Numerical Investigation of the Strain Stiffening Behavior of Mesenchymal Stem Cells on Elastic Substrates

Document Type : Mechanics article

Authors

1 MSc/University of Tehran

2 Assistant Professor/University of Tehran

Abstract

In order to accurately predict the cellular response, it is necessary, along with other factors, to consider the effect of the cell spreading on the substrate. Also, the core tensions, due to the cell spreading, play a crucial role in the fate of a stem cell. Therefore, the exact prediction of these tensions is of particular importance. The effect of the strain stiffening of a mesenchymal cell, in a two-dimensional model, was investigated numerically using finite element method, by exerting a time function displacement, to the cytoplasm boundary. Utilizing Schwartz-Christoffel transformation, a model for cell-spreading was proposed that can be used to achieve accurate cellular responses. Three different models are considered. In the first model, the cell is treated as a non-alive material. That is, the mechanical properties remain constant on the substrate. Two other models, the linear and exponential strain-stiffening, are active models. By comparing the results of these models with the experimental results, it was found that the assumption that the cell is inactive departs the response from the exact amount. Therefore, considering the cell’s living nature, in both linear and exponential models, leads to more similarity of the results, both the tension value and the slope of the variations, with the experimental observations. Furthermore, by increasing the amount of the cell spreading, the difference in the amount of the nucleus stress in active models with the inactive model increases, so that the predicted tension by the linear model reaches 2.3 times that predicted by the non-alive model.

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Main Subjects

References

 
[1] Wu, H.W., Lin, C.C., Hwang, S.M, Chang, Y.J., Lee, G.B. (2011). A Microfluidic Device for Chemical and Mechanical Stimulation of Mesenchymal Stem Cells, Microfluidics and Nanofluidics, Vol. 11, pp. 545–556.
[2] McBeath, R., Pirone, D.M., Nelson, C.M., Bhadriraju, K., Chen, C.S. (2004). Cell Shape, Cytoskeletal Tension, and RhoA Regulate Stem Cell Lineage Commitment, Developmental Cell, Vol. 6, pp. 483–495.
[3] Pek, Y.S., Wan, A.C., Ying, J.Y. (2010). The Effect of Matrix Stiffness on Mesenchymal Stem Cell Differentiation in a 3D Thixotropic Gel, Biomaterials, Vol. 31, pp. 385–391.
[4] Schätti, O., Grad, S., Goldhahn, J., Salzmann, G., Li, Z., Alini, M., et al. (2011). A Combination of Shear and Dynamic Compression Leads to Mechanically Induced Chondrogenesis of Human Mesenchymal Stem Cells, European Cells & Materials, Vol. 22, pp. 214–225.
[5] Sim, W.Y., Park, S.W., Park, S.H., Min, B.H., Park, S.R., Yang, S.S. (2007). A Pneumatic Micro Cell Chip for the Differentiation of Human Mesenchymal Stem Cells Under Mechanical Stimulation, Lab on a Chip, Vol. 7, pp. 1775–1782.
[6] Zhao, F., Chella, R., Ma, T. (2015). . Effects of Shear Stress on 3‐D Human Mesenchymal Stem Cell Construct Development in a Perfusion Bioreactor System: Experiments and Hydrodynamic Modeling Biotechnology and Bioengineering, Vol. 15, pp. 584–595.
[7] Vaziri. A., Mofrad. M.R. (2007). Mechanics and Deformation of the Nucleus in Micropipette Aspiration Experiment, Journal of Biomechanics, Vol. 40, pp. 2053–2062.
[8] Dailey, H.L., Ricles, L.M., Yalcin, H.C., Ghadiali, S.N. (1985). Image-Based Finite Element Modeling of Alveolar Epithelial Cell Injury During Airway Reopening, Journal of Applied Physiology, Vol. 106, pp. 221–232.
[9] Deshpande, V.S., McMeeking, R.M., Evans, A.G. (2006). A Bio-Chemo-Mechanical Model for Cell Contractility, Proceedings of the National Academy of Sciences of the United States of America, Vol. 103, pp. 14015–14020.
[10] Deshpande, V.S., Mrksich, M., McMeeking, R.M., Evans, A.G. (2008). A Bio-Mechanical Model for Coupling Cell Contractility with Focal Adhesion Formation, Journal of the Mechanics and Physics of Solids, Vol. 56, pp. 1484–1510.
[11] McGarry, J.P., Fu, J., Yang, M.T., Chen, C.S., McMeeking, R.M., Evans, A.G., et al. (2009). Simulation of the Contractile Response of Cells on an Array of Micro-Posts, Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences, Vol. 367, pp. 3477–3497.
[12] Alihemmati, Z., Vahidi, B., Haghighipour, N., Salehi, M. (2017). Computational Simulation of Static/Cyclic Cell Stimulations to Investigate Mechanical Modulation of an Individual Mesenchymal Stem Cell Using Confocal Microscopy, Materials Science & Engineering C-Materials for Biological Applications, Vol. 70, pp. 494–504.
[13] Ghaemi, R.V., Vahidi, B., Sabour, M.H., Haghighipour, N., Alihemmati, Z.  (2016). Fluid–Structure Interactions Analysis of Sear-Induce Modulation of a Mesenchymal Stem Cell: an Image-Based Study, Artificial Organs, Vol. 40, pp. 278–287.
[14] Mullen, C.A., Vaughan, T.J., Voisin, M.C., Brennan, M.A., Layrolle, P., McNamara, L.M. (2014). Cell Morphology and Focal Adhesion Location Alters Internal Cell Stress, Journal of The Royal Society Interface, Vol. 11.
[15] Jean, R.P., Gray, D.S., Spector, A.A., Chen, C.S. (2004). Characterization of the Nuclear Deformation Caused by Changes in Endothelial Cell Shape, Journal of Biomechanical Engineering, Vol. 126, pp. 552–558.
[16] Vishavkarma, R., Raghavan, S., Kuyyamudi, C., Majumder, A., Dhawan, J., Pullarkat, P.A. (2014). Role of Actin Filaments in Correlating Nuclear Shape and Cell Spreading, Public Library of Science, Vol. 9.
[17] Wang, N., Stamenovic, D. (2000). Contribution of Intermediate Filaments to Cell Stiffness, Stiffening, and Growth, American Journal of Physiology-Cell Physiology, Vol. 279, pp. 181-194.
[18] Thoumine, O., Cardoso, O., Meister, J., Majumder (1999). Chang in the Mechanical Properties of Fibroblasts during Spreading: a Micromanipulation Study, European Biophysics Journal, Vol. 28, pp. 222-234.
[19] McGarry, J.G., Prendergast, P.J. (2004). A Three Dimensional Finite Element Model of an Adherent Eukaryotic Cell, European Cells and Materials, Vol. 7, pp. 27-34.
 
