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Hydration and radiation effects on the residual stress state of cortical bone
Acta Biomaterialia 9 (2013) 9503–9507
Contents lists available at ScienceDirect
Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat
Hydration and radiation effects on the residual stress state of cortical bone Patrick K.M. Tung a, Stephen Mudie b, John E. Daniels a,⇑ a b
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia The Australian Synchrotron, Clayton, Victoria 3168, Australia
a r t i c l e
i n f o
Article history: Received 17 April 2013 Received in revised form 23 June 2013 Accepted 22 July 2013 Available online 31 July 2013 Keywords: Residual stress Hydroxyapatite Collagen Hydration Radiation damage
a b s t r a c t The change in the biaxial residual stress state of hydroxyapatite crystals and collagen fibrillar structure in sections of bovine cortical bone has been investigated as a function of dehydration and radiation dose using combined small- and wide-angle X-ray scattering. It is shown that dehydration of the bone has a pronounced effect on the residual stress state of the crystalline phase, while the impact of radiation damage alone is less dramatic. In the initial hydrated state, a biaxial compressive stress of approximately 150 MPa along the bone axis exists in the hydroxyapatite crystals. As water evaporates from the bone material, the stress state moves to a tensile state of approximately 100 MPa. The collagen fibrillar structure is initially in a tensile residual stress state when the bone is hydrated and the state increases in magnitude slightly with dehydration. Radiation dose in continually hydrated samples also reduces the initial biaxial compressive stress magnitude in the hydroxyapatite phase; however, the stress remains compressive. Radiation exposure alone does not appear to affect the stress state of the collagen fibrillar structure. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Structural biological materials are of great interest to researchers across multiple fields due to their remarkable mechanical properties. Cortical bone, for example, shows an excellent combination of strength, toughness and ductility in a lightweight structure built from simple motifs [1]. Such mechanical properties exhibited by cortical bone are attributed to its hierarchical structure, which consists of crystalline hydroxyapatite nanoparticles incorporated into a collagen fibrillar structure, which are in turn structured at the mesoscopic scale [1]. A critical constituent of the cortical bone structure is water. It is of vital importance, as hydrated and dehydrated cortical bone have vastly different mechanical properties, yet the mechanisms that drive this disparity are still unclear [2]. Studies have revealed that hydrated bone typically has higher ductility and toughness compared to dehydrated bone [3]. In order to understand the deformation mechanisms that give rise to the exceptional mechanical properties, it is essential that the effect of water in bone mechanics receives considerable attention. In biomimetics, information derived from research into bone hydration may be applied to the development of enhanced materials inspired by the multi-length-scale structure of bone [4]. Additionally, computer modelling of bone can be refined to attempt
⇑ Corresponding author. Tel.: +61 2 9385 5607; fax: +61 2 9385 6565. E-mail address: [email protected] (J.E. Daniels).
to reflect its true properties [5], which has many potential medical implications. One of the key experimental techniques for understanding the structure property relationships in bone has been synchrotron Xray scattering. This technique is extremely powerful at probing the multi-length-scale structure of cortical bone and characterizing applied and residual stress states of the bone constituents. Residual stresses are of particular interest as they remain in the structure after external forces have been removed from the material and have significant influence on mechanical properties [6]. Residual stresses occur at multiple length scales, from the microscale residual stresses of the hydroxyapatite crystals in collagen fibrillar structures to the macroscale stresses associated with whole bone growth. It has been noted that the macroscale residual stress is released when the bone is cut into smaller pieces [7]. Numerous studies have employed synchrotron radiation to elucidate the residual stress in both hydroxyapatite crystals and collagen fibrils within the cortical bone material [7–12]. The sin2w method was used to determine the residual stress of a bulk bovine femoral diaphysis [13,14] and found hydroxyapatite particles to be under tensile stress at the surface, transitioning to compressive stress a few millimetres below the surface [15]. Hydration as a variable in the stress state of cortical bone has also been considered [9]. Here, the authors showed decreasing compressive residual stress state in the hydroxyapatite nanoparticles along the bone axis as the bone hydrates. Another important consideration in making such quantitative studies about the structure of biological materials is the magnitude
1742-7061/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actbio.2013.07.028
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of radiation dose that the material receives during measurement. It has been shown by Barth et al. [16] that radiation doses considerably degrade the strength, ductility and toughness of human cortical bone due to mechanisms at various length scales, including degradation of collagen molecules and reduced fibrillar sliding. This is likely related to the observed changes in residual elastic strains in hydroxyapatite nanocrystals and collagen structures that have been found due to increasing radiation exposure [17]. Such information about the impact of radiation on bone material is also important for understanding the function of bone grafts which have undergone sterilization at high radiation doses [18]. The aim of this study was to quantitatively determine the effects of hydration and X-ray radiation dose on the residual stress states of the constituents of cortical bone. Small- and wide-angled X-ray scattering (SAXS/WAXS) was employed to examine the diffraction profiles of collagen and hydroxyapatite nanoparticles, respectively. This was performed on both dehydrating and constantly hydrated samples over a period of approximately 6 h, to a maximum radiation exposure of 2600 kGy. The biaxial residual stresses along the bone axis were assessed by the sin2w method, whereby measuring the change in d-spacing with corresponding w rotations away from the bone long axis allows the internal residual stress state to be quantified.
