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Similar damage initiation but different failure behavior in trabecular and cortical bone tissue
J O U R N A L O F T H E M E C H A N I C A L B E H AV I O R O F B I O M E D I C A L M AT E R I A L S
4 (2011) 1787–1796
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/jmbbm
Research paper
Similar damage initiation but different failure behavior in trabecular and cortical bone tissue M.E. Szabó a , J. Zekonyte b , O.L. Katsamenis a , M. Taylor a , P.J. Thurner a,∗ a Bioengineering Science Research Group, School of Engineering Sciences, Faculty of Engineering and the Environment, University of
Southampton, Southampton, SO17 1BJ, UK b National Centre for Advanced Tribology at Southampton, School of Engineering Sciences, Faculty of Engineering and the Environment, University of Southampton, Southampton, SO17 1BJ, UK
A R T I C L E
I N F O
A B S T R A C T
Article history:
The mechanical properties of bone tissue are reflected in its micro- and nanostructure
Received 6 April 2011
as well as in its composition. Numerous studies have compared the elastic mechanical
Received in revised form
properties of cortical and trabecular bone tissue and concluded that cortical bone tissue is
20 May 2011
stiffer than trabecular bone tissue. This study compared the progression of microdamage
Accepted 28 May 2011
leading to fracture and the related local strains during this process in trabecular and cortical
Published online 6 June 2011
bone tissue. Unmachined single bovine trabeculae and similarly-sized cortical bovine bone samples were mechanically tested in three-point bending and concomitantly imaged to
Keywords:
assess local strains using a digital image correlation technique. The bone whitening effect
Cortical
was used to detect microdamage formation and propagation. This study found that cortical
Trabeculae
bone tissue exhibits significantly lower maximum strains (trabecular 36.6% ± 14% vs.
Microdamage
cortical 22.9% ± 7.4%) and less accumulated damage (trabecular 16100 ± 8800 pix/mm2
Strain
vs. cortical 8000 ± 3400 pix/mm2 ) at failure. However, no difference was detected for the
Three-point bending
maximum local strain at whitening onset (trabecular 5.8% ± 2.6% vs. cortical 7.2% ± 3.1%). The differences in elastic modulus and mineral distribution in the two tissues were investigated, using nanoindentation and micro-Raman imaging, to explain the different mechanical properties found. While cortical bone was found to be overall stiffer and more highly mineralized, no apparent differences were noted in the distribution of modulus values or mineral density along the specimen diameter. Therefore, differences in the mechanical behavior of trabecular and cortical bone tissue are likely to be in large part due to microstructural (i.e. orientation and distribution of cement lines) and collagen related compositional differences. c 2011 Elsevier Ltd. All rights reserved. ⃝
1.
Introduction
Understanding the relationship between the mechanical function and the structure of the materials that make up
bone might inspire the design of new materials (Weiner and Wagner, 1998). Cortical and trabecular bone tissue differ in their structure, with cortical tissue consisting of osteons and plexiform lamellae aligned in the longitudinal direction of
∗ Corresponding author. Tel.: +44 0 2380 594640; fax: +44 0 2380 593016. E-mail address: [email protected] (P.J. Thurner). c 2011 Elsevier Ltd. All rights reserved. 1751-6161/$ - see front matter ⃝ doi:10.1016/j.jmbbm.2011.05.036
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the bone and single trabeculae containing trabecular bone packets with boundary layers at various angles compared to the longitudinal axis of the trabecula (Choi and Goldstein, 1992). The different structure of the two types of bone tissue may lead to differences in their mechanical properties. Examining the mechanical properties of the two types of bone tissue is important in informing computer models, which are widely used to e.g. design implants and to predict the macroscopic mechanical properties of bone. In the nineteenth century Wolff (1892) suggested that cortical and trabecular bone were the same material from a mechanical point of view. Today, however, there is a general agreement in the literature that cortical bone tissue has a higher Young’s modulus compared to trabecular bone tissue (Guo, 2001). Despite numerous studies comparing the elastic properties of these two tissues (Guo, 2001; Rho et al., 1993; Kuhn et al., 1989; Choi et al., 1990; Mente and Lewis, 1989; Zysset et al., 1999), it seems that only a few studies investigated their mechanical properties related to the damage process (Bayraktar et al., 2004; Choi and Goldstein, 1992). Bayraktar et al. (2004) studied yield properties and found a lower calibrated (by combining finite element with measured apparent mechanical properties) tensile yield strain for trabecular tissue compared to measured values for cortical bone tissue. Choi and Goldstein (1992) compared the fatigue properties of trabecular and cortical bone tissue and found that the machined trabeculae had a lower fatigue strength compared to similarly sized cortical bone samples. To further investigate the damage properties of the two tissues, the aim of this study was to find out whether the local strains and microdamage associated with the damage process differ for unmachined single trabeculae and cortical tissue. If they do, can it be explained by compositional differences, more precisely by the putative uneven mineral distribution along the diameter of single trabeculae due to bone remodeling (van der Linden et al., 2001)?
2.
Materials and methods
2.1.
Three-point bending
2.1.1.
Sample preparation
Single trabeculae The proximal end of a frozen bovine femur, acquired from a meat wholesaler, was first cut off from the rest of the femur. Then, the proximal femur was cut with a bandsaw (BG 200, Medoc, Logrono, Spain) along the longitudinal and transverse directions, resulting in several cm-sized pieces. These pieces were cleaned of marrow using a cold water jet, produced by connecting a plastic pipette tip to a water tap through a plastic tube. Once the marrow had been removed, the individual trabeculae were revealed. The pieces cut were kept hydrated in tap water during the cutting process and subsequently stored in Hank’s Buffered Salt Solution (HBSS) of pH = 7.4. Initially, eight individual trabeculae were excised from the bone pieces using a pair of scissors and a scalpel. Following application of the speckle pattern (see below), each trabecula retrieved was wrapped in gauze
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soaked with HBSS and stored at −20 ◦ C in sealed plastic bags until testing. The pieces from which the trabeculae were excised were stored in the same manner and later reused again to harvest additional trabeculae. From the used pieces an additional twelve trabeculae were excised, which were similarly wrapped in saline-soaked gauze and stored at −20 ◦ C in sealed plastic bags until testing. In total, twenty individual trabeculae were used for this study, the data from these samples were used in a previous study (Szabó et al., 2011). They were divided into two groups regarding sample preparation: the group of twelve samples was subjected to a supplementary freeze-thaw cycle compared to the initial group of eight trabeculae. However, no significant difference was found performing a two-tailed Student’s t-test on the data assuming unequal variance for the two groups and using a significance level of 0.05. Therefore, the data of both groups were merged. Care was taken in choosing trabeculae to match the 2 mm span of the three-point-bending jig. This selection was regardless of trabecula orientation and the loading experienced in vivo. The exact location from which the trabeculae were excised within the proximal femur was not noted. The cross-sectional dimensions (0.1–1 mm) at midspan were measured in two approximately orthogonal directions, using a digital caliper. Cortical samples The distal part of the same bovine frozen femur as used for excising single trabeculae was cut in cm-sized pieces with a bandsaw (see above). The bone pieces were wrapped in saline-soaked gauze and stored at −20 ◦ C in sealed plastic bags. From the frozen pieces approximately 350 µm thick slabs were cut with a low-speed saw (IsoMet, Buehler, Lake Bluff, IL, USA). The precise location from which the cortical samples were cut was not noted. The slabs were wrapped in saline-soaked gauze and stored at −20 ◦ C in sealed plastic bags. Prior to testing, twenty longitudinally oriented, approximately 6 mm long samples of rectangular cross-section (approximately 350 µm × 350 µm) were cut from the slabs with the low-speed saw. The width and height of the cortical beams were measured towards the edges of the beam using a digital caliper, to avoid any potential damage caused by the calipers at midspan. Finally, the speckle pattern was applied to the samples (see below).
2.1.2.
Speckle pattern
To detect surface strains, a point grid pattern was printed on the sample surface eventually facing the camera using an inkjet printer (D2460 deskjet, Hewlett Packard, USA). First, the printing of a grid, created using graphics software (PhotoPaint X4, Corel, Ottawa, Canada), at a resolution of 1200 dpi was started. As soon as the printer started printing on the paper, it was stopped and opened to access the location just about to be printed. Double-sided sticky tape was applied to this paper zone and samples, rinsed with distilled water, were placed on it. Then, the printer was set to continue, creating an ink grid on the specimens as shown in Fig. 2.
2.1.3.
