Skip to main content
SpringerLink
Log in

Modeling of Bone Adaption Processes

  • Living reference work entry
  • First Online:
Encyclopedia of Continuum Mechanics

Synonyms

Bone adaption; Bone remodeling; Stress shielding

Definitions

A new paradigm is stated in order to push mechanically driven bone adaption simulations into clinical practice. Low-parametrized 3D modeling approaches are needed which describe the essential phenomena in a sufficient manner. Furthermore, suitable techniques for the determination of patient individual model parameters and boundary conditions are necessary. In this paper a low-parametrized simple bone remodeling theory is outlined in the framework of thermodynamic consistent constitutive theory of materials. Furthermore a goal-oriented strategy for patient individual modeling is outlined.

Introduction

Bones are living organs which adapt themselves to their mechanical demand. In adults under usual activity, bone is continuously maintained by the cellular activity; however for a longer resting time or low-gravity environment, a significant loss of bone mass happens, whereas bone mass increases when the physical activity...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Ackermann MJ (1999) The visible human project: a resource for education. Acad Med 74(6):667–670

    Article  Google Scholar 

  • Austmann RL, Milner JA, Holdsworth DW, Dunning CE (2008) The effect of the density-modulus relationship selected to apply material properties in a finite element model of long bone. J Biomech 41:3171–3176

    Article  Google Scholar 

  • Beaupré G, Orr T, Carter D (1990) An approach for time-dependent bone modeling and remodeling-application: a preliminary remodeling simulation. J Orthop Res 8(5):662–670

    Article  Google Scholar 

  • Bergmann G, Bender A, Dymke J, Duda G, Damm P (2016) Standardized loads acting in hip implants. Plos one. https://doi.org/10.1371/journal.pone.0155612

  • Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35:268–308

    Article  Google Scholar 

  • Braun A, Sabah A (2009) Zwei-Jahres-Ergebnisse einer modularen Kurzschaft-Hftendoprothese. Z Orthop Unfall 147:700–706

    Article  Google Scholar 

  • Burr DB, Martin RB, Schaffler MB, Radin EL (1985) Bone remodeling in response to in vivo fatigue microdamage. J Biomech 18(3):189–200

    Article  Google Scholar 

  • Carter DR, Hayes WC (1977) The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg Am 59:954–962

    Article  Google Scholar 

  • Carter D, Orr T, Fyhrie D (1989) Relationships between loading history and femoral cancellous bone architecture. J Biomech 22(3):231–244

    Article  Google Scholar 

  • Doblaré M, Garcıa J (2001) Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement. J Biomech 34(9):1157–1170

    Article  Google Scholar 

  • Ehrlich PJ, Lanyon LE (2002) Mechanical strain and bone cell function: a review. Osteoporos Int 13:688–700

    Article  Google Scholar 

  • Floerkemeier T, Gronewold J, Berner S (2013) The influence on resection hight on proximal femoral strain patterns after Metha short stem hip arthropasty. Int Orthop 37(3):369–377

    Google Scholar 

  • Frost HM (1987) Bone mass and the mechanostat: a proposal. Anat Rec 219:1–9

    Google Scholar 

  • Frost HM (1998) From wolff’s law to the mechanostat: a new face of physiology. J Orthop Sci 3:282–286

    Google Scholar 

  • Gomez-Benito MJ, Garcia-Aznar JM, Doblare M (2005) Finite element prediction of proximal femoral fracture patterns under different loads. J Biomech Eng 127: 9–14

    Google Scholar 

  • Hambli R (2014) Connecting mechanics and bone cell activities in the bone remodeling process: an integrated finite element modeling. Front Bioeng Biotechnol 2(6):1–12

    Google Scholar 

  • Jacobs CR, Levenston ME, Beaupre GS, Simo JC, Carter DR (1995) Numerical instabilities in bone remodeling simulations: the advantage of a node-based finite element approach. J Biomech 28:449–459

    Article  Google Scholar 

  • Kastl S, Sommer T, Klein P, Hohenberger W, Engelke K (2002) Accuracy and precision of bone mineral density and bone mineral content in excised rat humeri using fan beam dual-energy x-ray absorptiometry. Bone 30(1):243–246

    Article  Google Scholar 

  • Krstin N, Nackenhorst U, Lammering R (2000) Zur konstitutiven beschreibung des anisotropen beanspruchungsadaptiven knochenumbaus. Technische Mechanik 20(1):31–40

    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

    Article  MathSciNet  Google Scholar 

  • Lemaitre J, Chaboche JL (1990) Mechanics of solid materials. Cambridge University Press, Cambridge

    Google Scholar 

  • von Lewinski G, Flörkemeier T (2015) 10-year experience with short stem total hip arthropasty. Orthopedics 38(3):51–56

    Google Scholar 

  • Lutz A (2011) Ein integrales modellierungskonzept zur numerischen simulation der osseointegration und langzeitstabilität von endoprothesen. PhD thesis, Institut für Baumechanik und Numerische Mechanik, Leibniz Universität Hannover

