Continuum-Based Modelling Approaches for Cell Mechanics

Authors: Yogesh D. Bansod, Jiri Bursa

Abstract:

The quantitative study of cell mechanics is of paramount interest, since it regulates the behaviour of the living cells in response to the myriad of extracellular and intracellular mechanical stimuli. The novel experimental techniques together with robust computational approaches have given rise to new theories and models, which describe cell mechanics as combination of biomechanical and biochemical processes. This review paper encapsulates the existing continuum-based computational approaches that have been developed for interpreting the mechanical responses of living cells under different loading and boundary conditions. The salient features and drawbacks of each model are discussed from both structural and biological points of view. This discussion can contribute to the development of even more precise and realistic computational models of cell mechanics based on continuum approaches or on their combination with microstructural approaches, which in turn may provide a better understanding of mechanotransduction in living cells.

Keywords: Cell mechanics, computational models, continuum approach, mechanical models.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1107928

References:

[1] Yeung, E. Evans, “Cortical Shell-Liquid Core Model for Passive Flow of Liquid-Like Spherical Cells into Micropipets,” Biophys J., vol. 56, no. 1, pp. 139–149, 1989.
[2] C. Dong, R. Skalak, and K. L. Sung, “Cytoplasmic Rheology of Passive Neutrophils,” Biorheology, vol. 28, no. 6, pp. 557–567, 1991.
[3] M. A. Tsai, R. S. Frank, and R. E. Waugh, “Passive Mechanical Behaviour of Human Neutrophils: Power-Law fluid,” Biophysical Journal, vol. 65, no. 5, pp. 2078–2088, 1993.
[4] C. Dong, R. Skalak, K. L. Sung, G. W. Schmid-Schonbein, and S. Chien, “Passive Deformation Analysis of Human Leukocytes,” Journal of Biomechanical Engineering, vol. 110, no. 1, pp. 27–36, 1988.
[5] B. Fabry, G. Maksym, J. Butler, M. Glougauer, D. Navajas, and J. Fredberg, “Scaling the Microrheology of Living Cells,” The American Physical Society, vol. 87, no. 14, pp. 148102, 2001.
[6] V. S. Deshpande, R. M. McMeeking, and A. G. Evans, “A Bio-Chemo- Mechanical Model for Cell Contractility,” Proc. Natl. Acad. Sci. U.S.A, vol. 103, no. 38, pp. 14015–14020, 2006.
[7] R. Blumenfeld, “Isostaticity and Controlled Force Transmission in the Cytoskeleton: A Model Awaiting Experimental Evidence,” Biophys Journal, vol. 91, pp. 1970-1983, 2006.
[8] F. C. Mackintosh, J. Kas, and P. A. Janmey, “Elasticity of Semi-flexible Biopolymer Networks,” Phys. Rev. Lett., vol. 75, no. 24, pp. 4425– 4428, 1995.
[9] P. Onck, T. Koeman, T. van Dillen, and E. van der Giessen, “Alternative Explanation of Stiffening in Cross-Linked Semi-flexible Networks,” Phys. Rev. Lett., vol. 95, pp. 178102, 2005.
[10] D. Head, A. Levine, and F. MacKintosh, “Distinct Regimes of Elastic Response and Deformation Modes of Cross-Linked Cytoskeletal and Semi-flexible Polymer Networks,” Phys. Rev. E, vol. 68, pp. 061907, 2003.
[11] H. Isambert, A. Maggs, “Dynamics and Rheology of Actin Solutions,” Macromolecules, vol. 29, no. 3, pp. 1036-1040, 1996.
[12] T. Kim, W. Hwang, and R. Kamm, “Computational Analysis of a Cross- Linked Actin-Like Network,” Experimental Mechanics, vol. 49, no. 1, pp. 91-104, 2009.
[13] M. Coughlin, D. Stamenovic, “A Prestressed Cable Network Model of the Adherent Cell Cytoskeleton,” Biophysical Journal, vol. 84, no. (2 Pt 1), pp. 1328-1336, 2003.
[14] D. Stamenovic, M. Coughin, “The Role of Prestress and Architecture of the Cytoskeleton and Deformability of Cytoskeletal Filaments in Mechanics of Adherent Cells: A Quantitative Analysis,” Journal of Theoretical Biology, vol. 201, no. 1, pp. 63-74, 1999.
