0
Research Papers

Computational Analysis of Fluid Flow Within a Device for Applying Biaxial Strain to Cultured Cells

[+] Author and Article Information
Jason Lee

Department of Biomedical Engineering,
University of Texas at Austin,
Austin, TX 78712

Aaron B. Baker

Department of Biomedical Engineering,
University of Texas at Austin,
107 West Dean Keeton Street,
BME 5.202D, C0800,
Austin, TX 78712
e-mail: abbaker1@gmail.com

1Corresponding author.

Manuscript received September 5, 2014; final manuscript received January 10, 2015; published online March 5, 2015. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 137(5), 051006 (May 01, 2015) (7 pages) Paper No: BIO-14-1441; doi: 10.1115/1.4029638 History: Received September 05, 2014; Revised January 10, 2015; Online March 05, 2015

In vitro systems for applying mechanical strain to cultured cells are commonly used to investigate cellular mechanotransduction pathways in a variety of cell types. These systems often apply mechanical forces to a flexible membrane on which cells are cultured. A consequence of the motion of the membrane in these systems is the generation of flow and the unintended application of shear stress to the cells. We recently described a flexible system for applying mechanical strain to cultured cells, which uses a linear motor to drive a piston array to create biaxial strain within multiwell culture plates. To better understand the fluidic stresses generated by this system and other systems of this type, we created a computational fluid dynamics model to simulate the flow during the mechanical loading cycle. Alterations in the frequency or maximal strain magnitude led to a linear increase in the average fluid velocity within the well and a nonlinear increase in the shear stress at the culture surface over the ranges tested (0.5–2.0 Hz and 1–10% maximal strain). For all cases, the applied shear stresses were relatively low and on the order of millipascal with a dynamic waveform having a primary and secondary peak in the shear stress over a single mechanical strain cycle. These findings should be considered when interpreting experimental results using these devices, particularly in the case when the cell type used is sensitive to low magnitude, oscillatory shear stresses.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Mammoto, T., Mammoto, A., and Ingber, D. E., 2013, “Mechanobiology and Developmental Control,” Annu. Rev. Cell Dev. Biol., 29, pp. 27–61. [CrossRef] [PubMed]
Chiu, J. J., and Chien, S., 2011, “Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives,” Physiol. Rev., 91(1), pp. 327–387. [CrossRef] [PubMed]
Koskinas, K. C., Chatzizisis, Y. S., Baker, A. B., Edelman, E. R., Stone, P. H., and Feldman, C. L., 2009, “The Role of Low Endothelial Shear Stress in the Conversion of Atherosclerotic Lesions From Stable to Unstable Plaque,” Curr. Opin. Cardiol., 24(6), pp. 580–590. [CrossRef] [PubMed]
Makale, M., 2007, “Cellular Mechanobiology and Cancer Metastasis,” Birth Defects Res., Part C, 81(4), pp. 329–343. [CrossRef]
Suresh, S., 2007, “Biomechanics and Biophysics of Cancer Cells,” Acta Biomater., 3(4), pp. 413–438. [CrossRef] [PubMed]
Laplaca, M. C., and Prado, G. R., 2010, “Neural Mechanobiology and Neuronal Vulnerability to Traumatic Loading,” J. Biomech., 43(1), pp. 71–78. [CrossRef] [PubMed]
