Bone morphology allows estimation of loading history in a murine model of bone adaptation

  • Patrik Christen
  • Bert van RietbergenEmail author
  • Floor M. Lambers
  • Ralph Müller
  • Keita Ito
Open Access
Original Paper


Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.


Bone loading estimation Bone adaptation Micro-finite element analysis Bone remodeling algorithm Murine caudal vertebra 



Funding from the European Union for the osteoporotic virtual physiological human project (VPHOP FP7-ICT2008-223865) is gratefully acknowledged.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  1. Abel R, Macho GA (2011) Ontogenetic changes in the internal and external morphology of the ilium in modern humans. J Anatomy 218(3): 324–335. doi: 10.1111/j.1469-7580.2011.01342.x CrossRefGoogle Scholar
  2. Adams DJ, Spirt AA, Brown TD, Fritton SP, Rubin CT, Brand RA (1997) Testing the daily stress stimulus theory of bone adaptation with natural and experimentally controlled strain histories. J Biomech 30(7): 671–678CrossRefGoogle Scholar
  3. Ashman RB, Rho JY (1988) Elastic modulus of trabecular bone material. J Biomech 21(3): 177–181CrossRefGoogle Scholar
  4. Beaupre GS, Orr TE, Carter DR (1990) An approach for time-dependent bone modeling and remodeling-application: a preliminary remodeling simulation. J Orthop Res 8(5): 662–670. doi: 10.1002/jor.1100080507 CrossRefGoogle Scholar
  5. Bevill G, Eswaran SK, Farahmand F, Keaveny TM (2009) The influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties. Bone 44(4): 573–578. doi: 10.1016/j.bone.2008.11.015 CrossRefGoogle Scholar
  6. Bona MA, Martin LD, Fischer KJ (2006) A contact algorithm for density-based load estimation. J Biomech 39(4): 636–644. doi: 10.1016/j.jbiomech.2005.01.006 CrossRefGoogle Scholar
  7. Burger EH, Klein-Nulend J (1999) Mechanotransduction in bone—role of the lacuno-canalicular network. FASEB J 13(Suppl): S101–112Google Scholar
  8. Burra S, Jiang JX (2009) Connexin 43 hemichannel opening associated with Prostaglandin E(2) release is adaptively regulated by mechanical stimulation. Commun Integr Biol 2(3): 239–240CrossRefGoogle Scholar
  9. Carter DR (1982) The relationship between in vivo strains and cortical bone remodeling. Crit Rev Biomed Eng 8(1): 1–28Google Scholar
  10. Cowin SC (1987) Bone remodeling of diaphyseal surfaces by torsional loads: theoretical predictions. J Biomech 20(11–12): 1111– 1120CrossRefGoogle Scholar
  11. Ding M, Odgaard A, Danielsen CC, Hvid I (2002) Mutual associations among microstructural, physical and mechanical properties of human cancellous bone. J Bone Joint Surg Br 84(6): 900–907CrossRefGoogle Scholar
  12. Elliott DM, Sarver JJ (2004) Young investigator award winner: validation of the mouse and rat disc as mechanical models of the human lumbar disc. Spine Phil Pa (1976)29(7): 713–722CrossRefGoogle Scholar
  13. Fischer KJ, Jacobs CR, Carter DR (1995) Computational method for determination of bone and joint loads using bone density distributions. J Biomech 28(9): 1127–1135CrossRefGoogle Scholar
  14. Fischer KJ, Jacobs CR, Levenston ME, Cody DD, Carter DR (1998) Bone load estimation for the proximal femur using single energy quantitative CT data. Comput Methods Biomech Biomed Eng 1(3): 233–245CrossRefGoogle Scholar
  15. Fischer KJ, Jacobs CR, Levenston ME, Cody DD, Carter DR (1999) Proximal femoral density patterns are consistent with bicentric joint loads. Comput Methods Biomech Biomed Eng 2(4): 271–283CrossRefGoogle Scholar
  16. Forwood MR, Turner CH (1995) Skeletal adaptations to mechanical usage: results from tibial loading studies in rats. Bone 17(Suppl 4): 197S–205SGoogle Scholar
  17. Frost HM (1964) The laws of bone structureGoogle Scholar
  18. Frost HM (1987) Bone “mass” and the “mechanostat”: a proposal. Anat Rec 219(1): 1–9. doi: 10.1002/ar.1092190104 MathSciNetCrossRefGoogle Scholar
  19. Frost HM (1997) On our age-related bone loss: insights from a new paradigm. J Bone Miner Res 12(10): 1539–1546. doi: 10.1359/jbmr.1997.12.10.1539 CrossRefGoogle Scholar
  20. Giesen EB, van Eijden TM (2000) The three-dimensional cancellous bone architecture of the human mandibular condyle. J Dent Res 79(4): 957–963CrossRefGoogle Scholar
  21. Goldstein SA, Matthews LS, Kuhn JL, Hollister SJ (1991) Trabecular bone remodeling: an experimental model. J Biomech 24(Suppl 1): 135–150CrossRefGoogle Scholar
  22. Harada S, Rodan GA (2003) Control of osteoblast function and regulation of bone mass. Nature 423(6937): 349–355. doi: 10.1038/nature01660 CrossRefGoogle Scholar
  23. Hildebrand T, Laib A, Muller R, Dequeker J, Ruegsegger P (1999) Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res 14(7): 1167–1174. doi: 10.1359/jbmr.1999.14.7.1167 CrossRefGoogle Scholar
  24. Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ (1987) Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 20(11–12): 1135–1150CrossRefGoogle Scholar
