Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site

In the context of reconciling the mechanical properties of trabecular bone measured from in vitro mechanical testing with the true in situ behavior, recent attention has focused on the "side-artifact" which results from interruption of the trabecular network along the sides of machined specimens. The objective of this study was to compare the magnitude of the side-artifact error for measurements of elastic modulus vs. yield stress and to determine the dependence of these errors on anatomic site and trabecular micro-architecture. Using a series of parametric variations on micro-CT-based finite element models of trabecular bone from the human vertebral body (n=24) and femoral neck (n=10), side-artifact correction factors were quantified as the ratio of the side-artifact-free apparent mechanical property to the corresponding property measured in a typical experiment. The mean (+/-SD) correction factors for yield stress were 1.32+/-0.17 vs. 1.20+/-0.11 for the vertebral body and femoral neck (p<0.05), respectively, and the corresponding factors for modulus were 1.24+/-0.09 vs. 1.10+/-0.04 (p<0.0001). Correction factors were greater for yield stress than modulus (p<0.003), but no anatomic site effect was detected (p>0.29) after accounting for variations in bone volume fraction (BV/TV). Approximately 30-55% of the variation in the correction factors for modulus and yield stress could be accounted for by BV/TV or micro-architecture, representing an appreciable systematic component of the error. Although some scatter in the correction factor-BV/TV relationships may confound accurate correction of modulus and yield stress for individual specimens, side-artifact correction is nonetheless essential for obtaining accurate mean estimates of modulus and yield stress for a cohort of specimens. We conclude that appreciation and correction for the differential effects of the side-artifact in modulus vs. yield stress and their dependence on BV/TV may improve the interpretation of measured elastic and failure properties for trabecular bone.     

Comparison of trabecular bone behavior in core and whole bone samples using high-resolution modeling of a vertebral body

Computational analysis of trabecular bone normally involves the modeling of (experimental tests of) cored samples. However, the lack of constraint on the sides of the extracted trabecular bone samples limits the information that can be inferred regarding true in situ behavior. Here, the element-by-element voxel-based finite element method was applied via, a custom-written software suite (FEEBE), to a 72 μm resolution model of an ovine vertebra. The difference between the apparent modulus of eight concentric core cylinders when modeled as part of the whole bone (containing 84 × 10⁶ degrees of freedom) and independent of the whole bone was investigated. The results showed that cored trabecular bone apparent modulus depended significantly on the core diameter when modeled as an extracted core (r ² = 0.975) and as part of a whole bone (r ² = 0.986). The cause of this result was separated into the side-artifact effect and bone volume fraction (BV/TV) effect. For the independently modeled cores, the apparent modulus of an inner core region of interest varied with increasing thickness of the outer annulus. This was attributed to the side-artifact effect, given that the BV/TV of the core region was constant. Within the whole trabecular structure, the side artifact was eliminated as the entire bone structure was modeled. However, a BV/TV effect influenced the apparent modulus depending on the size of the core selected for determining apparent modulus. Changing the size of the core varied the overall BV/TV of the core, and this significantly (r ² = 0.999) influences the apparent modulus. Therefore, determining a ‘true’ apparent modulus for trabecular bone was not achievable. The independently modeled cores consistently under-predict the in vivo apparent modulus. It is recommended that if a ‘true’ apparent modulus is required, the BV/TV at which it is required needs to be first determined. Apparent modeling of entire bones at microscale resolution allowed regions of low and high tissue strains to be identified, consistent with patterns of trabecular bone remodeling and resorption reported in literature. The basivertebral vein cavity underwent the highest strains within the entire vertebral body, suggesting that failure might initiate here, despite containing visibly thicker struts and plate trabeculae. Although computationally expensive, analysis of the entire vertebral body provided a full picture of in situ trabecular bone deformation.     

Fast and accurate specimen-specific simulation of trabecular bone elastic modulus using novel beam-shell finite element models

Elastic modulus and strength of trabecular bone are negatively affected by osteoporosis and other metabolic bone diseases. Micro-computed tomography-based beam models have been presented as a fast and accurate way to determine bone competence. However, these models are not accurate for trabecular bone specimens with a high number of plate-like trabeculae. Therefore, the aim of this study was to improve this promising methodology by representing plate-like trabeculae in a way that better reflects their mechanical behavior. Using an optimized skeletonization and meshing algorithm, voxel-based models of trabecular bone samples were simplified into a complex structure of rods and plates. Rod-like and plate-like trabeculae were modeled as beam and shell elements, respectively, using local histomorphometric characteristics. To validate our model, apparent elastic modulus was determined from simulated uniaxial elastic compression of 257 cubic samples of trabecular bone (4mm×4mm×4mm; 30μm voxel size; BIOMED I project) in three orthogonal directions using the beam-shell models and using large-scale voxel models that served as the gold standard. Excellent agreement (R(2)=0.97) was found between the two, with an average CPU-time reduction factor of 49 for the beam-shell models. In contrast to earlier skeleton-based beam models, the novel beam-shell models predicted elastic modulus values equally well for structures from different skeletal sites. It allows performing detailed parametric analyses that cover the entire spectrum of trabecular bone microstructures.     

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.     

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.     

Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A microCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure (N) and effective strain (Deltasigma/E(0)): N=1.394x10(-25)(Deltasigma/E(0))(-12.17), r(2)=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.     

