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Biomechanical Modelling of Cells in Mechanoregulation

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Cellular and Biomolecular Mechanics and Mechanobiology

Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 4))

Abstract

Many cells are mechanoregulated; their activities are performed at a rate partly determined by the biophysical stimulus acting on them. Computer simulations that would capture this could be used to predict the effect of physical exercise on tissue health. They could also be used to simulate how the tissues surrounding a medical device would respond to the placement of that device. Since cells are the actors within tissues, such simulations require models of how cells themselves are mechanoregulated. In this chapter, we review how mechanoregulation simulations may be built up from models in three ways: cells as simple points, cells as multiple points, cells as structures. In particular, a computer simulation method for tissue differentiation using cells as points is also given, and an approach for extending it to include cells as multiple points is presented. Cells as structures in the form of a hybrid tensegrity-continuum model is presented, and its potential for use in mechanoregulation simulations is discussed.

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References

  1. Lacroix, D., Prendergast, P.J., Li, G., Marsh, D.: Biomechanical model to simulate tissue differentiation and bone regeneration: application to fracture healing. Med. Biol. Eng. Comput. 40, 14–21 (2002)

    Article  Google Scholar 

  2. Geris, L., Gerisch, A., van der Sloten, J., Weiner, R., Oosterwyck, H.V.: Angiogenesis in bone fracture healing: a bioregulatory model. J. Theor. Biol. 251, 137–158 (2008)

    Article  Google Scholar 

  3. Graner, F., Glazier, J.A.: Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69(13), 2013 (1992)

    Article  Google Scholar 

  4. Ouchi, N., Glazier, J., Rieu, J., Upadhyaya, A., Sawada, Y.: Improving the realism of the cellular Potts model in simulations of biological cells. Physica A 329(3–4), 451–458 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kamm, R.D., McVittie, A.K., Bathe, M.: On the role of continuum models in mechanobiology. In: Casey, J., Bao, G. (eds.) Mechanics in Biology, pp. 1–11 (2000)

    Google Scholar 

  6. Ingber, D.E.: Tensegrity: the architectural basis of cellular mechanotransduction. Annu. Rev. Physiol. 59, 575–599 (1997)

    Article  Google Scholar 

  7. Slomka, N., Gefen, A.: Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics. J. Biomech. 43(9), 1806–1816 (2010)

    Article  Google Scholar 

  8. McGarry, J.P., Fu, J., Yang, M.T., Chen, C.S., McMeeking, R.M., Evans, A.G., Deshpande, V.S.: Simulation of the contractile response of cells on an array of micro-posts. Philos. Transact. A Math. Phys. Eng. Sci. 367(1902), 3477–3497 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Maurin, B., Cañadas, P., Baudriller, H., Montcourrier, P., Bettache, N.: Mechanical model of cytoskeleton structuration during cell adhesion and spreading. J. Biomech. 41(9), 2036–2041 (2008)

    Article  Google Scholar 

  10. Prendergast, P.J.: What Matters in Bioengineering, An Inaugral Lecture for the Chair of Bioengineering. Trinity College Dublin School of Engineering, Dublin (2008)

    Google Scholar 

  11. Prendergast, P.J., Checa, S., Lacroix, D.: Computational models of tissue differentiation. In: De, S., Guilak, F., Mofrad, R. (eds.) Computational Modeling in Biomechanics, pp. 335–372. Springer, New York (2010)

    Google Scholar 

  12. Checa, S., Byrne, D.P., Prendergast, P.J.: Predictive modelling in mechanobiology: combining algorithms for cell activities in response to physical stimuli using a lattice-modelling approach. In: Computer Methods in Mechanics, pp. 423–435. Springer (2010)

    Google Scholar 

  13. Checa, S., Sandino, C., Byrne, D.P., Kelly, D.J., Lacroix, D., Prendergast, P.J.: Computational techniques for selection of biomaterial scaffolds for tissue engineering. In: Fernandes, P.R., Bártolo, p. (eds.) Advances of modeling in Tissue Engineering. Springer (2010, in press)

