A novel micromorphic approach captures non-locality in continuum bone remodelling

References

• Arndt D, Bangerth W, Feder M, Fehling M, Gassmöller R, Heister T, Heltai L, Kronbichler M, Maier M, Munch P, et al. 2022. The deal.ii library, version 9.4. J Numer Math. 30(3):231–246. doi:10.1515/jnma-2022-0054.
   Google Scholar
• Bagge M. 2000. A model of bone adaptation as an optimization process. J Biomech. 33(11):1349–1357. doi:10.1016/s0021-9290(00)00124-x.
   PubMed Web of Science ®Google Scholar
• Bangerth W, Hartmann R, Kanschat G. 2007. Deal.ii—a general-purpose object-oriented finite element library. ACM Trans Math Softw. 33(4):24–es. doi:10.1145/1268776.1268779.
   Web of Science ®Google Scholar
• Bangerth W, Heister T, Kanschat G, Maier M. 2022. The deal.ii finite element library. [accessed 2022 Sept 16]. Available from: https://www.dealii.org/.
   Google Scholar
• Carter DR, Beauprè GS. 2000. Skeletal function and form: mechanobiology of skeletal development, aging, and regeneration. Cambridge University Press. doi:10.1017/CBO9780511574993.
   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
• Coelho P, Fernandes P, Rodrigues H, Cardoso J, Guedes J. 2009. Numerical modeling of bone tissue adaptation - a hierarchical approach for bone apparent density and trabecular structure. J Biomech. 42(7):830–837. doi:10.1016/j.jbiomech.2009.01.020.
   PubMed Web of Science ®Google Scholar
• Fernandes P, Rodrigues H, Guedes J, Coelho P. 2012. Multiscale modelling on bone mechanics – application to tissue engineering and bone quality analysis. IFAC Proc Vol. 45(2):1013–1017. doi:10.3182/20120215-3-AT-3016.00179.
   Google Scholar
• Frost HM. 1987. Bone mass and the mechanostat: a proposal. Anat Rec. 219(1):1–9. doi:10.1002/ar.1092190104.
   PubMedGoogle Scholar
• Galilei G. 1638. Discorsi e dimostrazioni matematiche intorno á due nuove scienze attenenti alla meccanica e i movimenti locali.
   Google Scholar
• Gibson LJ, Ashby MF. 1982. The mechanics of three-dimensional cellular materials. Proc R Soc London A Math Phys Sci. 382:43–59.
   Web of Science ®Google Scholar
• Gitman IM. 2012. Anisotropic gradient elasticity for modelling bone tissue. Comput Mater Sci. 52(1):136–138. doi:10.1016/j.commatsci.2011.06.022.
   Web of Science ®Google Scholar
• Haj AE, Minter S, Rawlinson S, Suswillo R, Lanyon L. 1990. Cellular responses to mechanical loading in vitro. J Bone Miner Res. 5(9):923–932. doi:10.1002/jbmr.5650050905.
   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 Methods Eng. 36(5):837–854. doi:10.1002/nme.1620360508.
   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. doi:10.1016/0020-7683(94)90178-3.
   Web of Science ®Google Scholar
• Hirschberger CB. 2008. A treatise on micromorphic continua. theory, homogenization, computation [doctoral thesis]. Kaiserslautern: Technische Universit Kaiserslautern. ISBN: 978-3-939432-80-7.
   Google Scholar
• Hirschberger CB, Kuhl E, Steinmann P. 2007. On deformational and configurational mechanics of micromorphic hyperelasticity - theory and computation. Comput Methods Appl Mech Eng. 196(41-44):4027–4044. doi:10.1016/j.cma.2007.02.015.
   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 Biomech. 28/(4):449–459. doi:10.1016/0021-9290(94)00087-k.
   PubMed Web of Science ®Google Scholar
• Klein-Nulend J. 2010. Mechanosensing in bone. Clinic Rev Bone Miner Metab. 8(4):161–162. doi:10.1007/s12018-011-9085-7.
