NANO LETTERS
Nanoscale Deformation Mechanisms in Bone
2005 Vol. 5, No. 10 2108-2111
Himadri S. Gupta,*,† Wolfgang Wagermaier,† Gerald A. Zickler,† D. Raz-Ben Aroush,‡ Se´rgio S. Funari,§ Paul Roschger,| H. Daniel Wagner,‡ and Peter Fratzl† Max Planck Institute of Colloids and Interfaces, MPI-KG Golm, D-14424 Potsdam, Germany, Department of Materials and Interfaces, Weizmann Institute of Science, RehoVot, Israel, HASYLAB-DESY, Notkestrasse 85, Hamburg, Germany, and Ludwig Boltzmann Institute of Osteology, Vienna, Austria Received August 11, 2005; Revised Manuscript Received September 13, 2005
ABSTRACT Deformation mechanisms in bone matrix at the nanoscale control its exceptional mechanical properties, but the detailed nature of these processes is as yet unknown. In situ tensile testing with synchrotron X-ray scattering allowed us to study directly and quantitatively the deformation mechanisms at the nanometer level. We find that bone deformation is not homogeneous but distributed between a tensile deformation of the fibrils and a shearing in the interfibrillar matrix between them.
Most natural biological materials have a hierarchical structure from the molecular to the macroscopic level.1 Their mechanical response and fracture properties arise from the properties of the individual elements at each level in the hierarchy as well as from the interaction between these elements across the different length scales,1,2 as in bone,2,3 nacre,4,5 deep-sea silicate sponges,6 and wood.7 In particular, the composite nature of such materials at the nanometer level is crucial to their overall structural and physiological function. Considering bone specifically, it consists at the nanometer level of type I collagen molecules (300 nm long, 1.1-1.5 nm wide) interspersed with irregularly shaped nanocrystal platelets of carbonated apatite (3-5 nm thick and a lateral size of ∼ 50 nm8). A composite of these two constituents forms the mineralized collagen fibril, with typically a diameter of 100 nm.9 The fibrils are hierarchically organized into lamellae and further on into the compact bone material, which, in combination with a cellular trabecular bone material, forms the organ bone. Partly due to this structural complexity, it is difficult to quantify separately the deformation mechanisms at the fibrillar level and their relation to the macroscopic fracture properties and plastic deformation of bone. A better understanding of such mechanisms would be of importance in designing biomimetic * Author to whom correspondence should be addressed. Phone: ++49331-567-9438. Fax: ++49-331-567-9402. E-mail: himadri.gupta@ mpikg-golm.mpg.de. † Max Planck Institute of Colloids and Interfaces. ‡ Weizmann Institute of Science. § HASYLAB-DESY. || Ludwig Boltzmann Institute of Osteology. 10.1021/nl051584b CCC: $30.25 Published on Web 09/22/2005
© 2005 American Chemical Society
nanostructured materials as bone replacements10 as well as in the field of clinical bone fracture studies.11 Most research into such mechanisms at the nanometer level has focused on the structure of the mineralized matrixsfor example, confocal,12 electron,13 and atomic force microscopic14 studies now provide detailed pictures of the mineralized matrix of bone down to a few nanometers. By investigation of the fracture surfaces with these techniques, mechanisms for controlling deformability have been proposed (for example, crack-bridging15 or microcracking12). Here, in contrast, by combining structural and mechanical techniques at the same time on the same sample, we look directly and quantitatively at the in situ nanometer-level mechanisms as bone deforms. A crucial question regarding the material-level deformation mechanisms of bone concerns the interplay between the strains in the collagen, mineral, and noncollagenous protein components of bone. Although most modeling work assumes that the nanometer-scale interface between the organic and the inorganic phases is strong, the interfacial strength has not been measured.16 Indeed, the deformation mechanisms at the microstructural level would be expected to be quite different for different types (covalent, ionic, or van der Waals) and strengths of interactions between the different phases. Although the macroscopic mechanical parameters, such as failure strain and strength, can be correlated to different modes of deformation with an appropriate parameter fit,17,18 a direct measurement of the deformation of the phases at the fibril level is still lacking. To quantify the fibrillar deformation mechanisms in bone, we carried out in situ tensile testing of hydrated bovine