    Google Scholar 

  14. Sloot, P.M.A., Hoekstra, A.G.: Multi-scale modelling in computational biomedicine. Brief. Bioinform. 11(1), 142–152 (2010)

    Article  Google Scholar 

  15. Boyle, C., Lennon, A., Early, M., Kelly, D., Lally, C., Prendergast, P.: Computational simulation methodologies for mechanobiological modelling: a cell-centred approach to neointima development in stents. Philos. Trans. R. Soc. A Math. Phys. 368(1921), 2919–2935 (2010)

    Google Scholar 

  16. Codling, E.A., Plank, M.J., Benhamou, S.: Random walk models in biology. J. R. Soc. Interface 5(25), 813–834 (2008)

    Article  Google Scholar 

  17. Checa, S., Prendergast, P.J.: A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach. Ann. Biomed. Eng. 37(1), 129–145 (2009)

    Article  Google Scholar 

  18. Pérez, M.A., Prendergast, P.J.: Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation. J. Biomech. 40(10), 2244–2253 (2007)

    Article  Google Scholar 

  19. Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  20. Chen, F., Song, L., Mauck, R.L., Li, W.J., Tuan, R.S.: Mesenchymal stem cells. In: Lanza, R., Langer, R.S., Vacanti J. (eds.) Principles of Tissue Engineering, 3rd edn. Elsevier Academic Press, Burlington (2007)

    Google Scholar 

  21. Minguell, J.J., Erices, A., Conget, P.: Mesenchymal stem cells. Exp. Biol. Med. 226, 507–520 (2001)

    Google Scholar 

  22. Kearney, E.M., Prendergast, P.J., Campbell, V.A.: Mechanisms of strain-mediated mesenchymal stem cell apoptosis. J. Biomech. Eng. 130, 061004 (2008)

    Article  Google Scholar 

  23. Kearney, E.M., Farrell, E., Prendergast, P.J., Campbell, V.A., Tensile.: Strain as a regulator of Mesenchymal stem cell osteogenesis. Ann. Biomed. Eng. 38(5), 1767–1779 ( 2010)

    Google Scholar 

  24. Pauwels, F.: A new theory of the influence of mechanical stimuli on the differentiation of supporting tissue. The tenth contribution to the functional anatomy and causal morphology of the supporting structure. Zeitschrift für Anatomie und Entwicklungsgeschichte, pp. 478–515 (1960)

    Google Scholar 

  25. Carter, D., Blenman, P., Beaupre, G.: Correlations between mechanical stress history and tissue differentiation in initial fracure healing. J. Orthop. Res. 6, 736–748 (1988)

    Article  Google Scholar 

  26. Claes, L.E., Heigele, C.A.: Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J. Biomech. 32, 255–266 (1999)

    Article  Google Scholar 

  27. Prendergast, P.J., Huiskes, R., Soballe, K.: ESB Research Award 1996. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J. Biomech. 30, 539–548 (1997)

    Article  Google Scholar 

  28. Isaksson, H., van Donkelaar, C.C., Huiskes, R., Ito, K.: Corroboration of mechanoregulatory algorithms for tissue differentiation during fracture healing: comparison with in vivo results. J. Orthop. Res. 24, 898–907 (2006)

    Article  Google Scholar 

  29. Hayward, L.N., Morgan, E.F.: Assessment of a mechano-regulation theory of skeletal tissue differentiation in an in vivo model of mechanically induced cartilage formation. Biomech. Model. Mechanobiol 8(6), 447–455 (2009)

    Google Scholar 

  30. Geris, L., Vandamme, K., Naert, I., Vander Sloten, J., Duyck, J., Van Oosterwyck, H.: Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber. J. Biomech. 41, 145–154 (2008)

