Abstract
Bone regeneration is a common biological process occurring, for example, during fracture healing or osseo-integration of prostheses. Computer simulation of bone regeneration is difficult to carry out because it is a complex sequence of cell-mediated processes regulated by mechanobiological stimuli. An algorithm to predict the time-course of intramembranous and endochondral ossification has been developed. The algorithm assumes that there are precursor cells in the undifferentiated tissue and that these cells differentiate into either fibroblasts (to form fibrous connective tissue), chondrocytes (to form cartilaginous tissue) or osteoblasts (to form bone), based on a combination of biophysical stimuli derived from strain in the collagenous matrix and flow of the interstitial fluid. Both these stimuli are known to deform the precursor cells, and the authors hypothesise that this causes activation of cell differentiation pathways. The observation that precursor cells take time to spread throughout the fracture callus has been included in the algorithm. The algorithm was tested in an investigation of the fracture healing of a long bone using an axisymmetric finite element model. The spatio-temporal sequence of tissue phenotypes that appear in the course of fracture healing was successfully simulated. Furthermore, the origin of the precursor cells (either surrounding muscle, bone marrow or periosteum) was predicted to have a fundamental effect on the healing pattern and on the rate of reduction of the interfragmentary strain (IFS). The initial IFS=0.15 drops to 0.01 within seven iterations if cells originated from the surrounding soft tissue, but took more than 50% longer if cells originated in the inner cambium layer of the periosteum, and four times longer if precursor cells originated from the bone marrow only.
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Abbreviations
- σ1,2,3 :
-
principal stresses
- D :
-
diffusion co-efficient
- E :
-
average Young's modulus
- E granulation :
-
Young's modulus of granulation tissues
- E tissue :
-
Young's modulus of differentiated tissue
- H :
-
hydrostatic stress
- n :
-
cell density
- n max :
-
maximum cell density
- OI :
-
osteogenic index
- S :
-
octahedral shear stress
References
Blenman, P. R., Carter, D. R., andBeaupré, G. S. (1989): ‘Role of mechanical loading in the progressive ossification of a fracture callus’,J. Orthop. Res.,7, pp. 398–407
Carter, D. R., Blenman, P. R., andBeaupré, G. S. (1988): ‘Correlations between mechanical stress history and tissue differentiation in initial fracture healing’,J. Orthop. Res.,6, pp. 736–748
Claes, L. E., Heigele, C. A., Neidlinger-Wilke, C., Kaspar, D., Seidl, W., Margevivius, J., andAugat, P. (1998): ‘Effects of mechanical factors on the fracture healing process’,Clin. Orthop. Rel. Res.,355S, pp. 132–147
Claes, L. E., andHeigele, C. A. (1999): ‘Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing’,J. Biomech.,32, pp. 255–266
Cowin, S. C. (1999): ‘Bone poroelasticity’,J. Biomech.,32, pp. 217–238
Einhorn, T. A. (1998): ‘The cell and molecular biology of fracture healing’,Clin. Orthop. Rel. Res.,355S, pp. 7–21
Gardner, T. A., Stoll, T., Marks, L., andKnothe Tate, M. (2000): ‘The influence of mechanical stimulus on the pattern of tissue differentiation in a long bone fracture-an FEM study’,J. Biomech.,33, pp. 415–425
Hori, R. Y., andLewis, J. L. (1982): ‘Mechanical properties of the fibrous tissue found at the bone-cement interface following total joint replacement’,J. Biomed. Mater. Res.,16, pp. 911–927
Huiskes, R., van Driel, W. D., Prendergast, P. J., andSøballe, K. (1997): ‘A biomechanical regulatory model of peri-prosthetic tissue differentiation’,J. Mater. Sci. Mater. Med.,8, pp. 785–788
Iwaki, A., Jingushi, S., Oda, Y., Izumi, T., Shida, J. I., Tsuneyoshi, M., andSugioka, Y. (1997): ‘Localization and quantification of proliferating cells during rat fracture repair: detection of proliferating cell nuclear antigen by immunohistochemistry’,J. Bone Min. Res.,12, pp. 96–102
Kuiper, J. H., Ashton, B. A., andRichardson, J. B. (2000): ‘Computer simulation of fracture callus formation and stiffness restoration’. Proceedings of 12th Conference of European Society of Biomechanics, p. 61, urwww.biomechanics.ie/esb2000
Lacroix, D., andPrendergast, P. J. 2000a: ‘A homogenization procedure to prevent numerical instabilities in poroelastic tissue differentiation models’. Proceedings of 8th Symposium on Computational Methods in Orthopaedic Biomechanics, urwww.me.gatech.edu/pre-ORS/
Lacroix, D., andPrendergast, P. J. 2000b: ‘A 3D finite element model of a tibia to simulate the regenerative and resportive phases during fracture healing’. Proceedings of 12th Conference of European Society of Biomechanics, p. 60, urwww.biomechanics.ie/esb2000.
