Elastic anisotropy of uniaxial mineralized collagen fibers measured using two-directional indentation. Effects of hydration state and indentation depth.

Mineralized turkey leg tendon (MTLT) is an attractive model of mineralized collagen fibers, which are also present in bone. Its longitudinal structure is advantageous for the relative simplicity in modeling, yet its anisotropic elastic properties remain unknown. The aim of this study was to quantify the extent of elastic anisotropy of mineralized collagen fibers by using nano- and microindentation to probe a number on MTLT samples in two orthogonal directions. The large dataset allowed the quantification of the extent of anisotropy, depending on the final indentation depth and on the hydration state of the sample. Anisotropy was observed to increase with the sample re-hydration process. Artifacts of indentation in a transverse direction to the main axis of the mineralized tendons in re-hydrated condition were observed. The indentation size effect, that is, the increase of the measured elastic properties with decreasing sampling volume, reported previously on variety of materials, was also observed in MTLT. Indentation work was quantified for both directions of indentation in dried and re-hydrated conditions. As hypothesized, MTLT showed a higher extent of anisotropy compared to cortical and trabecular bone, presumably due to the alignment of mineralized collagen fibers in this tissue.

Introduction

Mineralized turkey leg tendon (MTLT) is a tissue containing longitudinally arranged collagen fibers that normally mineralize over time, which makes them attractive models to study mechanisms of mineralization (Landis et al., 1996; Landis and Silver, 2002). The tendons undergo a gradual mineralization from a point mid-way along the tendon in the proximal direction, giving possibilities to study different stages of the process, depending on the distance from the mineralization front. Constituents of MTLT are similar to those of bone, being mainly collagen, of which 90% is the type I collagen (Landis and Silver, 2002; Fritsch and Hellmich, 2007), the mineral — hydroxyapatite and water. The mineral content of tendons in animals 24 weeks old was reported to be slightly lower than that of human bone (Gupta et al., 2004), but within the bone mineralization level for tendons extracted from older turkeys (Spiesz et al., 2012).

Two distinct morphologies of MTLT are shown in Fig. 1. One morphology, called the circumferential zone, consists of densely packed mineralized collagen fibers and is placed around large pores of the tendon (blood vessels). The other morphology, called the interstitial zone, is located between the large pores and has a more sparse structure and higher microporosity (Spiesz et al., 2012). The zones had different morphology and composition, and therefore were treated separately in this study.

Fig. 1

Circumferential (CIR) and interstitial (INT) zones of MTLT in two orthogonal directions (axial — AXI and transverse — TRV) as seen by backscattered electron imaging (a)–(d) and scanning probe microscopy (e)–(h). (a), (b) Bar −50 μm; (c), (d) Bar −25 μm; (e)–(h) Bar −5 μm.

Indentation is a technique used for quantifying the elastic properties of inhomogeneous materials at the micro- and nanolevel. It could be considered as a non-destructive technique that often does not require complicated sample preparation or mounting and can be performed multiple times on the same sample. In this technique the indentation modulus of rate-independent, elasto-plastic materials can be evaluated on the basis of the elastic contact theory (Oliver and Pharr, 1992; Fischer-Cripps, 2002; Oyen, 2011). For bulk isotropic materials, the indentation modulus is directly related to the elastic modulus and Poisson’s ratio (Oliver and Pharr, 1992; Rho et al., 1999; Ebenstein and Pruitt, 2006). However, for anisotropic and/or more complex material systems, such as bone or MTLT, the indentation modulus is related to the stiffness tensor by a more complex function (Swadener and Pharr, 2001), but can be estimated using iterative schemes (Franzoso and Zysset, 2009). Many nano- and microindentation results of mineralized tissues available so far have been obtained in the dried state. However, due to the important role of hydration in collagen properties, nanoindentation in physiological conditions is gaining acceptance (Hengsberger et al., 2002; Wolfram et al., 2010b). This enables the simulation of collagenous tissues conditions closer to the in vivo state, in which hydrated tissues are often swollen, giving rise to markedly different elastic properties. In trabecular bone, the stiffness anisotropy changes with re-hydration (Wolfram et al., 2010b), which suggests the volume changes are anisotropic, which was also observed macroscopically on MTLT (Lees and Page, 1992).