  25. Huiskes R, Weinans H, van Rietbergen B (1992) The relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials. Clin Orthop Relat Res 274: 124–134Google Scholar
  26. Jepsen KJ (2009) Systems analysis of bone. Wiley Interdiscip Rev Syst Biol Med 1(1): 73–88. doi: 10.1002/wsbm.15 MathSciNetCrossRefGoogle Scholar
  27. Karasik D, Kiel DP (2010) Evidence for pleiotropic factors in genetics of the musculoskeletal system. Bone 46(5): 1226–1237. doi: 10.1016/j.bone.2010.01.382 CrossRefGoogle Scholar
  28. Lambers FM, Kuhn G, Gerhard FA, Müller R (2009) Load induced bone adaptation monitored with in vivo micro-computed tomography. In: Book of abstracts ICCB 2009, IV international congress on computational bioengineering, Bertinoro, Italy, ISSN 2036-9247 (, September 16–18, p 139
  29. Lawson CL, Hanson RJ (1974) Solving least squares problems. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  30. Lim TH, Hong JH (2000) Poroelastic properties of bovine vertebral trabecular bone. J Orthop Res 18(4): 671–677. doi: 10.1002/jor.1100180421 CrossRefGoogle Scholar
  31. Manolagas SC (2000) Birth and death of bone cells: basic regulatory mechanisms and implications for the pathogenesis and treatment of osteoporosis. Endocr Rev 21(2): 115–137CrossRefGoogle Scholar
  32. Mori S, Burr DB (1993) Increased intracortical remodeling following fatigue damage. Bone 14(2): 103–109CrossRefGoogle Scholar
  33. Mullender MG, Huiskes R (1995) Proposal for the regulatory mechanism of Wolff’s law. J Orthop Res 13(4): 503–512. doi: 10.1002/jor.1100130405 CrossRefGoogle Scholar
  34. Pressel T, Bouguecha A, Vogt U, Meyer-Lindenberg A, Behrens BA, Nolte I, Windhagen H (2005) Mechanical properties of femoral trabecular bone in dogs. Biomed Eng Online 4(1): 17. doi: 10.1186/1475-925X-4-17 CrossRefGoogle Scholar
  35. Rath AL, Bonewald LF, Ling J, Jiang JX, Van Dyke ME, Nicolella DP (2010) Correlation of cell strain in single osteocytes with intracellular calcium, but not intracellular nitric oxide, in response to fluid flow. J Biomech 43(8): 1560–1564. doi: 10.1016/j.jbiomech.2010.01.030 CrossRefGoogle Scholar
  36. Robling AG, Castillo AB, Turner CH (2006) Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 8: 455–498. doi: 10.1146/annurev.bioeng.8.061505.095721 CrossRefGoogle Scholar
  37. Rubin CT, Lanyon LE (1987) Kappa Delta Award paper. Osteoregulatory nature of mechanical stimuli: function as a determinant for adaptive remodeling in bone. J Orthop Res Offic Publ Orthop Res Soc 5(2): 300–310. doi: 10.1002/jor.1100050217 Google Scholar
  38. Ruimerman R, Van Rietbergen B, Hilbers P, Huiskes R (2005) The effects of trabecular-bone loading variables on the surface signaling potential for bone remodeling and adaptation. Ann Biomed Eng 33(1): 71–78CrossRefGoogle Scholar
  39. Schulte FA, Lambers FM, Kuhn G, Muller R (2011) In vivo micro-computed tomography allows direct three-dimensional quantification of both bone formation and bone resorption parameters using time-lapsed imaging. Bone 48(3): 433–442. doi: 10.1016/j.bone.2010.10.007 CrossRefGoogle Scholar
  40. van Rietbergen B, Weinans H, Huiskes R, Odgaard A (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28(1): 69–81CrossRefGoogle Scholar
  41. Wang Q, Xie H, Tang P, Yao Q, Huang P, Chen P, Huang F (2009) A study on the mechanical properties of beagle femoral head using the digital speckle correlation method. Med Eng Phys 31(10): 1228–1234. doi: 10.1016/j.medengphy.2009.07.021 CrossRefGoogle Scholar
  42. Webster D, Wasserman E, Ehrbar M, Weber F, Bab I, Muller R (2010) Mechanical loading of mouse caudal vertebrae increases trabecular and cortical bone mass-dependence on dose and genotype. Biomech Model Mechanobiol 9(6): 737–747. doi: 10.1007/s10237-010-0210-1 CrossRefGoogle Scholar
  43. Webster DJ, Morley PL, van Lenthe GH, Muller R (2008) A novel in vivo mouse model for mechanically stimulated bone adaptation—a combined experimental and computational validation study. Comput Methods Biomech Biomed Eng 11(5): 435–441. doi: 10.1080/10255840802078014 CrossRefGoogle Scholar
  44. Whitehouse WJ, Dyson ED (1974) Scanning electron microscope studies of trabecular bone in the proximal end of the human femur. J Anat 118(Pt 3): 417–444Google Scholar
  45. Wolff J (1892) Das Gesetz der Trasnformation der Knochen. Verlag von August Hirschwalden, BerlinGoogle Scholar
  46. Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA (1999) Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech 32(10): 1005–1012CrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Patrik Christen
    • 1
  • Bert van Rietbergen
    • 2
    Email author
  • Floor M. Lambers
    • 3
  • Ralph Müller
    • 4
  • Keita Ito
    • 5
  1. 1.Orthopaedic Biomechanics, Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Orthopaedic Biomechanics, Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.Institute for BiomechanicsETH ZurichZurichSwitzerland
  4. 4.Institute for BiomechanicsETH ZurichZurichSwitzerland
  5. 5.Orthopaedic Biomechanics, Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations