Identifying novel clinical surrogates to assess human bone fracture toughness

Abstract

Fracture risk does not solely depend on strength but also on fracture toughness, i.e. the ability of bone material to resist crack initiation and propagation. Because resistance to crack growth largely depends on bone properties at the tissue level including collagen characteristics, current X-ray based assessment tools may not be suitable to identify age-, disease-, or treatment-related changes in fracture toughness. To identify useful clinical surrogates that could improve the assessment of fracture resistance, we investigated the potential of ¹H nuclear magnetic resonance spectroscopy (NMR) and reference point indentation (RPI) to explain age-related variance in fracture toughness. Harvested from cadaveric femurs (62 human donors), single-edge notched beam (SENB) specimens of cortical bone underwent fracture toughness testing (R-curve method). NMR-derived bound water showed the strongest correlation with fracture toughness properties (r=0.63 for crack initiation, r=0.35 for crack growth, and r=0.45 for overall fracture toughness; p<0.01). Multivariate analyses indicated that the age-related decrease in different fracture toughness properties were best explained by a combination of NMR properties including pore water and RPI-derived tissue stiffness with age as a significant covariate (adjusted R² = 53.3%, 23.9%, and 35.2% for crack initiation, crack growth, and overall toughness, respectively; p<0.001). These findings reflect the existence of many contributors to fracture toughness and emphasize the utility of a multimodal assessment of fracture resistance. Exploring the mechanistic origin of fracture toughness, glycation-mediated, non-enzymatic collagen crosslinks and intra-cortical porosity are possible determinants of bone fracture toughness and could explain the sensitivity of NMR to changes in fracture toughness. Assuming fracture toughness is clinically important to the ability of bone to resist fracture, our results suggest that improvements in fracture risk assessment could potentially be achieved by accounting for water distribution (quantitative ultrashort echo-time magnetic resonance imaging) and by a local measure of tissue resistance to indentation (RPI).

Introduction

Fracture resistance of bone depends on yield strength, the ability of bone to withstand high force or stress without appreciable permanent deformation as well as fracture toughness, the ability of bone to resist crack initiation and propagation. These two attributes describe different aspects of the mechanical behavior of bone and, as such, high yield strength does not necessarily mean low or high fracture toughness.⁽¹⁾ Reduced bone strength typically results from a loss of bone mass and correlates well with areal bone mineral density (aBMD) as measured by dual-energy X-ray absorptiometry (DXA), the clinical gold standard to assess fracture risk. Fractures however are not solely the manifestation of low bone strength or low aBMD.⁽²⁾ For fractures to occur, damage must form and propagate. Fracture resistance thus depends on the ability of bone to resist damage initiation, accumulation, and propagation. While strength characterizes some of this ability, there are other mechanical properties – fatigue life, toughness, and fracture toughness – that specifically assess various damaging mechanisms of energy dissipation during fracture. The idea that fracture toughness at the apparent level could also significantly contribute to the overall fracture resistance is gaining prominence in recent years as an apparent compromise in fracture toughness mechanisms could underpin the occurrence of atypical femoral fractures^(3,4) and may explain why patients with type 2 diabetes are at higher risk of fracture despite a normal aBMD.^(5,6)

There are multiple ways to characterize the fracture toughness of a material. Whether determined as the critical stress state beyond which the crack begins to grow (stress intensity factor K), the non-linear elastic energy dissipated prior to and during fracture (J-integral), or the toughness evolution with crack extension (crack resistance curve or R-curve), fracture toughness of bone decreases with advancing age.^(7–10) Like strength, it is related to apparent bone density,^(11,12) but fracture toughness also largely depends on microstructural and compositional properties at the material level such as tissue orientation,^(12–14) cement line properties,⁽¹⁵⁾ osteon density,⁽¹⁶⁾ tissue heterogeneity,⁽¹⁷⁾ water content,^(11,18) accumulation of in vivo microdamage,^(19,20) or accumulation of advanced glycation end-products (AGEs).^(8,21) As X-rays are insensitive to numerous deleterious changes within bone tissue, bone densitometry may not be suitable to identify age-, disease-, or treatment-related changes in fracture toughness. This would explain to some extent the lack of specificity of aBMD in identifying certain individuals at imminent risk of a devastating fracture. ^(22–24)

