A predictive, two-dimensional model with good absolute accuracy for flow and mass transfer in cross-flow hollow fiber membrane artificial lungs is developed. The proposed model is able to predict the gas transfer to water flowing outside and perpendicular to hollow fibers in the artificial lung. The model uses a finite element technique to solve the Navier-Stokes equations and the convection-diffusion equation on the computational domain of a unit fiber cell. Subsequent stream-wise and cross-wise unit fiber cells are then coupled/assembled to the relationship between the oxygen transfer rate and flow rate of a cross-flow hollow fiber membrane artificial lung. The model is compared to experimental water data obtained by perfusing three commercial artificial lungs with water.
ShahV.L.. Blood flow. In: MujumdarA.S., ed. Advances in transport processes.New Dehli: Wiley Eastern Limited, 1980; pp. 1–57.
2.
WeissmanM.H., MockrosL.F.. Oxygen and carbon dioxide transfer in membrane oxygenators. Med Biol Eng1969; 7: 169–84.
3.
VillarroelF., LanhamC.E.. A design calculation method for capillary tube oxygenators. Med Biol Eng1973; 11: 732–42.
4.
SmebyL., GrimsrudL.. Theoretical investigation of mass transfer in membrane oxygenators. Med Biol Eng1974; 12: 698–705.
5.
OomersJ.M., SpaanJ.A.. A generalized advancing front model describing the oxygen transport in flowing blood. In: Proceedings of the 2nd International Symposium on Oxygen Transport to Tissue; 1975. Mainz, West Germany: Plenum; 1975.
BakerD.A., HolteJ.E., PatankarS.V.. Computationally two-dimensional finite-difference model for hollow-fibre blood-gas exchange devices. Medical and Biological Engineering and Computing1991; 29: 482–8.
12.
DierickxP.W., De WachterD.S., VerdonckP.R.. Blood flow around hollow fibers. Int J Artif Organs2000; 23(9): 610–17.
13.
BirdR.B., StewartW.E., LightfootE.N.. Transport phenomena.John Wiley & Sons, 1960; p. 197.
14.
ErgunS.. Fluid flow through packed columns. Chemical Engineering Progress1952; 48(2): 89–94.
15.
MortimerC.. Chemistry, a conceptual approach.New York: D. Van Nostrand Company, 1979; p. 300.
16.
ChenC.J., WungT.S.. Finite analytic solution of convective heat transfer for tube arrays in crossfiow: part II - heat transfer analysis. Transactions of the ASME. Journal of Heat Transfer1989; 111: 641–8.
17.
ThewsG.. Em Verbahren zur Berchnung des O2-Diffusions-koeffizienten aus Messungen der Sauerstoffdiffusion in Häemoglobin und Myoglobin Lösungen. Pfiueger Arch Gesamte Physiol Menschen Tiere1957; 265: 138–53.
18.
PerryR.H., GreenD.W.. Perry's chemical engineers’ handbook, 6 ed.New York: McGaw Hill, 1984; pp. 1203–5.
19.
VaslefS.N., MockrosL.F., AndersonR.W., LeonardR.. Use of a mathematical model to predict oxygen transfer rates in hollow fiber membrane oxygenators. ASAIO Trans1994; 40: 990–6.
20.
CuvelierC., SegalA., van SteenhovenA.A.. Finite element methods and Navier-Stokes equations.Dordrecht: D Reidel Publishing Company, 1986; 1153–65.
21.
SegalG., VuikK., KasselsK.. On the implementation of symmetric and antisymmetric periodic boundary conditions for incompressible flow. International Journal for Numerical Methods in Fluids1994; 18: 1153–65.
22.
MizukamiA., HughesT.J.. A Petrov-Galerkin finite element method for convection-dominated flows: an accurate upwinding technique for satisfying the maximum principle. Computer Methods in Applied Mechanics and Engineering1985; 50: 181–93.
23.
NiranjanS.C., ClarkJ.W., SanK.Y., ZwischenbergerJ.B., BidaniA.. Analysis of factors affecting gas exchange in intravascular blood gas exchanger. J Appl Physiol1994; 77(4): 1716–30.
24.
LeonardE.F., JorgansenS.B.. The analysis of convection and diflusion in capillary beds. Annu Rev Biophys Bioeng1974; 3: 293–339.