[15] D. E. Ingber, “Cellular Tensegrity—Defining New Rules of Biological Design that Govern the Cytoskeleton,” J. Cell Sci., vol. 104, pp. 613– 627, 1993.
[16] J. Milan, S. Wendling-Mansuy, M. Jean, and P. Chabrand, “Divided Medium-Based Model for Analyzing the Dynamic Reorganization of the Cytoskeleton during Cell Deformation,” Biomech Model Mechanobiol, vol. 6, no. 6, pp. 373–390, 2007.
[17] B. Maurin, P. Canadas, H. Baudriller, P. Montcourrier, and N. Bettache, “Mechanical Model of Cytoskeleton Structuration during Cell Adhesion and Spreading,” Journal of Biomechanics, vol. 41, no. 9, pp. 2036-2041, 2008.
[18] C. S. Peskin, G. M. Odell, and G. F. Oster, “Cellular Motions and Thermal Fluctuations: The Brownian Ratchet,” Biophysical Journal, vol. 65, pp. 316–324, 1993.
[19] A. Mogilner, G. Oster, “Cell Motility Driven by Actin Polymerization,” Biophysical Journal, vol. 71 no. 6, pp. 3030-3045, 1996.
[20] A. Zemel, I, Bischofs, and S. Safran, “Active Elasticity of Gels with Contractile Cells,” Physical Review Letters, vol. 97, no. 12, pp. 128103, 2006.
[21] R. De, A. Zemel, and S. A. Safran, “Dynamics of Cell Orientation,” Nature Physics, vol. 3, pp. 655, 2007.
[22] R. Kaunas, H. J. Hsu, “A Kinematic Model of Stretch-Induced Stress Fiber Turnover and Reorientation,” Journal of Theoretical Biology, vol. 257, no. 2, pp. 320–330, 2009.
[23] F. J. Vernerey, M. Farsad, “A Constrained Mixture Approach to Mechano-Sensing and Force Generation in Contractile Cells,” J. Mech. Behav. Biomed. Mater., vol. 4, no. 8, pp. 1683–1699, 2011.
[24] M. Maraldi, K. Garikipati, “The Mechanochemistry of Cytoskeletal Force Generation,” Biomechanics and Modeling in Mechanobiology, vol. 14, pp. 59-72, 2015.
[25] J. Li, M. Dao, C. T. Lim, and S. Suresh, “Spectrin-Level Modeling of the Cytoskeleton and Optical Tweezer Stretching of the Erythrocyte,” Biophysical Journal, vol. 88, pp. 3707 -3719, 2005.
[26] X. Li, Z. Peng, H. Lei, M. Dao, and G. E. Karniadakis, “Probing Red Blood Cell Mechanics, Rheology and Dynamics with a Two-Component Multi-Scale Model,” Phil. Trans. R. Soc. A, vol. 372, pp. 20130389, 2014.
[27] J. Satcher, C. Dewey, “Theoretical Estimates of Mechanical Properties of the Endothelial Cell Cytoskeleton,” Biophysical Journal, vol. 71, no. 1, pp. 109–118, 1996.
[28] G. Forgacs, “Commentary on the Possible Role of Cytoskeletal Filamentous Network in Intracellular Signalling: An Approach Based on Percolation,” Journal of Cell Science, vol. 108, pp. 2131-2143, 1995.
[29] D. Stamenovic, S. Mijailovich, I. Norrelkykke, J. Chen, and N. Wang, “Cell Prestress. II. Contribution of Microtubules,” The American Physiological Society, vol. 282, pp. C617-C624, 2002b.
[30] Vaziri, A. Gopinath, “Cell and Biomolecular Mechanics in Silico,” Nature Materials, vol. 7, pp. 15 – 23, 2008.
[31] C. T. Lim, E. H. Zhou, and S. T. Quek, “Mechanical Models for Living Cells-A Review,” J. Biomech, vol. 39, no. 2, pp. 195–216, 2006.
[32] D. Needham, R. M. Hochmuth, “Rapid Flow of Passive Neutrophils into a 4 Microns Pipet and Measurement of Cytoplasmic Viscosity,” ASME J. Biomech. Eng, vol. 112, no. 3, pp. 269–276, 1990.