    Article  Google Scholar 

  31. Carter, D.R., Beaupre, G.S., Giori, N.J., Helms, J.A.: Mechanobiology of skeletal regeneration. Clin. Orthop. Relat. Res. 355 Suppl. S41–S55 (1998)

    Google Scholar 

  32. Lacroix, D., Prendergast, P.J.: A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J. Biomech. 35, 1163–1171 (2002)

    Article  Google Scholar 

  33. Byrne, D.P., Lacroix, D., Planell, J.A., Kelly, D.J., Prendergast, P.J.: Simulation of tissue differentiation in a scaffold as a function of porosity, Young’s modulus and dissolution rate: application of mechanobiological models in tissue engineering. Biomaterials 28, 5544–5554 (2007)

    Article  Google Scholar 

  34. Kelly, D.J., Prendergast, P.J.: Prediction of the optimal mechanical properties for a scaffold used in osteochondral defect repair. Tissue Eng. 12, 2509–2519 (2006)

    Article  Google Scholar 

  35. Huiskes, R., Van Driel, W.D., Prendergast, P.J., Soballe, K.: A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation. J. Mater. Sci.: Mater. Med. 8, 785–788 (1997)

    Article  Google Scholar 

  36. Ambard, D., Swider, P.: A predictive mechano-biological model of the bone-implant healing. Eur. J. Mech. A Solids 25, 927–937 (2006)

    Article  MATH  Google Scholar 

  37. Isaksson, H., Comas, O., van Donkelaar, C.C., Mediavilla, J., Wilson, W., Huiskes, R., Ito, K.: Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity. J. Biomech. 40, 2002–2011 (2007)

    Article  Google Scholar 

  38. Loboa, E.G., Fang, T.D., Parker, D.W., Warren, S.M., Fong, K.D., Longaker, M.T., Carter, D.R.: Mechanobiology of mandibular distraction osteogenesis: finite element analyses with a rat model. J. Orthop. Res. 23, 663–670 (2005)

    Article  Google Scholar 

  39. Morgan, E.F., Longaker, M.T., Carter, D.R.: Relationships between tissue dilatation and differentiation in distraction osteogenesis. Matrix Biol. 25, 94–103 (2006)

    Article  Google Scholar 

  40. Boccaccio, A., Prendergast, P.J., Pappalettere, C., Kelly, D.J.: Tissue differentiation and bone regeneration in an osteotomized mandible: a computational analysis of the latency period. Med. Biol. Eng. Comput. 46, 283–298 (2008)

    Article  Google Scholar 

  41. Geris, L., Van Oosterwyck, H., Vander Sloten, J., Duyck, J., Naert, I.: Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants. Comput. Methods Biomech. Biomed. Eng. 6, 277–288 (2003)

    Article  Google Scholar 

  42. Gomez-Benito, M.J., Garcia-Aznar, J.M., Kuiper, J.H., Doblare, M.: Influence of fracture gap size on the pattern of long bone healing: a computational study. J. Theor. Biol. 235, 105–119 (2005)

    Article  MathSciNet  Google Scholar 

  43. Liu, X., Niebur, G.L.: Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm. Biomech. Model. Mechanobiol. 7, 335–344 (2008)

    Article  Google Scholar 

  44. Isaksson, H., van Donkelaar, C.C., Huiskes, R., Ito, K.: A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity. J. Theor. Biol. 252, 230–246 (2008)

    Article  Google Scholar 

  45. Checa, S., Prendergast, P.J.: A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach. Ann. Biomed. Eng. 37, 129–145 (2009)

    Article  Google Scholar 

  46. Guldberg, R.E., Caldwell, N.J., Guo, X.E., Goulet, R.W., Hollister, S.J., Goldstein, S.A.: Mechanical stimulation of tissue repair in the hydraulic bone chamber. J. Bone Miner. Res. 12, 1295–1302 (1997)