Therefore, we investigated the potential of two clinically translatable technologies to become surrogates of fracture toughness assessment. First, ¹H nuclear magnetic resonance spectroscopy (NMR) allows one to evaluate the concentration of water interacting with the matrix (bound water) and water residing in pores (pore water).^(25–27) Hydration and porosity are known determinants of fracture toughness of bone^(11,18) and are quantifiable by clinical magnetic resonance imaging (MRI).^(28,29) The second technology is reference point indentation (RPI),^(30,31) an instrument designed for clinical measurements of bone material properties by indenting a patient’s tibia. In particular, RPI could be sensitive to some of the intrinsic toughening mechanisms in bone tissue⁽³²⁾ as it generates microdamage ahead of the probe tip. Based on a large dataset of human samples (62 donors), our approach compares the ability of ¹H NMR, RPI, and micro-computed tomography (μCT) (used as a surrogate of X-ray-based measurements) to explain age-related changes in fracture toughness. In addition, glycation-mediated, non-enzymatic collagen cross-links were measured because their accumulation in tissue, together with increased porosity, are thought to impair fracture toughness.⁽²¹⁾

Material and methods

Bone sample preparation and study design

All cadaveric tissues used in this work were stored fresh-frozen and obtained from the Musculoskeletal Transplant Foundation (Edison, NJ), the Vanderbilt Donor Program (Nashville, TN), and the National Disease Research Interchange (Philadelphia, PA). Cortical bone samples were extracted from the lateral quadrant of the femoral mid-shaft of sixty-two human donors (30 male donors, aged 21 – 98 years old, mean ± standard deviation: 63.5 ± 23.7 years; and 32 female donors, aged 23 –101 years old, 64.4 ± 21.3 years). Single-edge notched beam (SENB) specimens (one per donor, N=62) were cut using a circular low-speed, diamond-embedded saw (660, South Bay Technology, Inc., San Clemente, CA) and machined using an end mill to a specimen thickness B = 1.9–3.3 mm, width W = 4–6.8 mm, and length L = 19–31 mm, with B = 0.5.W as per the fracture toughness test standard ASTM E1820.⁽³³⁾ Micro-notches were created using a low-speed saw and sharpened further into a pre-crack by means of a razor blade lubricated with 1 μm diamond solution to give original crack size a₀ = 0.9–1.9 mm.

The measuring sequence – schematically described in Fig. 1 – consisted of 1) imaging the notched region of the specimen with micro-computed tomography (μCT), 2) performing fracture toughness test until fracture, 3) extracting two bone segments from each SENB specimen for further analysis by ¹H NMR spectroscopy and high performance liquid chromatography (HPLC), respectively. The specimens were stored in phosphate-buffered saline (PBS) soaked gauze at −20°C between each phase of the experimental protocol. Reference point indentation (RPI) was carried out on the surface of the NMR specimens. An additional measurement campaign was performed to obtain RPI measures closer to a clinical setting, that is, indenting through the periosteum. The thickness (B) of the SENB specimen precluded RPI along the periosteal edge. Instead, RPI was performed on the opposite medial quadrant (Fig. 1).

Figure 1.

Schematic of bone analysis. Upon imaging the notched region of the specimen with micro-computed tomography (μCT) to determine intra-cortical porosity and volumetric bone mineral density, each single-edge notched beam (SENB) specimen underwent fracture toughness testing. After testing, a segment of the SENB specimen (~5 × 5 × 2.5 mm³) was analyzed by ¹H nuclear magnetic resonance (NMR) spectroscopy to determine the fraction of bound and pore water (i.e., water volume per apparent bone volume). A second bone segment (~2 × 2 × 2.5 mm³) was analyzed by high performance liquid chromatography (HPLC) to determine pentosidine, a glycation-mediated, non-enzymatic collagen crosslink.

Micro-computed tomography analysis (μCT)

Prior to fracture toughness testing, SENB specimens were scanned (μCT50, Scanco Medical, Switzerland) at an isotropic voxel size of 5 μm using the same settings (tube voltage: 90 kVp; beam current: 200 μA; 1000 projections per 360° rotation; integration time: 400 ms) and a hydroxyapatite phantom calibration with the manufacturer’s beam hardening correction.⁽³⁴⁾ Upon reconstruction, μCT images were post-processed with a Gaussian filter to suppress image noise (sigma = 1.8 and support of 3). The scanned region was 1.3 mm wide and encompassed the notch (Fig. 1), allowing for the precise determination of the original crack size (a₀). A volume of interest (VOI) was selected in front of the original crack tip of each specimen (Fig. 1). Apparent volumetric bone mineral density (avBMD) was defined as the mean of volumetric bone mineral density for all voxels within the total volume of the VOI. Tissue mineral density (TMD) was defined as the mean of volumetric bone mineral density for all voxels assigned to the matrix (voxels with a bone mineral density more than 660 mgHA/cm³). Intracortical porosity (Ct.Po) was computed as the ratio of the voxels with a bone mineral density less than 600 mgHA/cm³ per total number of voxels in the VOI (noise filter set to sigma = 2.0 and support of 2).