Fig. 1. Schematic of the experimental setup showing the diffraction images and the rotation axis, w, of the bone samples.
times in order to vary the radiation dose received. Within each set of 4 samples, a delay between the initial and subsequent measurements was varied from 15 min to approximately 3 h. The saline filled capillary showed no significant difference in WAXS scattered intensity to those in air, thus the additional water content was considered negligible for the remainder of the analysis.
2. Experimental 2.3. Data analysis 2.1. Sample preparation A bovine femur bone of a cow approximately 2 years old was purchased from a local supplier. The epiphyses of the femur were removed with a hacksaw and the surface of the remaining diaphysis was sanded down using 120 then 180 grade sandpaper to produce a homogeneous surface. A 5 cm thick cross-section was cut out from the shaft and attached to a piece of Perspex. A diamond saw (Struers Minitom) was used to extract 10 separate 1 1 10 mm3 samples from the centre of the compact cortical bone under water irrigation. Samples of this size possess limited macroscale residual stresses associated with the whole bone growth, and the stresses measured will be associated with the microscale structure of the material. The long edge of the samples was parallel to the bone axis. Prior to X-ray scattering measurements, samples were stored in refrigerated saline solution to ensure hydration. 2.2. X-ray measurements X-ray scattering experiments were carried out on the SAXS/ WAXS beamline of the Australian Synchrotron. The beam size used was 250 250 lm and the beam energy was 12 keV (k = 1.0322 Å). Silver behenate was used as a calibration standard to refine detector parameters, including distance, beam centre and tilts. A schematic of the setup is shown in Fig. 1. The rectangular bone samples were placed into sealed 1 mm diameter Kapton capillaries and mounted such that they could be rotated in the plane tilted 8° from perpendicular to the direction of the beam. This tilt was necessary to allow for measurement of SAXS and WAXS scattering information, where the scattering vector, q, could be adjusted from parallel to perpendicular to the long bone axis. Diffraction patterns were taken at every 10° rotation increment for a total of 90°, to obtain 10 diffraction images for each sample. Two sets of samples were measured: four samples were kept continuously in saline solution and four were allowed to dry for the duration of the X-ray measurements. The sequence of data collection was staggered throughout the eight samples, where samples in each set of four would be tested a unique number of
The data collection strategy produced 10 SAXS and WAXS diffraction images per measurement. Diffraction images from both SAXS and WAXS were integrated using the software package fit2D [19] to produce an intensity vs. q-vector profile. The SAXS pattern was ‘‘caked’’ (refer to Fig. 1) into 10° sectors to assess the anisotropy of the diffraction image. Characteristic peaks from both the SAXS and WAXS patterns were used to evaluate the nanoscale lattice spacing of the collagen fibril structure and hydroxyapatite nanoparticles, respectively. The (0 0 2) diffraction peak from the hydroxyapatite phase in the WAXS pattern and the third-order collagen peak in the SAXS pattern are fitted using asymmetric pseudo-Voigt functions. The variation of the positions and intensities of these peaks was assessed as a function of rotation angle, w, away from the bone long axis during the dehydration and radiation exposures. The biaxial residual stress was calculated from the shifts in lattice spacing that occur as a function of angle, w, between the scattering vector and the long bone axis according to Eqs. (1) and (2) below [14]. The sin2w method, which monitors the shifts in lattice spacings that occur from w-rotations, was used to calculate the biaxial residual stress state of the hydroxyapatite crystals [14]. In our case, the residual stress is calculated using the rotation angles from 0 to 50°, as patterns from 60–90° have significant scattered intensity from non-fibril hydroxyapatite.
ru ¼ 1
m00
½hkl ½hkl S d/;w¼0 2 2
1 1þv S2 ¼ 2 E
ð1Þ
ð2Þ
where ru is the biaxial residual stress, m00 is the gradient of the data ½hkl in a d-spacing vs. sin2w graph, 12 S2 is an X-ray elasticity constant ½hkl (XEC), d/;w¼0 is the d-spacing at w = 0 and {hkl} is the specfic reflection. The residual stress, presented in megapascals, requires the approximation of an XEC for the material, which is a set of macroscopic elastic constants used in stress measurements by Xray diffraction. This method is described in more detail by He [14]. In the case of collagen, the XEC is taken as 0.4 103 MPa1
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(where E = 3.75 GPa and v = 0.5) [20] and for hydroxyapatite crystals an XEC of 10.2 106 MPa1 was used [8]. 2.4. Estimation of radiation dose For the current experimental setup, the radiation dose on the sample is calculated from the incident X-ray flux of 1 1012 photons s–1 and reported mass attenuation coefficient of cortical bone of 20 cm2 g–1 [21,22]. The exposure time for each stress measurement was 20 s. From these values the total irradiation dose is calculated as,
Total irradiated dose ¼
ð1 expapl Þ ð/eEÞ t M
ð3Þ
where a (cm2 g1) is the mass attenuation coefficient, q (g cm3) is the density, l (cm) is the thickness of the material, / (photons s1) is the radiation flux, e (J eV1) is the elementary charge of 1.6 1019, E (eV) is the energy of the beam, M (kg) is the mass of the sample and t (s) is the exposure time. The irradiated mass was calculated with the assumption that the irradiated area was 500 500 lm due to the eccentricity of the rotation axis. 3. Results and discussion Fig. 2 shows the typical WAXS diffraction patterns of a bovine cortical bone where the sample is rotated such that the scattering vector is sampled in 10° increments from parallel to perpendicular to the bone axis. The preferred orientation of the hydroxyapatite nanocrystals with their [0 0 2] direction parallel to the long axis of the bone is clear from the variation in intensity of the peak at 18.8 nm1 in Fig. 2. Likewise, Fig. 3 shows the variation in the intensity of the third-order collagen peak at 0.1 nm1 for the same sequence of rotation angles, clearly indicating a preferred orientation of the collagen molecules along the bone axis. These results demonstrate the strong crystallographic texture and aligned collagen structure in cortical bone.