Uversky, V. N., and Eliezer, D., 2009, “Biophysics of Parkinson's Disease: Structure and Aggregation of Alpha-Synuclein,” Curr. Protein Pept. Sci., 10(5), pp. 483–499. [CrossRef] [PubMed]
Brown, T. D., 2000, “Techniques for Mechanical Stimulation of Cells In Vitro: A Review,” J. Biomech., 33(1), pp. 3–14. [CrossRef] [PubMed]
Kim, D. H., Wong, P. K., Park, J., Levchenko, A., and Sun, Y., 2009, “Microengineered Platforms for Cell Mechanobiology,” Annu. Rev. Biomed. Eng., 11, pp. 203–233. [CrossRef] [PubMed]
Schulz, R. M., and Bader, A., 2007, “Cartilage Tissue Engineering and Bioreactor Systems for the Cultivation and Stimulation of Chondrocytes,” Eur. Biophys. J., 36(4–5), pp. 539–568. [CrossRef] [PubMed]
Lee, A. A., Delhaas, T., Waldman, L. K., MacKenna, D. A., Villarreal, F. J., and McCulloch, A. D., 1996, “An Equibiaxial Strain System for Cultured Cells,” Am. J. Physiol., 271(4 Pt. 1), p. C1400. [PubMed]
Lee, J., Wong, M., Smith, Q., and Baker, A. B., 2013, “A Novel System for Studying Mechanical Strain Waveform-Dependent Responses in Vascular Smooth Muscle Cells,” Lab Chip, 13(23), pp. 4573–4582. [CrossRef] [PubMed]
Schaffer, J. L., Rizen, M., L'Italien, G. J., Benbrahim, A., Megerman, J., Gerstenfeld, L. C., and Gray, M. L., 1994, “Device for the Application of a Dynamic Biaxially Uniform and Isotropic Strain to a Flexible Cell Culture Membrane,” J. Orthop. Res., 12(5), pp. 709–719. [CrossRef] [PubMed]
Sotoudeh, M., Jalali, S., Usami, S., Shyy, J. Y., and Chien, S., 1998, “A Strain Device Imposing Dynamic and Uniform Equi-Biaxial Strain to Cultured Cells,” Ann. Biomed. Eng., 26(2), pp. 181–189. [CrossRef] [PubMed]
Bieler, F. H., Ott, C. E., Thompson, M. S., Seidel, R., Ahrens, S., Epari, D. R., Wilkening, U., Schaser, K. D., Mundlos, S., and Duda, G. N., 2009, “Biaxial Cell Stimulation: A Mechanical Validation,” J. Biomech., 42(11), pp. 1692–1696. [CrossRef] [PubMed]
Simmons, C. S., Sim, J. Y., Baechtold, P., Gonzalez, A., Chung, C., Borghi, N., and Pruitt, B. L., 2011, “Integrated Strain Array for Cellular Mechanobiology Studies,” J. Micromech. Microeng., 21(5), pp. 54016–54025. [CrossRef] [PubMed]
Vande Geest, J. P., Di Martino, E. S., and Vorp, D. A., 2004, “An Analysis of the Complete Strain Field Within Flexercell Membranes,” J. Biomech., 37(12), pp. 1923–1928. [CrossRef] [PubMed]
Chatzizisis, Y. S., Coskun, A. U., Jonas, M., Edelman, E. R., Feldman, C. L., and Stone, P. H., 2007, “Role of Endothelial Shear Stress in the Natural History of Coronary Atherosclerosis and Vascular Remodeling: Molecular, Cellular, and Vascular Behavior,” J. Am. Coll. Cardiol., 49(25), pp. 2379–2393. [CrossRef] [PubMed]
Hsiai, T. K., Cho, S. K., Wong, P. K., Ing, M., Salazar, A., Sevanian, A., Navab, M., Demer, L. L., and Ho, C. M., 2003, “Monocyte Recruitment to Endothelial Cells in Response to Oscillatory Shear Stress,” FASEB J., 17(12), pp. 1648–1657. [CrossRef] [PubMed]
Hwang, J., Saha, A., Boo, Y. C., Sorescu, G. P., McNally, J. S., Holland, S. M., Dikalov, S., Giddens, D. P., Griendling, K. K., Harrison, D. G., and Jo, H., 2003, “Oscillatory Shear Stress Stimulates Endothelial Production of O2- From p47phox-Dependent NAD(P)H Oxidases, Leading to Monocyte Adhesion,” J. Biol. Chem., 278(47), pp. 47291–47298. [CrossRef] [PubMed]
