Bone fracture healing within a continuum bone remodelling framework

References

• Ament C, Hofer E. 2000. A fuzzy logic model of fracture healing. J Biomech. 33(8):961–968.
   PubMed Web of Science ®Google Scholar
• Bailón-Plaza A, van der Meulen MC. 2003. Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing. J Biomech. 36(8):1069–1077.
   PubMed Web of Science ®Google Scholar
• Carlier A, Geris L, Lammens J, van Oosterwyck H. 2015. Bringing computational models of bone regeneration to the clinic. Wiley Interdiscip Rev Syst Biol Med. 7(4):183–194.
   PubMed Web of Science ®Google Scholar
• Carter DR, Beauprè GS. 2001. Skeletal function and form: Mechanobiology of skeletal development, aging, and regeneration. Cambridge (MA): Cambridge University Press.
   Google Scholar
• Carter DR, Blenman PR, Beaupré GS. 1988. Correlations between mechanical stress history and tissue differentiation in initial fracture healing. J Orthop Res. 6(5):736–748.
   PubMed Web of Science ®Google Scholar
• Carter DR, Hayes WC. 1977. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg Am. 59(7):954–962.
   PubMed Web of Science ®Google Scholar
• Falcinelli C, Schileo E, Baruffaldi F, Cristofolini L, Taddei F. 2017. The effect of computed tomography current reduction on proximal femur subject-specific finite element models. J Mech Med Biol. 17(01):1750012.
   Google Scholar
• Frost HM. 1987. Bone “mass” and the “mechanostat”: a proposal. Anat Rec. 219(1):1–9.
   PubMedGoogle Scholar
• Geris L, Reed AAC, Vander Sloten J, Simpson AHRW, van Oosterwyck H. 2010a. Occurrence and treatment of bone atrophic non-unions investigated by an integrative approach. PLoS Comput Biol. 6(9):e1000915.
   PubMed Web of Science ®Google Scholar
• Geris L, Sloten JV, van Oosterwyck H. 2010b. Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions. Biomech Model Mechanobiol. 9(6):713–724.
   PubMed Web of Science ®Google Scholar
• Ghiasi MS, Chen J, Vaziri A, Rodriguez EK, Nazarian A. 2017. Bone fracture healing in mechanobiological modeling: a review of principles and methods. Bone Rep. 6:87–100.
   PubMedGoogle Scholar
• Ghiasi MS, Chen JE, Rodriguez EK, Vaziri A, Nazarian A. 2019. Computational modeling of human bone fracture healing affected by different conditions of initial healing stage. BMC Musculoskelet Disord. 20(1):562.
   PubMed Web of Science ®Google Scholar
• Gibson LJ, Ashby MF. 1982. The mechanics of three-dimensional cellular materials. Proc Roy Soc Lond Math Phys Sci. 382:43–59.
   Web of Science ®Google Scholar
• Gibson LJ. 2005. Biomechanics of cellular solids. J Biomech. 38(3):377–399.
   PubMed Web of Science ®Google Scholar
• Goolsby MA, Boniquit N. 2017. Bone health in athletes. Sports Health. 9(2):108–117.
   PubMedGoogle Scholar
• Hak DJ, Fitzpatrick D, Bishop JA, Marsh JL, Tilp S, Schnettler R, Simpson H, Alt V. 2014. Delayed union and nonunions: epidemiology, clinical issues, and financial aspects. Injury. 45(Suppl. 2):S3–S7.
   PubMed Web of Science ®Google Scholar
• Harrigan TP, Hamilton JJ. 1993. Finite element simulation of adaptive bone remodelling: a stability criterion and a time stepping method. Int J Numer Meth Engng. 36(5):837–854.
   Web of Science ®Google Scholar
• Harrigan TP, Hamilton JJ. 1994. Necessary and sufficient conditions for global stability and uniqueness in finite element simulations of adaptive bone remodeling. Int J Solids Struct. 31(1):97–107.
