Abstract
Different mechanical stimuli are applied to the substrate of a microchip and a cellular scaffold to simulate in vivo biomechanical environment, but few studies have been performed to measure the stress inside the substrate and the scaffold. In this study, a novel technique of computing the stress field inside a scaffold using optically measured deformation field has been developed. The effectiveness of our proposed technique is evaluated using a polymer block undergoing indentation deformation. The deformation field in the cross section of a block under indentation loading was measured using a particle image analysis method, and the accuracy of the displacement measurement method was verified. The measured displacement fields were mapped into the cross sectional surface of a block model, and FE analysis was performed to compute the stress fields. The stress field estimated from the inverse analysis using the measured displacement fields agree with that of the direct force loading simulation, and the relative error of maximum stress was less than 3%. The indentation forces also agreed well with those in the direct force loading FE analysis, and the errors were less than 8%.
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References
Gillespie, P. G. and Walker, R. G., “Molecular Basis of Mechanosensory Transduction,” Nature, Vol. 413, No. 6852, pp. 194–202, 2001.
Wang, H.-B., Dembo, M., Hanks, S. K., and Wang, Y.-l., “Focal Adhesion Kinase is involved in Mechanosensing during Fibroblast Migration,” Proceedings of the National Academy of Sciences, Vol. 98, No. 20, pp. 11295–11300, 2001.
Chen, C. S., “Mechanotransduction -A Field Pulling Together?” Journal of Cell Science, Vol. 121, No. 20, pp. 3285–3292, 2008.
Burton, K. and Taylor, D. L., “Traction Forces of Cytokinesis Measured with Optically Modified Elastic Substrata,” Nature, Vol. 385, No. 6615, pp. 450, 1997.
Schwarz, U. S., Balaban, N. Q., Riveline, D., Bershadsky, A., Geiger, B., and Safran, S., “Calculation of Forces at Focal Adhesions from Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization,” Biophysical Journal, Vol. 83, No. 3, pp. 1380–1394, 2002.
Engler, A., Bacakova, L., Newman, C., Hategan, A., Griffin, M., and Discher, D., “Substrate Compliance Versus Ligand Density in Cell on Gel Responses,” Biophysical Journal, Vol. 86, No. 1, pp. 617–628, 2004.
Cesa, C. M., Kirchgeßner, N., Mayer, D., Schwarz, U. S., Hoffmann, B., and Merkel, R., “Micropatterned Silicone Elastomer Substrates for High Resolution Analysis of Cellular Force Patterns,” Review of Scientific Instruments, Vol. 78, No. 3, Paper No. 034301, 2007.
Pelham, R. J. and Wang, Y.-l., “High Resolution Detection of Mechanical Forces Exerted by Locomoting Fibroblasts on the Substrate,” Molecular Biology of the Cell, Vol. 10, No. 4, pp. 935–945, 1999.
Yang, Z., Lin, J.-S., Chen, J., and Wang, J. H., “Determining Substrate Displacement and Cell Traction Fields -A New Approach,” Journal of Theoretical Biology, Vol. 242, No. 3, pp. 607–616, 2006.
Ng, S. S., Li, C., and Chan, V., “Experimental and Numerical Determination of Cellular Traction Force on Polymeric Hydrogels,” Interface Focus, Vol. 1, No. 5, pp. 777–791, 2011.
Tolic-Nørrelykke, I. M., Butler, J. P., Chen, J., and Wang, N., “Spatial and Temporal Traction Response in Human Airway Smooth Muscle Cells,” American Journal of Physiology-Cell Physiology, Vol. 283, No. 4, pp. C1254–C1266, 2002.
Dembo, M. and Wang, Y.-L., “Stresses at the Cell-to-Substrate Interface during Locomotion of Fibroblasts,” Biophysical Journal, Vol. 76, No. 4, pp. 2307–2316, 1999.
Butler, J. P., Tolic-Nø rrelykke, I. M., Fabry, B., and Fredberg, J. J., “Traction Fields, Moments, and Strain Energy that Cells Exert on their Surroundings,” American Journal of Physiology-Cell Physiology, Vol. 282, No. 3, pp. C595–C605, 2002.
