Increased bone strength is associated with improved bone microarchitecture in intact female rats treated with strontium ranelate: A finite element analysis study

Bone 48 (2011) 1109–1116

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Bone j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / b o n e

Increased bone strength is associated with improved bone microarchitecture in intact female rats treated with strontium ranelate: A finite element analysis study Steven K. Boyd a,b,⁎, Eva Szabo a,b, Patrick Ammann c a b c

Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, Canada Roger Jackson Centre for Health and Wellness, University of Calgary, Calgary, Canada Service of Bone Diseases, World Health Organization Collaborating Center for Osteoporosis Prevention, Geneva, Switzerland

a r t i c l e

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Article history: Received 23 July 2010 Revised 7 January 2011 Accepted 10 January 2011 Available online 27 January 2011 Edited by: H. Genant Keywords: Strontium ranelate Osteoporosis Micro-computed tomography Finite element analysis Bone microarchitecture Bone strength

a b s t r a c t Strontium ranelate has been previously shown to act on bone metabolism and to be effective in postmenopausal osteoporosis treatment by preventing vertebral and non-vertebral fractures. Animal studies explicitly demonstrated that bone strength was improved with strontium ranelate treatment, but the contribution of either improved bone microarchitecture or intrinsic quality of the bone tissue is not clear. Therefore, the purpose of this research was to address this issue by using the unique capability of finite element (FE) analysis to integrate both intrinsic bone quality properties from nano-indentation and microarchitecture measured by micro-computed tomography (μCT). The two groups included intact female Fischer rats fed a normal diet (controls, N = 12) or a diet containing strontium ranelate (900 mg/kg/day; N = 12) for a period of 104 weeks. The L5 vertebra was scanned by μCT and a morphological analysis of the vertebral body was performed. Subsequently, those μCT data were the basis of FE models with added virtual endcaps that simulated axial compression tests. The FE models were solved with the vertebral bodies only and repeated with the vertebral processes intact. In the initial stages, the intrinsic bone properties were kept constant between the control and the treated animals in order to independently study the impact of microarchitectural changes on bone strength. Morphological data indicated a significant improvement in bone microarchitecture associated with strontium ranelate compared to controls, including a 40% (p b 0.01) higher trabecular thickness, a 28% (p b 0.01) higher cortical thickness, and no significant change in the number of trabeculae (p = 0.56). The poor correlation of bone strontium content against bone volume fraction (BV/TV) (R2 = 0.013, p = 0.74) and BMD (R2 = 0.153, p = 0.23) indicated that the morphological data were not biased by the presence of strontium in bone. The FE simulations demonstrated a 22% (p b 0.01) increase of stiffness and 29% (p b 0.01) increase in strength compared to controls. The magnitudes were greater, but the relative differences were similar when the entire intact vertebra was modeled compared to the vertebral body alone. Adjusting the FE models to account for differences in intrinsic bone tissue quality between control and treated animals resulted in an even higher bone strength with strontium ranelate. Furthermore, load transfer in strontium ranelate treated animals shifted from an equal distribution between cortical and trabecular compartments to more load being supported by the trabecular bone (a shift of 8%, p b 0.02). Tissue-level stresses were reduced on average (− 7%, p b 0.01) and more homogeneously distributed. Together, these findings indicated that, independently from bone strontium content, microarchitectural adaptations played a major role in the increased bone strength associated with strontium ranelate exposure and that the changes in load distribution resulted in patterns that were more favorable to resisting fracture. © 2011 Elsevier Inc. All rights reserved.

Introduction Strontium ranelate efficacy has been demonstrated in postmenopausal osteoporosis treatment by reduction of vertebral and nonvertebral fractures [1–3]. In vitro studies suggest a dual mechanism of action where strontium ranelate both decreases bone resorption [4–7] ⁎ Corresponding author at: Schulich School of Engineering, University of Calgary, 2500 University Drive, N.W., Calgary, Alberta T2N 1N4, Canada. Fax: +1 403 282 8406. E-mail address: [email protected] (S.K. Boyd). 8756-3282/$ – see front matter © 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.bone.2011.01.004

and enhances bone formation [5,8,9]. In ovariectomized rats, strontium ranelate prevents bone loss by decreasing resorption while maintaining bone formation [10] and this has been shown to lead to improved bone microarchitecture and bone strength [11]. These effects have also been observed in intact (i.e., not ovariectomized) animals after treatment with strontium ranelate [12]. While it is clear that strontium ranelate increases bone strength in the rat vertebrae, the relative importance of improved microarchitecture [12,13] and improved intrinsic bone tissue quality [14] on bone strength are still to be clarified.

