Microfluidics and Nanofluidics

, Volume 15, Issue 3, pp 285–296 | Cite as

Mathematical analysis of oxygen transfer through polydimethylsiloxane membrane between double layers of cell culture channel and gas chamber in microfluidic oxygenator

  • Min-Cheol KimEmail author
  • Raymond H. W. Lam
  • Todd ThorsenEmail author
  • H. Harry Asada
Research Paper


For successful cell culture in microfluidic devices, precise control of the microenvironment, including gas transfer between the cells and the surrounding medium, is exceptionally important. The work is motivated by a polydimethylsiloxane (PDMS) microfluidic oxygenator chip for mammalian cell culture suggesting that the speed of the oxygen transfer may vary depending on the thickness of a PDMS membrane or the height of a fluid channel. In this paper, a model is presented to describe the oxygen transfer dynamics in the PDMS microfluidic oxygenator chip for mammalian cell culture. Theoretical studies were carried out to evaluate the oxygen profile within the multilayer device, consisting of a gas reservoir, a PDMS membrane, a fluid channel containing growth media, and a cell culture layer. The corresponding semi-analytical solution was derived to evaluate dissolved oxygen concentration within the heterogeneous materials, and was found to be in good agreement with the numerical solution. In addition, a separate analytical solution was obtained to investigate the oxygen pressure drop (OPD) along the cell layer due to oxygen uptake of cells, with experimental validation of the OPD model carried out using human umbilical vein endothelial cells cultured in a PDMS microfluidic oxygenator. Within the theoretical framework, the effects of several microfluidic oxygenator design parameters were studied, including cell type and critical device dimensions.


PDMS Human Umbilical Vein Endothelial Cell Microfluidic Device Oxygen Transfer PDMS Membrane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank the Singapore-MIT Alliance of Research and Technology for financial supports of this work. The authors would like to acknowledge the financial supports from Croucher Foundation, Early Career Scheme of Hong Kong Research Grant Council (Project# RGC124212), and the National Science Foundation under Grant No. EFRI-0735997 and Grant No. STC-0902396. The authors thank Sukhyun Song for his assistance on the HUVEC culture experiment.

Supplementary material

10404_2013_1142_MOESM1_ESM.doc (2.2 mb)
Supplementary material 1 (DOC 2208 kb)


