Published Dec 7, 2015


Google Scholar
Search GoogleScholar

Daniel Ricardo Suárez, PhD



It is well known that the mechanical environment affects biological tissues. The importance of theories and models that aim at explaining the role of the mechanical stimuli in process such as differentiation and adaptation of tissues is highlighted because if those theories can explain the tissue’s response to mechanical loading and to its environment, it becomes possible to predict the consequences of mechanical stimuli on growth, adaptation and ageing of tissues. This review aims to present an overview of the various theories and models on tissue differentiation and adaptation of tissues and their mathematical implementation. Although current models are numerically well defined and are able to resemble the tissue differentiation and adaptation processes, they are limited by (1) the fact that some of their input parameters are likely to be site- and species-dependent, and (2) their verification is done by data that may make the model results redundant. However, some theories do have predictive power despite the limitations of generalization. It seems to be a matter of time until new experiments and models appear with predictive power and where rigorous verification can be performed.


Computational biology, Mechanobiology, finite element, tissue growth, tissue differentiation, skeletal regenerationbiología computacional, mecanobiología, elementos finitos, diferenciación de tejidos

[1] D. R. Carter, M. C. van der Meulen, and G. S. Beaupre, “Mechanical factors in bone growth and development,” Bone, vol. 18, pp. 5S-10S, Jan, 1996.
[2] D. E. Ingber, “Mechanobiology and diseases of mechanotransduction,” Ann. Med., vol. 35, pp. 564-577, 2003.
[3] H. Isaksson, “Recent advances in mechanobiological modeling of bone regeneration,” Mech. Res. Commun., vol. 42, pp. 22-31, 2012.
[4] D. R. Carter and G. S. Beaupré, Skeletal Function and Form: Mechanobiology of Skeletal Development, Aging, and Regeneration. Cambridge University Press, 2007.
[5] W. Roux, “Der zuchtende Kampf der Teile, oder die ‘Teilau-slese’ im Organismus (Theorie der “funktionellen Anpassung”),” Wilhelm Engelmann, Leipzig, 1891.
[6] S. Perren and J. Cordey, “The concept of interfragmentary strain,” Current Concepts of Internal Fixation of Fractures, pp. 63-77, 1980.
[7] D. R. Carter, “Mechanical loading history and skeletal biology,” J. Biomech., vol. 20, pp. 1095-1109, 1987.
[8] L. Claes and C. Heigele, “Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing,” J. Biomech., vol. 32, pp. 255-266, 1999.
[9] P. Prendergast, R. Huiskes, and K. Søballe, “Biophysical stimuli on cells during tissue differentiation at implant interfaces,” J. Biomech., vol. 30, pp. 539-548, 1997.
[10] H. Isaksson, C. C. van Donkelaar, R. Huiskes, and K. Ito, “A mechano-regulatory bonehealing model incorporating cell-phenotype specific activity,” J. Theor. Biol., vol. 252, pp. 230-246, 2008.
[11] F. Pauwels, “Grundriß einer Biomechanik der Frakturheilung. Verh dtsch orthop Ges 34. Kongreß 62–108,” Ges Abh Springer, Berlin, 1980.
[12] H. M. Frost, The Laws of Bone Structure. CC Thomas, 1964.
[13] C. H. Turner, “Homeostatic control of bone structure: an application of feedback theory,” Bone, vol. 12, pp. 203-217, 1991.
[14] M. C. van der Meulen and R. Huiskes, “Why mechanobiology?: A survey article,” J. Biomech., vol. 35, pp. 401-414, 2002.
[15] F. Guilak, D. L. Butler, S. A. Goldstein, and F. P. Baaijens, “Biomechanics and mechanobiology in functional tissue engineering,” J. Biomech., vol. 47, pp. 1933-1940, 2014.
[16] A. Carlier, L. Geris, J. Lammens, and H. Van Oosterwyck, “Bringing computational models of bone regeneration to the clinic,” Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 2015.
[17] D. C. Betts and R. Müller, “Mechanical Regulation of Bone Regeneration: Theories, Models, and Experiments,” Frontiers in Endocrinology, vol. 5, 2014.
[18] L. Geris, J. Vander Sloten, and H. Van Oosterwyck, “In silico biology of bone modelling and remodelling: regeneration,” Philos. Trans. A. Math. Phys. Eng. Sci., vol. 367, pp. 2031-2053, May 28, 2009.
[19] R. Hart, “Bone modeling and remodeling: Theories and computation,” in Bone Mechanics Handbook, second edition ed., S. C. Cowin, Ed. Boca Raton: CRC Press, 2001, pp. (31) 1.
[20] H. Weinans and P. Prendergast, “Tissue adaptation as a dynamical process far from equilibrium,” Bone, vol. 19, pp. 143-149, 1996.
[21] D. R. Carter, G. S. Beaupré, N. J. Giori and J. A. Helms, “Mechanobiology of skeletal regeneration,” Clin. Orthop., vol. 355, pp. S41-S55, 1998.
