Compressive axial mechanical properties of rat bone as functions of bone volume fraction, apparent density and micro-ct based mineral density

Counter-effect of constrained dynamic loading on osteoporosis in ovariectomized mice

In recent years, dynamic mechanical loading has been shown to effectively enhance bone remodeling. The current study attempted to research the counter-effect of constrained dynamic loading on osteoporosis (OP) in ovariectomized (OVX) mice. Female Kunming (KM) mice were randomly divided into 2 groups: SHAM and OVX. The right ulnas of the OVX mice were subjected to a 4-week constrained dynamic loading protocol, and the mechanical properties, trabecular micromorphology parameters and biochemical indices of osteogenesis were evaluated. We detected higher levels of tissue alkaline phosphatase (AKP) and serum bone gamma-carboxyglutamic-acid-containing proteins (BGPs), better trabecular micromorphology parameters and ulnar mechanical properties in the loading group than in the nonloading group. In summary, constrained dynamic loading could prevent ovariectomy-induced osteoporosis by facilitating osteogenesis, improving trabecular microstructure and enhancing bone mechanical properties.

Improved prediction of rat cortical bone mechanical behavior using composite beam theory to integrate tissue level properties

Tissue level characteristics of bone can be measured by nanoindentation and microspectroscopy, but are challenging to translate to whole bone mechanical behavior in this hierarchically structured material. The current study calculated weighted section moduli from microCT attenuation values based on tissue level relationships (Z(lin,a) and Z(lin,b)) between mineralization and material properties to predict whole bone mechanical behavior. Z(lin,a) was determined using the equation of the best fit linear regression between indentation modulus from nanoindentation and mineral:matrix ratio from Raman spectroscopy. To better represent the modulus of unmineralized tissue, a second linear regression with the intercept fixed at 0 was used to calculate Z(lin,b). The predictive capability of the weighted section moduli calculated using a tissue level relationship was compared with average tissue level properties and weighted section moduli calculated using an apparent level relationship (Z(exp)) between Young's Modulus and mineralization. A range of bone mineralization was created using vitamin D deficiency in growing rats. After 10 weeks, left femurs were scanned using microCT and tested to failure in 3 point bending. Contralateral limbs were used for co-localized tissue level mechanical properties by nanoindentation and compositional measurements by Raman microspectroscopy. Vitamin D deficiency reduced whole bone stiffness and strength by ∼35% and ∼30%, respectively, but only reduced tissue mineral density by ∼10% compared with Controls. Average tissue level properties did not correlate with whole bone mechanical behavior while Z(lin,a), Z(lin,b), and Z(exp) predicted 54%, 66%, and 80% of the failure moment respectively. This study demonstrated that in a model for varying mineralization, the composite beam model in this paper is an improved method to extrapolate tissue level data to macro-scale mechanical behavior.

Finite element analysis of a micromechanical model of bone and a new 3D approach to validation

Finite Element Analysis (FEA) is now widely used to analyse the mechanical behaviour of bone structures. Ideally, simulations are validated against experimental data. To date, validation of Finite Element Models (FEMs) has been 2 Dimensional (2D) only, being based on comparison with surface-mounted strain gauge readings. In this study we present a novel 3-Dimensional (3D) approach to validation that allows comparison of modelled with experimental results between any two points in 3D space throughout the structure, providing magnitude and direction data for comparison, internally and externally. Specifically, we validate a FEM of a rat tibia, including trabecular network geometry, using a material testing stage housed within a microCT scanner. We further apply novel landmark based morphometric approaches to more effectively compare modelled and experimental results. 542 landmark points on the cortical and trabecular bone surfaces of the model were selected and validated in 3D against experimental data. This approach may hold considerable potential in fields wherein a better understanding of the mechanical behaviour of trabecular networks is important, e.g., the studies of osteoporosis and trabecular loss after orthopaedic implant insertion.