[33] E. Evans, A. Yeung, “Apparent Viscosity and Cortical Tension of Blood Granulocytes Determined by Micropipet Aspiration,” Biophys J., vol. 56, no. 1, pp. 151–160, 1989.
[34] R. Tran-Son-Tay, D. Needham, A. Yeung, and R. M. Hochmuth, “Time- Dependent Recovery of Passive Neutrophils after Large Deformation,” Biophys J., vol. 60, no. 4, pp. 856–866, 1991.
[35] R. M. Hochmuth, H. P. Ting-Beall, B. B. Beaty, D. Needham, and R. Tran- Son-Tay. “Viscosity of Passive Human Neutrophils Undergoing Small Deformations,” Biophysical Journal, vol. 64, no. 5, pp. 1596– 1601, 1993b.
[36] D. Needham, R. Hochmuth, “A Sensitive Measure of Surface Stress in the Resting Neutrophil,” Biophys J., vol. 61, no. 6, pp. 1664–1670, 1992.
[37] F. Guilak, J. R. Tedrow, and R. Burgkart, “Viscoelastic Properties of the Cell Nucleus,” Biochemical and Biophysical Research Communications, vol. 269, no. 3, pp. 781–786, 2000.
[38] N. Caille, O. Thoumine, Y. Tardy, and J. J. Meister, “Contribution of the Nucleus to the Mechanical Properties of Endothelial Cells,” Journal of Biomechanics, vol. 35, no. 2, pp. 177–187, 2002.
[39] A. J. Maniotis, C. S. Chen, and D. E. Ingber, “Demonstration of Mechanical Connections between Integrins, Cytoskeletal Filaments, and Nucleoplasm that Stabilize Nuclear Structure,” Proceeding of the National Academy of Sciences of the United States of America, vol. 94, pp. 849–854, 1997a.
[40] H. C. Kan, H. S. Udaykumar, W. Shyy, and R. Tran-Son-Tay, “Hydrodynamics of a Compound Drop with Application to Leukocyte Modelling,” Physics of Fluids, vol. 10, no. 4, pp. 760–774, 1998.
[41] R. Tran-Son-Tay, H. C. Kan, H. S. Udaykumar, E. Damay, and W. Shyy, “Rheological Modelling of Leukocytes,” Medical & Biological Engineering & Computing, vol. 36, no. 2, pp. 246–250, 1998.
[42] H. C. Kan, W. Shyy, H. S. Udaykumar, P. Vigneron, and R. Tran-Son- Tay, “Effects of nucleus on leukocyte recovery,” Annals of Biomedical Engineering, vol. 27, no. 5, pp. 648–655, 1999.
[43] J. L. Drury, M. Dembo, “Aspiration of Human Neutrophils: Effects of Shear Thinning and Cortical Dissipation,” Biophysical Journal, vol. 81, no. 6, pp. 3166–3177, 2001.
[44] M. Rodriguez, N. J. Sniadecki, In Computational Modelling of Biomechanics in the Musculoskeletal System: Tissues, Replacements and Regeneration. 1st ed. Woodhead Publishing, 2014.
[45] B. Fabry, G. N. Maksym, J. P. Butler, M. Glogauer, Navajas D, N. A. Taback, E. J. Millet, J. J. Fredberg, “Time Scale and Other Invariants of Integrative Mechanical Behaviour in Living Cells,” Physical Review E, vol. 68, no 4, pp. 041914, 2003.
[46] C. Dong, R. Skalak, “Leukocyte Deformability: finite Element Modeling of Large Viscoelastic Deformation,” Journal of Theoretical Biology, vol. 158, no. 2, pp. 173–193, 1992.
[47] R. M. Hochmuth, “Measuring the Mechanical Properties of Individual Human Blood Cells,” ASME J. Biomech. Eng, vol. 115, no. 4B, pp. 515–519, 1993.
[48] M. Mofrad, H. Karcher, and R. Kamm, “Continuum Elastic or Viscoelastic Models of the Cell,” In Cytoskeletal Mechanics models and measurements, 1st edition, M. Mofrad, R. Kamm, Editors. USA: Cambridge University Press, 2006; pp. 71-83.
[49] D. Theret, M. Levesque, M. Sato, R. Nerem, and L. Wheeler, “The Application of a Homogeneous Half-Space Model in the Analysis of Endothelial-Cell Micropipette Measurements,” ASME J Biomech Eng., vol. 110, pp. 190–199, 1988.
