A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models

International Journal for Numerical Methods in Biomedical Engineering

Volumn 30, Issue 2, 2014, Pages 204-231

  Xiao, Nan ^a,b   Alastruey, Jordi ^a   Figueroa, C Alberto ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

^b Stanford University   (United States)

Author keywords

Arterial hemodynamics; Fluid structure interaction; Full aorta model; Outflow boundary condition estimation; Pulse wave propagation; Spatially varying mechanical properties; Windkessel

Indexed keywords

ABDOMINAL AORTA; ARTERIAL HEMODYNAMICS; ARTERY; ARTICLE; BIOLOGICAL MODEL; BLOOD PRESSURE; COMMON CAROTID ARTERY; COMPARATIVE STUDY; COMPUTER SIMULATION; DIASTOLE; FLUID-STRUCTURE INTERACTION; FULL AORTA MODEL; HEMODYNAMICS; HUMAN; METABOLISM; OUTFLOW BOUNDARY CONDITION ESTIMATION; PHYSIOLOGY; PULSE WAVE PROPAGATION; SPATIALLY VARYING MECHANICAL PROPERTIES; THORACIC AORTA; WINDKESSEL;

ARTERIAL HEMODYNAMICS; FLUID-STRUCTURE INTERACTION; FULL AORTA MODEL; OUTFLOW BOUNDARY CONDITION ESTIMATION; PULSE WAVE PROPAGATION; SPATIALLY VARYING MECHANICAL PROPERTIES; WINDKESSEL;

AORTA, ABDOMINAL; AORTA, THORACIC; ARTERIES; BLOOD PRESSURE; CAROTID ARTERY, COMMON; COMPUTER SIMULATION; DIASTOLE; HEMODYNAMICS; HUMANS; MODELS, CARDIOVASCULAR;

EID: 84894918142     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.2598     Document Type: Article

References (66)