   Web of Science ®Google Scholar
• Holzapfel GA. 2001. Nonlinear solid mechanics – a continuum approach for engineering. West Sussex: John Wiley and Sons.
   Google Scholar
• Isaksson H, Wilson W, van Donkelaar CC, Huiskes R, Ito K. 2006. Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing. J Biomech. 39(8):1507–1516.
   PubMed Web of Science ®Google Scholar
• Jacobs CE, Levenston ME, Beauprè GS, Simo JC, Carter DR. 1995. Numerical instabilities in bone remodeling simulations: the advantages of a node-based finite element approach. J Biomechanics. 28(4):449–459.
   PubMed Web of Science ®Google Scholar
• Klopfer T, Hemmann P, Schreiner AJ, Bahrs C. 2019. Proximale femurfraktur. Trauma Berufskrankh. 21(2):86–94.
   Google Scholar
• Kuhl E, Steinmann P. 2003. Theory and numerics of geometrically non-linear open system mechanics. Int J Numer Meth Engng. 58(11):1593–1615.
   Web of Science ®Google Scholar
• Lacroix D, Prendergast PJ, Li G, Marsh D. 2002. Biomechanical model to simulate tissue differentiation and bone regeneration: application to fracture healing. Med Biol Eng Comput. 40(1):14–21.
   PubMed Web of Science ®Google Scholar
• Liedtke H, McBride A, Sivarasu S, Roche S. 2017. Computational simulation of bone remodelling post reverse total shoulder arthroplasty. arXiv preprint arXiv:170508324.
   Google Scholar
• Papastavrou A, Schmidt I, Deng K, Steinmann P. 2020a. On age-dependent bone remodeling. J Biomech. 103:109701.
   PubMed Web of Science ®Google Scholar
• Papastavrou A, Schmidt I, Steinmann P. 2020b. On biological availability dependent bone remodeling. Comput Methods Biomech Biomed Engin. 23(8):432–444.
   PubMed Web of Science ®Google Scholar
• Pauwels F. 1960. Eine neue theorie ber den einflu mechanischer reize auf die differenzierung der stützgewebe. Z Anat Entwickl Gesch. 121(6):478–515.
   PubMedGoogle Scholar
• Pauwels F. 1980. Biomechanics of the locomotor apparatus: Contributions on the functional anatomy of the locomotor apparatus. Berlin, Heidelberg: Springer Berlin Heidelberg.
   Google Scholar
• Prendergast PJ. 1997. Finite element models in tissue mechanics and orthopaedic implant design. Clin Biomech (Bristol, Avon). 12(6):343–366.
   PubMed Web of Science ®Google Scholar
• Rho JY, Ashman RB, Turner CH. 1993. Young’s modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. 26(2):111–119.
   PubMed Web of Science ®Google Scholar
• Roux W. 1895. Gesammelte abhandlungen über entwicklungsmechanik der organismen. W Engelmann.
   Google Scholar
• Schmidt I, Papastavrou A, Steinmann P. 2021. Concurrent consideration of cortical and cancellous bone within continuum bone remodelling. Comput Methods Biomech Biomed Engin. 24(11):1274–1212.
   PubMed Web of Science ®Google Scholar
• Singaram S, Naidoo M. 2019. The physical, psychological and social impact of long bone fractures on adults: a review. Afr J Prim Health Care Fam Med. 11(1):e1–e9.
   PubMed Web of Science ®Google Scholar
• Wang M, Yang N, Wang X. 2017. A review of computational models of bone fracture healing. Med Biol Eng Comput. 55(11):1895–1914.
   PubMed Web of Science ®Google Scholar
• Wehner T, Claes L, Niemeyer F, Nolte D, Simon U. 2010. Influence of the fixation stability on the healing time-a numerical study of a patient-specific fracture healing process. Clin Biomech (Bristol, Avon). 25(6):606–612.
   PubMed Web of Science ®Google Scholar