[50] M. Sato, D. P. Theret, L. T. Wheeler, N. Ohshima, and R. M. Nerem, “Application of the Micropipette Technique to the Measurement of Cultured Porcine Aortic Endothelial Cell Viscoelastic Properties,” Journal of Biomechanical Engineering, vol. 112, no. 3, pp. 263–268, 1990.
[51] M. A. Haider, F. Guilak, “An Axisymmetric Boundary Integral Model for Incompressible Linear Viscoelasticity: Application to the Micropipette Aspiration Contact Problem,” ASME J. Biomech. Eng., vol. 122, no. 3, pp. 236–244, 2000.
[52] M. Rodriguez, N. Sniadecki, “Review on Cell Mechanics: Experimental and Modelling Approaches,” Applied Mechanics Review, vol. 65, pp. 060801, 2013.
[53] J. Bursa, R. Lebis, and J. Holata, “Tensegrity Finite Element Models of Mechanical Tests of Individual Cells,” Technology and Health Care, vol. 20, no. 2, pp. 135-150, 2012.
[54] M. M. Nava, M. T. Raimondi, R. Pietrabissa, “Bio-Chemo-Mechanical Models for Nuclear Deformation in Adherent Eukaryotic Cells,” Biomechanics and Modeling in Mechanobiology, vol. 13, no. 5, pp. 929- 943, 2014.
[55] S. Moreno-Flores, R. Benitez, and J. L. Toca-Herrera, “Stress Relaxation and Creep on Living Cells with the Atomic Force Microscope: A Means to Calculate Elastic Moduli and Viscosities of Cell Components,” Nanotechnology, vol. 21, pp. 445101, 2010.
[56] J. McGarry, P. McHugh, “Modelling of in vitro Chondrocyte Detachment,” J. Mech Phys Solids, vol. 56, no. 4, pp. 1554–1565, 2008.
[57] J. McGarry, “Characterization of Cell Mechanical Properties by Computational Modeling of Parallel Plate Compression,” Ann Biomed Eng, vol. 37, no. 11, pp. 2317–2325, 2009.
[58] P. A. Dimilla, K. Barbee, and D. A. Lauffenburger, “Mathematical Model for the Effects of Adhesion and Mechanics on Cell Migration Speed,” Biophys. J, vol. 60, no. 1, pp. 15–37, 1991.
[59] J. Milner, M. Grol, K. Beaucage, S. Dixon, and D. W. Holdsworth, “Finite- Element Modeling of Viscoelastic Cells during High- Frequency Cyclic Strain,” Journal of Funct Biomater, vol. 3, no. 1, pp. 209–224, 2012.
[60] J. Chen, “Nano-biomechanics of Living Cells: A Review,” Interface Focus, vol. 4, no. 2, pp. 20130055, 2014.
[61] G. G. Bilodeau, “Regular Pyramid Punch Problem,” Journal of Applied Mechanics, vol. 59, no. 3, pp. 519–523, 1992.
[62] D. Shin, K. Athanasiou, “Cytoindentation for Obtaining Cell Biomechanical Properties,” Journal of Orthopaedic Research, vol. 17, no. 6, pp. 880–890, 1999.
[63] S. M. Mijailovich, M. Kojic, M. Zivkovic, B. Fabry, and J. J. Fredberg, “A finite Element Model of Cell Deformation during Magnetic Bead Twisting,” Journal of Applied Physiology, vol. 93, no. 4, pp. 1429–1436, 2002.
[64] E. J. Koay, A. C. Shieh, and K. A. Athanasiou, “Creep Indentation of Single Cells,” Journal of Biomechanical Engineering, vol. 125, no. 3, pp. 334–341, 2003.
[65] X. Zeng, S. Li, “Modelling and Simulation of Substrate Elasticity Sensing in Stem Cells,” Comput Methods Biomech Biomed Eng, vol. 14, no. 5, pp. 447–458, 2011a.
[66] X. Zeng, S. Li, “Multi-scale Modeling and Simulation of Soft Adhesion and Contact of Stem Cells,” J Mech Behav Biomed Mater, vol. 4, no. 2, pp. 180–189, 2011b.