Testing procedure
Each sample was placed on a three-point-bending jig (support length = 2 mm, radius of all three rollers = 0.25 mm) in a bath filled with 10 mM Phosphate Buffered Saline (PBS)
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solution of pH ≈ 7.4. The bath was mounted on the platform of the mechanical tester (ElectroForce3200, Bose, Eden Prairie, MN, USA). Load was applied via a rounded plunger fixed to the mechanical tester, controlled by the provided WinTest software. During testing, fiber optic lights (DC-950H, Dolan-Jenner, Boxborough, MA, USA) illuminated the specimen from the two sides. A three-axis stage was used for positioning the high-speed camera (Ultima 512, Photron, San Diego, CA, USA), which recorded the bending tests using commercial software (Photron FASTCAM Viewer 2.4.5.1, Motion Engineering, Indianapolis, IN, USA). The three-point bending tests were planned to be run in displacement control. However, this proved to be impossible due to technical problems encountered with the mechanical tester. Due to small displacements involved in these experiments, the proportional integral derivative (PID) feedback parameters could not be optimally set while ensuring stable control of the testing machine. In fact, instability of the testing machine was observed at the failure point of individual samples. In order to prevent damage to the jig and to the load cell (5 lb, model 31, Honeywell Sensotec, Columbus, OH, USA), the tests on single trabeculae were carried out without PID control, in so-called direct command mode. Cortical bone samples were tested with very mild PID control (P = 0.01, I = 0.00035, D = 0, O = −37) to avoid instability at sample failure. Further preventive measures were taken to avoid collision between the plunger and the rollers, by setting up the experiment such that the plunger, pulled to its ultimate downward position, did not touch the rollers. The testing procedure consisted of two stages. First, the plunger was manually lowered until it touched the top part of the sample being tested. Contact was defined as a preload of 0.01 N. Then, the specimen was loaded past the failure stage, with a displacement rate varying between 0.01 and 1.28 mm/s for single trabeculae. The changing nature of the loading rate was not expected to influence the results significantly based on a previous study where we tested the strain rate sensitivity of single trabeculae. The displacement rate was set to 0.01 mm/s for cortical samples. The displacement was measured using a built-in linear variable differential transformer (LVDT). The actuator/sensor system has a maximum travel of 12.5 mm and a resolution of 1 µm. Our study was not focused on delivering elastic material constants but rather local strains and damage accumulation. Therefore we did not consider the effects of load frame or load cell compliance, which means that the values reported are likely slightly underestimating the true Young’s moduli of the samples. Parallel to this, the high-speed camera recorded the mechanical test with a frame rate varying from 60 to 250 frames/s, matching the respective data acquisition rates used. The waveform generation at the tester was started right after the camera recording started. This time delay was to ensure that the video footage showed the beginning of the mechanical experiment, and provided a point of synchronization.
Nanoindentation
2.2.1.
Sample preparation
Six single trabeculae were excised from a frozen proximal bovine femur: five samples from a different femur than used
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for the bending tests and one sample from the same femur. The cross-sectional dimensions of the single trabeculae varied between 300 and 740 mm. Five cortical samples were retained for nanoindentation tests using the pieces left after testing and from the pieces remaining from the sample cutting process. All samples were first rinsed in distilled water and then let to dry. All samples were embedded in transparent cold-setting resin (Epofix, Struers, Rotherham, UK) except for the single trabecula sample from the femur used for the bending tests of this study which was embedded in a non-transparent hot curing Technovit resin for practical reasons. First, a baselayer was poured in the mould and when the layer hardened, the sample was placed on top. Before pouring the top layer over the sample, the mix was let to cure for 30 min–1 h to avoid infiltration of the resin into the bone tissue. 1 mm thick slices were cut from the resulting resin blocks, outside the damaged region of each sample, using a low-speed saw. Each slice was glued onto a metal disk. Then, the samples were polished for several minutes using sandpaper of increasingly finer grit size (400, 600 and 1200 grit) as well as diamond suspensions (6, 3, 1 and 0.25 mm particle size). Between each polishing step, the particles were removed from the polished surface of each sample by placing the sample in an ultrasonic bath for 30 s.
2.2.2.
Testing procedure
Nanoindentation of each bone sample was performed using a depth sensing indentation instrument (Nano Test Platform 2, Micro Materials Ltd., Wrexham, UK). This pendulum-based nanoindentation system is extensively explained elsewhere (Beake et al., 2002; Beake and Leggett, 2002). Indentations were carried out using a Berkovich diamond indenter in loadcontrolled mode. The maximum loading force was set to 30 mN. The loading and unloading rates were kept constant, with the loading and unloading times set to 30 s. A dwell time of 50 s was selected at maximum load to reduce the influence of creep. A matrix of 100 to 150 indents (depending on the sample size) was imprinted onto the bone surface to measure the distribution of mechanical properties for each specimen. After indentation, all samples were imaged using an optical profilometer (InfiniteFocus, Alicona Imaging, Austria).
2.3.
Micro-Raman
Compositional analysis and imaging were performed by means of µ-Raman microscopy (inVia Raman microscope, Renishaw, New Mills, UK) on one trabecular and one cortical bone sample, selected from the ones used for nanoindentation. Two laser lines, namely 532 and 785 nm, were used for mapping the samples. The spectra were obtained by focusing the laser beam on the sample surface via a 20x objective lens, using an exposure time of 1 s and a spectral resolution of 1 cm−1 . A computer-controlled, motorized XYZ stage was moving the sample by 25 µm after every acquisition until the whole sample was scanned.
2.4. 2.2.
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Data analysis
From the cortical and trabecular datasets, the longitudinal tensile strain at failure and at whitening onset, the Young’s modulus and the maximum amount of whitening until failure were derived. Four calculated values in the trabecular dataset
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exceeding the mean by more than four times the standard deviation were excluded from further analysis, where the mean and standard deviation were taken after exclusion. The parameters derived for cortical and trabecular tissue were compared using a two-tailed Student’s t-test assuming unequal variance and a significance threshold of 0.05.
2.4.1.
Young’s modulus
The force–displacement data were obtained from the mechanical tester. The linearly elastic region of the force– displacement curves was manually selected, and a linear curve was fitted to these data points, which gave the slope in the elastic region. An elliptical shape was assumed for the single trabeculae when determining the cross-sectional area, second moment of area and the shear coefficient. The elliptical approximation was based on the cross-sections of the six single trabeculae (prepared for nanoindentation) viewed under a microscope. For the cortical samples a shear coefficient value of 0.850 and for the single trabeculae, depending on the geometry, values varying between 0.828 and 0.904 were used (Cowper, 1966), assuming a Poisson’s ratio value of 0.3. The slope, the shear coefficient and the Poisson’s ratio along with the variables derived from geometrical measurements of the samples (i.e.: crosssectional area and second moment of area) were incorporated in the Timoshenko formula (1) (Gere and Timoshenko, 1991; Wang, 1995), to obtain the Young’s modulus of the samples examined. 24(1 + ν)I Pl3 1+ (1) vmax = 48EI AKl2 where vmax denotes the deflection at midspan, P the applied force, l the support length, E the Young’s modulus, I the second moment of area, ν the Poisson’s ratio, A the crosssectional area of the beam and K the shear coefficient. For each specimen, the Young’s modulus was calculated. The mean and standard deviation were calculated for the trabecular and cortical Young’s modulus values, respectively (Fig. 1(a)).
2.4.2.
Microdamage
The whitening effect (Burstein et al., 1973; Currey and Brear, 1974; Currey et al., 1995) was used to detect microdamage (Thurner et al., 2006a,b). To quantify whitening, the images recorded by the high-speed camera were processed, as previously described (Thurner et al., 2006a) using a custom LabVIEW program (Jungmann, 2006). Briefly, a threshold was defined, based on the brightest pixel found on the bone surface in the first few frames of each video. All pixels above the threshold were counted as whitened pixels in subsequent frames. Finally, plotting the number of whitened pixels against the frame number, a whitening curve was obtained. The whitening effect itself is depicted on Fig. 2. The amount of whitening just prior to failure, used as an indicator of the amount of microdamage, was normalized by dividing the number of whitened pixels by the cross-sectional area of the corresponding specimen. As we assume whitening to scale with volume, normalization should reduce the effect of the sample geometry. Resulting mean and standard deviation values of whitening were compared for trabecular and cortical bone tissue (Fig. 1(d)).
2.4.3.
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Strain
Strain maps were generated based on recorded images using commercial digital image correlation software (Vic-2D 2009, Correlated Solutions, Columbia, SC, USA). To obtain strain maps covering the area of interest, the subset size was set between 21 and 33 pixels (depending on the sample) and the step size to 1. A decay filter (90% center-weighted Gaussian filter) of size 15 was applied to smooth the calculated strain maps. This provided real-time strain measurements and therefore, strain maps matched with the different phases of whitening (Fig. 2). For each sample, the longitudinal Lagrangian strain maps corresponding to whitening initiation and failure (first visible crack) were retained for further analysis. The bottom extreme tensile zone was selected at midspan, and the maximum tensile strain value noted at whitening initiation and failure, respectively. These values were compared for trabecular and cortical bone tissue (Fig. 1(b) and (c)).