According to the conventional plasticity theory, the measurement of the indentation modulus should be independent of indentation depth, but the so called indentation size effect, which describes the increase of indentation modulus with decreasing sampling volume, was reported before (Swadener and Pharr, 2001; Zhang et al., 2008; Voyiadjis and Peters, 2010). This issue is not yet resolved quantitatively, even though some modeling attempts were done (Begley and Hutchinson, 1998; Shu and Fleck, 1998).

The aim of this study was to measure the elastic properties of mineralized turkey leg tendons in two orthogonal directions. Availability of such data set is limited in literature, to the authors’ knowledge, but could be very useful for the attempts to understand mechanical behavior of uniaxial mineralized collagen fibril arrays (Reisinger et al., 2010). Effects of sample re-hydration on the measured indentation modulus in the two directions were also investigated. Two hierarchical levels of the tissue organization were investigated using nano- and microindentation, contributing to the knowledge of the indentation size effects observed in mineralized tissues.

Materials and methods

Samples

Highly mineralized parts of ten digital flexor tendons of domestic turkeys (Bigi et al., 1996; Lees et al., 1994; Gupta et al., 2004) older than 24 weeks were used in this study. Approximately 10 millimeter-long specimens (about 40%–60% of the hard, highly mineralized part of a tendon), extracted from 8 legs, were used. Five cut sections were performed in each sample, as shown in Fig. 2, resulting in one transverse sample of approximately 10 mm in length and four axial samples. A total number of 49 tendon sections (one axial section was destroyed during processing) were embedded in epoxy resin (EpoFix, Struers, Ballerup, Denmark) without dehydration of the sample or resin infiltration, allowing subsequent re-hydration for indentation. The specimens were mounted on glass slides and polished using a silicon carbide paper series, followed by a 1 μm diamond suspension on a polishing cloth with a semi-automatic polishing machine (PM5, Logitech, UK). A similar procedure was successfully used for bone sections preparation for indentation (Wolfram et al., 2010a,b). Two morphological zones present in MTLT (Spiesz et al., 2012), the circumferential and the interstitial, were investigated separately by indentation. The mineralization within a morphology zone measured using quantitative backscattered electron imaging was homogeneous. The interstitial zone showed a higher porosity than the circumferential one (Spiesz et al., 2012).

Fig. 2

MTLT two-directional sample extraction scheme resulting in axial (AXI) and transverse samples (TRV). MTLT is schematically represented as mineralized collagen fibers arranged longitudinally along the tendon’s main axis .

Morphological analyses

The morphology of MTLT was observed using two imaging techniques: quantitative backscattered electron imaging (qBEI) and scanning probe microscopy mode of the indenter. qBEI images were captured using a digital scanning electron microscope with a four-quadrant semiconductor backscattered electron detector (DSM 962, Zeiss), at a working distance of 15 mm. The probe current was adjusted to 110±0.4 pA and the electron beam energy used was 20 keV (Roschger et al., 1998). Images with magnifications of 50 and 400x were captured, which yielded imaged areas of approximately 2.0×2.5 mm and 250×315 μm, respectively (see Fig. 1). The regions were chosen randomly, ensuring that both types of morphology are visible in each image. Additionally, topography scans were obtained using the Hysitron Triboindenter with a Berkovich tip, the same as the one used for indentation (see Section 2.3.2) with a scan rate of 0.3 Hz.

Indentation

Selection of regions of interest

Regions of interest for indentation were selected within the tissue previously imaged with qBEI. In each section of a tendon, 6–10 400x qBEI images containing both circumferential and interstitial zones were taken, defining the regions of interest for indentation. In each of these, 30–60 single indents were placed using a light microscope of the indenter to position indents avoiding lacunae, micropores or surface preparation defects. Over 3000 indentations with 2500 nm (dried and physiological conditions of indentation) and over 2000 indents of approximately 900–1000 nm in depth (dried conditions) were performed in site matched zones of the 49 specimens. The difference between what we refer to as microindentation (final indentation depth of about 2.5 μm) and nanoindentation (about 900 nm) for MTLT is barely a factor of 3 in depth. Nevertheless, in microindentation, greater influence of microporosity is expected, as the size of an indent may cover more than one fiber. Additionally, the micropores are partially invisible when choosing the indentation sites. In nanoindentation, the influence of microporosity is minimized, as the resulting deformed volume is smaller than a fiber and all indents were inspected for a visible influence of surface defects (also micropores visible with the scanning probe microscopy).

