A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart.


Journal

International journal for numerical methods in biomedical engineering
ISSN: 2040-7947
Titre abrégé: Int J Numer Method Biomed Eng
Pays: England
ID NLM: 101530293

Informations de publication

Date de publication:
03 2023
Historique:
revised: 13 12 2022
received: 12 08 2022
accepted: 19 12 2022
pubmed: 30 12 2022
medline: 16 3 2023
entrez: 29 12 2022
Statut: ppublish

Résumé

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

Identifiants

pubmed: 36579792
doi: 10.1002/cnm.3678
doi:

Types de publication

Journal Article Research Support, Non-U.S. Gov't

Langues

eng

Sous-ensembles de citation

IM

Pagination

e3678

Informations de copyright

© 2023 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

Références

Benjamin EJ, Blaha MJ, Chiuve SE, et al. Heart disease and stroke statistics-2017 update: a report from the American Heart Association. Circulation. 2017;135(10):e146-e603. doi:10.1161/CIR.0000000000000485
Gerach T, Schuler S, Fröhlich J, et al. Electro-mechanical whole-heart digital twins: a fully coupled multi-physics approach. Mathematics. 2021;9(11):1247. doi:10.3390/math9111247
Gray RA, Pathmanathan P. Patient-specific cardiovascular computational modeling: diversity of personalization and challenges. J Cardiovasc Transl Res. 2018;11(2):80-88. doi:10.1007/s12265-018-9792-2
Karabelas E, Longobardi S, Fuchsberger J, et al. Global sensitivity analysis of four chamber heart hemodynamics using surrogate models. IEEE Trans Biomed Eng. 2022;69(10):3216-3223. doi:10.1109/TBME.2022.3163428
Niederer SA, Lumens J, Trayanova NA. Computational models in cardiology. Nat Rev Cardiol. 2019;16(2):100-111. doi:10.1038/s41569-018-0104-y
Quarteroni A, Lassila T, Rossi S, Ruiz-Baier R. Integrated heart-coupling multiscale and multiphysics models for the simulation of the cardiac function. Comput Methods Appl Mech Eng. 2017;314:345-407. doi:10.1016/j.cma.2016.05.031
Quarteroni A, Dede' L, Manzoni A, Vergara C. Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications. Cambridge University Press; 2019.
Katz AM. Physiology of the Heart. Lippincott Williams & Wilkins; 2010.
Klabunde R. Cardiovascular Physiology Concepts. Lippincott Williams & Wilkins; 2011.
Hosoi A, Washio T, Ji O, Kadooka Y, Nakajima K, Hisada T. A multi-scale heart simulation on massively parallel computers. Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis. 2010;1-11.
Ji O, Washio T, Sugiura S, Hisada T. Clinical and pharmacological application of multiscale multiphysics heart simulator, UT-heart. Korean J Physiol Pharmacol. 2019;23(5):295-303. doi:10.4196/kjpp.2019.23.5.295
Santiago A, Aguado-Sierra J, Zavala-Aké M, et al. Fully coupled fluid-electro-mechanical model of the human heart for supercomputers. Int J Numer Methods Biomed Eng. 2018;34(12):e3140. doi:10.1002/cnm.3140
Arevalo HJ, Vadakkumpadan F, Guallar E, et al. Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models. Nat Commun. 2016;7(1):1-8. doi:10.1038/ncomms11437
Bucelli M, Salvador M, Dede' L, Quarteroni A. Multipatch isogeometric analysis for electrophysiology: simulation in a human heart. Comput Methods Appl Mech Eng. 2021;376:113666. doi:10.1016/j.cma.2021.113666
Del Corso G, Verzicco R, Viola F. A fast computational model for the electrophysiology of the whole human heart. J Comput Phys. 2022;457:111084. doi:10.1016/j.jcp.2022.111084
Gillette K, Gsell MA, Prassl AJ, et al. A framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs. Med Image Anal. 2021;71:102080. doi:10.1016/j.media.2021.102080
Piersanti R, Africa PC, Fedele M, et al. Modeling cardiac muscle fibers in ventricular and atrial electrophysiology simulations. Comput Methods Appl Mech Eng. 2021;373:113468. doi:10.1016/j.cma.2020.113468
Romero D, Sebastian R, Bijnens BH, et al. Effects of the Purkinje system and cardiac geometry on biventricular pacing: a model study. Ann Biomed Eng. 2010;38(4):1388-1398. doi:10.1007/s10439-010-9926-4
