Increased tissue-level storage modulus and hardness with age in male cortical bone and its association with decreased fracture toughness

Abstract

The incidence of bone fracture increases with age, due to both declining bone quantity and quality. Towards the goal of an improved understanding of the causes of the age-related decline in the fracture toughness of male cortical bone, nanoindentation experiments were performed on femoral diaphysis specimens from men aged 21–98 years. Because aged bone has less matrix-bound water and dry bone is less viscoelastic, we used a nanoindentation method that is sensitive to changes in viscoelasticity. Given the anisotropy of bone stiffness, longitudinal (n = 26) and transverse (n = 25) specimens relative to the long axis of the femur diaphysis were tested both dry in air and immersed in phosphate buffered saline solution. Indentation stiffness (storage modulus) and hardness increased with age, while viscoelasticity (loss modulus) was independent of donor age. The increases in indentation stiffness and hardness with age were best explained by increased mineralization with age. Indentation stiffness and hardness were negatively correlated with previously acquired fracture toughness parameters, which is consistent with a tradeoff between material strength and toughness. In keeping with the complex structure of bone, a combination of tissue-level storage modulus or hardness, bound water, and osteonal area in regression models best explained the variance in the fracture toughness of male human cortical bone. On the other hand, viscoelasticity was unchanged with age and was not associated with fracture toughness. In conclusion, the age-related increase in stiffness and hardness of male cortical bone may be one of the multiple tissue-level characteristics that contributes to decreased fracture toughness.

Graphical Abstract

1. Introduction

The incidence of bone fracture increases with age and is a problem with significant societal costs [1–4]. For example, about 30% of people with a hip fracture will die in the following year [4]. Although fragility fractures are commonly associated with elderly women, men suffer from osteoporosis as well. The hip fracture incidence in men is approximately that of women who are 5 years younger [1], and approximately 1 out of every 4 hip fracture cases in the United States occur in men [4]. Traditionally, the increase in fracture incidence among the elderly is attributed to declining bone mass with age. Thus, the criterion used to diagnose osteoporosis, areal bone mineral density (aBMD) by dual-energy X-ray absorptiometry below a threshold, is primarily based on a measure of bone mass. However, the probability of a fracture increases with age independently of aBMD [1–3]. For the same aBMD, an 80 year old woman has a hip fracture probability that is 3 to 6 times greater than that of a 50 year old woman [2]. Thus, with age there is a decline in both bone quantity and quality, where quality in the present study refers to the determinants of fracture resistance for a given quantity of bone. In a large observational study, only 21% of the male non-vertebral fractures occurred in osteoporotic men, which demonstrates the shortcomings in using aBMD as the sole predictor of fracture risk [1]. The motivation of this study is the expectation that an improved understanding of the mechanisms behind the age-related decline in bone quality will inform better diagnostic and treatment options.

The fracture resistance of cortical bone is especially important because 80% of fractures are non-vertebral and occur at sites which are predominantly cortical [5]. Because of its greater surface area, trabecular bone loss begins earlier than cortical bone loss. For men, around 42% of total lifetime trabecular bone loss occurs before 50 years of age, compared to 15% for cortical bone [6]. Thus, the increase in fracture incidence in the elderly occurs after substantial trabecular bone loss has already occurred and is at a time when bone loss is predominantly cortical. The importance of cortical bone at a common fracture site, the femoral neck, has been demonstrated in a study in which complete removal of all trabecular bone only resulted in a failure load decrease of 7% [7]. A decline in cortical bone quality can therefore substantially reduce whole-bone fracture resistance.

Bone fractures in an increasingly brittle fashion with age, characterized by reduced strain at failure [8, 9] and straighter crack paths [10, 11]. A number of compositional and structural properties have been linked to declining bone quality with age, such as increased porosity [12], in vivo microdamage accumulation [13], increased advanced glycation end-products (AGEs) [14], increased osteon density (#/mm²) [15] but decreased osteonal area fraction (mm²/mm²) [16], and decreased bound water content [17]. Other changes with age during adulthood in male cortical bone, such as those of matrix mineralization and stiffness, are still inconclusive, due to insufficient or discordant findings. Given the number of concurrent changes with age at varying length scales, it is a challenge to determine the relative contribution of a given property change on fracture toughness. Whole-bone fracture resistance is further complicated by factors separate from bone quality, such as total bone mass and its distribution.

Nanoindentation is a useful technique in bone mechanics investigations because it is capable of measuring the mechanical properties of small volumes of material, independent of porosity (surface voids such as Haversian canals, lacunae, etc. can be avoided). This study was designed to identify mechanical property changes with age in adult male cortical bone at the tissue level. Similar indentation and compositional studies have found substantial variation between individuals and indicated that changes with age, if any, were likely to be modest [18–20]. Therefore, specimens from a relatively large number of donors (n = 30), over a wide age range (21–98 years) were used. Because bone matrix properties vary spatially within the lamellar structure of cortical bone and between tissue types, it is necessary to sample a number of different regions in order to accurately characterize a given specimen. In this study, each specimen was tested with 64 indents, distributed among 8 osteons and 8 neighboring interstitial sites, which are the remnants of osteons as bone remodels. Given the anisotropy of bone and the importance of water to bone’s mechanical properties, longitudinally and transversely sectioned specimens from each donor were tested in both wet and dry conditions. Since declining matrix-bound water has been associated with the age-related decline in bone quality and since matrix hydration affects bone viscoelasticity, the nanoindentation method used to characterize the tissue-level properties of bone was designed to be sensitive to possible changes in viscoelasticity with age. Including mechanical, compositional, and micro-structural properties of cortical bone acquired in previous studies [16, 21] from the same donors, we were able to address several questions: If the nanomechanical properties change with age, were any compositional changes responsible? Are the nanoindentation and fracture data correlated? What combination of parameters best predicted the fracture toughness data? Together these experimental analyses test the hypothesis that changes in tissue-level mechanical properties, as determined by dynamic nanoindentation, are indicative of the age-related decline in the fracture toughness of male cortical bone.

2. Material and Methods

2.1. Study Design

This study consists of indentation, fracture, compositional, and structural data from human cortical bone samples extracted from the lateral quadrant of the mid-shaft of fresh-frozen cadaveric femurs. Provided by 2 procurement agencies of tissue allografts (NDRI, Philadelphia, PA and MTF Biologics, Edison, NJ), the cadaveric femurs came from 30 male donors, aged 21–98 years. Thus, these samples covered nearly 8 decades of adult male aging.

