Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 5, pp 1697–1708 | Cite as

Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation

  • Young Kwan Kim
  • Yoshitaka Kameo
  • Sakae Tanaka
  • Taiji Adachi
Original Paper


To understand Wolff’s law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling.


Bone adaptation Wolff’s law Biological rationale Model reduction Multiscale biomechanics Mechanobiology 



This work was partially supported by the Advanced Research and Development Programs for Medical Innovation from the Japan Agency for Medical Research and Development (AMED-CREST).


  1. Aarden EM, Burger EH, Nijweide PJ (1994) Function of osteocytes in bone. J Cell Biochem 55:287–299. doi: 10.1002/jcb.240550304 CrossRefGoogle Scholar
  2. Adachi T, Kameo Y, Hojo M (2010) Trabecular bone remodelling simulation considering osteocytic response to fluid-induced shear stress. Philos T R Soc A 368:2669–2682. doi: 10.1098/rsta.2010.0073 MathSciNetCrossRefzbMATHGoogle Scholar
  3. Adachi T, Osako Y, Tanaka M et al (2006) Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. Biomaterials 27:3964–3972. doi: 10.1016/j.biomaterials.2006.02.039 CrossRefGoogle Scholar
  4. Adachi T, Tomita Y, Sakaue H, Tanaka M (1997) Simulation of trabecular surface remodeling based on local stress nonuniformity. JSME Int Ser C 40:782–792CrossRefGoogle Scholar
  5. 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 123:403–409. doi: 10.1115/1.1392315 CrossRefGoogle Scholar
  6. Burger EH, Klein-Nulend J (1999) Mechanotransduction in bone—role of the lacuno-canalicular network. FASEB J 13:S101–S112Google Scholar
  7. Busse B, Djonic D, Milovanovic P et al (2010) Decrease in the osteocyte lacunar density accompanied by hypermineralized lacunar occlusion reveals failure and delay of remodeling in aged human bone. Aging Cell 9:1065–1075. doi: 10.1111/j.1474-9726.2010.00633.x CrossRefGoogle Scholar
  8. Canalis E (2003) Mechanisms of glucocorticoid-induced osteoporosis. Curr Opin Rheumatol 15:454–457. doi: 10.1097/00002281-200307000-00013 CrossRefGoogle Scholar
  9. Carter DR (1984) Mechanical loading histories and cortical bone remodeling. Calcif Tissue Int 36(Suppl 1):S19–S24CrossRefGoogle Scholar
  10. Carter DR, Fyhrie DP, Whalen RT (1987) Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. J Biomech 20:785–794. doi: 10.1016/0021-9290(87)90058-3 CrossRefGoogle Scholar
  11. Colloca M, Blanchard R, Hellmich C et al (2014) A multiscale analytical approach for bone remodeling simulations: Linking scales from collagen to trabeculae. Bone 64:303–313. doi: 10.1016/j.bone.2014.03.050 CrossRefGoogle Scholar
  12. Cowin SC (1985) The relationship between the elasticity tensor and the fabric tensor. Mech Mater 4:137–147. doi: 10.1016/0167-6636(85)90012-2 CrossRefGoogle Scholar
  13. Cowin SC, Hegedus DH (1976) Bone remodeling I: theory of adaptive elasticity. J Elast 6:313–326MathSciNetCrossRefzbMATHGoogle Scholar
  14. Cowin SC, Weinbaum S, Zeng Y (1995) A case for bone canaliculi generated as the anatomical potential. J Biomech 28:1281–1297. doi: 10.1016/0021-9290(95)00058-P CrossRefGoogle Scholar
  15. Del Fattore A, Cappariello A, Teti A (2008) Genetics, pathogenesis and complications of osteopetrosis. Bone 42:19–29. doi: 10.1016/j.bone.2007.08.029 CrossRefGoogle Scholar
  16. Doane DP, Seward LE (2011) Measuring skewness: a forgotten statistic? J Stat Educ 19:1–18Google Scholar
  17. Feng X, McDonald JM (2011) Disorders of bone remodeling. Sci York 6:121–145. doi: 10.1146/annurev-pathol-011110-130203 Google Scholar
  18. Frenkel B, Hong A, Baniwal SK et al (2010) Regulation of adult bone turnover by sex steroids. J Cell Physiol 224:305–310. doi: 10.1002/jcp.22159 CrossRefGoogle Scholar
  19. Fritsch A, Hellmich C (2007) “Universal” microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: Micromechanics-based prediction of anisotropic elasticity. J Theor Biol 244:597–620. doi: 10.1016/j.jtbi.2006.09.013 CrossRefGoogle Scholar
  20. Hambli R (2010) Application of neural networks and finite element computation for multiscale simulation of bone remodeling. J Biomech Eng 132:114502. doi: 10.1115/1.4002536 CrossRefGoogle Scholar