[67] Y. Cao, R. Bly, W. Moore, Z. Gao, A. Cuitino, and W. Soboyejo, “On the Measurement of Human Osteosarcoma Cell Elastic Modulus Using Shear Assay Experiment,” J Mater Sci., vol. 18, no. 1, pp. 103–109, 2007.
[68] M. Ferko, A. Bhatnagar, M. Garcia, and P. Butler, “Finite-Element Stress Analysis of a Multicomponent Model of Sheared and Focally- Adhered Endothelial Cells,” Ann Biomed Eng. vol. 35, no. 2, pp. 858– 859, 2007.
[69] C. Nelson, R. Jean, J. Tan, W. Liu, N. Sniadecki, A. Spector, and C. Chen, “Emergent Patterns of Growth Controlled by Multicellular Form and Mechanics,” Proc Natl Acad Sci USA, vol. 102, no. 33, pp. 11594– 11599, 2005.
[70] T. Ohashi, Y. Ishii, Y. Ishikawa, T. Matsumoto, and M. Sato, “Experimental and Numerical Analyses of Local Mechanical Properties Measured by Atomic Force Microscopy for Sheared Endothelial Cells,” Biomed Mater Eng, vol. 12, no. 3, pp. 319–327, 2002.
[71] F. Guilak, G. Erickson, and H. Ting-Beall, “The Effects of Osmotic Stress on the Viscoelastic and Physical Properties of Articular Chondrocytes,” Biophysics Journal, vol. 82, no. 2, pp. 720–727, 2002.
[72] M. Sato, N. Ohshima, and R. M. Nerem, “Viscoelastic Properties of Cultured Porcine Aortic Endothelial Cells Exposed to Shear Stress,” Journal of Biomechanics, vol. 29, no. 4, pp. 461–467, 1996.
[73] G. W. Schmid-Schonbein, K. L. Sung, H. Tozeren, R. Skalak, and S. Chien, “Passive Mechanical Properties of Human Leukocytes,” Biophysical Journal, vol. 36, no. 1, pp. 243–256, 1981.
[74] J. Qiu, A. Baik, X. Lu, E. Hillman, Z. Zhuang, C. Dong, and E. Guo, “A Non-Invasive Approach to Determine Viscoelastic Properties of an Individual Adherent Cell Under Fluid Flow,” Journal of Biomechanics, vol. 47, no. 6, pp. 1537–1541, 2014.
[75] P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of Soft Glassy Materials,” Physical Review Letters, vol. 78, no. 10, pp. 2020- 2023, 1997.
[76] P. Sollich, “Rheological Constitutive Equation for a Model of Soft Glassy Materials,” Physical Review Letters, vol. 8, pp. 738-759, 1998.
[77] P. Bursac, G. Lenormand, B. Fabry, M. Oliver, D. A. Weitz, V. Viasnoff, J. P. Butler, and J. J. Fredberg, “Cytoskeletal Remodelling and Slow Dynamics in the Living Cell,” Nat Mater, vol. 4, no. 7, pp. 557-61, 2005.
[78] P. Kollmannsberger, B. Fabry, "Active Soft Glassy Rheology of Adherent Cells," Soft Matter, vol 5, no. 9, pp, 1771-1774, 2009.
[79] B. Hoffman, J. Crocker, “Cell Mechanics: Dissecting the Physical Responses of Cells to Force,” Annual Review of Biomedical Engineering, vol. 11, pp. 259-288, 2009.
[80] D. Stamenovic, B. Suki, B. Fabry, N. Wang, and J. Fredberg, “Rheology of Airway Smooth Muscle Cells is Associated with Cytoskeletal Contractile Stress,” Journal of Appl. Physiol, vol. 96, no. 5, pp. 1600- 1605, 2004.
[81] A. Vaziri, Z. Xue, R. D. Kamm, M. R. Mofrad, “A Computational Study on Power-Law Rheology of Soft Glassy Materials with Application to Cell Mechanics,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 31–32, pp. 2965–2971, 2007.
[82] E. H. Zhou, F. Xu, S. T. Quek, and C. T. Lim, “A Power-Law Rheology- Based Finite Element Model for Single Cell Deformation,” Biomech Model Mechanobiol, vol. 11, no. 7, pp. 1075-84, 2012.