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Although dual X-ray absorptiometry (DXA) is the clinical standard to assess bone mineral density (BMD), that measure is confounded by changes in microarchitecture, intrinsic bone tissue quality and the effects of a heavy strontium (Sr2+) atom [15]. Thus, bone strength cannot be directly inferred from BMD, and alternative surrogates for bone strength are needed [16]. Until now, studies have mainly used classical destructive biomechanics, but a promising non-destructive approach exists based on the finite element (FE) method. The FE method provides a novel approach to assess bone strength, particularly when combined with specimen-specific high-resolution data obtained from micro-computed tomography (μCT), from which the bone microarchitecture can be easily obtained [17]. Alternatively, the FE method has the unique capability to integrate both intrinsic bone tissue properties and microarchitecture in order to elucidate their relative contributions to bone strength [18]. It also can provide insight into the relative load carried by trabecular and cortical bone compartments [19] and shifts in intrinsic tissue stress distributions are related to treatment interventions [20]. Finally, the FE method also provides an opportunity to investigate effects of different biomechanical testing approaches, for example, whether it is necessary to remove vertebral processes prior to compression testing. This is particularly relevant to investigations of new treatments such as strontium ranelate as it is possible that cortical bone (of which processes are primarily composed) is more greatly affected than trabecular bone, therefore the impact of strontium ranelate may be greater with processes included in the analysis. Thus, the goal of this study was to use μCT-based FE analysis to investigate the relative contribution of two important determinants of bone strength (microarchitecture and intrinsic tissue properties) due to strontium ranelate in intact female rats. A complementary secondary goal was to understand how these changes may influence bone loading patterns in the trabecular and cortical compartments.

The segmentation of the cortical and trabecular compartments was performed using an automated segmentation routine [21], and the masks generated were verified by manual inspection. These masks were the basis to perform separate morphological analysis for the cortical and trabecular compartments and to distinguish those compartments in the finite element models so that relative loading could be determined. The vertebral processes were identified by manual segmentation so that FE modeling could be performed with and without the intact vertebral body. Morphological analysis of the bone microarchitecture was determined for the vertebral body, including bone volume fraction (BV/TV), trabecular thickness (Tb.Th), trabecular number (Tb.N), trabecular separation (Tb.Sp), connectivity density (Conn.D) and cortical thickness (Ct.Th) [22,23]. Bone mineral density (BMD) of the vertebral bodies were determined and expressed as linear attenuation (1/cm) rather than units of hydroxyapatite (HA). Finite element analysis Finite element models were generated to simulate axial compression testing of all the L5 vertebrae. As per bone mechanical testing [14], virtual embedding of the caudal and cranial surfaces in methylmethacrylate cement endcaps was performed to ensure parallel surfaces for application of the axial load. Alternatively, cutting the caudal and cranial surfaces would have compromised the structural integrity of the bone and altered its normal load carrying capacity. Each end of the vertebrae was embedded 0.66 mm into an endcap that was 1.89 mm thick and approximately 5 mm in diameter. The 3D images representing the segmented trabecular and cortical compartments, and the methylmethacrylate endcaps, were resampled by a factor of two to reduce data

