Computational investigation of ultrastructural behavior of bone using a cohesive finite element approach

  • Mohammad Maghsoudi-Ganjeh
  • Liqiang Lin
  • Xiaodu WangEmail author
  • Xiaowei ZengEmail author
Original Paper


Bone ultrastructure at sub-lamellar length scale is a key structural unit in bone that bridges nano- and microscale hierarchies of the tissue. Despite its influence on bulk response of bone, the mechanical behavior of bone at ultrastructural level remains poorly understood. To fill this gap, in this study, a two-dimensional cohesive finite element model of bone at sub-lamellar level was proposed and analyzed under tensile and compressive loading conditions. In the model, ultrastructural bone was considered as a composite of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM) that is comprised of hydroxyapatite (HA) polycrystals bounded via thin organic interfaces of non-collagenous proteins (NCPs). The simulation results indicated that in compression, EFM dictated the pre-yield deformation of the model, then damage was initiated via relative sliding of HA polycrystals along the organic interfaces, and finally shear bands were formed followed by delamination between MCF and EFM and local buckling of MCF. In tension, EFM carried the most of load in pre-yield deformation, and then an array of opening-mode nano-cracks began to form within EFM after yielding, thus gradually transferring the load to MCF until failure, which acted as crack bridging filament. The failure modes, stress–strain curves, and in situ mineral strain of ultrastructural bone predicted by the model were in good agreement with the experimental observations reported in the literature, thus suggesting that this model can provide new insights into sub-microscale mechanical behavior of bone.


Bone ultrastructure Collagen fibrils Extrafibrillar matrix Organic interface Cohesive finite element modeling Bone mechanical response 



Research reported in this publication was supported by a Grant from National Science Foundation (CMMI-1538448) and a Grant from the University of Texas at San Antonio, Office of the Vice President for Research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Abueidda DW, Sabet FA, Jasiuk IM (2017) Modeling of stiffness and strength of bone at nanoscale. J Biomech Eng 139(5):051006–051006-10. CrossRefGoogle Scholar
  2. Al-Qtaitat AI, Aldalaen SM (2014) A review of non-collagenous proteins; their role in bone. Am J Life Sci 2:351–355CrossRefGoogle Scholar
  3. Balooch M, Habelitz S, Kinney JH et al (2008) Mechanical properties of mineralized collagen fibrils as influenced by demineralization. J Struct Biol 162:404–410CrossRefGoogle Scholar
  4. Bishop N (2016) Bone material properties in osteogenesis imperfecta. J Bone Miner Res 31:699–708CrossRefGoogle Scholar
  5. Boskey AL (2013) Bone composition: relationship to bone fragility and antiosteoporotic drug effects. BoneKEy Rep 2:447CrossRefGoogle Scholar
  6. Boskey AL, Coleman R (2010) Aging and bone. J Dent Res 89:1333–1348CrossRefGoogle Scholar
  7. Boyce TM, Fyhrie DP, Glotkowski MC et al (1998) Damage type and strain mode associations in human compact bone bending fatigue. J Orthop Res 16:322–329CrossRefGoogle Scholar
  8. Buehler MJ (2007) Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization. Nanotechnology 18:295102CrossRefGoogle Scholar
  9. Cassella JP, Stamp TCB, Ali SY (1996) A morphological and ultrastructural study of bone in osteogenesis imperfecta. Calcif Tissue Int 58:155–165CrossRefGoogle Scholar
