Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface method.
cardiac hemodynamics
cardiac modeling
valves
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:
24 Aug 2023
24 Aug 2023
Historique:
revised:
05
06
2023
received:
19
08
2022
accepted:
30
07
2023
medline:
24
8
2023
pubmed:
24
8
2023
entrez:
24
8
2023
Statut:
aheadofprint
Résumé
A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. These oscillations can strongly affect valve dynamics models driven by the blood flow, making unlikely to recovering physiological dynamics. Hence, prescribed opening and closing times are usually employed, or the isovolumetric phases are neglected altogether. In this article, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., Biomech Model Mechanobiol 2017, 16, 1779-1803) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., Int J Numer Methods Biomed Eng 2020, 36, e3223) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. Finally, we demonstrate that by the new method the cardiac valves can open and close without prescribing any opening/closing times.
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
e3767Subventions
Organisme : Ministero dell'Istruzione, dell'Università e della Ricerca
ID : 2017AXL54F
Informations de copyright
© 2023 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.
Références
Quarteroni A, Dede' L, Manzoni A, et al. 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.
Formaggia L, Lamponi D, Tuveri M, Veneziani A. Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput Methods Biomech Biomed Eng. 2006;9(5):273-288.
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(December):1-13.
Bucelli M, Dede' L, Quarteroni A, Vergara C. Partitioned and monolithic FSI schemes for the numerical simulation of the heart. Commun Comput Phys. 2022;32:1217-1256.
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.
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.
Nordsletten D, McCormick M, Kilner PJ, Hunter P, Kay D, Smith NP. 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.
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.
Bucelli M, Zingaro A, Africa PC, Fumagalli I, Dede' L, Quarteroni AM. A mathematical model that integrates cardiac electrophysiology, mechanics and fluid dynamics: application to the human left heart. Int J Numer Methods Biomed Eng. 2022;39:e3678.
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.
Watanabe H, Hisada T, Sugiura S, Okada J, Fukunari H. Computer simulation of blood flow, left ventricular wall motion and their interrelationship by fluid-structure interaction finite element method. JSME Int J Ser C Mech Syst Mach Elem Manuf. 2002;45(4):1003-1012.
Viola F, Meschini V, Verzicco R. Fluid-structure-electrophysiology interaction (FSE) in the leftheart: a multi-way coupled computational model. Eur J Mech-B/Fluids. 2020;79:212-232.
Choi YJ, Constantino J, Vedula V, Trayanova N, Mittal R. A new MRI-based model of heart function with coupled hemodynamics and application to normal and diseased canine left ventricles. Front Bioeng Biotechnol. 2015;3:140.
Tagliabue A, Dede' L, Quarteroni A. Fluid dynamics of an idealized left ventricle: the extended Nitsche's method for the treatment of heart valves as mixed time varying boundary conditions. Int J Numer Methods Fluids. 2017;85(3):135-164.
Zingaro A, Dede' L, Menghini F, Quarteroni A. Hemodynamics of the heart's left atrium based on a variational multiscale-LES numerical method. Eur J Mech-B/Fluids. 2021;89:380-400.
Domenichini F, Pedrizzetti G, Baccani B. Three-dimensional filling flow into a model left ventricle. J Fluid Mech. 2005;539:179-198.
Baccani B, Domenichini F, Pedrizzetti G. Vortex dynamics in a model left ventricle during filling. Eur J Mech-B/Fluids. 2002;21(5):527-543.
Mittal R, Seo Jung H, Vedula V, et al. Computational modeling of cardiac hemodynamics: current status and future outlook. J Comput Phys. 2016;305:1065-1082.
Corti M, Zingaro A, Dede' L, Quarteroni A. Impact of atrial fibrillation on left atrium haemodynamics: a computational fluid dynamics study. Comput Biol Med. 2022;150:106143.
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.
This A, Morales Hernán G, Bonnefous O, Fernández Miguel A, Gerbeau J-F. A pipeline for image based intracardiac CFD modeling and application to the evaluation of the PISA method. Comput Methods Appl Mech Eng. 2020;358:112627.
Chnafa C, Mendez S, Nicoud F. Image-based large-eddy simulation in a realistic left heart. Comput Fluids. 2014;94:173-187.