[83] J. Alcaraz, L. Buscemi, M. Grabulosa, X. Trepat, B. Fabry, R. Farre, and D. Navajas, Microrheology of Human Lung Epithelial Cells Measured by Atomic Force Microscopy,” Biophys. J, vol. 84, no. 3, pp. 2071– 2079, 2003.
[84] M. R. Mofrad, “Rheology of the Cytoskeleton,” Annu. Rev. Fluid Mech, vol. 41, pp. 433-453, 2009.
[85] D. Stamenovic, N. Rosenblatt, M. Montoya-Zavala, B. Matthews, S. Hu, B. Suki, N. Wang, and D. Ingber, “Rheological Behaviour of Living Cells is Timescale-Dependent,” Biophysical Journal, vol. 93, no. 8, pp. 39–41, 2007.
[86] K. Mandadapu, S. Govindjee, and M. Mofrad, “On the Cytoskeleton and Soft Glassy Rheology,” Journal of Biomechanics, vol. 41, no. 7, pp. 1467-1478, 2008.
[87] P. Kollmannsberger, B. Fabry, “Linear and Nonlinear Rheology of Living Cells,” Annual Review of Materials Research, vol. 41, pp. 75-97, 2011.
[88] D. Wirtz, “Particle-Tracking Microrheology of Living Cells: Principles and Applications,” Annual Review of Biophysics, vol. 38, pp. 301-326, 2009.
[89] R. Pritchard, Y. Huang, and E. Terentjev, “Mechanics of Biological Networks: From the Cell Cytoskeleton to Connective Tissue,” Soft Matter, vol. 10, pp. 1864-1884, 2014.
[90] E. Moeendarbary, A. R. Harris, “Cell Mechanics: Principles, Practices, and Prospects,” WIREs Syst Biol Med, vol. 6, pp. 371–388, 2014.
[91] F. Guilak, M. Haider, L. Setton, T. Laursen, and F. Baaijens. “Multiphasic Models of the Cell Mechanics,” in Cytoskeletal Mechanics Models and Measurements, M. Mofrad, R. Kamm, editors. USA: Cambridge University Press. 2006, pp. 84-102.
[92] F. Guilak, V. C. Mow, “The Mechanical Environment of the Chondrocyte: a Biphasic finite Element Model of Cell–Matrix Interactions in Articular Cartilage,” Journal of Biomechanics, vol. 33, no. 12, pp. 1663–1673, 2000.
[93] L. G. Alexopoulos, G. M. Williams, M. L. Upton, L. A. Setton, and F. Guilak, “Osteoarthritic Changes in the Biphasic Mechanical Properties of the Chondrocyte Pericellular Matrix in Articular Cartilage,” J. Biomech, vol. 38, no. 3, pp. 509–517, 2005.
[94] N. O. Chahine, C. T. Hung, and G. A. Ateshian, “In-Situ Measurements of Chondrocyte Deformation under Transient Loading,” Eur. Cell Mater, vol. 13, pp. 100–111, 2007.
[95] R. K. Korhonen, P. Julkunen, W. Wilson, and W. Herzog, “Importance of Collagen Orientation and Depth-Dependent Fixed Charge Densities of Cartilage on Mechanical behaviour of Chondrocytes,” ASME Journal Biomech. Eng, vol. 130, no. 2, pp. 021003, 2008.
[96] E. Kim, F. Guilak, and M. A. Haider. “An Axisymmetric Boundary Element Model for Determination of Articular Cartilage Pericellular Matrix Properties in situ via Inverse Analysis of Chondron Deformation,” ASME J. Biomech. Eng, vol. 132, no. 3, pp. 031011, 2010.
[97] S. K. Han, S. Federico, and W. Herzog, “A Depth-Dependent Model of the Pericellular Microenvironment of Chondrocytes in Articular Cartilage,” Comput Methods Biomech Biomed Eng, vol. 14, pp. 657–64, 2011.
[98] E. Moo, W. Herzog, S. Han, N. Abu Osman, B. Pingguan-Murphy, and S. Federico, “Mechanical Behaviour of in-situ Chondrocytes Subjected to Different Loading Rates: A finite Element Study,” Biomech Model Mechanobiol, vol. 11, pp. 983–93, 2012.