Fig. 3. Intergrated intensity profile of the SAXS diffraction pattern where the scattering vector is parallel and perpendicular to the bone long axis.
Fig. 4. Biaxial residual stress in hydroxyapatite crystals as a function of drying time for four samples during dehydration. The insets show the sin2w plots for typical tensile and compressive residual stress states, prior and subsequent to significant dehydration, respectively. Each trace represents a different sample.
Fig. 2. Intergrated intensity profile of the WAXS diffraction pattern where the scattering vector is rotated in 10° increments from the bone long axis. The inset shows a representative peak fit using an asymmetric pseudo-Voigt peak shape.
Fig. 4 shows the biaxial residual stress along the bone axis in the hydroxyapatite nanoparticles calculated by the sin2w method as a function of time for four hydrated samples m which were allowed to then dehydrate in air. It is clear that they are initially under significant biaxial compressive stress, where the lattice spacing
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along the bone long axis is less than perpendicular to the bone long axis (Fig. 4, bottom inset). Upon commencing measurements, the compressive biaxial residual stress immediately falls and becomes tensile along the bone axis within a few minutes of the start of dehydration (Fig. 4, top inset). For the samples measured, the time between the initial data acquisition and the next subsequent acquisition was varied. In each case, the first subsequent measurement showed a dramatic change in the stress state of the crystalline component of the bone material. However, the magnitude of the change is correlated to the time between measurements and not the total number of measurements. This indicates that the variations observed here are primarily due to sample hydration and not initial radiation doses, although, as shown later, initial radiation effects may be included, though they are of significantly lower magnitude. It should be noted that the longitudinal strain component (the lattice spacing along the bone axis) decreases with increasing drying time. This shows that the full deviatoric stress state of the hydroxyapatite particles is complex and incorporates both an isotropic and a biaxial component, which vary during drying. The variation in the initial residual stress values of each sample is attributed to the positions from the bulk bone specimen that they were segmented from. Yamada and Tadano [7] observed macroscale residual stress variations in the bone cross-section which likely affects the microscale stresses developed during bone growth. It is also noted that the biaxial residual stress of the hydroxyapatite particles along the bone axis in the dehydrating samples slowly decreases after its maximum tensile value is reached. The mechanism for this is unclear; however, it could be that subsequent radiation damage in the already dehydrated samples is the cause. The collagen residual stress state for the same set of dehydrating samples is shown in Fig. 5. Here, an initial biaxial tensile stress along the bone axis is observed as evidenced by the slightly higher d-spacing along the bone axis as opposed to angles away from the bone axis (Fig. 5, inset). The trend of stress in the collagen fibrillar structure shows a slightly increasing biaxial tensile stress with time during the drying process. The significant variation in the initial value of the collagen stress for each sample is again attributed to the various positions within the cortical bone macrostructure that samples have been sectioned from, as described above. The second set of samples were placed inside saline-filled capillaries during identical X-ray scattering measurements. As there is
an absence of dehydration in these samples, the residual stress was measured only against the doses of radiation each sample received. Here, the magnitude of the initial compressive biaxial residual stress of the crystalline hydroxyapatite component also decreased with subsequent X-ray measurements, as shown in Fig. 6. However, the dramatic move from compressive to tensile biaxial stress observed in the dehydrating samples was not observed here. The reduction in the compressive stress is more subtle and generally resulted in an approximately 50% reduction in the compressive residual stress value during the measurement sequence. At no time during the measurements was the residual stress state of the hydroxyapatite crystals in the hydrated samples observed to become tensile. For the same sample set, no significant change in collagen structure observed by the SAXS patterns could be observed (Fig. 7). Such a change in the biaxial residual stress state of the hydroxyapatite phase with hydration level (Fig. 4) will certainly have an effect on the material mechanical properties. In particular, it would be expected that the tensile strength along the long bone axis would be dramatically reduced after dehydration. Initially the brittle crystalline component is under a compressive stress and thus tensile loads would act to relieve that stress; however, once the brittle crystalline component is under tensile load (after dehydration), further loading would likely result in fracture and failure of that structural component. These results correlate with the changes in tensile strength properties that have been observed in cortical bone before and after dehydration, where the elastic modulus is larger in dehydrated bone [3]. These results also provide some insight to the mechanism by which radiation affects the properties of bone. Barth et al. [23] have shown that the mechanical properties of bone are dramatically affected by X-ray irradiation doses of the order of a few hundred kilograys. The authors used UV Raman spectroscopy to observe variations in the collagen structure, which they conclude is a contributing factor to the degradation of mechanical properties. These observed changes correlate closely with the change in residual stress state from the current radiation dose study. Using the SAXS/WAXS method, the direct structure of the collagen is not accessible; however, the breakdown of the collagen structure within the bone fibrils has likely led to the relief of the initial residual stress state of the hydroxyapatite phase. The compressive biaxial residual stress state along the bone axis is reduced by 50% by radiation doses ofthe order of approximately 1500 kGy.