The primary indentation parameters reported in this study are storage modulus (E′), loss modulus (E″), and hardness (H). To study the effect of hydration, indentation experiments were conducted with the bone specimens tested dry in air (dry condition) and immersed in phosphate buffered saline (PBS) solution (wet condition). There were 2 cortical femur specimens for each donor, with one specimen being longitudinally sectioned and the other transversely sectioned, relative to the long axis of the femur. Because bone mechanical properties vary spatially, each indentation test consisted of a large number of indents, spread between a number of regions of interest. In each indentation experiment, indents were split between osteonal and interstitial locations. Therefore, the 4 variables in the human femur indentation data were:

1. Condition (wet vs. dry)

2. Section (longitudinal vs. transverse)

3. Age (21–98 years)

4. Location (osteonal vs. interstitial)

Details on the acquisition of the mechanical, compositional, and micro-structural properties (Table 1) can be found in our previously published studies [16, 21]. Briefly, single edge notched bend (SENB) specimens were tested in 3-point bending. The fracture parameters of interest in this study were K_init (critical stress intensity at crack initiation) and the J-integral (J-integral value at failure). The micro-structural parameters were PoreWater (pore water volume fraction), and OstAr (osteonal area fraction). PoreWater is a bulk measure of the volume of voids within a volume of cortical bone, while OstAr is a measure of the proportion of the cross-sectional area occupied by osteonal bone. PoreWater was measured by ¹H nuclear magnetic resonance (¹H NMR) spectroscopy [21] and OstAr by quantitative backscattered electron imaging (qBEI) [16]. The compositional parameters were TMD (tissue mineral density), BoundWater (bound water volume fraction), PE (pentosidine crosslinking concentration) [21], and Ca wt.% [16] (Table 1). TMD and qBEI Ca wt.% are measures of the degree of bone mineralization. BoundWater quantifies the volume of water within the bone matrix.

Table 1:

Summary of human femur fracture, compositional, and structural parameter data

Name	Description	Measurement Technique
Kinit	Critical stress intensity at crack initiation	SENB 3-point bending
J-integral	J-integral value at failure	”
TMD	Tissue mineral density	μCT
PoreWater	Pore water volume fraction	1H NMR
BoundWater	Bound water volume fraction	”
PE	Pentosidine crosslinking concentration	HPLC
OstAr	Osteonal area fraction	qBEI
Ca wt.%	Degree of mineralization	”

SENB = single edge notched bend

μCT = micro-computed tomography

¹H NMR = ¹H nuclear magnetic resonance spectroscopy

HPLC = high-performance liquid chromatography

qBEI = quantitative backscattered electron imaging

Along with correlations with age, changes with age were assessed by splitting the donors into two age groups: young (age ≤ 60 years, n = 14) and aged (age > 60 years, n = 16). Sixty years was chosen as the age cutoff for two reasons. First, this age cutoff gives nearly equal group sizes. Second, bone turnover in adult men progressively decreases to a minimum at around 60 years of age [22]. For all donors, the mean age ± standard deviation was 63.5 ± 23.7 years. For the young and aged groups, these values were 42.1 ± 14.5 years and 82.1 ± 10.5 years, respectively.

2.2. Specimen Preparation

The transverse set of nanoindentation specimens was created by cutting ~3 mm thick cross-sections from the SENB specimens, away from the region of fracture. Comparably-sized longitudinal nanoindentation specimens neighbored the transverse specimens and included the surface along the SENB specimens. Surfaces were first ground (Exakt 400CS Grinder) with wet silicon carbide paper starting with 800 grit or 1200 grit and ending on 4000 grit (Exakt Technologies, Oklahoma City, OK). After confirming that none of the scratches from grinding with 1200 grit were present, the surfaces were then polished (Buehler Vibromet 2 Polisher) on a synthetic cloth containing 0.05 μm aluminum oxide suspension (MasterPrep, Buehler, Lake Bluff, IL). Note that the qBEI and nanoindentation transverse specimens were the same, with qBEI being performed first.

2.3. Indentation Theory and Equations

2.3.1. Quasi-static Indentation

Nanoindentation uses an indenter tip of known geometry and load-displacement data obtained during the loading and unloading of the indenter to measure mechanical properties of small volumes of material. Most commonly, Young’s modulus (E) and hardness (H) are measured using the Oliver-Pharr method [23]. During indentation both the indenter and the indented material deform elastically, and the effective elastic modulus of the combined testing system and specimen is known as the reduced modulus (E_R). The reduced modulus, measured contact stiffness (S), and indenter projected contact area (A_c) are related by

$$E_R=\frac{\sqrt{\pi }}{2\beta }\frac{S}{\sqrt{A_c}}$$ (1)

where β is a constant which depends upon indenter geometry. Once E_R has been calculated using Equation 1, E can be calculated by

$$\frac{1}{E_R}=\frac{1-v^2}{E}+\frac{1-v_i^2}{E_i}$$ (2)

where E_i and v_i are Young’s modulus and Poisson’s ratio, respectively, of the indenter tip. Finally, v is Poisson’s ratio of the indented material, which is often assumed. The contact stiffness, S, can be calculated from the initial portion of the unloading curve as dP/dh, for load on sample P and displacement into surface h. The contact area, A_c, is a function of indenter contact depth (h_c), which can be calculated from the shape of the indenter tip, but in practice the tip area function is generally determined by indenting a reference material. The contact depth, h_c, is less than the total displacement of the indenter tip for materials which exhibit sink-in, due to elastic displacement of the material’s surface and can be computed from:

$$h_c=h-\epsilon \frac{P}{S}$$ (3)

In Equation 3, ε is a constant based on indenter geometry whose value is close to 0.75. Hardness is calculated as the ratio of maximum load (P_max) to A_c at that peak load.

$$H=\frac{P_{max}}{A_c}$$ (4)

2.3.2. Viscoelasticity

Viscoelastic materials exhibit both elastic and viscous mechanical properties. When subjected to deformation, part of the input energy is stored elastically and part is dissipated as heat. Viscoelastic materials demonstrate time-dependent behavior such as creep and stress relaxation. When a linear viscoelastic material is subjected to a harmonic stress, the resulting strain is also harmonic but is delayed relative to the input stress according to:

$$\sigma ={\sigma }_o\text{sin}\left(\omega t\right)$$ (5)

$$\epsilon ={\epsilon }_0\text{sin}\left(\omega t+\delta \right)$$ (6)

were σ is stress, σ₀ is stress amplitude, ε is strain, ε₀ is strain amplitude, ω is angular frequency, t is time, and δ is the phase lag between the input stress and the resulting strain. The stress-strain relationship of a viscoelastic material under harmonic loading can be described by the storage modulus (E′) and loss modulus (E″):

$$E^{\prime }=\frac{{\sigma }_o}{{\epsilon }_0}\text{cos}\left(\delta \right)$$ (7)

$$E^{″}=\frac{{\sigma }_o}{{\epsilon }_0}\text{sin}\left(\delta \right)$$ (8)

E′ is in-phase with the input stress and describes the elastic behavior of the material, while E″ is 90° out-of-phase and describes its viscous behavior.