Trayanova NA. Whole-heart modeling: applications to cardiac electrophysiology and electromechanics. Circ Res. 2011;108(1):113-128. doi:10.1161/CIRCRESAHA.110.223610
Vergara C, Lange M, Palamara S, Lassila T, Frangi AF, Quarteroni A. A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network. J Comput Phys. 2016;308:218-238. doi:10.1016/j.jcp.2015.12.016
Augustin CM, Crozier A, Neic A, et al. Patient-specific modeling of left ventricular electromechanics as a driver for haemodynamic analysis. EP Europace. 2016;18:iv121-iv129. doi:10.1093/europace/euw369
Baillargeon B, Rebelo N, Fox DD, Taylor RL, Kuhl E. The living heart project: a robust and integrative simulator for human heart function. Eur J Mech: A/Solids. 2014;48:38-47. doi:10.1016/j.euromechsol.2014.04.001
Dede' L, Gerbi A, Quarteroni A. Segregated algorithms for the numerical simulation of cardiac electromechanics in the left human ventricle. Springer; 2020:81-116.
Fedele M, Piersanti R, Regazzoni F, et al. A comprehensive and biophysically detailed computational model of the whole human heart electromechanics. arXiv Preprint arXiv:2207.12460 2022. doi: 10.48550/arXiv.2207.12460
Gerbi A, Dede' L, Quarteroni A. A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle. Math Eng. 2019;1(1):1-37. doi:10.3934/Mine.2018.1.1
Gurev V, Lee T, Constantino J, Arevalo H, Trayanova NA. Models of cardiac electromechanics based on individual hearts imaging data: image-based electromechanical models of the heart. Biomech Model Mechanobiol. 2011;10(3):295-306. doi:10.1007/s10237-010-0235-5
Levrero-Florencio F, Margara F, Zacur E, et al. Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: effect of mechanical parameters on physiologically relevant biomarkers. Comput Methods Appl Mech Eng. 2020;361:112762. doi:10.1016/j.cma.2019.112762
Pfaller MR, Hörmann JM, Weigl M, et al. The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling. Biomech Model Mechanobiol. 2019;18(2):503-529. doi:10.1007/s00791-002-0081-9
Piersanti R, Regazzoni F, Salvador M, et al. 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics. Comput Methods Appl Mech Eng. 2022;391:114607. doi:10.1016/j.cma.2022.114607
Regazzoni F, Salvador M, Africa PC, Fedele M, Dede L, Quarteroni A. A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation. J Comput Phys. 2022;457:111083. doi:10.1016/j.jcp.2022.111083
Salvador M, Fedele M, Africa PC, et al. Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia. Comput Biol Med. 2021;136:104674. doi:10.1016/j.compbiomed.2021.104674
Strocchi M, Gsell MA, Augustin CM, et al. Simulating ventricular systolic motion in a four-chamber heart model with spatially varying Robin boundary conditions to model the effect of the pericardium. J Biomech. 2020;101:109645. doi:10.1016/j.jbiomech.2020.109645
Usyk TP, LeGrice IJ, McCulloch AD. Computational model of three-dimensional cardiac electromechanics. Comput Vis Sci. 2002;4(4):249-257. doi:10.1007/s00791-002-0081-9
Chnafa C, Mendez S, Nicoud F. Image-based large-eddy simulation in a realistic left heart. Comput Fluids. 2014;94:173-187. doi:10.1016/j.compfluid.2014.01.030
Collia D, Zovatto L, Pedrizzetti G. Analysis of mitral valve regurgitation by computational fluid dynamics. APL Bioeng. 2019;3(3):036105. doi:10.1063/1.5097245
Kronborg J, Svelander F, Eriksson-Lidbrink S, et al. Computational analysis of flow structures in turbulent ventricular blood flow associated with mitral valve intervention. Front Physiol. 2022;13:752. doi:10.3389/fphys.2022.806534
Rigatelli G, Chiastra C, Pennati G, Dubini G, Migliavacca F, Zuin M. Applications of computational fluid dynamics to congenital heart diseases: a practical review for cardiovascular professionals. Expert Rev Cardiovasc Ther. 2021;19(10):907-916. doi:10.1080/14779072.2021.1999229
