A Biomechanical Approach for Bone Regeneration Inside Scaffolds Embedded with BMP-2

  • C. Gorriz
  • F. Ribeiro
  • J. M. Guedes
  • J. Folgado
  • P. R. FernandesEmail author
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 51)


Scaffold-based strategies for Bone Tissue Engineering have been seen as a solution to repair bone in situations of large defect size and disease. Nevertheless, the factors that conduct to an optimal scaffold performance haven’t been fully determined yet in spite of the intense research work on this field. This work presents the development of a computational model to analyse concurrently the process of degradation and the cell/tissue invasion in an artificial bone substitute embedded with BMP-2. The computational procedure comprises a degradation model which takes in account the hydrolysis process and its enhancement by autocatalysis and a mechano-regulated bone tissue regeneration model based on cell differentiation and growth theories including the effect of BMP-2. It assumes the domain of study to be only a representative volume element of a periodic scaffold constituted by several volume elements with periodic properties. The effective elastic and permeability properties are computed using an asymptotic homogenization method. Results show that the inclusion of BMP-2 in the scaffold leads to an increase on bone formation velocity. At the end of the process the quantity of bone is not significantly different with and without BMP-2, but an early bone formation contributes to a better mechanical stability of the bone substitute.


Bone scaffolds Biodegradation Bone regeneration BMP-2 Tissue Engineering 



Authors would like to tank to Fundação para a Ciência e Tecnologia (Portugal) for the support through project PTDC/BBB-BMC/5655/2014 and LAETA project UID/EMS/50022/2019.


