Resonance in the mouse tibia as a predictor of frequencies and locations of loading-induced bone formation

Abstract

To enhance new bone formation for the treating of patients with osteopenia and osteoporosis, various mechanical loading regimens have been developed. Although a wide spectrum of loading frequencies is proposed in those regimens, a potential linkage between loading frequencies and locations of loading-induced bone formation is not well understood. In this study, we addressed a question: Does mechanical resonance play a role in frequency-dependent bone formation? If so, can the locations of enhanced bone formation be predicted through the modes of vibration? Our hypothesis is that mechanical loads applied at a frequency near the resonant frequencies enhance bone formation, specifically in areas that experience high principal strains. To test the hypothesis, we conducted axial tibia loading using low, medium, or high frequency to the mouse tibia, as well as finite element analysis. The experimental data demonstrated dependence of the maximum bone formation on location and frequency of loading. Samples loaded with the low-frequency waveform exhibited peak enhancement of bone formation in the proximal tibia, while the high-frequency waveform offered the greatest enhancement in the midshaft and distal sections. Furthermore, the observed dependence on loading frequencies was correlated to the principal strains in the first five resonance modes at 8.0–42.9 Hz. Collectively, the results suggest that resonance is a contributor to the frequencies and locations of maximum bone formation. Further investigation of the observed effects of resonance may lead to the prescribing of personalized mechanical loading treatments.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. Chattah NL, Sharir A, Weiner S, Shahar R (2009) Determining the elastic modulus of mouse cortical bone using electronic speckle pattern interferometry (ESPI) and micro computed tomography: a new approach for characterizing small-bone material properties. Bone 45(1):84–90

    Article  Google Scholar 

  2. Christiansen BA, Bayly PV, Silva MJ (2008) Constrained tibial vibration in mice: a method for studying the effects of vibrational loading of bone. J Biomech Eng 130(4):044502

    Article  Google Scholar 

  3. De Souza RL, Matsuura M, Eckstein F, Rawlinson SCF, 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 

  4. Dodge T, Wanis M, Ayoub R, Zhao L, Watts NB, Bhattacharya A, Akkus O, Robling A, Yokota H (2012) Mechanical loading, damping, and load-driven bone formation in mouse tibiae. Bone 51(4):810–818

    Article  Google Scholar 

  5. Donahue SW, Jacobs CR, Donahue HJ (2001) Flow-induced calcium oscillations in rat osteoblasts are age, loading frequency, and shear stress dependent. Am J Physiol Cell Physiol 281(5):C1635–C1641

    Google Scholar 

  6. Fortis AP, Kostopoulos V, Panagiotopoulos E, Tsantzalis S, Kokkinos A (2004) Viscoelastic properties of cartilage-subchondral bone complex in osteoarthritis. J Med Eng Technol 28(5):223–226

    Article  Google Scholar 

  7. Grimston SK, Watkins MP, Brodt MD, Silva MJ, Civitelli R (2012) Enhanced periosteal and endocortical responses to axial tibial compression loading in conditional connexin43 deficient mice. PLoS One 7(9):e44222

    Article  Google Scholar 

  8. Guo LX, Zhang M, Zhang YM, Teo EC (2009) Vibration modes of injured spine at resonant frequencies under vertical vibration. Spine 34(19):E682–E688

    Google Scholar 

  9. Harvey N, Dennison E, Cooper C (2010) Osteoporosis: impact on health and economics. Nat Rev Rheumatol 6(2):99–105

    Article  Google Scholar 

  10. Hight TK, Piziali RL, Nagel DA (1980) Natural frequency analysis of a human tibia. J Biomech 13(2):139–147

    Article  Google Scholar 

  11. Hobatho MC, Darmana R, Pastor P, Barrau JJ, Laroze S, Morucci JP (1991) Development of a three-dimensional finite element model of a human tibia using experimental modal analysis. J Biomech 24(6):371–383

    Article  Google Scholar 

  12. Hsieh YF, Turner CH (2001) Effects of loading frequency on mechanically induced bone formation. J Bone Miner Res 16(5):918–924

    Article  Google Scholar 

  13. Huang TH, Lin SC, Chang FL, Hsieh SS, Liu SH, Yang RS (2003) Effects of different exercise modes on mineralization, structure, and biomechanical properties of growing bone. J Appl Physiol 95(1):300–307

    Google Scholar 

  14. Kameo Y, Adachi T, Hojo M (2011) Effects of loading frequency on the functional adaptation of trabeculae predicted by bone remodeling simulation. J Mech Behav Biomed Mater 4(6):900–908

    Article  Google Scholar 

  15. Kanis JA, Oden A, McCloskey EV, Johansson H, Wahl DA, Cooper C (2012) A systematic review of hip fracture incidence and probability of fracture worldwide. Osteoporos Int 23(9):2239–2256

    Article  Google Scholar 

  16. Kim KJ, Hwang IK (2006) Prediction of resonance characterisitics of the forearm bones using finite element analysis. J Musculoskelet Res 10(4):205–215

    Article  MathSciNet  Google Scholar 

  17. Kim YH, Byun CH, Oh TY (2006) Effect of osteoporosis on natural frequencies in mouse femur: vibration test and micro-CT based finite element analysis. Key Eng Mater 326–328:851–854

    Article  Google Scholar 

  18. Kwon RY, Meays DR, Meilan AS, Jones J, Miramontes R, Kardos N, Yeh JC, Frangos JA (2012) Skeletal adaptation to intramedullary pressure-induced interstitial fluid flow is enhanced in mice subjected to targeted osteocyte ablation. PLoS One 7(3):e33336

    Article  Google Scholar 

  19. Lakes R (1999) Viscoelastic solids. CRC Press, Boca Raton

    Google Scholar 

  20. Lam H, Brink P, Qin YX (2010) Skeletal nutrient vascular adaptation induced by external oscillatory intramedullary fluid pressure intervention. J Orthop Surg Res 5:18

    Article  Google Scholar 

  21. Lau RY, Guo X (2011) A review on current osteoporosis research: with special focus on disuse bone loss. J Osteoporos 2011:293808

    Article  Google Scholar 

  22. Martinez MD, Schmid GJ, McKenzie JA, Ornitz DM, Silva MJ (2010) Healing of non-displaced fractures produced by fatigue loading of the mouse ulna. Bone 46(6):1604–1612

    Article  Google Scholar 

  23. Ozcivici E, Luu YK, Rubin CT, Judex S (2010) Low-level vibrations retain bone marrow’s osteogenic potential and augment recovery of trabecular bone during reambulation. PLoS One 5(6):e11178

    Article  Google Scholar 

  24. Parfitt MA, Drezner MK, Glorieux FH, Kanis JA, Malluche H, Meunier PJ, Ott SM, Recker RR (1987) Bone histomorphometry: standardization of nomenclature, symbols, and units. J Bone Miner Res 2(6):595–610

    Article  Google Scholar 

  25. Robling AG, Niziolek PJ, Baldridge LA, Condon KW, Allen MR, Alam I, Mantila SM, Gluhak-Heinrich J, Bellido TM, Harris SE, Turner CH (2008) Mechanical stimulation of bone in vivo reduces osteocyte expression of Sost/sclerostin. J Biol Chem 283(9):5866–5875

    Article  Google Scholar 

  26. Sample SJ, Behan M, Smith L, Oldenhoff WE, Markel MD, Kalscheur VL, Hao Z, Miletic V, Muir P (2008) Functional adaptation to loading of a single bone is neuronally regulated and involves multiple bones. J Bone Miner Res 23(9):1372–1381

    Google Scholar 

  27. Silva MJ, Brodt MD, Hucker WJ (2005) Finite element analysis of the mouse tibia: estimating endocortical strain during three-point bending in SAMP6 osteoporotic mice. Anat Rec A Discov Mol Cell Evol Biol 283(2):380–390

    Google Scholar 

  28. Tanaka SM, Alam IM, Turner CH (2003) Stochastic resonance in osteogenic response to mechanical loading. FASEB J 17(2):313–314

    Google Scholar 

  29. Taylor WR, Roland E, Ploeg H, Hertig D, Klabunde R, Warner MD, Hobatho MC, Rakotomanana L, Clift SE (2002) Determination of orthotropic bone elastic constants using FEA and modal analysis. J Biomech 35(6):767–773

    Google Scholar 

  30. Tsuchikane A, Nakatsuchi Y, Nomura A (1995) The influence of joints and soft tissue on the natural frequency of the human tibia using the impulse response method. Proc Inst Mech Eng H 209(3):149–155

    Article  Google Scholar 

  31. van den Bergh JP, van Geel TA, Geusens PP (2012) Osteoporosis, frailty and fracture: implications for case finding and therapy. Nat Rev Rheumatol 8(3):163–172

    Article  Google Scholar 

  32. Warden SJ, Turner CH (2004) Mechanotransduction in the cortical bone is most efficient at loading frequencies of 5–10 Hz. Bone 34(2):261–270

    Article  Google Scholar 

  33. Warden SJ, Robling AG, Sanders MS, Bliziotes MM, Turner CH (2005) Inhibition of the serotonin (5-hydroxytryptamine) transporter reduces bone accrual during growth. Endocrinology 146(2):685–693

    Article  Google Scholar 

  34. 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(1):372–379

    Article  Google Scholar 

  35. Zhang P, Su M, Tanaka SM, Yokota H (2006) Knee loading stimulates cortical bone formation in murine femurs. BMC Musculoskelet Disord 7:73

    Article  Google Scholar 

  36. Zhang P, Su M, Liu Y, Hsu A, Yokota H (2007a) Knee loading dynamically alters intramedullary pressure in mouse femora. Bone 40(2):538–543

    Google Scholar 

  37. Zhang P, Tanaka SM, Sun Q, Turner CH, Yokota H (2007b) Frequency-dependent enhancement of bone formation in murine tibiae and femora with knee loading. J Bone Miner Metab 25(6):383–391

    Google Scholar 

Download references

Acknowledgments

This study was in part supported by the grant NIH R01 AR052144. The authors report no conflicts of interest.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hiroki Yokota.

Additional information

Liming Zhao and Todd Dodge contributed equally.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zhao, L., Dodge, T., Nemani, A. et al. Resonance in the mouse tibia as a predictor of frequencies and locations of loading-induced bone formation. Biomech Model Mechanobiol 13, 141–151 (2014). https://doi.org/10.1007/s10237-013-0491-2

Download citation

Keywords

  • Tibia
  • Loading
  • Resonance frequency
  • Bone mineral density
  • Finite element analysis
  • Strain