  1. Allen JW, Bhatia SN (2003) Formation of steady-state oxygen gradients in vitro—application to liver zonation. Biotechnol Bioeng 82(3):253–262CrossRefGoogle Scholar
  2. Beebe DJ, Mensing GA, Walker GM (2002) Physics and applications of microfluidics in biology. Annu Rev Biomed Eng 4:261–286CrossRefGoogle Scholar
  3. Brischwein M, Motrescu ER, Cabala R et al (2003) Functional cellular assays with multiparametric silicon sensor chips. Lap Chip 3(4):234–240CrossRefGoogle Scholar
  4. Chakraborty S, Balakotaiah V, Bidani A (2007) Multiscale model for pulmonary oxygen uptake and its application to quantify hypoxemia in hepatopulmonary syndrome. J Theor Biol 244(2):190–207MathSciNetCrossRefGoogle Scholar
  5. Conte SD, deBoor C (1972) Elementary numerical analysis. McGraw-Hill, New YorkzbMATHGoogle Scholar
  6. Cuvelier D, Thery M, Chu YS et al (2007) The universal dynamics of cell spreading. Curr Biol 17(8):694–699CrossRefGoogle Scholar
  7. De Bartolo L, Salerno S, Morelli S et al (2006) Long-term maintenance of human hepatocytes in oxygen-permeable membrane bioreactor. Biomaterials 27(27):4794–4803CrossRefGoogle Scholar
  8. Farahat WA, Wood LB, Zervantonakis IK et al (2012) Ensemble analysis of angiogenic growth in three-dimensional microfluidic cell cultures. PLoS ONE 7(5):e37333CrossRefGoogle Scholar
  9. Fredman TP (2003) An analytical solution method for composite layer diffusion problems with an application in metallurgy. Heat Mass Transf 39(4):285–295Google Scholar
  10. Germain S, Monnot C, Muller L, Eichmann A (2010) Hypoxia-driven angiogenesis: role of tip cells and extracellular matrix scaffolding. Curr Opin Hematol 17(3):245–251Google Scholar
  11. Higgins JM, Eddington DT, Bhatia SN, Mahadevan L (2007) Sickle cell vasoocclusion and rescue in a microfluidic device. Proc Natl Acad Sci USA 104(51):20496–20500CrossRefGoogle Scholar
  12. Houston KS, Weinkauf DH, Stewart FF (2002) Gas transport characteristics of plasma treated poly (dimethylsiloxane) and polyphosphazene membrane materials. J Membr Sci 205(1–2):103–112CrossRefGoogle Scholar
  13. Kane BJ, Zinner MJ, Yarmush ML, Toner M (2006a) Liver-specific functional studies in a microfluidic array of primary mammalian hepatocytes. Anal Chem 78(13):4291–4298CrossRefGoogle Scholar
  14. Kane BJ, Zinner MJ, Yarmush ML, Toner M (2006b) Liver-specific functional studies in a microfluidic array of primary mammalian hepatocytes. Anal Chem 78(13):4291–4298CrossRefGoogle Scholar
  15. Lam RHW, Kim MC, Thorsen T (2009) Culturing aerobic and anaerobic bacteria and mammalian cells with a microfluidic differential oxygenator. Anal Chem 81(14):5918–5924CrossRefGoogle Scholar
  16. Leclerc E, Sakai Y, Fujii T (2004) Microfluidic PDMS (polydimethylsiloxane) bioreactor for large-scale culture of hepatocytes. Biotechnol Prog 20(3):750–755CrossRefGoogle Scholar
  17. Masterton WL, Hurley CN (2002) Chemistry: principles and reactions. Thomson Books/Cole, BelmontGoogle Scholar
  18. McDonald JC, Duffy DC, Anderson JR et al (2000) Fabrication of microfluidic systems in poly(dimethylsiloxane). Electrophoresis 21(1):27–40CrossRefGoogle Scholar
  19. Mulholland GP, Cobble MH (1972) Diffusion through composite media. Int J Heat Mass Transf 15(1):147–160CrossRefGoogle Scholar
  20. Park J, Bansal T, Pinelis M, Maharbiz MM (2006) A microsystem for sensing and patterning oxidative microgradients during cell culture. Lab Chip 6(5):611–622CrossRefGoogle Scholar
  21. Pathi P, Ma T, Locke BR (2005) Role of nutrient supply on cell growth in bioreactor design for tissue engineering of hematopoietic cells. Biotechnol Bioeng 89(7):743–758CrossRefGoogle Scholar
  22. Patton JN, Palmer AF (2006) Numerical simulation of oxygen delivery to muscle tissue in the presence of hemoglobin-based oxygen carriers. Biotechnol Prog 22(4):1025–1049CrossRefGoogle Scholar
  23. Polinkovsky M, Gutierrez E, Levchenko A, Groisman A (2009) Fine temporal control of the medium gas content and acidity and on-chip generation of series of oxygen concentrations for cell cultures. Lab Chip 9(8):1073–1084CrossRefGoogle Scholar
