Skip to main content

Cortical Bone Adaptation to Mechanical Environment: Strain Energy Density Versus Fluid Motion

  • Chapter
  • First Online:
Biomanufacturing

Abstract

This chapter presents an in silico study to compare the osteogenic potentials of normal strain-derived strain energy density (SED) and fluid shear. In vivo studies reported that mechanical loading promotes osteogenesis (i.e., new bone formation) at the sites elevated normal strain magnitude. Accordingly, in silico models assumed normal strain-derived SED as an osteogenic stimulus to predict the site-specific new bone formation. Nevertheless, there are in vivo studies where new bone formation is noticed at the sites of minimal normal strain magnitude especially near the neutral axis of bending. It is anticipated that SED as stimulus will have limited success in explaining such new bone distribution. Thus, there is no unifying principle that can relate the new bone formation to mechanical environment. A secondary component of mechanical environment, i.e., canalicular fluid flow derived shear, is reported as a potential stimulus of osteogenesis in the literature; however, their exact role is not well established. Therefore, this chapter presents an in silico model which studies site-specific new bone formation as a function of SED and fluid shear, individually and in their combination. The model simulates experimental new bone formation reported in different in vivo animal loading studies. The chapter also concludes that fluid shear closely fits the new bone formation near the minimal strain sites, and both SED and fluid shear contribute collectively to new bone formation. The findings presented in the chapter may be useful in the design of biomechanical strategies to cure bone loss and also in the improvement of the design of orthopedic implants.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Lau RY, Guo X (2011) A review on current osteoporosis research: with special focus on disuse bone loss. J Osteoporos 2011:1–6

    Article  Google Scholar 

  2. Kennel KA, Drake MT (2009) Adverse effects of bisphosphonates: implications for osteoporosis management. Mayo Clin Proc 84(7):632–638

    Google Scholar 

  3. Rubin C, Recker R, Cullen D, Ryaby J, McCabe J, McLeod K (2003) Prevention of postmenopausal bone loss by a low-magnitude, high-frequency mechanical stimuli: a clinical trial assessing compliance, efficacy, and safety. J Bone Miner Res 19:343–351

    Article  Google Scholar 

  4. Rubin CT, Lanyon LE (1985) Regulation of bone mass by mechanical strain magnitude. Calcif Tissue Int 37:411–417

    Article  CAS  Google Scholar 

  5. Kotha SP, Hsieh Y-F, Strigel RM, Müller R, Silva MJ (2004) Experimental and finite element analysis of the rat ulnar loading model—correlations between strain and bone formation following fatigue loading. J Biomech 37:541–548

    Article  CAS  Google Scholar 

  6. De Souza RL, Matsuura M, Eckstein F, Rawlinson SC, Lanyon LE, Pitsillides AA (2005) Non-invasive axial loading of mouse tibiae increases cortical bone formation and modifies trabecular organization: a new model to study cortical and cancellous compartments in a single loaded element. Bone 37:810–818

    Article  Google Scholar 

  7. Sample SJ, Collins RJ, Wilson AP, Racette MA, Behan M, Markel MD, Kalscheur VL, Hao Z, Muir P (2010) Systemic effects of ulna loading in male rats during functional adaptation. J Bone Miner Res 25:2016–2028

    Article  Google Scholar 

  8. Gross TS, Srinivasan S, Liu CC, Clemens TL, Bain SD (2002) Noninvasive loading of the murine tibia: an in vivo model for the study of mechanotransduction. J Bone Miner Res 17:493–501

    Article  Google Scholar 

  9. Akhter MP, Cullen DM, Recker RR (2002) Bone adaptation response to sham and bending stimuli in mice. J Clin Densitom 5:207–216

    Article  CAS  Google Scholar 

  10. Silva MJ, Brodt MD (2008) Mechanical stimulation of bone formation is normal in the samp6 mouse. Calcif Tissue Int 82:489–497