In addition, 16 NMR specimens (Fig. 1) were also scanned by μCT and analyzed using the same settings and parameters as the notch scans to verify two assumptions: 1) the porosity remains relatively constant throughout the whole SENB specimen, that is Ct.Po^NMR and Ct.Po are similar and 2) porosity determined from ¹H NMR highly correlates with porosity assessed from μCT images.

Fracture toughness testing

Fracture toughness testing procedures adhered to the guidelines of ASTM Standard E1820.⁽³³⁾ SENB specimens were subjected to three-point bending. The samples were positioned horizontally on two 1 mm diameter supports with a ~20 mm span S (equal to 4×W)⁽³³⁾ and loaded mid-span (in-line with notch), using an axial servo-hydraulic testing system (DynaMight 8841, Instron, Norwood, MA), to propagate a crack normal to the osteonal direction (Fig. 1 and 2A). The force-displacement data was recorded at 50 Hz as the hydrated bone was tested in displacement control to failure with a progressive, multiple loading (+0.07 mm at 0.01 mm/s)-unloading (−0.04 mm at 0.015 mm/s)-dwell scheme (Fig. 2B).

Figure 2.

Measuring the fracture toughness of human cortical bone using the R-curve method. The single-edge notched-beam specimen (A) was subjected to a progressive load-unload-reload scheme (B) with rest insertion before reloading in order to capture images of the crack. Three representative images after 1, 15, and 23 cycles show the crack propagation during testing (A). Using a non-linear, elastic fracture mechanics approach, the specimen geometry, and the slope of unloading curve to estimate crack length (B), the J-integral was computed as a function stable crack extension (C). Then, crack growth toughness was determined as the slope of fracture toughness per cycle of loading vs. the square root of crack extension (D).

Human cortical bone exhibits non-linear mechanical behavior (i.e., a significant amount of plastic deformation), and as such, its fracture behavior must be studied in the framework of elastic-plastic fracture mechanics as pointed out by others.^(10,35,36) This comes down to characterizing the so-called rising R-curve, which evaluates the fracture resistance in terms of the J-integral, as a function of stable crack extension Δa (Fig. 2). Crack lengths (a_i) were computed from the unloading compliance data C_i (Fig. 2B) and specimen geometry by solving the following equation (Eq A1.10 in ASTM E1820)⁽³³⁾ for each cycle i:

$$C_i=\frac{1}{E^{\prime }·B}·{\left(\frac{s}{W-a_i}\right)}^2·\left[1.193-1.98\left(\frac{a_i}{W}\right)+4.478{\left(\frac{a_i}{W}\right)}^2-4.443{\left(\frac{a_i}{W}\right)}^3+1.739{\left(\frac{a_i}{W}\right)}^4\right]$$ (1)

where E′=E/(1−ν²), ν is the Poisson’s ratio (taken to equal 0.3), and E is the specimen-specific flexural Young’s modulus computed as follows:

$$E=\frac{\delta S^3}{48·I}=\frac{\delta S^3}{4·B·{(W-a_0)}^3}$$

where δ is the initial stiffness during R-curve testing. We verified that this estimated modulus matched the modulus derived from eq. 1 for C₀ and a₀. The value of J was calculated for each cycle by adding its elastic and plastic components and correcting for crack growth:

$$J_i=\frac{{K_i}^2}{E^{\prime }}+J_{pl(i)}$$ (2)

The detailed equations used to compute the stress-intensity K and the plastic component of J are provided in ASTM E1820⁽³³⁾ (precisely, Eq. A1.2, A1.3, A1.8 and A1.9). Conditions for J-dominance were met (i.e. W-a₀, B>10(J/σ), where σ is the yield stress) for all 62 fracture tests. Note that we chose to use a smaller ratio a₀/W (0.26±0.03) than the one recommended by ASTM E1820 to provide more crack events before complete failure occurred. Since fracture toughness properties depend on this ratio,⁽³⁷⁾ the absolute values in the present work tend to be higher than what other studies report for human cortical bone.

Three parameters of interest were retrieved from the R-curve: J-integral and the critical stress intensities required to initiate cracks (K_init) and to sustain subsequent crack growth (K_grow). Precisely, J-int is the value of J at failure. Crack initiation toughness K_init was back-calculated from J_Ic using the K-J equivalence relationship K_J = (E′.J)^1/2 (Fig. 2C). Crack growth toughness K_grow was defined as the slope of the linearized plot K_J vs (Δa)^{1/2 (38)} (Fig. 2D). K_grow could not be calculated for specimens that exhibit highly brittle behavior, i.e. when the crack propagation is rapidly unstable and leads to failure immediately after reaching the peak force. This was the case for 11 samples out of 62.