Spühler JH, Jansson J, Jansson N, Hoffman J. A High Performance Computing Framework for Finite Element Simulation of Blood Flow in the Left Ventricle of the Human Heart. Springer; 2020:155-164.
Terahara T, Kuraishi T, Takizawa K, Tezduyar TE. Computational flow analysis with boundary layer and contact representation: II. Heart valve flow with leaflet contact. J Mech. 2022;38:185-194. doi:10.1093/jom/ufac013
This A, Boilevin-Kayl L, Fernández MA, Gerbeau JF. Augmented resistive immersed surfaces valve model for the simulation of cardiac hemodynamics with isovolumetric phases. Int J Numer Methods Biomed Eng. 2020;36(3):e3223. doi:10.1002/cnm.3223
VedulaV SJH, LardoAC MR. Effect of trabeculae and papillary muscles on the hemodynamics of the left ventricle. Theor Comput Fluid Dyn. 2016;30(1):3-21. doi:10.1007/s00162-015-0349-6
Zingaro A, Dede' L, Menghini F, Quarteroni A. Hemodynamics of the heart's left atrium based on aVariational multiscale-LES numerical method. Eur J Mech: B/Fluids. 2021;89:380-400. doi:10.1016/j.euromechflu.2021.06.014
Zingaro A, Fumagalli I, Dede' L, et al. A geometric multiscale model for the numerical simulation of blood flow in the human left heart. Discr Contin Dyn Syst-S. 2022;15(8):2391-2427. doi:10.3934/dcdss.2022052
Cheng Y, Oertel H, Schenkel T. Fluid-structure coupled CFD simulation of the left ventricular flow during filling phase. Ann Biomed Eng. 2005;33(5):567-576. doi:10.1007/s10439-005-4388-9
Einstein DR, Del Pin F, Jiao X, et al. Fluid-structure interactions of the mitral valve and left heart: comprehensive strategies, past, present and future. Int J Numer Methods Biomed Eng. 2010;26(3-4):348-380. doi:10.1002/cnm.1280
Feng L, Gao H, Griffith B, Niederer S, Luo X. Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve. Int J Numer Methods Biomed Eng. 2019;35(11):e3254. doi:10.1002/cnm.3254
Gao H, Feng L, Qi N, Berry C, Griffith BE, Luo X. A coupled mitral valve-left ventricle model with fluid-structure interaction. Med Eng Phys. 2017;47:128-136. doi:10.1016/j.medengphy.2017.06.042
Hirschhorn M, Tchantchaleishvili V, Stevens R, Rossano J, Throckmorton A. Fluid-structure interaction modeling in cardiovascular medicine-A systematic review 2017-2019. Med Eng Phys. 2020;78:1-13. doi:10.1016/j.medengphy.2020.01.008
Brenneisen J, Daub A, Gerach T, et al. Sequential coupling shows minor effects of fluid dynamics on myocardial deformation in a realistic whole-heart model. Front Cardiovasc Med. 2021;8:1-13. doi:10.3389/fcvm.2021.768548
Khodaei S, Henstock A, Sadeghi R, et al. Personalized intervention cardiology with transcatheter aortic valve replacement made possible with a non-invasive monitoring and diagnostic framework. Sci Rep. 2021;11(1):1-28. doi:10.1038/s41598-021-85500-2
Nordsletten D, McCormick M, Kilner P, Hunter P, Kay D, Smith N. Fluid-solid coupling for the investigation of diastolic and systolic human left ventricular function. Int J Numer Methods Biomed Eng. 2011;27(7):1017-1039. doi:10.1002/cnm.1405
Zhang Q, Hisada T. Analysis of fluid-structure interaction problems with structural buckling and large domain changes by ALE finite element method. Comput Methods Appl Mech Eng. 2001;190(48):6341-6357. doi:10.1016/S0045-7825(01)00231-6
Bucelli M, Gabriel MG, Gigante G, Quarteroni A, Vergara C. A stable loosely-coupled scheme for cardiac electro-fluidstructure interaction. arXiv preprint arXiv:2210.00917 2022.
Gerbi A. Numerical approximation of cardiac electro-fluid-mechanical models. PhD thesis EPFL, Lausanne, Switzerland; 2018.
Sugiura S, Okada JI, Washio T, Hisada T. UT-Heart: A Finite Element Model Designed for the Multiscale and Multiphysics Integration of our Knowledge on the Human Heart. Springer; 2022:221-245.
Verzicco R. Electro-fluid-mechanics of the heart. J Fluid Mech. 2022;941:941. doi:10.1017/jfm.2022.272
Kariya T, Washio T, Ji O, et al. Personalized perioperative multi-scale, multi-physics heart simulation of double outlet right ventricle. Ann Biomed Eng. 2020;48(6):1740-1750. doi:10.1007/s10439-020-02488-y