[22] I. Owan, D. B. Burr, C. H. Turner, J. Qiu, Y. Tu, J. E. Onyia, and R. L. Duncan, “Mechanotransduction in bone: osteoblasts are more responsive to fluid forces than mechanical strain,” Am. J. Physiol.-Cell Ph., vol. 273, pp. C810-C815, 1997.
[23] P. Prendergast, “Computational mechanobiology,” in Computational Bioengineering: Current Trends and Applications. s. p.: Imperial College Press, 2004, pp. 117-133.
[24] V. Mow, “Biphasic creep and stress relaxation of articular cartilage in compression,” J. Biomech. Eng., vol. 102, pp. 73-84, 1980.
[25] G. N. Duda, Z. M. Maldonado, P. Klein, M. O. Heller, J. Burns. and H. Bail, “On the influence of mechanical conditions in osteochondral defect healing,” J. Biomech., vol. 38, pp. 843-851, 2005.
[26] A. Bailon-Plaza and M. C. Van Der Meulen, “A mathematical framework to study the effects of growth factor influences on fracture healing,” J. Theor. Biol., vol. 212, pp. 191-209, 2001.
[27] A. Bailon-Plaza and M. van der Meulen, “Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing,” J. Biomech., vol. 36, pp. 1069-1077, 2003.
[28] S. R. Moore, G. M. Saidel, U. Knothe and M. L. K. Tate, “Mechanistic, mathematical model to predict the dynamics of tissue genesis in bone defects via mechanical feedback and mediation of biochemical factors,” PLoS Computational Biology, vol. 10, pp. e1003604, 2014.
[29] L. Geris, A. Gerisch, J. V. Sloten, R. Weiner, and H. V. Oosterwyck, “Angiogenesis in bone fracture healing: a bioregulatory model,” J. Theor. Biol., vol. 251, pp. 137-158, 2008.
[30] E. Loboa, T. Wren, G. Beaupre and D. Carter, “Mechanobiology of soft skeletal tissue differentiation—a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications,” Biomechanics and Modeling in Mechanobiology, vol. 2, pp. 83-96, 2003.
[31] M. Levenston, E. Frank and A. Grodzinsky, “Variationally derived 3-field finite element formulations for quasistatic poroelastic analysis of hydrated biological tissues,” Comput. Methods Appl. Mech. Eng., vol. 156, pp. 231-246, 1998.
[32] B. R. Simon, “Multiphase poroelastic finite element models for soft tissue structure,” Appl. Mech. Rev., vol. 45, 1992.
[33] P. Prendergast and M. Van der Meulen, “Mechanics of bone regeneration,” in Bone Mechanics Handbook. Boca Raton: CRC Press, 2001, pp. 32-31.
[34] J. D. Murray, “Mechanical models for generating pattern and form in development”, Mathematical Biology, 1993.
[35] D. R. Carter and G. S. Beaupré, Skeletal Function and Form: Mechanobiology of Skeletal Development, Aging, and Regeneration. Cambridge: Cambridge University Press, 2001.
[36] D. R. Carter, G. S. Beaupré, M. Wong, R. L. Smith, T. P. Andriacchi, and D. J. Schurman, “The mechanobiology of articular cartilage development and degeneration,” Clin. Orthop., vol. 427, pp. S69-S77, 2004.
[37] R. Huiskes, W. Van Driel, P. Prendergast, and K. Søballe, “A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation,” J. Mater. Sci. Mater. Med., vol. 8, pp. 785-788, 1997.
[38] D. Lacroix, P. Prendergast, G. Li, and D. Marsh, “Biomechanical model to simulate tissue differentiation and bone regeneration: application to fracture healing,” Medical and Biological Engineering and Computing, vol. 40, pp. 14-21, 2002.
[39] D. Kelly and P. J. Prendergast, “Mechano-regulation of stem cell differentiation and tissue regeneration in osteochondral defects,” J. Biomech., vol. 38, pp. 1413-1422, 2005.
[40] K. Søballe, “Hydroxyapatite ceramic coating for bone implant fixation: mechanical and histological studies in dogs,” Acta Orthopaedica, vol. 64, pp. 1-58, 1993.
[41] C. R. Jacobs and D. J. Kelly, “Cell mechanics: The role of simulation,” in Advances on Modeling in Tissue Engineering. New York: Springer, 2011, pp. 1-14.
[42] D. R. Carter, “Mechanical loading histories and cortical bone remodeling,” Calcif. Tissue Int., vol. 36, pp. S19-S24, 1984.
[43] J. E. Bertram and S. M. Swartz, “The ‘Law of Bone Transformation’: A Case of Crying Wolff?” Biol Rev, vol. 66, pp. 245-273, 1991.
[44] H. Khayyeri, H. Isaksson and P. J. Prendergast, “Corroboration of computational models for mechanoregulated stem cell differentiation,” Comput. Methods Biomech. Biomed. Engin., vol. 18, pp. 15-23, 01/02; 2014/11, 2015.
How to Cite
Suárez, D. R. (2015). Theories of mechanically induced tissue differentiation and adaptation in the musculoskeletal system. Ingenieria Y Universidad, 20(1), 21–40.
Bioengineering and chemical engineering

Most read articles by the same author(s)