¹H Nuclear magnetic resonance spectroscopy

Recent work has shown that transverse relaxation time constant (T₂) from ¹H NMR can separate proton signals from collagen-bound water (~400 μs) and pore water (~1 ms – 1s).^(25,26) Along with a microsphere of water as a reference volume (T₂ ~ 2 s), bone specimens were inserted into a custom-built, low proton, loop-gap-style radio-frequency (RF) coil⁽²⁶⁾ and placed in a 4.7T horizontal-bore magnet (Varian Medical Systems, Santa Clara, CA). Upon 90°/180° RF pulses of ~ 5/10 μs duration, Carr-Purcell-Meiboom-Gill (CPMG) measurements with 10,000 echoes were collected at 100 μs spacing, yielding data that were fitted with multiple exponential decay functions to generated a T₂ spectrum using the freely available MERA toolbox⁽³⁹⁾ for MATLAB® (details available in Horch et al.⁽²⁶⁾).

Given the known water volume in the microsphere, the integrated areas of bound water (T₂ = 150 μs − 1 ms) and pore water (T₂ = 1 ms − 600 ms) were compared to the area of the reference sample (T₂ = 600 ms-10 s) (Fig. 1) and converted into water volumes. Finally, these volumes were divided by the specimen volume (calculated from Archimedes’ principle) to give bound water (bw) and pore water (pw) volume fractions.

Reference point indentation

The tissue-level mechanical properties of cortical bone were assessed using a BioDent™ instrument (Active Life Scientific, Inc., Santa Barbara, CA).^(40–43) The general principle of RPI consists of measuring the displacement of a stainless steel test probe (375 μm diameter, 90° cono-spherical, 2.5 μm radius tip) that cyclically indents into the bone to a given load (20 cycles at 2 Hz with a maximum force of 10 N per cycle in this study). There is a short dwell period (166 ms) between loading and unloading. Throughout RPI testing, the samples were kept hydrated with PBS. The raw load vs. displacement data was processed using a custom MATLAB® code⁽⁴³⁾ to determine a number of indentation resistance properties. Although a multitude of parameters can be computed from a single acquisition, most of them are inter-correlated, and therefore provide redundant information.⁽⁴³⁾ Moreover, the parameters related to the first cycle typically present higher scatter.⁽⁴³⁾ Hence, we decided to retain two parameters commonly reported in RPI studies, namely total indentation increase (TID) and indentation distance increase (IDI), as well as two parameters known to correlate with tissue age and toughness, that is the average value from the cycle 3 to 20 of energy dissipation (avED) and loading slope (avLS).⁽⁴³⁾

Ten RPI measurements were collected every 2 mm on the medial quadrant of the midshaft, below the periosteum (Fig. 1). Five RPI measures were acquired on the surface of the NMR sample (indentation orthogonal to the osteon direction). Extreme outliers among the indentations per tested surface for any given RPI property were identified using the generalized extreme studentized deviate procedure⁽⁴⁴⁾ and discarded from further analysis (1.7% and 3.3% of the measurements on periosteum and NMR samples, respectively) and the average value per tested surface was computed from the remaining measurements.

High performance liquid chromatography

A small piece of bone (~ 10–50 mg) was cut from the corner of the SENB specimen (Fig. 1). The sample was first fully demineralized in 20% EDTA (0.68M, pH 7.4), then hydrolyzed (110°C, 20–24h) in 6N HCl (10μL/mg bone). After removing the acid with a vacuum concentrator (Savant SPD131DDA SpeedVac with cold-trap; Thermo Scientific; USA), the hydrosylate was re-suspended in ultrapure water, split (nominal ratio 50:50), and dried in the vacuum concentrator.

For crosslinking assay, the residue of one split sample was re-suspended in a dissolving buffer containing an internal standard (1.5 μM pyridoxine). The solution was filtered and diluted with buffer (0.5% (v/v) heptafluorobutyric acid in 10% (v/v) acetonitrile), and a 50 μL sample was injected into a HPLC system (Beckman-Coulter System Gold 126) fitted with a silica-based column (Waters Spherisorb®). Varying concentrations of pentosidine (PE) from the International Maillard Reaction Society combined with a fixed amount of pyridoxine were used as standards. PE concentration was calculated from the chromatograms recorded using a Waters fluorescence detector (328/378 nm excitation/emission).

PE concentration was then normalized by its respective collagen amount, as determined by a hydroxyproline assay⁽⁴⁵⁾ on the second split sample. Briefly, amino acids and internal standard (α-amino-butyric acid (α-ABA)) were derivatized with phenyl isothiocyanate (PITC). The derivatives were re-suspended in a buffer (5% acetonitrile in 5mM disodium phosphate), along with standards of varying concentrations of hydroxyproline (Hyp) and proline, and injected into the same HPLC system but with a Pico•Taq® column and a UV detector. The mole of Hyp per mass of bone calculated from the chromatograms was divided by 14% (amount of hydroxyproline in type I collagen) and by 0.3 (molecular weight of collagen in μg/pmol)⁽⁴⁶⁾ to give PE concentration as mmol/mol of collagen (PE_coll).