Can micro-imaging based analysis methods quantify structural integrity of rat vertebrae with and without metastatic involvement?

This study compares the ability of μCT image-based registration, 2D structural rigidity analyses and multimodal continuum-level finite element (FE) modeling in evaluating the mechanical stability of healthy, osteolytic, and mixed osteolytic/osteoblastic metastatically involved rat vertebrae. μMR and μCT images (loaded and unloaded) were acquired of lumbar spinal motion segments from 15rnu/rnu rats (five per group). Strains were calculated based on image registration of the loaded and unloaded μCT images and via analysis of FE models created from the μCT and μMR data. Predicted yield load was also calculated through 2D structural rigidity analysis of the axial unloaded μCT slices. Measures from the three techniques were compared to experimental yield loads. The ability of these methods to predict experimental yield loads were evaluated and image registration and FE calculated strains were directly compared. Quantitatively for all samples, only limited weak correlations were found between the image-based measures and experimental yield load. In comparison to the experimental yield load, we observed a trend toward a weak negative correlation with median strain calculated using the image-based strain measurement algorithm (r=-0.405, p=0.067), weak significant correlations (p<0.05) with FE based median and 10th percentile strain values (r=-0.454, -0.637, respectively), and a trend toward a weak significant correlation with FE based mean strain (r=-0.366, p=0.09). Individual group analyses, however, yielded more and stronger correlations with experimental results. Considering the image-based strain measurement algorithm we observed moderate significant correlations with experimental yield load (p<0.05) in the osteolytic group for mean and median strain values (r=-0.840, -0.832, respectively), and in the healthy group for median strain values (r=-0.809). Considering the rigidity-based predicted yield load, we observed a strong significant correlation with the experimental yield load in the mixed osteolytic/osteoblastic group (r=0.946) and trend toward a moderate correlation with the experimental yield load in the osteolytic group (r=0.788). Qualitatively, strain patterns in the vertebral bodies generated using image registration and FEA were well matched, yet quantitatively a significant correlation was found only between mean strains in the healthy group (r=0.934). Large structural differences in metastatic vertebrae and the complexity of motion segment loading may have led to varied modes of failure. Improvements in load characterization, material properties assignments and resolution are necessary to yield a more generalized ability for image-based registration, structural rigidity and FE methods to accurately represent stability in healthy and pathologic scenarios.

Changes in proximal femur bone properties following ovariectomy and their association with resistance to fracture

Bone strength depends on several material and structural properties, but findings concerning the best predictors of bone mechanical performance are conflicting. The aim of this study was to investigate how a broad set of bone properties in the proximal femur are influenced by age and hormonal status, and how these properties together determine bone strength. Twenty-five Wistar rats were ovariectomized (OVX, n = 13) or sham operated (SHAM, n = 12) at 5 months of age, and killed after 9 months. Another group of rats was killed at 5 months as baseline control (BSL, n = 7). At sacrifice, serum 17β-estradiol and bone turnover marker concentrations were determined in the serum. Both femurs were collected for assessment of trabecular microarchitecture, femoral neck geometry, radiographic absorptiometry, calcium and phosphate content, and biomechanical properties. While stiffness was mostly associated with proximal femur trabecular microarchitecture and mineralization degree, bone strength was mostly linked to bone size and femoral neck geometry, which predicted almost 50% of its variance. Despite the decrease in cortical and trabecular bone as well as in mineralization degree following estrogen loss, bone strength was not reduced in OVX animals compared to BSL or sham-operated rats. This was due to a change in femoral neck geometry as well as to an increase in femur size in OVX, which apparently compensated their lower bone volume and mineral content, thereby preserving bone strength. Estrogen loss leads to a deterioration of bone tissue quality, but bone strength was preserved at the expense of geometric adaptations.

Assessment of axial bone rigidity in rats with metabolic diseases using CT-based structural rigidity analysis

Objectives

This study aims to assess the correlation of CT-based structural rigidity analysis with mechanically determined axial rigidity in normal and metabolically diseased rat bone.