Yin, W., Shanmugavelayudam, S. K., and Rubenstein, D. A., 2011, “The Effect of Physiologically Relevant Dynamic Shear Stress on Platelet and Endothelial Cell Activation,” Thromb. Res., 127(3), pp. 235–241. [CrossRef] [PubMed]
Awolesi, M. A., Widmann, M. D., Sessa, W. C., and Sumpio, B. E., 1994, “Cyclic Strain Increases Endothelial Nitric Oxide Synthase Activity,” Surgery, 116(2), pp. 439–444. [PubMed]
Xiao, Z., Zhang, Z., Ranjan, V., and Diamond, S. L., 1997, “Shear Stress Induction of the Endothelial Nitric Oxide Synthase Gene is Calcium-Dependent but Not Calcium-Activated,” J. Cell. Physiol., 171(2), pp. 205–211. [CrossRef] [PubMed]
Boutahar, N., Guignandon, A., Vico, L., and Lafage-Proust, M. H., 2004, “Mechanical Strain on Osteoblasts Activates Autophosphorylation of Focal Adhesion Kinase and Proline-Rich Tyrosine Kinase 2 Tyrosine Sites Involved in ERK Activation,” J. Biol. Chem., 279(29), pp. 30588–30599. [CrossRef] [PubMed]
Kapur, S., Baylink, D. J., and Lau, K. H., 2003, “Fluid Flow Shear Stress Stimulates Human Osteoblast Proliferation and Differentiation Through Multiple Interacting and Competing Signal Transduction Pathways,” Bone, 32(3), pp. 241–251. [CrossRef] [PubMed]
Iwasaki, H., Eguchi, S., Ueno, H., Marumo, F., and Hirata, Y., 2000, “Mechanical Stretch Stimulates Growth of Vascular Smooth Muscle Cells Via Epidermal Growth Factor Receptor,” Am. J. Physiol. Heart Circ. Physiol., 278(2), pp. H521–H529. [PubMed]
Ueba, H., Kawakami, M., and Yaginuma, T., 1997, “Shear Stress as an Inhibitor of Vascular Smooth Muscle Cell Proliferation. Role of Transforming Growth Factor-Beta 1 and Tissue-Type Plasminogen Activator,” Arterioscler. Thromb. Vasc. Biol., 17(8), pp. 1512–1516. [CrossRef] [PubMed]
Song, G., Ju, Y., Shen, X., Luo, Q., Shi, Y., and Qin, J., 2007, “Mechanical Stretch Promotes Proliferation of Rat Bone Marrow Mesenchymal Stem Cells,” Colloids Surf. B, 58(2), pp. 271–277. [CrossRef]
Yourek, G., McCormick, S. M., Mao, J. J., and Reilly, G. C., 2010, “Shear Stress Induces Osteogenic Differentiation of Human Mesenchymal Stem Cells,” Regener. Med., 5(5), pp. 713–724. [CrossRef]
Thompson, M. S., Abercrombie, S. R., Ott, C. E., Bieler, F. H., Duda, G. N., and Ventikos, Y., 2011, “Quantification and Significance of Fluid Shear Stress Field in Biaxial Cell Stretching Device,” Biomech. Model Mechanobiol., 10(4), pp. 559–564. [CrossRef] [PubMed]
Davies, P. F., Remuzzi, A., Gordon, E. J., Dewey, C. F., Jr., and Gimbrone, M. A., Jr., 1986, “Turbulent Fluid Shear Stress Induces Vascular Endothelial Cell Turnover In Vitro,” Proc. Natl. Acad. Sci. USA, 83(7), pp. 2114–2117. [CrossRef]
Ziegler, T., Bouzourene, K., Harrison, V. J., Brunner, H. R., and Hayoz, D., 1998, “Influence of Oscillatory and Unidirectional Flow Environments on the Expression of Endothelin and Nitric Oxide Synthase in Cultured Endothelial Cells,” Arterioscler. Thromb. Vasc. Biol., 18(5), pp. 686–692. [CrossRef] [PubMed]
White, F. M., 2003, Fluid Mechanics, McGraw-Hill, Boston, MA.
Voyvodic, P. L., Min, D., Liu, R., Williams, E., Chitalia, V., Dunn, A. K., and Baker, A. B., 2014, “Loss of Syndecan-1 Induces a Pro-Inflammatory Phenotype in Endothelial Cells With a Dysregulated Response to Atheroprotective Flow,” J. Biol. Chem., 289(14), pp. 9547–9559. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