Statistical analysis

A preliminary analysis on a subset of 16 specimens determined whether (i) the porosity at the notched region (Ct.Po) is equivalent to the porosity of the NMR specimens (Ct.Po^NMR), and (ii) pore water is equivalent to porosity assessed from μCT images (Ct.Po^NMR). Because porosities were not normally distributed, both these comparisons were tested using Wilcoxon signed rank test and Spearman correlation, respectively.

Because gender did not significantly explain the variance in fracture toughness properties, it was not included as a covariate in further analysis. As several properties did not follow a normal distribution (Shapiro-Wilk Test), Spearman correlation coefficients were used to evaluate the association between fracture toughness properties (K_init, K_grow, J-int) and potential explanatory variables, namely age, apparent volumetric bone mineral density measured from CT (vBMD), NMR outcomes (bw, pw), and RPI properties (TID, IDI, avED, avLS) (Table 1). Including age as a covariate, linear regressions on fracture toughness properties were used to identify parameters that improved the ability of age to explain the variance in fracture toughness (Table 2). Upon examining inter-correlations between the explanatory variables with Spearman’s correlation coefficient (Supplemental Table 1), low correlated parameters (r<0.55) were considered as independent predictors in a backward, stepwise, multiple regression with the fracture toughness parameters as dependent variables to determine which combination of parameters/modalities best explain the variance in fracture toughness properties (i.e., highest adjusted R², Table 2). Lastly, to explore the mechanistic origin of fracture toughness, we extended our search for fracture toughness predictors to non-clinically translatable parameters, namely intra-cortical porosity (measured via μCT), non-enzymatic collagen cross-links level or AGE content, and tissue mineral density (Table 3).

Table 1.

Correlation between fracture toughness properties and proposed explanatory variables (Spearman correlation coefficients (r) are indicated when significant at p<0.05). For RPI, properties from indentations through the periosteum are listed above the properties from indentations on the NMR specimen (italics)

r	age	avBMD	bw	pw	TID	IDI	avED	avLS
Kinit (n=62)	−0.48	0.29	0.63	−0.53	−0.44	ns	−0.32	0.24*
					ns	−0.26	−0.33	0.36
Kgrow (n=51)	−0.34	0.26*	0.35	ns	ns	ns	ns	ns
					ns	ns	ns	ns
J-int (n=62)	−0.38	ns	0.45	−0.34	ns	ns	−0.39	0.44
					ns	ns	ns	0.22*

^*p<0.08

Table 2.

Linear combination of significant parameters across modalities including age of the donor for each fracture toughness property (models applied on bootstrapped data with 1000 replicates)

Fracture toughness property	Explanatory variables	Linear model	Adj-R2 (%)
Kinit	age + bone density	−0.05·age + 0.02·avBMD	40.8
	age + NMR	7.80 − 0.03·age + 0.30·bw − 0.34·pw	47.0
	age + RPIa	−0.05·age − 0.08·TID + 19.74·avLS	37.9
	best combination	−0.03·age + 0.30·bw − 0.30·pw + 19.86·avLS	53.3
Kgrow	age + bone density*	8.32 − 0.05·age	17.1
	age + NMR*
	age + RPIa	49.75 − 0.68·age − 88.04·avLS + 1.32·age·avLS	23.9
	best combination		23.9
J-int	age + bone density*	18.61 − 0.09·age	12.8
	age + NMR	22.55 − 0.07·age − 0.62·pw	18.6
	age + RPIa	−17.75 − 0.09·age + 77.9·avLS	30.9
	Best combination	−0.07·age − 0.49·pw + 71.98·avLS	35.2

^aIndentations through the periosteum

^*The explanatory variable was not significant in the multivariate model

Table 3.

Mechanistic origin of changes in fracture toughness. Spearman correlation coefficients (r) are indicated when significant at p<0.05. Linear multivariate analysis was applied on bootstrapped data with 1000 replicates.

	Spearman correlation coefficient			Multivariate analysis Best combination*	Adj-R2 (%)
	Ct.Po	PEcoll	TMD
Kinit	−0.51	−0.34	−0.28	12.24 − 0.19·Ct.Po − 0.0003·PEcoll	42.2
Kgrow	−0.27**	ns	ns	ns	ns
J-int	−0.23**	−0.32	−0.32	18.61 − 0.25· Ct.Po − 0.007· PEcoll	21.1

^*age was not included as a covariate in the multilinear model because of the strong correlation between age and PE_coll (r = 0.65)

^**p<0.07

The correlations and simple linear regressions were performed using the MATLAB Statistics Toolbox (The Mathworks Inc., Natick, MA). The general linear models including the stepwise regression were applied on bootstrapped data (1000 replicates) to account for the non-normality of most parameters (STATA 12, StataCorp LP, College Station, TX). Statistical results were considered significant for p-values less than 0.05, unless otherwise stated.