2.3.3. Dynamic Indentation

E′ and E″ of a viscoelastic material can be measured by nanoindentation through the use of the continuous stiffness measurement (CSM) technique. In CSM a small harmonic load is superimposed on the much larger load required to drive the indenter into the sample. Contact stiffness can be continuously measured as the ratio of harmonic load amplitude to harmonic displacement amplitude. In practice, a lock-in amplifier is used to measure S and δ. The harmonic motion of the instrument can be modeled as a damped harmonic oscillator:

$$m{h}^{″}+C_m{h}^{\prime }+k_{m}h=Fcos\left(\omega t\right)$$ (9)

where m is the oscillator mass, h is displacement, C_m is the damping coefficient, k_m is the stiffness coefficient, F is the driving force with angular frequency ω, and t is time. Dynamic indenter-sample contact is described by a spring and dashpot mechanical model where the sample and instrument are in parallel and are each described by a spring and a dashpot in parallel:

$$k_m=k_i+k_s$$ (10)

$$C_m=C_i+C_S$$ (11)

where the subscript m denotes the measured value, i the instrument, and s the sample. It is therefore necessary to correct measurements for the dynamics of the instrument. It is possible to the solve for the sample values, k_s and ωC_s, using

$$k_s=S_m\text{cos}\left({\delta }_m\right)-S_i\text{cos}\left({\delta }_i\right)$$ (12)

$$\omega C_s=S_m\text{sin}\left({\delta }_m\right)-S_i\text{sin}\left({\delta }_i\right)$$ (13)

where S_m and δ_m are the measured harmonic stiffness and phase angle with the indenter in contact with the sample. S_i and δ_i are the same values, except when the indenter is not in contact with the sample, i.e. in free space.

The viscoelastic equations corresponding to Equation 1 give the reduced storage (${E^{\prime }}_R$) and loss (${E^{″}}_R$) moduli:

$${E^{\prime }}_R=\frac{\sqrt{\pi }}{2\beta }\frac{k_s}{\sqrt{A_c}}$$ (14)

$${E^{″}}_R=\frac{\sqrt{\pi }}{2\beta }\frac{\omega C_s}{\sqrt{A_c}}$$ (15)

Finally, using Equation 2 to solve for E′ from ${E^{\prime }}_R$ and E″ from ${E^{″}}_R$ and using the fact that the diamond tip is not viscoelastic gives:

$$E^{\prime }=\left(1-v^2\right){\left(\frac{1}{{E^{\prime }}_R}-\frac{1-v_i^2}{E_i}\right)}^{-1}$$ (16)

$$E^{″}=\left(1-v^2\right){E^{″}}_R$$ (17)

2.3.4. Summary of Calculations

In summary, the steps to calculate E′, E″, and H were:

1. Measure P, h, S_m, δ_m, S_i, and δ_i

2. Calculate k_s and ωC_s from Equations 12 and 13

3. Calculate h_c from Equation 3 (using k_s in the place of S)

4. Calculate A_c from a previously measured tip area function (A_c = f(h_c))

5. Calculate ${E^{\prime }}_R$ and ${E^{″}}_R$ from Equations 14 and 15

6. Calculate E′, E″, and H from Equations 16, 17, and 4

Input values for the Berkovich diamond tip were:

• ε = 0.75

• β = 1.034

• E_i = 1143 GPa

• v_i = 0.3

The Poisson’s ratio of bone used was v = 0.3.

2.4. Indentation Experiments

2.4.1. Equipment

Nanoindentation experiments were conducted using a NanoIndenter XP instrument (Agilent Technologies, Oak Ridge, TN) with a Berkovich diamond tip (Micro Star Technologies, Huntsville, TX). The Berkovich tip is a 3-sided pyramidal indenter with a centerline-face angle of 65.3°. The tip area function was periodically calibrated using a fused silica reference material. A MATLAB GUI was developed for indentation site selection, with desired indent locations selected individually by mouse click. Adequate spacing (30 μm, i.e. 30x the end-of-loading displacement target) between indents and between indents and pores was ensured by a circular region drawn around each selected indent location. For areas free of surface features needing to be avoided, indents could also be placed as a rectangular array.

To generate physiologically accurate mechanical data, bone specimens must be tested in a hydrated state. For the wet condition nanoindentation experiments, the bone specimens were fully immersed in 0.01 M phosphate buffered saline solution (PBS, Sigma-Aldrich P3813, Saint Louis, MO). PBS solution was used for the hydrated tests, as opposed to distilled water, in order to prevent mineral dissolution from the surface of the bone specimens. The sample holder consisted of an inner sample puck surrounded by an outer hollow cylinder. Both components were stainless steel. The sample puck could slide vertically within the outer cylinder, which enabled the sample surface to be set a fixed distance from the top surface of the outer cylinder (1.3 mm). A polyurethane O-ring housed in grooves around the perimeter of the inner sample puck kept the PBS solution from leaking through the gap between the puck and the outer cylinder. In order for the sample to remain immersed through the duration of an experiment, it was necessary to compensate for evaporative liquid loss. This was done by a syringe pump with liquid-level feedback, comprised of two probes and a voltage divider circuit. The liquid-level voltage was measured after the completion of each indent. Thus, the syringe pump was not active while an indent was in progress. The syringe pump was connected to the specimen holder via a small hole in the cylindrical outer ring. The syringe tip was passed through a tapered round plug, which was then inserted into the hole. Thus, PBS was added to the sample well in a bottom-up fashion (Figure S1).

2.4.2. Indentation Method

The first stage of this study was the development of an indentation method which could accurately measure the viscoelasticity of bone and its potential change with age. The method was required to work equally well in the wet and dry hydration conditions. After making contact with the sample, load on sample was increased until the displacement target of 1 μm was reached. Loading was exponential, at a Ṗ/P rate of 0.5 s⁻¹, where Ṗ is the loading rate and P is the load on sample. For a geometrically self-similar indenter like the Berkovich, a constant Ṗ/P results in a constant indentation strain rate when the hardness does not vary with depth. This step typically took slightly under 20 seconds. Next, the CSM was turned with a harmonic displacement target of 4 nm and an oscillation frequency of 45 Hz. This oscillation frequency was selected for experimental, not physiological reasons, as it was not clear what the most physiologically relevant oscillation frequency would be regarding bone fracture.

Once the harmonic displacement target was reached, the next step was a 2 minute hold, which was the primary data acquisition step. Viscoelastic materials such as bone, demonstrate indenter creep into the sample under constant load. The rate of displacement is greatest at the start of the hold and decreases progressively throughout the hold segment. There are a couple of advantages to a longer hold time. First, the data are more consistent during the more steady-state situation of minimal creep. Second, noise in the data can be averaged out over longer data acquisition times. Data acquisition was at a rate of 5 Hz, and the indentation parameters (E′, E″, H, etc.) were calculated continuously during the 2 minute hold segment. The final values were taken as the averages over the last minute of the hold period.

After the end of hold segment, the indenter was unloaded from the sample to a distance of 1 μm and oscillated in free space for 15 seconds. As discussed in the Dynamic Indentation section, E′ and E″ cannot be accurately determined without an accurate characterization of the instrument’s dynamics (S_i and δ_i). The instrument’s dynamics vary with position within the indenter’s range of travel and could potentially change with time over the course of months of experiments. Additionally, it was unknown to what extent the instrument’s dynamics would be sensitive to immersion in PBS in the wet tests. For these reasons, it was decided that the most accurate method would be to measure S_i and δ_i for each indent, near the surface of each sample.