Bakir AA, Al Abed A, Stevens MC, Lovell NH, Dokos S. A multiphysics biventricular cardiac model: simulations with a left-ventricular assist device. Front Physiol. 2018;9:1259.
Viola F, Meschini V, Verzicco R. Fluid-structure-electrophysiology interaction (FSEI) in the left-heart: a multi-way coupled computational model. Eur J Mech: B/Fluids. 2020;79:212-232. doi:10.1016/j.euromechflu.2019.09.006
Viola F, Meschini V, Verzicco R. Effects of stenotic aortic valve on the left heart hemodynamics: A fluid-structureelectrophysiology approach. arXiv Preprint arXiv:2103.14680, 2021. doi: 10.48550/arXiv.2103.14680
Nash MP, Panfilov AV. Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. Prog Biophys Mol Biol. 2004;85(2-3):501-522. doi:10.1016/j.pbiomolbio.2004.01.016
Viola F, Spandan V, Meschini V, et al. FSEI-GPU: GPU accelerated simulations of the fluid-structure-electrophysiology interaction in the left heart. Comput Phys Commun. 2022;273:108248. doi:10.1016/j.cpc.2021.108248
Viola F, Del Corso G, De Paulis R, Verzicco R. GPU accelerated digital twins of the human heart open new routes for cardiovascular research. Research Square Preprint 2022.
Battista NA, Miller LA. Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart development. Biomath. 2017;6(2):ID-1711297. doi:10.11145/j.biomath.2017.11.297
Salvador M, Regazzoni F, Pagani S, Trayanova N, Quarteroni A. The role of mechano-electric feedbacks and hemodynamic coupling in scar-related ventricular tachycardia. Comput Biol Med. 2022;142:105203. doi:10.1016/j.compbiomed.2021.105203
Regazzoni F, Dede' L, Quarteroni A. Biophysically detailed mathematical models of multiscale cardiac active mechanics. PLoS Comput Biol. 2020;16(10):e1008294. doi:10.1371/journal.pcbi.1008294
Bucelli M, Dede' L, Quarteroni A, Vergara C. Partitioned and monolithic FSI schemes for the numerical simulation of the heart. Commun Comput Phys. 2022.
Hirschvogel M, Bassilious M, Jagschies L, Wildhirt SM, Gee MW. A monolithic 3D-0D coupled closed-loop model of the heart and the vascular system: experiment-based parameter estimation for patient-specific cardiac mechanics. Int J Numer Methods Biomed Eng. 2017;33(8):e2842. doi:10.1002/cnm.2842
Zingaro A, Bucelli M, Fumagalli I, Dede' L, Quarteroni A. Modeling isovolumetric phases in cardiac flows by an augmented resistive immersed implicit surface method. arXiv Preprint arXiv:2208.09435, 2022. doi: 10.48550/arXiv.2208.09435
Hughes TJ. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Courier Corporation; 2012.
Quarteroni A. Numerical Models for Differential Problems. Springer; 2017.
Africa PC. Lifex: a flexible, high performance library for the numerical solution of complex finite element problems. arXiv Preprint arXiv:2207.14668 2022. doi: 10.48550/arXiv.2207.14668
Africa PC, Piersanti R, Fedele M, Dede' L, Quarteroni A. Lifex-heart module: a high-performance simulator for the cardiac function package 1: fiber generation. arXiv Preprint arXiv:2201.03303 2022. doi: 10.48550/arXiv.2201.03303
Official lifex website. Accessed: October 4, 2022. https://lifex.gitlab.io/.
Roberts DE, Hersh LT, Scher AM. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ Res. 1979;44(5):701-712. doi:10.1161/01.RES.44.5.701
Eriksson TS, Prassl AJ, Plank G, Holzapfel GA. Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction. Math Mech Solids. 2013;18(6):592-606. doi:10.1177/1081286513485779
Gil D, Aris R, Borras A, Ramírez E, Sebastian R, Vazquez M. Influence of fiber connectivity in simulations of cardiac biomechanics. Int J Comput Assist Radiol Surg. 2019;14(1):63-72. doi:10.1007/s11548-018-1849-9
Doste R, Soto-Iglesias D, Bernardino G, et al. A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts. Int J Numer Methods Biomed Eng. 2019;35(4):e3185. doi:10.1002/cnm.3185