Results

Correlations with fracture toughness

All the fracture toughness properties – crack initiation toughness (K_init), crack growth toughness (K_grow), and overall resistance to crack propagation (J-init) – decreased with age (Table 1). However, the correlation between fracture toughness and age was not particularly strong with age only explaining 13% to 23% of the variance (Fig. 3A). The NMR-derived bound water (bw) had the strongest correlation with K_init and J-init (Table 1). Whereas the 3 fracture toughness properties increased with an increase in bw (Fig. 3B), they decreased with an increase in NMR-derived pore water (pw), except for K_grow, which was not significantly correlated with pw (Fig. 3C). Lower resistance of bone to micro-indentation at the tissue-level (that is, higher TID, IDI and avED, and lower avLS) was associated with lower K_init and J-int at the apparent level (Table 1). The correlation trends were similar whether RPI was performed through the periosteum (surrogate of clinical setting) or on the surface of the NMR sample. Apparent volumetric mineral bone density (avBMD) was weakly correlated with only K_init.

Figure 3.

Age-related changes in fracture toughness. Crack initiation toughness, crack growth toughness, and total energy dissipated during these processes decreased with age (A). Fracture toughness was directly correlated with bound water (B) and inversely correlated with pore water (C).

Multivariate explanation of fracture toughness

Since our potential clinical surrogates (bw, IDI, etc.) did not strongly correlate with fracture toughness on their own (Table 1 and Fig. 3), we performed a multivariate analysis. When either NMR properties or RPI properties were combined with age, the explanation of the variance in K_init and J-init improved (compare R² values in Fig. 3 to adjusted R² values in Table 2). This improvement was greater than what was obtained combining age and avBMD (Table 2). With age still as a significant covariate, a combination of NMR-derived properties (bw and pw) and one RPI property (avLS) provided the best explanation of K_init (adjusted R² = 53.3%, p<10⁻⁵), whereas a combination of pw and avLS provided the best explanation of J-int. Only the linear combination of age and avLS (a RPI parameter related to bone matrix hardness) including a significant interaction (adj-R² = 23.9%, p=0.001) helped improve the explanation of the variance in crack growth toughness (K_grow).

Determinants of fracture toughness

As for the effect of microstructure and matrix properties on fracture toughness, intracortical porosity, tissue mineral density, and pentosidine levels were all negatively associated with K_init and J-int (Table 3). The combination of Ct.Po and PE_coll best explained the variance in fracture toughness properties (Table 3). Porosity was the only factor that significantly correlated with crack growth toughness.

To explore why the NMR measurements could be predictive of fracture toughness, we compared them to the aforementioned determinants. Specifically, we expected bw to be sensitive to changes in the matrix tissue, i.e. PE_coll and TMD; and pw to reflect differences in the microstructure (Ct.Po). We found that, similarly to the correlations observed for the fracture toughness properties, bound water was negatively correlated with pentosidine levels (r = −0.31, p = 0.014) and TMD (r = −0.42, p = 0.001 for all 62 specimens and r = −0.74, p = 0.0001 for 14 NMR specimens that were imaged by μCT but excluding 2 highly porous outliers). The ancillary analysis of the paired 16 specimens showed that porosity was similar between NMR specimen and notched region (Wilcoxon signed rank test p-value equal to 0.079 and R² = 93.7%, Fig. 4A). A direct comparison on the NMR samples showed a high correlation between pw and Ct.Po^NMR (R² = 66.1% for the 16 specimens, R² = 93.8% after removing two outliers, Fig. 4B), confirming that pore water derived from NMR is a valid measure to assess intracortical porosity. The remarkably high porosities (>35%) of the two outliers could explain the discrepancies between μCT and NMR since pores at the surface of the bone specimen are accounted for in the computation of porosity with μCT but not NMR (Fig. S1). Looking at the whole dataset, the NMR-derived porosity and the porosity assessed from μCT were also highly correlated (R² = 56.0%; R² = 78.1% after removing two outliers, Fig. 4C).

Figure 4.

Strong correlations between μCT-derived porosity and NMR-derived pore water. The porosity of the NMR specimens correlated with the μCT-derived porosity (5 μm voxel size) near the notch of the same SENB specimens (A). For this subset of NMR specimens, porosity strongly correlated with pore water especially when 2 highly porous specimens were excluded (B). For all specimens excluding the 2 outliers, porosity near the notch directly correlated with pore water of the SENB portion (C).