parallel-fibered bone, concurrently measuring the small-angle X-ray scattering (SAXS) pattern, using high-brilliance synchrotron radiation. The principle of the test is to measure the changes in both fibril and tissue strain with applied stress, in real time. Because the collagen molecules are staggered axially along the fibril,19 a periodic electron density profile exists along the fibril axis (the D-period ≈ 64-67 nm), with the less dense regions referred to as the “gap” zones. Mineral particles nucleate and form first in the gap zones.8 Hence, the mineral density along the fibril axis is a step function (step length ≈ 0.46D20), which results in a series of Bragg reflections with period 2π/D ≈ 0.094-0.098 nm-1. When a fibril is stretched, the gap zones move apart, and the fibril strain is measured from the percentage shift in D, as measured from the SAXS pattern.21-23 The real-time acquisition of a sequence of sufficiently intense SAXS patterns is possible at third-generation synchrotron sources, because of the high photon flux. Hence when synchrotron diffraction is combined with a micromechanical test setup, the macroscopic and nanometer-level strains can be measured simultaneously. Such experiments have been performed for native unmineralized collagen,21 cross-link-deficient collagen,22 and mineralized tendon,23 but, to the best of our knowledge, not for bone. We carried out strain-controlled tensile tests of parallelfibered bone from femoral bovine bone, at constant strain rate, using a tensile stage made at our internal Max Planck Institute workshop and adapted to beamline A2, HASYLABDESY (Hamburg, Germany). To minimize tissue strain measurement errors arising from compliance effects in our microtensile tests, we used noncontact video extensometry to measure tissue strain T. The tissue strain is defined as the percent increase in separation between two reference points on the bone sample, relative to their separation when the sample is unstressed. The typical load-deformation curve of bone showed an initial elastic range up to 0.5-0.6% strain, followed by a slower rate of stress increase with strain following the elastic/inelastic transition (in the postyield regime). We used the third-order peak for measuring the changes in the fibril D-period. Figure 1 shows the ratio of the fibril strain F to tissue strain T as a function of the elastic modulus of the specimen. The elastic modulus was not varied in a controlled way but had a naturally occurring scatter in the samples tested. The figure includes (a) samples that were either stretched continuously to failure in the elastic regime and (b) samples loaded stepwise to successively higher stress levels, allowed to relax, following which the SAXS patterns were measured at different points along the sample length. The ratio lies between 0 and 1 and increases with the elastic modulus. Since the modulus increases with mineral content, this figure shows that for samples with higher mineral content the difference between fibril and tissue strain decreases. To show what happens to the fibrils in the postyield regime, in Figure 2 we show the variation of fibrillar strain with tissue strain for one sample. The first SAXS pattern was taken at zero applied strain, and from tissue strains of ∼0.4%, SAXS patterns were continually taken up to sample Nano Lett., Vol. 5, No. 10, 2005
Figure 1. Fibril strain F is less than the total applied tissue strain T and increases with increasing elastic modulus. The solid line is a visual guide. Triangles are averages of strain values at five spatially separated points along the tissue (error bars are standard deviations), and circles are measured at a single point on the tissue.
Figure 2. Fibrils stretch with increasing tissue strain up to around the elastic/inelastic transition point, then approach a constant value. In the sample shown, the solid lines show the initial increase of fibril strain and the final saturation value of ∼0.5%. The dotted line denotes the elastic/inelastic transition. Inset: Macroscopic stress vs tissue strain for the same sample.
failure at ∼1.3% tissue strain. The inset shows the stresstissue strain curve. For tissue strains e0.7%, the fibril and tissue strain both increase. For larger strains, we see a leveling off of the fibril strain, approaching a constant value of ∼ 0.5%. Because this saturation occurs after the elastic/ inelastic transition, we conjecture that when the tissue is strained beyond the yield point the fibrils do not stretch any more, but they also do not relax back to zero strain. To check that the fibril strain was homogeneous along the sample, stepwise straining experiments were carried out, and the SAXS pattern at five equidistantly spaced points along the sample length were measured (Figure 3). For a given tissue strain, there are no significant variations of fibril strain across the sample. Hence, the average of the fibril strain 2109
Figure 3. Bone fibrillar deformation is homogeneous along the length of the sample, and hence the difference between fibril and tissue strain is most likely not due to local strain variations. SAXS patterns corresponding to the five points at each tissue strain value are taken at 1 mm intervals along the length of the sample. The gray symbols give the average of the five points (error bars are standard deviations), and gray lines show the increase and final saturation value (analogous to Figure 2). Each set of five points are clearly separated in the vertical direction relative to the other sets, implying relative spatial homogeneity of fibril strain deformation.
