Modelling left ventricular function under assist device support

International Journal for Numerical Methods in Biomedical Engineering

Volumn 27, Issue 7, 2011, Pages 1073-1095

  Mccormick, M ^a   Nordsletten, D ^b   Kay, D ^a   Smith, N ^a,b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Arbitrary Lagrangian Eulerian; Fictitious domain; Finite elasticity; Fluid mechanics; LVAD; Mechanical heart modelling

Indexed keywords

ARBITRARY LAGRANGIAN EULERIAN; FICTITIOUS DOMAINS; FINITE ELASTICITY; LVAD; MECHANICAL HEART;

CONTACTS (FLUID MECHANICS); ELASTICITY; ENERGY TRANSFER; FINITE DIFFERENCE METHOD; FLUID MECHANICS; FLUIDS; RIGID STRUCTURES;

COMPUTER SIMULATION;

EID: 79959722838     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1428     Document Type: Article

References (57)

1. Arabia F, Smith R, Rose D, Arzouman D, Sethi G, Copeland J. The success rates of long-term circulatory assist devices used currently for bridge to heart transplantation. The ASAIO Journal 1996 42:542-546.
2. Klotz S, Deng M, Stypmann J. Left ventricular pressure and volume unloading during pulsatile versus nonpulsatile left ventricular assist device support. Annals of Thoracic Surgery 2004; 77:143-149.
3. Opie L. Heart Physiology (4th edn), Lippincott Williams and Wilkins: Philadelphia, 2004.
4. Mancini D, Beniaminovits A, Levin H. The low incidence of myocardial recovery after left ventricular assist device implantation in patients with chronic heart failure. Circulation 1998; 98:2383-2389.
5. Birks E, Yacoub M, Banner N, Khaghani A. The role of bridge to transplantation: should LVAD patients be transplanted. Current Opinion in Cardiology 2004; 19:148-153.
6. Burkhoff D, Klotz S, Mancini D. LVAD induced reverse remodeling: basic and clinical implications for myocardial recovery. Journal of Cardiac Failure 2006; 12:227-239.
7. Williams M, Oz M. The Indications and patient selection for mechanical ventricular assistance. Annals of Thoracic Surgery 2001; 71:86-91.
8. Yang G, Merrifield R, Sharmeen M, Kilner P. Flow and myocardial interaction: an imaging perspective. Philosophical Transactions of the Royal Society 2007; 362:1329-1341.
9. Kilner P, Yang G, Wilkes A, Mohiaddin R, Firmin D, Yacoub M. The asymmetric redirection of flow through the heart. Nature 2000; 404:759-761.
10. Kilner P, Henein M, Gibson D. Our tortuous heart in dynamic mode: an echocardiographic study of mitral flow and movement in exercising subjects. Heart Vessels 1997; 12:103-110.
11. McQueen D. Peskin, C. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Computers and Graphics 2000; 34:56-60.
12. Peskin C, McQueen DM. Fluid dynamics of the heart and its valves. In Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, Othmer HG, Adler FR, Lewis MA, Dallon JC (eds). Prentice-Hall: Englewood Cliffs, NJ, 1996; 309-337.
13. Peskin C. Fiber architecture of the left ventricular wall: an asymptotic analysis. Communications on Pure and Applied Mathematics 1989; 42:79-113.
14. 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 International Journal 2002; 45:1003-1012.
15. Nordsletten D, McCormick M, Kilner P, Kay D, Smith N. Fluid-solid coupling for the investigation of diastolic and systolic human left ventricular function. International Journal for Numerical Methods in Biomedical Engineering, DOI: 10.1002/cnm.1405.
16. Reesink K, Dekker A, der Nagel TV, Beghi C, Leonardi F, Botti P, Cicco GD, Lorusso R, der Veen FV, Maessen J. Suction due to left ventricular assist: implications for device control and management. Artificial Organs 2007; 31:542-549.
17. Bertrand F, Tanguy P, Thibault F. A three-dimensional fictitious domain method for incompressible fluid flow problems. International Journal for Numerical Methods in Fluids 1997; 25:719-736.
18. Baaijens F. A fictitious domain/mortar element method for fluid-structure interaction. International Journal for Numerical Methods in Fluids 2001; 35:743-761.
19. van Loon R, Anderson P, van de Vosse F. A fluid-structure interaction method with solid-rigid contact for heart valve dynamics. Journal of Computational Physics 2006; 217:806-823.
20. Peskin C. Flow patterns around heart valves: a numerical method. Journal of Computational Physics 1972; 10:252-271.
21. Glowinski R, Pan T, Hesla T, Joseph D. A distributed lagrange multiplier/fictitious domain method for particulate flows. International Journal of Multiphase Flow 1999; 25:755-794.
22. Diaz-Goano C, Minev P, Nandakumar K. A distributed Lagrange multiplier/fictitious domain method for particulate flos. Journal of Computational Physics 2003; 192:105-123.
23. Wan D, Turek S. Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows. Journal of Computational Physics 2007; 222:28-56.
24. Glowinski R, Pan T, Hesla T, Joseph D, Periaux J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. Journal of Computational Physics 2001; 169:363-426.
