Continuum remodeling revisited

Deformation rate driven functional adaptation using a hypoelastic constitutive law
Original Paper

Abstract

Recent research effort in bone remodeling has been directed toward describing interstitial fluid flow in the lacuno-canalicular system and its potential as a cellular stimulus. Regardless of the precise contents of the mechanotransduction “black box”, it seems clear that the fluid flow on which the remodeling is predicated cannot occur under static loading conditions. In an attempt to help continuum remodeling simulations catch up with cellular and subcellular research, this paper presents a simple, strain rate driven remodeling algorithm for density allocation and principal material direction rotations. An explicit finite element code was written and deployed on a supercomputer which discretizes the remodeling process and uses an objective hypoelastic constitutive law to simulate trabecular realignment. Results indicate that a target strain rate for this dynamic approach is |DI*|  =  1.7% per second which seems reasonable when compared to observed strain rates. Simulations indicate that a morpho-mechanically realistic three-dimensional bone can be synthesized by applying a few dynamic loads at the envelope of common daily physiological rates, even with no static loading component.

Keywords

Bone remodeling Dynamic stimulus Hypoelastic Three-dimensional Finite element analysis Cyberinfrastructure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Batra NN, Ying YJ, Yellowley CE, You L, Malone AM, Kim CH, Jacobs CR (2006) Effects of short-term recovery periods on fluid-induced signaling in osteoblastic cells. J Biomech (in press)Google Scholar
  2. Beaupré GS, Orr TE, Carter DR (1990) An approach for time-dependent bone modeling and remodeling—theoretical development. J Orthop Res 8:651–661CrossRefGoogle Scholar
  3. Bergmann G (2001) Loading of the hip joint compact disc. In: Bergmann G (ed) HIP98. Free University of Berlin, BerlinGoogle Scholar
  4. Burger EH, Veldhuijzen J (1993) Bone In: Hall BK (ed) Influence of mechanical factors on bone formation, resorption and growth in vitro, vol 7. CRC Press, Boca Raton, pp 37–56Google Scholar
  5. Burr DB, Milgrom C, Fyhrie D, Forwood M, Nyska M, Finestone A, Hoshaw S, Saiag E, Simkin A (1996) In vivo measurement of human tibial strains during vigorous activity. Bone 18(5):405–410CrossRefGoogle Scholar
  6. Carter DR, Orr TE, Fyhrie DP (1989) Relationships between loading history and femoral cancellous bone architecture. J Biomech 22(3):231–244CrossRefGoogle Scholar
  7. Cowin SC (1986) Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech 108:83–86CrossRefGoogle Scholar
  8. Currey JD (2003) The many adaptations of bone. J Biomech 36: 1487–1495CrossRefGoogle Scholar
  9. Donahue SW, Donahue HJ, Jacobs CR (2003a) Osteoblastic cells have refractory periods for fluid-flow-induced intracellular calcium oscillations for short bouts of flow and display multiple low-magnitude oscillations during long-term flow. J Biomech 36(1):35–43CrossRefGoogle Scholar
  10. Donahue TL, Haut TR, Yellowley CE, Donahue HJ, Jacobs CR (2003b) Mechanosensitivity of bone cells to oscillating fluid flow induced shear stress may be modulated by chemotransport. J Biomech 36(9):1363–1371CrossRefGoogle Scholar
  11. Ebbecke B, Nackenhorst U (2004) Simulation of stress adaptive bone remodelling- towards an individual therapy in endoprosthetics. PAMM 4(1):250–251CrossRefGoogle Scholar
  12. Edlich M, Yellowley CE, Jacobs CR, Donahue HJ (2004) Cycle number and waveform of fluid flow affect bovine articular hondrocytes. Biorheology 41:315–322Google Scholar
  13. García JM, Rueberg T, Doblaré M (2005) A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity. Biomech Model Mechanobiol (in press)Google Scholar
  14. Gurtin ME (2003) An introduction to continuum mechanics. Academic, San DiegoGoogle Scholar
  15. Han Y, Cowin S, Schaffler MB, Weinbaum S (2004) Mechanotransduction and strain amplification in osteocyte cell processes. Proc Nat Acad Sci 101(47):16689–16694CrossRefGoogle Scholar
  16. Heiner A, Brown TD (2001) Structural properties of a new design of composite replicate femurs and tibias. J Biomech 34: 773–781CrossRefGoogle Scholar
  17. Hung CT, Pollack SR, Reilly TM, Brighton CT (1995) Real time calcium response of cultured bone cells to fluid flow. Clin 313:256–269Google Scholar
  18. Impelluso TJ, Negus CH (2005) Biomechanics and the cyber-infrastructure: delivering the bone and other models to the surgeon. In: Zeman M (ed) Computational modeling of tissue surgery Chapter 10. WIT Press, Southhampton, pp. 1–30Google Scholar
  19. Jacobs CR, Beaupré GS, Simo JC, Carter DR (1996) A principal stress-based approach to the simulation of anisotropic bone adaptation to mechanical loading. In: Middleton J, Pande GN, Williams KR (eds) Gordon and Breach, Computer methods in biomechanics and biomedical engineering. Amsterdam, pp 85–94Google Scholar
