Nanomechanical properties of mineralised collagen microfibrils based on finite elements method: biomechanical role of cross-links

Hierarchical structures in bio-composites such as bone tissue have many scales or levels and synergic interactions between the different levels. They also have a highly complex architecture in order to fulfil their biological and mechanical functions. In this study, a new three-dimensional (3D) model based on the finite elements (FEs) method was used to model the relationship between the hierarchical structure and the properties of the constituents at the sub-structure scale (mineralised collagen microfibrils) and to investigate their apparent nanomechanical properties. The results of the proposed FE simulations show that the elastic properties of microfibrils depend on different factors such as the number of cross-links, the mechanical properties and the volume fraction of phases. The results obtained under compression loading at a small deformation < 2% show that the microfibrils have a Young's modulus (Ef) ranging from 0.4 to 1.16 GPa and a Poisson's ratio ranging from 0.26 to 0.3. These results are in excellent agreement with experimental data (X-ray, AFM and MEMS) and molecular simulations.

[1]  T J Sims,et al.  Mechanical Properties of Adult Vertebral Cancellous Bone: Correlation With Collagen Intermolecular Cross‐Links , 2002, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[2]  J. W. SMITH,et al.  Molecular Pattern in Native Collagen , 1968, Nature.

[3]  N Guzelsu,et al.  Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory. , 2003, Journal of biomechanical engineering.

[4]  P. Hauschka,et al.  Nucleation and inhibition of hydroxyapatite formation by mineralized tissue proteins. , 1996, The Biochemical journal.

[5]  M. Grynpas,et al.  Changes in bone mineralization, architecture and mechanical properties due to long-term (1 year) administration of pamidronate (APD) to adult dogs , 1992, Osteoporosis International.

[6]  N. Sasaki,et al.  Stress-strain curve and Young's modulus of a collagen molecule as determined by the X-ray diffraction technique. , 1996, Journal of biomechanics.

[7]  D J Prockop,et al.  Radial packing, order, and disorder in collagen fibrils. , 1995, Biophysical journal.

[8]  T. Irving,et al.  The in situ supermolecular structure of type I collagen. , 2001, Structure.

[9]  Allen J. Bailey,et al.  Molecular mechanisms of ageing in connective tissues , 2001, Mechanisms of Ageing and Development.

[10]  Bernd Eggers,et al.  Bones Structure And Mechanics , 2016 .

[11]  Ridha Hambli,et al.  Failure of Mineralized Collagen Microfibrils Using Finite Element Simulation Coupled to Mechanical Quasi-brittle Damage , 2011, 1107.1027.

[12]  C. M. Agrawal,et al.  Age-related changes in the collagen network and toughness of bone. , 2002, Bone.

[13]  L Kinzl,et al.  Correlation of bone mineral density with strength and microstructural parameters of cortical bone in vitro. , 2002, Bone.

[14]  Vashishith.  EFFECTS OF NON-ENZYMATIC GLYCATION ON CANCELLOUS BONE FRAGILITY , 2005 .

[15]  N. Sasaki,et al.  Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of structural hierarchy. , 1996, Journal of biomechanics.

[16]  J. Nyman,et al.  Age‐related factors affecting the postyield energy dissipation of human cortical bone , 2007, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[17]  A. Redaelli,et al.  Molecular assessment of the elastic properties of collagen-like homotrimer sequences , 2005, Biomechanics and modeling in mechanobiology.

[18]  Kai-Nan An,et al.  Flexibility of type I collagen and mechanical property of connective tissue. , 2004, Biorheology.

[19]  Markus J Buehler,et al.  Entropic elasticity controls nanomechanics of single tropocollagen molecules. , 2007, Biophysical journal.

[20]  M. Buehler.  Nanomechanics of collagen fibrils under varying cross-link densities: atomistic and continuum studies. , 2008, Journal of the mechanical behavior of biomedical materials.

[21]  Markus J. Buehler,et al.  Theoretical and computational hierarchical nanomechanics of protein materials: Deformation and fracture , 2008 .