1. Hughes T, Lubliner J. On the one-dimensional theory of blood flow in the larger vessels. Mathematical Biosciences 1973; 18:161-170.
2. Stergiopulos N, Young DF, Rogge TR. Computer simulation of arterial flow with applications to arterial and aortic stenoses. Journal of Biomechanics 1992; 25(12):1477-88.
3. Reymond P, Bohraus Y, Perren F, Lazeyras F, Stergiopulos N. Validation of a patient-specific 1-D model of the systemic arterial tree. American Journal of Physiology Heart and Circulatory Physiology 2011; 301:H1173-H1182.
4. Olufsen M, Peskin C, Kim W, Pedersen E, Nadim A, Larsen J. Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Annals of Biomedical Engineering 2000; 28:1281-1299.
5. Formaggia L, Lamponi D, Quarteroni A. One-dimensional models for blood flow in arteries. Journal of Engineering Mathematics 2003; 47:251-276.
6. Sherwin SJ, Franke V, Peiro J, Parker KH. One-dimensional modelling of a vascular network in space-time variables. Journal of Engineering Mathematics 2003; 47(3):217-250.
7. Bessems D, Rutten M, vande Vosse F. A wave propagation model of blood flow in large vessels using an approximate velocity profile function. Journal of Fluid Mechanics 2007; 580:145-168.
8. Mynard J, Nithiarasu P. A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Communications in Numerical Methods in Engineering 2008; 24:367-417.
9. Alastruey J, Khir AW, Matthys KS, Segers P, Sherwin SJ, Verdonck PR, Parker KH, Peiró J. Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements. Journal of Biomechanics 2011; 44(12):2250-8.
10. Müller L, Toro E. Well balanced high-order solver for blood flow in networks of vessels with variable properties. International Journal for Numerical Methods in Biomedical Engineering 2013. DOI: 10.1002/cnm.2580.
11. Perktold K, Rappitsch G. Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. Journal of Biomechanics 1995; 28(7):845-56.
12. Taylor CA, Hughes TJR, Zarins CK. Finite element modeling of blood flow in arteries. Computer Methods in Applied Mechanics and Engineering 1998; 158:155-196.
13. Quarteroni A, Tuveri M, Veneziani A. Computational vascular fluid dynamics: problems, models and methods. Computing and Visualization in Science March 2000; 2:163-97.
14. Steinman D, Milner J, Norley C, Lownie S, Holdsworth D. Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. American Journal of Neuroradiology 2003; 24(4):559-566. 4th World Congress of Biomechanics, Calgary, Canada, Aug, 2002.
15. Cebral J, Castro M, Burgess J, Pergolizzi R, Sheridan M, Putman C. Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models. American Journal of Neuroradiology 2005; 26(10):2550-2559.
16. Gerbeau JF, Vidrascu M, Frey P. Fluid-structure interaction in blood flows on geometries based on medical imaging. Computers and Structures 2005; 83(2-3):155-165.
17. Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes TJR, Taylor CA. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Computer Methods in Applied Mechanics and Engineering 2006; 195(41-43):5685-5706.
18. vande Vosse F, Stergiopulos N. Pulse wave propagation in the arterial tree. Annual Review of Fluid Mechanics 2011; 43:467-499.
19. Alastruey J, Parker K, Sherwin S. Arterial pulse wave haemodynamics. BHR Group's 11th International Conference on Pressure Surges, Lisbon, Portugal, 24th - 26th October, 2012; 401-442, Code 95139. ISBN: 978 1 85598 133 1.
20. Parker K. An introduction to wave intensity analysis. Medical and Biological Engineering and Computing 2009; 47:175-188.
21. Steele B, Wan J, Ku J, Hughes T, Taylor C. In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts. IEEE Transactions on Biomedical Engineering 2003; 50(6):649-656.
22. Matthys KS, Alastruey J, Peiro J, Khir AW, Segers P, Verdonck PR, Parker KH, Sherwin SJ. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. Journal of Biomechanics 2007; 40(15):3476-3486.
23. Humphrey J, Strumpf R, Yin F. Determination of a constitutive relation for passive myocardium: II. Parameter-estimation. Journal of Biomechanical Engineering - Transactions of the ASME 1990; 112(3):340-346.
24. Xiong G, Figueroa CA, Xiao N, Taylor CA. Simulation of blood flow in deformable vessels using subject-specific geometry and spatially varying wall properties. International Journal for Numerical Methods in Biomedical Engineering 2011; 27(7):1000-1016.
25. Prasad A, Xiao N, Gong XY, Zarins C, Figueroa CA. A computational framework for investigating the positional stability of aortic endografts. Biomechanics and Modeling in Mechanogiology 2013. DOI: 10.1007/s10237-012-0450-3.
26. Taylor CA, Figueroa CA. Patient-specific modeling of cardiovascular mechanics. Annual Review of Biomedical Engineering 2009; 11:109-134. Annual Reviews. Palo Alto, CA USA.
27. Moore S, Moorhead K, Chase J, David T, Fink J. One-dimensional and three-dimensional models of cerebrovascular flow. Journal of Biomechanical Engineering-Transactions of the ASME 2005; 127(3):440-449.
28. Grinberg L, Cheever E, Anor T, Madsen JR, Karniadakis GE. Modeling blood flow circulation in intracranial arterial networks: a comparative 3D/1D simulation study. Annals of Biomedical Engineering 2011; 39(1):297-309.
29. Reymond P, Perren F, Lazeyras F, Stergiopulos N. Patient-specific mean pressure drop in the systemic arterial tree, a comparison between 1-D and 3-D models. Journal of Biomechanics 2012; 45:2499-2505.
30. Xiao N, Humphrey JD, Figueroa CA. Multi-scale computational model of three-dimensional hemodynamics within a deformable full-body arterial network. Journal of Computational Physics 2013; 244:22-40.
31. Passerini T, deLuca M, Formaggia L, Quarteroni A, Veneziani A. A 3D/1D geometrical multiscale model of cerebral vasculature. Journal of Engineering Mathematics 2009; 64(4):319-330.
32. van de Vosse FN, Stergiopulos N. Pulse wave propagation in the arterial tree. Annual Review of Fluid Mechanics 2011; 43:467-499. Annual Reviews. Palo Alto, CA USA.
