Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 1, pp 83–95 | Cite as

Large-scale microstructural simulation of load-adaptive bone remodeling in whole human vertebrae

  • Sandro D. Badilatti
  • Patrik Christen
  • Alina Levchuk
  • Javad Hazrati Marangalou
  • Bert van Rietbergen
  • Ian Parkinson
  • Ralph MüllerEmail author
Original Paper


Identification of individuals at risk of bone fractures remains challenging despite recent advances in bone strength assessment. In particular, the future degradation of the microstructure and load adaptation has been disregarded. Bone remodeling simulations have so far been restricted to small-volume samples. Here, we present a large-scale framework for predicting microstructural adaptation in whole human vertebrae. The load-adaptive bone remodeling simulations include estimations of appropriate bone loading of three load cases as boundary conditions with microfinite element analysis. Homeostatic adaptation of whole human vertebrae over a simulated period of 10 years is achieved with changes in bone volume fraction (BV/TV) of less than 5 %. Evaluation on subvolumes shows that simplifying boundary conditions reduces the ability of the system to maintain trabecular structures when keeping remodeling parameters unchanged. By rotating the loading direction, adaptation toward new loading conditions could be induced. This framework shows the possibility of using large-scale bone remodeling simulations toward a more accurate prediction of microstructural changes in whole human bones.


Bone adaptation Bone remodeling simulations Human vertebra Bone loading estimation Microfinite element modeling 



The authors thank Dr. Friederike Schulte for her work on the \({\upmu }\hbox {CT}\) datasets and gratefully acknowledge funding from the European Union Osteoporotic Virtual Physiological Human Project (VPHOP FP7-ICT2008-223865) and the Swiss National Supercomputing Center in Lugano, Switzerland, for computational time (CSCS ID 5372).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10237_2015_715_MOESM1_ESM.avi (2.8 mb)
Online Resource 1: Adaptation of the X-shaped trabecula to uniaxial compressive loading.
10237_2015_715_MOESM2_ESM.avi (2.7 mb)
Online Resource 2: Adaptation of the Y-shaped trabecula to uniaxial compressive loading.
10237_2015_715_MOESM3_ESM.avi (2.9 mb)
Online Resource 3: Adaptation of the Z-shaped trabecula to uniaxial compressive loading.
10237_2015_715_MOESM4_ESM.avi (131.9 mb)
Online Resource 4: Adaptation of trabecular bone with different number of load cases.