[22]  Ridha Hambli,et al.  Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation , 2011, Biomechanics and modeling in mechanobiology.

[23]  Christian Hellmich,et al.  Mineral–collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach , 2004 .

[24]  V. Monnier.  Toward a Maillard reaction theory of aging. , 1989, Progress in clinical and biological research.

[25]  K. Heiple,et al.  Contribution of collagen and mineral to the elastic-plastic properties of bone. , 1975, The Journal of bone and joint surgery. American volume.

[26]  P. Boesecke,et al.  In situ multi-level analysis of viscoelastic deformation mechanisms in tendon collagen. , 2010, Journal of structural biology.

[27]  Michele Vendruscolo,et al.  Role of Intermolecular Forces in Defining Material Properties of Protein Nanofibrils , 2007, Science.

[28]  Christian Hellmich,et al.  Mechanical behavior of hydroxyapatite biomaterials: an experimentally validated micromechanical model for elasticity and strength. , 2009, Journal of biomedical materials research. Part A.

[29]  N. Sasaki,et al.  Viscoelastic properties of bone as a function of water content. , 1995, Journal of biomechanics.

[30]  J. Katz,et al.  On the anisotropic elastic properties of hydroxyapatite. , 1971, Journal of biomechanics.

[31]  M. Morris,et al.  Highly Ordered Interstitial Water Observed in Bone by Nuclear Magnetic Resonance , 2004, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[32]  F. Tay,et al.  Hierarchical and non-hierarchical mineralisation of collagen. , 2011, Biomaterials.

[33]  I. Rangelow,et al.  Hierarchical interconnections in the nano-composite material bone: Fibrillar cross-links resist fracture on several length scales , 2006 .

[34]  Tony M. Keaveny,et al.  BONE MECHANICS , 2005 .

[35]  M. Urist,et al.  Bone cell differentiation and growth factors. , 1983, Science.

[36]  D. Eyre,et al.  Advances in collagen cross-link analysis. , 2008, Methods.

[37]  K. An,et al.  Stretching short biopolymers using optical tweezers. , 2001, Biochemical and biophysical research communications.

[38]  H. Kahn,et al.  Nano measurements with micro-devices: mechanical properties of hydrated collagen fibrils , 2006, Journal of The Royal Society Interface.

[39]  R. Mayne.  Cartilage collagens. What is their function, and are they involved in articular disease? , 1989, Arthritis and rheumatism.

[40]  W. Walsh,et al.  Compressive properties of cortical bone: mineral-organic interfacial bonding. , 1994, Biomaterials.

[41]  D. Vashishth,et al.  Influence of nonenzymatic glycation on biomechanical properties of cortical bone. , 2001, Bone.

[42]  John D. Currey,et al.  Bones: Structure and Mechanics , 2002 .

[43]  E. Pearce.  Ion displacement following the adsorption of anionic macromolecules on hydroxyapatite , 2006, Calcified Tissue International.

[44]  Kai-Nan An,et al.  Stretching type II collagen with optical tweezers. , 2004, Journal of biomechanics.

[45]  P. Fratzl,et al.  Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. , 2000, Biophysical journal.

[46]  C. M. Agrawal,et al.  The role of collagen in determining bone mechanical properties , 2001, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[47]  W. Hayes,et al.  Mechanical properties of trabecular bone from the proximal femur: a quantitative CT study. , 1990, Journal of computer assisted tomography.

[48]  Markus J. Buehler,et al.  Atomistic and continuum modeling of mechanical properties of collagen: Elasticity, fracture, and self-assembly , 2006 .

[49]  Steve Weiner,et al.  THE MATERIAL BONE: Structure-Mechanical Function Relations , 1998 .

[50]  Kai-Nan An,et al.  Direct quantification of the flexibility of type I collagen monomer. , 2002, Biochemical and biophysical research communications.

[51]  T. Aigner,et al.  Collagens--structure, function, and biosynthesis. , 2003, Advanced drug delivery reviews.

[52]  D. Vashishth.  The role of the collagen matrix in skeletal fragility , 2007, Current Osteoporosis Reports.