2.4.4. Elastic modulus and hardness determined by nanoindentation During nanoindentation experiments a series of force vs. displacement curves were recorded. The analysis was performed using analytical software provided by MicroMaterials, where the unloading portion of the curve was fitted to a power law function to determine the hardness and elastic modulus of bone samples (Oliver and Pharr, 1992). The physical aspects of nanoindentation analysis are explained in detail by Beake et al. (2002), Beake and Leggett (2002), and therefore will not be repeated here. The sample hardness (H) was calculated from the maximum load (Fmax ) and projected area of contact, Ac , determined through a series of indentations at different loads on calibration sample of fused silica, by: H=
Fmax . Ac
(2)
The Young’s modulus (or elastic modulus), E, of the sample was determined from 1 − ν2i 1 1 − ν2 = + Er E Ei
(3)
where ν is the Poisson’s ratio of the sample (assumed to be 0.3), Er is the reduced modulus of the sample derived from the load vs. displacement curves (Oliver and Pharr, 1992), νi is the Poisson’s ratio of the indenter (0.07) and Ei is the Young’s modulus for the indenter (1141 GPa). Maps of the elastic modulus and hardness were generated to determine the distribution of the mechanical properties of cortical and trabecular bone tissues. These maps were further processed by eliminating values where surface defects interfered with points of measurement. Fig. 3 shows an example of an optical image of trabecular bone sample after indentation, as well as maps of the hardness and elastic modulus for the same sample. Statistical histograms of the modulus and hardness were also obtained, and mean values were calculated.
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Fig. 1 – Comparison of the measured mechanical parameters for trabecular and cortical bone tissue, showing mean and standard deviation values.
Fig. 2 – Recorded images demonstrating whitening progression and corresponding longitudinal local strain maps at various stages (from top to bottom: at the beginning of the test, at the onset of whitening and at failure) during three-point bending of a single trabecula (left two columns) and a similar-sized cortical bone sample (right two columns). The same geometric and strain scale apply to all images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2.4.5. Mineral to matrix ratio calculation and µ-Raman mapping The fluorescent background was removed from the raw spectra in Matlab using a modified 5th order polynomial fit algorithm (Lieber and Mahadevan-Jansen, 2003); the spectra were then smoothed for noise reduction and the ratio of ν1 PO3− peak (960 cm−1 ) over C–H2 wag (1450 cm−1 ) was 4
measured for every one of them (Fig. 6). It is known that the intensity of a certain peak is proportional to the amount of scatterers (molecules per cubic centimetre) (McCreery, 2000), therefore the ratio of two peaks which correspond to different scatterers is a normalized magnitude which describes the relative concentrations of those two scatterers. The Raman spectrum of bone tissue can be divided into two main regions,
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Fig. 3 – (a) Optical image of a single trabecula used for nanoindentation and µ-Raman experiments. Red dots indicate the place of indents. Maps of (b) Young’s modulus, E and (c) hardness, H. (d) Mineral to matrix ratio µ-Raman map for the same sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
i.e. the lower frequency region (400–1100 cm−1 ) where the mineral-related bands are present and the higher frequency region (1100–1550 cm−1 ) where the matrix-specific peaks occur. The mineral’s phosphate ν2 and ν4 vibration modes occur at 438 and 589 cm−1 while the predominant v1 vibration mode of PO−3 appears at ∼960 cm−1 . Matrix-related bands 4 are the Amide III band at ∼1255 cm−1 , which along with Amide I band at ∼1675 cm−1 (not shown in Fig. 6) mainly correspond to collagen and the C-H2 -wag which is due to both collagenous and noncollagenous moieties (Kazanci et al., 2006). In this study the predominant peak of PO−3 and the 4 C-H2 wag were selected as the markers of the mineral and the matrix phase, respectively. Finally, µ-Raman compositional images were reconstructed by mapping those ratio values.
3.
Results
The Young’s modulus values ranged from 4.09 to 15.10 GPa for cortical bone and from 1.85 to 13.93 GPa for trabecular bone. Cortical tissue was found to have a significantly higher Young’s modulus than single trabeculae (p-value = 1.9E × 10−4 ), as shown in Fig. 1(a) and Table 1. The amount of microdamage (normalized whitening) ranged from 2.6 to 14.8 × 103 pix/mm2 for cortical bone and from 5.6 to 38.7 × 103 pix/mm2 for trabecular bone. Significantly more microdamage occurred prior to failure in
single trabeculae than in cortical bone tissue (p-value = 0.003), see Fig. 1(d) and Table 1. The maximum tensile strain at failure ranged from 14.07% to 37.24% for cortical bone, and from 14.22% to 61.65% for trabecular bone. The maximum tensile strains measured at failure were significantly higher in trabeculae than in cortical bone tissue (p-value = 0.005), see Fig. 1(b) and Table 1. However, no significant difference was observed for the maximum tensile strains at microdamage initiation in the two distinct bone tissues (p-value = 0.136), see Fig. 1(c) and Table 1. The maximum tensile strain at whitening onset ranged from 3.44% to 14.41% for cortical bone, and from 1.95% to 11.44% for trabecular bone. The elastic modulus (ENI ) and hardness (H) of single trabeculae and cortical bone obtained by nanoindentation showed a significant difference. Average values for 5 samples (80–90 indents on each sample) of cortical bone were ENI = 23.17 ± 2.75 GPa and H = 1.08 ± 0.17 GPa, and for 6 samples (at least 90 indents on each sample) of single trabeculae were ENI = 18.72 ± 2.42 GPa and H = 0.76 ± 0.13 GPa (cf. Table 1). For cortical bone, a significantly higher modulus and hardness were found compared to single trabeculae (p-valueH = 6.12E× 10−4 and p-valueENI = 1.23E × 10−4 ). Similar results were obtained by Turner et al. (1999), who showed a difference in elastic modulus of trabeculae and cortical bone obtained by nanoindentation. Visually comparing the elastic modulus maps for both bone tissues, no apparent difference in
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Table 1 – Comparison of the mechanical and compositional parameters for trabecular and cortical bone tissue, showing mean, standard deviation, sample number (n) and p-value.
Young’s modulus (GPa) Maximum normalized whitening at failure (pix/mm2 ) Maximum tensile strain at failure (%) Maximum tensile strain at whitening onset (%) Indentation modulus (GPa) Hardness (GPa) Mineral/matrix ratio
Single trabeculae (mean ± SD (n)) Cortical bone (mean ± SD (n))
p-value
5.2 ± 3.1 (20) 16100 ± 8800 (16) 36.6 ± 14 (13) 5.80 ± 2.62 (18) 18.72 ± 2.42 (6) 0.76 ± 0.13 (6) 5.2 ± 0.8 (1a )
0.002 0.003 0.005 0.136 0.0001 0.0006 <0.0001
9.2 ± 2.9 (20) 8000 ± 3400 (20) 22.9 ± 7.4 (20) 7.2 ± 3.1 (20) 23.17 ± 2.75 (5) 1.08 ± 0.17 (5) 6.1 ± 0.7 (1a )
a Only one cortical and one trabecular bone sample were investigated with µ-Raman imaging. The t-test was performed assuming each image
point to be an independent measurement.
Fig. 4 – (a) Optical image of a cortical bone sample cut perpendicular to the bone’s long axis, used for nanoindentation and µ-Raman experiments. Red dots indicate the place of indents. Maps of (b) Young’s modulus, E and (c) hardness, H. (d) Mineral to matrix ratio µ-Raman map for the same sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the distribution of mechanical properties along the sample diameter was noted. Micro-Raman mappings of the mineral to matrix ratio of cortical and trabecular samples are shown in Figs. 3 and 4. The distributions of mineral to matrix ratios within the samples are also presented in Fig. 5. A direct comparison of µ-Raman maps (i.e. the distribution of high to low mineralized areas within the sample) with ENI and H maps showed no obvious correlation between areas of high mineral to matrix
ratio with those of high elastic modulus or high stiffness and vice versa. On the other hand, the fact that cortical bone exhibited an overall higher modulus than trabecular bone is inline with the µ-Raman measurements. As can be seen in Fig. 5 and Table 1, cortical bone was found to be significantly more mineralized, having a mineral to matrix ratio of 6.1 ± 0.7 compared to 5.2 ± 0.8 for trabecular bone (p-value < 0.0001). This is in agreement with a previous compositional study reporting similar results (Paschalis et al., 1997).
