Numerical treatment of boundary conditions to replace lateral branches in hemodynamics

International Journal for Numerical Methods in Biomedical Engineering

Volumn 28, Issue 12, 2012, Pages 1165-1183

  Porpora, A ^a   Zunino, P ^a,b   Vergara, C ^c   Piccinelli, M ^d  

^a POLITECNICO DI MILANO   (Italy)

^b PA 15260   (United States)

^c UNIVERSITY OF BERGAMO   (Italy)

^d EMORY UNIVERSITY   (United States)

Author keywords

Fluid structure interaction problems; Lateral branch exclusion; Vascular reconstruction; Weak enforcement of boundary conditions

Indexed keywords

COMPLIANT WALLS; COMPUTATIONAL DOMAINS; COMPUTATIONAL HEMODYNAMICS; FLOW RATE CONDITIONS; FLUID-STRUCTURE INTERACTION PROBLEM; GEOMETRICAL RECONSTRUCTION; LATERAL BRANCH EXCLUSION; NUMERICAL RESULTS; NUMERICAL TREATMENTS; VASCULAR RECONSTRUCTION;

COMPUTER SIMULATION; HEMODYNAMICS; NUMERICAL METHODS;

BOUNDARY CONDITIONS;

ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; BIOMEDICAL ENGINEERING; COMPUTER SIMULATION; HEMODYNAMICS; HISTOLOGY; HUMAN; IMAGE PROCESSING; MECHANICAL STRESS; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; PHYSIOLOGY; PRESSURE; THORACIC AORTA;

AORTA, THORACIC; BIOMECHANICS; BIOMEDICAL ENGINEERING; COMPUTER SIMULATION; HEMODYNAMICS; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; MODELS, CARDIOVASCULAR; PRESSURE; STRESS, MECHANICAL;

EID: 84872387511     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.2488     Document Type: Article

References (39)