  24. Poulsen L, Zebger I, Tofte P et al (2003) Oxygen diffusion in bilayer polymer films. J Phys Chem B 107(50):13885–13891CrossRefGoogle Scholar
  25. Radisic M, Deen W, Langer R, Vunjak-Novakovic G (2005) Mathematical model of oxygen distribution in engineered cardiac tissue with parallel channel array perfused with culture medium containing oxygen carriers. Am J Physiol Heart Circ Physiol 288(3):H1278–H1289CrossRefGoogle Scholar
  26. Radisic M, Malda J, Epping E, Geng W, Langer R, Vunjak-Novakovic G (2006a) Oxygen gradients correlate with cell density and cell viability in engineered cardiac tissue. Biotechnol Bioeng 93(2):332–343CrossRefGoogle Scholar
  27. Radisic M, Park H, Chen F et al (2006b) Biomirnetic approach to cardiac tissue engineering: oxygen carriers and channeled scaffolds. Tissue Eng 12(8):2077–2091CrossRefGoogle Scholar
  28. Roy P, Baskaran H, Tilles AW, Yarmush ML, Toner M (2001) Analysis of oxygen transport to hepatocytes in a flat-plate microchannel bioreactor. Ann Biomed Eng 29(11):947–955CrossRefGoogle Scholar
  29. Shiku H, Saito T, Wu CC et al (2006) Oxygen permeability of surface-modified poly(dimethylsiloxane) characterized by scanning electrochemical microscopy. Chem Lett 35(2):234–235CrossRefGoogle Scholar
  30. Sud D, Mehta G, Mehta K et al (2006) Optical imaging in microfluidic bioreactors enables oxygen monitoring for continuous cell culture. J Biomed Optics 11(5):050504CrossRefGoogle Scholar
  31. Szita N, Boccazzi P, Zhang Z et al (2005) Development of a multiplexed microbioreactor system for high-throughput bioprocessing. Lab Chip 5(8):819–826CrossRefGoogle Scholar
  32. Tan JL, Tien J, Pirone M, Gray DS et al (2003) Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc Natl Acad Sci USA 100(4):1484–1489CrossRefGoogle Scholar
  33. Thorsen T, Maerkl SJ, Quake SR (2002) Microfluidic large-scale integration. Science 298(5593):580–584CrossRefGoogle Scholar
  34. Toh YC, Zhang C, Zhang J et al (2007) A novel 3D mammalian cell perfusion-culture system in microfluidic channels. Lab Chip 7(3):302–309CrossRefGoogle Scholar
  35. Tourovskaia A, Figueroa-Masot X, Folch A (2005) Differentiation-on-a-chip: a microfluidic platform for long-term cell culture studies. Lab Chip 5(1):14–19CrossRefGoogle Scholar
  36. Valeur B, Brochon JC (2001) New trends in fluorescence spectroscopy: applications to chemical and life. Springer, New York, p 236CrossRefGoogle Scholar
  37. Vickerman V, Blundo J, Chung S, Kamm R (2008) Design, fabrication and implementation of a novel multi-parameter control microfluidic platform for three-dimensional cell culture and real-time imaging. Lab Chip 8(9):1468–1477CrossRefGoogle Scholar
  38. Vollmer AP, Prostein RF, Gilbert R, Thorsen T (2005) Development of an integrated microfluidic platform for dynamic oxygen sensing and delivery in a flowing medium. Lab Chip 5(10):1059–1066CrossRefGoogle Scholar
  39. Wang Z, Kim MC, Marquez M, Thorsen T (2007) High-density microfluidic arrays for cell cytotoxicity analysis. Lab Chip 7(6):740–745CrossRefGoogle Scholar
  40. Zanzotto A, Szita N, Schmidt MA, Jensen KF (2002) 2nd annual international IEEE-EMBS special topic conference on microtechnologies in medicine & biology 164–168. Madison, Wisconsin, USAGoogle Scholar
  41. Zhang ZY, Boccazzi P, Choi HG et al (2006) Microchemostat—microbial continuous culture in a polymer-based, instrumented microbioreactor. Lab Chip 6(7):906–913CrossRefGoogle Scholar
  42. Ziomek E, Kirkpatrick N, Reid ID (1991) Effect of poldimethyl siloxane oxygen carriers on the biological bleaching of hardwood kraft pulp by trametes-versicolor. Appl Microbiol Biotechnol 35(5):669–673CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.BioSystem and Micromechanics (BioSyM) IRGSingapore-MIT Alliance for Research and TechnologySingaporeSingapore
  3. 3.Department of Mechanical and Biomedical EngineeringCity University of Hong KongHong KongChina

Personalised recommendations