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Discussion
Our results are in good agreement with previous communications, summarized by Guo (2001), showing a higher Young’s modulus for cortical, compared to trabecular, bone tissue. The higher degree of mineralization of cortical bone contributes to a stiffer, but on the other hand a more brittle tissue compared to single trabeculae (Currey, 2003). The Raman results are in overall agreement with the nanoindentation results, showing cortical tissue with a higher mineralization and Young’s modulus compared to trabecular tissue. Yet, we could not find an obvious local correlation between mineral to matrix intensity and indentation modulus. The study presented here provides insight into the failure process of cortical and trabecular bone tissue. We found that individual trabeculae fail at a significantly higher strain, and are hence more ductile, compared to similarly sized cortical bone samples. Interestingly, this is accompanied by a significantly increased microdamage accumulation (as assessed by whitening). In contrast, microdamage seems to initiate at similar strains in both tissues. Possible causes for the difference in failure behavior between trabecular and cortical bone tissue, are structural and/or compositional differences. Cortical bovine bone is plexiform as well as osteonal and has mostly longitudinal lamellar boundaries and cement lines, whereas trabecular bone packets form cement lines that are also diagonal to the long axis of the samples. The importance of the increased number of cement lines in trabecular tissue was suggested by Choi et al. (1990) and Choi and Goldstein (1992). Both cement lines and lamellar interfaces are likely considerably lower in stiffness compared to cortical bone (Dong et al., 2005; Seto et al., 2008). Therefore, it seems possible that these interfaces could prevent, otherwise catastrophic, cracks from propagating through the stiffer matrix. Furthermore, the presence of interfaces in high numbers or different orientations may lead to a higher amount of microdamage being generated prior to failure. In addition, due to remodeling, single trabeculae can have less mineralized, and hence less stiff (Gupta et al., 2006), outer layers, which could also lead to an increase of damage tolerance. To uncover possible differences in the mineral and elastic modulus distribution, micro-Raman and nanoindentation tests were carried out on cortical and trabecular bone samples. The elastic modulus and mineral to matrix maps were visually compared, however a less stiff or lowly mineralized outer layer for trabecular tissue was not detectable. This might be due to the fact that bovine bone was used for this study. Bovine individual trabeculae may be different from human trabeculae, reported (van der Linden et al., 2001; Busse et al., 2009) to display an inhomogeneous mineral distribution, with a lower mineral content on the surface layer compared to the middle. The proposed effect of non-uniform mineral distribution on trabecular strains is confirmed in a finite element study (van Ruijven et al., 2007), where the incorporation of a nonuniform bone mineral distribution obtained from microcomputed tomography scans led to significantly increased strains in trabecular bone. However, a recent finite element study (Gross et al., 2011) using synchrotron radiation microcomputed tomography concluded that mineral heterogeneity
Fig. 5 – Comparison between the mineral to matrix ratios of cortical and trabecular bone samples. (left) Mineral to matrix ratios distribution and (right) Gaussian fit for these data sets.
Fig. 6 – Typical spectrum obtained from the bone tissue before (red dashed line) and after (black solid line) background correction. The main phosphate and matrix-related bands are also presented. The 5th order polynomial curve (green solid line) was independently calculated for every single spectrum. Note that the raw spectrum has been Y offset in order to fit within the corrected spectrum region. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
in trabecular bone led only to a minor decrease (1%–4%) of the apparent stiffness. It might be that mineral inhomogeneity influences local strains more than the apparent stiffness. The experiments performed within this study were not free of limitations; difficulties were faced when determining the geometry of the trabecular samples. The exact final position of the trabecula being bent was only defined once placed on the jig. This way, the sample height could easily be deduced from the images, whereas no additional information could be gained regarding sample width. However, the
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sample’s rough dimensions were known by making two orthogonal measurements at the centre of the sample before positioning it on the rollers. These values combined with the known height were used to define the geometry and used in the analysis. 2D strain calculations were carried out, which assume a flat surface, whereas in reality the surface of an individual trabecula is curved. This discrepancy is unlikely to influence the results of this study since only the longitudinal strains were analyzed. However, it must be noted that out of plane strains could not be accounted for in the 2D strain analysis. Also, the maximum strain most probably occurs at the very bottom of each single trabecula, an area which was not captured by the camera in this study. The reported strain values were compared to previous experimental studies. The trabecular failure strain values are consistent with the findings of Yeh et al., measuring trabecular tissue strain at the point of fracture exceeding 20% (26.6% ± 2.8%) for hydrated samples in cantilever bending, using optical markers. Recently, Busse et al. (2009) reported displacement values, which according to linear elastic theory correspond to even higher strains, i.e. sample average maximum tensile strains of 36% at failure and 18% at yield for dry single trabeculae in three-point bending. The strains measured here at whitening onset are higher than those measured at the emergence of the dark zone in cortical bone (Sun et al., 2010), reporting an average strain of 1.1% ± 0.65%. Sun et al. measured five points on the edge of the dark zone in each sample to calculate an average value. We measured the highest value for strain initiation which can explain why we obtain higher strains for damage initiation. However, our cortical tissue failure strain values are considerably higher compared to tensile failure strains measured on mm-sized moist human cortical bone samples of different age (Burstein et al., 1976; McCalden et al., 1993), but are comparable to the strain results of a recent study (Sun et al., 2010). McCalden et al. (1993) reported ultimate strain values between 4% and 1% and Burstein et al. (1976) between 3.4% and 2.4% with increasing age. This discrepancy might be attributed to the difference in sample scale and loading type. Recently, Sun et al. (2010) reported local strains up to 14% in notched cortical bone samples subjected to tensile strain. Results in a similar range (∼10%) just prior to failure during tensile testing of cortical bone samples have also been reported by Benecke et al. (2009). Based on the results of this study, when creating bone models, trabecular tissue should be assigned a significantly lower Young’s modulus, but significantly higher failure strain and microdamage accumulation capacity than cortical bone tissue. Importantly, our results let us speculate about the biological implication of the extensive propensity of trabecular bone to accumulate microdamage, or in other words, the ability of trabecular bone to keep its structural integrity intact. An individual trabecula would very likely be resorbed as a consequence of a microfracture and hence, would decrease the mechanical competence of the trabecular network overall. However, if a single trabecula is damaged but not completely separated, bone remodeling can still occur. Conflict of interest statement None of the authors have any conflict of interest with regards to this study.
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Acknowledgments We are gratefully indebted to the School of Engineering Sciences, University of Southampton for financial support of this study and to Dr. Harold M.H. Chong for providing access to the µ-Raman Microscopy facility. Funding for instrumentation was in part provided by NIH Grant R01 GM65354. REFERENCES
Bayraktar, H.H., Morgan, E.F., Niebur, G.L., Morris, G.E., Wong, E.K., Keaveny, T.M., 2004. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. Journal of Biomechanics 37, 27–35. Beake, B., Leggett, G.J., Alexander, M.R., 2002. Characterization of the mechanical properties of plasma-polymerized coatings by nanoindentation and tribology. Journal of Materials Science 37, 4919–4927. Beake, B., Leggett, G.J., 2002. Nanoindentation and nanoscratch testing uniaxially and biaxially drawn poly(ethylene terephtalate) film. Polymer 43, 319–327. Benecke, G., Kerschnitzki, M., Fratzl, P., Gupta, H.S., 2009. Digital image correlation shows localized deformation bands in inelastic loading of fibrolamellar bone. Journal of Materials Research 24, 421–429. Burstein, A.H., Reilly, D.T., Frankel, V.H., 1973. Failure characteristics of bone and bone tissue. In: Perspectives in Biomedical Engineering. Macmillan, London, pp. 131–134. Burstein, A.H., Reilly, D.T., Martens, M., 1976. Aging of bone tissue: mechanical properties. The Journal of Bone and Joint Surgery 58, 82–86. Busse, B., Hahn, M., Soltau, M., Zustin, J., Püschel, K., Duda, G.N., Amling, M., 2009. Increased calcium content and inhomogeneity of mineralization render bone toughness in osteoporosis: mineralization, morphology and biomechanics of human single trabeculae. Bone 45, 1034–1043. Choi, K., Goldstein, S.A., 1992. A comparison of the fatigue behavior of human trabecular and cortical bone tissue. Journal of Biomechanics 25, 1371–1381. Choi, K., Kuhn, J.L., Ciarelli, M.J., Goldstein, S.A., 1990. The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. Journal of Biomechanics 23, 1103–1113. Cowper, G.R., 1966. The shear coefficient in Timoshenko’s beam theory. Journal of Applied Mechanics 33, 335–340. Currey, J.D., Brear, K., 1974. Tensile yield in bone. Calcified Tissue Research 15, 173–179. Currey, J.D., Zioupos, P., Sedman, A., 1995. Microstructureproperty relations in vertebrate bony hard tissues: microdamage and toughness. In: BIOMIMETICS Design and Processing of Materials. AIP Press, Woodbury, NY. Currey, J.D., 2003. How well are bones designed to resist fracture? Journal of Bone and Mineral Research 18, 591–598. Dong, X.N., Zhang, X., Guo, X.E., 2005. Interfacial strength of cement lines in human cortical bone. Mechanics and Chemistry of Biosystems 2, 63–68. Gere, J.M., Timoshenko, S.P., 1991. Mechanics of Materials. Chapman & Hall, London. Gross, T., Pahr, D.H., Peyrin, F., Zysset, P.K., 2011. The influence of mineral heterogeneity on the apparent elastic properties of human cancellous bone: a srmct based finite element study. In: Proceedings of the 57th Annual Meeting of the Orthopaedic Research Society, Long Beach, CA, USA. Guo, X., 2001. Mechanical properties of cortical bone and cancellous bone tissue. In: Cowin, S.C. (Ed.), Bone Mechanics Handbook. CRC Press, Boca Raton, FL, pp. 10.1–10.23.
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Sun, X., Jeon, J.H., Blendell, J., Akkus, O., 2010. Visualization of a phantom post-yield deformation process in cortical bone. Journal of Biomechanics 43, 1989–1996. Szabó, M.E, Taylor, M., Thurner, P.J., 2011. Mechanical properties of single bovine trabeculae are unaffected by strain rate. Journal of Biomechanics 44, 962–967. Thurner, P.J., Erickson, B., Jungmann, R., Schriock, Z., Weaver, J.C., Fantner, G.E., Schitter, G., Morse, D.E., Hansma, P.K., 2006a. High-speed photography of compressed human trabecular bone correlates whitening to microscopic damage. Engineering Fracture Mechanics 74, 1928–1941. Thurner, P.J., Erickson, B., Schriock, Z., Langan, J., Scott, J., Zhao, M., Weaver, J.C., Fantner, G.E., Turner, P., Kindt, J.H., Schitter, G., Morse, D.E., Hansma, P.K., 2006b. High-speed photography of the development of microdamage in trabecular bone during compression. Journal of Materials Research 21, 1093–1100. Turner, C.H., Rho, J., Takano, Y., Tsui, T.Y., Pharr, G.M., 1999. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. Journal of Biomechanics 32, 437–441. van der Linden, J.C., Birkenhager-Frenkel, D.H., Verhaar, J.A.N., Weinans, H., 2001. Trabecular bone’s mechanical properties are affected by its non-uniform mineral distribution. Journal of Biomechanics 34, 1573–1580. van Ruijven, L.J., Mulder, L., van Eijden, T.M.G.J., 2007. Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone. Journal of Biomechanics 40, 1211–1218. Wang, C., 1995. Timoshenko beam-bending solutions in terms of Euler–Bernoulli solutions. Journal of Engineering Mechanics 121, 763–765. Weiner, S., Wagner, H.D., 1998. Material bone: structuremechanical function relations. Annual Review of Materials Science 28, 271–298. Wolff, J., 1892. Das Gesetz der Transformation der Knochen. A. Hirchwild, Berlin. Zysset, P.K., Guo, X.E., Hoffler, C.E., Moore, K.E., Goldstein, S.A., 1999. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. Journal of Biomechanics 32, 1005–1012.
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Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/jmbbm
Research paper
Similar damage initiation but different failure behavior in trabecular and cortical bone tissue M.E. Szabó a , J. Zekonyte b , O.L. Katsamenis a , M. Taylor a , P.J. Thurner a,∗ a Bioengineering Science Research Group, School of Engineering Sciences, Faculty of Engineering and the Environment, University of
Southampton, Southampton, SO17 1BJ, UK b National Centre for Advanced Tribology at Southampton, School of Engineering Sciences, Faculty of Engineering and the Environment, University of Southampton, Southampton, SO17 1BJ, UK
A R T I C L E
I N F O
A B S T R A C T
Article history:
The mechanical properties of bone tissue are reflected in its micro- and nanostructure
Received 6 April 2011
as well as in its composition. Numerous studies have compared the elastic mechanical
Received in revised form
properties of cortical and trabecular bone tissue and concluded that cortical bone tissue is
20 May 2011
stiffer than trabecular bone tissue. This study compared the progression of microdamage
Accepted 28 May 2011
leading to fracture and the related local strains during this process in trabecular and cortical
Published online 6 June 2011
bone tissue. Unmachined single bovine trabeculae and similarly-sized cortical bovine bone samples were mechanically tested in three-point bending and concomitantly imaged to
Keywords:
assess local strains using a digital image correlation technique. The bone whitening effect
Cortical
was used to detect microdamage formation and propagation. This study found that cortical
Trabeculae
bone tissue exhibits significantly lower maximum strains (trabecular 36.6% ± 14% vs.
Microdamage
cortical 22.9% ± 7.4%) and less accumulated damage (trabecular 16100 ± 8800 pix/mm2
Strain
vs. cortical 8000 ± 3400 pix/mm2 ) at failure. However, no difference was detected for the
Three-point bending
maximum local strain at whitening onset (trabecular 5.8% ± 2.6% vs. cortical 7.2% ± 3.1%). The differences in elastic modulus and mineral distribution in the two tissues were investigated, using nanoindentation and micro-Raman imaging, to explain the different mechanical properties found. While cortical bone was found to be overall stiffer and more highly mineralized, no apparent differences were noted in the distribution of modulus values or mineral density along the specimen diameter. Therefore, differences in the mechanical behavior of trabecular and cortical bone tissue are likely to be in large part due to microstructural (i.e. orientation and distribution of cement lines) and collagen related compositional differences. c 2011 Elsevier Ltd. All rights reserved. ⃝
1.
Introduction
Understanding the relationship between the mechanical function and the structure of the materials that make up
bone might inspire the design of new materials (Weiner and Wagner, 1998). Cortical and trabecular bone tissue differ in their structure, with cortical tissue consisting of osteons and plexiform lamellae aligned in the longitudinal direction of
∗ Corresponding author. Tel.: +44 0 2380 594640; fax: +44 0 2380 593016. E-mail address: [email protected] (P.J. Thurner). c 2011 Elsevier Ltd. All rights reserved. 1751-6161/$ - see front matter ⃝ doi:10.1016/j.jmbbm.2011.05.036
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the bone and single trabeculae containing trabecular bone packets with boundary layers at various angles compared to the longitudinal axis of the trabecula (Choi and Goldstein, 1992). The different structure of the two types of bone tissue may lead to differences in their mechanical properties. Examining the mechanical properties of the two types of bone tissue is important in informing computer models, which are widely used to e.g. design implants and to predict the macroscopic mechanical properties of bone. In the nineteenth century Wolff (1892) suggested that cortical and trabecular bone were the same material from a mechanical point of view. Today, however, there is a general agreement in the literature that cortical bone tissue has a higher Young’s modulus compared to trabecular bone tissue (Guo, 2001). Despite numerous studies comparing the elastic properties of these two tissues (Guo, 2001; Rho et al., 1993; Kuhn et al., 1989; Choi et al., 1990; Mente and Lewis, 1989; Zysset et al., 1999), it seems that only a few studies investigated their mechanical properties related to the damage process (Bayraktar et al., 2004; Choi and Goldstein, 1992). Bayraktar et al. (2004) studied yield properties and found a lower calibrated (by combining finite element with measured apparent mechanical properties) tensile yield strain for trabecular tissue compared to measured values for cortical bone tissue. Choi and Goldstein (1992) compared the fatigue properties of trabecular and cortical bone tissue and found that the machined trabeculae had a lower fatigue strength compared to similarly sized cortical bone samples. To further investigate the damage properties of the two tissues, the aim of this study was to find out whether the local strains and microdamage associated with the damage process differ for unmachined single trabeculae and cortical tissue. If they do, can it be explained by compositional differences, more precisely by the putative uneven mineral distribution along the diameter of single trabeculae due to bone remodeling (van der Linden et al., 2001)?
2.
Materials and methods
2.1.
Three-point bending
2.1.1.