Hur, S. S., Zhao, Y., Li, Y.-S., Botvinick, E., and Chien, S., “Live Cells Exert 3-Dimensional Traction Forces on their Substrata,” Cellular and Molecular Bioengineering, Vol. 2, No. 3, pp. 425–436, 2009.
Maskarinec, S. A., Franck, C., Tirrell, D. A., and Ravichandran, G., “Quantifying Cellular Traction Forces in Three Dimensions,” Proceedings of the National Academy of Sciences, Vol. 106, No. 52, pp. 22108–22113, 2009.
Toyjanova, J., Bar-Kochba, E., López-Fagundo, C., Reichner, J., Hoffman-Kim, D., and Franck, C., “High Resolution, Large Deformation 3D Traction Force Microscopy,” PLoS One, Vol. 9, No. 4, Paper No. e90976, 2014.
Hsiai, T. K., “Mechanosignal Transduction Coupling between Endothelial and Smooth Muscle Cells: Role of Hemodynamic Forces,” American Journal of Physiology-Cell Physiology, Vol. 294, No. 3, pp. C659–C661, 2008.
Polacheck, W. J., Li, R., Uzel, S. G., and Kamm, R. D., “Microfluidic Platforms for Mechanobiology,” Lab on a Chip, Vol. 13, No. 12, pp. 2252–2267, 2013.
Davis, C. A., Zambrano, S., Anumolu, P., Allen, A. C., Sonoqui, L., and Moreno, M. R., “Device-Based In Vitro Techniques for Mechanical Stimulation of Vascular Cells: A Review,” Journal of Biomechanical Engineering, Vol. 137, No. 4, Paper No. 040801, 2015.
Lee, J. N., Jiang, X., Ryan, D., and Whitesides, G. M., “Compatibility of Mammalian Cells on Surfaces of Poly (Dimethylsiloxane),” Langmuir, Vol. 20, No. 26, pp. 11684–11691, 2004.
Chung, C., Chen, Y.-J., Chen, P.-C., and Chen, C.-Y., “Fabrication of PDMS Passive Micromixer by Lost-Wax Casting,” Int. J. Precis. Eng. Manuf., Vol. 16, No. 9, pp. 2033–2039, 2015.
Keane, R. D. and Adrian, R. J., “Theory of Cross-Correlation Analysis of PIV Images,” Applied Scientific Research, Vol. 49, No. 3, pp. 191–215, 1992.
Sadek, S., Iskander, M.G., and Liu, J., “Accuracy of Digital Image Correlation for Measuring Deformation in Transparent Media,” Journal of Computing in Civil Engineering, Vol. 17, No. 2, pp. 88–96, 2003.
Sabass, B., Gardel, M. L., Waterman, C. M., and Schwarz, U. S., “High Resolution Traction Force Microscopy Based on Experimental and Computational Advances,” Biophysical Journal, Vol. 94, No. 1, pp. 207–220, 2008.
Guo, Z., You, S., Wan, X., and Bicanic, N., “A FEM-Based Direct Method for Material Reconstruction Inverse Problem in Soft Tissue Elastography,” Computers & Structures, Vol. 88, No. 23, pp. 1459–1468, 2010.
Nicholson, D. W., “On Finite Element Analysis of an Inverse Problem in Elasticity,” Inverse Problems in Science and Engineering, Vol. 20, No. 5, pp. 735–748, 2012.
Domke, J. and Radmacher, M., “Measuring the Elastic Properties of Thin Polymer Films with the Atomic Force Microscope,” Langmuir, Vol. 14, No. 12, pp. 3320–3325, 1998.
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Kang, MJ., Rhee, K. Computation of stress field in a polymer scaffold from optically measured deformation field using particle images. Int. J. Precis. Eng. Manuf. 18, 1021–1026 (2017). https://doi.org/10.1007/s12541-017-0120-6
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DOI: https://doi.org/10.1007/s12541-017-0120-6