Methods Animals Twenty-four intact female Fischer rats aged 6–7 weeks old (Charles River) were divided equally into two experimental groups (N = 12 each) and either received laboratory chow (UAR, Villemoisson, France) or oral strontium ranelate (Les Laboratoires Servier, Neuilly, France) mixed into their diet at a dose of 900 mg/kg/day for 104 weeks. This dose of strontium ranelate leads to a strontium serum circulating level in the rats corresponding to twice the human therapeutic level. Animals were killed, and lumbar spine was immediately excised, wrapped in wet gauze, and frozen at − 18 °C until testing. Further details of these animals are available from an earlier study [14]. Micro-computed tomography The vertebrae L5 excised from the lumbar spine were scanned in air by μCT (μCT 40, Scanco Medical, Switzerland) with a nominal isotropic resolution of 16 μm (50 kVp, 144 μA, 200 ms integration time). These data were Gaussian filtered (σ = 0.7, support = 1) and globally thresholded to extract the mineralized phase. In order to avoid possible confounding effects of the heavy strontium atom (Sr2+) that may artefactually increase bone volume, an adaptive thresholding routine based on automatically finding the middle of a bi-modal histogram of a centrally located 1003-voxel sub-volume was applied to each bone (N = 24; Image Processing Language v5.08a) to extract the mineralized phase. In a previous study [12], the bone strontium content was analyzed by ICP-OES for each animal on the adjacent vertebra L4 and expressed as Sr/(Sr + Ca) mol/mol%, and these data were used here to test if the quantity of Sr2+ in the bone biased the morphological outcomes.

Fig. 1. Adaptive thresholding was applied to the 24 bone samples to account for differences in tissue mineralization. The left column shows the raw data and extracted mineralized phase for one vertebra from the control group. The right column shows the same for a vertebra from the strontium ranelate group.

S.K. Boyd et al. / Bone 48 (2011) 1109–1116

set size and automatically converted into FE meshes using the voxel conversion approach (323 μm voxels from 16.63 μm) [17]. Linear FE models were generated containing three phases of materials. The methylmethacrylate endcaps were assigned an elastic modulus of 3000 MPa and a Poisson's ratio of 0.3 [24]. In a previous study using nanoindentation [14], no difference was found between the intrinsic tissue properties of the cortical and trabecular bone compartments. However, that study found strontium ranelate was associated with a 15.1% increase in intrinsic bone tissue modulus when testing was performed under physiological conditions but was not significantly different from untreated controls under dry conditions (modulus of 19,310 MPa and a Poisson's ratio of 0.3). Therefore, our FE analysis was performed in two steps. First, it was performed under the assumption of the same tissue moduli for both experimental groups (19,310 MPa; 0.3 Poisson's ratio), and this allowed us to isolate the effects of microarchitectural differences on bone strength. Subsequently, the analysis was repeated with an augmented tissue modulus of 15.1% for the strontium ranelate group in accordance with the physiological nanoindentation tests, and this allowed incorporation of differences in intrinsic bone tissue modulus. All tests were performed with the cortical and trabecular compartments having the same tissue modulus. Boundary conditions for the models were applied to simulate uniaxial compression. Nodes on the caudal endcap were fixed in the axial (Z) direction and free to move in the transverse (XY) plane. Nodes on the cranial endcap had an axial (Z) displacement equivalent to 1% compressive strain applied. All models were solved on a desktop workstation (MacPro, OS X v10.5.6; 2 ×2.8 GHz Quad-Core Intel Xeon) using in-house designed software (FAIM, v4.1). Results included the reaction force [N] resulting from application of 1% strain, bone stiffness [N/mm], load sharing between the cortical and trabecular compartments [%] measured at the mid-transverse plane, and tissue von Mises stress [MPa] distribution. To characterize the histograms, we reported the mean, standard deviation, kurtosis (a measure of the peakedness of the histogram) and skewness (a measure of the

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asymmetry of the histogram) for data representing the whole bone, as well as the cortical and trabecular compartments separately. Finally, the estimated failure load [N] was determined using the so-called ‘Pistoia criterion’ [25,26] based on the assumption that failure occurs when more than 2% of the bone volume exceeds 0.7% energyequivalent strain. Together, these data provide insight into the mechanical properties of the vertebrae at the continuum level (equivalent to mechanical testing), as well as insight into the relative load carried by cortical and trabecular bone and distribution of tissue level stress that may indicate potential stress raisers (i.e., fracture initiation points). A sub-group of the 24 models described above were re-tested under identical conditions but with the vertebral body intact (N = 6 controls, N = 6 strontium ranelate). The same outcomes were determined and compared with their counterparts that had the vertebral processes removed. These data were used to investigate whether the inclusion of the vertebral processes changed the relative differences in bone mechanics between treated and untreated animals. Statistical analysis Descriptive statistics for all morphological and FE results were provided, including group mean, standard deviation, coefficient of variation, minimum and maximum values. Student t-tests were performed to determine differences between the two experimental groups (significance defined when p-value b 0.05). Pearson's correlation was performed between bone strontium content and BV/TV or BMD. Results Adaptive thresholding performed well at extracting the mineralized phase from the μCT images based on a qualitative comparison of segmented images with their gray-scale counterparts (Fig. 1). As

Fig. 2. Automatic segmentation algorithm identified the cortical and cancellous regions of the vertebrae. Light gray represents the cortical bone; dark gray represents the cancellous bone of a representative vertebra from the control and strontium ranelate groups. Morphological analysis was confined to the vertebral body.