[99] H. Guo, S. A. Maher, and P. A. Torzilli, “A Biphasic Multiscale Study of the Mechanical Microenvironment of Chondrocytes within Articular Cartilage under Unconfined Compression,” J Biomech, vol. 47, no. 11, pp. 2721-2729, 2014.
[100]G. T. Charras, J. C. Yarrow, M. A. Horton, L. Mahadevan, T. J. Mitchison, “Non-Equilibration of Hydrostatic Pressure in Blebbing Cells,” Nature, vol. 435, pp. 365-369, 2005.
[101]M. Herant, W. A. Marganski, and M. Dembo, “The Mechanics of Neutrophils: Synthetic Modeling of Three Experiments” Biophys Journal, .vol. 84, pp. 3389-3413, 2003.
[102]E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan , and G. T. Charras, “The Cytoplasm of Living Cells Behaves as a Poroelastic Material,” Nature Materials, vol. 12, pp. 253–261, 2013.
[103]L. Cao, F. Guilak, and L. A. Setton, “Pericellular Matrix Mechanics in the Anulus Fibrosus Predicted by a Three-Dimensional Finite Element Model and in situ Morphology,” Cell. Mol. Bioeng, .vol. 2, no. 3, .pp 306–319, 2009.
[104]P. Julkunen, W. Wilson, J. S. Jurvelin, and R. K. Korhonen, “Composition of the Pericellular Matrix Modulates the Deformation Behaviour of Chondrocytes in Articular Cartilage under Static Loading,” Med. Biol. Eng. Comput, vol. 47, no. 12, pp. 1281–1290, 2009.
[105]C. Y. Huang, M. A. Soltz, M. Kopacz, V. C. Mow, and G. A. Ateshian, “Experimental Verification of the Roles of Intrinsic Matrix Viscoelasticity and Tension-Compression Nonlinearity in the Biphasic Response of Cartilage,” ASME J. Biomech. Eng, vol. 125, no. 1, pp. 84– 93, 2003.
[106]F. P. Baaijens, W. R. Trickey, T. A. Laursen, and F. Guilak, “Large Deformation finite Element Analysis of Micropipette Aspiration to Determine the Mechanical Properties of the Chondrocyte,” Ann Biomed Eng, vol. 33, pp. 494–501, 2005.
[107]N. D. Leipzig, K. A. Athanasiou, “Unconfined creep compression of chondrocytes,” Journal of Biomechanics, vol. 38, no. 1, pp. 77–85, 2005.
[108]W. R. Trickey, F.P. Baaijens, T. A. Laursen, L. G. Alexopoulos, and F. Guilak, “Determination of the Poisson’s Ratio of the Cell: Recovery Properties of Chondrocytes after Release from Complete Micropipette Aspiration,” Journal of Biomechanics, vol. 39, no. 1, pp. 78–87, 2006.
[109]N. Wang, J. D. Tytell, and D. E. Ingber. “Mechanotransduction at a Distance: Mechanically Coupling the Extracellular Matrix with the Nucleus,” Nature Reviews Molecular Cell Biology, vol. 10, pp. 75–82, 2009.
[110]V. S. Deshpande, R. M. McMeeking, A. G. Evans, “A Model for the Contractility of the Cytoskeleton Including the Effects of Stress-Fibre Formation and Dissociation,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 463, no. 2079, pp. 787–815, 2007.
[111]V. S. Deshpande, M. Mrksich, R. M. McMeeking, and A. G. Evans, “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, 2008.
[112]E. L. Elson, G. M. Genin, “The Role of Mechanics in Actin Stress Fiber Kinetics,” Experimental Cell Research, vol. 319, no. 16, pp. 2490-2500, 2013.
[113]D. Mitrossilis, J. Fouchard, A. Guiroy, N. Desprat, N. Rodriguez, B. Fabry, A. Asnacios, “Single-Cell Response to Stiffness Exhibits Muscle- Like Behaviour,” Proc. Natl. Acad. Sci. U.S.A., vol. 106, no. 43, pp. 18243–18248, 2009.
[114]J. P. McGarry, J. Fu, M. T. Yang, C. S. Chen, R. M. McMeeking, A. G. Evans, and V. S. Deshpande, “Simulation of the Contractile Response of Cells on an Array of Micro-Posts,” Philos. Trans. R. Soc. London, Ser. A, vol. 367, no. 1902, pp. 3477–3497, 2009.