  10. Chamay A (1970) Mechanical and morphological aspects of experimental overload and fatigue in bone. J Biomech 3:263–270CrossRefGoogle Scholar
  11. Ciuchi IV, Olariu CS, Mitoseriu L (2013) Determination of bone mineral volume fraction using impedance analysis and Bruggeman model. Mater Sci Eng B 178:1296–1302CrossRefGoogle Scholar
  12. De Falco P, Barbieri E, Pugno N, Gupta HS (2017) Staggered fibrils and damageable interfaces lead concurrently and independently to hysteretic energy absorption and inhomogeneous strain fields in cyclically loaded antler bone. ACS Biomater Sci Eng 3:2779–2787CrossRefGoogle Scholar
  13. Ebacher V, Guy P, Oxland TR, Wang R (2012) Sub-lamellar microcracking and roles of canaliculi in human cortical bone. Acta Biomater 8:1093–1100CrossRefGoogle Scholar
  14. Ebacher V, Tang C, McKay H et al (2007) Strain redistribution and cracking behavior of human bone during bending. Bone 40:1265–1275CrossRefGoogle Scholar
  15. Fantner GE, Hassenkam T, Kindt JH et al (2005) Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat Mater 4:612–616CrossRefGoogle Scholar
  16. Fantner GE, Adams J, Turner P et al (2007) Nanoscale ion mediated networks in bone: osteopontin can repeatedly dissipate large amounts of energy. Nano Lett 7:2491–2498CrossRefGoogle Scholar
  17. Fazzalari NL, Forwood MR, Manthey BA et al (1998) Three-dimensional confocal images of microdamage in cancellous bone. Bone 23:373–378CrossRefGoogle Scholar
  18. Fratzl P (2008) Collagen structure and mechanics. Springer, BerlinGoogle Scholar
  19. Fratzl P, Weinkamer R (2007) Nature’s hierarchical materials. Prog Mater Sci 52:1263–1334CrossRefGoogle Scholar
  20. Fratzl-Zelman N, Schmidt I, Roschger P et al (2014) Mineral particle size in children with osteogenesis imperfecta type I is not increased independently of specific collagen mutations. Bone 60:122–128CrossRefGoogle Scholar
  21. Gao H, Ji B, Jäger IL et al (2003) Materials become insensitive to flaws at nanoscale: lessons from nature. Proc Natl Acad Sci 100:5597–5600CrossRefGoogle Scholar
  22. Gautieri A, Vesentini S, Redaelli A, Buehler MJ (2011) Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. Nano Lett 11:757–766CrossRefGoogle Scholar
  23. Georgiadis M, Müller R, Schneider P (2016) Techniques to assess bone ultrastructure organization: orientation and arrangement of mineralized collagen fibrils. J R Soc Interface 13:20160088CrossRefGoogle Scholar
  24. Grandfield K, Vuong V, Schwarcz HP (2018) Ultrastructure of bone: hierarchical features from nanometer to micrometer scale revealed in focused ion beam sections in the TEM. Calcif Tissue Int. CrossRefGoogle Scholar
  25. Gupta HS, Seto J, Wagermaier W et al (2006) Cooperative deformation of mineral and collagen in bone at the nanoscale. Proc Natl Acad Sci U S A 103:17741–17746CrossRefGoogle Scholar
  26. Hamed E, Jasiuk I (2012) Elastic modeling of bone at nanostructural level. Mater Sci Eng R Rep 73:27–49CrossRefGoogle Scholar
  27. Hang F, Gupta HS, Barber AH (2014) Nanointerfacial strength between non-collagenous protein and collagen fibrils in antler bone. J R Soc Interface 11:20130993CrossRefGoogle Scholar
  28. Hassenkam T, Fantner GE, Cutroni JA et al (2004) High-resolution AFM imaging of intact and fractured trabecular bone. Bone 35:4–10CrossRefGoogle Scholar
  29. Ingram RT, Clarke BL, Fisher LW, Fitzpatrick LA (1993) Distribution of noncollagenous proteins in the matrix of adult human bone: evidence of anatomic and functional heterogeneity. J Bone Miner Res 8:1019–1029CrossRefGoogle Scholar