Rossi S, Lassila T, Ruiz-Baier R, Sequeira A, Quarteroni A. Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. Eur J Mech: A/Solids. 2014;48:129-142. doi:10.1016/j.euromechsol.2013.10.009
Bayer JD, Blake RC, Plank G, Trayanova NA. A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann Biomed Eng. 2012;40(10):2243-2254. doi:10.1007/s10439-012-0593-5
Colli Franzone P, Pavarino LF, Scacchi S. Mathematical Cardiac Electrophysiology. Springer; 2014.
Sundnes J, Lines GT, Cai X, Nielsen BF, Mardal KA, Tveito A. Computing the Electrical Activity in the Heart. Springer Science & Business Media; 2007.
Ten Tusscher KH, Panfilov AV. Alternans and spiral breakup in a human ventricular tissue model. Am J Phys Heart Circ Phys. 2006;291(3):H1088-H1100. doi:10.1152/ajpheart.00109.2006
Collet A. Numerical Modeling of the Cardiac Mechano-Electric Feedback within a Thermo-Electro-Mechanical Framework. Study of its Consequences on Arrhythmogenesis. PhD thesis. Université de Liège, Liège, Belgique; 2015.
Timmermann V, Dejgaard LA, Haugaa KH, et al. An integrative appraisal of mechano-electric feedback mechanisms in the heart. Prog Biophys Mol Biol. 2017;130:404-417.
Costabal FS, Hurtado DE, Kuhl E. Generating Purkinje networks in the human heart. J Biomech. 2016;49(12):2455-2465. doi:10.1016/j.jbiomech.2015.12.025
Landajuela M, Vergara C, Gerbi A, Dede' L, Formaggia L, Quarteroni A. Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. Int J Numer Methods Biomed Eng. 2018;34(7):e2984. doi:10.1002/cnm.2984
Jacob R, Dierberger B, Kissling G. Functional significance of the frank-Starling mechanism under physiological and pathophysiological conditions. Eur Heart J. 1992;13(suppl_E):7-14. doi:10.1093/eurheartj/13.suppl_E.7
Opie LH. Heart Physiology: From Cell to Circulation. Lippincott Williams & Wilkins; 2004.
Bers D. Excitation-Contraction Coupling and Cardiac Contractile Force. Springer Science & Business Media; 2001.
Regazzoni F, Quarteroni A. An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics. Comput Methods Appl Mech Eng. 2021;373:113506. doi:10.1016/j.cma.2020.113506
Ogden R. Non-Linear Elastic Deformations. Courier Corporation; 2013.
Ambrosi D, Pezzuto S. Active stress vs. active strain in mechanobiology: constitutive issues. J Elast. 2012;107(2):199-212. doi:10.1007/s10659-011-9351-4
Göktepe S, Kuhl E. Electromechanics of the heart: a unified approach to the strongly coupled excitation-contraction problem. Comput Mech. 2010;45(2):227-243. doi:10.1007/s00466-009-0434-z
Pathmanathan P, Chapman S, Gavaghan D, Whiteley J. Cardiac electromechanics: the effect of contraction model on the mathematical problem and accuracy of the numerical scheme. Q J Mech Appl Math. 2010;63(3):375-399. doi:10.1093/qjmam/hbq014
Smith N, Nickerson D, Crampin E, Hunter P. Multiscale computational modelling of the heart. Acta Numer. 2004;13:371-431. doi:10.1017/S0962492904000200
Guccione JM, McCulloch AD. Finite Element Modeling of Ventricular Mechanics. Springer; 1991:121-144.
Zygote Media Group Inc. Zygote solid 3D heart generation II developement report. Technical Report. 2014.
Donea J, Giuliani S, Halleux JP. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluidstructure interactions. Comput Methods Appl Mech Eng. 1982;33(1-3):689-723. doi:10.1016/0045-7825(82)90128-1
Hughes TJR, Liu WK, Zimmermann TK. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng. 1981;29(3):329-349. doi:10.1016/0045-7825(81)90049-9
Stein K, Tezduyar T, Benney R. Mesh moving techniques for fluid-structure interactions with large displacements. J Appl Mech. 2003;70(1):58-63. doi:10.1115/1.1530635
Alharbi Y, Al Abed A, Bakir AA, et al. Fluid structure computational model of simulating mitral valve motion in a contracting left ventricle. Comput Biol Med. 2022;148:105834.
Hoffman J, Jansson J, Stöckli M. Unified continuum modeling of fluid-structure interaction. Math Models Methods Appl Sci. 2011;21(3):491-513. doi:10.1142/S021820251100512X
