Converging Parallel Plate Flow Chambers for Studies on the Effect of the Spatial Gradient of Wall Shear Stress on Endothelial Cells


Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.

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Lu, Y. , Li, W. , Oraifige, I. and Wang, W. (2014) Converging Parallel Plate Flow Chambers for Studies on the Effect of the Spatial Gradient of Wall Shear Stress on Endothelial Cells. Journal of Biosciences and Medicines, 2, 50-56. doi: 10.4236/jbm.2014.22008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] DeBakey, M.E., Lawrie, G.M. and Glaeser, D.H. (1985) Patterns of Atherosclerosis and Their Surgical Significance. Annals of Surgery, 201, 115-131.
[2] Caro, C.G., Fitz-Gerald, J.M. and Schroter, R.C. (1971) Atheroma and Arterial Wall Shear Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism for Atherogenesis. Proceedings of the Royal Society B: Biological Sciences, 177, 109-159.
[3] Lei, M., Kleinstreuer, C. and Truskey, G.A. (1995) Numerical Investigation and Prediction of Atherogenic Sites in Branching Arteries. ASME Journal of Biomechanical Engineering, 117, 350-357.
[4] Ojha, M. (1994) Wall Shear Stress Temporal Gradient and Anastomotic Intimal Hyperplasia. Circulation Research, 74, 1227-1231.
[5] He, X. and Ku, D.N. (1996) Pulsatile Flow in the Human Left Coro-nary Artery Bifurcation: Average Conditions. ASME Journal of Biomechanical Engineering, 118, 74-82.
[6] Buchanan, J.R., Kleistreuer, C., Truskey, G.A. and Lei, M. (1999) Relation between Non-Uniform Hemodynamics and Sites of Altered Permeability and Lesion Growth at the Rabbit Aorta-Celiac Junction. Atherosclerosis, 143, 27-40.
[7] LaMack, J.A. and Friedman, M.H. (2007) Individual and Combined Effects of Shear Stress Magnitude and Spatial Gradient on Endothelial Cell Gene Expression. American Journal of Physiology—Heart and Circulatory Physiology, 293, H2853-H2859.
[8] Shimogonya, Y., Ishikawa, T., Imai, Y., Matsuki, N. and Yama-guchi, T. (2009) Can Temporal Fluctuation in Spatial Wall Shear Stress Gradient Initiate a Cerebral Aneurysm? A Proposed Novel Hemodynamic Index, the Gradient Oscillatory Number (GON). Journal of Biomechanics, 42, 550-554.
[9] Davies, P.F. (1995) Flow Mediated Endothelial Mechano-transduction. Physiological Reviews, 75, 519-560.
[10] Chien, S. (2008) Effects of Disturbed Flow on Endothelial Cells. Annals of Biomedical Engineering, 36, 554-562.
[11] Dewey, C.F. (1994) Effects of Fluid Flow on Living Vascular Cells. ASME Journal of Biomechanical Engineering, 106, 31-35.
[12] Goldstein, A.S. and DiMilla, P.A. (1998) Comparison of Converging and Diverging Radial Flow for Measuring Cell Adhesion. AIChE Journal, 44, 465-473.
[13] Frangos, J.A., Eskin S.G., McIntire, L.V. and Ives, C.L. (1985) Flow Effects on Prostacyclin Production by Cultured Human Endothelial Cells. Science, 227, 1477-1479.
[14] Zeng, L., Xiao, Q., Margariti, A., Zhang, Z., Zampetaki, A., Patel, S., Capogrossi, M. C., Hu, Y. and Xu, Q. (2006) HDAC3 is Crucial in Shear- and VEGF-Induced Stem Cell Differentiation toward Endothelial Cells. Journal of Cell Biology, 174, 1059-1069.
[15] Brown, T.D. (2000) Techniques for Mechanical Stimulation of Cells in vitro: a Review. Journal of Biomechanics, 33, 3-14.
[16] DePaola, N., Gimbrone, M.A., Davies, P.F. and Dewey, C.F. (1993) Vascular Endothelium Responds to Fluid Shear Stress Gradients. Arteriosclerosis, Thrombosis, and Vascular Biology, 12, 1254-1257.
[17] Watkins, N.V., Caro, C.G. and Wang, W. (2002) Parallel-Plate Flow Chamber for Studies of 3D Flow-Endothelium Interaction. Biorheology, 39, 337-342.
[18] Qin, K., Jiang, W., Li, X. and Liu, Z. (1998) On Analysis of the Steady Flow in an Irrectangular Paral-lel-Plate Flow Chamber. Applied Mathematics and Mechanics, 19, 851-859.
[19] Usami, S., Chen, H.H., Zhao, Y., Chien, S. and Skalak, R. (1993) Design and Construction of a Linear Shear Stress Flow Chamber. Annals of Biomedical Engineering, 21, 77-83.
[20] Tsou, J.K., Gower, R.M., Ting, H.J., Schaff, U.Y., Insan, M.F., Passerini, A.G. and Simon, S.I. (2008) Spatial Regulation of Inflammation by Human Aortic Endothelial Cells in a Linear Gradient of Shear Stress. Microcirculation, 15, 311-323.
[21] Dolan, J.M., Meng, H., Singh, S., Paluch, R. and Kolega, J. (2011) High Fluid Shear Stress and Spatial Shear Stress Gradients Affect Endothelial Proliferation, Survival, and Alignment. Annals of Biomedical Engineering, 39, 1620-1631.

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