1. Perktold K, Hilbert D. Numerical simulation of pulsatile flow in a carotid bifurcation model. Journal of Biomedical Engineering 1986; 8(3):193-199.
2. Heywood JG, Rannacher R, Turek S. Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1996; 22(5):325-352.
3. Formaggia L, Quarteroni A (eds). AV. Cardiovascular Mathematics-Modeling and Simulation of the Circulatory System, Springer, 2009.
4. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A. Numerical treatment of defective boundary conditions for the Navier-Stokes equations. SIAM Journal on Numerical Analysis 2002; 40(1):376-401. (electronic).
5. Veneziani A, Vergara C. Flow rate defective boundary conditions in haemodynamics simulations. International Journal for Numerical Methods in Fluids 2005; 47(8-9):803-816, DOI: 10.1002/fld.843.
6. Veneziani A, Vergara C. An approximate method for solving incompressible Navier-Stokes problems with flow rate conditions. Computer Methods in Applied Mechanics and Engineering 2007; 196(9-12):1685-1700, DOI: 10.1016/j.cma.2006.09.011.
7. Formaggia L, Veneziani A, Vergara C. A new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics. SIAM Journal on Numerical Analysis 2008; 46(6):2769-2794.
8. Vignon-Clementel IE, AlbertoFigueroa C, Jansen KE, Taylor CA. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Computer Methods in Applied Mechanics and Engineering 2006; 195(29-32):3776-3796.
9. Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Computer Methods in Biomechanics and Biomedical Engineering 2010; 13(5):625-640.
10. Zunino P. Numerical approximation of incompressible flows with net flex defective boundary conditions by means of penalty techniques. Computer Methods in Applied Mechanics and Engineering 2009; 198(37-40):3026-3038, DOI: 10.1016/j.cma.2009.05.010.
11. Nitsche JA. Uber ein variationsprinzip zur lozung von dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind. Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 1970/71; 36:9-15.
12. Vergara C. Nitsche's method for defective boundary value problems in incompressible fluid-dynamics. Journal of Scientific Computing 2011; 46(1):100-123, DOI: 10.1007/s10915-010-9389-7.
13. Bazilevs Y, Gohean J, Hughes T, Moser R, Zhang Y. Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Computer Methods in Applied Mechanics and Engineering 2009; 198(45-46):3534-3550.
14. Esmaily Moghadam M, Bazilevs Y, Hsia T, Vignon-Clementel IE, Marsden AL. A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Computational Mechanics 2011:1-15. Article in Press.
15. Kim HJ, Figueroa CA, Hughes TJR, Jansen KE, Taylor CA. Augmented lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow. Computer Methods in Applied Mechanics and Engineering 2009; 198(45-46):3551-3566.
16. Vincent P, Hunt A, Grinberg L, Sherwin S, Weinberg P. A realistic representation of the rabbit aorta for use in computational haemodynamic studies. ASME Summer Bioengineering Conference, AMER SOC Mechanical Engineers 2009:985-986.
17. Moireau P, Xiao N, Astorino M, Figueroa CA, Chapelle D, Taylor CA, Gerbeau JF. External tissue support and fluid-structure simulation in blood flows. Biomechanics and Modeling in Mechanobiology 2011, DOI: 10.1007/s10237-011-0289-z.
18. Nobile F, Vergara C. An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM Journal on Scientific Computing 2008; 30(2):731-763, DOI: 10.1137/060678439.
19. Vincent PE, Plata AM, Hunt AAE, Weinberg PD, Sherwin SJ. Blood flow in the rabbit aortic arch and descending thoracic aorta. Journal of the Royal Society Interface 2011, DOI: 10.1098/rsif.2011.0116.
20. Kazakidi A, Plata AM, Sherwin SJ, Weinberg PD. Effect of reverse flow on the pattern of wall shear stress near arterial branches. Journal of the Royal Society Interface 2011, DOI: 10.1098/rsif.2011.0108s.
21. Kazakidi A, Sherwin S, Weinberg P. Effect of reynolds number and flow division on patterns of haemodynamic wall shear stress near branch points in the descending thoracic aorta. Journal of the Royal Society Interface 2009; 6(35):539-548, DOI:10.1098/rsif.2008.0323.
22. Kim HJ, Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA. Developing computational methods for three-dimensional finite element simulations of coronary blood flow. Finite Elements in Analysis and Design 2010; 46(6):514-525.
23. Kim HJ, Vignon-Clementel IE, Figueroa CA, Ladisa JF, Jansen KE, Feinstein JA, Taylor CA. On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Annals of Biomedical Engineering 2009; 37(11):2153-2169.
24. Antiga L, Piccinelli M, Botti L, Ene-Iordache B, Remuzzi A, Steinman D. An image-based modeling framework for patient-specific computational hemodynamics. Medical and Biological Engineering and Computing 2008; 46(11):1097-1112.
25. Olufsen M. Structured tree outflow condition for blood flow in larger systemic arteries. American Journal of Physiology - Heart and Circulatory Physiology 1999; 276(1):H257-H268.
26. Juntunen M, Stenberg R. Nitsche's method for general boundary conditions. Mathematics of Computation 2009; 78(267):1353-1374, DOI: 10.1090/S0025-5718-08-02183-2.
27. Caiazzo A, Fernández MA, Gerbeau JF, Martin V. Projection schemes for fluid flows through a porous interface. SIAM Journal on Scientific Computing 2011; 33(2):541-564.
28. Quarteroni A, Valli A. Numerical Approximation of Partial Differential Equations, Springer Series in Computational Mathematics, Springer-Verlag:Berlin, 1994.
29. Hughes TJR, Liu WK, Zimmermann TK. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering 1981; 29(3):329-349.
30. Donea J. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering 1982; 33:689-723.
31. Causin P, Gerbeau J, Nobile F. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Computer Methods in Applied Mechanics and Engineering 2005; 194(42-44):4506-4527.
32. Piperno S, Farhat C. Design of efficient partitioned procedures for transient solution of aerolastic problems. Revue Européenne Eléments Finis 2000; 9(6-7):655-680.
33. Badia S, Nobile F, Vergara C. Fluid-structure partitioned procedures based on Robin transmission conditions. Journal of Computation Physics 2008; 227:7027-7051.
34. Heil M. An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering 2004; 193:1-23.
35. Bazilevs Y, Calo V, Zhang Y, Hughes T. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Computational Mechanics 2006; 38:310-322.
36. Gee M, Kuttler U, Wall W. Truly monolithic algebraic multigrid for fluid-structure interaction. International Journal for Numerical Methods in Engineering 2011; 85(8):987-1016.
37. Fernández M, Gerbeau J, Grandmont C. A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. International Journal for Numerical Methods in Engineering 2007; 69(4):794-821.
38. Badia S, Quaini A, Quarteroni A. Splitting methods based on algebraic factorization for fluid-structure interaction. SIAM Journal on Scientific Computing 2008; 30(4):1778-1805.
39. Nobile F, Pozzoli M, Vergara C. Time accurate partitioned algorithms for the solution of fluid-structure interaction problems in haemodynamics. 2011. Submitted.