Spühler JH, Hoffman J. An interface-tracking unified continuum model for fluid-structure interaction with topology change and full-friction contact with application to aortic valves. Int J Numer Methods Eng. 2021;122(19):5258-5278. doi:10.1002/nme.6384
Johnson AA, Tezduyar TE. Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng. 1994;119(1-2):73-94. doi:10.1016/0045-7825(94)00077-8
Jasak H, Tukovic Z. Automatic mesh motion for the unstructured finite volume method. Trans FAMENA. 2006;30(2):1-20.
Corti M, Zingaro A, Quarteroni AM, et al. Impact of atrial fibrillation on left atrium haemodynamics: a computational fluid dynamics study. Comput Biol Med. 2022;150:106143. doi:10.1016/j.compbiomed.2022.106143
Fedele M, Faggiano E, Dede' L, Quarteroni A. A patient-specific aortic valve model based on moving resistive immersed implicit surfaces. Biomech Model Mechanobiol. 2017;16(5):1779-1803. doi:10.1007/s10237-017-0919-1
Fumagalli I, Fedele M, Vergara C, et al. An image-based computational hemodynamics study of the systolic anterior motion of the mitral valve. Comput Biol Med. 2020;123:103922. doi:10.1016/j.compbiomed.2020.103922
Fumagalli I, Vitullo P, Vergara C, et al. Image-based computational hemodynamics analysis of systolic obstruction in hypertrophic cardiomyopathy. Front Physiol. 2022;12:2437. doi:10.3389/fphys.2021.787082
Fumagalli I. A reduced 3D-0D FSI model of the aortic valve including leaflets curvature. arXiv preprint arXiv:2106.00571 2021. doi: 10.48550/arXiv.2106.00571
Astorino M, Gerbeau JF, Pantz O, Traoré KF. Fluid-structure interaction and multi-body contact: application to aortic valves. Comput Methods Appl Mech Eng. 2009;198(45-46):3603-3612. doi:10.1016/j.cma.2008.09.012
Dabiri Y, Yao J, Sack KL, Kassab GS, Guccione JM. Tricuspid valve regurgitation decreases after mitraclip implantation: fluid structure interaction simulation. Mech Res Commun. 2019;97:96-100. doi:10.1016/j.mechrescom.2019.04.009
Hsu MC, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJ. Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech. 2014;54(4):1055-1071. doi:10.1007/s00466-014-1059-4
Luraghi G, Wu W, De Gaetano F, et al. Evaluation of an aortic valve prosthesis: fluid-structure interaction or structural simulation? J Biomech. 2017;58:45-51. doi:10.1016/j.jbiomech.2017.04.004
Spühler JH, Jansson J, Jansson N, Hoffman J. 3D fluid-structure interaction simulation of aortic valves using a unified continuum ALE FEM model. Front Physiol. 2018;9:363. doi:10.3389/fphys.2018.00363
Terahara T, Takizawa K, Tezduyar TE, Bazilevs Y, Hsu MC. Heart valve isogeometric sequentially-coupled FSI analysis with the space-time topology change method. Comput Mech. 2020;65:1167-1187. doi:10.1007/s00466-019-01813-0
Bluestein D, Einav S. Transition to turbulence in pulsatile flow through heart valves - a modified stability approach. J Biomech Eng. 1994;116(4):477-487. doi:10.1115/1.2895799
Verkaik AC, Bogaerds ACB, Storti F, Van DeVosse F. A coupled overlapping domain method for the computation of transitional flow through artificial heart valves. Proceedings of the ASME Summer Bioengineering Conference. Am Soc Mech Eng. 2012;217-218.
Vignon-Clementel IE, Figueroa C, Jansen K, Taylor C. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput Methods Biomech Biomed Engin. 2010;13(5):625-640. doi:10.1080/10255840903413565
Bazilevs Y, Calo V, Cottrell J, Hughes T, Reali A, Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng. 2007;197(1-4):173-201. doi:10.1016/j.cma.2007.07.016
Bertoglio C, Caiazzo A. A tangential regularization method for backflow stabilization in hemodynamics. J Comput Phys. 2014;261:162-171. doi:10.1016/j.jcp.2013.12.057
Esmaily M, Bazilevs Y, Hsia TY, Vignon-Clementel IE, Marsden AL. A comparison of outlet boundary treatments for prevention of backflowdivergence with relevance to blood flowsimulations. Comput Mech. 2011;48(3):277-291. doi:10.1007/s00466-011-0599-0
