.; Vicente, A.; Solaz, E.; Calaforra, O.; Redon, J., Pulse pressure amplification and its determinants, Blood Press., 25, 21-27 (2016) · doi:10.3109/08037051.2015.1090713 |
| [32] | Quarteroni, A.; Manzoni, A.; Vergara, C., The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications, Acta Numer., 26, 365-590 (2017) · Zbl 1376.92016 · doi:10.1017/S0962492917000046 |
| [33] | Quarteroni, A.; Tuveri, M.; Veneziani, A., Computational vascular fluid dynamics: problems, models and methods, Comput. Visual. Sci., 2, 163-197 (2000) · Zbl 1096.76042 · doi:10.1007/s007910050039 |
| [34] | Richter, T., Goal-oriented error estimation for fluid-structure interaction problems, Comput. Methods Appl. Mech. Eng., 223-224, 28-42 (2012) · Zbl 1253.74037 · doi:10.1016/j.cma.2012.02.014 |
| [35] | Richter, T., A monolithic geometric multigrid solver for fluid-structure interactions in ALE formulation, Int. J. Numer. Methods Eng., 104, 372-390 (2015) · Zbl 1352.76066 · doi:10.1002/nme.4943 |
| [36] | Richter, T.: Fluid-structure Interactions: Models, Analysis and Finite Elements. Lecture Notes in Computational Science and Engineering, vol. 118. Springer International Publishing (2017) · Zbl 1374.76001 |
| [37] | Richter, T., Mizerski, J.: The candy wrapper problem-a temporal multiscale approach for Pde/Pde systems. In: ENUMATH 2019. Springer (2020) |
| [38] | Richter, T., Wick, T.: On time discretizations of fluid-structure interactions. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds.) Multiple Shooting and Time Domain Decomposition Methods. Contributions in Mathematical and Computational Science, vol. 9, pp. 377-400. Springer (2015) · Zbl 1382.76195 |
| [39] | Shojima, M.; Oshima, M.; Takagi, K.; Torii, R.; Hayakawa, M.; Katada, K.; Morita, A.; Kirino, T., Magnitude and role of wall shear stress on cerebral aneurysm, Stroke, 35, 2500-2505 (2004) · doi:10.1161/01.STR.0000144648.89172.0f |
| [40] | Steinman, D.: Assumptions in modelling of large artery hemodynamics. In: Ambrosi, D., Quarteroni, A., Rozza, G (eds.) Modeling of Physiological Flows. MS&A - Modeling, Simulation and Applications, vol. 5, pp. 1-18. Springer, Milano (2012) |
| [41] | Taylor, CA; Draney, MT; Ku, JP; Parker, D.; Steele, BN; Wang, K.; Zarins, CK, Predictive medicine: Computational techniques in therapeutic decision-making, Comput. Aided Surg., 4, 231-247 (1999) · doi:10.3109/10929089909148176 |
| [42] | Taylor, CA; Fonte, TA; Min, JK, Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve: scientific basis, J. Am. Coll. Cardiol., 61, 2233-2241 (2013) · doi:10.1016/j.jacc.2012.11.083 |
| [43] | Tonino, PA; de Bruyne, B.; Pijls, NH; Siebert, U.; Ikeno, F.; van’t Veer, M.; Klauss, V.; Manoharan, G.; Engstrøm, T.; Oldroyd, KG; Lee, PNV; MacCarthy, PA; Fearon, WF, Fractional flow reserve versus angiography for guiding percutaneous coronary intervention, Engl. J. Med., 360, 213-224 (2009) · doi:10.1056/NEJMoa0807611 |
| [44] | Torii, R.; Keegan, J.; Wood, NB; Dowsey, AW; Hughes, AD; Yang, G-Z; Firmin, DN; Thom, SAMcG; Xu, XY, MR image-based geometric and hemodynamic investigation of the right coronary artery with dynamic vessel motion, Ann. Biomed. Eng., 38, 2606-2620 (2010) · doi:10.1007/s10439-010-0008-4 |
| [45] | Yang, Y.; Jäger, W.; Neuss-Radu, M.; Richter, T., Mathematical modeling and simulation of the evolution of plaques in blood vessels, J. Math. Biol., 72, 973-996 (2016) · Zbl 1343.35190 · doi:10.1007/s00285-015-0934-8 |
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