Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls

SIAM Journal on Numerical Analysis

Volumn 39, Issue 5, 2001, Pages 1488-1511

  Quarteroni, Alfio ^a,b   Veneziani, Alessandro ^b   Zunino, Paolo ^a  

^a EPFL   (Switzerland)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Computational hemodynamics; Coupling of heterogeneous models; Finite element methods; Mass transfer processes

Indexed keywords

EID: 0036411415     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900369714     Document Type: Article

References (31)

1. D.A. BAKER, J.E. HOLTE, AND S.V. PATANKAR, Computationally two-dimensional finite-difference model for hollow-fibre blood-gas exchange devices, Med. Biol. Engrg. Comput., 29 (1991), pp. 482-488.
2. C.G. CARO, J.M. FITZGERALD, AND R.C. SCHROTER, Atheroma and wall shear: Observation, correlation and proposal of a shear dependent mass transfer mechanism of atherogenesis, Proc. Roy. Soc. London Ser. A, 177 (1971), pp. 109-159.
3. T.E. DILLER, B.B. MIKIC, AND P.A. DRINKER, Shear-induced augmentation of oxygen transfer in blood, J. Biomech. Engrg., 102 (1980), pp. 67-72.
4. T.K. GOLDSTICK AND P.B. DOBRIN, Arterial wall oxygen transport and its relationship to atherogenesis, in Handbook of Bioengineering, R. Skalak and S. Chen, eds., McGraw-Hill, New York, 1987, Chap. 22.
5. J. HEYWOOD, The Navier-Stokes equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), pp. 639-681.
6. J. HEYWOOD AND R. RANNACHER, Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization, SIAM J. Numer. Anal., 19 (1982), pp. 275-311.
7. E. HOPF, Über die Aufgangswertaufgabe fur die hydrodynamischen Grundliechungen, Math. Nachr., 4 (1951), pp. 213-231.
8. J.R. HUGHES AND M. MALLET, A new finite element formulation for computational fluid dynamics. III. The generalized streamline operator for multidimensional advective-diffusive systems, Comput. Methods Appl. Mech. Engrg., 58 (1986), pp. 305-328.
9. H. JO, R.O. DULL, T.M. HOLLIS, AND J.M. TARBELL, Endothelial albumin permeability is shear dependent, time dependent and reversible, Amer. J. Physiol., 260 (1991), pp. H1992-H1996.
10. G. KARNER AND K. PERKTOLD, Numerical modeling of mass transport in the arterial wall, in Proceedings of the 1999 Bioengineering Conference, BED, Vol. 42, V.K. Goal, R.L. Spilker, G.A. Ateshian, and L.J. Solawsky, eds., ASME, New York, 1999, pp. 739-740
11. G. KARNER, K. PERKTOLD, H.-P. ZEHENTNER, AND M. PROSI, Mass transport in large arteries and through the arterial wall, in Intra and Extracorporeal Cardiovascular Fluid Dynamics, Vol. 2, Fluid-Structure Interaction, Adv. Fluid Mech. 23, P. Verdonck and K. Perktold, eds., WIT Press-Computational Mechanics, Southampton, Bellerica, MA, 2000, pp. 209-247.
12. K.H. KELLER, Effect of fluid shear on mass transport in flowing blood, Fed. Proc., 30 (1971), pp. 1591-1599.
13. J. LERAY, Etude de diverses équations intégrales et de quelques problèmes que pose l'hydrodynamique, J. Math. Pures Appl., 12 (1933), pp. 1-82.
14. J. LERAY, Essai sur les mouvement d'un liquide visqueux emplissant l'espace, Acta. Math., 63 (1934), pp. 193-248.
15. J. LERAY, Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J. Math. Pures Appl., 13 (1934), pp. 331-418.
16. J.L. LIONS AND E. MAGENES, Problèmes aux Limites non Homogènes et Applications 1, Dunod, Paris, 1968.
17. P.-L. LIONS, On the Schwarz alternating method. III. A variant for nonoverlapping subdomains, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Houston, 1989, SIAM, Philadelphia, 1990, pp. 202-223.
18. J.A. MOORE AND C.R. ETHIER, Oxygen mass transfer calculations in large arteries, J. Biomech. Engrg., 119 (1997), pp. 469-475.
19. W. NICHOLS AND M. O'ROURKE, EDS., McDonald's Blood Flow in Arteries, 3rd ed., Edward Arnold, London, 1990.
20. A. QUARTERONI, F. SALERI, AND A. VENEZIANI, Analysis of the Yosida method for the incompressible Navier-Stokes equations, J. Math. Pures Appl. (9), 78 (1999), pp. 473-503.
21. A. QUARTERONI, F. SALERI, AND A. VENEZIANI, Factorization methods for the numerical approximation of the incompressible Navier-Stokes equations, Comput. Meth. Appl. Mech. Engrg., 188 (2000), pp. 505-526.
22. A. QUARTERONI, M. TUVERI, AND A. VENEZIANI, Computational vascular fluid dynamics: Problems, models and methods, Comput. Visualisation Sci., 2 (2000), pp. 163-197.
23. A. QUARTERONI, A. VENEZIANI, AND P. ZUNINO, A domain decomposition method for advection-diffusion processes with application to blood solutes, SIAM J. Sci. Comput., to appear.
24. A. QUARTERONI AND A. VALLI, Numerical Approximation of Partial Differential Equations, Springer-Verlag, Berlin, 1994.
25. A. QUARTERONI AND A. VALLI, Domain Decomposition Methods for Partial Differential Equations, Oxford University Press, Oxford, 1999.
26. G. RAPPITSCH AND K. PERKTOLD, Pulsatile albumin transport in large arteries: A numerical simulation study, J. Biomech. Engrg., 118 (1996), pp. 511-519.
27. G. RAPPITSCH, K. PERKTOLD, AND E. PERNKOPF, Numerical modelling of shear-dependent mass transfer in large arteries, Internat. J. Numer. Methods Fluids, 25 (1997), pp. 847-857.
28. R. TEMAM, Navier-Stokes Equations: Theory and Numerical Analysis, 3rd ed., North-Holland, Amsterdam, 1984.
29. R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, SIAM, Philadelphia, 1983.
30. N.L. WANG AND K.H. KELLER, Solute transport induced by erythrocyte motions in shear flow, Trans. Amer. Soc. Artif. Intern. Organs, 25 (1979), pp. 14-17.
31. N.L. WANG AND K.H. KELLER, Augmented transport of extracellular solutes in concentrated erythrocyte suspensions in Couette flow, J. Colloid Inter. Sci., 103 (1985), pp. 210-225.