2.4.3. Experimental Procedure

To set up an indentation experiment, the samples were first removed from the freezer and mounted on the sample puck using cyanoacrylate adhesive. Next, the sample surface and indentation tip were gently cleaned with a methanol-moistened wipe (Kimwipe, Kimberly-Clark Professional). The specimen and outer cylinder heights were then set, and the indent locations were selected and imaged. The 64 indents per test were divided between 8 regions of interest, with each region being an osteonal area and a nearby interstitial area containing 4 indents apiece (Figure 1). In transverse sections, osteons were identified by circumferential lamellae around a central Haversian canal. All non-osteonal regions were considered interstitial. The osteonal – interstitial distinction was less clear-cut for the longitudinal sections (Figure 1b). Again, the defining feature of an osteon was lamellae around a central Haversian canal. In this case, the Haversian canal has the shape of an elongated ellipse. Interstitial regions were non-adjacent to Haversian canals and had a less distinctly lamellar structure than the osteonal regions. For the wet experiments, the specimen was then immersed, and the syringe pump was turned on. After experimental setup there was a 2 hour delay to allow the system to reach thermal equilibrium and for the wet specimens to become fully hydrated. After testing, the indents were imaged, and it was confirmed that the indents were placed accurately. For the wet tests, it was first necessary to turn off the syringe pump, remove the liquid, and clean the sample surface first. Note that the residual dry indentations were larger and more distinct than the wet ones, presumably due to greater viscoelastic recovery in the wet case.

Figure 1:

Examples of osteonal and interstitial indents for the longitudinal (a) and transverse (b) specimens.

2.5. Data Analysis

2.5.1. Indent Exclusion

Due to the large number of indents in this study (>7,500), it was necessary to develop an automated procedure to identify and exclude spurious indentation data. Bad indentation data could be caused by software issues such as missing data index markers (Ex: end of loading, start of hold, etc.) or by experimental issues such as false surface finds or too short of an approach distance. The largest experimental issue was precipitation of salt from the PBS solution onto the indenter shaft, which could impair indenter motion. Automated indent exclusion functioned in two stages. First, each indent was checked for 13 different exclusion criteria (Supplemental Information), based off of the expected behavior of an idealized indent in bone. Second, outliers among the remaining indents were removed to catch any questionable data that may have been missed in the first step. Outliers were identified by $\left|\widehat{z}\right|>2$, where $\widehat{z}$ was the robust z-score estimate:

$$\widehat{z}=\frac{X_i-\text{median}\left(X\right)}{1.4826*\text{MAD}\left(X\right)}$$ (18)

for data set X, where MAD is median absolute deviation:

$$\text{MAD}=\text{median}\left(X_i-\text{median}\left(X\right)\right)$$ (19)

This value was chosen as ≈95% of normally distributed data lies within 2 standard deviations of the mean. The parameters used for outlier exclusion were E’, E″, H, and δ. Indentation outlier exclusion was performed separately for each section–condition combination.

2.5.2. Indent-level to Specimen-level Values

All of the statistical calculations in this study, aside from the site-matched indentation–qBEI Ca wt.% correlations, were done with specimen-level data as inputs, meaning a single representative value for each specimen. The calculation of the representative specimen values proceeded in two steps. First, the osteonal and interstitial averages were determined. These location-specific values were used in calculations for which indent location was considered. For calculations in which indent location was not considered, the representative specimen-level value used was the average of the osteonal and interstitial specimen-level representative values (i.e., (osteonal mean + interstitial mean)/2). The average of the osteonal and interstitial representative values was used because there were often not an equal number of osteonal and interstitial indents.

2.5.3. Specimen Exclusion

The original human femur dataset consisted of specimens from 30 donors (1 longitudinal section and 1 transverse section). However, the final dataset was smaller than this because some specimens were excluded. First, one donor was excluded as an extreme Porosity outlier, where Porosity was calculated from the μCT images. The Porosity robust z-score estimate (same $\widehat{z}$ parameter as was described in Indent Exclusion) for this donor was 21.4. No other donor had a Porosity $\widehat{z}$ greater than 5.9. Thus, the bones from this donor were not representative of those from the other 29 donors, and their inclusion could have skewed the results. For all of the other fracture, compositional, and structural parameters, no $\widehat{z}$ value was greater than 5.1.

Next, for the indentation data, 3 longitudinal and 4 transverse specimens were excluded. The 3 longitudinal section exclusions were due to experimental issues during wet testing. For example, the surface of the specimen may not have remained submerged, or salt buildup could have interfered with the motion of the indenter. One of the excluded transverse specimens was damaged and could not be tested. The other 3 transverse specimens were excluded due to having a measured surface tilt greater than 4° in either the wet or dry experiments. Unlike the longitudinal specimens, the transverse specimens were tested with qBEI before the indentation experiments. The residual adhesive from mounting the transverse experiments for qBEI testing was difficult to cleanly remove, given the small size of the specimens and the fact that the polished top surface could not be touched. Thus, some of the specimens were not mounted perfectly flat for indentation. Surface tilt leads to an underestimation of the actual projected contact area of the indenter and consequently an overestimation in E′, E″, and H. For somewhat blunt tips such as the Berkovich (centerline-to-face angle of 65.3°), this error can be appreciable even at relatively low surface tilt angles. Surface tilt was calculated by fitting a plane to the non-excluded indent surface displacements.

The final number of specimens per age group and per section is listed in Table 2. All calculations were done with the maximum amount of available data, rather than restricting the set of specimens to only those with no missing data. For example, the correlation between K_init and ge had 29 data points, while the correlation between E′–longitudinal–wet and Age had 26 data points. As can be seen in Table 2, when grouped by age, the young and aged groups had a roughly equal number of data points. Note that one of the excluded longitudinal specimens was from the oldest donor. Consequently, the donor age range covered by the longitudinal indentation data (21–97 years) was 1 year less than for the transverse indentation data (21–98 years).

Table 2:

Number of donors and samples by measurement category

	Fracture, Composition, Structure	Indentation: longitudinal	Indentation: transverse
Young	14	13	12
Aged	15	13	13
Total	29	26	25

Young = Age ≤ 60 years

Aged = Age > 60 years

2.5.4. Statistical Analysis

All statistical hypothesis tests used were either nonparametric or robust. This was done because the data were generally not normally distributed and to reduce the influence of extreme values. A significance level of 0.05 was used for all statistical hypothesis tests. In tables, results with 0.05 < p < 0.10 are also reported with an asterisk. Otherwise, the difference or correlation was denoted not significant (−). All hypothesis tests were double-sided. Correlations were calculated as Spearman rank correlations (r_s). Best-fit lines, as well as some linear regression models, were calculated via iteratively reweighted least squares (IRLS), using the Huber weight function and tuning constant of 1.345σ. The Wilcoxon rank sum test was used for comparisons between 2 unpaired groups: wet vs. dry, longitudinal vs. transverse, and young vs. aged. The Wilcoxon signed rank test was used for the osteonal vs. interstitial comparison and to test the distribution of indent-level site-matched indentation–qBEI correlations (null hypothesis: median(r_s) = 0). For boxplots the maximum whisker length was 1.5 times the interquartile range, and values outside of this range were plotted as outliers (red plus signs).