   Google Scholar
• Kuhl E. 2004. Theory and numerics of open system continuum thermodynamics - spatial and material settings [habilitation]. Technische Universität Kaiserslautern.
   Google Scholar
• Kuhl E, Menzel A, Steinmann P. 2003. Computational modeling of growth - a critical review, a classification of concepts and two new consistent approaches. Comput Mech. 32(1–2):71–88. doi:10.1007/s00466-003-0463-y.
   Web of Science ®Google Scholar
• Kuhl E, Steinmann P. 2003. Theory and numerics of geometrically non-linear open system mechanics. Int J Numer Methods Eng. 58(11):1593–1615. doi:10.1002/nme.827.
   Web of Science ®Google Scholar
• McBride A, Davydov D, Steinmann P. 2020. Modelling the flexoelectric effect in solids: a micromorphic approach. Comput Methods Appl Mech Eng. 371:113320. doi:10.1016/j.cma.2020.113320.
   Web of Science ®Google Scholar
• Mullender M, Huiskes R, Weinans H. 1994. A physiological approach to the simulation of bone remodeling as a self-organizational control process. J Biomech. 27(11):1389–1394. doi:10.1016/0021-9290(94)90049-3.
   PubMed Web of Science ®Google Scholar
• Papastavrou A, Schmidt I, Deng K, Steinmann P. 2020a. On age-dependent bone remodeling. J Biomech. 103:109701. doi:10.1016/j.jbiomech.2020.109701.
   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. doi:10.1080/10255842.2020.1736050.
   PubMed Web of Science ®Google Scholar
• Park J, Park S, Kang I, Noh G. 2022a. Biomechanical effects of bone quality and design features in dental implants in long-term bone stability. J Comput Des Eng. 9(5):1538–1548. doi:10.1093/jcde/qwac069.
   Web of Science ®Google Scholar
• Park S, Park J, Kang I, Lee H, Noh G. 2022b. Effects of assessing the bone remodeling process in biomechanical finite element stability evaluations of dental implants. Comput Methods Prog Biomed. 221:106852.
   PubMed Web of Science ®Google Scholar
• Parkinson IH, Fazzalari NL. 2013. Characterisation of trabecular bone structure. Berlin Heidelberg: Springer; p. 31–51.
   Google Scholar
• Schaller E, Javili A, Schmidt I, Papastavrou A, Steinmann P. 2022. A peridynamic formulation for nonlocal bone remodelling. Comput Methods Biomech Biomed Eng. 25(16):1835–1851. doi:10.1080/10255842.2022.2039641.
   PubMed Web of Science ®Google Scholar
• Scheiner S, Pivonka P, Hellmich C. 2013. Coupling systems biology with multiscale mechanics, for computer simulations of bone remodeling. Comput Methods Appl Mech Eng. 254:181–196. doi:10.1016/j.cma.2012.10.015.
   Web of Science ®Google Scholar
• Schmidt I. 2022. Modelling and simulation of bone adaption processes [Doctoral dissertation]. Erlangen: Friedrich-Alexander-Universität Erlangen-Nürnberg.
   Google Scholar
• Schmidt I, Albert J, Ritthaler M, Papastavrou A, Steinmann P. 2021a. Bone fracture healing within a continuum bone remodelling framework. Comput Methods Biomech Biomed Eng. 25(9):1040–1050. doi:10.1080/10255842.2021.1998465.
   PubMed Web of Science ®Google Scholar
• Schmidt I, Papastavrou A, Steinmann P. 2021b. Concurrent consideration of cortical and cancellous bone within continuum bone remodelling. Comput Methods Biomech Biomed Eng. 24(11):1274–1285. doi:10.1080/10255842.2021.1880573.
   PubMed Web of Science ®Google Scholar
• Coreform L. 2022. Coreform cubit. [accessed 2022 Jun 27]. Available from: https://coreform.com/products/coreform-cubit/.
   Google Scholar
• Autodesk I. 2022. Autodesk meshmixer. [accessed 2022 Jul 01]. Available from: https://meshmixer.com/.
   Google Scholar