Sample preparation
Single trabeculae The proximal end of a frozen bovine femur, acquired from a meat wholesaler, was first cut off from the rest of the femur. Then, the proximal femur was cut with a bandsaw (BG 200, Medoc, Logrono, Spain) along the longitudinal and transverse directions, resulting in several cm-sized pieces. These pieces were cleaned of marrow using a cold water jet, produced by connecting a plastic pipette tip to a water tap through a plastic tube. Once the marrow had been removed, the individual trabeculae were revealed. The pieces cut were kept hydrated in tap water during the cutting process and subsequently stored in Hank’s Buffered Salt Solution (HBSS) of pH = 7.4. Initially, eight individual trabeculae were excised from the bone pieces using a pair of scissors and a scalpel. Following application of the speckle pattern (see below), each trabecula retrieved was wrapped in gauze
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soaked with HBSS and stored at −20 ◦ C in sealed plastic bags until testing. The pieces from which the trabeculae were excised were stored in the same manner and later reused again to harvest additional trabeculae. From the used pieces an additional twelve trabeculae were excised, which were similarly wrapped in saline-soaked gauze and stored at −20 ◦ C in sealed plastic bags until testing. In total, twenty individual trabeculae were used for this study, the data from these samples were used in a previous study (Szabó et al., 2011). They were divided into two groups regarding sample preparation: the group of twelve samples was subjected to a supplementary freeze-thaw cycle compared to the initial group of eight trabeculae. However, no significant difference was found performing a two-tailed Student’s t-test on the data assuming unequal variance for the two groups and using a significance level of 0.05. Therefore, the data of both groups were merged. Care was taken in choosing trabeculae to match the 2 mm span of the three-point-bending jig. This selection was regardless of trabecula orientation and the loading experienced in vivo. The exact location from which the trabeculae were excised within the proximal femur was not noted. The cross-sectional dimensions (0.1–1 mm) at midspan were measured in two approximately orthogonal directions, using a digital caliper. Cortical samples The distal part of the same bovine frozen femur as used for excising single trabeculae was cut in cm-sized pieces with a bandsaw (see above). The bone pieces were wrapped in saline-soaked gauze and stored at −20 ◦ C in sealed plastic bags. From the frozen pieces approximately 350 µm thick slabs were cut with a low-speed saw (IsoMet, Buehler, Lake Bluff, IL, USA). The precise location from which the cortical samples were cut was not noted. The slabs were wrapped in saline-soaked gauze and stored at −20 ◦ C in sealed plastic bags. Prior to testing, twenty longitudinally oriented, approximately 6 mm long samples of rectangular cross-section (approximately 350 µm × 350 µm) were cut from the slabs with the low-speed saw. The width and height of the cortical beams were measured towards the edges of the beam using a digital caliper, to avoid any potential damage caused by the calipers at midspan. Finally, the speckle pattern was applied to the samples (see below).
2.1.2.
Speckle pattern
To detect surface strains, a point grid pattern was printed on the sample surface eventually facing the camera using an inkjet printer (D2460 deskjet, Hewlett Packard, USA). First, the printing of a grid, created using graphics software (PhotoPaint X4, Corel, Ottawa, Canada), at a resolution of 1200 dpi was started. As soon as the printer started printing on the paper, it was stopped and opened to access the location just about to be printed. Double-sided sticky tape was applied to this paper zone and samples, rinsed with distilled water, were placed on it. Then, the printer was set to continue, creating an ink grid on the specimens as shown in Fig. 2.
2.1.3.
Testing procedure
Each sample was placed on a three-point-bending jig (support length = 2 mm, radius of all three rollers = 0.25 mm) in a bath filled with 10 mM Phosphate Buffered Saline (PBS)
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solution of pH ≈ 7.4. The bath was mounted on the platform of the mechanical tester (ElectroForce3200, Bose, Eden Prairie, MN, USA). Load was applied via a rounded plunger fixed to the mechanical tester, controlled by the provided WinTest software. During testing, fiber optic lights (DC-950H, Dolan-Jenner, Boxborough, MA, USA) illuminated the specimen from the two sides. A three-axis stage was used for positioning the high-speed camera (Ultima 512, Photron, San Diego, CA, USA), which recorded the bending tests using commercial software (Photron FASTCAM Viewer 2.4.5.1, Motion Engineering, Indianapolis, IN, USA). The three-point bending tests were planned to be run in displacement control. However, this proved to be impossible due to technical problems encountered with the mechanical tester. Due to small displacements involved in these experiments, the proportional integral derivative (PID) feedback parameters could not be optimally set while ensuring stable control of the testing machine. In fact, instability of the testing machine was observed at the failure point of individual samples. In order to prevent damage to the jig and to the load cell (5 lb, model 31, Honeywell Sensotec, Columbus, OH, USA), the tests on single trabeculae were carried out without PID control, in so-called direct command mode. Cortical bone samples were tested with very mild PID control (P = 0.01, I = 0.00035, D = 0, O = −37) to avoid instability at sample failure. Further preventive measures were taken to avoid collision between the plunger and the rollers, by setting up the experiment such that the plunger, pulled to its ultimate downward position, did not touch the rollers. The testing procedure consisted of two stages. First, the plunger was manually lowered until it touched the top part of the sample being tested. Contact was defined as a preload of 0.01 N. Then, the specimen was loaded past the failure stage, with a displacement rate varying between 0.01 and 1.28 mm/s for single trabeculae. The changing nature of the loading rate was not expected to influence the results significantly based on a previous study where we tested the strain rate sensitivity of single trabeculae. The displacement rate was set to 0.01 mm/s for cortical samples. The displacement was measured using a built-in linear variable differential transformer (LVDT). The actuator/sensor system has a maximum travel of 12.5 mm and a resolution of 1 µm. Our study was not focused on delivering elastic material constants but rather local strains and damage accumulation. Therefore we did not consider the effects of load frame or load cell compliance, which means that the values reported are likely slightly underestimating the true Young’s moduli of the samples. Parallel to this, the high-speed camera recorded the mechanical test with a frame rate varying from 60 to 250 frames/s, matching the respective data acquisition rates used. The waveform generation at the tester was started right after the camera recording started. This time delay was to ensure that the video footage showed the beginning of the mechanical experiment, and provided a point of synchronization.
Nanoindentation
2.2.1.
Sample preparation
Six single trabeculae were excised from a frozen proximal bovine femur: five samples from a different femur than used
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for the bending tests and one sample from the same femur. The cross-sectional dimensions of the single trabeculae varied between 300 and 740 mm. Five cortical samples were retained for nanoindentation tests using the pieces left after testing and from the pieces remaining from the sample cutting process. All samples were first rinsed in distilled water and then let to dry. All samples were embedded in transparent cold-setting resin (Epofix, Struers, Rotherham, UK) except for the single trabecula sample from the femur used for the bending tests of this study which was embedded in a non-transparent hot curing Technovit resin for practical reasons. First, a baselayer was poured in the mould and when the layer hardened, the sample was placed on top. Before pouring the top layer over the sample, the mix was let to cure for 30 min–1 h to avoid infiltration of the resin into the bone tissue. 1 mm thick slices were cut from the resulting resin blocks, outside the damaged region of each sample, using a low-speed saw. Each slice was glued onto a metal disk. Then, the samples were polished for several minutes using sandpaper of increasingly finer grit size (400, 600 and 1200 grit) as well as diamond suspensions (6, 3, 1 and 0.25 mm particle size). Between each polishing step, the particles were removed from the polished surface of each sample by placing the sample in an ultrasonic bath for 30 s.
2.2.2.
Testing procedure
Nanoindentation of each bone sample was performed using a depth sensing indentation instrument (Nano Test Platform 2, Micro Materials Ltd., Wrexham, UK). This pendulum-based nanoindentation system is extensively explained elsewhere (Beake et al., 2002; Beake and Leggett, 2002). Indentations were carried out using a Berkovich diamond indenter in loadcontrolled mode. The maximum loading force was set to 30 mN. The loading and unloading rates were kept constant, with the loading and unloading times set to 30 s. A dwell time of 50 s was selected at maximum load to reduce the influence of creep. A matrix of 100 to 150 indents (depending on the sample size) was imprinted onto the bone surface to measure the distribution of mechanical properties for each specimen. After indentation, all samples were imaged using an optical profilometer (InfiniteFocus, Alicona Imaging, Austria).
2.3.
Micro-Raman
Compositional analysis and imaging were performed by means of µ-Raman microscopy (inVia Raman microscope, Renishaw, New Mills, UK) on one trabecular and one cortical bone sample, selected from the ones used for nanoindentation. Two laser lines, namely 532 and 785 nm, were used for mapping the samples. The spectra were obtained by focusing the laser beam on the sample surface via a 20x objective lens, using an exposure time of 1 s and a spectral resolution of 1 cm−1 . A computer-controlled, motorized XYZ stage was moving the sample by 25 µm after every acquisition until the whole sample was scanned.
2.4. 2.2.
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Data analysis
From the cortical and trabecular datasets, the longitudinal tensile strain at failure and at whitening onset, the Young’s modulus and the maximum amount of whitening until failure were derived. Four calculated values in the trabecular dataset
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exceeding the mean by more than four times the standard deviation were excluded from further analysis, where the mean and standard deviation were taken after exclusion. The parameters derived for cortical and trabecular tissue were compared using a two-tailed Student’s t-test assuming unequal variance and a significance threshold of 0.05.
2.4.1.