Indentation protocol

MTLT was considered to be a linear viscoelastic material under small strains, an assumption based on previous macroscopic tensile tests (unpublished data) and its similarity of mineralization to bone. Two machines were used: the Nano-Hardness Tester, CSM Instruments, Peseux, Switzerland (for microindentation) and the TriboIndenter, Hysitron, USA (for nanoindentation). In this study MTLT samples were indented in two orthogonal directions (axial and transverse) to the main axis of a tendon.

Indentations were performed in both dried and physiological conditions to evaluate re-hydration effects on MTLT’s stiffness. Microindentation in physiological conditions was performed in a specially designed fluid cell, using Hank’s Balanced Salts Solution (HBSS; VWR, Vienna, Austria) as a re-hydration medium. Samples were re-hydrated for at least 1 h before indentation.

In all cases, a Berkovich indenter was used and measurements were conducted in a load control. The indentation protocol involved trapezoidal loading/unloading at a constant rate of 120 mN/s, with 60 s holding time at maximum load to minimize the viscoelastic and/or viscoplastic effects. In microindentation, this load controlled protocol was performed until the displacement limit of 2500 nm, and, in nanoindentation, until the load limit of 9000 μN. As no protocols for indentation of mineralized tendons were available in the literature, the two indentation depths were chosen based on previous experiments on mineralized tissues (mainly cortical and trabecular bone): for microindentation — (Wolfram et al., 2010a,b) and for nanoindentation — (Franzoso and Zysset, 2009). Indentation moduli were calculated according to the method of Oliver and Pharr (1992).

Because this study was not focused on time dependence, a homogeneous loading rate was used in all indentations. MTLT was considered to have a no more rate-dependent behavior than other mineralized tissues on which nano- and microindentations have previously been successfully performed (Ebenstein and Pruitt, 2006; Oyen, 2006).

Statistical analyses

All indents located close to scratches or other surface defects (including pores) were discarded as outliers. Earlier studies on mineralization of the two zones of morphology had shown low heterogeneity of mineralization within a zone (Spiesz et al., 2012). This allowed defining additional statistical outliers of indentation moduli as values higher than 1.5 times the interquartile range above the third quartile and below the first quartile (Crawley, 2005). A Welch two-tailed -test (Crawley, 2005) was used to compare the groups. The differences were shown using the box and whisker plots that represent the sample medians (horizontal bar) and the top/bottom border of the box represents the interquartile range (see Figs. 3–5). Whiskers represent maximum/minimum value (after removal of the outliers). This representation of the data has the advantage of showing the nature of variation in the results and skewness of the distribution (Crawley, 2005), rather than merely showing the means and standard deviations. A significance level of was used in this study.

Indentation work

The work of indentation was calculated for the microindentation experiments. Application of the force to the indenter and the resulting displacement represents the work done on the system, and is manifested as plastic and elastic strains in the specimen (Fischer-Cripps, 2002). During unloading, energy is released by the material. The area enclosed by the loading and unloading curve represents the energy lost in plastic deformation (plastic work). The elastic energy stored was evaluated by integration of the area under the unloading curve, until the end of the holding phase (elastic work).

Stiffness tensor estimation

An iterative scheme proposed by Franzoso and Zysset (2009) was used to estimate a stiffness tensor based on indentation moduli in two orthogonal directions. The scheme is based on a procedure inverse to the one proposed by Swadener and Pharr (2001), which allows calculation of the indentation moduli in a given direction knowing the material’s stiffness tensor.