    Article  CAS  Google Scholar 

  11. Zhang P, Tanaka SM, Jiang H, Su M, Yokota H (2006) Diaphyseal bone formation in murine tibiae in response to knee loading. J Appl Physiol 100:1452–1459

    Article  Google Scholar 

  12. Meakin LB, Price JS, Lanyon LE (2014) The contribution of experimental in vivo models to understanding the mechanisms of adaptation to mechanical loading in bone. Front Endocrinol. https://doi.org/10.3389/fendo.2014.00154

  13. Sugiyama T, Price JS, Lanyon LE (2010) Functional adaptation to mechanical loading in both cortical and cancellous bone is controlled locally and is confined to the loaded bones. Bone 46:314–321

    Article  Google Scholar 

  14. Chennimalai Kumar N, Dantzig JA, Jasiuk IM (2012) Modeling of cortical bone adaptation in a rat ulna: effect of frequency. Bone 50:792–797

    Article  CAS  Google Scholar 

  15. Hambli R, Katerchi H, Benhamou C-L (2011) Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation. Biomech Model Mechanobiol 10:133–145

    Article  Google Scholar 

  16. Tiwari AK, Prasad J (2017) Computer modelling of bone’s adaptation: the role of normal strain, shear strain and fluid flow. Biomech Model Mechanobiol 16:395–410

    Article  Google Scholar 

  17. Gross TS, Edwards JL, Mcleod KJ, Rubin CT (1997) Strain gradients correlate with sites of periosteal bone formation. J Bone Miner Res 12:982–988

    Article  CAS  Google Scholar 

  18. Judex S, Gross TS, Zernicke RF (1997) Strain gradients correlate with sites of exercise-induced bone-forming surfaces in the adult skeleton. J Bone Miner Res 12:1737–1745

    Article  CAS  Google Scholar 

  19. Srinivasan S, Gross T (1999) Canalicular fluid flow in bone: a basis for bone formation at sites of minimal strain. In: 45th annual meeting, Orthopaedic Research Society, 1999

    Google Scholar 

  20. Qin YX, Lin W, Rubin C (2001) The relationship between bone fluid flow and adaptation as stimulated by intramedullary hydraulic loading. Trans Orth Res Soc 26:319

    Google Scholar 

  21. Qin Y-X, Kaplan T, Saldanha A, Rubin C (2003) Fluid pressure gradients, arising from oscillations in intramedullary pressure, is correlated with the formation of bone and inhibition of intracortical porosity. J Biomech 36:1427–1437

    Article  Google Scholar 

  22. Hu M, Cheng J, Bethel N, Serra-Hsu F, Ferreri S, Lin L, Qin Y-X (2014) Interrelation between external oscillatory muscle coupling amplitude and in vivo intramedullary pressure related bone adaptation. Bone 66:178–181

    Article  Google Scholar 

  23. Steck R, Niederer P, Tate MK (2000) A finite difference model of load-induced fluid displacements within bone under mechanical loading. Med Eng Phys 22:117–125

    Article  CAS  Google Scholar 

  24. Tate MLK, Knothe U, Niederer P (1998) Experimental elucidation of mechanical load-induced fluid flow and its potential role in bone metabolism and functional adaptation. Am J Med Sci 316:189–195

    Google Scholar 

  25. Tate MK, Steck R, Forwood M, Niederer P (2000) In vivo demonstration of load-induced fluid flow in the rat tibia and its potential implications for processes associated with functional adaptation. J Exp Biol 203:2737–2745

    Google Scholar 

  26. Weinbaum S, Cowin S, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J Biomech 27:339–360

    Article  CAS  Google Scholar 

  27. Carriero A, Pereira AF, Wilson AJ, Castagno S, Javaheri B, Pitsillides AA, Marenzana M, Shefelbine SJ (2018) Spatial relationship between bone formation and mechanical stimulus within cortical bone: combining 3D fluorochrome mapping and poroelastic finite element modelling. Bone Rep 8:72–80

