Advertisement

Computational Mechanics

, Volume 52, Issue 6, pp 1463–1473 | Cite as

Experimental and computational validation of Hele-Shaw stagnation flow with varying shear stress

  • Brandon J. TefftEmail author
  • Adrian M. Kopacz
  • Wing Kam Liu
  • Shu Q. Liu
Original Paper

Abstract

An in vitro flow model system with continuous variation of fluid shear stress can be used to test cell responses to a range of shear stresses. In this investigation, we validated such a flow system computationally for steady and unsteady flow conditions and experimentally for steady flow conditions. The unsteady flow validation is important for studying cells such as endothelial cells that experience unsteady flow conditions in their native environment. The system is capable of exposing cells in different regions of the chamber to steady or unsteady shear stress conditions with average values ranging linearly from 0 to 30 dyn/cm\(^{2}\). These tests and analyses demonstrate that the variable-width parallel plate flow system can be used to test the influence of a range of steady and unsteady fluid shear stress levels on cell activities.

Keywords

Flow chamber Unsteady flow Shear stress Endothelial cells adhesion 

Notes

Acknowledgments

This work was supported by National Science Foundation (NSF) CMMI Grant 0856333. WKL was partially supported by the World Class University Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (R33-10079). This research used resources of the QUEST cluster at Northwestern University and the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357.

Conflict of interest No competing financial interests exist.