    Google Scholar 

  • Lutz A, Nackenhorst U (2009) A computational approach on the osseointegration of bone implants based on a bio-active interface theory. GAMM-Mitteilungen 32(2):178

    Article  MathSciNet  Google Scholar 

  • Lutz A, Nackenhorst U (2010) Numerical investigations on the biomechanical compatibility of hip-joint endoprostheses. Arch Appl Mech 80(5):503–512

    Article  Google Scholar 

  • Lutz A, Nackenhorst U (2012) Numerical investigations on the osseointegration of uncemented endoprostheses based on bio-active interface theory. Comput Mech 50(3):367–381

    Article  MathSciNet  Google Scholar 

  • Morgan EF, Bayraktar HH, Keaveny TM (2003) Trabecular bone modulus-density relationship depend on anatomic site. J Biomech 36:897–904

    Article  Google Scholar 

  • Mullender M, Haj AJE, Yang Y, van Duin MA, Burger EH, Klein-Nulend J (2004) Mechanotransduction of bone cells in vitro: mechanobiology of bone tissue. Med Biol Eng Comput 42(1):14–21

    Article  Google Scholar 

  • Nackenhorst U (1997) Numerical simulation of stress stimulated bone remodeling. Tech Mech 17(1):31–40

    Google Scholar 

  • Nackenhorst U, Krstin N, Lammering R (2000) A constitutive law for anisotropic stress adaptive bone remodeling. ZAMM Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 80(S2):399–400

    Article  Google Scholar 

  • O’Connor J, Borges LMA, Duda FP, da Cruz AGB (2016) Bone density growth. Biomechanics of healthy and prosthetic femur after a total hip arthroplasty. In: Proceedings of XXXVII Latin-American congress on computational methods in engineering (CILAMCE 2016)

    Google Scholar 

  • Prendergast PJ (1997) Finite element models in tissue mechanics and orthoportho implant design. Clin Biomech 12(6):343–366

    Google Scholar 

  • Rice JC, Cowin SC, Bowman JA (1988) On the dependence of the elasticity and strength of cancellous bone on appearent density. J Biomech 21:155–168

    Article  Google Scholar 

  • Robling AG, Castillo AB, Turner CH (2006) Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 8:455–498

    Article  Google Scholar 

  • Sarkalkan N, Weinans H, Sadpoor AA (2014) Statistical shape and appearence models of bones. Bone 60: 129–140

    Article  Google Scholar 

  • Szmukler-Moncler S, Salama H, Reingewirtz Y, Dubruille JH (1998) Timing and loading effect on micromotion on dental implant interface: review of experimental literature. J Biomed Mater Res 43:192–203

    Google Scholar 

  • Verborgt O, Gibson GJ, Schaffler MB (2000) Loss of osteocyte integrity in association with microdamage and bone remodeling after fatigue in vivo. J Bone Miner Res 14(1):60–67

    Article  Google Scholar 

  • Viceconti M, Casali M, Massari B, Christofolini L, Bassini S, Toni A (1996) The ‘standardized femur program’ proposal for a reference geometry to be used for the creation of finite element models of the femur. J Biomech 29(9):1241

    Article  Google Scholar 

  • Viceconti M, Ansaloni M, Baleani M, Toni A (2003) The muscle standardized femur: a step forward in the replication of numerical studies in biomechanics. Proc Instn Mech Engrs Part H J Eng Med 217:105–110

    Article  Google Scholar 

  • Webster D, Müller R (2011) In silico models of bone remodeling fram macro to nano – from organ to cell. WIREs Syst Biol Med 3(2):241–251

    Google Scholar 

  • Weinans H, Huiskes R, Grootenboer H (1992) The behavior of adaptive bone-remodeling simulation models. J Biomech 25(12):1425–1441

    Article  Google Scholar 

  • Wolff J (1982) Das Gesetz der Transformation der Knochen. Hirschwald

    Google Scholar 

  • Yagiura M, Ibaraki T (2001) On metaheuristic algorithms for combinatorial optimization problems. Syst Comput Jpn 32:33–55

    Article  Google Scholar 

  • Zysset PK, Curnier A (1996) A 3D damage model for trabecular bone based on fabric tensors. J Biomech 29(12):1549–1558

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by several grants from the German Research Foundation within the framework of GRK 615 and under contracts DFG-NA330-6 and DFG-NA330-8. We express our gratitude for that funding.

Author information

Authors and Affiliations

  1. Leibniz University Hannover, Hannover, Germany

    Udo Nackenhorst

Authors
  1. Udo Nackenhorst
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Udo Nackenhorst .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Chair of Continuum Mechanics, Ruhr-University-Bochum, Bochum, Germany

    Daniel Balzani

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Nackenhorst, U. (2018). Modeling of Bone Adaption Processes. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_33-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_33-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation