Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Abueidda DW, Sabet FA, Jasiuk IM (2017) Modeling of stiffness and strength of bone at nanoscale. J Biomech Eng 139(5):051006–051006-10. https://doi.org/10.1115/1.4036314

    Article  Google Scholar 

  • Al-Qtaitat AI, Aldalaen SM (2014) A review of non-collagenous proteins; their role in bone. Am J Life Sci 2:351–355

    Article  Google Scholar 

  • Balooch M, Habelitz S, Kinney JH et al (2008) Mechanical properties of mineralized collagen fibrils as influenced by demineralization. J Struct Biol 162:404–410

    Article  Google Scholar 

  • Bishop N (2016) Bone material properties in osteogenesis imperfecta. J Bone Miner Res 31:699–708

    Article  Google Scholar 

  • Boskey AL (2013) Bone composition: relationship to bone fragility and antiosteoporotic drug effects. BoneKEy Rep 2:447

    Article  Google Scholar 

  • Boskey AL, Coleman R (2010) Aging and bone. J Dent Res 89:1333–1348

    Article  Google Scholar 

  • Boyce TM, Fyhrie DP, Glotkowski MC et al (1998) Damage type and strain mode associations in human compact bone bending fatigue. J Orthop Res 16:322–329

    Article  Google Scholar 

  • Buehler MJ (2007) Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization. Nanotechnology 18:295102

    Article  Google Scholar 

  • Cassella JP, Stamp TCB, Ali SY (1996) A morphological and ultrastructural study of bone in osteogenesis imperfecta. Calcif Tissue Int 58:155–165

    Article  Google Scholar 

  • Chamay A (1970) Mechanical and morphological aspects of experimental overload and fatigue in bone. J Biomech 3:263–270

    Article  Google Scholar 

  • Ciuchi IV, Olariu CS, Mitoseriu L (2013) Determination of bone mineral volume fraction using impedance analysis and Bruggeman model. Mater Sci Eng B 178:1296–1302

    Article  Google Scholar 

  • 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 3:2779–2787

    Article  Google Scholar 

  • Ebacher V, Guy P, Oxland TR, Wang R (2012) Sub-lamellar microcracking and roles of canaliculi in human cortical bone. Acta Biomater 8:1093–1100

    Article  Google Scholar 

  • Ebacher V, Tang C, McKay H et al (2007) Strain redistribution and cracking behavior of human bone during bending. Bone 40:1265–1275

    Article  Google Scholar 

  • 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 4:612–616

    Article  Google Scholar 

  • 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 7:2491–2498

    Article  Google Scholar 

  • Fazzalari NL, Forwood MR, Manthey BA et al (1998) Three-dimensional confocal images of microdamage in cancellous bone. Bone 23:373–378

    Article  Google Scholar 

  • Fratzl P (2008) Collagen structure and mechanics. Springer, Berlin

    Google Scholar 

  • Fratzl P, Weinkamer R (2007) Nature’s hierarchical materials. Prog Mater Sci 52:1263–1334

    Article  Google Scholar 

  • 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 60:122–128

    Article  Google Scholar 

  • Gao H, Ji B, Jäger IL et al (2003) Materials become insensitive to flaws at nanoscale: lessons from nature. Proc Natl Acad Sci 100:5597–5600

    Article  Google Scholar 

  • Gautieri A, Vesentini S, Redaelli A, Buehler MJ (2011) Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. Nano Lett 11:757–766

    Article  Google Scholar 

  • Georgiadis M, Müller R, Schneider P (2016) Techniques to assess bone ultrastructure organization: orientation and arrangement of mineralized collagen fibrils. J R Soc Interface 13:20160088

    Article  Google Scholar 

  • 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. https://doi.org/10.1007/s00223-018-0454-9

    Google Scholar 

  • 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 103:17741–17746

    Article  Google Scholar 

  • Hamed E, Jasiuk I (2012) Elastic modeling of bone at nanostructural level. Mater Sci Eng R Rep 73:27–49

    Article  Google Scholar 

  • Hang F, Gupta HS, Barber AH (2014) Nanointerfacial strength between non-collagenous protein and collagen fibrils in antler bone. J R Soc Interface 11:20130993

    Article  Google Scholar 

  • Hassenkam T, Fantner GE, Cutroni JA et al (2004) High-resolution AFM imaging of intact and fractured trabecular bone. Bone 35:4–10

    Article  Google Scholar 

  • 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 8:1019–1029

    Article  Google Scholar 

  • Jasiuk I, Ostoja-Starzewski M (2004) Modeling of bone at a single lamella level. Biomech Model Mechanobiol 3:67–74