    Article  Google Scholar 

  28. Tiwari AK, Kumar R, Tripathi D, Badhyal S (2018) In silico modeling of bone adaptation to rest-inserted loading: strain energy density versus fluid flow as stimulus. J Theor Biol 446:110–127

    Article  Google Scholar 

  29. Kuruvilla SJ, Fox SD, Cullen DM, Akhter MP (2008) Site specific bone adaptation response to mechanical loading. J Musculoskelet Neuronal Interact 8:71–78

    CAS  PubMed  Google Scholar 

  30. Wagner DW, Chan S, Castillo AB, Beaupre GS (2013) Geometric mouse variation: implications to the axial ulnar loading protocol and animal specific calibration. J Biomech 46:2271–2276

    Article  Google Scholar 

  31. LaMothe JM (2004) Rest insertion combined with high-frequency loading enhances osteogenesis. J Appl Physiol 96:1788–1793

    Article  Google Scholar 

  32. Srinivasan S, Gross T (2013) Concurrent optimization of Cyclosporin A and mechanical loading identifies multiple optima to rescue senescentbone adaptation. In: Orthopaedic Research Society, 2013

    Google Scholar 

  33. Lynch ME, Main RP, Xu Q, Schmicker TL, Schaffler MB, Wright TM, van der Meulen MCH (2011) Tibial compression is anabolic in the adult mouse skeleton despite reduced responsiveness with aging. Bone 49:439–446

    Article  Google Scholar 

  34. Yang H, Embry RE, Main RP (2017) Effects of loading duration and short rest insertion on cancellous and cortical bone adaptation in the mouse tibia. PLoS ONE 12:e0169519

    Article  Google Scholar 

  35. Matsumoto HN, Koyama Y, Takakuda K (2008) Effect of mechanical loading timeline on periosteal bone formation. J Biomech Sci Eng 3:176–187

    Article  Google Scholar 

  36. Roberts MD, Santner TJ, Hart RT (2009) Local bone formation due to combined mechanical loading and intermittent hPTH-(1-34) treatment and its correlation to mechanical signal distributions. J Biomech 42:2431–2438

    Article  CAS  Google Scholar 

  37. Sakai D, Kii I, Nakagawa K, Matsumoto HN, Takahashi M, Yoshida S, Hosoya T, Takakuda K, Kudo A (2011) Remodeling of actin cytoskeleton in mouse periosteal cells under mechanical loading induces periosteal cell proliferation during bone formation. PLoS ONE 6:e24847

    Article  CAS  Google Scholar 

  38. Weatherholt AM, Fuchs RK, Warden SJ (2013) Cortical and trabecular bone adaptation to incremental load magnitudes using the mouse tibial axial compression loading model. Bone 52:372–379

    Article  Google Scholar 

  39. Patel TK, Brodt MD, Silva MJ (2014) Experimental and finite element analysis of strains induced by axial tibial compression in young-adult and old female C57Bl/6 mice. J Biomech 47:451–457

    Article  Google Scholar 

  40. Mosley J, March B, Lynch J, Lanyon L (1997) Strain magnitude related changes in whole bone architecture in growing rats. Bone 20:191–198

    Article  CAS  Google Scholar 

  41. Wallace I, Demes B, Mongle C, Pearson O, Polk J, Carrier D et al (2014) Exercise-induced bone formation is poorly linked to local strain magnitude in the sheep tibia. PLoS ONE 9(6):e99108

    Article  Google Scholar 

  42. Birkhold AI, Razi H, Duda GN, Weinkamer R, Checa S, Willie BM (2014) Mineralizing surface is the main target of mechanical stimulation independent of age: 3D dynamic in vivo morphometry. Bone 66:15–25

    Article  Google Scholar 

  43. Yang H, Butz KD, Duffy D, Niebur GL, Nauman EA, Main RP (2014) Characterization of cancellous and cortical bone strain in the in vivo mouse tibial loading model using microCT-based finite element analysis. Bone 66:131–139