  21. Hambli R (2011) Numerical procedure for multiscale bone adaptation prediction based on neural networks and finite element simulation. Finite Elem Anal Des 47:835–842. doi: 10.1016/j.finel.2011.02.014 CrossRefGoogle Scholar
  22. 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. doi: 10.1007/s10237-010-0222-x CrossRefGoogle Scholar
  23. Han Y, Cowin SC, Schaffler MB, Weinbaum S (2004) Mechanotransduction and strain amplification in osteocyte cell processes. Proc Natl Acad Sci USA 101:16689–16694. doi: 10.1073/pnas.0407429101 CrossRefGoogle Scholar
  24. Hasegawa M, Adachi T, Takano-Yamamoto T (2015) Computer simulation of orthodontic tooth movement using CT image-based voxel finite element models with the level set method. Comput Methods Biomech Biomed Eng. doi: 10.1080/10255842.2015.1042463 Google Scholar
  25. Hirayama T, Danks L, Sabokbar A, Athanasou N (2002) Osteoclast formation and activity in the pathogenesis of osteoporosis in rheumatoid arthritis. Rheumatology (Oxford) 41:1232–1239. doi: 10.1093/rheumatology/41.11.1232 CrossRefGoogle Scholar
  26. Huiskes R, Ruimerman R, van Lenthe GH, Janssen JD (2000) Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 405:704–706. doi: 10.1038/35015116 CrossRefGoogle Scholar
  27. Huiskes R, Weinans H, Grootenboer HJ et al (1987) Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 20:1135–1150. doi: 10.1016/0021-9290(87)90030-3 CrossRefGoogle Scholar
  28. Jing D, Lu XL, Luo E et al (2013) Spatiotemporal properties of intracellular calcium signaling in osteocytic and osteoblastic cell networks under fluid flow. Bone 53:531–540. doi: 10.1016/j.bone.2013.01.008 CrossRefGoogle Scholar
  29. Kameo Y, Adachi T (2014a) Interstitial fluid flow in canaliculi as a mechanical stimulus for cancellous bone remodeling: in silico validation. Biomech Model Mechanobiol 13:851–860. doi: 10.1007/s10237-013-0539-3 CrossRefGoogle Scholar
  30. Kameo Y, Adachi T (2014b) Modeling trabecular bone adaptation to local bending load regulated by mechanosensing osteocytes. Acta Mech 225:2833–2840. doi: 10.1007/s00707-014-1202-5 CrossRefGoogle Scholar
  31. Kameo Y, Adachi T, Hojo M (2009) Fluid pressure response in poroelastic materials subjected to cyclic loading. J Mech Phys Solids 57:1815–1827. doi: 10.1016/j.jmps.2009.08.002 MathSciNetCrossRefzbMATHGoogle Scholar
  32. Kameo Y, Ootao Y, Ishihara M (2016) Theoretical investigation of the effect of bending loads on the interstitial fluid flow in a poroelastic lamellar trabecula. J Biomech Sci Eng 11:15–00663. doi: 10.1299/jbse.15-00663 CrossRefGoogle Scholar
  33. Kufahl RH, Saha S (1990) A theoretical model for stress-generated fluid flow in the canaliculi-lacunae network in bone tissue. J Biomech 23:171–180. doi: 10.1016/0021-9290(90)90350-C CrossRefGoogle Scholar
  34. Kumar NC, Jasiuk I, Dantzig J (2011) Dissipation energy as a stimulus for cortical bone adaptation. J Mech Mater Struct 6:303–319CrossRefGoogle Scholar
  35. Lacroix D, Chateau A, Ginebra MP, Planell JA (2006) Micro-finite element models of bone tissue-engineering scaffolds. Biomaterials 27:5326–5334. doi: 10.1016/j.biomaterials.2006.06.009 CrossRefGoogle Scholar
  36. Milovanovic P, Zimmermann EA, Hahn M et al (2013) Osteocytic canalicular networks: Morphological implications for altered mechanosensitivity. ACS Nano 7:7542–7551. doi: 10.1021/nn401360u CrossRefGoogle Scholar
  37. Mosekilde L (2008) Primary hyperparathyroidism and the skeleton. Clin Endocrinol (Oxf) 69:1–19. doi: 10.1111/j.1365-2265.2007.03162.x CrossRefGoogle Scholar
  38. 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
  39. Nguyen AM, Jacobs CR (2013) Emerging role of primary cilia as mechanosensors in osteocytes. Bone 54:196–204. doi: 10.1016/j.bone.2012.11.016 CrossRefGoogle Scholar
  40. Phillips AT, Villette CC, Modenese L (2015) Femoral bone mesoscale structural architecture prediction using musculoskeletal and finite element modelling. Int Biomech 2:43–61. doi: 10.1080/23335432.2015.1017609 CrossRefGoogle Scholar
  41. Redlich K, Smolen JS (2012) Inflammatory bone loss: pathogenesis and therapeutic intervention. Nat Rev Drug Discov 11:234–250. doi: 10.1038/nrd3669 CrossRefGoogle Scholar