    Article  Google Scholar 

  • Ji B (2008) A study of the interface strength between protein and mineral in biological materials. J Biomech 41:259–266

    Article  Google Scholar 

  • 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 147:111–120

    Article  Google Scholar 

  • Katz JL, Ukraincik K (1971) On the anisotropic elastic properties of hydroxyapatite. J Biomech 4:221–227

    Article  Google Scholar 

  • 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 18:135102

    Article  Google Scholar 

  • 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 65:236–247

    Article  Google Scholar 

  • Lai ZB, Wang M, Yan C, Oloyede A (2014) Molecular dynamics simulation of mechanical behavior of osteopontin-hydroxyapatite interfaces. J Mech Behav Biomed Mater 36:12–20

    Article  Google Scholar 

  • Li Y, Aparicio C (2013) Discerning the subfibrillar structure of mineralized collagen fibrils: a model for the ultrastructure of bone. PLoS ONE 8:e76782

    Article  Google Scholar 

  • 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 98:203–220

    Google Scholar 

  • 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 65:224–235

    Article  Google Scholar 

  • Lin L, Wang X, Zeng X (2017b) Computational modeling of interfacial behaviors in nanocomposite materials. Int J Solids Struct 115–116:43–52

    Article  Google Scholar 

  • 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 52:51–62

    Article  Google Scholar 

  • 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 4:943–952

    Article  Google Scholar 

  • Mbuyi-Muamba JM, Dequeker J, Gevers G (1989) Collagen and non-collagenous proteins in different mineralization stages of human femur. Acta Anat (Basel) 134:265–268

    Article  Google Scholar 

  • 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:e29258

    Article  Google Scholar 

  • McNamara LM (2017) 2.10 Bone as a material. In: Ducheyne P (ed) Comprehensive biomaterials II. Elsevier, Oxford, pp 202–227

    Chapter  Google Scholar 

  • Morgan S, Poundarik AA, Vashishth D (2015) Do non-collagenous proteins affect skeletal mechanical properties? Calcif Tissue Int 97:281–291

    Article  Google Scholar 

  • Nair AK, Gautieri A, Chang S-W, Buehler MJ (2013) Molecular mechanics of mineralized collagen fibrils in bone. Nat Commun 4:1724

    Article  Google Scholar 

  • 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 126:256–269

    Article  Google Scholar 

  • 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 29:13873–13882

    Article  Google Scholar 

  • Nikolov S, Raabe D (2008) Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization. Biophys J 94:4220–4232

    Article  Google Scholar 

  • 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 2:613–619

    Article  Google Scholar 

  • Olszta MJ, Cheng X, Jee SS et al (2007) Bone structure and formation: a new perspective. Mater Sci Eng R Rep 58:77–116

    Article  Google Scholar 

  • 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 31:1050–1059

    Article  Google Scholar 

  • Piekarski K (1973) Analysis of bone as a composite material. Int J Eng Sci 11:557–565

    Article  Google Scholar 

  • Poundarik AA, Diab T, Sroga GE et al (2012) Dilatational band formation in bone. Proc Natl Acad Sci 109:19178–19183

    Article  Google Scholar 

  • Qin Z, Gautieri A, Nair AK et al (2012) Thickness of hydroxyapatite nanocrystal controls mechanical properties of the collagen–hydroxyapatite interface. Langmuir 28:1982–1992

    Article  Google Scholar 

  • Reilly DT, Burstein AH (1974) Review article. The mechanical properties of cortical bone. J Bone Jt Surg Am 56:1001–1022

    Article  Google Scholar 

  • Reisinger AG, Pahr DH, Zysset PK (2011) Elastic anisotropy of bone lamellae as a function of fibril orientation pattern. Biomech Model Mechanobiol 10:67–77

    Article  Google Scholar 

  • Reznikov N, Shahar R, Weiner S (2014) Bone hierarchical structure in three dimensions. Acta Biomater 10:3815–3826

    Article  Google Scholar 

  • Rho J-Y, Kuhn-Spearing L, Zioupos P (1998) Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92–102

    Article  Google Scholar 

  • Ritchie RO (2010) How does human bone resist fracture? Ann N Y Acad Sci 1192:72–80

    Article  Google Scholar 

  • Ritchie RO (2011) The conflicts between strength and toughness. Nat Mater 10:817–822

    Article  Google Scholar 

  • 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 18:617–628

    Article  Google Scholar 

  • Rodriguez-Florez N, Oyen ML, Shefelbine SJ (2013) Insight into differences in nanoindentation properties of bone. J Mech Behav Biomed Mater 18:90–99