Methods

A total of 30 rats were divided equally into normal, ovariectomized, and partially nephrectomized groups. Cortical and trabecular bone segments from each animal underwent micro-CT to assess their average and minimum axial rigidities using structural rigidity analysis. Following imaging, all specimens were subjected to uniaxial compression and assessment of mechanically-derived axial rigidity.

Results

The average structural rigidity-based axial rigidity was well correlated with the average mechanically-derived axial rigidity results (R2 = 0.74). This correlation improved significantly (p < 0.0001) when the CT-based Structural Rigidity Analysis (CTRA) minimum axial rigidity was correlated to the mechanically-derived minimum axial rigidity results (R2 = 0.84). Tests of slopes in the mixed model regression analysis indicated a significantly steeper slope for the average axial rigidity compared with the minimum axial rigidity (p = 0.028) and a significant difference in the intercepts (p = 0.022). The CTRA average and minimum axial rigidities were correlated with the mechanically-derived average and minimum axial rigidities using paired t-test analysis (p = 0.37 and p = 0.18, respectively).

Conclusions

In summary, the results of this study suggest that structural rigidity analysis of micro-CT data can be used to accurately and quantitatively measure the axial rigidity of bones with metabolic pathologies in an experimental rat model. It appears that minimum axial rigidity is a better model for measuring bone rigidity than average axial rigidity.

Assessment of axial bone rigidity in rats with metabolic diseases using CT-based structural rigidity analysis

Objectives

This study aims to assess the correlation of CT-based structural rigidity analysis with mechanically determined axial rigidity in normal and metabolically diseased rat bone.

Methods

A total of 30 rats were divided equally into normal, ovariectomized, and partially nephrectomized groups. Cortical and trabecular bone segments from each animal underwent micro-CT to assess their average and minimum axial rigidities using structural rigidity analysis. Following imaging, all specimens were subjected to uniaxial compression and assessment of mechanically-derived axial rigidity.

Results

The average structural rigidity-based axial rigidity was well correlated with the average mechanically-derived axial rigidity results (R² = 0.74). This correlation improved significantly (p < 0.0001) when the CT-based Structural Rigidity Analysis (CTRA) minimum axial rigidity was correlated to the mechanically-derived minimum axial rigidity results (R² = 0.84). Tests of slopes in the mixed model regression analysis indicated a significantly steeper slope for the average axial rigidity compared with the minimum axial rigidity (p = 0.028) and a significant difference in the intercepts (p = 0.022). The CTRA average and minimum axial rigidities were correlated with the mechanically-derived average and minimum axial rigidities using paired t-test analysis (p = 0.37 and p = 0.18, respectively).

Conclusions

In summary, the results of this study suggest that structural rigidity analysis of micro-CT data can be used to accurately and quantitatively measure the axial rigidity of bones with metabolic pathologies in an experimental rat model. It appears that minimum axial rigidity is a better model for measuring bone rigidity than average axial rigidity.

Non-invasive assessment of failure torque in rat bones with simulated lytic lesions using computed tomography based structural rigidity analysis

This study applies CT-based structural rigidity analysis (CTRA) to assess failure torque of rat femurs with simulated lytic defects at different locations (proximal and distal femur) and diameters (25% and 50% of the cross-section at the site), and compared the results to those obtained from mechanical testing. Moreover, it aims to compare the correlation coefficients between CTRA-based failure torque and DXA-based aBMD versus actual failure torque. Twenty rats were randomly assigned to four equal groups of different simulated lesions based on size and location. Femurs from each animal underwent micro-computed tomography to assess three-dimensional micro-structural data, torsional rigidity using structural rigidity analysis and dual energy X-ray absorptiometry to assess bone mineral density. Following imaging, all specimens were subjected to torsion. Failure torque predicted from CT-derived structural rigidity measurements was better correlated with mechanically derived failure torque [R(2)=0.85] than was aBMD from DXA [R(2)=0.32]. In summary, the results of this study suggest that computed tomography based structural rigidity analysis can be used to accurately and quantitatively measure the mechanical failure torque of bones with osteolytic lesions in an experimental rat model. Structural rigidity analysis can provide more accurate predictions on maximal torque to mechanical failure than dual energy X-ray absorptiometry based on bone mineral density.