2.5.5. Fracture Regression Models

Linear regression models were created to determine which combination of parameters best predicted the fracture data and whether the inclusion of indentation data significantly improved explanation of the variance in fracture toughness with respect to compositional and microstructural terms. The predictor or explanatory variables used were the indentation, compositional, and microstructural parameters which had significant correlations with the fracture parameter response variable. With this restricted set of predictor variables, each possible model with up to 4 terms was evaluated using ordinary least squares (OLS). The selected models were those with the highest Adjusted-R² value for each fracture parameter. The selected OLS models were also rerun with IRLS, since OLS models can be sensitive to influential data points. To avoid multicollinearity amongst the predictor variables, models with a variance inflation factor (VIF) greater than 5 were excluded (the VIFs in the selected models were ≤ 1.5). To enable a comparison of the relative importance of each predictor variable despite differing units, the coefficients were standardized. Given a regression equation with unstandardized coefficients (α),

$$Y={\alpha }_1{X}_1+{\alpha }_2{X}_2+\cdots +{\alpha }_k{X}_k$$ (20)

the standardized coefficients (β) were calculated by:

$${\beta }_i=\frac{Std\left(X_i\right)}{Std\left(Y\right)}*{\alpha }_i$$ (21)

The magnitude of a standardized coefficient is an estimate of the change in the response variable (number of standard deviations) for a one standard deviation change in the associated predictor variable.

3. Results

3.1. Hardness was the primary difference in nano-mechanical properties between osteonal and interstitial sites of cortical bone

Interstitial hardness (H) was greater than osteonal H, irrespective of section or condition (Table S1). The only section–condition combination in which the osteonal vs. interstitial difference was not statistically significant was longitudinal–dry, and in this instance the difference trended toward H of interstitial tissue being greater than of osteonal tissue (0.05 < p < 0.10). On the other hand, there was no consistent osteonal vs. interstitial difference for storage modulus (E′) or loss modulus (E″) among the 4 combinations with tissue-level E′ and E″ being both higher and lower in interstitial tissue compared to osteonal tissue or not significantly different between the sites (Table S1). Moreover, the significant differences in mean osteonal and mean interstitial values for E′ and E″ were within 4%, while for H, the significant differences were 9% (transverse–wet), 9% (longitudinal–wet), and 6% (transverse–dry).

3.2. Storage modulus, loss modulus, and hardness depended on hydration and orientation of osteons relative to loading direction of the indenter tip

Taking the average of osteonal and interstitial measurements, hydration condition and indentation direction significantly affected storage modulus, loss modulus, and hardness (Table 3). Indentation H and E′ were highly correlated in each experiment (r_s = 0.72–0.89, p < 0.001), whereas H and E″ were mostly uncorrelated. Therefore, the results for E′ and H were generally similar. Relative to the dry-in-air state, specimen hydration had the effect of lowering matrix stiffness (E′) and hardness while increasing viscoelasticity (E″). Indentation measurements parallel to the preferential osteonal orientation (transverse specimens) had higher E′, E″, and H values than measurements normal to the preferential osteonal orientation (longitudinal specimens).

Table 3:

Effect of hydration and orientation of osteons relative to the loading direction on tissue-level nanomechanical properties

Parameter	Section	Wet Mean (SD)	Dry Mean (SD)	Difference (%)a	p-value
E′ (GPa)	Longitudinal	14.1 (1.0)	17.1 (0.8)	+19.5	<0.001
	Transverse	20.4 (1.6)	26.7 (1.5)	+26.9	<0.001
	Difference (%)b	+36.5	+43.8
	p-value	<0.001	<0.001
E″ (GPa)	Longitudinal	0.61 (0.02)	0.40 (0.01)	−42.0	<0.001
	Transverse	0.66 (0.03)	0.47 (0.03)	−34.4	<0.001
	Difference (%)b	+8.0	+15.7
	p-value	<0.001	<0.001
H (GPa)	Longitudinal	0.40 (0.04)	0.51 (0.03)	+24.0	<0.001
	Transverse	0.54 (0.04)	0.87 (0.08)	+47.5	<0.001
	Difference (%)b	+28.7	+52.0
	p-value	<0.001	<0.001

^aPercent difference = 100 × (Dry – Wet) / [0.5 × (Wet + Dry)]

^bPercent difference = 100 × (Transverse – Longitudinal) / [0.5 × (Longitudinal + Transverse)]

Specimen-level values calculated as (osteonal mean + interstitial mean)/2

p-value = Wilcoxon rank sum test p-value

3.3. Storage modulus and hardness increased with age but loss modulus did not

When grouped by age, aged E′ was greater than young E′ for longitudinal–wet, transverse–wet, and longitudinal–dry conditions (Table 4, Figure 2). However, there was no significant young vs. aged difference for the transverse–dry case. The aging trends for H were the same as for E′, except that there was not a significant change with age in the longitudinal–dry case. The magnitudes of the changes with age as a continuous variable were calculated from iteratively reweighted least squares fits with Age as the predictor variable (Figure 3). For the wet hydration condition, irrespective of section, E′ was ~15% greater at the oldest donor age (97 years for longitudinal, 98 years for transverse) compared to the youngest donor age (21 years). The magnitudes of these overall changes were 1.9 GPa for the longitudinal specimens and 2.8 GPa for the transverse specimens, or 0.25 GPa/decade and 0.37 GPa/decade, respectively. Relative to the fit value at 21 years these are increases of 1.9% and 2.0% per decade, respectively. In the longitudinal–dry case, the age-related increase in E′ was 1.3 GPa, or 8% (0.17 GPa/decade or 1.0%/decade). The aging trend for H was slightly weaker than the aging trend for E′, as H increased ~12–13% (1.6%/decade) from the youngest to the oldest donor for the wet hydration condition, irrespective of section. In contrast, when grouped by age, there were no significant differences in E″ between the young and aged groups (Table 4).

Table 4:

Comparison of indentation data between young and aged age groups

Parameter	Section	Condition	Young Mean (SD)	Aged Mean (SD)	p-value
E′ (GPa)	Longitudinal	Wet	13.4 (0.9)	14.7 (0.6)	<0.001
		Dry	16.6 (0.7)	17.6 (0.4)	0.001
	Transverse	Wet	19.5 (1.7)	21.2 (1.0)	0.006
		Dry	26.7 (1.5)	26.8 (1.5)	–
E″ (GPa)	Longitudinal	Wet	0.61 (0.02)	0.61 (0.02)	–
		Dry	0.40 (0.01)	0.40 (0.01)	–
	Transverse	Wet	0.65 (0.03)	0.67 (0.03)	–
		Dry	0.46 (0.04)	0.47 (0.02)	–
H (GPa)	Longitudinal	Wet	0.38 (0.04)	0.42 (0.03)	0.021
		Dry	0.50 (0.03)	0.52 (0.03)	–
	Transverse	Wet	0.51 (0.04)	0.56 (0.03)	0.011
		Dry	0.88 (0.08)	0.86 (0.07)	–

Young = age ≤ 60 years, Aged = age > 60 years

p-value = Wilcoxon rank sum test p-value

– denotes p > 0.10

Figure 2:

Effect of age group on E′ and H data. Significant age group differences are indicated by the comparison lines located above the boxes. Wet vs. dry and longitudinal vs. transverse comparison lines are not shown, since in each instance dry > wet and transverse > longitudinal (Table 3).