[115]A. Pathak, V. S. Deshpande, A. Evans, and R. McMeeking, “Simulations of Cell Behaviour on Substrates of Variegated Stiffness and Architecture,” in Computer Models in Biomechanics from Nano to Macro, G. A. Holzapfel, E. Kuhl, Dordrecht: Springer Science + Business Media Dordrecht, 2013, 25-41.
[116]W. Ronan, V. S. Deshpande, R. M. McMeeking, and J. P. McGarry, “Cellular Contractility and Substrate Elasticity: A Numerical Investigation of the Actin Cytoskeleton and Cell Adhesion,” Biomechanics and Modeling in Mechanobiology, vol. 13, no. 2, 417- 435, 2014.
[117]A. Pathak, V. S. Deshpande, R. M. McMeeking, and A. G. Evans, “The Simulation of Stress Fibre and Focal Adhesion Development in Cells on Patterned Substrates,” J. R. Soc. Interface, vol. 5, no. 22, pp. 507–524, 2008.
[118]Z. Wei, V. S. Deshpande, R. M. McMeeking RM, Evans AG. “Analysis and Interpretation of Stress Fiber Organization in Cells Subject to Cyclic Stretch,” ASME J. Biomech. Eng. vol. 130, no. 3, pp. 031009, 2008.
[119]S. J. Han, N. J. Sniadecki, “Simulations of the Contractile Cycle in Cell Migration Using a Bio-Chemical-Mechanical Model,” Comput Methods Biomech Biomed Engin, vol. 14, no. 5, pp. 459-68, 2011.
[120]A. Pathak, R. M. McMeeking, A. G. Evans, and V. S. Deshpande, “An Analysis of the Co-Operative Mechano-Sensitive Feedback between Intracellular Signalling, Focal Adhesion Development, and Stress Fiber Contractility,” J. Appl. Mech, vol. 78, no. 4, pp. 041001, 2011.
[121]E. P. Dowling, W. Ronan, and J. P. McGarry, “Computational Investigation of in situ Chondrocyte Deformation and Actin Cytoskeleton Remodelling under Physiological Loading,” Acta Biomater, vol. 9, no. 4, pp. 5943–5955, 2013
[122]R. Blumenfeld, “Stresses in Granular Systems and Emergence of Force Chains,” Phys. Rev. Lett, vol. 93, pp. 108301–108304, 2004.
[123]R. Blumenfeld, “Stress Transmission in Planar Disordered Solid Foams,” J Phys A: Math Gen, vol. 36, pp. 2399-2411, 2003.
[124]R. C. Ball, R. Blumenfeld, “The Stress field in Granular Systems: Loop Forces and Potential Formulation,” Phys. Rev. Lett. vol. 88 pp. 115505– 115508, 2002.
[125]D. Stamenović, N. Wang, “Stress Transmission within the Cell,” Comprehensive Physiology, vol. 1, pp. 499–524, 2011.
[126]R. Satcher, Jr. C. Dewey, and J. Hartwig, “Mechanical Remodelling of the Endothelial Surface and Actin Cytoskeleton Induced by Fluid Flow,” Microcirculation, vol. 4, no. 4, pp. 8-453, 1998.
[127]D. Ingber, N. Wang, and D. Stamenovi, “Tensegrity, Cellular Biophysics, and the Mechanics of Living Systems,” Progress in Physics, vol. 77, no. 4, pp. 046603, 2014.
[128]S. Hu, J. Chen, B. Fabry, Y. Numaguchi, A. Gouldstone, D. E. Ingber, J. J. Fredberg, J. P. Butler, and N. Wang, “Intracellular Stress Tomography Reveals Stress Focusing and Structural Anisotropy in Cytoskeleton of Living Cells,” Am J Physiol. Cell Physiol., vol. 285, pp. C1082-1090, 2003.
[129]D. Kardas, U. Nackenhrost, and D. Balzani, “Computational Model for the Cell-Mechanical Response of the Osteocyte Cytoskeleton Based on Self-Stabilizing Tensegrity Structures,” Biomech. Model Mechanobiol., vol. 12, pp. 167-183, 2013.
[130]E. Robert, “Cellular and Molecular Structure as a Unifying Framework for Whole-Cell Modeling,” Curr. Opin. Struct. Biol, vol. 25, pp. 86-91, 2014.