5 Discussion and Conclusions
We have presented in this paper a general constitutive theory for growth, differentiation and damage of living tissues. This model is assumed to be controlled by mechanical influences, although other effects could also be included, such as chemical reactions, growth factors, and so on. The governing equations have been derived by considering the extracellular matrix concentration and the cellular population.
Following the framework of this formulation, one theoretical particularization has been developed to show its potential: the modelling of bone fracture healing. It is a complex process where growth, differentiation and damage act on the tissue.
Although the particularization shown here presents some simplifications (small deformations, no residual stresses, null cell-matrix interaction and so on) the global formulation proposed is sufficiently general to be used in other biomechanical applications, such as limb lengthening, tendons and vessel growth and remodelling.
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References
Barber, C. B., Dobkin, D. P., and Huhdanpaa, H. (1996). The quickhull algorithm for convex hulls. ACM Trans. Math. Software 22:469–483.
Burr, D. B., Turner, C. H., Naick, P., Forwood, M. R., Ambrosius, W., Hasan, M. S., and Pidaparti, R. (1998). Does microdamage accumulation affect the mechanical properties of bone? J. Biomech. 31:337–345.
Carter, D. R., Beaupre, G. S., Giori, N. J., and Helms, J. A. (1998). Mechanobiology of skeletal regeneration. Clin. Orthop. S355:S41–S55.
Claes, L., Augat, P., Suger, G., and Wilke, H. J. (1997). Influence of size and stability of the osteotomy gap on the success of fracture healing. J. Orthop. Res. 15:577–584.
Cowin, S. C., and Hegedus, D. H. (1976). Bone remodelling I: Theory of adaptive elasticity. J. Elasticity 6:313–326.
Cowin, S. C. (2004). Tissue growth and remodeling. Ann. Rev. Biomed. Eng. 6:77–107.
García-Aznar, J. M., Kuiper, J. H., Gómez-Benito, M. J., Doblaré, M., and Richardson, J. B. (2005). Computational simulation of fracture healing. J. Biomech. in press.
Garikipati, K., Arruda, E. M., Grosh, K., Narayanan, H., and Calve, S. (2004). A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics. J. Mech. Phys. Solids 52:1595–1626.
Gómez-Benito, M. J., García-Aznar, J. M., Kuiper, J. H., and Doblaré, M. (2005). Influence of fracture gap size on the pattern of long bone healing: A computational study. J. Theoret. Biol. in press.
Humphrey, J. D. (1995). Mechanics of the arterial wall: Review and directions. Crit. Rev. Biomed. Eng. 23:1–162.
Kuhl, E., and Steinmann, P. (2003). Theory and numerics of geometrically non-linear open system mechanics. Int. J. Numer. Meth. Eng. 58: 1593–1615.
Kuhl, E., and Steinmann, P. (2004). Computational modeling of healing: An application of the material force method. Biomech. Model. Mechanobio. 2:187–203.
Levick, J. R. (1987). Flow through interstitium and other fibrous matrices. Q. J. Exp. Physiol. 72:409–438.
Lubarda, V. A., and Hoger, A. (2002). On the mechanics of solids with a growing mass. Int. J. Solids Structures 39:4627–4664.
Oster, G. F., Murray, J. D., and Harris, A. K. (1983). Mechanical aspects of mesenchymal morphogenesis. J. Embryol. Exp. Morph. 78:83–125.
Prendergast, P. J., Huiskes, R., and Soballe, K. (1997). Biophysical stimuli on cells during tissue differentiation at implant interfaces. J. Biomech. 6: 539–548.
Skalak, R., Dasgupta, G., Moss, M., Otten, E., Dullemeijer, P., and Vilmann, H. (1982). Analytical description of growth. J. Theoret. Biol. 94:555–577.
Taber, L. A. (1995). Biomechanics of growth, remodelling, and morphognesis. Appl. Mech. Rev. 48:487–545.
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Doblaré, M., García-Aznar, J.M., Gómez-Benito, M.J. (2006). A Mechanobiological Formulation of Bone Healing. In: Holzapfel, G.A., Ogden, R.W. (eds) Mechanics of Biological Tissue. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31184-X_8
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DOI: https://doi.org/10.1007/3-540-31184-X_8
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