Figure 4. Nanometer-level model for the deformation in mineralized collagen fibrils and extrafibrillar matrix. The white arrows indicate the direction of the relative motion of fibrils under applied tensile load in the vertical direction. The parallelogram between the fibrils shows the direction of shear stress in the extrafibrillar matrix; the magnitude of shear strain is highly exaggerated for visual clarity.
values across the length (5 mm) can be considered representative of the sample under investigation. On the basis of these results, a simple structural model for bone deformation at the nanostructural level is shown in Figure 4. The tensile strain is divided into two contributions: (i) a tensile stretching of the mineralized collagen fibrils, as visualized by an increase of the axial collagen 2110
period D, and (ii) a predominantly shear deformation of the interfibrillar matrix. This matrix is also mineralized to some extent, which affects its deformability. Hence, we conjecture that a comparably small fraction of interfibrillar mineral may have a significant impact on the mechanical behavior of bone tissue.24 Beyond the yield point, the mechanisms observed at the micron length scale, such as microcracking12 and ligament bridging,15 do not seem to cause relaxation of fibril strain, as seen from Figure 2. Since the fibers are surrounded by extrafibrillar matrix, a possible mechanism could be that a critical interfacial shear strength between the fibril and the matrix is exceeded when the bone is stretched above the yield point. When this happens, matrix flows past the fibrils, resulting in frictional losses. In this interpretation, such a stick/slip matrix flow past the mineralized fibrils could transmit a constant flow shear stress between fibrils, maintaining a constant strain in the fibrils beyond the yield point. As a corollary, no softening in the stress-strain curve would be expected, which is consistent with experimental observations. The large work of fracture under the yield portion of the stress-strain curve may arise directly due to this frictional dissipation in bone at the nanoscale, as has recently been proposed, via sacrificial bonds, to occur in bone.25 We suggest that the macroscopic yield stress (∼60-80 MPa for our slow strain rates) is close to the shear strength between the fibril and the extrafibrillar matrix. In the yield regime, the phenomenon of diffuse microcracking, observed using light and confocal microscopy for a range of bone tissues subjected to impact loading,26 could arise due to the formation of gaps axially between the fibrils. The composite bone material would hence show irreversible deformation, even though the individual fibrils may not be composed of a plastic (or ductile) material. In summary, the fiber matrix shearing mechanisms here are reminiscent of the lap-joint model16,17 for bone deformation at the level of the individual collagen molecule and mineral particles but are operative at the next level of hierarchical architecture.2 Regarding the mechanical properties of the bone nanocomposite, our proposed model brings out the crucial role of the fibril-matrix interface region, which is an amorphous, hydrated interfibrillar matrix consisting of proteins (e.g., osteopontin27,28) and protein-polysaccharide complexes such as proteoglycans.29,30 The combination of a stiff element with a surrounding, more ductile one at the nanometer scale is also found in tendon22 and nacre, among other biological composites. It appears that the coupling of a stiff fibrous material (here, the mineralized fibril) with a more ductile extrafibrillar material and the creation of a high specific area due to the nanometer scale of the constituents are common features in natural composite materials, resulting in a stiff structure with a relatively high work of fracture. Acknowledgment. We thank G. Benecke, M. Dommach, W. Katz, M. Kerschnitzki, P. Leibner, A. M. Martins, W. Nierenz, and H. Pitas for technical assistance. H.S.G. thanks Ingo Burgert and Oskar Paris for very interesting discussions. H.S.G., W.W., H.D.W., and P.F. thank the German-Israeli Nano Lett., Vol. 5, No. 10, 2005
Foundation (Project No. I-800-180.10\2003) for financial support for collaboration. P.R. acknowledges support from the Austrian Social Insurance for Occupational Risk, the WGKK (Social Health Insurance Vienna), and the Austrian Science Fund (Project No. P16880-B13). Supporting Information Available: Materials and methods. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Currey, J. D. Hierarchies in biomineral structures. Science 2005, 309, 253. (2) Weiner, S.; Wagner, H. D. The material bone: Structure mechanical function relations. Annu. ReV. Mater. Sci. 1998, 28, 271-298. (3) Rho, J. Y.; Kuhn-Spearing, L.; Zioupos, P. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 1998, 20 (2), 92-102. (4) Li, X.; Chang, W.-C.; Chao, Y. J.; Wang, R.; Chang, M. Nanoscale structural and mechanical characterization of a natural nanocomposite material: The shell of red abalone. Nano Lett. 2004, 4 (4), 613617. (5) Kamat, S.; Su, X.; Ballarini, R.; Heuer, A. H. Structural basis for the fracture toughness of the shell of the conch Strombus gigas. Nature 2000, 405 (6790), 1036-1040. (6) Aizenberg, J.; Weaver, J. C.; Thanawala, M. S.; Sundar, V. C.; Morse, D. E.; Fratzl, P. Skeleton of Euplectella sp.: Structural hierarchy from the nanoscale to the macroscale. Science 2005, 309, 275. (7) Keckes, J.; Burgert, I.; Fruhmann, K.; Muller, M.; Kolln, K.; Hamilton, M.; Burghammer, M.; Roth, S. V.; Stanzl-Tschegg, S.; Fratzl, P. Cell-wall recovery after irreversible deformation of wood. Nat. Mater. 2003, 2 (12), 810-814. (8) Landis, W. J.; Hodgens, K. J.; Arena, J.; Song, M. J.; McEwen, B. F. Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography. Microsc. Res. Tech. 1996, 33 (2), 192-202. (9) Rubin, M. A.; Jasiuk, L.; Taylor, J.; Rubin, J.; Ganey, T.; Apkarian, R. P. TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone 2003, 33 (3), 270-282. (10) Hartgerink, J. D.; Beniash, E.; Stupp, S. I. Self-assembly and mineralization of peptide-amphiphile nanofibers. Science 2001, 294 (5547), 1684-1688. (11) Zioupos, P. Ageing human bone: Factors affecting its biomechanical properties and the role of collagen. J. Biomater. Appl. 2001, 15 (3), 187-229. (12) Zioupos, P. On microcracks, microcracking, in-vivo, in-vitro, in-situ and other issues. J. Biomech. 1999, 32 (2), 209-211. (13) Braidotti, P.; Branca, F. P.; Stagni, L. Scanning electron microscopy of human cortical bone failure surfaces. J. Biomech. 1997, 30 (2), 155-62. (14) Hassenkam, T.; Fantner, G. E.; Cutroni, J. A.; Weaver, J. C.; Morse, D. E.; Hansma, P. K. High-resolution AFM imaging of intact and fractured trabecular bone. Bone 2004, 35 (1), 4-10.