Fig. 5. Biaxial residual stress in drying collagen fibrils as a function of drying time. Each trace represents a different sample.
Fig. 6. Biaxial residual stress in hydroxyapatite crystals of hydrated samples as a function of irradiated dose. Each trace represents a different sample.
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DP130100415. The authors acknowledge the provision of beamtime under Australian Synchrotron proposal number AS113/ SAXS4041. Appendix A. Figures with essential colour discrimination Certain figures in this article, particularly Figs. 1–7, are difficult to interpret in black and white. The full colour images can be found in the on-line version, at http://dx.doi.org/10.1016/j.actbio.2013. 07.028.
References
Fig. 7. Biaxial residual stress in hydrated collagen as a function of irradiated dose. Each trace represents a different sample.
Both the hydrated and dry samples had clear indications of radiation damage after the experiments. Discoloration of the surface at the point of the beam intersection had occurred and it was observed that the samples fractured preferentially at this point during unmounting. It is clear from the results of this study that X-ray scattering experiments on bone materials should be performed with care of the hydration and radiation dose applied to the samples. It should also be noted that the dehydration rate of cortical bone will certainly be a function of the sample size. Here, very small samples were used that dehydrated rapidly. Experiments where in situ hydration is not possible would be likely to be improved by using larger samples; however, data to confirm this should be collected for any in situ experiments conducted. 4. Conclusion Water content has a significant effect on the residual stress of both hydroxyapatite crystals and the collagen structure in bone. The biaxial residual stress of hydroxyapatite is compressive along the bone axis when hydrated, and transitions into tensile stress as the bone dehydrates; for samples of geometry of 1 1 10 mm3, this transition occurs within 15 min and begins to plateau after approximately 1 h. The hydrated collagen begins under biaxial tensile stress and the stress increases at a slow rate as the bone dehydrates. Effects of hydration appear to occur independently of radiation dose. The effect of radiation damage in constantly hydrated specimens is less pronounced, though still evident. The biaxial compressive residual stress in hydroxyapatite decreases by approximately 50% from its initial value under irradiation doses up to 1500 kGy. There was no quantifiable effect on the stress state of collagen in bone due to radiation dose. Acknowledgements J.E.D. acknowledges financial support from an AINSE Research Fellowship. This work was supported under ARC Discovery Project
[1] Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci 2007;52:1263–334. [2] Nyman JS, Roy A, Shen XM, Acuna RL, Tyler JH, Wang XD. The influence of water removal on the strength and toughness of cortical bone. J Biomech 2006;39:931–8. [3] Seto J, Gupta HS, Zaslansky P, Wagner HD, Fratzl P. Tough lessons from bone: extreme mechanical anisotropy at the mesoscale. Adv Funct Mater 2008;18:1905–11. [4] Bhushan B. Biomimetics: lessons from nature – an overview. Philos Trans R Soc London, A 2009;367:1445–86. [5] Weinans H, Huiskes R, Grootenboer HJ. The behavior of adaptive boneremodelling simulation models. J Biomech 1992;25:1425–41. [6] Tadano S, Okoshi T. Residual stress in bone structure and tissue of rabbit’s tibiofibula. Bio-Med Mater Eng 2006;16:11–21. [7] Yamada S, Tadano S. Residual stress around the cortical surface in bovine femoral diaphysis. J Biomech Eng-Trans ASME 2010;132:044503-1–3-4. [8] Almer JD, Stock SR. Internal strains and stresses measured in cortical bone via high-energy X-ray diffraction. J Struct Biol 2005;152:14–27. [9] Almer JD, Stock SR. Micromechanical response of mineral and collagen phases in bone. J Struct Biol 2007;157:365–70. [10] Stock SR, Yuan F, Brinson LC, Almer JD. Internal strain gradients quantified in bone under load using high-energy X-ray scattering. J Biomech 2011;44:291–6. [11] Hoo RP, Fratzl P, Daniels JE, Dunlop JWC, Honkimaki V, Hoffman M. Cooperation of length scales and orientations in the deformation of bovine bone. Acta Biomater 2011;7:2943–51. [12] Yamada S, Tadano S, Fujisaki K. Residual stress distribution in rabbit limb bones. J Biomech 2011;44:1285–90. [13] Liu C, Huntz A-M, Lebrun J-L. Origin and development of residual stresses in the Ni–NiO system: in situ studies at high temperature by X-ray diffraction. Mater. Sci. Eng., A 1993;160:113–26. [14] He BB. Stress Measurement. Two-Dimensional X-ray Diffraction. Hoboken, NJ: John Wiley Sons; 2009. [15] Yamada S, Tadano S, Todoh M, Fujisaki K. Residual stress distribution in the bovine femoral diaphysis measured by synchrotron. J Biomech Sci Eng 2011;6:114–24. [16] Barth HD, Zimmermann EA, Schaible E, Tang SY, Alliston T, Ritchie RO. Characterization of the effects of X-ray irradiation on the hierarchical structure and mechanical properties of human cortical bone. Biomaterials 2011;32:8892–904. [17] Singhal A, Deymier-Black AC, Almer JD, Dunand DC. Effect of high-energy Xray doses on bone elastic properties and residual strains. J Mech Behav Biomed Mater 2011;4:1774–86. [18] Currey JD, Foreman J, Laketic I, Mitchell J, Pegg DE, Reilly GC. Effects of ionizing radiation on the mechanical properties of human bone. J Orthop Res 1997;15:111–7. [19] Hammersley AP, Svensson SO, Hanfland M, Fitch AN, Hausermann D. Twodimensional detector software: from real detector to idealized image or twotheta scan. High Pressure Res 1996;14:235–48. [20] Wenger MPE, Bozec L, Horton MA, Mesquida P. Mechanical properties of collagen fibrils. Biophys J 2007;93:1255–63. [21] Zhou H, Keall PJ, Graves EE. A bone composition model for Monte Carlo X-ray transport simulations. Med Phys 2009;36:1008–18. [22] White DR, Peaple LHJ, Crosby TJ. Measured attenuation coefficients at low photon energies (9.88–59.32 keV) for 44 materials and tissues. Radiat Res 1980;84:239–52. [23] Barth HD, Launey ME, MacDowell AA, Ager JW, Ritchie RO. On the effect of Xray irradiation on the deformation and fracture behavior of human cortical bone. Bone 2010;46:1475–85.
Contents lists available at ScienceDirect
Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat
Hydration and radiation effects on the residual stress state of cortical bone Patrick K.M. Tung a, Stephen Mudie b, John E. Daniels a,⇑ a b
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia The Australian Synchrotron, Clayton, Victoria 3168, Australia
a r t i c l e
i n f o
Article history: Received 17 April 2013 Received in revised form 23 June 2013 Accepted 22 July 2013 Available online 31 July 2013 Keywords: Residual stress Hydroxyapatite Collagen Hydration Radiation damage
a b s t r a c t The change in the biaxial residual stress state of hydroxyapatite crystals and collagen fibrillar structure in sections of bovine cortical bone has been investigated as a function of dehydration and radiation dose using combined small- and wide-angle X-ray scattering. It is shown that dehydration of the bone has a pronounced effect on the residual stress state of the crystalline phase, while the impact of radiation damage alone is less dramatic. In the initial hydrated state, a biaxial compressive stress of approximately 150 MPa along the bone axis exists in the hydroxyapatite crystals. As water evaporates from the bone material, the stress state moves to a tensile state of approximately 100 MPa. The collagen fibrillar structure is initially in a tensile residual stress state when the bone is hydrated and the state increases in magnitude slightly with dehydration. Radiation dose in continually hydrated samples also reduces the initial biaxial compressive stress magnitude in the hydroxyapatite phase; however, the stress remains compressive. Radiation exposure alone does not appear to affect the stress state of the collagen fibrillar structure. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Structural biological materials are of great interest to researchers across multiple fields due to their remarkable mechanical properties. Cortical bone, for example, shows an excellent combination of strength, toughness and ductility in a lightweight structure built from simple motifs [1]. Such mechanical properties exhibited by cortical bone are attributed to its hierarchical structure, which consists of crystalline hydroxyapatite nanoparticles incorporated into a collagen fibrillar structure, which are in turn structured at the mesoscopic scale [1]. A critical constituent of the cortical bone structure is water. It is of vital importance, as hydrated and dehydrated cortical bone have vastly different mechanical properties, yet the mechanisms that drive this disparity are still unclear [2]. Studies have revealed that hydrated bone typically has higher ductility and toughness compared to dehydrated bone [3]. In order to understand the deformation mechanisms that give rise to the exceptional mechanical properties, it is essential that the effect of water in bone mechanics receives considerable attention. In biomimetics, information derived from research into bone hydration may be applied to the development of enhanced materials inspired by the multi-length-scale structure of bone [4]. Additionally, computer modelling of bone can be refined to attempt
⇑ Corresponding author. Tel.: +61 2 9385 5607; fax: +61 2 9385 6565. E-mail address: [email protected] (J.E. Daniels).