Figure 3:

Scatterplots of E′ and H vs. ge in the wet hydration condition. The legend contains information on the aging trend, as determined by the iteratively reweighted least squares (IRLS) best fit line shown in each plot. Both E′ and H increased with age, and the relative magnitude of the aging trend was the same for the longitudinal and transverse sections.

3.4. Fracture toughness negatively correlated with measurements of storage modulus and hardness, which were dependent on mineralization

There were significant correlations between E′ and H and the fracture toughness parameters, each of which was negative (Table 5). The J-integral, the energy dissipated per unit increase in crack surface area at failure, was more consistently correlated with E′ and H than was K_init, the critical stress intensity at crack initiation. Specifically, H and the J-integral were negatively correlated for each of the 4 section–condition combinations, except for transverse–dry, while the only significant correlation between H and K_init was for the longitudinal–wet case. The correlations between E′ and the fracture toughness parameters were the same as those for H, except that there was no significant correlation in the transverse–wet case. Loss modulus, on the other hand, did not correlate with K_init or J-integral, irrespective of the section orientation and hydration state.

Table 5:

Correlations (r_s) between nanoindentation data and fracture and compositional data

Parameter	Section	Condition	Kinit	J-integral	TMD	Bound Water	PE
E′	Longitudinal	Wet	−0.53	−0.56	0.40	−0.38*	–
		Dry	–	−0.50	0.62	−0.40	–
	Transverse	Wet	–	–	0.38*	–	0.46
		Dry	–	–	0.40	–	0.37*
E″	Longitudinal	Wet	–	0.36*	–	–	–
		Dry	–	–	–	–	−0.34*
	Transverse	Wet	–	–	–	–	–
		Dry	−0.37*	–	–	−0.54	–
H	Longitudinal	Wet	−0.40	−0.43	–	–	–
		Dry	–	−0.49	–	–	–
	Transverse	Wet	–	−0.41	–	–	–
		Dry	–	–	–	–	–

^*denotes 0.05 < p < 0.10

– denotes p > 0.10

The compositional parameter that most consistently correlated with E′ was tissue mineral density (TMD), as for all 4 experiments E′ and TMD were positively correlated (p ≤ 0.065, Figure 4). BoundWater (bulk bound water volume fraction) and PE (pentosidine crosslinking concentration) each had orientation-dependent correlations with E′. For the longitudinal sections, E′ and BoundWater were negatively correlated (p ≤ 0.056), while for the transverse sections, PE and E′ were positively correlated (p ≤ 0.066). Surprisingly, there were no significant correlations between H and the compositional parameters. For E″, the only correlation with any of the compositional parameters was an unexpected negative correlation with BoundWater in the transverse–dry case only.

Figure 4:

Scatterplots of E′ vs. tissue mineral density (TMD), with I LS best fit lines. As seen in the correlation information in the legends, E′ and TMD were positively correlated for each of the 4 section–condition combinations (p ≤ 0.065).

To directly assess the dependence of local mineralization on the indentation parameters, the locations of transverse section indents were identified on the qBEI images, and for each specimen the correlation between the indentation data and the extracted local qBEI Ca wt.% was calculated (Table 6). The observed correlations are consistent with the other matrix mineralization parameter in this study, TMD. Namely, E′ was positively correlated with qBEI Ca wt.% in both the wet and dry cases, while E″ and qBEI Ca wt.% were uncorrelated. However, while H and TMD, a bulk measurement away from the sites of nanoindentation, were uncorrelated, site-matched H and qBEI Ca wt.% were weakly correlated in both the wet and dry cases.

Table 6:

Site-matched indentation–qBEI Ca wt.% indent-level correlation data. Indent-level correlations between the nanoindentation and qBEI Ca wt.% data were calculated for each sample, and the null hypothesis tested by the Wilcoxon signed-rank test was that the median indent-level correlation coefficient was equal to zero.

Parameter	Condition	rs Mean (SD)	p-value
E′	Wet	0.23 (0.21)	<0.001
	Dry	0.23 (0.21)	<0.001
E″	Wet	−0.04 (0.25)	–
	Dry	0.06 (0.19)	–
H	Wet	0.28 (0.21)	<0.001
	Dry	0.31 (0.16)	<0.001

r_s = Spearman rank correlation coefficient

p-value = Wilcoxon signed-rank test p-value

– denotes p > 0.10

3.5. Storage modulus and hardness helped bound water and/or microstructural parameters explain the variance in crack initiation toughness and overall energy dissipated during crack growth, respectively

Linear regression models were created to determine which combination of parameters, not including Age, best predicted the fracture data (Table 7). The best-fit models (highest adj-R² with significant explanatory variables) indicate that the nano-mechanical measurements, which included anisotropy (2 orthogonal directions), helped known determinants explain the variance in K_init and final J-integral. The most important takeaway from these models is their multifactorial nature. The K_init prediction model was a function of indentation (longitudinal–wet E′), compositional (BoundWater), and microstructural (PoreWater, OstAr) terms. Likewise, the J-integral model was a function of indentation (longitudinal–wet H, transverse–wet H) and microstructural (OstAr) terms.

Table 7:

Regression models of fracture. The upper equation for each fracture parameter is the OLS model with the highest Adj-R² value out of all possible models with up to 4 terms, where the explanatory variables were restricted to only those with a significant correlation with the fracture response variable (Tables 5, S2). The lower equation is the IRLS model created with the same terms as in the OLS model above. Coefficients are standardized and ordered by decreasing magnitude.

Fracture Parameter	Equation	Adj-R2	n
Kinit	−0.32·E′L,Wet+ 0.26·BoundWater − 0.24·PoreWater + 0.22·OstAr	0.39	26
	−0.43·E′L,Wet + 0.35·BoundWater + 0.22·OstAr − 0.18·PoreWater	N/Aa
j-integral	0.65·OstAr − 0.32·HL,Wet − 0.22·HT,Wet	0.46	23
	0.59·OstAr − 0.34·HL,Wet − 0.26·HT,wet	N/A

^anot applicable because the iterative reweighting method increases the adjusted coefficient of determination relative to OLS regression

n = number of data points

4. Discussion

This is the first study to demonstrate a consistent aging trend in tissue-level mechanical behavior using nanoindentation analysis of adult human cortical bone. Specifically, in this sample of male cortical femur specimens from donors aged 21–98 years, nanoindentation stiffness (storage modulus) and hardness were found to increase with age, while viscoelasticity (loss modulus) was unchanged. Importantly, the magnitude of the aging trend (as a percentage relative to the fit value at 21 years) was the same whether the indentation direction was parallel (longitudinal sections) or normal (transverse sections) to the osteonal orientation (Figure 3). Additionally, the absence of a significant aging trend (Table 4) when tested in the dry condition (except for longitudinal E′, where the magnitude of the aging trend was merely reduced) supports the critical role of water on the mechanical properties of bone [24].