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Table 1 Morphology. Group

Descriptors

BV/TV [%]

Tb.Th* [mm]

Tb.N* [mm−1]

Tb.Sp* [mm]

Conn.D [mm−3]

Ct.Th* [mm]

BMD [1/cm]

Control

Mean SD %CV Min Max Mean SD %CV Min Max p-value % change (SR)

61.79 6.38 10.32 52.47 74.31 72.20 7.83 10.84 59.75 83.76 b 0.01 17.00%

0.17 0.02 12.17 0.14 0.21 0.24 0.04 17.29 0.18 0.33 b0.01 40.00%

5.07 0.19 3.83 4.90 5.51 5.09 0.31 6.11 4.34 5.47 0.56 0.00%

0.15 0.02 13.11 0.11 0.17 0.13 0.01 8.46 0.12 0.15 b0.01 −13.00%

33.31 8.16 24.5 19.73 50.98 22.05 4.71 21.36 15.29 31.28 0.03 −34.00%

0.20 0.01 6.14 0.18 0.22 0.26 0.06 21.59 0.20 0.42 b0.01 28.00%

2.98 0.16 5.36 2.79 3.36 4.15 0.24 5.69 3.82 4.49 b 0.01 40.00%

Strontium ranelate 900 mg/kg/day

Microarchitecture and density of the vertebral body (vertebral processes excluded) of control (N = 12) and strontium ranelate (N = 12) groups. Mean, standard deviation (SD), percent coefficient of variation (%CV), minimum and maximums for each group are shown. The percent differences of the strontium ranelate (SR) group compared to control, and associated p-value indicating statistical significance (p b 0.05) for each parameter are also shown. * indicates direct measurements of these indices were performed.

expected, due to higher BMD, the average global threshold for the strontium ranelate group was higher than the normal controls, with averages of 34.2% versus 27.3% of maximum gray-scale value, respectively. However, the poor correlation of bone strontium content against bone volume fraction (BV/TV) (R2 = 0.013, p = 0.74, N = 11) and BMD (R2 = 0.153, p = 0.23, N = 11) indicated that the morphological data was not biased by the presence of strontium in bone. The automated segmentation algorithm successfully identified the trabecular and cortical compartments for each bone (Fig. 2). Morphological parameters The bone microarchitecture (Table 1) was markedly different between the two experimental groups for all parameters except trabecular number (Tb.N, p = 0.56). The strontium ranelate group had higher trabecular BV/TV (+17%, p b 0.01) as well as higher bone mineral density (BMD, +40%, p b 0.01) compared to controls. Thus, the microarchitecture did not differ in terms of topology (i.e., Tb.N remained constant) but was characterized by a significantly higher trabecular thickness (Tb.Th, + 40%, p b 0.01) and corresponding lower trabecular separation (Tb.Sp, −13%, p b 0.01). This augmented trabecular structure is consistent with the overall increase in BMD in the strontium ranelate group. Interestingly, although Tb.N was the same between experimental groups, the connectivity density was lower in the strontium ranelate group, which likely indicates that small openings (i.e., remodeling spaces) had been closed. In accordance with the higher thickness in the trabecular region, the