  1. Adachi T, Tsubota K, Tomita Y, Hollister SJ (2001) Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. J Biomech Eng Trans Asme 123:403–409CrossRefGoogle Scholar
  2. Al Nazer R, Lanovaz J, Kawalilak C, Johnston JD, Kontulainen S (2012) Direct in vivo strain measurements in human bone-a systematic literature review. J Biomech 45:27–40. doi: 10.1016/j.jbiomech.2011.08.004 CrossRefGoogle Scholar
  3. Arjmand N, Shirazi-Adl A, Bazrgari B (2006) Wrapping of trunk thoracic extensor muscles influences muscle forces and spinal loads in lifting tasks. Clin Biomech 21:668–675. doi: 10.1016/j.clinbiomech.2006.03.006 CrossRefGoogle Scholar
  4. Boutroy S, Bouxsein ML, Munoz F, Delmas PD (2005) In vivo assessment of trabecular bone microarchitecture by high-resolution peripheral quantitative computed tomography. J Clin Endocrinol Metab 90:6508–6515. doi: 10.1210/jc.2005-1258 CrossRefGoogle Scholar
  5. Briggs AM, Perilli E, Parkinson IH, Kantor S, Wrigley TV, Fazzalari NL, Wark JD (2012) Measurement of subregional vertebral bone mineral density in vitro using lateral projection dual-energy X-ray absorptiometry: validation with peripheral quantitative computed tomography. J Bone Miner Metab 30:222–231CrossRefGoogle Scholar
  6. Burr DB (2002) Targeted and nontargeted remodeling. Bone 30:2–4CrossRefGoogle Scholar
  7. Calisse J, Rohlmann A, Bergmann G (1999) Estimation of trunk muscle forces using the finite element method and in vivo loads measured by telemeterized internal spinal fixation devices. J Biomech 32:727–731CrossRefGoogle Scholar
  8. Chevalier Y, Pahr D, Zysset PK (2009) The role of cortical shell and trabecular fabric in finite element analysis of the human vertebral body. J Biomech Eng 131:111003. doi: 10.1115/1.3212097 CrossRefGoogle Scholar
  9. Christen D, Melton LJ 3rd, Zwahlen A, Amin S, Khosla S, Müller R (2013a) Improved fracture risk assessment based on nonlinear micro-finite element simulations from HRpQCT images at the distal radius. J Bone Miner Res 28:2601–2608. doi: 10.1002/jbmr.1996 CrossRefGoogle Scholar
  10. Christen P, Ito K, Ellouz R, Boutroy S, Sornay-Rendu E, Chapurlat RD, van Rietbergen B (2014) Bone remodelling in humans is load-driven but not lazy. Nat Commun 5:4855. doi: 10.1038/ncomms5855 CrossRefGoogle Scholar
  11. Christen P, Ito K, Knippels I, Müller R, van Lenthe GH, van Rietbergen B (2013b) Subject-specific bone loading estimation in the human distal radius. J Biomech 46:759–766. doi: 10.1016/j.jbiomech.2012.11.016 CrossRefGoogle Scholar
  12. Christen P, Ito K, Müller R, Rubin MR, Dempster DW, Bilezikian JP, van Rietbergen B (2012) Patient-specific bone modelling and remodelling simulation of hypoparathyroidism based on human iliac crest biopsies. J Biomech 45:2411–2416. doi: 10.1016/j.jbiomech.2012.06.031 CrossRefGoogle Scholar
  13. Christen P, Ito K, Santos AA, Müller R, van Bert R (2013c) Validation of a bone loading estimation algorithm for patient-specific bone remodelling simulations. J Biomech 46:941–948. doi: 10.1016/j.jbiomech.2012.12.012 CrossRefGoogle Scholar
  14. Christen P, van Rietbergen B, Lambers FM, Müller R, Ito K (2011) Bone morphology allows estimation of loading history in a murine model of bone adaptation. Biomech Model Mechanobiol. doi: 10.1007/s10237-011-0327-x Google Scholar
  15. Dunlop JW, Hartmann MA, Brechet YJ, Fratzl P, Weinkamer R (2009) New suggestions for the mechanical control of bone remodeling. Calcif Tissue Int 85:45–54. doi: 10.1007/s00223-009-9242-x CrossRefGoogle Scholar
  16. Eriksen EF, Melsen F, Sod E, Barton I, Chines A (2002) Effects of long-term risedronate on bone quality and bone turnover in women with postmenopausal osteoporosis. Bone 31:620–625CrossRefGoogle Scholar
  17. Fields AJ, Eswaran SK, Jekir MG, Keaveny TM (2009) Role of trabecular microarchitecture in whole-vertebral body biomechanical behavior. J Bone Miner Res 24:1523–1530. doi: 10.1359/jbmr.090317 CrossRefGoogle Scholar
  18. Flaig C, Arbenz P (2011) A scalable memory efficient multigrid solver for micro-finite element analyses based on CT images. Parallel Comput 37:846–854CrossRefGoogle Scholar