References

  1. 1.
    Ando J, Yamamoto K (2011) Effects of shear stress and stretch on endothelial function. Antioxid Redox Signal 15(5):1389–1403. doi: 10.1089/ars.2010.3361 CrossRefGoogle Scholar
  2. 2.
    Buga GM, Gold ME, Fukuto JM, Ignarro LJ (1991) Shear stress-induced release of nitric oxide from endothelial cells grown on beads. Hypertension 17(2):187–193CrossRefGoogle Scholar
  3. 3.
    Frangos JA, Eskin SG, McIntire LV, Ives CL (1985) Flow effects on prostacyclin production by cultured human endothelial cells. Science 227(4693):1477–1479CrossRefGoogle Scholar
  4. 4.
    Nigro P, Abe J, Berk BC (2011) Flow shear stress and atherosclerosis: a matter of site specificity. Antioxid Redox Signal 15(5):1405–1414. doi: 10.1089/ars.2010.3679 CrossRefGoogle Scholar
  5. 5.
    Herring MB (1991) Endothelial cell seeding. J Vasc Surg 13(5):731–732CrossRefGoogle Scholar
  6. 6.
    Usami S, Chen HH, Zhao Y, Chien S, Skalak R (1993) Design and construction of a linear shear stress flow chamber. Ann Biomed Eng 21(1):77–83CrossRefGoogle Scholar
  7. 7.
    Gimbrone MA Jr, Nagel T, Topper JN (1997) Biomechanical activation: an emerging paradigm in endothelial adhesion biology. J Clin Invest 99(8):1809–1813. doi: 10.1172/JCI119346 CrossRefGoogle Scholar
  8. 8.
    Coskun AU, Yeghiazarians Y, Kinlay S, Clark ME, Ilegbusi OJ, Wahle A, Sonka M, Popma JJ, Kuntz RE, Feldman CL, Stone PH (2003) Reproducibility of coronary lumen, plaque, and vessel wall reconstruction and of endothelial shear stress measurements in vivo in humans. Catheter Cardiovasc Interv 60(1):67–78CrossRefGoogle Scholar
  9. 9.
    Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46(1):17–29. doi: 10.1007/S00466-009-0423-2 MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE–VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Method Eng 19(2):171–225. doi: 10.1007/S11831-012-9071-3 MathSciNetCrossRefGoogle Scholar
  11. 11.
    Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space-time finite element computation of arterial fluid–structure interactions. Comput Mech 46(1):31–41. doi: 10.1007/S00466-009-0425-0 MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50(6):675–686. doi: 10.1007/S00466-012-0760-4 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the deforming-spatial-domain/stabilized space-time formulation. Comput Method Appl Mech Eng 195(13–16):1885–1895. doi: 10.1016/J.Cma.2005.05.050 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38(4–5):482–490. doi: 10.1007/S00466-006-0065-6 CrossRefzbMATHGoogle Scholar
  15. 15.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43(1):151–159. doi: 10.1007/S00466-008-0325-8 CrossRefzbMATHGoogle Scholar
  16. 16.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms. Comput Mech 46(1):43–52. doi: 10.1007/S00466-009-0439-7 CrossRefzbMATHGoogle Scholar
  17. 17.
    Yee A, Sakurai Y, Eskin SG, McIntire LV (2006) A validated system for simulating common carotid arterial flow in vitro: alteration of endothelial cell response. Ann Biomed Eng 34(4):593–604. doi: 10.1007/s10439-006-9078-8 CrossRefGoogle Scholar
  18. 18.
    Truskey GA, Yuan F, Katz DF (2004) Transport phenomena in biological systems. Pearson Prentice Hall, Upper Saddle RiverGoogle Scholar
  19. 19.
    Loudon C, Tordesillas A (1998) The use of the dimensionless Womersley number to characterize the unsteady nature of internal flow. Theor Biol 191:63–78CrossRefGoogle Scholar
  20. 20.
    Yakhot A, Arad M (1999) Numerical invesitagtion of a laminar pulsating flow in a rectangular duct. Int J Numer Methods Fluids 29:935–950CrossRefzbMATHGoogle Scholar
  21. 21.
    Bacabac RG, Smit TH, Cowin SC, Van Loon JJ, Nieuwstadt FT, Heethaar R, Klein-Nulend J (2005) Dynamic shear stress in parallel-plate flow chambers. J Biomech 38(1):159–167. doi: 10.1016/j.jbiomech.2004.03.020 Google Scholar
  22. 22.
    Nauman EA, Risic KJ, Keaveny TM, Satcher RL (1999) Quantitative assessment of steady and pulsatile flow fields in a parallel plate flow chamber. Ann Biomed Eng 27(2):194–199Google Scholar
  23. 23.
    Vogel M, Franke J, Frank W, Schroten H (2007) Flow in the well: computational fluid dynamics is essential in flow chamber construction. Cytotechnology 55:41–54CrossRefGoogle Scholar
  24. 24.
    Womersley JR (1955) Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 127(3):553–563Google Scholar
  25. 25.
    He X, Ku DN, Moore JE Jr (1993) Simple calculation of the velocity profiles for pulsatile flow in a blood vessel using mathematica. Ann Biomed Eng 21(1):45–49Google Scholar
  26. 26.
    Koelsch B, Rimann M, Hall H (2007) Design of a flow chamber to study shear stress induced endothelial cell orientation on/within different modified 3D-fibrin matrices. Eur Cell Matrix 14(Supp 3):49–50Google Scholar
  27. 27.
    Munson B, Young DF, Okiishi TH (1990) Fundamentals of fluid mechanics, 3rd edn. Wiley, New YorkGoogle Scholar
  28. 28.
    Schlichting H (1968) Boundary layer theory. McGraw-Hill, New York Google Scholar
  29. 29.
    Bowen BD (1985) Streaming potential in the hydrodynamic entrance region of cylindrical and rectangular capillaries. J Colloid Interface 106:367–376CrossRefGoogle Scholar
  30. 30.
    Chung BJ, Roberton AM, Peters DG (2003) The numerical design of a parallel plate flow chamber for investigation of endothelial cell response to shear stress. Comput Struct 81:535–546CrossRefGoogle Scholar
  31. 31.
    Cao J, Usami S, Dong C (1997) Development of a side-view chamber for studying cell-surface adhesion under flow conditions. Ann Biomed Eng 25(3):573–580CrossRefGoogle Scholar
  32. 32.
    Hughes TJR, Cliffs E (1987) The finite element method. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  33. 33.
    Tezduyar TE (1992) Stabilized finite-element formulations for incompressible-flow computations. Adv Appl Mech 28:1–44MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible-flow computations with stabilized bilinear and linear equal-order-interpolation velocity–pressure elements. Comput Method Appl M 95(2):221–242CrossRefzbMATHGoogle Scholar
  35. 35.
    Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Method Appl M 190(3–4):411–430CrossRefzbMATHGoogle Scholar
  36. 36.
    Frangos JA, McIntire LV, Eskin SG (1988) Shear stress induced stimulation of mammalian cell metabolism. Biotechnol Bioeng 32:1053–1060CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Brandon J. Tefft
    • 1
    • 5
    Email author
  • Adrian M. Kopacz
    • 2
  • Wing Kam Liu
    • 2
    • 3
    • 4
  • Shu Q. Liu
    • 1
  1. 1.Department of Biomedical EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.King Abdulaziz University (KAU)JeddahSaudi Arabia
  4. 4.Sung Kyun Kwan UniversitySeoulSouth Korea
  5. 5.Mayo ClinicRochesterUSA

Personalised recommendations