cortex thickness was also significantly higher (Ct.Th, +28%, p b 0.01) in the strontium ranelate group than in the control group. Finite element analysis The analysis of the FE models (with vertebral processes removed) revealed a significant difference in bone strength consistent with the morphological data (Table 2). Models took an average of 15 minutes to solve on desktop workstations. The effect of strontium ranelate was to increase both stiffness (+22%, p b 0.01) and estimated failure load (+ 29%, p b 0.01) of the vertebrae when the 19,340 MPa tissue modulus was applied to both experimental groups. When the FE models of the strontium ranelate group were re-run with the tissue modulus augmented by + 15.1%, i.e., to 22,260 MPa, the mechanical strength needed for a 1% strain increased, as indicated by the stiffness (+31%, p b 0.01) and estimated failure load (+48%, p b 0.01). Load sharing in the vertebrae differed between the experimental groups. In comparison to the control group where sharing between the cortical and trabecular bone compartments was evenly split (50.5% versus 49.5%), strontium ranelate resulted in a statistically significant shift in loading to the trabecular compartment (46.4% versus 53.6%, p = 0.02 and p b 0.01, respectively). Visualization of each FE model superimposed with the von Mises stress represented by color mapping (Fig. 3) was performed to ensure consistency for each model (i.e., the endcaps did not extend into the vertebral processes, and von Mises stress was continuous). The distribution of von Mises stress was determined for each FE model of

Table 2 FEM Strength. Group

Descriptors

Elements [M]

Nodes [M]

RFz [N]

LS.Cort [%]

LS.Trab [%]

Fail Load [N]

Stiffness [N/mm]

Control

Mean SD %CV Min Max Mean SD %CV Min Max p-value % change (SR)

2.83 0.06 1.98 2.74 2.92 2.99 0.07 2.34 2.89 3.09 b0.01 6.00%

3.05 0.06 2.1 2.97 3.16 3.17 0.06 1.97 3.07 3.27 b0.01 4.00%

514.66 35.85 6.97 472.9 590 614.03 33.55 5.46 566.7 659.1 b0.01 19.00%

50.51 3.97 7.86 43.54 56.76 46.37 2.48 5.34 40.69 50.28 0.02 −8.00%

49.51 3.95 7.99 43.35 56.46 53.63 2.47 4.61 49.72 59.27 b0.01 8.00%

264.08 31.42 11.9 229.3 328.5 341.57 36.46 10.67 300.4 421.4 b 0.01 29.00%

5733.42 387.95 6.77 5325 6442 6990.92 354.42 5.07 6417 7564 b 0.01 22.00%

Strontium ranelate 900 mg/kg/day

The mechanical properties assessed by finite element (FE) analysis simulating axial compression of control (N = 12) and strontium ranelate (N = 12) groups (vertebral body). Table includes data on model size, reaction force at 1% strain (RFz), load sharing (LS), and failure load and bone stiffness. p-values indicating statistical significance (p b 0.05) for each parameter are also indicated.

S.K. Boyd et al. / Bone 48 (2011) 1109–1116

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Fig. 3. A frontal cut of a representative vertebra from the strontium ranelate group (left) and control group (right). Colors represent the magnitude of tissue von Mises stress (MPa). Representative samples were chosen based on having the mean stiffness [N/mm] of each experimental group.

the vertebral body, and histogram results were determined for the whole bone, as well as for the cortical and trabecular compartments separately (Table 3). Strontium ranelate resulted in a lower von Mises stress in the tissue (− 7%, p b 0.01), and the decrease was greater in the cortical (− 9%) than the trabecular (−5%) compartments. Overall, strontium ranelate treatment was associated with a more homogeneously distributed von Mises stress distribution as reflected by the substantial (+ 76%, p b 0.01) increase in kurtosis of the histograms. The increased kurtosis of the cortical (210%) and trabecular (52%) compartments suggests that reductions of stresses raisers occurred substantially in all regions of the bone. Lastly, the analysis of vertebrae with the vertebral processes intact was repeated and compared to the results from tests with the vertebral body alone (Table 4; Fig. 4). The FE models took an average of 56 minutes to solve on our desktop workstations. Including the vertebral processes resulted in models with approximately 50–60% more elements, and the represented increase in bone mass led to a substantial increase in failure load and stiffness. The increases were similar for both strontium ranelate and control groups and affected

the failure load estimates (46–47%) more than the stiffness outcome (17–21%). Notably, the relative increase of failure load and stiffness of the strontium ranelate group compared to controls was similar to the previous tests with the processes removed (see Table 2), although smaller groups were analyzed (N = 6/group). These results indicated that performing the axial compression tests without the intact vertebral processes provides an acceptable test to determine the effects of strontium ranelate on bone strength. Despite there being an increase in bone strength when the processes are included (they provide support to the vertebrae), the relative changes between the strontium ranelate and control groups are not altered. Discussion This FE analysis provides a unique opportunity to integrate two important determinants of bone strength in association with strontium ranelate treatment, that is, the effects on bone microarchitecture and intrinsic tissue quality. While both determinants have previously been shown to be related to increased bone strength,