25. Hart JD, Peters G, Schreuers P, Baaijens F. A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. Journal of Biomechanics 2003; 36, 103-112.
26. Stijnen J, Hart JD, Bovendeerd P, van de Vosse F. Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves. Journal of Fluids and Structures 2004; 19:835-850.
27. Nordsletten D, Hunter P, Smith N. Conservative and non-conservative arbitrary Lagrangian-Eulerian forms for ventricular flows. International Journal for Numerical Methods in Biomedical Engineering 2008; 56:1457-1463.
28. Nordsletten D, Kay D, Smith N. A non-conforming monolithic finite element method for problems of coupled mechanics. Journal of Computational Physics 2010; 20:7571-7593.
29. Girault V, Raviart P. Finite Element Methods for Navier-Stokes Equations. Springer: Berlin, 1986.
30. Nobile F. Numerical approximation of fluid-structure interaction problems with application to haemodynamics. Ph.D. Thesis, Ecole Polytechnique Federale de Lausanne, 2001.
31. Nordsletten D, Smith N, Kay D. A preconditioner for the finite element approximation to the ALE Navier-Stokes equations. SIAM Journal on Scientific Computing 32:521-543.
32. Oertel H, Spiegel K, Donisi S. Modelling the Human Cardiac Fluid Mechanics. Universitatsverlag karlsruhe, 2006.
33. Hirt C, Amsden A, Cook J. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 1974; 14:227-253.
34. Donea J, Huerta A, Ponthot J, A. Rodr'iguez-Ferran Arbitrary Lagrangian-Eulerian methods. Encyclopedia of Computational Mechanics 2004; 1. DOI: 10.1002/0470091355.ecm009.
35. Costa K, Holmes J, McCulloch A. Modeling cardiac mechanical properties in three dimensions. Philosophical Transactions of the Royal Society 2001; 359:1233-1250.
36. Huyghe J, Arts T, Campen D, Reneman R. The Porous medium finite element model of the beating left ventricle. American Journal of Physiology 1992; 262:H1256-H1267.
37. Nash M. Mechanics and material properties of the heart using an anatomically accurate mathematical model. Ph.D. Thesis, University of Auckland, 1998.
38. Nash M, Hunter P. Computational mechanics of the heart. Journal of Elasticity 2000; 61:113-141.
39. Nickerson D, Smith N, Hunter P. A model of cardiac cellular electromechanics. Philosophical Transactions of the Royal Society 2001; 359:1159-1172.
40. Stevens C, Remme E, LeGrice I, Hunter P. Ventricular mechanics in diastole: material parameter sensitivity. Journal of Biomechanics 2003; 36:737-748.
41. Stevens C. An anatomically-based computational study of cardiac mechanics and myocardial infarction. Ph.D. Thesis, 2002.
42. Lemmon J, Yoganathan A. Computational modeling of left heart diastolic function: examination of ventricular dysfunction. Journal of Elasticity 2000; 122:297-303.
43. Brezzi F, Douglas J, Duran R, Fortin M. Mixed finite elements for second order elliptic problems in three variables. Numerical Mathematics 1987; 51:237-250.
44. Gresho P, Sani R. Incompressible Flow and the Finite Element Method II, Isothermal Laminar Flow. Wiley: New York, 1998.
45. Quarteroni A, Valli A. Numerical Approximation of Partial Differential Equations. Springer: Berlin, 1994.
46. Zienkiewicz O, Taylor R. The Finite Element Method. Elsevier: Amsterdam, 2000.
47. Dennis J, Schnabel R. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall Inc.: New York, 1996.
48. Dennis S, Chang G. Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. Journal of Fluid Mechanics 1970; 42:471-489.
49. Fornberg B. A numerical study of steady viscous flow past a circular cylinder. Journal of Fluid Mechanics 1980; 98:819-855.
50. McCormick M, Nordsletten D, de Vecchi A, Kay D, Smith N. Fluid-mechanics simulations of ventricular function under LVAD support. Conference: Medical Physics and Biomedical Engineering, Munich, 2009.
51. LeGrice I, Smaill B, Chai L, Edgar S, Gavin J, Hunter P. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. American Journal of Physiology 1995; 269:H571-H582.
52. LeGrice I, Hunter P, Young A, Smaill B. The architecture of the heart: a data-based model. Philosophical Transactions of the Royal Society 2001; 359:1217-1232.
53. Rajagopal M, Chung J, Bullivant D, Nielsen P, Nash M. Determining the finite elasticity reference state from a loaded configuration. International Journal for Numerical Methods in Engineering 2007; 72:1434-1451.
54. Niederer S, Smith N. An improved numerical method for strong coupling of excitation and contraction models in the heart. Progress in Biophysics and Molecular Biology 2008; 96:90-111.
55. Nordsletten D, Niederer S, Nash M, Hunter P, Smith N. Coupling multi-physics models to cardiac mechanics. Progress in Biophysics and Molecular Biology, 2009.
56. Pantalos G, Koenig S, Gillars K, Giridharan G, Ewert D. Characterisation of an adult mock circulation for testing cardiac support devices. ASAIO 2004; 50:37-46.
57. Kerckhoffs P, Neal M, Gu Q, Bassingthwaighte J, Omens J. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Annals of Biomedical Engineering 2007; 35:1-18.