33. Formaggia L, Quarteroni A, Vergara C. On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. Journal of Computational Physics 2012; 244:97-112.
34. Peiró J, Veneziani A. Reduced models of the cardiovascular system. In Cardiovascular Mathematics Modeling and Simulation of the Circulatory System, Formaggia L, Quarteroni A, Veneziani A (eds). Springer-Verlag (Milano), 2009; 347-394.
35. Smith NP, Pullan AJ, Hunter PJ. An anatomically based model of transient coronary blood flow in the heart. SIAM Journal on Applied Mathematics 2002; 62(3):990-1018.
36. Čanić S, Kim E. Mathematical analysis of the quasilinear effects in a hyperbolic model of blood flow through compliant axi-symmetric vessels. Mathematicsl Methods in the Applied Sciences 2003; 26:1161-1186.
37. Quarteroni A, Formaggia L. Mathematical modelling and numerical simulation of the cardiovascular system. In Modelling of Living Systems, Ayache N (ed.). Elsevier (Amsterdam), 2004.
38. Alastruey J, Parker KH, Peiró J, Sherwin SJ. Lumped parameter outflow models for 1-D blood flow simulations: Effect on pulse waves and parameter estimation. Communications in Computational Physics 2008; 4:317-336.
39. 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; 11(1-2):1-18.
40. Vignon-Clementel IE, Figueroa CA, 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.
41. 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):625-40.
42. 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.
43. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32(1-3):199-259.
44. Franca LP, Frey SL. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1992; 99(2-3):209-233.
45. Whiting CH, Jansen KE. A stabilized finite element method for the incompressible Navier-Stokes equations using a hierarchical basis. International Journal for Numerical Methods in Fluids 2001; 35(1):93-116.
46. Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method. Journal of Applied Mechanics 1993; 6:371-375.
47. Jansen KE, Whiting CH, Hulbert GM. A generalized- α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering 2001; 190(31):305-319.
48. Figueroa CA, Baek S, Taylor CA, Humphrey JD. A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Computer Methods in Applied Mechanics and Engineering 2009; 198(45-46):3583-3602.
49. Baek S, Gleason RL, Rajagopal KR, Humphrey JD. Theory of small on large: potential utility in computations of fluid-solid interactions in arteries. Computer Methods in Applied Mechanics and Engineering 2007; 196(31-32):3070-3078.
50. Alastruey J, Passerini T, Formaggia L, Peiró J. Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation. Journal of Engineering Mathematics 2012; 77(1):19-37.
51. Simon AC, Safar ME, Levenson JA, London GM, Levy BI, Chau NP. An evaluation of large arteries compliance in man. American Journal of Physiology Heart and Circulatory Physiology 1979; 237(5):H550-H554.
52. Alastruey J, Parker KH, Peiró J, Sherwin SJ. Analysing the pattern of pulse waves in arterial networks: a time-domain study. Journal of Engineering Mathematics 2009; 64(4):331-351.
53. Spilker RL, Taylor CA. Tuning multidomain hemodynamic simulations to match physiological measurements. Annals of Biomedical Engineering 2010; 38(8):2635-2648.
54. Devault K, Gremaud PA, Novak V, Olufsen MS, Vernieres G, Zhao P. Blood flow in the circle of Willis: modeling and calibration. Multiscale Modeling and Simulation 2008; 7(2):888-909.
55. Nichols WW, O'Rourke MF. McDonald's Blood Flow in Arteries: Theoretical, Experimental, and Clinical Principles, Vol.11, Hodder Arnold. Oxford University Press: New York, 2005.
56. Reymond P, Merenda F, Perren F, Rüfenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. American Journal of Physiology Heart and Circulatory Physiology 2009; 297(1):H208-H222.
57. Yearwood TL, Chandran KB. Experimental investigation of steady flow through a model of the human aortic arch. Journal of Biomechanics 1980; 13(12):1075-88.
58. Sun H, Kuban BD, Schmalbrock P, Friedman MH. Measurement of the geometric parameters of the aortic bifurcation from magnetic resonance images. Annals of Biomedical Engineering 1994; 22(3):229-39.
59. Shin IY, Chung YG, Shin WH, Im SB, Hwang SC, Kim BT. A morphometric study on cadaveric aortic arch and its major branches in 25 Korean adults: the perspective of endovascular surgery. Journal of Korean Neurosurgical Society 2008; 44(2):78-83.
60. Wang JJ, O'Brien AB, Shrive NG, Parker KH, Tyberg JV. Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. American Journal of Physiology Heart and Circulatory Physiology 2003; 284:H1358-H1368.
61. Aguado-Sierra J, Alastruey J, Wang JJ, Hadjiloizou N, Davies JE, Parker KH. Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries. Proceedings of the Institution of Mechanical Engineers Part H-Journal of Engineering in Medicine 2008; 222:403-416.
62. Čanić S, Lamponi D, Mikelić A, Tambača J. Self-consistent effective equations modeling blood flow in medium-to-large compliant arteries. Multiscale Modeling and Simulation 2005; 3:559-596.
63. Robertson AM, Sequeira A. A director theory approach for modeling blood flow in the arterial system: an alternative to classical 1D models. Mathematical Models and Methods in Applied Sciences 2005; 15:871-906.
64. Azer K, Peskin CS. A one-dimensional model of blood flow in arteries with friction and convection based on the Womersley velocity profile. Cardiovascular Engineering 2007; 7:51-73.
65. Riley WA, Barnes RW, Evans GW, Burke GL. Ultrasonic measurement of the elastic modulus of the common carotid artery. The atherosclerosis risk in communities (ARIC) study. Stroke 1992; 23(7):952-956.
66. Cheng C, Herfkens RJ, Taylor CA. Abdominal aortic hemodynamic conditions in healthy subjects aged 50-70 at rest and during lower limb exercise: in vivo quantification using MRI. Atherosclerosis 2003; 168(2):323-331.