Table 3 FEM Tissue stress and strain distribution. Group

Control

Strontium ranelate 900 mg/kg/day

Descriptors

Mean SD %CV Min Max Mean SD %CV Min Max p-value % change (SR)

Vertebral body

Cortical compartment

Trabecular compartment

Ave [MPa]

SD [MPa]

Skew

Kurt

Ave [MPa]

SD [MPa]

Skew

Kurt

Ave [MPa]

SD [MPa]

Skew

Kurt

121.18 2.5 2.07 118.6 125.1 112.68 3.8 3.37 106 116.7 b0.01 −7.00%

56.9 5.78 10.15 44.64 63.2 48.94 4.73 9.67 38.08 54.98 b0.01 −14.00%

1.04 0.17 16.35 0.71 1.29 1.26 0.12 9.88 1.07 1.45 b0.01 21.00%

1.16 0.48 41.95 0.58 2.3 2.03 0.64 31.39 0.92 3.12 b0.01 76.00%

135.31 3.11 2.3 128.2 139.5 122.99 7.69 6.25 106.8 130.6 b0.01 −9.00%

61.55 6.61 10.75 48.78 70.07 54.54 5.35 9.81 42.23 60.63 0.02 −11.00%

0.75 0.14 19.19 0.55 0.95 0.92 0.17 18.14 0.73 1.25 0.02 23.00%

0.28 0.42 150.64 −0.33 0.87 0.86 0.73 85.83 −0.19 2.12 0.01 210.00%

112.44 3.53 3.14 108.9 119.4 106.42 2.54 2.38 101.8 110.4 0.01 −5.00%

51.91 4.95 9.54 40.72 57.51 43.72 5.18 11.85 32.85 50.95 b0.01 −16.00%

1.22 0.25 20.12 0.7 1.53 1.47 0.23 15.7 1.19 1.88 0.02 20.00%

2.11 0.82 38.82 0.59 3.79 3.2 1.01 31.59 1.96 5.03 b0.01 52.00%

The distribution of tissue stresses (von Mises) in the whole vertebral body, as well as separately for the cortical and trabecular regions of control (N = 12) and strontium ranelate (N = 12) groups. The mean and standard deviation of the tissue stress, and the skewness (Skew) and kurtosis (Kurt) of the distribution are presented. p-values indicating statistical significance (p b 0.05) for each parameter are also indicated.

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Table 4 FEM testing with vertebral processes. Group

Descriptors

Elements [M]

Nodes [M]

RFz [N]

Fail load [N]

Stiffness [N/mm]

Control

Mean SD %CV Min Max Mean SD %CV Min Max p-value % change (SR) % change (versus control w/o processes) % change (versus SR w/o processes)

4.38 0.22 4.93 4.12 4.64 5.03 0.37 7.4 4.55 5.36 b 0.01 15.00% 54.00% 68.00%

4.98 0.27 5.49 4.64 5.31 5.63 0.39 6.85 5.14 6 0.03 13.00% 62.00% 77.00%

638.47 58.51 9.16 565.2 705.4 717.67 48.55 6.76 653.2 775 0.09 12.00% 21.00% 17.00%

389.95 42.92 11.01 351.3 453.2 490.88 40.43 8.24 429.9 541.1 0.01 26.00% 47.00% 46.00%

7074.67 643.87 9.1 6452 7856 8107.33 545.36 6.73 7601 8983 0.04 15.00% 21.00% 17.00%

Strontium ranelate 900 mg/kg/day

Control SR

Finite element (FE) results when the vertebral processes are included in the analysis. The percent change of the strontium ranelate group (N = 6) relative to the controls (N = 6) and associated p-values are shown. Subsequently, the last two rows indicate the percent change of each FE outcome when the processes are included compared to the vertebral body alone for each the strontium ranelate and control groups.

the results of this study suggest that the augmented microarchitecture can explain the improved strength independently from the increased intrinsic tissue modulus. At the tissue level, strontium ranelate treatment resulted in a shift of load carried by the cortical bone to the trabecular compartment and a reduced likelihood of stress concentrations reflected by the more homogeneous distribution of

tissue stresses. These tissue-level mechanisms are consistent with the increased bone strength by FE analysis, and the results were consistent regardless of whether the vertebral processes were removed or not. The morphological results presented here are on the whole consistent with the findings of Ammann et al. [14], although only a

Fig. 4. Finite element models were generated that included the vertebrae and endcaps. Models were created for vertebral bodies with (top row) and without (bottom row) the processes intact.