Young’s modulus
The force–displacement data were obtained from the mechanical tester. The linearly elastic region of the force– displacement curves was manually selected, and a linear curve was fitted to these data points, which gave the slope in the elastic region. An elliptical shape was assumed for the single trabeculae when determining the cross-sectional area, second moment of area and the shear coefficient. The elliptical approximation was based on the cross-sections of the six single trabeculae (prepared for nanoindentation) viewed under a microscope. For the cortical samples a shear coefficient value of 0.850 and for the single trabeculae, depending on the geometry, values varying between 0.828 and 0.904 were used (Cowper, 1966), assuming a Poisson’s ratio value of 0.3. The slope, the shear coefficient and the Poisson’s ratio along with the variables derived from geometrical measurements of the samples (i.e.: crosssectional area and second moment of area) were incorporated in the Timoshenko formula (1) (Gere and Timoshenko, 1991; Wang, 1995), to obtain the Young’s modulus of the samples examined. 24(1 + ν)I Pl3 1+ (1) vmax = 48EI AKl2 where vmax denotes the deflection at midspan, P the applied force, l the support length, E the Young’s modulus, I the second moment of area, ν the Poisson’s ratio, A the crosssectional area of the beam and K the shear coefficient. For each specimen, the Young’s modulus was calculated. The mean and standard deviation were calculated for the trabecular and cortical Young’s modulus values, respectively (Fig. 1(a)).
2.4.2.
Microdamage
The whitening effect (Burstein et al., 1973; Currey and Brear, 1974; Currey et al., 1995) was used to detect microdamage (Thurner et al., 2006a,b). To quantify whitening, the images recorded by the high-speed camera were processed, as previously described (Thurner et al., 2006a) using a custom LabVIEW program (Jungmann, 2006). Briefly, a threshold was defined, based on the brightest pixel found on the bone surface in the first few frames of each video. All pixels above the threshold were counted as whitened pixels in subsequent frames. Finally, plotting the number of whitened pixels against the frame number, a whitening curve was obtained. The whitening effect itself is depicted on Fig. 2. The amount of whitening just prior to failure, used as an indicator of the amount of microdamage, was normalized by dividing the number of whitened pixels by the cross-sectional area of the corresponding specimen. As we assume whitening to scale with volume, normalization should reduce the effect of the sample geometry. Resulting mean and standard deviation values of whitening were compared for trabecular and cortical bone tissue (Fig. 1(d)).
2.4.3.
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Strain
Strain maps were generated based on recorded images using commercial digital image correlation software (Vic-2D 2009, Correlated Solutions, Columbia, SC, USA). To obtain strain maps covering the area of interest, the subset size was set between 21 and 33 pixels (depending on the sample) and the step size to 1. A decay filter (90% center-weighted Gaussian filter) of size 15 was applied to smooth the calculated strain maps. This provided real-time strain measurements and therefore, strain maps matched with the different phases of whitening (Fig. 2). For each sample, the longitudinal Lagrangian strain maps corresponding to whitening initiation and failure (first visible crack) were retained for further analysis. The bottom extreme tensile zone was selected at midspan, and the maximum tensile strain value noted at whitening initiation and failure, respectively. These values were compared for trabecular and cortical bone tissue (Fig. 1(b) and (c)).
2.4.4. Elastic modulus and hardness determined by nanoindentation During nanoindentation experiments a series of force vs. displacement curves were recorded. The analysis was performed using analytical software provided by MicroMaterials, where the unloading portion of the curve was fitted to a power law function to determine the hardness and elastic modulus of bone samples (Oliver and Pharr, 1992). The physical aspects of nanoindentation analysis are explained in detail by Beake et al. (2002), Beake and Leggett (2002), and therefore will not be repeated here. The sample hardness (H) was calculated from the maximum load (Fmax ) and projected area of contact, Ac , determined through a series of indentations at different loads on calibration sample of fused silica, by: H=
Fmax . Ac
(2)
The Young’s modulus (or elastic modulus), E, of the sample was determined from 1 − ν2i 1 1 − ν2 = + Er E Ei
(3)
where ν is the Poisson’s ratio of the sample (assumed to be 0.3), Er is the reduced modulus of the sample derived from the load vs. displacement curves (Oliver and Pharr, 1992), νi is the Poisson’s ratio of the indenter (0.07) and Ei is the Young’s modulus for the indenter (1141 GPa). Maps of the elastic modulus and hardness were generated to determine the distribution of the mechanical properties of cortical and trabecular bone tissues. These maps were further processed by eliminating values where surface defects interfered with points of measurement. Fig. 3 shows an example of an optical image of trabecular bone sample after indentation, as well as maps of the hardness and elastic modulus for the same sample. Statistical histograms of the modulus and hardness were also obtained, and mean values were calculated.
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Fig. 1 – Comparison of the measured mechanical parameters for trabecular and cortical bone tissue, showing mean and standard deviation values.
Fig. 2 – Recorded images demonstrating whitening progression and corresponding longitudinal local strain maps at various stages (from top to bottom: at the beginning of the test, at the onset of whitening and at failure) during three-point bending of a single trabecula (left two columns) and a similar-sized cortical bone sample (right two columns). The same geometric and strain scale apply to all images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2.4.5. Mineral to matrix ratio calculation and µ-Raman mapping The fluorescent background was removed from the raw spectra in Matlab using a modified 5th order polynomial fit algorithm (Lieber and Mahadevan-Jansen, 2003); the spectra were then smoothed for noise reduction and the ratio of ν1 PO3− peak (960 cm−1 ) over C–H2 wag (1450 cm−1 ) was 4
measured for every one of them (Fig. 6). It is known that the intensity of a certain peak is proportional to the amount of scatterers (molecules per cubic centimetre) (McCreery, 2000), therefore the ratio of two peaks which correspond to different scatterers is a normalized magnitude which describes the relative concentrations of those two scatterers. The Raman spectrum of bone tissue can be divided into two main regions,
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Fig. 3 – (a) Optical image of a single trabecula used for nanoindentation and µ-Raman experiments. Red dots indicate the place of indents. Maps of (b) Young’s modulus, E and (c) hardness, H. (d) Mineral to matrix ratio µ-Raman map for the same sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
i.e. the lower frequency region (400–1100 cm−1 ) where the mineral-related bands are present and the higher frequency region (1100–1550 cm−1 ) where the matrix-specific peaks occur. The mineral’s phosphate ν2 and ν4 vibration modes occur at 438 and 589 cm−1 while the predominant v1 vibration mode of PO−3 appears at ∼960 cm−1 . Matrix-related bands 4 are the Amide III band at ∼1255 cm−1 , which along with Amide I band at ∼1675 cm−1 (not shown in Fig. 6) mainly correspond to collagen and the C-H2 -wag which is due to both collagenous and noncollagenous moieties (Kazanci et al., 2006). In this study the predominant peak of PO−3 and the 4 C-H2 wag were selected as the markers of the mineral and the matrix phase, respectively. Finally, µ-Raman compositional images were reconstructed by mapping those ratio values.
3.
Results
The Young’s modulus values ranged from 4.09 to 15.10 GPa for cortical bone and from 1.85 to 13.93 GPa for trabecular bone. Cortical tissue was found to have a significantly higher Young’s modulus than single trabeculae (p-value = 1.9E × 10−4 ), as shown in Fig. 1(a) and Table 1. The amount of microdamage (normalized whitening) ranged from 2.6 to 14.8 × 103 pix/mm2 for cortical bone and from 5.6 to 38.7 × 103 pix/mm2 for trabecular bone. Significantly more microdamage occurred prior to failure in
single trabeculae than in cortical bone tissue (p-value = 0.003), see Fig. 1(d) and Table 1. The maximum tensile strain at failure ranged from 14.07% to 37.24% for cortical bone, and from 14.22% to 61.65% for trabecular bone. The maximum tensile strains measured at failure were significantly higher in trabeculae than in cortical bone tissue (p-value = 0.005), see Fig. 1(b) and Table 1. However, no significant difference was observed for the maximum tensile strains at microdamage initiation in the two distinct bone tissues (p-value = 0.136), see Fig. 1(c) and Table 1. The maximum tensile strain at whitening onset ranged from 3.44% to 14.41% for cortical bone, and from 1.95% to 11.44% for trabecular bone. The elastic modulus (ENI ) and hardness (H) of single trabeculae and cortical bone obtained by nanoindentation showed a significant difference. Average values for 5 samples (80–90 indents on each sample) of cortical bone were ENI = 23.17 ± 2.75 GPa and H = 1.08 ± 0.17 GPa, and for 6 samples (at least 90 indents on each sample) of single trabeculae were ENI = 18.72 ± 2.42 GPa and H = 0.76 ± 0.13 GPa (cf. Table 1). For cortical bone, a significantly higher modulus and hardness were found compared to single trabeculae (p-valueH = 6.12E× 10−4 and p-valueENI = 1.23E × 10−4 ). Similar results were obtained by Turner et al. (1999), who showed a difference in elastic modulus of trabeculae and cortical bone obtained by nanoindentation. Visually comparing the elastic modulus maps for both bone tissues, no apparent difference in
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Table 1 – Comparison of the mechanical and compositional parameters for trabecular and cortical bone tissue, showing mean, standard deviation, sample number (n) and p-value.