Bazilevs Y, Takizawa K, Tezduyar TE. Computational Fluid-Structure Interaction: Methods and Applications. John Wiley & Sons; 2013.
Blanco PJ, Feijóo RA. A 3D-1D-0D computational model for the entire cardiovascular system. Mec Comput. 2010;29(59):5887-5911.
Quarteroni A, Veneziani A, Vergara C. Geometric multiscale modeling of the cardiovascular system, between theory and practice. Comput Methods Appl Mech Eng. 2016;302:193-252. doi:10.1016/j.cma.2016.01.007
Janela J, Moura dAB, Sequeira A. Comparing absorbing boundary conditions for a 3D non Newtonian fluid-structure interaction model for blood flow in arteries. Mec Comput. 2010;29(59):5961-5971.
Regazzoni F. Mathematical Modeling and Machine Learning for the Numerical Simulation of Cardiac Electromechanics. PhD thesis. Politecnico di Milano, Milano, Italy; 2020.
Krishnamoorthi S, Sarkar M, Klug WS. Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology. Int J Numer Methods Biomed Eng. 2013;29(11):1243-1266. doi:10.1002/cnm.2573
Pathmanathan P, Mirams GR, Southern J, Whiteley JP. The significant effect of the choice of ionic current integration method in cardiac electro-physiological simulations. Int J Numer Methods Biomed Eng. 2011;27(11):1751-1770. doi:10.1002/cnm.1438
Africa PC, Salvador M, Gervasio P, Dede L, Quarteroni A. A matrix-free high-order solver for the numerical solution of cardiac electrophysiology. arXiv Preprint arXiv:2205.05136 2022. doi: 10.48550/arXiv.2205.05136
Saad Y. Iterative Methods for Sparse Linear Systems. SIAM; 2003.
Xu J, Zikatanov L. Algebraic multigrid methods. Acta Numer. 2017;26:591-721. doi:10.1017/S0962492917000083
Salvador M, Dede' L, Quarteroni A. An intergrid transfer operator using radial basis functions with application to cardiac electromechanics. Comput Mech. 2020;66:491-511. doi:10.1007/s00466-020-01861-x
Fedele M, Quarteroni A. Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function. Int J Numer Methods Biomed Eng. 2021;37(4):e3435. doi:10.1002/cnm.3435
VMTK. Accessed October 4, 2022, http://www.vmtk.org/. code repository: https://github.com/marco-fedele/vmtk.
Arndt D, Bangerth W, Blais B, et al. The deal.II library, version 9.2. J Numer Math. 2020;28(3):131-146. doi:10.1515/jnma-2020-0043
Arndt D, Bangerth W, Davydov D, et al. The deal.II finite element library: design, features, and insights. Comput Math Appl. 2021;81:407-422. doi:10.1016/j.camwa.2020.02.022
Official deal.ii. Accessed: October 4, 2022. https://www.dealii.org/.
Maceira AM, Prasad SK, Khan M, Pennell DJ. Normalized left ventricular systolic and diastolic function by steady state free precession cardiovascular magnetic resonance. J Cardiovasc Magn Reson. 2006;8(3):417-426. doi:10.1080/10976640600572889
Clay S, Alfakih K, Radjenovic A, Jones T, Ridgway JP. Normal range of human left ventricular volumes and mass using steady state free precession MRI in the radial long axis orientation. MAGMA. 2006;19(1):41-45. doi:10.1007/s10334-005-0025-8
Sugimoto T, Dulgheru R, Bernard A, et al. Echocardiographic reference ranges for normal left ventricular 2D strain: results from the EACVI NORRE study. Eur Heart J Cardiovasc Imaging. 2017;18(8):833-840. doi:10.1093/ehjci/jex140
Hammermeister K, Brooks R, Warbasse J. The rate of change of left ventricular volume in man: I. validation and peak systolic ejection rate in health and disease. Circulation. 1974;49(4):729-738. doi:10.1161/01.CIR.49.4.729
Fabian J, Epstein E, Coulshed N. Duration of phases of left ventricular systole using indirect methods. I. Normal subjects. Br Heart J. 1972;34(9):874-881. doi:10.1136/hrt.34.9.874
Benchimol A, Ellis JG. A study of the period of isovolumic relaxation in normal subjects and in patients with heart disease. Am J Cardiol. 1967;19(2):196-206. doi:10.1016/0002-9149(67)90533-4
LittleWC DTR. Clinical evaluation of left ventricular diastolic performance. Prog Cardiovasc Dis. 1990;32(4):273-290. doi:10.1016/0033-0620(90)90017-V