  19. Frost HM (2003) Bone’s mechanostat: a 2003 update. Anat Rec A Discov Mol Cell Evol Biol 275:1081–1101. doi: 10.1002/ar.a.10119 CrossRefGoogle Scholar
  20. Glover SJ, Garnero P, Naylor K, Rogers A, Eastell R (2008) Establishing a reference range for bone turnover markers in young, healthy women. Bone 42:623–630. doi: 10.1016/j.bone.2007.12.218 CrossRefGoogle Scholar
  21. Homminga J, Van-Rietbergen B, Lochmuller EM, Weinans H, Eckstein F, Huiskes R (2004) The osteoporotic vertebral structure is well adapted to the loads of daily life, but not to infrequent “error” loads. Bone 34:510–516. doi: 10.1016/j.bone.2003.12.001 CrossRefGoogle Scholar
  22. Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ (1987) Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 20:1135–1150CrossRefGoogle Scholar
  23. Hulme PA, Boyd SK, Ferguson SJ (2007) Regional variation in vertebral bone morphology and its contribution to vertebral fracture strength. Bone 41:946–957. doi: 10.1016/j.bone.2007.08.019 CrossRefGoogle Scholar
  24. Jacobs CR, Temiyasathit S, Castillo AB (2010) Osteocyte mechanobiology and pericellular mechanics. Ann Rev Biomed Eng 12:369–400. doi: 10.1146/annurev-bioeng-070909-105302 CrossRefGoogle Scholar
  25. Johnell O, Kanis J (2005) Epidemiology of osteoporotic fractures. Osteoporos Int 16(Suppl 2):S3–7. doi: 10.1007/s00198-004-1702-6 CrossRefGoogle Scholar
  26. Johnell O, Kanis JA (2006) An estimate of the worldwide prevalence and disability associated with osteoporotic fractures. Osteoporos Int 17:1726–1733. doi: 10.1007/s00198-006-0172-4 CrossRefGoogle Scholar
  27. Kanis JA et al (1994) Assessment of fracture risk and its application to screening for postmenopausal osteoporosis—synopsis of a who report. Osteoporosis Int 4:368–381CrossRefGoogle Scholar
  28. Kanis JA et al (2008) European guidance for the diagnosis and management of osteoporosis in postmenopausal women. Osteoporos Int 19:399–428. doi: 10.1007/s00198-008-0560-z CrossRefGoogle Scholar
  29. Kanis JA, Johnell O (2005) Requirements for DXA for the management of osteoporosis in Europe. Osteoporos Int 16:229–238. doi: 10.1007/s00198-004-1811-2 CrossRefGoogle Scholar
  30. Keller TS, Kosmopoulos V, Lieberman IH (2005) Vertebroplasty and kyphoplasty affect vertebral motion segment stiffness and stress distributions: a microstructural finite-element study. Spine 30:1258–1265CrossRefGoogle Scholar
  31. Kemmler W, Lauber D, Weineck J, Hensen J, Kalender W, Engelke K (2004) Benefits of 2 years of intense exercise on bone density, physical fitness, and blood lipids in early postmenopausal osteopenic women: results of the Erlangen Fitness Osteoporosis Prevention Study (EFOPS). Arch Intern Med 164:1084–1091. doi: 10.1001/archinte.164.10.1084 CrossRefGoogle Scholar
  32. Khosla S et al (2006) Effects of sex and age on bone microstructure at the ultradistal radius: a population-based noninvasive in vivo assessment. J Bone Miner Res 21:124–131. doi: 10.1359/JBMR.050916 CrossRefGoogle Scholar
  33. Kim DG, Christopherson GT, Dong XN, Fyhrie DP, Yeni YN (2004) The effect of microcomputed tomography scanning and reconstruction voxel size on the accuracy of stereological measurements in human cancellous bone. Bone 35:1375–1382. doi: 10.1016/j.bone.2004.09.007 CrossRefGoogle Scholar
  34. Krug R, Burghardt AJ, Majumdar S, Link TM (2010) High-resolution imaging techniques for the assessment of osteoporosis. Radiol Clin North Am 48:601–621. doi: 10.1016/j.rcl.2010.02.015 CrossRefGoogle Scholar
  35. Levchuk A et al (2014) The clinical biomechanics award 2012—presented by the European Society of Biomechanics: large scale simulations of trabecular bone adaptation to loading and treatment. Clin Biomech 29:355–362. doi: 10.1016/j.clinbiomech.2013.12.019 CrossRefGoogle Scholar
  36. Lochmuller EM, Müller R, Kuhn V, Lill CA, Eckstein F (2003) Can novel clinical densitometric techniques replace or improve DXA in predicting bone strength in osteoporosis at the hip and other skeletal sites? J Bone Miner Res 18:906–912CrossRefGoogle Scholar