    Article  Google Scholar 

  • Rubin MA, Jasiuk I, Taylor J et al (2003) TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone 33:270–282

    Article  Google Scholar 

  • 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 57:128–138

    Article  Google Scholar 

  • Schwarcz HP, McNally EA, Botton GA (2014) Dark-field transmission electron microscopy of cortical bone reveals details of extrafibrillar crystals. J Struct Biol 188:240–248

    Article  Google Scholar 

  • Schwarcz HP, Abueidda D, Jasiuk I (2017) The ultrastructure of bone and its relevance to mechanical properties. Front Phys 5:39

    Article  Google Scholar 

  • 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 13:740–747

    Article  Google Scholar 

  • Schwiedrzik J, Taylor A, Casari D et al (2017) Nanoscale deformation mechanisms and yield properties of hydrated bone extracellular matrix. Acta Biomater 60:302–314

    Article  Google Scholar 

  • 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 29:2537–2544

    Article  Google Scholar 

  • Siegmund T, Allen MR, Burr DB (2008) Failure of mineralized collagen fibrils: modeling the role of collagen cross-linking. J Biomech 41:1427–1435

    Article  Google Scholar 

  • Sroga GE, Vashishth D (2012) Effects of bone matrix proteins on fracture and fragility in osteoporosis. Curr Osteoporos Rep 10:141–150

    Article  Google Scholar 

  • Su X, Sun K, Cui FZ, Landis WJ (2003) Organization of apatite crystals in human woven bone. Bone 32:150–162

    Article  Google Scholar 

  • Tai K, Ulm F-J, Ortiz C (2006) Nanogranular origins of the strength of bone. Nano Lett 6:2520–2525

    Article  Google Scholar 

  • Tertuliano OA, Greer JR (2016) The nanocomposite nature of bone drives its strength and damage resistance. Nat Mater 15:1195–1202

    Article  Google Scholar 

  • Thurner PJ (2009) Atomic force microscopy and indentation force measurement of bone. Wiley Interdiscip Rev Nanomed Nanobiotechnol 1:624–649

    Article  Google Scholar 

  • Urist MR, Strates BS (2009) The classic: bone morphogenetic protein. Clin Orthop 467:3051–3062

    Article  Google Scholar 

  • 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 17:449–464

    Article  Google Scholar 

  • Viswanath B, Raghavan R, Ramamurty U, Ravishankar N (2007) Mechanical properties and anisotropy in hydroxyapatite single crystals. Scr Mater 57:361–364

    Article  Google Scholar 

  • Wagermaier W, Klaushofer K, Fratzl P (2015) Fragility of bone material controlled by internal interfaces. Calcif Tissue Int 97:201–212

    Article  Google Scholar 

  • Wallace JM (2012) Applications of atomic force microscopy for the assessment of nanoscale morphological and mechanical properties of bone. Bone 50:420–427

    Article  Google Scholar 

  • Wang Y, Ural A (2018) Mineralized collagen fibril network spatial arrangement influences cortical bone fracture behavior. J Biomech 66:70–77

    Article  Google Scholar 

  • Wang X, Shen X, Li X, Agrawal CM (2002) Age-related changes in the collagen network and toughness of bone. Bone 31:1–7

    Article  Google Scholar 

  • Wang Z, Vashishth D, Picu RC (2018) Bone toughening through stress-induced non-collagenous protein denaturation. Biomech Model Mechanobiol 17:1093–1106

    Article  Google Scholar 

  • Weiner S, Traub W (1992) Bone structure: from angstroms to microns. FASEB J 6:879–885

    Article  Google Scholar 

  • Wilson EE, Awonusi A, Morris MD et al (2005) Highly ordered interstitial water observed in bone by nuclear magnetic resonance. J Bone Miner Res 20:625–634

    Article  Google Scholar 

  • Wilson EE, Awonusi A, Morris MD et al (2006) Three structural roles for water in bone observed by solid-state NMR. Biophys J 90:3722–3731

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA

    Mohammad Maghsoudi-Ganjeh, Liqiang Lin, Xiaodu Wang & Xiaowei Zeng

Authors
  1. Mohammad Maghsoudi-Ganjeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liqiang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaodu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaowei Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xiaodu Wang or Xiaowei Zeng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maghsoudi-Ganjeh, M., Lin, L., Wang, X. et al. Computational investigation of ultrastructural behavior of bone using a cohesive finite element approach. Biomech Model Mechanobiol 18, 463–478 (2019). https://doi.org/10.1007/s10237-018-1096-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-018-1096-6

Keywords

Search

Navigation