  42. Reina-Romo E, Gómez-Benito MJ, Sampietro-Fuentes A et al (2011) Three-dimensional simulation of mandibular distraction osteogenesis: Mechanobiological analysis. Ann Biomed Eng 39:35–43. doi: 10.1007/s10439-010-0166-4 CrossRefGoogle Scholar
  43. 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
  44. Scheiner S, Pivonka P, Hellmich C (2013) Coupling systems biology with multiscale mechanics, for computer simulations of bone remodeling. Comput Methods Appl Mech Eng 254:181–196. doi: 10.1016/j.cma.2012.10.015 MathSciNetCrossRefzbMATHGoogle Scholar
  45. Sharma GB, Debski RE, McMahon PJ, Robertson DD (2010) Effect of glenoid prosthesis design on glenoid bone remodeling: adaptive finite element based simulation. J Biomech 43:1653–1659. doi: 10.1016/j.jbiomech.2010.03.004 CrossRefGoogle Scholar
  46. Swan CC, Lakes RS, Brand R a, Stewart KJ (2003) Micromechanically based poroelastic modeling of fluid flow in Haversian bone. J Biomech Eng 125:25–37. doi: 10.1115/1.1535191 CrossRefGoogle Scholar
  47. Temiyasathit S, Jacobs CR (2010) Osteocyte primary cilium and its role in bone mechanotransduction. Ann N Y Acad Sci 1192:422–428. doi: 10.1111/j.1749-6632.2009.05243.x CrossRefGoogle Scholar
  48. Tsubota K, Adachi T (2005) Spatial and temporal regulation of cancellous bone structure: characterization of a rate equation of trabecular surface remodeling. Med Eng Phys 27:305–11. doi: 10.1016/j.medengphy.2004.09.013
  49. Tsubota K, Adachi T (2006) Simulation study on local and integral mechanical quantities at single trabecular level as candidates of remodeling stimuli. J Biomech Sci Eng 1:124–135. doi: 10.1299/jbse.1.124 CrossRefGoogle Scholar
  50. Tsubota K, Adachi T, Tomita Y (2002) Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state. J Biomech 35:1541–1551. doi: 10.1016/S0021-9290(02)00173-2 CrossRefGoogle Scholar
  51. Tsubota K, Suzuki Y, Yamada T et al (2009) Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: approach to understanding Wolff’s law. J Biomech 42:1088–1094. doi: 10.1016/j.jbiomech.2009.02.030 CrossRefGoogle Scholar
  52. Unger JF, Könke C (2008) Coupling of scales in a multiscale simulation using neural networks. Comput Struct 86:1994–2003. doi: 10.1016/j.compstruc.2008.05.004 CrossRefGoogle Scholar
  53. van Hove RP, Nolte PA, Vatsa A et al (2009) Osteocyte morphology in human tibiae of different bone pathologies with different bone mineral density - Is there a role for mechanosensing? Bone 45:321–329. doi: 10.1016/j.bone.2009.04.238 CrossRefGoogle Scholar
  54. van Oers RFM, Wang H, Bacabac RG (2015) Osteocyte shape and mechanical loading. Curr Osteoporos Rep 13:61–66. doi: 10.1007/s11914-015-0256-1 CrossRefGoogle Scholar
  55. 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 28:69–81. doi: 10.1016/0021-9290(95)80008-5 CrossRefGoogle Scholar
  56. Villette CC, Phillips AT (2016) Informing phenomenological structural bone remodelling with a mechanistic poroelastic model. Biomech Model Mechanobiol 15:69–82. doi: 10.1007/s10237-015-0735-4 CrossRefGoogle Scholar
  57. Weinbaum S, Cowin SC, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J Biomech 27:339–360. doi: 10.1016/0021-9290(94)90010-8 CrossRefGoogle Scholar
  58. Whitehouse WJ (1974) The quantitative morphology of anisotropic trabecular bone. J Microsc 101:153–168. doi: 10.1111/j.1365-2818.1974.tb03878.x CrossRefGoogle Scholar
  59. Wolff J (1869) Ueber die bedeutung der architectur der spongiösen substanz für die frage vom knochenwachsthum. ZBT Med Wiss 6:223–234Google Scholar
  60. Wolff J (1892) Das gesetz der transformation der knochen. Hirschwald, BerlinGoogle Scholar
  61. Xia SL, Ferrier J (1992) Propagation of a calcium pulse between osteoblastic cells. Biochem Biophys Res Commun 186:1212–1219. doi: 10.1016/S0006-291X(05)81535-9 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Young Kwan Kim
    • 1
    • 2
  • Yoshitaka Kameo
    • 2
  • Sakae Tanaka
    • 1
  • Taiji Adachi
    • 2
  1. 1.Department of Orthopaedic Surgery, Faculty of MedicineThe University of TokyoTokyoJapan
  2. 2.Department of Biosystems Science, Institute for Frontier Life and Medical SciencesKyoto UniversityKyotoJapan

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