  1. 1.
    Fu Q, Saiz E, Rahaman MN, Tomsia AP (2011) Bioactive glass scaffolds for bone tissue engineering: state of the art and future perspectives. Mater Sci Eng C 31(7):1245–1256CrossRefGoogle Scholar
  2. 2.
    Hollister SJ, Lin CY (2007) Computational design of tissue engineering scaffold. Comput Methods Appl Mech Eng 196:31–32CrossRefGoogle Scholar
  3. 3.
    Dias MR, Guedes JM, Flanagan CL, Hollister SJ, Fernandes PR (2014) Optimization of scaffold design for bone tissue engineering: a computational and experimental study. Med Eng Phys 36(4):448–457CrossRefGoogle Scholar
  4. 4.
    Castilho M, Dias M, Gbureck U, Groll J, Fernandes P, Pires I, Gouveia B, Rodrigues J, Vorndran E (2013) Fabrication of computationally designed scaffolds by low temperature 3D printing. Biofabrication 5:035012CrossRefGoogle Scholar
  5. 5.
    Chao G, Xiaobo S, Chenglin C, Yinsheng D, Yuepu P, Pinghua L (2009) A cellular automaton simulation of the degradation of porous polylactide scaffold: I. Effect of porosity. Mater Sci Eng C 29(6):1950–1958CrossRefGoogle Scholar
  6. 6.
    Göpferich A, Langer R (1993) Modeling of polymer erosion. Macromolecules 26(16):4105–4112CrossRefGoogle Scholar
  7. 7.
    Göpferich A (1997) Polymer bulk erosion. Macromolecules 30(9):2598–2604CrossRefGoogle Scholar
  8. 8.
    Mohammadi Y, Jabbari E (2006) Monte Carlo simulation of degradation of porous poly (lactide) scaffolds, 1. Macromol Theory Simul 15(9):643–653CrossRefGoogle Scholar
  9. 9.
    Chen Y, Zhou S, Li Q (2011) Mathematical modeling of degradation for bulkerosive polymers: applications in tissue engineering scaffolds and drug delivery systems. Acta Biomater 7(3):1140–1149CrossRefGoogle Scholar
  10. 10.
    Sanz-Herrera J, Garcia-Aznar J, Doblare M (2007) A mathematical approach for tissue regeneration inside a specific type of scaffold. Biomech Model Mechanobiol 7:355–366CrossRefGoogle Scholar
  11. 11.
    Adachi T, Osako Y, Tanaka M, Hojo M, Hollister SJ (2006) Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. Biomaterials 27:3964–3972CrossRefGoogle Scholar
  12. 12.
    Gorriz C, Ribeiro F, Guedes JM, Fernandes PR (2015) A biomechanical approach for bone regeneration inside scaffolds. Procedia Eng 110:82–89CrossRefGoogle Scholar
  13. 13.
    Schindeler A, McDonald MM, Bokko P, Little DG (2008) Bone remodeling during fracture repair: the cellular picture. Semin Cell Dev Biol 19(5):459–466CrossRefGoogle Scholar
  14. 14.
    Gerhart TN, Kirker-Head CA, Kriz MJ, Holtrop ME, Hennig GE, Hipp J, Schelling SH, Wang E (1993) Healing segmental femoral defects in sheep using recombinant human bone morphogenetic protein. Clin Orthop Relat Res 293:317–326Google Scholar
  15. 15.
    Boyne P, Marx RE, Nevins M, Lazaro E, Le Lilly AM, Nummikoski P (1997) A feasibility study evaluating rhbmp-2/absorbable collagen sponge for maxillary sinus floor augmentation. Int J Period Restor Dent 17:11–25Google Scholar
  16. 16.
    Wang X, Nyman JS, Dong X, Leng H, Reyes M (2010) Fundamental biomechanics in bone tissue engineering. Synth Lect Tissue Eng 2(1):1–225CrossRefGoogle Scholar
  17. 17.
    Ribeiro FO, Gomez-Benito MJ, Folgado J, Fernandes PR, Garcia-Aznar JM (2015) In silico mechano-chemical model of bone healing for regeneration of critical defects: the effect of BMP-2. PLoS ONE 10(6):e0127722CrossRefGoogle Scholar
  18. 18.
    Guedes JM, Kikuchi N (1990) Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng 83:143–198MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Chen Y, Zhou S, Li Q (2011) Mathematical modeling of degradation for bulk-erosive polymers: applications in tissue engineering scaffolds and drug delivery systems. Acta Biomater 7(3):1140–1149CrossRefGoogle Scholar
  20. 20.
    Gómez-Benito MJ, García-Aznar JM, Kuiper JH, Doblaré M (2005) Influence of fracture gap size on the pattern of long bone healing: a computational study. J Theor Biol 235(1):105–119MathSciNetCrossRefGoogle Scholar
  21. 21.
    Dias MR, Fernandes PR, Guedes JM, Hollister SJ (2012) Permeability analysis of scaffolds for bone tissue engineering. J Biomech 45(6):938–944CrossRefGoogle Scholar
  22. 22.
    Wu XS, Wang N (2001) Synthesis, characterization, biodegradation, and drug delivery application of biodegradable lactic/glycolic acid polymers. Part II: Biodegradation. J Biomater Sci Polym Ed 12(1):21–34Google Scholar
  23. 23.
    Oh SH, Kang SG, Lee JH (2006) Degradation behavior of hydrophilized PLGA scaffolds prepared by melt-molding particulate-leaching method: comparison with control hydrophobic one. J Mater Sci Mater Med 17(2):131–137CrossRefGoogle Scholar
  24. 24.
    Rahman CV, Ben-David D, Dhillon A, Kuhn G, Gould TW, Müller R, Rose FR, Shakesheff KM, Livne E (2014) Controlled release of BMP-2 from a sintered polymer scaffold enhances bone repair in a mouse calvarial defect model. J Tissue Eng Regen Med 8(1):59–66CrossRefGoogle Scholar
  25. 25.
    Cowan CM, Aghaloo T, Chou YF, Walder B, Zhang X, Soo C, Wu B (2007) MicroCT evaluation of three-dimensional mineralization in response to BMP-2 doses in vitro and in critical sized rat calvarial defects. Tissue Eng 13(3):501–512CrossRefGoogle Scholar
  26. 26.
    Byrne DP, Lacroix D, Planell JA, Kelly DJ, Prendergast PJ (2007) 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(36):5544–5554CrossRefGoogle Scholar
  27. 27.
    Sanz-Herrera J, Doblaré M, GarcíaAznar J (2010) Scaffold microarchitecture determines internal bone directional growth structure: a numerical study. J Biomech 43(13):2480–2486CrossRefGoogle Scholar
  28. 28.
    Schofer MD, Roessler PP, Schaefer J, Theisen C, Schlimme S, Heverhagen JT, Paletta JR (2011) Electrospun PLLA nanofiber scaffolds and their use in combination with BMP-2 for reconstruction of bone defects. PLoS ONE 6(9):e25462CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • C. Gorriz
    • 1
  • F. Ribeiro
    • 1
  • J. M. Guedes
    • 1
  • J. Folgado
    • 1
  • P. R. Fernandes
    • 1
    Email author
  1. 1.IDMEC, Instituto Superior Técnico, Universidade de LisboaLisbonPortugal

Personalised recommendations