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subset of the current parameters (e.g., Ct.Th, Tb.N, Tb.Th and Tb.Sp) were reported previously. Comparing the morphological results for the strontium ranelate treatment group, we estimated a lower Ct.Th (−7%), lower Tb.Sp (−14%), higher Tb.Th (+ 28%) and higher Tb.N (+15%). However, the relative difference between strontium ranelate and control groups was similar for both studies (between − 2% and +11%). Differences in the morphological results are likely due to using different regions of interest (ROI) for the analysis. Ammann et al. [14] assessed the secondary spongiosa of the vertebral body, whereas in the current study the entire trabecular compartment of the L5 vertebral body was analyzed. The difference in ROI may be the reason we found no significant difference for Tb.N as opposed to the modest increase reported previously [14]. Interestingly, the muted change in Tb.N along with an increase in Tb.Th is consistent with findings of recently reported in vivo μCT studies where it was shown that a common mechanism of bone apposition was to build upon the existing microarchitecture network rather than by increasing the number of trabeculae [27–29]. It is unlikely that new bridging trabeculae can be formed by anti-osteoporosis treatments currently available, although there may be special cases where overwhelming bone apposition could lead to closing of inter-trabecular spaces. Overall, the findings here are consistent with previous results and show that strontium ranelate is associated with improved bone microarchitecture. Furthermore, the underlying biological mechanisms of strontium ranelate treatment—that is, reduced osteoclastic absorption and increased osteoblastic activity [30]—is consistent with the observed net gain in bone microarchitecture. The mechanical parameters determined by FE analysis demonstrated a clear improvement of bone strength. Because no significant difference was detected in dry condition testings, the same homogeneous, isotropic tissue modulus was used in FE models for both experimental groups. Hence, the augmented microarchitecture alone due to strontium ranelate treatment can explain the increase in mechanical parameters reported in Table 2, independently from effects of intrinsic tissue quality changes. Nevertheless, under physiological conditions, it has been shown [14] by nanoindentation that rats fed strontium ranelate have a +15.1% improvement in intrinsic bone quality of the L4 vertebra. When that augmented tissue modulus was taken into account in the FE models, then the increased stiffness was estimated to be +31% (compared to +22% in Table 2) and the increased failure load was estimated to be +48% (compared to +29% in Table 2). Therefore, FE results using the same or augmented tissue moduli for the strontium ranelate group both support that the improved microarchitecture independently contributed to improvements in bone strength. Both these FE results based on the L5 vertebrae, and experimental biomechanical testing on the L4 vertebrae performed previously, are consistent in showing an increase in bone strength with strontium ranelate. The improvement of maximal load measured from experimental testing was found to be +23% [14], whereas the FE results here indicated at least a +29% improvement. While the strength results are in agreement, it should be noted that the stiffness estimates differed in terms of both magnitude and statistical findings from the experimental tests. The magnitude of the FE estimated stiffness was greater for both control and strontium ranelate treated groups, and this may be attributed to a number of factors including (a) using an overestimated tissue modulus in the FE model (based on nanoindentation tests) and (b) having thinner methylmethacrylate endcaps than in experimental tests (i.e., a thin endcap would result in a less compliant endcap–bone– endcap test specimen). Combined, these factors would have had an additive effect. Also, it is important to recall that there may have been differences due to using different vertebra (L4 and L5), even if these differences are probably minor since the two considered vertebrae are adjacent. If the same vertebra had been used, it may have been possible to back-calculate tissue moduli [18] to verify that the nanoindentation results were representative of the whole bone. The other difference from experimental tests was that the improvement in stiffness (+22%)