Results

Microindentation in dried and physiological conditions

A higher indentation modulus was measured in the circumferential zone, as compared to interstitial one, using microindentation in axial and transverse directions (see Table 1). Also, a higher anisotropy extent was measured in the circumferential zone than in the interstitial one, see Table 1. Significant differences of indentation moduli in dried and physiological conditions, for both axial and transverse directions, were found when the circumferential and interstitial zones were treated separately, (-values below 0.05, see Fig. 3). Similarly, as for the trabecular bone (Wolfram et al., 2010a), re-hydration of the MTLT diminished the indentation modulus for both orthogonal directions and in both morphology zones.

Table 1

Extent of anisotropy measured with nano- and microindentation in two orthogonal directions, in dried (DRY) and re-hydrated (WET) conditions. Average indentation moduli in the axial and transverse direction , as well as standard deviations (in brackets), are given in GPa. CIR stands for the circumferential and INT for the interstitial zone. The differences of the anisotropy extent between the CIR and INT zones were not statistically significant.

Anisotropy extent	Microindentation		Nanoindentation
^indE_axi^indE_trv	WET	DRY	DRY
CIR	12.85(±1.57)2.85(±0.93)=4.50	13.68(±0.83)6.51(±1.03)=2.10	18.09(±2.86)10.16(±1.81)=1.78
INT	11.60(±1.22)2.76(±0.77)=4.20	12.18(±1.05)6.14(±1.08)=1.99	15.68(±3.86)9.92(±1.59)=1.60

Fig. 3

Re-hydration effects on microindentation moduli evaluated separately in the two morphology zones: circumferential (CIR) and interstitial (INT). Indentation moduli were measured in dried (DRY) and re-hydrated conditions (WET), in the two orthogonal directions (AXI, TRV). The level of significance noted in the figure (*) is . The horizontal solid bars represent medians, the top/bottom border of the box represent the interquartile range. Whiskers represent maximum/minimum value.

On average, the indentation modulus decreased by 5.4% in physiological conditions with respect to the dried ones, when measured in the axial direction. In the transverse direction the averaged measured stiffness decrease was 55.6%, but is likely overestimated due to swelling artifacts.

The total work, as well as the plastic and elastic work of microindentation, were calculated for measurements in dried and physiological conditions and showed similar trends as indentation moduli for the same cases. Plastic work is shown in Fig. 4a as an example.

Fig. 4

(a) Microindentation plastic work measured in dried (DRY) and re-hydrated (WET) conditions, in the two orthogonal directions (AXI, TRV), in the two morphology zones (CIR, INT), (b) ratio of elastic to plastic work averaged over the two morphology zones for simplification. The level of significance noted in the figure (*) is . The horizontal solid bars represent medians, the top/bottom border of the box represents the interquartile range. Whiskers represent maximum/minimum value.

Ratios of the elastic over plastic work , representing the fraction of elastic and dissipated energy were calculated to ensure the work was independent of the maximal load used in indentation (see Fig. 4(b)). Higher ratios were observed in the transverse direction of indentation (0.40 and 0.53 in dried and re-hydrated conditions, respectively) than in the axial one (0.23 and 0.18 in dried and re-hydrated conditions).

Nanoindentation in dried conditions

To compare with the results of microindentation in dried conditions, indents with the final depth of 900–1000 nm were performed on the same samples and in the same regions of interest. In nanoindentation, as in microindentation, the circumferential zone was stiffer in the axial and transverse directions than the interstitial zone, but only the difference in the axial moduli was significant (, see Fig. 5).

Fig. 5

Nanoindentation results in the two morphology zones (CIR, INT), dry indentation in two directions (AXI, TRV). The level of significance noted in the figure (*) is . The horizontal solid bars represent medians, the top/bottom border of the box represents the interquartile range. Whiskers represent maximum/minimum value.

The indentations were performed in load control and resulted in different final indentation depths (depending on the local stiffness of the tested area). The average final indentation depth in the axial direction of indentation was higher for the interstitial zone (990 ± 138 nm) than in the circumferential one (916 ± 64 nm). The final indentation depths were higher in the transverse direction of the indentation as compared to the axial directions. The final depth in the interstitial zone was again higher (1205 ± 155 nm) than in the circumferential one (1109 ± 79 nm).