Masci A, Alessandrini M, Forti D, et al. A proof of concept for computational fluid dynamic analysis of the left atrium in atrial fibrillation on a patient-specific basis. J Biomech Eng. 2020;142(1):011002.
Bennati L, Vergara C, Giambruno V, et al. An image-based computational fluid dynamics study of mitral regurgitation in presence of prolapse. Cardiovasc Eng Technol. 2023;14:457-475.
Bennati L, Giambruno V, Renzi F, et al. Turbulence and blood washout in presence of mitral regurgitation: a computational fluid-dynamics study in the complete left heart. bioRxiv; 2023;2023-03.
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.
Augustin Christoph M, Crozier A, Neic A, et al. Patient-specific modeling of left ventricular electromechanics as a driver for haemodynamic analysis. EP Europace. 2016;18(suppl_4):iv121-iv129.
This A, Boilevin-Kayl L, Fernández Miguel A, Gerbeau J-F. 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.
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 Dynam Syst S. 2022;15(8):2391-2427.
Zingaro A, Bucelli M, Piersanti R, Regazzoni F, Dede' L, Quarteroni A. An electromechanics-driven fluid dynamics model for the simulation of the whole human heart. arXiv Preprint arXiv:2301.02148; 2023.
Zingaro A, Vergara C, Dede' L, Regazzoni F, Quarteroni A. A comprehensive mathematical model for cardiac perfusion. arXiv Preprint arXiv:2303.13914; 2023.
Fedele M, Piersanti R, Regazzoni F, et al. A comprehensive and biophysically detailed computational model of the whole human heart electromechanics. Comput Methods Appl Mech Eng. 2023;410:115983.
Cheng R, Lai Yong G, Chandran Krishnan B. Three-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics. Ann Biomed Eng. 2004;32(11):1471-1483.
Espino Daniel M, Shepherd Duncan ET, Hukins David WL. Evaluation of a transient, simultaneous, arbitrary Lagrange-Euler based multi-physics method for simulating the mitral heart valve. Comput Methods Biomech Biomed Eng. 2014;17(4):450-458.
Basting S, Quaini A, Čanić S, Glowinski R. Extended ALE method for fluid-structure interaction problems with large structural displacements. J Comput Phys. 2017;331:312-336.
Jianhai Z, Dapeng C, Shengquan Z. ALE finite element analysis of the opening and closing process of the artificial mechanical valve. Appl Math Mech. 1996;17(5):403-412.
Nestola Maria GC, Faggiano E, Vergara C, et al. Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses. Comput Methods Biomech Biomed Eng. 2017;20(2):171-181.
Fernández Miguel A, Gerbeau J-F, Martin V. Numerical simulation of blood flows through a porous interface. ESAIM: Math Modell Numer Anal. 2008;42(6):961-990.
Astorino M, Hamers J, Shadden Shawn C, Gerbeau J-F. A robust and efficient valve model based on resistive immersed surfaces. Int J Numer Methods Biomed Eng. 2012;28(9):937-959.
Spühler Jeannette H, 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.
Alauzet F, Fabrèges B, Fernández Miguel A, Landajuela M. Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures. Comput Methods Appl Mech Eng. 2016;301:300-335.
Hansbo P, Larson Mats G, Zahedi S. Characteristic cut finite element methods for convection-diffusion problems on time dependent surfaces. Comput Methods Appl Mech Eng. 2015;293:431-461.
Erik B, Fernández Miguel A. An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes. Comput Methods Appl Mech Eng. 2014;279:497-514.
Mayer Ursula M, Popp A, Gerstenberger A, WallWolfgang A. 3D fluid-structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach. Comput Mech. 2010;46(1):53-67.
Massing A, Larson M, Logg A, Rognes M. A Nitsche-based cut finite element method for a fluid-structure interaction problem. Commun Appl Math Comput Sci. 2015;10(2):97-120.
Gerstenberger A, Wall Wolfgang A. An extended finite element method/Lagrange multiplier based approach for fluid-structure interaction. Comput Methods Appl Mech Eng. 2008;197(19-20):1699-1714.
Zonca S, Vergara C, Formaggia L. An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach. SIAM J Sci Comput. 2018;40(1):B59-B84.