  20. Jacobs CR, Yellowley CE, Davis BR, Zhou Z, Cimbala JM, Donahue HJ (1998) Differential effect of steady versus oscillating flow on bone cells. J Biomech 31(11):969–976CrossRefGoogle Scholar
  21. Judex S, Zernicke RF (2000) High-impact exercise and growing bone: relation between high strain rates and enhanced bone formation. J Appl Physiol 88: 2183–2191Google Scholar
  22. Klein-Nulend J, Roelofsen J, Semeins CM, Bronckers AL, Burger EH (1997) Mechanical stimulation of osteopontin mrna expression and synthesis in bone cell cultures. J Cell Physiol 170(2):174–181CrossRefGoogle Scholar
  23. Kuhl E, Balle F (2005) Computational modeling of hip replacement surgery: total hip replacement vs. hip resurfacing. Technische mechanik 25(2):107–114Google Scholar
  24. Kuhl E, Garikipati K, Arruda EM, Grosh K (2005) Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. J Mech Phys Solids 53(7):1552–1573CrossRefMathSciNetMATHGoogle Scholar
  25. Levenston ME, Beaupré GS, Carter DR (1998) Loading mode interactions in simulations of long bone cross-sectional adaptation. Comput Methods Biomech Biomed Eng 1:303–319CrossRefGoogle Scholar
  26. McGarry J, Klein-Nulend J, Pendergast P (2005) The effect of cytoskeletal disruption on pulsatile fluid flow-induced nitric oxide and prostaglandin E2 release in osteocytes and osteoblasts. Biochem Biophys Res Commun 330(1):341–348CrossRefGoogle Scholar
  27. Menzel A (2005). Modeling of anisotropic growth in biological tissues—a new approach and computational aspects. Biomech Model Mechanobiol 3(3):147–171CrossRefGoogle Scholar
  28. Mosley JR, Lanyon LE (1998) Strain rate as a controlling influence on adaptive modeling in response to dynamic loading of the ulna in growing male rats. Bone 23:313–318CrossRefGoogle Scholar
  29. Neidlinger-Wilke C, Stall I, Claes L, Brand R, Rubenacker S, Arand M, Kinzl L (1995) Human osteoblasts from younger normal and osteoporotic donors show differences in proliferation and TGF-β release in response to cyclic strain. J. Biomech 28:1411–1418CrossRefGoogle Scholar
  30. Owan I, Burr DB, Turner CH, Qiu J, Tu Y, Onyia JE, Duncan RL (1997) Mechanotransduction in bone: osteoblasts are more responsive to fluid forces than mechanical strain. Am J Physiol Cell Physiol 273:C810–C815Google Scholar
  31. Reich KM, Fangos JA (1991) Effect of flow on prostaglandin E2 and inositol trisphosphate levels in osteoblasts. Am J Physiol 261:C428–C432Google Scholar
  32. Robling AG, Hinant FM, Burr DB, Turner CH (2002) Shorter, more frequent mechanical loading sessions enhance bone mass. Med Sci Sports Exerc 34:196–202CrossRefGoogle Scholar
  33. Rubin CT, Lanyon LE (1984) Regulation of bone formation by applied dynamic loads. J Bone Joint Surg (Am) 66:397–402Google Scholar
  34. Smalt R, Mitchell FT, Howard RL, Chambers TJ (1997) Mechanotransduction in bone cells: induction of nitric oxide and prostaglandin synthesis by fluid shear stress, but not by mechanical strain. Adv Exp Med Biol 433:311–314Google Scholar
  35. Taylor D, O’Reilly P, Vallet L, Lee TC (2003) The fatigue strength of compact bone in torsion. J. Biomech 36:1103–1109CrossRefGoogle Scholar
  36. Truesdell C, Noll W (1965) The nonlinear field theories of mechanics. Springer, Berlin Heidelberg New YorkGoogle Scholar
  37. Turner CH (1998) Three rules for bone adaptation to mechanical stimuli. Bone 23(5):399–407CrossRefGoogle Scholar
  38. Umemura Y, Ishiko T, Yamauchi T, Kurono M, Mashiko S (1997) Five jumps per day increase bone mass and breaking force in rats. J Bone Miner Res 12:1480–1485CrossRefGoogle Scholar
  39. Underwood P (1983) Dynamic relaxation. In: Belytschko T, Hughes T (eds) Computational methods for transient analysis Chapter 5. Elsevier Science Publishers, New York, pp 246–265Google Scholar
  40. Weinbaum S, Cowin SC, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses on osteocytic processes. J. Biomech 27(3):339–360CrossRefGoogle Scholar
  41. Wirtz DC, Pandorf T, Portheine F, Radermacher K, Schiffers N, Prescher A, Weichert D, Forst R (2000) Critical evaluation of known bone material properties to realize anisotropic FE- simulation of the proximal femur. J Biomech 33:1325–1330CrossRefGoogle Scholar
  42. You L, Cowin S (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J. Biomech 34:1375–1386CrossRefGoogle Scholar
  43. You L, Yellowley CE, Donahue HJ, Zhang Y, Chen Q, Jacobs CR (2000) Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to loading-induced oscillatory fluid flow. J Biomech Eng 122: 387–393CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaSan Diego La JollaUSA
  2. 2.Department of Mechanical EngineeringSan Diego State UniversitySan DiegoUSA
  3. 3.L-3 Jaycor Simulation, Engineering and TestingSan DiegoUSA

Personalised recommendations