    Article  Google Scholar 

  47. Tagil, M., Aspenberg, P.: Cartilage induction by controlled mechanical stimulation in vivo. J. Orthop. Res. 17, 200–204 (1999)

    Article  Google Scholar 

  48. de Rooij, P.P., Siebrecht, M.A., Tagil, M., Aspenberg, P.: The fate of mechanically induced cartilage in an unloaded environment. J. Biomech. 34, 961–966 (2001)

    Article  Google Scholar 

  49. Hannink, G., Aspenberg, P., Schreurs, B.W., Buma, P.: Development of a large titanium bone chamber to study in vivo bone ingrowth. Biomaterials 27, 1810–1816 (2006)

    Article  Google Scholar 

  50. Perez, M.A., Prendergast, P.J.: Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation. J. Biomech. 40, 2244–2253 (2007)

    Article  Google Scholar 

  51. Lanza, R., Thomas, E., Thomson, J., Gearhart, J., Hogan, B., Melton, D., Pederson, R., Wilmut, I. (eds.) Essentials of Stem Cell Biology. Elsevier Academic Press, San Diego (2009)

    Google Scholar 

  52. Fletcher, E.C., Lesske, J., Qian, W., Miller, C.C., Unger, T.: Repetitive episodic hypoxia causes diurnal elevation of blood pressure in rats. Hypertension 19, 555–561 (1992)

    Google Scholar 

  53. Hulman, S., Falkner, B.: The effect of excess dietary sucrose on growth, blood pressure, and metabolism in developing Sprague–Dawley rats. Pediatr. Res. 36, 95–101 (1994)

    Article  Google Scholar 

  54. Grinnell, F.: Fibroblasts myofibroblasts, and wound contraction. J. Cell Biol. 124, 401–404 (1994)

    Article  Google Scholar 

  55. Tamariz, E., Grinnell, F.: Modulation of fibroblast morphology and adhesion during collagen matrix remodeling. Mol. Biol. Cell 13, 3915–3929 (2002)

    Article  Google Scholar 

  56. Fisher, J.P., Mikos, A.G., Bronzino, J.D. (eds.) Tissue Engineering. CRC Press, Boca Raton (2007)

    Google Scholar 

  57. Glazier, J.A., Graner, F.: Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47(3), 2128 (1993)

    Article  Google Scholar 

  58. Chen, N., Glazier, J.A., Izaguirre, J.A., Alber, M.S.: A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis. Comput. Phys. Commun. 176(11–12), 670–681 (2007)

    Article  Google Scholar 

  59. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087 (1953)

    Article  Google Scholar 

  60. Gusatto, É., Mombach, J.C.M., Cercato, F.P., Cavalheiro, G.H.: An efficient parallel algorithm to evolve simulations of the cellular potts model. Parallel Process. Lett. 15(1/2), 199–208 (2005)

    Article  MathSciNet  Google Scholar 

  61. van Oers, R.F.M., Ruimerman, R., Tanck, E., Hilbers, P.A.J., Huiskes, R.: A unified theory for osteonal and hemi-osteonal remodeling. Bone 42(2), 250–259 (2008)

    Article  Google Scholar 

  62. Merks, R.M., Brodsky, S.V., Goligorksy, M.S., Newman, S.A., Glazier, J.A.: Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev. Biol. 289(1), 44–54 (2006)

    Article  Google Scholar 

  63. Izaguirre, J.A., Chaturvedi, R., Huang, C., Cickovski, T., Coffland, J., Thomas, G., Forgacs, G., Alber, M., Hentschel, G., Newman, S.A., Glazier, J.A.: CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics 20(7), 1129–1137 (2004)

    Article  Google Scholar 

  64. Swat, M.H., Hester, S.D., Heiland, R.W., Zaitlen, B.L., Glazier, J.A., Shirinifard, A.: CompuCell3D Manual and Tutorial, Version 3.4.1. Biocomplexity Institute and Department of Physics, Indiana University, Bloomington (2009)

