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
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)
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)
Graner, F., Glazier, J.A.: Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69(13), 2013 (1992)
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)
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)
Ingber, D.E.: Tensegrity: the architectural basis of cellular mechanotransduction. Annu. Rev. Physiol. 59, 575–599 (1997)
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)
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)
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)
Prendergast, P.J.: What Matters in Bioengineering, An Inaugral Lecture for the Chair of Bioengineering. Trinity College Dublin School of Engineering, Dublin (2008)
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)
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)
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)
Sloot, P.M.A., Hoekstra, A.G.: Multi-scale modelling in computational biomedicine. Brief. Bioinform. 11(1), 142–152 (2010)
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)
Codling, E.A., Plank, M.J., Benhamou, S.: Random walk models in biology. J. R. Soc. Interface 5(25), 813–834 (2008)
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)
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)
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)
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)
Minguell, J.J., Erices, A., Conget, P.: Mesenchymal stem cells. Exp. Biol. Med. 226, 507–520 (2001)
Kearney, E.M., Prendergast, P.J., Campbell, V.A.: Mechanisms of strain-mediated mesenchymal stem cell apoptosis. J. Biomech. Eng. 130, 061004 (2008)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Ambard, D., Swider, P.: A predictive mechano-biological model of the bone-implant healing. Eur. J. Mech. A Solids 25, 927–937 (2006)
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)
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)
Morgan, E.F., Longaker, M.T., Carter, D.R.: Relationships between tissue dilatation and differentiation in distraction osteogenesis. Matrix Biol. 25, 94–103 (2006)
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)
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)
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)
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)
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)
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)
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)
Tagil, M., Aspenberg, P.: Cartilage induction by controlled mechanical stimulation in vivo. J. Orthop. Res. 17, 200–204 (1999)
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)
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)
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)
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)
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)
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)
Grinnell, F.: Fibroblasts myofibroblasts, and wound contraction. J. Cell Biol. 124, 401–404 (1994)
Tamariz, E., Grinnell, F.: Modulation of fibroblast morphology and adhesion during collagen matrix remodeling. Mol. Biol. Cell 13, 3915–3929 (2002)
Fisher, J.P., Mikos, A.G., Bronzino, J.D. (eds.) Tissue Engineering. CRC Press, Boca Raton (2007)
Glazier, J.A., Graner, F.: Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47(3), 2128 (1993)
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)
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)
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)
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)
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)
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)
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)
Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. J. ACM 13(4), 471–494 (1966)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, MIT USA (2001)
Wu, K., Otoo, E., Shoshani, A.: Optimizing connected component labeling algorithms (2005)
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
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)
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)
Guilak, F., Tedrow, J.R., Burgkart, R.: Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269(3), 781–786 (2000)
Ingber, D.: Tensegrity I. Cell structure and hierarchical systems biology. J. Cell Sci. 116(7), 1157–1173 (2003)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Miles, A.W., Tanner, K.E.: Strain Measurement in Biomechanics. Springer (1992)
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)
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)
Huiskes, R., Chao, E.Y.S.: A survey of finite element analysis in orthopaedic biomechanics: the first decade. J. Biomech. 16, 385–409 (1983)
Prendergast, P.J.: Finite element models in tissue mechanics and orthopaedic implant design. Clin. Biomech. 12, 343–368 (1997)
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)
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)
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)
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)
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
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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