(a) Photograph of device for applying mechanical stretch to culture cells. (b) Photograph of a single well with flexible cell culture substrate. (c) Diagram of the application of mechanical strain to the well through the displacement of the piston and the top view of the geometry of the culture well used for the studies.

Grahic Jump Location
Fig. 2

(a) Optimized mesh used in the simulations. (b) Displacement profile of piston. Dashed lines denote the location of the walls of the well. (c) Displacement of the bottom of the well during the simulation. Plotted are the shear stress of the bottom of the well during the motion. The displacement for 10% maximal strain at 1 Hz is shown.

Grahic Jump Location
Fig. 3

Maximal magnitude of velocity within the well at frequency plotted on a coronal plane cut through the center of the well (time point varied with frequency of loading). The plotted time was chosen as the time when there was the maximum velocity in the coronal slice from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Maximum strains of 1%, 5%, and 10% were investigated per frequency. Higher velocity is observed toward the middle of the well. To aid visualization, the displacement of the membrane is not shown in the simulation.

Grahic Jump Location
Fig. 4

Maximal magnitude of velocity within the system for each of the frequencies tested (0.5, 1, and 2 Hz) as the membrane displaces. The plotted time was chosen as the time when there was the maximum velocity in the horizontal slices from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Horizontal cut planes through the well with the bottom, middle, and top of the well are shown. Maximum strains of 1%, 5%, and 10% were investigated at each frequency. The bottom plane shows the velocity of the displacing surface, and the top plane shows the velocity at the top of the well. Higher velocity is observed toward the middle of the well. To aid visualization, the displacement of the membrane is not shown in the simulation.

Grahic Jump Location
Fig. 5

Fluid velocity and shear stress during mechanical loading, averaged over the entire well or culture surface. (a) Average fluid velocity for the entire well averaged over time in the final cycle of the simulation. (b) Average shear stress on the culture surface averaged over time in the final cycle of the simulation.

Grahic Jump Location
Fig. 6

Velocity isosurfaces for the time with maximal velocity for each frequency of loading (0.5, 1, and 2 Hz) as the membrane displaces. Maximum strains of 1%, 5%, and 10% were investigated at each frequency. The plotted time was chosen as the time when there was the maximum velocity in the well from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Each isosurface color shows a surface with a constant velocity within the well in millimeter per second. Higher velocity is observed toward the middle of the well.

Grahic Jump Location
Fig. 7

(a) Average shear stress over the first cycles of loading for the total, central, and outer regions of the bottom surface of the well. Conditions shown are for 10% maximal strain and 1 Hz frequency of loading. (b) Average shear stress on the bottom of the plate over the last cycle of the simulation.

Grahic Jump Location
Fig. 8

Maximal shear stress on the surfaces of the well during the loading cycle. Within each frequency group, the time point chosen is held constant and is set for the time of maximal shear stress. Maximum strains of 1%, 5%, and 10% were investigated per frequency. The plotted time was chosen as the time when there was the maximum shear stress on the well surfaces from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Higher shear stress is observed toward the wall. The quarter front wall has been removed to aid visualization.

Grahic Jump Location
Fig. 9

Circumferential average of shear stresses on the culture surface during last cycle of the simulation. The zero point indicates the center of the well with an average taken circumferentially at each radius. Graphs shown are for 10% maximal strain and 1 Hz frequency of loading.

Grahic Jump Location
Fig. 10

Circumferential average shear stress during last cycle of the simulation. The zero point indicates the center of the well with an average taken circumferentially at each radius. All frequencies (0.5, 1, and 2 Hz) and maximal strain (1%, 5%, and 10%) are shown.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In