to reflect its true properties [5], which has many potential medical implications. One of the key experimental techniques for understanding the structure property relationships in bone has been synchrotron Xray scattering. This technique is extremely powerful at probing the multi-length-scale structure of cortical bone and characterizing applied and residual stress states of the bone constituents. Residual stresses are of particular interest as they remain in the structure after external forces have been removed from the material and have significant influence on mechanical properties [6]. Residual stresses occur at multiple length scales, from the microscale residual stresses of the hydroxyapatite crystals in collagen fibrillar structures to the macroscale stresses associated with whole bone growth. It has been noted that the macroscale residual stress is released when the bone is cut into smaller pieces [7]. Numerous studies have employed synchrotron radiation to elucidate the residual stress in both hydroxyapatite crystals and collagen fibrils within the cortical bone material [7–12]. The sin2w method was used to determine the residual stress of a bulk bovine femoral diaphysis [13,14] and found hydroxyapatite particles to be under tensile stress at the surface, transitioning to compressive stress a few millimetres below the surface [15]. Hydration as a variable in the stress state of cortical bone has also been considered [9]. Here, the authors showed decreasing compressive residual stress state in the hydroxyapatite nanoparticles along the bone axis as the bone hydrates. Another important consideration in making such quantitative studies about the structure of biological materials is the magnitude
1742-7061/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actbio.2013.07.028
9504
P.K.M. Tung et al. / Acta Biomaterialia 9 (2013) 9503–9507
of radiation dose that the material receives during measurement. It has been shown by Barth et al. [16] that radiation doses considerably degrade the strength, ductility and toughness of human cortical bone due to mechanisms at various length scales, including degradation of collagen molecules and reduced fibrillar sliding. This is likely related to the observed changes in residual elastic strains in hydroxyapatite nanocrystals and collagen structures that have been found due to increasing radiation exposure [17]. Such information about the impact of radiation on bone material is also important for understanding the function of bone grafts which have undergone sterilization at high radiation doses [18]. The aim of this study was to quantitatively determine the effects of hydration and X-ray radiation dose on the residual stress states of the constituents of cortical bone. Small- and wide-angled X-ray scattering (SAXS/WAXS) was employed to examine the diffraction profiles of collagen and hydroxyapatite nanoparticles, respectively. This was performed on both dehydrating and constantly hydrated samples over a period of approximately 6 h, to a maximum radiation exposure of 2600 kGy. The biaxial residual stresses along the bone axis were assessed by the sin2w method, whereby measuring the change in d-spacing with corresponding w rotations away from the bone long axis allows the internal residual stress state to be quantified.
Fig. 1. Schematic of the experimental setup showing the diffraction images and the rotation axis, w, of the bone samples.
times in order to vary the radiation dose received. Within each set of 4 samples, a delay between the initial and subsequent measurements was varied from 15 min to approximately 3 h. The saline filled capillary showed no significant difference in WAXS scattered intensity to those in air, thus the additional water content was considered negligible for the remainder of the analysis.
2. Experimental 2.3. Data analysis 2.1. Sample preparation A bovine femur bone of a cow approximately 2 years old was purchased from a local supplier. The epiphyses of the femur were removed with a hacksaw and the surface of the remaining diaphysis was sanded down using 120 then 180 grade sandpaper to produce a homogeneous surface. A 5 cm thick cross-section was cut out from the shaft and attached to a piece of Perspex. A diamond saw (Struers Minitom) was used to extract 10 separate 1 1 10 mm3 samples from the centre of the compact cortical bone under water irrigation. Samples of this size possess limited macroscale residual stresses associated with the whole bone growth, and the stresses measured will be associated with the microscale structure of the material. The long edge of the samples was parallel to the bone axis. Prior to X-ray scattering measurements, samples were stored in refrigerated saline solution to ensure hydration. 2.2. X-ray measurements X-ray scattering experiments were carried out on the SAXS/ WAXS beamline of the Australian Synchrotron. The beam size used was 250 250 lm and the beam energy was 12 keV (k = 1.0322 Å). Silver behenate was used as a calibration standard to refine detector parameters, including distance, beam centre and tilts. A schematic of the setup is shown in Fig. 1. The rectangular bone samples were placed into sealed 1 mm diameter Kapton capillaries and mounted such that they could be rotated in the plane tilted 8° from perpendicular to the direction of the beam. This tilt was necessary to allow for measurement of SAXS and WAXS scattering information, where the scattering vector, q, could be adjusted from parallel to perpendicular to the long bone axis. Diffraction patterns were taken at every 10° rotation increment for a total of 90°, to obtain 10 diffraction images for each sample. Two sets of samples were measured: four samples were kept continuously in saline solution and four were allowed to dry for the duration of the X-ray measurements. The sequence of data collection was staggered throughout the eight samples, where samples in each set of four would be tested a unique number of
The data collection strategy produced 10 SAXS and WAXS diffraction images per measurement. Diffraction images from both SAXS and WAXS were integrated using the software package fit2D [19] to produce an intensity vs. q-vector profile. The SAXS pattern was ‘‘caked’’ (refer to Fig. 1) into 10° sectors to assess the anisotropy of the diffraction image. Characteristic peaks from both the SAXS and WAXS patterns were used to evaluate the nanoscale lattice spacing of the collagen fibril structure and hydroxyapatite nanoparticles, respectively. The (0 0 2) diffraction peak from the hydroxyapatite phase in the WAXS pattern and the third-order collagen peak in the SAXS pattern are fitted using asymmetric pseudo-Voigt functions. The variation of the positions and intensities of these peaks was assessed as a function of rotation angle, w, away from the bone long axis during the dehydration and radiation exposures. The biaxial residual stress was calculated from the shifts in lattice spacing that occur as a function of angle, w, between the scattering vector and the long bone axis according to Eqs. (1) and (2) below [14]. The sin2w method, which monitors the shifts in lattice spacings that occur from w-rotations, was used to calculate the biaxial residual stress state of the hydroxyapatite crystals [14]. In our case, the residual stress is calculated using the rotation angles from 0 to 50°, as patterns from 60–90° have significant scattered intensity from non-fibril hydroxyapatite.