As for what possibly influences microindentation, we found that the RPI properties did not correlate with TMD and weakly correlated with PE (periosteal IDI and avgED only), but surprisingly, some properties were not completely independent of porosity (Supplemental Table 2) regardless of whether indentation was performed on the periosteal surface or the NMR specimens.

Discussion

Mounting evidence, both from clinical reports and basic science research, indicate that fracture risk does not solely depend on strength but also on bone properties at the tissue level. In this context, there is a growing recognition of the importance of fracture toughness in assessing fracture risk as it is a measure of the ability of the tissue to resist crack initiation and propagation.⁽⁴⁷⁾ The relative insensitivity of DXA to bone quality motivates the search for novel clinical surrogates to assess attributes of bone other than bone mass and strength. For the first time, we show that NMR and to a lesser extent RPI have the potential to assess fracture toughness properties. Although the techniques presented in our work were applied to excised samples, both techniques can conceivably be translated to clinical assessment of fracture risk. Indeed, bound and pore water derived from ¹H NMR can be imaged in patients using selective radiofrequency pulse sequences with ultrashort echo-time magnetic resonance imaging (UTE-MRI)^(28,48) and RPI can be performed directly on the patient’s tibia.^(30,31) Findings from the multivariate analysis call for a multimodal assessment of fracture risk, thereby reflecting the existence of many contributors to fracture toughness.

Several phenomena occurring at different hierarchical levels of organization underpin the fracture toughness of bone. In any material, crack growth occurs when the stress near the tip of a pre-existing flaw reaches a critical value (K_init) and depends on the ability of the material to dissipate energy: the more energy-dissipation mechanisms that exist, the more difficult it is to break a material.⁽⁴⁹⁾ In bone, this mainly involves plasticity at the nanoscale through uncoiling of the collagen molecules and sliding of both mineralized collagen fibrils and individual collagen fibers.^(49–52) Once a crack starts propagating, additional toughening mechanisms come into play. At the ultrastructural level, bone toughening is achieved by the development of diffuse microdamage in the tissue surrounding the main crack^(53–55) as well as through mineralized collagen filaments that bridge the surfaces created by the crack extension.^(56–60) While submicron mechanisms govern crack initiation and growth, the latter is also largely influenced by larger scale toughening mechanisms. For example, cement lines can deflect the crack path,^{(10,14,32,61–63)} at least when the crack propagates perpendicular to the osteons^(10,13) at a relatively low strain rate.⁽⁶⁴⁾ In addition, an increased porosity induces larger stress concentrations in the matrix, thereby facilitating crack initiation and growth. Based upon these observations, non-enzymatic collagen cross-links, which stiffen the matrix and reduce its energy dissipation,^(52,65–67) as well as intracortical porosity have been naturally proposed as determinant factors of bone fracture toughness.⁽²¹⁾ Our findings support this supposition as porosity and pentosidine levels together explained up to 42% of the variance in fracture toughness (Table 3).

The aforementioned concepts on what dictates toughening mechanisms helps our understanding of why NMR-derived properties correlate with fracture toughness of human cortical bone. Matrix of more porous bone specimens are subjected to higher local stresses compared to less porous bone and subsequently will not resist as well to the departure of a crack from the initial notch. Hence, since pore water is directly related to intra-cortical porosity (Fig. 4) as reported by others,^(27,68,69) it is not surprising that increased pore water was associated with lower crack initiation toughness. The role of the bound water in fracture toughness likely occurs at the nanoscale in so far as hydration confers plasticity to collagen. Hence, a less hydrated matrix (i.e. lower bound water) could partially hinder the resistance to crack initiation and propagation, as observed in our study (Table 1). The negative correlation between bound water and pentosidine (also found in Nyman et al.⁽⁶⁸⁾) fits with the observation that chemical cross-linking changes the relaxation time of bound water in rat tail tendon⁽⁷⁰⁾ and causes dehydration of the fibers by drawing the collagen molecules closer together⁽⁷¹⁾ which could reduce sites of hydrogen bonding between water and collagen. Similarly, a decrease in bound water was associated with an increase of mineralization (TMD) also suggesting NMR-derived bw is sensitive to mineral aggregation displacing collagen-bound water.^(72–74) Additional investigations involving manipulation of the bone matrix are necessary to confirm that the degree of mineralization and non-enzymatic collagen crosslink concentrations are determinants of bw.