Young’s modulus (GPa) Maximum normalized whitening at failure (pix/mm2 ) Maximum tensile strain at failure (%) Maximum tensile strain at whitening onset (%) Indentation modulus (GPa) Hardness (GPa) Mineral/matrix ratio
Single trabeculae (mean ± SD (n)) Cortical bone (mean ± SD (n))
p-value
5.2 ± 3.1 (20) 16100 ± 8800 (16) 36.6 ± 14 (13) 5.80 ± 2.62 (18) 18.72 ± 2.42 (6) 0.76 ± 0.13 (6) 5.2 ± 0.8 (1a )
0.002 0.003 0.005 0.136 0.0001 0.0006 <0.0001
9.2 ± 2.9 (20) 8000 ± 3400 (20) 22.9 ± 7.4 (20) 7.2 ± 3.1 (20) 23.17 ± 2.75 (5) 1.08 ± 0.17 (5) 6.1 ± 0.7 (1a )
a Only one cortical and one trabecular bone sample were investigated with µ-Raman imaging. The t-test was performed assuming each image
point to be an independent measurement.
Fig. 4 – (a) Optical image of a cortical bone sample cut perpendicular to the bone’s long axis, used for nanoindentation and µ-Raman experiments. Red dots indicate the place of indents. Maps of (b) Young’s modulus, E and (c) hardness, H. (d) Mineral to matrix ratio µ-Raman map for the same sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the distribution of mechanical properties along the sample diameter was noted. Micro-Raman mappings of the mineral to matrix ratio of cortical and trabecular samples are shown in Figs. 3 and 4. The distributions of mineral to matrix ratios within the samples are also presented in Fig. 5. A direct comparison of µ-Raman maps (i.e. the distribution of high to low mineralized areas within the sample) with ENI and H maps showed no obvious correlation between areas of high mineral to matrix
ratio with those of high elastic modulus or high stiffness and vice versa. On the other hand, the fact that cortical bone exhibited an overall higher modulus than trabecular bone is inline with the µ-Raman measurements. As can be seen in Fig. 5 and Table 1, cortical bone was found to be significantly more mineralized, having a mineral to matrix ratio of 6.1 ± 0.7 compared to 5.2 ± 0.8 for trabecular bone (p-value < 0.0001). This is in agreement with a previous compositional study reporting similar results (Paschalis et al., 1997).
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Discussion
Our results are in good agreement with previous communications, summarized by Guo (2001), showing a higher Young’s modulus for cortical, compared to trabecular, bone tissue. The higher degree of mineralization of cortical bone contributes to a stiffer, but on the other hand a more brittle tissue compared to single trabeculae (Currey, 2003). The Raman results are in overall agreement with the nanoindentation results, showing cortical tissue with a higher mineralization and Young’s modulus compared to trabecular tissue. Yet, we could not find an obvious local correlation between mineral to matrix intensity and indentation modulus. The study presented here provides insight into the failure process of cortical and trabecular bone tissue. We found that individual trabeculae fail at a significantly higher strain, and are hence more ductile, compared to similarly sized cortical bone samples. Interestingly, this is accompanied by a significantly increased microdamage accumulation (as assessed by whitening). In contrast, microdamage seems to initiate at similar strains in both tissues. Possible causes for the difference in failure behavior between trabecular and cortical bone tissue, are structural and/or compositional differences. Cortical bovine bone is plexiform as well as osteonal and has mostly longitudinal lamellar boundaries and cement lines, whereas trabecular bone packets form cement lines that are also diagonal to the long axis of the samples. The importance of the increased number of cement lines in trabecular tissue was suggested by Choi et al. (1990) and Choi and Goldstein (1992). Both cement lines and lamellar interfaces are likely considerably lower in stiffness compared to cortical bone (Dong et al., 2005; Seto et al., 2008). Therefore, it seems possible that these interfaces could prevent, otherwise catastrophic, cracks from propagating through the stiffer matrix. Furthermore, the presence of interfaces in high numbers or different orientations may lead to a higher amount of microdamage being generated prior to failure. In addition, due to remodeling, single trabeculae can have less mineralized, and hence less stiff (Gupta et al., 2006), outer layers, which could also lead to an increase of damage tolerance. To uncover possible differences in the mineral and elastic modulus distribution, micro-Raman and nanoindentation tests were carried out on cortical and trabecular bone samples. The elastic modulus and mineral to matrix maps were visually compared, however a less stiff or lowly mineralized outer layer for trabecular tissue was not detectable. This might be due to the fact that bovine bone was used for this study. Bovine individual trabeculae may be different from human trabeculae, reported (van der Linden et al., 2001; Busse et al., 2009) to display an inhomogeneous mineral distribution, with a lower mineral content on the surface layer compared to the middle. The proposed effect of non-uniform mineral distribution on trabecular strains is confirmed in a finite element study (van Ruijven et al., 2007), where the incorporation of a nonuniform bone mineral distribution obtained from microcomputed tomography scans led to significantly increased strains in trabecular bone. However, a recent finite element study (Gross et al., 2011) using synchrotron radiation microcomputed tomography concluded that mineral heterogeneity
Fig. 5 – Comparison between the mineral to matrix ratios of cortical and trabecular bone samples. (left) Mineral to matrix ratios distribution and (right) Gaussian fit for these data sets.
Fig. 6 – Typical spectrum obtained from the bone tissue before (red dashed line) and after (black solid line) background correction. The main phosphate and matrix-related bands are also presented. The 5th order polynomial curve (green solid line) was independently calculated for every single spectrum. Note that the raw spectrum has been Y offset in order to fit within the corrected spectrum region. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
in trabecular bone led only to a minor decrease (1%–4%) of the apparent stiffness. It might be that mineral inhomogeneity influences local strains more than the apparent stiffness. The experiments performed within this study were not free of limitations; difficulties were faced when determining the geometry of the trabecular samples. The exact final position of the trabecula being bent was only defined once placed on the jig. This way, the sample height could easily be deduced from the images, whereas no additional information could be gained regarding sample width. However, the
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sample’s rough dimensions were known by making two orthogonal measurements at the centre of the sample before positioning it on the rollers. These values combined with the known height were used to define the geometry and used in the analysis. 2D strain calculations were carried out, which assume a flat surface, whereas in reality the surface of an individual trabecula is curved. This discrepancy is unlikely to influence the results of this study since only the longitudinal strains were analyzed. However, it must be noted that out of plane strains could not be accounted for in the 2D strain analysis. Also, the maximum strain most probably occurs at the very bottom of each single trabecula, an area which was not captured by the camera in this study. The reported strain values were compared to previous experimental studies. The trabecular failure strain values are consistent with the findings of Yeh et al., measuring trabecular tissue strain at the point of fracture exceeding 20% (26.6% ± 2.8%) for hydrated samples in cantilever bending, using optical markers. Recently, Busse et al. (2009) reported displacement values, which according to linear elastic theory correspond to even higher strains, i.e. sample average maximum tensile strains of 36% at failure and 18% at yield for dry single trabeculae in three-point bending. The strains measured here at whitening onset are higher than those measured at the emergence of the dark zone in cortical bone (Sun et al., 2010), reporting an average strain of 1.1% ± 0.65%. Sun et al. measured five points on the edge of the dark zone in each sample to calculate an average value. We measured the highest value for strain initiation which can explain why we obtain higher strains for damage initiation. However, our cortical tissue failure strain values are considerably higher compared to tensile failure strains measured on mm-sized moist human cortical bone samples of different age (Burstein et al., 1976; McCalden et al., 1993), but are comparable to the strain results of a recent study (Sun et al., 2010). McCalden et al. (1993) reported ultimate strain values between 4% and 1% and Burstein et al. (1976) between 3.4% and 2.4% with increasing age. This discrepancy might be attributed to the difference in sample scale and loading type. Recently, Sun et al. (2010) reported local strains up to 14% in notched cortical bone samples subjected to tensile strain. Results in a similar range (∼10%) just prior to failure during tensile testing of cortical bone samples have also been reported by Benecke et al. (2009). Based on the results of this study, when creating bone models, trabecular tissue should be assigned a significantly lower Young’s modulus, but significantly higher failure strain and microdamage accumulation capacity than cortical bone tissue. Importantly, our results let us speculate about the biological implication of the extensive propensity of trabecular bone to accumulate microdamage, or in other words, the ability of trabecular bone to keep its structural integrity intact. An individual trabecula would very likely be resorbed as a consequence of a microfracture and hence, would decrease the mechanical competence of the trabecular network overall. However, if a single trabecula is damaged but not completely separated, bone remodeling can still occur. Conflict of interest statement None of the authors have any conflict of interest with regards to this study.
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Acknowledgments We are gratefully indebted to the School of Engineering Sciences, University of Southampton for financial support of this study and to Dr. Harold M.H. Chong for providing access to the µ-Raman Microscopy facility. Funding for instrumentation was in part provided by NIH Grant R01 GM65354. REFERENCES
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