  37. Mc Donnell P, Harrison N, Liebschner MA, Mc Hugh PE (2009) Simulation of vertebral trabecular bone loss using voxel finite element analysis. J Biomech. doi:  10.1016/j.jbiomech.2009.07.038
  38. Morgan EF, Bayraktar HH, Keaveny TM (2003) Trabecular bone modulus-density relationships depend on anatomic site. J Biomech 36:897–904CrossRefGoogle Scholar
  39. Mullender MG, Huiskes R (1995) Proposal for the regulatory mechanism of Wolff’s law. J Orthop Res 13:503–512. doi: 10.1002/jor.1100130405 CrossRefGoogle Scholar
  40. Müller R (2005) Long-term prediction of three-dimensional bone architecture in simulations of pre-, peri- and post-menopausal microstructural bone remodeling. Osteoporos Int 16(Suppl 2):S25–35. doi: 10.1007/s00198-004-1701-7 CrossRefGoogle Scholar
  41. Perilli E, Briggs AM, Kantor S, Codrington J, Wark JD, Parkinson IH, Fazzalari NL (2012) Failure strength of human vertebrae: prediction using bone mineral density measured by DXA and bone volume by micro-CT. Bone 50:1416–1425. doi: 10.1016/j.bone.2012.03.002
  42. Polikeit A, Nolte LP, Ferguson SJ (2003) The effect of cement augmentation on the load transfer in an osteoporotic functional spinal unit: finite-element analysis. Spine 28:991–996. doi: 10.1097/01.BRS.0000061987.71624.17 Google Scholar
  43. Ruimerman R (2005) Modeling and remodeling in bone tissue electronic, University Library, Doctoral Thesis, TU Eindhoven.
  44. Ruimerman R, Hilbers P, van Rietbergen B, Huiskes R (2005) A theoretical framework for strain-related trabecular bone maintenance and adaptation. J Biomech 38:931–941. doi: 10.1016/j.jbiomech.2004.03.037 CrossRefGoogle Scholar
  45. Schulte FA, Ruffoni D, Lambers FM, Christen D, Webster DJ, Kuhn G, Müller R (2013a) Local mechanical stimuli regulate bone formation and resorption in mice at the tissue level. PloS One 8:e62172. doi: 10.1371/journal.pone.0062172 CrossRefGoogle Scholar
  46. Schulte FA et al (2013b) Strain-adaptive in silico modeling of bone adaptation—a computer simulation validated by in vivo micro-computed tomography data. Bone 52:485–492. doi: 10.1016/j.bone.2012.09.008 CrossRefGoogle Scholar
  47. Sugiyama T, Meakin LB, Browne WJ, Galea GL, Price JS, Lanyon LE (2012) Bones’ adaptive response to mechanical loading is essentially linear between the low strains associated with disuse and the high strains associated with the lamellar/woven bone transition. J Bone Miner Res 27:1784–1793. doi: 10.1002/jbmr.1599
  48. Viceconti M, Schileo E, Taddei F, Martelli S, Testi D (2010) Personalised multiscale models for risk fracture prediction. Osteoporos Int 21:1067–1071CrossRefGoogle Scholar
  49. Wegrzyn J et al (2010) Role of trabecular microarchitecture and its heterogeneity parameters in the mechanical behavior of ex vivo human L3 vertebrae. J Bone Miner Res 25:2324–2331. doi: 10.1002/jbmr.164 CrossRefGoogle Scholar
  50. Widmer RP, Ferguson SJ (2013) A comparison and verification of computational methods to determine the permeability of vertebral trabecular bone. Proc Inst Mech Eng H 227:617–628. doi: 10.1177/0954411912462814 CrossRefGoogle Scholar
  51. Wilcox RK, Allen DJ, Hall RM, Limb D, Barton DC, Dickson RA (2004) A dynamic investigation of the burst fracture process using a combined experimental and finite element approach. Eur Spine J 13:481–488. doi: 10.1007/s00586-003-0625-9 CrossRefGoogle Scholar
  52. Wolff J (2010) The classic: on the inner architecture of bones and its importance for bone growth. 1870. Clin Orthop Relat Res 468:1056–1065. doi: 10.1007/s11999-010-1239-2 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sandro D. Badilatti
    • 1
  • Patrik Christen
    • 1
  • Alina Levchuk
    • 1
  • Javad Hazrati Marangalou
    • 2
  • Bert van Rietbergen
    • 2
  • Ian Parkinson
    • 3
  • Ralph Müller
    • 1
    Email author
  1. 1.Institute for BiomechanicsETH ZurichZurichSwitzerland
  2. 2.Orthopaedic Biomechanics, Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.SA Pathology and University of AdelaideAdelaideAustralia

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