Emilsson K, Egerlid R, Nygren BM, Wandt B. Mitral annulus motion versus long-axis fractional shortening. Exp Clin Cardiol. 2006;11(4):302.
Hawthorne EW. Dynamic geometry of the left ventricle. Am J Cardiol. 1966;18(4):566-573. doi:10.1016/0002-9149(66)90012-9
Feher JJ. Quantitative Human Physiology: An Introduction. Academic Press; 2017.
Gulsin G, Singh A, McCann GP. Cardiovascular magnetic resonance in the evaluation of heart valve disease. BMC Med Imaging. 2017;17(1):1-14. doi:10.1186/s12880-017-0238-0
Kumar V, Abbas AK, Fausto N, Aster JC. Robbins and Cotran Pathologic Basis of Disease, Professional Edition e-book. Elsevier Health Science; 2014.
Stanfield CL. Principles of Human Physiology. Pearson; 2016.
Mark JB. Atlas of Cardiovascular Monitoring. Churchill Livingstone; 1998.
Murgo JP, Westerhof N, Giolma JP, Altobelli SA. Aortic input impedance in normal man: relationship to pressure wave forms. Circulation. 1980;62(1):105-116. doi:10.1161/01.CIR.62.1.105
Dusch MN, Thadani SR, Dhillon GS, Hope MD. Diastolic function assessed by cardiac MRI using longitudinal left ventricular fractional shortening. Clin Imaging. 2014;38(5):666-668. doi:10.1016/j.clinimag.2014.06.002
Pandian NG, Skorton DJ, Collins SM, Falsetti HL, Burke ER, Kerber RE. Heterogeneity of left ventricular segmental wall thickening and excursion in 2-dimensional echocardiograms of normal human subjects. Am J Cardiol. 1983;51(10):1667-1673. doi:10.1016/0002-9149(83)90207-2
Di Labbio G, Kadem L. Jet collisions and vortex reversal in the human left ventricle. J Biomech. 2018;78:155-160. doi:10.1016/j.jbiomech.2018.07.023
Pedrizzetti G, La Canna G, Alfieri O, Tonti G. The vortex-an early predictor of cardiovascular outcome? Nat Rev Cardiol. 2014;11(9):545-553. doi:10.1038/nrcardio.2014.75
Lee AW, Nguyen UC, Razeghi O, et al. A rule-based method for predicting the electrical activation of the heart with cardiac resynchronization therapy from non-invasive clinical data. Med Image Anal. 2019;57:197-213. doi:10.1016/j.media.2019.06.017
Ma X, Gao H, Griffith BE, Berry C, Luo X. Image-based fluid-structure interaction model of the human mitral valve. Comput Fluids. 2013;71:417-425. doi:10.1016/j.compfluid.2012.10.025
Jhun CS, Newswanger R, Cysyk JP, et al. Dynamics of blood flows in aortic stenosis: mild, moderate, and severe. ASAIO J. 2021;67(6):666-674. doi:10.1097/MAT.0000000000001296
Wood P. Aortic stenosis. Am J Cardiol. 1958;1(5):553-571. doi:10.1016/0002-9149(58)90138-3
Sahasakul Y, Edwards WD, Naessens JM, Tajik AJ. Age-related changes in aortic and mitral valve thickness: implications for two-dimensional echocardiography based on an autopsy study of 200 normal human hearts. Am J Cardiol. 1988;62(7):424-430. doi:10.1016/0002-9149(88)90971-X

Auteurs

Michele Bucelli (M)

MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.

Alberto Zingaro (A)

MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.

Pasquale Claudio Africa (PC)

MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.

Ivan Fumagalli (I)

MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.

Luca Dede' (L)

MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.

Alfio Quarteroni (A)

MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.
Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.

Articles similaires

[Redispensing of expensive oral anticancer medicines: a practical application].

Lisanne N van Merendonk, Kübra Akgöl, Bastiaan Nuijen
1.00
Humans Antineoplastic Agents Administration, Oral Drug Costs Counterfeit Drugs

Smoking Cessation and Incident Cardiovascular Disease.

Jun Hwan Cho, Seung Yong Shin, Hoseob Kim et al.
1.00
Humans Male Smoking Cessation Cardiovascular Diseases Female
Humans United States Aged Cross-Sectional Studies Medicare Part C
1.00
Humans Yoga Low Back Pain Female Male

Classifications MeSH