Nano Lett., Vol. 5, No. 10, 2005
(15) Nalla, R. K.; Kinney, J. H.; Ritchie, R. O. Mechanistic fracture criteria for the failure of human cortical bone. Nat. Mater. 2003, 2 (3), 164168. (16) Gao, H. J.; Ji, B. H.; Jager, I. L.; Arzt, E.; Fratzl, P. Materials become insensitive to flaws at nanoscale: Lessons from nature. Proc. Natl. Acad.Sci. U.S.A. 2003, 100 (10), 5597-5600. (17) Jager, I.; Fratzl, P. Mineralized collagen fibrils: A mechanical model with a staggered arrangement of mineral particles. Biophys. J. 2000, 79 (4), 1737-1746. (18) Akiva, U.; Wagner, H. D.; Weiner, S. Modelling the threedimensional elastic constants of parallel-fibred and lamellar bone. J. Mater. Sci. 1998, 33 (6), 1497-1509. (19) Veis, A. Collagen fibrillar structure in mineralized and nonmineralized tissues. Curr. Opin. Solid State Mater. Sci. 1997, 2 (3), 370-378. (20) Bigi, A.; Ripamonti, A.; Koch, M. H. J.; Roveri, N. Calcified turkey leg tendon as structural model for bone mineralization. Int. J. Biol. Macromol. 1988, 10 (5), 282-286. (21) Sasaki, N.; Shukunami, N.; Matsushima, N.; Izumi, Y. Time-resolved X-ray diffraction from tendon collagen during creep using synchrotron radiation. J. Biomech. 1999, 32 (3), 285-292. (22) Puxkandl, R.; Zizak, I.; Paris, O.; Keckes, J.; Tesch, W.; Bernstorff, S.; Purslow, P.; Fratzl, P. Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Philos. Trans. R. Soc. London, Ser. B 2002, 357 (1418), 191-197. (23) Gupta, H. S.; Messmer, P.; Roschger, P.; Bernstorff, S.; Klaushofer, K.; Fratzl, P. Synchrotron diffraction study of deformation mechanisms in mineralized tendon. Phys. ReV. Lett. 2004, 93 (15), 158101. (24) Currey, J. D. Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content. J. Biomech. 2004, 37 (4), 549-556. (25) Fantner, G.; Hassenkam, T.; Kindt, J. H.; Weaver, J. C.; Birkedal, H.; Pechenik, L.; Cutroni, J. A.; Cidade, G. A. G.; Stucky, G. D.; Morse, D. E.; Hansma, P. K. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat. Mater. 2005, 4, 612-616. (26) Zioupos, P.; Currey, J. D.; Sedman, A. J. An examination of the micromechanics of failure of bone and antler by acoustic-emission tests and laser-scanning-confocal-microscopy. Med. Eng. Phys. 1994, 16 (3), 203-212. (27) Sodek, J.; Ganss, B.; McKee, M. D. Osteopontin. Crit. ReV. Oral Biol. Med. 2000, 11 (3), 279-303. (28) Nanci, A. Content and distribution of noncollagenous matrix proteins in bone and cementum: Relationship to speed of formation and collagen packing density. J. Struct. Biol. 1999, 126 (3), 256-269. (29) Cribb, A. M.; Scott, J. E. Tendon response to tensile-stresssAn ultrastructural unvestigation of collagen-proteoglycan interactions in stressed tendon. J. Anat. 1995, 187, 423-428. (30) Scott, J. E. Elasticity in extracellular matrix ‘shape modules’ of tendon, cartilage, etc. A sliding proteoglycan-filament model. J. Physiol. 2003, 553 (2), 335-343.
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