Only a study with a large number of donors over a wide age range would be able to detect a modest change in properties with age. For example, in this study the change in E′ from 21 to 98 years of age for the transverse–wet specimens was 2.8 GPa, a 15% increase. On a per decade basis this would be a change of 0.36 GPa, or 1.9% of the youngest value. Also, note that due to the spatial variation in properties within a specimen, as well as individual differences between donors, bone nanoindentation studies inherently have a certain amount of data scatter. For example, the average standard deviation of E′ values for a given transverse–wet specimen in this study was 2.2 GPa. In other words, the per decade aging trend is only a fraction of the intra-specimen data spread. Clearly, studies with a small number of donors or a limited age range would be expected to miss an aging trend of this magnitude.

The work of Mirzaali et al. is the most similar to the present study and indented wet human cortical bone from with the largest number of donors (n = 39) to date [18]. Of the 39 donors, 20 were female and 19 were male. The male age range was 59–91 years and the female age range was 64–99 years, plus one donor aged 46 years. Both longitudinal and transverse sections were tested in only the wet condition. Elastic modulus (E) and H from quasi-static indentation tests did not change with age, with the exception of interstitial H for the transverse specimens, which decreased slightly with age. Hardness of the longitudinal specimens was on average 14% lower for the female specimens than for the male specimens. The average E difference between the male and female longitudinal specimens was 8% but was not described as being statistically significant. Similarly, E and H were not found to be gender-dependent for the transverse specimens.

Because this study and that of Mirzaali et al. are the only nanoindentation studies of aging in femoral diaphyseal cortical bone with more than 10 donors, it is worthwhile to consider possible explanations for the differing results. First, the trend of increasing stiffness and hardness with age in this study could be a false positive. However, this seems unlikely since the same result of E′ increasing with age occurred for both orthogonal orientations of the osteons relative to the loading direction in the wet testing condition, as well as in the longitudinal–dry case. Second, if male femoral cortical bone does generally tend to have an increase in E and H with age, then the result in Mirzaali et al. could be a false negative. In fact, given that the Mirzaali et al. male dataset came from 19 donors over an age range of 33 years, it would be difficult to detect an aging trend of the magnitude identified in this study. The dataset in this study came from 26 male donors over a 78 year age range. The measured aging trend could be gender-specific. The result in Mirzaali et al. of 14% lower H for the female longitudinal specimens hints at this possibility. Third, while both studies used cortical femoral specimens, the specimens were from different locations: proximal anterior-lateral in the case of Mirzaali et al. and lateral mid-shaft in this study. Lastly, was a difference in specimen preparations: Mirzaali et al. used embedded specimens, while those in this study were unembedded.

There are 2 other nanoindentation studies of aging trends in human cortical bone with more than 10 donors. Tjhia et al. tested embedded iliac crest specimens, presumably dry in air, from 32 female donors, split into 2 age groups [25]. The younger age group consisted of 20 donors aged 20–40 years, while the older age group had 12 donors aged 49–74 years. Indentation E and H were not seen to be significantly different between the two groups. Hoffler et al. used hydrated indentation to test femoral neck specimens from 27 donors. Data were collected for both cortical and trabecular locations. Sixteen of the donors were male and 11 were female. The respective age ranges were 40–85 years and 27–93 years. No trends with age or sex-related differences were seen. The difference in anatomical location between the previous studies and present precludes a meaningful comparison of the age-related changes in nanoindentation properties of bone. The femoral neck and iliac crest cortices are much thinner than that of the femoral diaphysis and are expected to have higher levels of bone turnover.

With 4 studies containing more than 20 specimens, there is a greater quantity of available nanoindentation data on aging trends in human trabecular bone than there is for cortical bone. By far the largest such study is that of Wolfram et al., with vertebral specimens from 104 donors, 54 female and 50 male, aged 21–94 years [26]. Indentation modulus was not found to change with age. However, elastic energy and dissipated energy (calculated from the area under the load–displacement curve) increased with age. This increase with age was attributed to an increase in maximum force. Unfortunately, H data were not given, although an increase in maximum force would likely translate to an increase in hardness. Hoffler et al. indented femoral neck specimens from 16 male and 11 female donors aged 40–85 years and 27–93 years, respectively, and observed no aging trends or gender differences [20]. Similarly, Ojanen et al. indented femoral neck trabeculae from 21 male donors aged 17–82 years and observed no indentation trends with age [27]. The work of Polly et al. is the only study aside from the present one to use dynamic nanoindentation to assess aging trends in adult human bone, wherein no difference in indentation storage or loss modulus was seen for trabecular bone from transiliac biopsies taken from 15 women before (49 ± 1.9 years) and after menopause (54.6 ± 2.2 years) [28]. Thus, trabecular bone indentation values are generally found not to change with age, although the increase in elastic and dissipated energies with age in Wolfram et al. is interesting. However, results from trabecular bone should not be expected to apply to cortical bone, due to the differences in mineralization and collagen orientation between the tissues. In particular, trabecular bone has a significantly higher surface area and rate of turnover.

Aging in male femoral cortical bone has also been investigated using scanning acoustic microscopy (SAM) by Malo et al. in which acoustic impedance is an indirect measure of stiffness [29]. Femoral shaft and femoral neck specimens were tested from 21 men aged 17–82 years. Measurements were performed for both cortical and trabecular bone types. In all cases, stiffness was found to increase with age. Thus, in both Malo et al. and in this study, tissue-level modulus was seen to increase with age for the male femoral cortex. Note that these are the two studies of aging in male cortical bone with the greatest number of donors at this time. Despite the difference in measurement techniques between the prior and present study, the magnitude of the age-related increase in modulus was similar: ~10% increase over 66 years compared with ~15% over 78 years. Notably, nanoindentation and SAM-derived measurements of bone tissue stiffness also correlated (R² = 0.61) when lamellae of secondary osteons in a transverse section of human femur were analyzed [30].

Of the 3 compositional parameters considered in this study (matrix mineralization, bound water content, pentosidine crosslinking concentration), it was matrix mineralization which was the best predictor of indentation stiffness and hardness, as seen in the positive correlations of E′ with TMD (Figure 4) and the site-matched correlations between E′ and H and qBEI Ca wt.% (Table 6). This dependence of bone mechanical properties on mineral content is readily understood, as for most two-component composites an increase in the volume fraction of the stiffer component will result in increased stiffness of the composite. On the other hand, in this study matrix viscoelasticity (E″) was independent of the level of mineralization. Presumably, this is due to the fact that the mineral platelets are not viscoelastic, while the amount of the viscoelastic collagen in the bone matrix is relatively constant after initial deposition.