  30. Jasiuk I, Ostoja-Starzewski M (2004) Modeling of bone at a single lamella level. Biomech Model Mechanobiol 3:67–74CrossRefGoogle Scholar
  31. Ji B (2008) A study of the interface strength between protein and mineral in biological materials. J Biomech 41:259–266CrossRefGoogle Scholar
  32. Kasugai S, Todescan R, Nagata T et al (1991) Expression of bone matrix proteins associated with mineralized tissue formation by adult rat bone marrow cells in vitro: inductive effects of dexamethasone on the osteoblastic phenotype. J Cell Physiol 147:111–120CrossRefGoogle Scholar
  33. Katz JL, Ukraincik K (1971) On the anisotropic elastic properties of hydroxyapatite. J Biomech 4:221–227CrossRefGoogle Scholar
  34. Kindt JH, Thurner PJ, Lauer ME et al (2007) In situ observation of fluoride-ion-induced hydroxyapatite–collagen detachment on bone fracture surfaces by atomic force microscopy. Nanotechnology 18:135102CrossRefGoogle Scholar
  35. Lai ZB, Yan C (2017) Mechanical behaviour of staggered array of mineralised collagen fibrils in protein matrix: effects of fibril dimensions and failure energy in protein matrix. J Mech Behav Biomed Mater 65:236–247CrossRefGoogle Scholar
  36. Lai ZB, Wang M, Yan C, Oloyede A (2014) Molecular dynamics simulation of mechanical behavior of osteopontin-hydroxyapatite interfaces. J Mech Behav Biomed Mater 36:12–20CrossRefGoogle Scholar
  37. Li Y, Aparicio C (2013) Discerning the subfibrillar structure of mineralized collagen fibrils: a model for the ultrastructure of bone. PLoS ONE 8:e76782CrossRefGoogle Scholar
  38. Lin L, Wang X, Zeng X (2014) Geometrical modeling of cell division and cell remodeling based on Voronoi tessellation method. CMES Comput Model Eng Sci 98:203–220Google Scholar
  39. Lin L, Samuel J, Zeng X, Wang X (2017a) Contribution of extrafibrillar matrix to the mechanical behavior of bone using a novel cohesive finite element model. J Mech Behav Biomed Mater 65:224–235CrossRefGoogle Scholar
  40. Lin L, Wang X, Zeng X (2017b) Computational modeling of interfacial behaviors in nanocomposite materials. Int J Solids Struct 115–116:43–52CrossRefGoogle Scholar
  41. Luczynski KW, Steiger-Thirsfeld A, Bernardi J et al (2015) Extracellular bone matrix exhibits hardening elastoplasticity and more than double cortical strength: evidence from homogeneous compression of non-tapered single micron-sized pillars welded to a rigid substrate. J Mech Behav Biomed Mater 52:51–62CrossRefGoogle Scholar
  42. Luo Q, Nakade R, Dong X et al (2011) Effect of mineral–collagen interfacial behavior on the microdamage progression in bone using a probabilistic cohesive finite element model. J Mech Behav Biomed Mater 4:943–952CrossRefGoogle Scholar
  43. Mbuyi-Muamba JM, Dequeker J, Gevers G (1989) Collagen and non-collagenous proteins in different mineralization stages of human femur. Acta Anat (Basel) 134:265–268CrossRefGoogle Scholar
  44. McNally EA, Schwarcz HP, Botton GA, Arsenault AL (2012) A model for the ultrastructure of bone based on electron microscopy of ion milled sections. PLoS ONE 7:e29258CrossRefGoogle Scholar
  45. McNamara LM (2017) 2.10 Bone as a material. In: Ducheyne P (ed) Comprehensive biomaterials II. Elsevier, Oxford, pp 202–227CrossRefGoogle Scholar
  46. Morgan S, Poundarik AA, Vashishth D (2015) Do non-collagenous proteins affect skeletal mechanical properties? Calcif Tissue Int 97:281–291CrossRefGoogle Scholar