ru ¼ 1
m00
½hkl ½hkl S d/;w¼0 2 2
1 1þv S2 ¼ 2 E
ð1Þ
ð2Þ
where ru is the biaxial residual stress, m00 is the gradient of the data ½hkl in a d-spacing vs. sin2w graph, 12 S2 is an X-ray elasticity constant ½hkl (XEC), d/;w¼0 is the d-spacing at w = 0 and {hkl} is the specfic reflection. The residual stress, presented in megapascals, requires the approximation of an XEC for the material, which is a set of macroscopic elastic constants used in stress measurements by Xray diffraction. This method is described in more detail by He [14]. In the case of collagen, the XEC is taken as 0.4 103 MPa1
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(where E = 3.75 GPa and v = 0.5) [20] and for hydroxyapatite crystals an XEC of 10.2 106 MPa1 was used [8]. 2.4. Estimation of radiation dose For the current experimental setup, the radiation dose on the sample is calculated from the incident X-ray flux of 1 1012 photons s–1 and reported mass attenuation coefficient of cortical bone of 20 cm2 g–1 [21,22]. The exposure time for each stress measurement was 20 s. From these values the total irradiation dose is calculated as,
Total irradiated dose ¼
ð1 expapl Þ ð/eEÞ t M
ð3Þ
where a (cm2 g1) is the mass attenuation coefficient, q (g cm3) is the density, l (cm) is the thickness of the material, / (photons s1) is the radiation flux, e (J eV1) is the elementary charge of 1.6 1019, E (eV) is the energy of the beam, M (kg) is the mass of the sample and t (s) is the exposure time. The irradiated mass was calculated with the assumption that the irradiated area was 500 500 lm due to the eccentricity of the rotation axis. 3. Results and discussion Fig. 2 shows the typical WAXS diffraction patterns of a bovine cortical bone where the sample is rotated such that the scattering vector is sampled in 10° increments from parallel to perpendicular to the bone axis. The preferred orientation of the hydroxyapatite nanocrystals with their [0 0 2] direction parallel to the long axis of the bone is clear from the variation in intensity of the peak at 18.8 nm1 in Fig. 2. Likewise, Fig. 3 shows the variation in the intensity of the third-order collagen peak at 0.1 nm1 for the same sequence of rotation angles, clearly indicating a preferred orientation of the collagen molecules along the bone axis. These results demonstrate the strong crystallographic texture and aligned collagen structure in cortical bone.
Fig. 3. Intergrated intensity profile of the SAXS diffraction pattern where the scattering vector is parallel and perpendicular to the bone long axis.
Fig. 4. Biaxial residual stress in hydroxyapatite crystals as a function of drying time for four samples during dehydration. The insets show the sin2w plots for typical tensile and compressive residual stress states, prior and subsequent to significant dehydration, respectively. Each trace represents a different sample.
Fig. 2. Intergrated intensity profile of the WAXS diffraction pattern where the scattering vector is rotated in 10° increments from the bone long axis. The inset shows a representative peak fit using an asymmetric pseudo-Voigt peak shape.