Given its complex hierarchical structure, bone fracture can be expected to be complex as well, and features at all length scales of the structural hierarchy have been identified which contribute to the fracture resistance of bone. In this study, the multifactorial nature of cortical bone fracture toughness was reflected in the regression models of fracture for the human femur specimens (Table 7). Specifically, K_init and J-integral were best predicted by a combination of indentation (E′, H), compositional (BoundWater), and structural (PoreWater, OstAr) parameters. In the mechanics of materials there is typically a tradeoff between a material’s strength and its toughness; increasing strength comes at the expense of decreased ductility. This strength– toughness tradeoff is seen in bone [31, 32], and explains why increased matrix stiffness (i.e. modulus) and hardness is detrimental to fracture resistance. Conversely, bound water content is beneficial to fracture toughness because water is a plasticizer for bone’s collagen component, increasing its ductility [17, 33]. Pore water content is negatively associated with fracture toughness because it is primarily a measure of porosity, and matrix voids act as stress concentrators and provide a ready path for crack propagation [34, 35]. Lastly, osteonal area fraction is beneficial because osteons are effective at halting crack growth or forcing crack deflection [36]. Osteonal regions are also tougher than interstitial regions because they are less mineralized [37] and have lower in vivo microdamage accumulation than interstitial regions [13]. Thus, the trend of increased bone matrix stiffness and hardness with age seen in this study is associated with decreased fracture resistance, however, due to the multifactorial nature of bone fracture it is only one of several contributing factors to the age-related decline in the fracture resistance of male cortical bone.

As discussed, the compositional parameter most strongly associated with indentation stiffness and hardness is matrix mineralization. It follows that the primary cause of the observed increases in E′ and H with age was the observed increase in mineralization with age (Table S2). It is clear that the level of bone mineralization increases with age until skeletal maturity. However, the available data are limited and inconclusive with respect to mineralization changes during adulthood. The largest study of age-related changes in the degree of mineralization is that of Bergot et al., using microradiography with anterior midfemoral cortical specimens from 193 donors [37]. The 99 female and 94 male specimens were divided into 7 decades between 20–29 years and 80–89 years of age. For males, interstitial mineralization was positively correlated with age (r = 0.212, p = 0.049), while osteonal mineralization was uncorrelated with age. For females, both osteonal and interstitial mineralization decreased with age (r = −0.249; p=0.013 and r = −0.222; p = 0.027, respectively). Until 50 years of age when menopause begins, mineralization was higher in females, but in the elderly groups mineralization was higher in males. The diverging aging trends seen for men and women highlight the necessity of treating male and female data separately; when the data were pooled no significant correlations with age were seen. Also, the relatively low correlation coefficients indicate that the mineralization trends with age were relatively modest and would likely be missed in studies with small sample sizes. For a least-squares fit to the data from the 29 specimens in this study, TMD increased from 956 mgHA/cm³ at 21 years to 1003 mgHA/cm³ at 98 years, a change of 5%. Such a change is consistent with the modest increase in male interstitial mineralization with age seen in Bergot et al. Another study in which mineralization, namely mineral-to-matrix ratio, was found to increase with age in the male femoral cortex is that of Yerramshetty et al., for 16 donors aged 52–85 years [38].

Because the overall level of mineralization is a function of the bone turnover rate [39, 40], studies of age-related changes in biochemical bone turnover markers (BTMs) can provide insight into mineralization aging trends, and due of the relative ease in collecting serum and urinary samples, there are several large studies of age-related changes of BTMs in men [41–44]. For example, Chaitou et al. collected BTM data for 1149 men aged 19–85 years [41]. These studies show that for men bone turnover is highest at 20–30 years of age and declines to a minimum around 50–60 years. With advancing age after 60 years, bone resorption increases slightly while bone formation remains stable or declines slightly [22, 41]. Histomorphometric data also demonstrate decreased bone turnover with age in men [45]. The changes with age for the human femur specimens in this study are consistent with the trend of decreased bone turnover with age seen in the BTM studies. Specifically, decreased bone turnover leads to an increase in average tissue age, which means a higher degree of average mineralization, which in turn means higher indentation stiffness and hardness.

Note that the general aging trends of bone turnover are different for men and women. Bone turnover in women increases during menopause as a result of decreased estrogen levels and remains elevated thereafter [46, 47]. Recall that the largest study of mineralization changes with age of the human femoral cortex, by Bergot et al., found a slight decline in mineralization with age for females and a slight increase in interstitial mineralization with age for males [37]. These diverging trends match with the theoretical expectations from the bone turnover studies. Namely, a decline in bone turnover with age in men, resulting in slightly increased mineralization with age, and an increase in bone turnover in women, resulting in slightly decreased mineralization with age. This also means that studies of aging in bone should be cautious about pooling male and female data.

A limitation of this study is that fact that the femoral diaphysis is not a typical fracture site, such as the femoral neck or distal radius. These common fracture sites have thinner cortices than the femoral shaft and consequently may be remodeled more frequently. However, while there may be some anatomical variation, because the rate of bone turnover is largely hormonally driven, aging trends in cortical bone are expected to be systemic. Note that Malo et al. found stiffness to increase with age in males at both the femoral shaft and the femoral neck [29]. Another potential limitation of this study is the fact that transverse specimens were vacuum desiccated for qBEI imaging prior to the nanoindentation experiments, while the longitudinal specimens were never vacuum desiccated. Out of the four section–condition combinations tested, only the transverse–dry case lacked an aging trend for E′. As seen in this study and others, bound water decreases with age in male cortical bone. By altering the matrix bound water content, the vacuum desiccation may have masked a previously present aging trend, as E′ and H were seen to increase with age in the subsequent wet tests. Lastly, the study did not include collagen orientation that can dictate tissue-level modulus along with mineralization.

The results from this study have implications for the use of bisphosphonates in the prevention of osteoporotic fractures. Bisphosphonates act by reducing bone turnover, which helps preserve bone mass in cases of elevated turnover, as is typical of postmenopausal osteoporosis. However, long-term bisphosphonate use is associated with fractures at “atypical” sites such as the femoral diaphysis [48]. This is likely because unremodeled tissue progressively becomes less tough over time due to increased mineralization, microdamage accumulation, decreased bound water, etc. (for an overview of a proposed pathologic mechanism, see [49]). In men, however, turnover is not normally elevated in old age, and this study demonstrates that male cortical bone becomes less tough with age, due in part to changes associated with increased tissue age. By further depressing the remodeling rate, the use of bisphosphonates could favor hypermineralization.

5. Conclusions

In the present study, the storage modulus and hardness of tissue in male femoral diaphysis specimens increased with age; and based on regression models with several compositional and microstructural explanatory variables, storage modulus from the longitudinal surface and hardness from both transverse and longitudinal surfaces were negative predictors of fracture toughness. On the other hand, viscoelasticity (loss modulus) did not vary with age, despite an age-related decrease in matrix-bound water, and did not correlate with the fracture parameters. For the hydrated specimens, the magnitude of the increase over the age range 21–98 years was ~15% for storage modulus and ~12–13% for hardness, irrespective of indentation direction (transverse and longitudinal sections). The increase in tissue-level stiffness and hardness is likely due to a subtle increase in mineralization with age. With respect to prior observations about bone turnover in men and principles of solid mechanics, a likely explanation for the associations observed in this study is:

$$\frac{\downarrow \text{ turnover }}{\text{ age }}\to \frac{\uparrow \text{ mineralization }}{\text{ age }}\to \frac{\uparrow \text{ stiffness}\text{and}\text{hardness }}{\text{ age }}=\frac{\downarrow \text{ fracture}\text{resistance }}{\text{ age }}.$$

Highlights.

• Indentation stiffness of adult male cortical bone increased with age

• The stiffness increase is attributed to increased mineralization

• Increasing tissue-level stiffness may be detrimental to fracture resistance