[53]  K. Mann,et al.  Identification of the noncollagenous proteins of bovine bone by two-dimensional gel electrophoresis , 1984, Calcified Tissue International.

[54]  J. Revel,et al.  Subfibrillar structure of type I collagen observed by atomic force microscopy. , 1993, Biophysical journal.

[55]  S A Goldstein,et al.  Type‐I collagen mutation compromises the post‐yield behavior of Mov13 long bone , 1996, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[56]  Wolfgang Wagermaier,et al.  Cooperative deformation of mineral and collagen in bone at the nanoscale , 2006, Proceedings of the National Academy of Sciences.

[57]  P. Fratzl,et al.  Collagen packing and mineralization. An x-ray scattering investigation of turkey leg tendon. , 1993, Biophysical journal.

[58]  Ridha Hambli,et al.  Finite Element 3D Modeling of Mechanical Behavior of Mineralized Collagen Microfibrils , 2011, Journal of applied biomaterials & biomechanics : JABB.

[59]  J. Rovenský,et al.  [Collagen in the treatment of rheumatic diseases--oral tolerance]. , 1999, Bratislavske lekarske listy.

[60]  Christian Hellmich,et al.  'Universal' microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. , 2007, Journal of theoretical biology.

[61]  Himadri S. Gupta,et al.  Structure and mechanical quality of the collagen–mineral nano-composite in bone , 2004 .

[62]  A J Bailey,et al.  Collagen cross-links in mineralizing tissues: a review of their chemistry, function, and clinical relevance. , 1998, Bone.

[63]  T. Irving,et al.  Microfibrillar structure of type I collagen in situ. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[64]  A S Posner,et al.  Crystal chemistry of bone mineral. , 1969, Physiological reviews.

[65]  J. Nyman,et al.  The influence of water removal on the strength and toughness of cortical bone. , 2006, Journal of biomechanics.

[66]  C. Lim,et al.  Nanostructure of collagen fibrils in human nucleus pulposus and its correlation with macroscale tissue mechanics , 2010, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[67]  J A McGeough,et al.  Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure. , 1993, The Journal of bone and joint surgery. American volume.

[68]  Thomas Siegmund,et al.  Failure of mineralized collagen fibrils: modeling the role of collagen cross-linking. , 2008, Journal of biomechanics.

[69]  S. Cowin.  Do liquid crystal-like flow processes occur in the supramolecular assembly of biological tissues? , 2004 .

[70]  A. Arsenault.  Image analysis of collagen-associated mineral distribution in cryogenically prepared turkey leg tendons , 2007, Calcified Tissue International.

[71]  U Ziese,et al.  Corneal collagen fibril structure in three dimensions: Structural insights into fibril assembly, mechanical properties, and tissue organization , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[72]  Salah Naili,et al.  Variational homogenization for modeling fibrillar structures in bone , 2009 .

[73]  Richard Weinkamer,et al.  Nature’s hierarchical materials , 2007 .

[74]  K. Mark.  Structure, Biosynthesis and Gene Regulation of Collagens in Cartilage and Bone , 2006 .

[75]  T. McMahon,et al.  The tensile behavior of demineralized bovine cortical bone. , 1996, Journal of biomechanics.

[76]  F Peyrin,et al.  Site-matched assessment of structural and tissue properties of cortical bone using scanning acoustic microscopy and synchrotron radiation μCT , 2006, Physics in medicine and biology.

[77]  Xiaodu Wang,et al.  The Toughness of Cortical Bone and Its Relationship with Age , 2004, Annals of Biomedical Engineering.

[78]  M. Harmand,et al.  Molecular interface characterization in human bone matrix. I. Biochemical and IR spectroscopic studies. , 1993, Biomaterials.

[79]  M. Saito,et al.  Collagen cross-links as a determinant of bone quality: a possible explanation for bone fragility in aging, osteoporosis, and diabetes mellitus , 2010, Osteoporosis International.

[80]  C. M. Agrawal,et al.  The use of dynamic mechanical analysis to assess the viscoelastic properties of human cortical bone. , 2001, Journal of biomedical materials research.