Fig. 4 shows the biaxial residual stress along the bone axis in the hydroxyapatite nanoparticles calculated by the sin2w method as a function of time for four hydrated samples m which were allowed to then dehydrate in air. It is clear that they are initially under significant biaxial compressive stress, where the lattice spacing
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along the bone long axis is less than perpendicular to the bone long axis (Fig. 4, bottom inset). Upon commencing measurements, the compressive biaxial residual stress immediately falls and becomes tensile along the bone axis within a few minutes of the start of dehydration (Fig. 4, top inset). For the samples measured, the time between the initial data acquisition and the next subsequent acquisition was varied. In each case, the first subsequent measurement showed a dramatic change in the stress state of the crystalline component of the bone material. However, the magnitude of the change is correlated to the time between measurements and not the total number of measurements. This indicates that the variations observed here are primarily due to sample hydration and not initial radiation doses, although, as shown later, initial radiation effects may be included, though they are of significantly lower magnitude. It should be noted that the longitudinal strain component (the lattice spacing along the bone axis) decreases with increasing drying time. This shows that the full deviatoric stress state of the hydroxyapatite particles is complex and incorporates both an isotropic and a biaxial component, which vary during drying. The variation in the initial residual stress values of each sample is attributed to the positions from the bulk bone specimen that they were segmented from. Yamada and Tadano [7] observed macroscale residual stress variations in the bone cross-section which likely affects the microscale stresses developed during bone growth. It is also noted that the biaxial residual stress of the hydroxyapatite particles along the bone axis in the dehydrating samples slowly decreases after its maximum tensile value is reached. The mechanism for this is unclear; however, it could be that subsequent radiation damage in the already dehydrated samples is the cause. The collagen residual stress state for the same set of dehydrating samples is shown in Fig. 5. Here, an initial biaxial tensile stress along the bone axis is observed as evidenced by the slightly higher d-spacing along the bone axis as opposed to angles away from the bone axis (Fig. 5, inset). The trend of stress in the collagen fibrillar structure shows a slightly increasing biaxial tensile stress with time during the drying process. The significant variation in the initial value of the collagen stress for each sample is again attributed to the various positions within the cortical bone macrostructure that samples have been sectioned from, as described above. The second set of samples were placed inside saline-filled capillaries during identical X-ray scattering measurements. As there is
an absence of dehydration in these samples, the residual stress was measured only against the doses of radiation each sample received. Here, the magnitude of the initial compressive biaxial residual stress of the crystalline hydroxyapatite component also decreased with subsequent X-ray measurements, as shown in Fig. 6. However, the dramatic move from compressive to tensile biaxial stress observed in the dehydrating samples was not observed here. The reduction in the compressive stress is more subtle and generally resulted in an approximately 50% reduction in the compressive residual stress value during the measurement sequence. At no time during the measurements was the residual stress state of the hydroxyapatite crystals in the hydrated samples observed to become tensile. For the same sample set, no significant change in collagen structure observed by the SAXS patterns could be observed (Fig. 7). Such a change in the biaxial residual stress state of the hydroxyapatite phase with hydration level (Fig. 4) will certainly have an effect on the material mechanical properties. In particular, it would be expected that the tensile strength along the long bone axis would be dramatically reduced after dehydration. Initially the brittle crystalline component is under a compressive stress and thus tensile loads would act to relieve that stress; however, once the brittle crystalline component is under tensile load (after dehydration), further loading would likely result in fracture and failure of that structural component. These results correlate with the changes in tensile strength properties that have been observed in cortical bone before and after dehydration, where the elastic modulus is larger in dehydrated bone [3]. These results also provide some insight to the mechanism by which radiation affects the properties of bone. Barth et al. [23] have shown that the mechanical properties of bone are dramatically affected by X-ray irradiation doses of the order of a few hundred kilograys. The authors used UV Raman spectroscopy to observe variations in the collagen structure, which they conclude is a contributing factor to the degradation of mechanical properties. These observed changes correlate closely with the change in residual stress state from the current radiation dose study. Using the SAXS/WAXS method, the direct structure of the collagen is not accessible; however, the breakdown of the collagen structure within the bone fibrils has likely led to the relief of the initial residual stress state of the hydroxyapatite phase. The compressive biaxial residual stress state along the bone axis is reduced by 50% by radiation doses ofthe order of approximately 1500 kGy.
Fig. 5. Biaxial residual stress in drying collagen fibrils as a function of drying time. Each trace represents a different sample.
Fig. 6. Biaxial residual stress in hydroxyapatite crystals of hydrated samples as a function of irradiated dose. Each trace represents a different sample.
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DP130100415. The authors acknowledge the provision of beamtime under Australian Synchrotron proposal number AS113/ SAXS4041. Appendix A. Figures with essential colour discrimination Certain figures in this article, particularly Figs. 1–7, are difficult to interpret in black and white. The full colour images can be found in the on-line version, at http://dx.doi.org/10.1016/j.actbio.2013. 07.028.
References
Fig. 7. Biaxial residual stress in hydrated collagen as a function of irradiated dose. Each trace represents a different sample.
Both the hydrated and dry samples had clear indications of radiation damage after the experiments. Discoloration of the surface at the point of the beam intersection had occurred and it was observed that the samples fractured preferentially at this point during unmounting. It is clear from the results of this study that X-ray scattering experiments on bone materials should be performed with care of the hydration and radiation dose applied to the samples. It should also be noted that the dehydration rate of cortical bone will certainly be a function of the sample size. Here, very small samples were used that dehydrated rapidly. Experiments where in situ hydration is not possible would be likely to be improved by using larger samples; however, data to confirm this should be collected for any in situ experiments conducted. 4. Conclusion Water content has a significant effect on the residual stress of both hydroxyapatite crystals and the collagen structure in bone. The biaxial residual stress of hydroxyapatite is compressive along the bone axis when hydrated, and transitions into tensile stress as the bone dehydrates; for samples of geometry of 1 1 10 mm3, this transition occurs within 15 min and begins to plateau after approximately 1 h. The hydrated collagen begins under biaxial tensile stress and the stress increases at a slow rate as the bone dehydrates. Effects of hydration appear to occur independently of radiation dose. The effect of radiation damage in constantly hydrated specimens is less pronounced, though still evident. The biaxial compressive residual stress in hydroxyapatite decreases by approximately 50% from its initial value under irradiation doses up to 1500 kGy. There was no quantifiable effect on the stress state of collagen in bone due to radiation dose. Acknowledgements J.E.D. acknowledges financial support from an AINSE Research Fellowship. This work was supported under ARC Discovery Project
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