McKibbin, B. (1978): ‘The biology of fracture healing in long bones’,J. Bone Joint Surg.,60B, 150–162
Mow, V. C., Kuei, S. C., Lai, W. M., andArmstrong, C. G. (1980): ‘Biphasic creep and stress relaxation of articular cartilage: theory and experiments’,J. Biomech. Eng.,102, pp. 73–84
Ochoa, J. A., andHillberry, B. M. (1992): ‘Permeability of bovine cancellous bone’. Transactions of 38th Meeting of Orthopaedic Research Society, p. 162
Olsen, L., Sherratt, J. A., andMaini, P. K. (1996): ‘A mathematical model for fibro-proliferative wound healing disorders’,Bull. Math. Biol.,58, pp. 787–808
Pauwels, F. (1941): ‘Grundrieß einer Biomechanik der Frakturheilung’. 34th Kongreß der Deutschen Orthopädischen Gesellschaft (Ferdinand Enke Verlag: Stuttgart, 1941), pp. 62–108. Translated as ‘Biomechanics of fracture healing’ in ‘Biomechanics of the locomotor apparatus’ byMaquet, P., andFurlong, R. (Springer, Berlin, 1980), pp. 107–137
Pauwels, F. (1960): ‘Eine Neue Theorie über den Einfluß Mechanischer Reize auf die Differenzierung der Stützgewebe’,Z. Anat. Entwickl. Gesch.,121, pp. 478–515. Translated as ‘A new theory concerning the influence of mechanical stimuli on the differentiation of the supporting tissues’ in ‘Biomechanics of the locomotor apparatus’ byMaquet, P., andFurlong, R. (Springer, Berlin, 1980), pp. 375–407
Perren, S. M. (1979): ‘Physical and biological aspects of fracture healing with special reference to internal fixation’,Clin. Orthop. Rel. Res.,138, p. 175
Prendergast, P. J., van Driel, W. D., andKuiper, J. H. (1996): ‘A comparison of finite element codes for the solution of biphasic poroelastic problems’,Proc. Inst. Mech. Eng. H,210, pp. 131–136
Prendergast, P. J., andvan der Meulen, M. C. H. (2001): ‘Mechanics of bone regeneration’ inCowin, S. C. (Ed.): Handbook of bone mechanics’ (CRC Press, Boca Raton, 2001), pp. 32.1–32.13
Prendergast, P. J. (1997): ‘Finite element models in tissue mechanics and orthopaedic implant design’,Clin. Biomech.,12, pp. 343–366
Prendergast, P. J., Huiskes, R., andSøballe, K. (1997): ‘Biophysical stimuli on cells during tissue differentiation at implant interfaces’,J. Biomech.,30, pp. 539–548
Rhinelander, F. W. (1974): ‘Tibial blood supply in relation to fracture healing’,Clin. Orthop. Rel. Res.,105, pp. 35–81
Sherratt, J. A., Martin, P., Murray, J. D., andLewis, J. (1992): ‘Mathematical models of would healing in embryonic and adult epidermis’,IMA J. Math. Appl. Med. Biol.,9, pp. 177–196
Tencer, A. F., andJohnson, J. (1994): Biomechanics in orthopaedic trauma’ (Martin Dinitz, London, 1994)
Yoo, J. U., andJohnstone, B. 1998. ‘The role of osteochondral progenitor cells in fracture repair’,Clin. Orthop. Rel. Res.,355, pp. 73–81
Zohar, R., Cheifetz, S., Mcculloch, C. A. G., andSodek, J. (1998): Analysis of intracellular osteopontin as a marker of osteoblastic cell differentiation and mesenchymal cell migration,Eur. J. Oral. Sci.,106, pp. 401–407
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Lacroix, D., Prendergast, P.J., Li, G. et al. Biomechanical model to simulate tissue differentiation and bone regeneration: Application to fracture healing. Med. Biol. Eng. Comput. 40, 14–21 (2002). https://doi.org/10.1007/BF02347690
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DOI: https://doi.org/10.1007/BF02347690