  47. Nair AK, Gautieri A, Chang S-W, Buehler MJ (2013) Molecular mechanics of mineralized collagen fibrils in bone. Nat Commun 4:1724CrossRefGoogle Scholar
  48. Nanci A (1999) Content and distribution of noncollagenous matrix proteins in bone and cementum: relationship to speed of formation and collagen packing density. J Struct Biol 126:256–269CrossRefGoogle Scholar
  49. Nikel O, Laurencin D, McCallum SA et al (2013) NMR investigation of the role of osteocalcin and osteopontin at the organic–inorganic interface in bone. Langmuir 29:13873–13882CrossRefGoogle Scholar
  50. Nikolov S, Raabe D (2008) Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization. Biophys J 94:4220–4232CrossRefGoogle Scholar
  51. Nyman JS, Leng H, Neil Dong X, Wang X (2009) Differences in the mechanical behavior of cortical bone between compression and tension when subjected to progressive loading. J Mech Behav Biomed Mater 2:613–619CrossRefGoogle Scholar
  52. Olszta MJ, Cheng X, Jee SS et al (2007) Bone structure and formation: a new perspective. Mater Sci Eng R Rep 58:77–116CrossRefGoogle Scholar
  53. Paschalis EP, Gamsjaeger S, Fratzl-Zelman N et al (2016) Evidence for a role for nanoporosity and pyridinoline content in human mild osteogenesis imperfecta. J Bone Miner Res 31:1050–1059CrossRefGoogle Scholar
  54. Piekarski K (1973) Analysis of bone as a composite material. Int J Eng Sci 11:557–565CrossRefGoogle Scholar
  55. Poundarik AA, Diab T, Sroga GE et al (2012) Dilatational band formation in bone. Proc Natl Acad Sci 109:19178–19183CrossRefGoogle Scholar
  56. Qin Z, Gautieri A, Nair AK et al (2012) Thickness of hydroxyapatite nanocrystal controls mechanical properties of the collagen–hydroxyapatite interface. Langmuir 28:1982–1992CrossRefGoogle Scholar
  57. Reilly DT, Burstein AH (1974) Review article. The mechanical properties of cortical bone. J Bone Jt Surg Am 56:1001–1022CrossRefGoogle Scholar
  58. Reisinger AG, Pahr DH, Zysset PK (2011) Elastic anisotropy of bone lamellae as a function of fibril orientation pattern. Biomech Model Mechanobiol 10:67–77CrossRefGoogle Scholar
  59. Reznikov N, Shahar R, Weiner S (2014) Bone hierarchical structure in three dimensions. Acta Biomater 10:3815–3826CrossRefGoogle Scholar
  60. Rho J-Y, Kuhn-Spearing L, Zioupos P (1998) Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92–102CrossRefGoogle Scholar
  61. Ritchie RO (2010) How does human bone resist fracture? Ann N Y Acad Sci 1192:72–80CrossRefGoogle Scholar
  62. Ritchie RO (2011) The conflicts between strength and toughness. Nat Mater 10:817–822CrossRefGoogle Scholar
  63. Roach HI (1994) Why does bone matrix contain non-collagenous proteins? The possible roles of osteocalcin, osteonectin, osteopontin and bone sialoprotein in bone mineralisation and resorption. Cell Biol Int 18:617–628CrossRefGoogle Scholar
  64. Rodriguez-Florez N, Oyen ML, Shefelbine SJ (2013) Insight into differences in nanoindentation properties of bone. J Mech Behav Biomed Mater 18:90–99CrossRefGoogle Scholar
  65. Rubin MA, Jasiuk I, Taylor J et al (2003) TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone 33:270–282CrossRefGoogle Scholar
  66. Samuel J, Park J-S, Almer J, Wang X (2016) Effect of water on nanomechanics of bone is different between tension and compression. J Mech Behav Biomed Mater 57:128–138CrossRefGoogle Scholar
  67. Schwarcz HP, McNally EA, Botton GA (2014) Dark-field transmission electron microscopy of cortical bone reveals details of extrafibrillar crystals. J Struct Biol 188:240–248CrossRefGoogle Scholar