    Google Scholar 

  65. Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. J. ACM 13(4), 471–494 (1966)

    Article  MATH  Google Scholar 

  66. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, MIT USA (2001)

    Google Scholar 

  67. Wu, K., Otoo, E., Shoshani, A.: Optimizing connected component labeling algorithms (2005)

    Google Scholar 

  68. McGarry, J.G., Prendergast, P.J.: A three-dimensional finite element model of an adherent eukaryotic cell. Eur. Cell Mater. 7, 27–33 (2004). discussion 33-34

    Google Scholar 

  69. De Santis, G., Boschetti, F., Lennon, A.B., Prendegast, P.J., Verdonck, P., Verhegghe, B.: How an eukaryotic cell senses the substrate stiffness? An exploration using a finite element model with cytoskeleton modelled as tensegrity structure. In: Proceedings of the ASME 2009 Summer Bioengineering Conference, American Society of Mechanical Engineers (ASME), Lake Tahoe, CA, USA (2009)

    Google Scholar 

  70. McGarry, J.P., Murphy, B.P., McHugh, P.E.: Computational mechanics modelling of cell-substrate contact during cyclic substrate deformation. J. Mech. Phys. Solids 53(12), 2597–2637 (2005)

    Article  MATH  Google Scholar 

  71. Guilak, F., Tedrow, J.R., Burgkart, R.: Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269(3), 781–786 (2000)

    Article  Google Scholar 

  72. Ingber, D.: Tensegrity I. Cell structure and hierarchical systems biology. J. Cell Sci. 116(7), 1157–1173 (2003)

    Article  Google Scholar 

  73. Brangwynne, C.P., MacKintosh, F.C., Kumar, S., Geisse, N.A., Talbot, J., Mahadevan, L., Parker, K.K., Ingber, D.E., Weitz, D.A.: Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol 173(5), 733–741 (2006)

    Article  Google Scholar 

  74. Kumar, S., Maxwell, I., Heisterkamp, A., Polte, T., Lele, T., Salanga, M., Mazur, E., Ingber, D.: Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. Biophys. J. 90(10), 3762–3773 (2006)

    Article  Google Scholar 

  75. Dahl, K.N., Booth-Gauthier, E.A., Ladoux, B.: In the middle of it all: mutual mechanical regulation between the nucleus and the cytoskeleton. J. Biomech. 43(1), 2–8 (2010)

    Google Scholar 

  76. Xue, F., McKayed, K., Lennon, A.B., Campbell, V.A., Prendergast, P.J.: Computational investigation of influence of age on biomechanics of mesenchymal stem cells. In: Proceedings of the 9th international symposium on computer methods in biomechanics and biomedical engineering 2010, Valencia, Paper 154, CDROM (2010, in press)

    Google Scholar 

  77. McGarry, J.G., Klein-Nulend, J., Mullender, M.G., Prendergast, P.J.: A comparison of strain and fluid shear stress in stimulating bone cell responses—a computational and experimental study. FASEB J. 19(3), 482–484 (2005)

    Google Scholar 

  78. De Santis, G., Lennon, A.B., Boschetti, F., Verhegghe, B., Verdonck, P., Prendergast, P.J.: Principle of matrix-elasticity sensing by cells. Eur. Cells Mater. (2010) (in press)

    Google Scholar 

  79. Hofmann, U.G., Rotsch, C., Parak, W.J., Radmacher, M.: Investigating the cytoskeleton of chicken cardiocytes with the atomic force microscope. J. Struct. Biol. 119(2), 84–91 (1997)

    Article  Google Scholar 

  80. Domke, J., Dannohl, S., Parak, W.J., Muller, O., Aicher, W.K., Radmacher, M.: Substrate dependent differences in morphology and elasticity of living osteoblasts investigated by atomic force microscopy. Colloids Surf. B Biointerfaces 19(4), 367–379 (2000)