Peskin CS. Flow patterns around heart valves: a numerical method. J Comput Phys. 1972;10(2):252-271.
Borazjani I, Ge L, Sotiropoulos F. High-resolution fluid-structure interaction simulations of flow through a bi-leaflet mechanical heart valve in an anatomic aorta. Ann Biomed Eng. 2010;38(2):326-344.
Griffith BE. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int J Numer Methods Biomed Eng. 2012;28(3):317-345.
Hsu M-C, Kamensky D, Bazilevs Y, Sacks Michael S, Hughes Thomas JR. Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech. 2014;54(4):1055-1071.
Wu Michael CH, Zakerzadeh R, Kamensky D, Kiendl J, Sacks Michael S, Hsu M-C. An anisotropic constitutive model for immersogeometric fluid-structure interaction analysis of bioprosthetic heart valves. J Biomech. 2018;74:23-31.
Liu Wing K, Liu Y, Farrell D, et al. Immersed finite element method and its applications to biological systems. Comput Methods Appl Mech Eng. 2006;195(13-16):1722-1749.
Yang J, Yu F, Krane M, Zhang LT. The perfectly matched layer absorbing boundary for fluid-structure interactions using the immersed finite element method. J Fluids Struct. 2018;76:135-152.
Nestola Maria GC, Becsek B, Zolfaghari H, et al. An immersed boundary method for fluid-structure interaction based on variational transfer. J Comput Phys. 2019;398:108884.
Oks D, Samaniego C, Houzeaux G, Butakoff C, Vázquez M. Fluid-structure interaction analysis of eccentricity and leaflet rigidity on thrombosis biomarkers in bioprosthetic aortic valve replacements. Int J Numer Methods Biomed Eng. 2022;38(12):e3649.
Glowinski R, Pan T-W, Periaux J. A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori. C R l'Acad Sci-Ser I-Math. 1997;324(3):361-369.
Astorino M, Gerbeau J-F, Pantz O, Traore K-F. Fluid-structure interaction and multi-body contact: application to aortic valves. Comput Methods Appl Mech Eng. 2009;198(45-46):3603-3612.
Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U. 3D simulation of wind turbine rotors at full scale. Part II: fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids. 2011;65(1-3):236-253.
Kamensky D, Hsu M-C, Schillinger D, et al. An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Methods Appl Mech Eng. 2015;284:1005-1053.
De Hart J, Peters GWM, Schreurs PJG, Baaijens FPT. A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. J Biomech. 2003;36(1):103-112.
Loon R, Anderson PD, Vosse FN. A fluid-structure interaction method with solid-rigid contact for heart valve dynamics. J Comput Phys. 2006;217(2):806-823.
Morsi Yos S, Yang William W, Wong Cynthia S, Das S. Transient fluid-structure coupling for simulation of a trileaflet heart valve using weak coupling. J Artif Organs. 2007;10(2):96-103.
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.
Marom G. Numerical methods for fluid-structure interaction models of aortic valves. Arch Comput Methods Eng. 2015;22(4):595-620.
Votta E, Le TB, Stevanella M, et al. Toward patient-specific simulations of cardiac valves: state-ofthe-art and future directions. J Biomech. 2013;46(2):217-228.
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.
Schenkel T, Malve M, Reik M, Markl M, Jung B, Oertel H. MRI-based CFD analysis of flow in a human left ventricle: methodology and application to a healthy heart. Ann Biomed Eng. 2009;37(3):503-515.
Bavo AM, Pouch Alison M, Degroote J, et al. Patient-specific CFD models for intraventricular flow analysis from 3D ultrasound imaging: comparison of three clinical cases. J Biomech. 2017;50:144-150.
Quarteroni A, Sacco R, Saleri F. Numerical Mathematics. Springer Science & Business Media; 2010.
Doyle MG, Tavoularis S, Bougault Y. Application of fluid-structure interaction to numerical simulations in the left ventricle. Trans Can Soc Mech Eng. 2015;39(4):749-766.
Küttler U, Förster C, Wall WA. A solution for the incompressibility dilemma in partitioned fluid-structure interaction with pure Dirichlet fluid domains. Comput Mech. 2006;38:417-429.
Perktold K, Thurner E, Kenner T. Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models. Med Biol Eng Comput. 1994;32(1):19-26.