[20] Speigel, M.R. (1964). Schaum's Outline of Theory and Problems of Complex Variables: with an Introduction to Conformal Mapping and Its Application, New York, McGraw Hill.
[21] Bonet, J., Wood, R.D. (2008). Nonlinear Continuum Mechanics for Finite Element Analysis, United Kingdom, Cambridge University Press.
[22] Docheva, D., Padula, D., Popov, C., Mutschler, W., Clausen-Schaumann, H., Schieker, M. (2008). Researching into the Cellular Shape, Volume and Elasticity of Mesenchymal Stem Cells, Osteoblasts and Osteosarcoma Cells by Atomic Force Microscopy, Journal of Cellular and Molecular Medicine, Vol. 12, pp. 537–552.
[23] Guilak, F., Tedrow, J.  Burgkart, R. (2000). Viscoelastic Properties of the Cell Nucleus, Biochemical and Biophysical Research Communication, Vol. 269, pp. 781–786.
[24] Zielinski, R., Mihai, C., Kniss, D., Ghadiali, S.N.  (2013). Finite Element Analysis of Traction Force Microscopy: Influence of Cell Mechanics, Adhesion, and Morphology, Journal of Biomechanical Engineering, Vol. 135.
 
 
 
 
Journal of Modeling in Engineering
Volume 16, Issue 55
December 2018
Pages 351-359

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History

  • Receive Date: 06 October 2017
  • Revise Date: 06 January 2018
  • Accept Date: 22 January 2018

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