Comparison between nano- and microindentation results

Indentation moduli measured with nanoindentation were higher than the ones measured with microindentation (see Table 1). The anisotropy extent measured with nanoindentation was lower compared to the one measured with microindentation in the same regions of interest as mentioned before (see Table 1). The circumferential zone of MTLT showed higher anisotropy compared to the interstitial one, both in nano- and microindentation, as well as in dried and re-hydrated conditions of microindentation, but the differences were not significant. Stiffness tensors of MTLT were estimated from micro- and nanoindentation results in the dried state, taking the average of all indents in the given indentation direction (see Fig. 6). The following transverse-isotropic stiffness tensors were estimated for MTLT from:

Fig. 6

Transverse-isotropic stiffness tensors estimated from the average indentation moduli in two orthogonal directions for the dried state micro- and nanoindentation in MTLT.

microindentation in two directions:

nanoindentation in two directions:

Discussion

The goal of this study was to quantify the extent of elastic anisotropy in MTLT using two-directional indentation. It was assumed that the anisotropy in this tissue would be higher than that measured in bone, because of the simple, uniaxial arrangement of the mineralized collagen fibers. In cortical and trabecular bone the fiber arrangement is much more complex, with ranges in average anisotropy extent lower than those seen in MTLT. Franzoso and Zysset (2009) had measured the extent of anisotropy of human cortical bone using nanoindentation in the dried state, which resulted in an average . Wolfram et al. (2010b) had found a lower anisotropy in trabecular bone (1.40 measured with microindentation in the re-hydrated and 1.19 in dried state). In this work, the anisotropy in MTLT was found to be the highest among those mineralized tissues (see Table 1). Similarly, the elasticity anisotropy ratio which had been obtained with acoustic microscopy by Lees and Page (1992) was 1.96 — higher than the anisotropy in bone, and within the range measured in this study for dried specimens.

The elastic anisotropy extent of a mineralized collagen fibril array had been predicted with a mean field micromechanical homogenization scheme by Reisinger et al. (2010). In their model, the mineralized collagen fibrils had been aligned uniaxially in arrays similar to MTLT. The extent of anisotropy quantified by a ratio of indentation moduli in the axial and transverse directions was found to be in the range of 1.5–2.0, depending on the overall mineralization of the array and stiffness of collagen used in the simulation. This is in agreement with the range measured using indentation in dried conditions in this work (see Table 1).

The anisotropy ratio measured in re-hydrated conditions (4.20–4.50) was outside of the range predicted by the simulations by Reisinger et al. (2010), which may be due to the highly reduced values of indentation modulus measured in the transverse direction. The stiffness changes in physiological conditions in this direction of indentation may be larger than the changes in vivo and may be due to the excessive bulging of the sample surface in this direction. The swelling in MTLT has been reported to be highly anisotropic at the macroscopic level (Lees and Page, 1992), which is confirmed here in the microscopic scale. Microindentation moduli in the transverse direction of MTLT in the re-hydrated state are on average 55.6% lower than the results obtained in the dried state. This appears to be due to an artifact originating from the swelling of the cut tissue surfaces, where the fibers are not constrained. In this study a surface swell of about 15–20 μm in the transverse samples under HBSS re-hydration was seen. The physiological process of swelling in the wet state may be rather less pronounced in vivo, as the fibers are constrained with one another. The indentation moduli had been shown to decrease by about 29% when going from the dried to the wet state in trabecular bone (Wolfram et al., 2010a). This decrease is greater than what we have measured in the axial direction of MTLT (average 5.4%). The swelling in the axial and transverse directions of MTLT are likely to be the two extremes. We note that the fibers in MTLT are aligned in a parallel manner along the long axis of the tendon, whereas the complex lamellar arrangement of mineralized collagen fibers in bone restricts the swelling, so that the average amount of decrease in the indentation moduli with re-hydration falls somewhat in the middle between the two extremes seen in MTLT.

The circumferential zone of MTLT showed higher anisotropy, in both micro- and nanoindentation than that of the interstitial zone. This could be caused by the slightly different composition of the two types of morphology. In the fibril-array model proposed by Reisinger et al. (2010), elastic anisotropy was found to be proportional to the volume fraction of the mineralized collagen fibrils in a fibril-array, so also proportional to the volume fraction of collagen in the array. This would suggest a higher volume fraction of collagen in the circumferential zone as a factor contributing to the higher anisotropy of this zone. Additionally, the volume fraction of fibers observed with light microscopy was also higher in this zone (Spiesz et al., 2012).