    Article  Google Scholar 

  44. Razi H, Birkhold AI, Zaslansky P, Weinkamer R, Duda GN, Willie BM, Checa S (2015) Skeletal maturity leads to a reduction in the strain magnitudes induced within the bone: a murine tibia study. Acta Biomater 13:301–310

    Article  Google Scholar 

  45. Srinivasan S, Weimer DA, Agans SC, Bain SD, Gross TS (2002) Low-magnitude mechanical loading becomes osteogenic when rest is inserted between each load cycle. J Bone Miner Res 17:1613–1620

    Article  Google Scholar 

  46. Srinivasan S, Agans SC, King KA, Moy NY, Poliachik SL, Gross TS (2003) Enabling bone formation in the aged skeleton via rest-inserted mechanical loading. Bone 33:946–955

    Article  Google Scholar 

  47. Srinivasan S, Ausk BJ, Prasad J, Threet D, Bain SD, Richardson TS, Gross TS (2010) Rescuing loading induced bone formation at senescence. PLoS Comput Biol 6:e1000924

    Article  Google Scholar 

  48. Kameo Y, Adachi T, Hojo M (2009) Fluid pressure response in poroelastic materials subjected to cyclic loading. J Mech Phys Solids 57:1815–1827

    Article  CAS  Google Scholar 

  49. Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185

    Article  CAS  Google Scholar 

  50. Pereira AF, Javaheri B, Pitsillides A, Shefelbine S (2015) Predicting cortical bone adaptation to axial loading in the mouse tibia. J R Soc Interface 12:20150590

    Article  Google Scholar 

  51. Kumar NC, Dantzig JA, Jasiuk IM, Robling AG, Turner CH (2010) Numerical modeling of long bone adaptation due to mechanical loading: correlation with experiments. Ann Biomed Eng 38:594–604

    Article  Google Scholar 

  52. Burr DB, Allen MR (eds) (2013) Basic and applied bone biology. Elsevier/Academic Press, Amsterdam

    Google Scholar 

  53. Birkhold AI, Razi H, Duda GN, Weinkamer R, Checa S, Willie BM (2016) The periosteal bone surface is less mechano-responsive than the endocortical. Sci Rep 6:23480

    Google Scholar 

  54. Srinivasan S, Gross T (2000) Canalicular fluid flow induced by bending of a long bone. Med Eng Phys 22:127–133

    Article  CAS  Google Scholar 

  55. Liu J, Shao XJ, Liu YS, Yue ZF (2008) Effect of cold expansion on fatigue performance of open holes. Mater Sci Eng, A 477:271–276

    Article  Google Scholar 

  56. Klein-Nulend J, Van der Plas A, Semeins C, Ajubi N, Frangos J, Nijweide P, Burger E (1995) Sensitivity of osteocytes to biomechanical stress in vitro. FASEB J 9:441–445

    Article  CAS  Google Scholar 

  57. Wang L, Wang Y, Han Y, Henderson SC, Majeska RJ, Weinbaum S, Schaffler MB (2005) In situ measurement of solute transport in the bone lacunar-canalicular system. Proc Natl Acad Sci USA 102:11911–11916

    Article  CAS  Google Scholar 

  58. Fan L, Pei S, Lucas LuX, Wang L (2016) A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone. Bone Res 4:16032

    Article  CAS  Google Scholar 

  59. Kerschnitzki M, Kollmannsberger P, Burghammer M, Duda GN, Weinkamer R, Wagermaier W, Fratzl P (2013) Architecture of the osteocyte network correlates with bone material quality. J Bone Miner Res 28:1837–1845

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abhishek Kumar Tiwari .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Tiwari, A.K., Prasad, J. (2019). Cortical Bone Adaptation to Mechanical Environment: Strain Energy Density Versus Fluid Motion. In: Prakash, C., et al. Biomanufacturing. Springer, Cham. https://doi.org/10.1007/978-3-030-13951-3_12

Download citation

Publish with us

Policies and ethics