Correlations between NMR-derived bulk properties and fracture toughness were modest (e.g. r = 0.63 between K_init and bw, see Table 1), but greater than those between fracture toughness and avBMD (r < 0.29), suggesting that information about water compartments in bone (bound and pore water) could be more valuable than a measure of bone mineral density to assess the ability of bone to resist fracture. These results extend the list of mechanical properties that are are related to or affected by changes in matrix water^(25,75–79) and pore water.⁽⁷⁸⁾ Although moderate, the present correlation coefficients are similar to those found in other studies between crack initiation toughness (stress intensity factor K_Ic or critical strain energy release G_c) and other bone characteristics, e.g. organic weight fraction (r=0.48),⁽¹⁷⁾ PE (r=−0.48),⁽⁸⁾ water content(r=−0.62),⁽¹¹⁾ microhardness (r=−0.51),⁽¹⁾ microdamage density (r=−0.40),⁽¹⁹⁾ or porosity (r=−0.61).⁽¹⁶⁾

Interestingly, NMR properties did not help improve the prediction of K_grow over age (Table 2) even though porosity is thought to influence both crack initiation and crack growth toughness. This shed lights on another feature that most likely affects fracture toughness: matrix heterogeneity. Indeed, based on fracture mechanics theory, a crack will propagate more readily in a homogeneous material than in a material offering structural/compositional interfaces.⁽⁸⁰⁾ A loss in tissue heterogeneity has been posited as an explanation for the occurrence of fractures associated with long-term anti-resorptive treatment, which leads to a more homogeneous matrix.^(4,81–83) Computational studies have also established the mechanical properties of the cement lines as an attribute likely to affect the propagation of the crack through bone tissue.^(62,84) Hence, by providing only a bulk measurement of bone tissue and therefore being insensitive to matrix heterogeneity and the microstructural barrier provided by cement lines, NMR-derived properties may not be suitable to detect changes in crack growth toughness.

As for RPI, the output properties of this instrument better explained age-related decrease in fracture toughness than avBMD. Precisely, it is easier for the probe tip to penetrate bone tissue (i.e. higher indentation distance, higher energy dissipated, lower loading slope) when bone material exhibits lower fracture toughness. In particular, RPI was the only technique among the three tested that improved the explanation of crack growth toughness from a coefficient of determination of 17.1% (age only) to 23.9% (Table 2). While this link between RPI and crack growth toughness concurs with fracture toughness tests conducted with compact tension specimens acquired from the tibia mid-shaft of four human donors,⁽³⁰⁾ weak correlations between RPI properties and fracture toughness (Table 1) are not entirely unexpected. The probe tip generates microdamage at the micro-scale, whereas apparent level fracture toughness depends on a crack propagating over millimeters and can take a tortuous path. It remains to be seen whether another reference point indenter, namely the OsteoProbe™, would provide stronger correlations with fracture toughness given that it uses a large impact load (~45 N) engaging more bone tissue and likely propagating more microcracks than the cyclic indentation method (10 N) of the BioDent™.

There is a possible limitation to the way bound and pore water were calculated. Indeed, by normalizing the water measurements by apparent total volume of bone (i.e. including both the matrix and porous space),^(26,27,85) pw and bw are inversely correlated to some extent. Consequently, for the same level of matrix hydration, a more porous specimen, i.e. with a lower matrix fraction, exhibits a lower bw. Nonetheless, the partial correlation between age and bound water when controlling for porosity (pw) remained significant (r = −0.47 with pw as a covariate, r = −0.52 otherwise), and so the age-related decrease in bound water is not strongly biased by any concomitant increase in porosity. This was also the case for the partial correlations between bw and the fracture toughness properties K_init (r = 0.49), J-int (r = 0.33), and K_grow (r = 0.33). Moreover, bw and pw together significantly contributed to K_init (Table 2). This was possible to test because of the large size of the cohort with more than 60 human donors (unusual for a basic science study). Care was taken to balance gender (32 female, 30 male) and age (from 23 to 98 years old, mean±std = 64±22 y.o.).

In summary, the findings of the present work stress the necessity of a multimodal assessment of fracture toughness. After investigating the potential of several techniques sensitive to different features and length scales of bone, an explanation of variance in fracture toughness can be best achieved by a combination of bound and pore water plus indentation resistance properties as determined by ¹H NMR and RPI, respectively. This supports the potential of MRI and RPI to complement DXA in clinical assessment of fracture risk, especially in diseases likely affecting material properties more so than areal BMD, e.g. type 2 diabetes.

Supplementary Material

Supp FigureS1

Supplemental Figure 1: Schematic representation of the calculation of porosity via μCT (left) and NMR (right). Using μCT, the total volume is computed as the outside contour (green) of the specimen. Any pixel that is not bone within this contour is assigned to porosity. Using NMR, the total volume is calculated using Archimedes’ principle, which ignores all the “entering” pores. As a result, the pore water only accounts for the water trapped inside a pore and is thereby significantly lower than the porosity computed from μCT. For most of the samples, the pores located on the outer contour of the bone are rather small compared to the overall porosity, yielding to similar results between Ct.Po and pw (Fig. 3B), but the discrepancy between μCT and NMR will occur for specimen that exhibit remarkably high porosities (it was the case for 2 out 62 specimens in our study).