The higher anisotropy of the indentation moduli results from the microindentation rather than from nanoindentation (see Table 1). This may be due to the higher impact of microporosity on the indentation modulus obtained in the microindentation in the transverse direction of MTLT. Additional compliance coming from bending of the mineralized collagen fibers of MTLT could be expected, if obscured longitudinal micropores are present close to or within the indentation deformation zone. This is less likely the case for nanoindentation, where the deformed volume is smaller. Also the final indentation depth in nanoindentation in the transverse direction is higher than that in the axial direction. Due to the assumed indentation depth effects, the indentation moduli values may be underestimated. This would cause the overestimation of the stiffness anisotropy ratio of nanoindentation measurements in MTLT. Additionally, damage accumulation (reduction of stiffness) under the tip may be dependent on the indentation depth.

The extent of mineralization of the MTLT was shown to be similar to that of human bone (Gupta et al., 2004). Differences in the morphology of the two zones were studied recently (Spiesz et al., 2012) suggesting some modeling/remodeling occurs in the tissue. The circumferential zone seems to be a newer one that is deposited on the edges of the vascular channels (large pores in Fig. 1(a) and (b)). The interstitial zone with the large mineralized fibers seems to be a product of mineralization of the large collagen fibers already existing in tendon. The different origins of the two tissue types may result in different mineral distributions (between the fibrils and extrafibrillar matrix) and mineral orientations. The newly built circumferential tissue is likely to be more similar to bone in the mineralization process, as both collagen fibrils and mineral may be laid down approximately at the same time. This may result in a high infiltration of the mineral into the fibril. On the other hand, the large collagenous fibers mineralizing after the fiber assembly may result in a lower infiltration rate and therefore higher extrafibrillar mineralization. The orientation of the extra- and intrafibrillar mineral also may be different. The intrafibrillar mineral likely follows the arrangement of the collagen fibrils, what causes high orientation (Fratzl and Weinkamer, 2007) and potentially enhances the stiffness. The extrafibrillar mineral may be less oriented (Fritsch and Hellmich, 2007), but modeling of the mineralized collagen fibrils has shown an increase in stiffness related to placing more mineral in the extrafibrillar space (Nikolov and Raabe, 2008), (Reisinger et al., 2010). The differences in the mineral distribution in the zones may be one of the factors explaining the difference in stiffness. Unfortunately, detailed experimental analyzes of this problem remain unavailable in literature.

The differences in the total indentation work measured in axial or transverse directions seem to be mainly influenced by the changing plastic work (see Fig. 4(a)). Interestingly the elastic work is comparable in both indentation directions and for both dried and physiological conditions.

The ratios of elastic and plastic work suggest that more energy is dissipated in the indentation in axial direction than in the transverse one. This may be caused by an anisotropic post-yield behavior of MTLT. More energy is dissipated during indentation in axial direction, as more fibers-slippage is likely to occur there. Also shear strain between the fibers is likely to be higher there than in transverse direction. Similar results were observed by Hengsberger et al. (2002) in indentation of human osteons. Dark (thick) lamellae, where the fibers are arranged mostly in the direction along the osteon main axis (Ascenzi and Lomovtsev, 2006; Spiesz et al., 2011) showed more dissipation, which could be a similar situation to indentation of MTLT in axial direction of the fibers. Less dissipation was measured in bright (thin) lamellae, similar to transverse direction of indentation in MTLT.

The measurements performed here are indentations in a porous media and in this sense fulfill the conditions of the half-space indentation in a homogenized sense, nevertheless the nano- and microindentation are valid methods for evaluating the average elastic properties of mineralized tissues (Hengsberger et al., 2002; Oyen, 2006; Donnelly et al., 2006; Lewis and Nyman, 2008; Wolfram et al., 2010a,b), as well as other natural and engineering materials (Berke et al., 2009; Jaeger et al., 2011).