Taylor CA, Hughes TJR, Zarins CK. Finite element modeling of blood flow in arteries. Comput Methods Appl Mech Eng. 1998;158(1-2):155-196.
Formaggia L, Quarteroni A, Veneziani A. Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System. Springer Science & Business Media; 2010.
Donea J, Giuliani S, Halleux J-P. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput Methods Appl Mech Eng. 1982;33(1-3):689-723.
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.
Fumagalli I. A reduced 3D-0D FSI model of the aortic valve including leaflets curvature. arXiv Preprint arXiv:2106.00571; 2021.
Quarteroni A. Numerical Models for Differential Problems. Springer; 2017.
Tezduyar TE. Stabilized finite element formulations for incompressible flow computations. In: Hutchinson John W, Wu Theodore Y, eds. Advances in Applied Mechanics. Elsevier; 1991:1-44.
Bazilevs Y, Calo VM, Cottrell JA, Hughes Thomas JR, 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.
Forti D, Dede' L. Semi-implicit BDF time discretization of the Navier-stokes equations with VMS-LES modeling in a high performance computing framework. Comput Fluids. 2015;117:168-182.
Jasak H, Tukovic Z. Automatic mesh motion for the unstructured finite volume method. Transa FAMENA. 2006;30(2):1-20.
Africa PC. lifex: a flexible, high performance library for the numerical solution of complex finite elements. SoftwareX. 2022;20:101252.
Africa PC, Piersanti R, Fedele M, Dede' L, Quarteroni A. Lifex-fiber: an open tool for myofibers generation in cardiac computational models. BMC Bioinform. 2023;24(1):143.
Arndt D, Bangerth W, Blais B, et al. The deal.II library, version 9.3. J Numer Math. 2021;29:29-186.
Arndt D, Bangerth W, Davydov D, et al. The deal.II finite element library: design, features, and insights. Comput Math Appl. 2020;81:407-422.
Official deal.ii website. https://www.dealii.org/
Africa PC, Fumagalli I, Bucelli M, et al. lifex-cfd: an open-source computational fluid dynamics solver for cardiovascular applications. arXiv preprint arXiv:2304.12032 2023.
Africa PC, Fumagalli I, Bucelli M, et al. Lifex-cfd: an open-source computational fluid dynamics solver for cardiovascular applications. arXiv Preprint arXiv:2304.12032; 2023. doi:10.5281/zenodo.7852089
Blanco Pablo J, Feijoo Raul A. A 3D-1D-0D computational model for the entire cardiovascular system. Mecan Comput. 2010;24:5887-5911.
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.
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.
Inc Zygote Media Group. Zygote solid 3D heart generation II development report. Technical Development of 3D Anatomical Systems; 2014.
Antiga L, Piccinelli M, Botti L, Ene-Iordache B, Remuzzi A, Steinman DA. An imagebased modeling framework for patient-specific computational hemodynamics. Med Biol Eng Comput. 2008;46(11):1097-1112.
Fedele M, Quarteroni AM. Polygonal surface processing and mesh generation tools for numerical simulations of the complete cardiac function. Int J Numer Methods Biomed Eng. 2021;37:e3435.
De Boor C. A Practical Guide to Splines. Springer-Verlag; 1978.
Korakianitis T, Shi Y. Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves. J Biomech. 2006;39(11):1964-1982.
Ten Tusscher Kirsten HWJ, Panfilov AV. Alternans and spiral breakup in a human ventricular tissue model. Am J Physiol Heart Circ Physiol. 2006;291(3):H1088-H1100.
Colli FP, Pavarino LF, Scacchi S. Mathematical Cardiac Electrophysiology. Springer; 2014.
Salvador M, Regazzoni F, Pagani S, et al. The role of mechano-electric feedbacks and hemodynamic coupling in scar-related ventricular tachycardia. Comput Biol Med. 2022;142:105203.
Regazzoni F, Dede' L, Quarteroni A. Biophysically detailed mathematical models of multiscale cardiac active mechanics. PLoS Comput Biol. 2020;16(10):e1008294.
Usyk TP, Mazhari R, McCulloch AD. Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle. J Elast Phys Sci Solids. 2000;61(1):143-164.