  68. Schwarcz HP, Abueidda D, Jasiuk I (2017) The ultrastructure of bone and its relevance to mechanical properties. Front Phys 5:39CrossRefGoogle Scholar
  69. Schwiedrzik J, Raghavan R, Bürki A et al (2014) In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone. Nat Mater 13:740–747CrossRefGoogle Scholar
  70. Schwiedrzik J, Taylor A, Casari D et al (2017) Nanoscale deformation mechanisms and yield properties of hydrated bone extracellular matrix. Acta Biomater 60:302–314CrossRefGoogle Scholar
  71. Seref-Ferlengez Z, Basta-Pljakic J, Kennedy OD et al (2014) Structural and mechanical repair of diffuse damage in cortical bone in vivo. J Bone Miner Res 29:2537–2544CrossRefGoogle Scholar
  72. Siegmund T, Allen MR, Burr DB (2008) Failure of mineralized collagen fibrils: modeling the role of collagen cross-linking. J Biomech 41:1427–1435CrossRefGoogle Scholar
  73. Sroga GE, Vashishth D (2012) Effects of bone matrix proteins on fracture and fragility in osteoporosis. Curr Osteoporos Rep 10:141–150CrossRefGoogle Scholar
  74. Su X, Sun K, Cui FZ, Landis WJ (2003) Organization of apatite crystals in human woven bone. Bone 32:150–162CrossRefGoogle Scholar
  75. Tai K, Ulm F-J, Ortiz C (2006) Nanogranular origins of the strength of bone. Nano Lett 6:2520–2525CrossRefGoogle Scholar
  76. Tertuliano OA, Greer JR (2016) The nanocomposite nature of bone drives its strength and damage resistance. Nat Mater 15:1195–1202CrossRefGoogle Scholar
  77. Thurner PJ (2009) Atomic force microscopy and indentation force measurement of bone. Wiley Interdiscip Rev Nanomed Nanobiotechnol 1:624–649CrossRefGoogle Scholar
  78. Urist MR, Strates BS (2009) The classic: bone morphogenetic protein. Clin Orthop 467:3051–3062CrossRefGoogle Scholar
  79. Vercher-Martínez A, Giner E, Belda R et al (2018) Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach. Biomech Model Mechanobiol 17:449–464CrossRefGoogle Scholar
  80. Viswanath B, Raghavan R, Ramamurty U, Ravishankar N (2007) Mechanical properties and anisotropy in hydroxyapatite single crystals. Scr Mater 57:361–364CrossRefGoogle Scholar
  81. Wagermaier W, Klaushofer K, Fratzl P (2015) Fragility of bone material controlled by internal interfaces. Calcif Tissue Int 97:201–212CrossRefGoogle Scholar
  82. Wallace JM (2012) Applications of atomic force microscopy for the assessment of nanoscale morphological and mechanical properties of bone. Bone 50:420–427CrossRefGoogle Scholar
  83. Wang Y, Ural A (2018) Mineralized collagen fibril network spatial arrangement influences cortical bone fracture behavior. J Biomech 66:70–77CrossRefGoogle Scholar
  84. Wang X, Shen X, Li X, Agrawal CM (2002) Age-related changes in the collagen network and toughness of bone. Bone 31:1–7CrossRefGoogle Scholar
  85. Wang Z, Vashishth D, Picu RC (2018) Bone toughening through stress-induced non-collagenous protein denaturation. Biomech Model Mechanobiol 17:1093–1106CrossRefGoogle Scholar
  86. Weiner S, Traub W (1992) Bone structure: from angstroms to microns. FASEB J 6:879–885CrossRefGoogle Scholar
  87. Wilson EE, Awonusi A, Morris MD et al (2005) Highly ordered interstitial water observed in bone by nuclear magnetic resonance. J Bone Miner Res 20:625–634CrossRefGoogle Scholar
  88. Wilson EE, Awonusi A, Morris MD et al (2006) Three structural roles for water in bone observed by solid-state NMR. Biophys J 90:3722–3731CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe University of Texas at San AntonioSan AntonioUSA

Personalised recommendations