Quantitative (31)P NMR spectroscopy and (1)H MRI measurements of bone mineral and matrix density differentiate metabolic bone diseases in rat models

In this study, bone mineral density (BMD) of normal (CON), ovariectomized (OVX), and partially nephrectomized (NFR) rats was measured by (31)P NMR spectroscopy; bone matrix density was measured by (1)H water- and fat-suppressed projection imaging (WASPI); and the extent of bone mineralization (EBM) was obtained by the ratio of BMD/bone matrix density. The capability of these MR methods to distinguish the bone composition of the CON, OVX, and NFR groups was evaluated against chemical analysis (gravimetry). For cortical bone specimens, BMD of the CON and OVX groups was not significantly different; BMD of the NFR group was 22.1% (by (31)P NMR) and 17.5% (by gravimetry) lower than CON. For trabecular bone specimens, BMD of the OVX group was 40.5% (by (31)P NMR) and 24.6% (by gravimetry) lower than CON; BMD of the NFR group was 26.8% (by (31)P NMR) and 21.5% (by gravimetry) lower than CON. No significant change of cortical bone matrix density between CON and OVX was observed by WASPI or gravimetry; NFR cortical bone matrix density was 10.3% (by WASPI) and 13.9% (by gravimetry) lower than CON. OVX trabecular bone matrix density was 38.0% (by WASPI) and 30.8% (by gravimetry) lower than CON, while no significant change in NFR trabecular bone matrix density was observed by either method. The EBMs of OVX cortical and trabecular specimens were slightly higher than CON but not significantly different from CON. Importantly, EBMs of NFR cortical and trabecular specimens were 12.4% and 26.3% lower than CON by (31)P NMR/WASPI, respectively, and 4.0% and 11.9% lower by gravimetry. Histopathology showed evidence of osteoporosis in the OVX group and severe secondary hyperparathyroidism (renal osteodystrophy) in the NFR group. These results demonstrate that the combined (31)P NMR/WASPI method is capable of discerning the difference in EBM between animals with osteoporosis and those with impaired bone mineralization.

Application of structural rigidity analysis to assess fidelity of healed fractures in rat femurs with critical defects

Approximately 6 million fractures occur each year in the United States, with an estimated medical and loss of productivity cost of $99 billion. As our population ages, it can only be expected that these numbers will continue to rise. While there have been recent advances in available treatments for fractures, assessment of the healing process remains a subjective process. This study aims to demonstrate the use of micro-computed tomography (microCT)-based structural rigidity analysis to accurately and quantitatively assess the progression of fracture healing over time in a rat model. The femora of rats with simulated lytic defects were injected with human BMP-2 cDNA at various time points postinjury (t = 0, 1, 5, 10 days) to accelerate fracture healing, harvested 56 days from time of injury, and subjected to microCT imaging to obtain cross-sectional data that were used to compute torsional rigidity. The specimens then underwent torsional testing to failure using a previously described pure torsional testing system. Strong correlations were found between measured torsional rigidity and computed torsional rigidity as calculated from both average (R2 = 0.63) and minimum (R2 = 0.81) structural rigidity data. While both methods were well correlated across the entire data range, minimum torsional rigidity was a better descriptor of bone strength, as seen by a higher Pearson coefficient and smaller y-intercept. These findings suggest considerable promise in the use of structural rigidity analysis of microCT data to accurately and quantitatively measure fracture-healing progression.