    Google Scholar 

  81. Mathur, A.B., Collinsworth, A.M., Reichert, W.M., Kraus, W.E., Truskey, G.A.: Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy. J. Biomech. 34(12), 1545–1553 (2001)

    Article  Google Scholar 

  82. Prendergast, P.J.: Biomechanical Techniques for Pre-Clinical Testing of Prostheses and Implants, Lecture Notes. Institute for Fundamental Technological Research, Polish Academy of Sciences, Warsaw (2001)

    Google Scholar 

  83. Miles, A.W., Tanner, K.E.: Strain Measurement in Biomechanics. Springer (1992)

    Google Scholar 

  84. Lennon, A.B., Prendergast, P.J. (eds.): Finite Element Modelling in Biomechanics and Mechanobiology with papers on patient-specific analysis, high resolution analysis, and applications in orthopaedics, cardiology, and cellular bioengineering. Trinity Centre for Bioengineering, Trinity College, Dublin (2007)

    Google Scholar 

  85. Campbell, V.A., O'Connell, B.: Cellular & molecular biomechanics. In: Lee, T.C., Niederer, P.F. (eds.) Basic Engineering for Medics and Biologists—an ESEM primer, pp. 202–213. IOS Press, Amsterdam (2010)

    Google Scholar 

  86. Huiskes, R., Chao, E.Y.S.: A survey of finite element analysis in orthopaedic biomechanics: the first decade. J. Biomech. 16, 385–409 (1983)

    Article  Google Scholar 

  87. Prendergast, P.J.: Finite element models in tissue mechanics and orthopaedic implant design. Clin. Biomech. 12, 343–368 (1997)

    Article  Google Scholar 

  88. Kiousis, D.E., Gasser, T.C., Holzapfel, G.A.: A numerical model to study the interaction of vascular stents with human atherosclerotic lesions. Ann. Biomed. Eng. 35(11), 1857–1869 (2007)

    Article  Google Scholar 

  89. Perillo-Marcone, A., Alonso-Vazquez, A., Taylor, M.: Assessment of the effect of mesh density on the material property discretisation within QCT-based FE-models: a practical example using the implanted proximal tibia. Comput. Methods Biomech. Biomed. Eng. 6(1), 17–20 (2003)

    Article  Google Scholar 

  90. Capelli, C., Taylor, A.M., Migliavacca, F., Bonhoeffer, P., Schievano, S.: Patient-specific reconstructed anatomies and computer simulations are fundamental for selecting medical device treatment: application to a new percutaneous pulmonary valve. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 368(1921), 3027–3038 (2010)

    Google Scholar 

  91. Reggiani, B., Cristofolini, L., Varini, E., Viceconti, M.: Predicting the subject-specific primary stability of cementless implants during pre-operative planning: preliminary validation of subject-specific finite-element models. J. Biomech. 40(11), 2552–2558 (2007)

    Article  Google Scholar 

  92. Khayyeri, H., Checa, S., Tägil, M., Aspenberg, P., Prendergast, P.J.: Individual-specific cell process rates explains variability in tissue differentiation experiment. In: Proceedings of the 17 Congress of the European Society of Biomechanics, European Society of Biomechanics, Edinburgh, Scotland, UK (2010); CDROM

    Google Scholar 

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Acknowledgments

Our research reported in this chapter has been funded in recent years by a Principal Investigator grant from Science Foundation Ireland to Prof. P. J. Prendergast (Grant No. 06/IN.1/B86) and by a Research Frontiers Grant (No. 08/RFP/ENM1361).

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Lennon, A.B., Khayyeri, H., Xue, F., Prendergast, P.J. (2010). Biomechanical Modelling of Cells in Mechanoregulation. In: Gefen, A. (eds) Cellular and Biomolecular Mechanics and Mechanobiology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/8415_2010_32

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