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associated with strontium ranelate based on FE results was statistically significant but not in experimental testing [12,14]. This is likely because of the variability inherent in mechanical testing (e.g., sample alignment, endcap embedding, etc.) that can be strictly controlled in FE models thereby improving the sensitivity to detect differences in the experimental groups. In summary, although there were differences in the stiffness results, both FE and experimental testing agree in that there was a significant improvement in bone strength associated with strontium ranelate. Using the FE models, the patterns of internal load distribution were found to be improved in the strontium ranelate treatment group. At the mid-plane of the vertebrae, the load shifted from being equally distributed in the cortical and trabecular compartments, to a small shift (+ 8%) from the cortical to the trabecular compartment. Also, the spatial distribution of von Mises stress in the tissue was changed as reflected by the histograms showing a reduction in the average stress (−7%) and an increase in the homogeneity of the stress throughout the vertebra (i.e., kurtosis improved by 76%). How these changes directly impact bone strength is open to interpretation; however, a more homogeneous tissue-level stress distribution is indicative of fewer stress concentrations, and this in turn may lead to better resistance to fracture. This concept is supported by the fact that bone strength was increased as assessed by FE (+29%) as well as mechanical testing (+23%) [14]. The changes in microarchitecture appear to translate into improved distribution of tissue-level stresses that is conducive to improved bone strength. The FE method also provides a unique opportunity to explore the implications of cutting the processes prior to axial testing because the same bone can be tested repeatedly with different conditions without destroying the specimen. The inclusion of the processes resulted in an expected increase in the strength of the vertebra because they function to reinforce the vertebral body. In fact, removing the processes results in an unnatural mechanical situation for the vertebra, and load transfer in the vertebral body under compression could be compromised. Nevertheless, despite the decreased stability of the vertebra, the relative difference in strength between the control and strontium ranelate groups is similar. This has implications for mechanical testing because it is significantly easier to perform testing without the processes attached. It also has implications for FE modeling because the inclusion of the processes significantly increases the number of degrees of freedom in the models and hence increases the computational load (i.e., a 4-fold increase in computation time). These data suggest that not only is removal of the processes convenient but it also does not reduce the sensitivity to detect differences in experimental groups. Some limitations of this study should be noted. We generated the FE models after reducing the resolution by a factor of two to reduce computation time, resulting in a 32 μm voxel size. However, since the average Tb.Th ranged between 170 μm and 240 μm, the 32 μm voxel size was still sufficient to represent the trabecular microarchitecture. Another limitation is that the so-called Pistoia criterion [25] was specifically developed for lower resolution μCT data, whereas the data in this study are much higher resolution. Nevertheless, the fact that the strength estimates compared well with experimental results indicates that the FE model was successful at estimating strength. Lastly, the presence of the heavier Sr2+ atom makes image processing a challenge when using global thresholds to isolate the mineralized phase from gray-scale μCT data. If we had opted to use the same global threshold for all specimens, then the presence of Sr2+ would have resulted in an artificially augmented architecture. We addressed that issue by using an adaptive thresholding technique to avoid bias between the control and strontium ranelate groups. A stronger threshold on average was determined and applied for the strontium ranelate groups than the controls. To confirm our thresholding method, we followed up with a qualitative evaluation of the thresholds (Fig. 1) and also tested that the correlations between the bone strontium content and BV/TV or BMD were not significant,

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further supporting that there was no bias in the interpretation of the effects of strontium ranelate on bone microarchitecture. Had the same global threshold been applied to all bones, then undoubtedly the improved microarchitecture and strength associated with strontium ranelate would have been even more pronounced. In conclusion, we found by an FE analysis approach that improved bone strength of the L5 vertebrae due to strontium ranelate treatment at 900 mg/kg/day of intact rats is due to augmented microarchitecture, independently from bone strontium content and intrinsic tissue quality. Furthermore, tissue-level stresses were reduced on average and more homogeneously distributed, indicating that the changes in load distribution resulted in patterns that were more favorable to resisting fracture.

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Conflict of interest There is no conflict of interest. Acknowledgments Dr. Boyd holds a Senior Scholar position from Alberta Innovates– Health Solutions, funded by the Alberta Heritage Foundation for Medical Research (AHFMR) endowment fund. This study was funded by a research grant provided by the Institut de Recherches Internationales Servier (IRIS).

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