[81]  J. Currey.  Role of collagen and other organics in the mechanical properties of bone , 2003, Osteoporosis International.

[82]  M. R. Dodge,et al.  Stress-strain experiments on individual collagen fibrils. , 2008, Biophysical journal.

[83]  S. Rackovsky,et al.  Computational study of packing a collagen‐like molecule: Quasi‐hexagonal vs “Smith” collagen microfibril model , 1996, Biopolymers.

[84]  B F McEwen,et al.  Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography , 1996, Microscopy research and technique.

[85]  Markus J Buehler,et al.  Molecular structure, mechanical behavior and failure mechanism of the C-terminal cross-link domain in type I collagen. , 2011, Journal of the mechanical behavior of biomedical materials.

[86]  Michael D Morris,et al.  Three structural roles for water in bone observed by solid-state NMR. , 2006, Biophysical journal.

[87]  Elliot P. Douglas,et al.  Bone structure and formation: A new perspective , 2007 .

[88]  I. Jasiuk,et al.  TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. , 2003, Bone.

[89]  R. G. Paul,et al.  Mechanisms of maturation and ageing of collagen , 1998, Mechanisms of Ageing and Development.

[90]  M Raspanti,et al.  Tapping-mode atomic force microscopy in fluid of hydrated extracellular matrix. , 2001, Matrix biology : journal of the International Society for Matrix Biology.

[91]  Mehdi Balooch,et al.  In situ atomic force microscopy of partially demineralized human dentin collagen fibrils. , 2002, Journal of structural biology.

[92]  J. Currey,et al.  The relationship between the stiffness and the mineral content of bone. , 1969, Journal of biomechanics.

[93]  Jan Feijen,et al.  Micromechanical testing of individual collagen fibrils. , 2006, Macromolecular bioscience.

[94]  Alberto Redaelli,et al.  Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. , 2011, Nano letters.

[95]  Ridha Hambli,et al.  Physically based 3D finite element model of a single mineralized collagen microfibril. , 2012, Journal of theoretical biology.

[96]  R. Hambli.  Apparent damage accumulation in cancellous bone using neural networks. , 2011, Journal of the mechanical behavior of biomedical materials.

[97]  S. Lees.  A mixed packing model for bone collagen , 2006, Calcified Tissue International.

[98]  D. Eyre,et al.  Collagen cross-linking in human bone and articular cartilage. Age-related changes in the content of mature hydroxypyridinium residues. , 1988, The Biochemical journal.

[99]  P. Odetti,et al.  Advanced Glycation End Products and Bone Loss during Aging , 2005, Annals of the New York Academy of Sciences.

[100]  M. Shimokomaki,et al.  Age related changes in the reducible cross‐links of collagen , 1971, FEBS letters.

[101]  A. Hiltner,et al.  Hierarchical structure of collagen composite systems: lessons from biology , 1991 .

[102]  P. Delmas,et al.  Bisphosphonates alter trabecular bone collagen cross-linking and isomerization in beagle dog vertebra , 2008, Osteoporosis International.

[103]  Peter Fratzl,et al.  Collagen : structure and mechanics , 2008 .

[104]  Fang Yuan,et al.  A new model to simulate the elastic properties of mineralized collagen fibril , 2011, Biomechanics and modeling in mechanobiology.

[105]  R. Pidaparti,et al.  Bone mineral lies mainly outside collagen fibrils: predictions of a composite model for osteonal bone. , 1996, Journal of biomechanics.

[106]  W. Friess,et al.  Collagen--biomaterial for drug delivery. , 1998, European journal of pharmaceutics and biopharmaceutics : official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V.

[107]  Dinesh R. Katti,et al.  Mechanics of molecular collagen is influenced by hydroxyapatite in natural bone , 2007 .

[108]  T. Irving,et al.  On the packing structure of collagen: response to Okuyama et al.'s comment on Microfibrillar structure of type I collagen in situ , 2009 .

[109]  P. Delmas,et al.  The role of collagen in bone strength , 2005, Osteoporosis International.