Biomechanical properties across trabeculae from the proximal femur of normal and ovariectomised sheep

The elastic behaviour of trabecular bone is a function not only of bone volume and architecture, but also of tissue material properties. Variation in tissue modulus can have a substantial effect on the biomechanical properties of trabecular bone. However, the nature of tissue property variation within a single trabecula is poorly understood. This study uses nanoindentation to determine the mechanical properties of bone tissue in individual trabeculae. Using an ovariectomised ovine model, the modulus and hardness distribution across trabeculae were measured. In both normal and ovariectomised bone, the modulus and hardness were found to increase towards the core of the trabeculae. Across the width of the trabeculae, the modulus was significantly less in the ovariectomised bone than in the control bone. However, in contrast to this hardness was found not to differ significantly between the two groups. This study provides valuable information on the variation of mechanical material properties in healthy and diseased trabecular bone tissue. The results of the current study will be useful in finite element modelling where more accurate values of trabecular bone modulus will enable the prediction of the macroscale behaviour of trabecular bone.     

Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling

An assessment of the mechanical properties of trabecular bone is important in determining the fracture risk of human bones. Many uncertainty factors contribute to the dispersion of the estimated mechanical properties of trabecular bone. This study was undertaken in order to propose a computational scheme that will be able to predict the effective apparent elastic moduli of trabecular bone considering the uncertainties that are primarily caused by image-based modelling and trabecular stiffness orientation. The effect of image-based modelling which focused on the connectivity was also investigated. A stochastic multi-scale method using a first-order perturbation-based and asymptotic homogenisation theory was applied to formulate the stochastically apparent elastic properties of trabecular bone. The effective apparent elastic modulus was predicted with the introduction of a coefficient factor to represent the variation of bone characteristics due to inter-individual differences. The mean value of the predicted effective apparent Young's modulus in principal axis was found at approximately 460 MPa for respective 15.24% of bone volume fraction, and this is in good agreement with other experimental results. The proposed method may provide a reference for the reliable evaluation of the prediction of the apparent elastic properties of trabecular bone.     

Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation

Assessment of the mechanical properties of trabecular bone is of major biological and clinical importance for the investigation of bone diseases, fractures and their treatments. Finite element (FE) methods are getting increasingly popular for quantifying the elastic and failure properties of trabecular bone. In particular, voxel-based FE methods have been previously used to calculate the effective elastic properties of trabecular microstructures. However, in most studies, bone tissue moduli were assumed or back-calculated to match the apparent elastic moduli from experiments, which often lead to surprisingly low values when compared to nanoindentation results. In this study, voxel-based FE analysis of trabecular bone is combined with physical measures of volume fraction, micro-CT (microCT) reconstructions, uniaxial mechanical tests and specimen-specific nanoindentation tests for proper validation of the method. Cylindrical specimens of cancellous bone were extracted from human femurs and their volume fraction determined with Archimede's method. Uniaxial apparent modulus of the specimens was measured with an improved tension-compression testing protocol that minimizes boundary artefacts. Their microCT reconstructions were segmented to match the measured bone volume fraction and used to create full-size voxel models with 30-45 microm element size. For each specimen, linear isotropic elastic material properties were defined based on specific nanoindentation measurements of its embedded bone tissue. Linear FE analyses were finally performed to simulate the uniaxial mechanical tests. Additional parametric analyses were performed to evaluate the potential errors on the predicted apparent modulus arising from variations in segmentation threshold, tissue modulus, and the use of 125-mm(3) cubic sub-regions. The results demonstrate an excellent correspondence between experimental measures and FE predictions of uniaxial apparent modulus. In conclusion, the adopted voxel-based FE approach is found to be a robust method to predict the linear elastic properties of human cancellous bone, provided segmentation of the microCT reconstructions is carefully calibrated, tissue modulus is known a priori and the entire region of interest is included in the analysis.     

Modeling modulus reduction in bovine trabecular bone damaged in compression.

Loading bone beyond its yield point creates microdamage, leading to reduction in stiffness. Previously, we related microdamage accumulation to changes in mechanical properties. Here, we develop a model that predicts stiffness loss based on the presence of microdamage. Modeling is done at three levels: (1) a single trabecula, (2) a cellular solid consisting of intact, damaged, and fractured trabeculae, and (3) a specimen with a localized damage band. Predictions of a reduced modulus agree well with experimental measured modulus reductions of post-yield compression of bovine trabecular bone. The predicted reduced modulus is relatively insensitive to changes in the input parameters.     

Effect of trabecular curvature on the stiffness of trabecular bone

Simplified structural models of trabecular bone have been used to model various forms of trabecular variability. The structural effects of variability of direction, length and thickness of the trabeculae have been studied using 'lattice-type' finite element models. However, many of the trabeculae are not perfectly straight, and have a small degree of curvature. The objective of this study is to quantify the influence of small curvatures of the trabeculae on the effective modulus of trabecular bone, in the principal material direction. An analytical analysis of the effect of curvature on a single trabecula is performed, utilizing the concept of cellular-solid models. Closed-form expressions are derived for the effect of curvature on the flexibility in the principal material direction. For comparison, expressions are derived for the flexibility of a straight oblique element, representing angular variability. A quantitative comparison is presented, which is dependent on the thickness of the trabeculae. It was found that small curvatures have a large effect on the stiffness of the trabecular structure. This effect is largest for thin trabeculae, and decreases for thick trabeculae. The stiffness of the trabecular structure can be reduced by a factor of up to four for thin trabeculae and up to two for thick trabeculae, even for small curvatures. The flexibility of curved elements is found to be larger than the flexibility of oblique elements with similar eccentricities. Thus it seems that curvature might play a role in determining the effective modulus of trabecular bone.     

Age-related changes in microarchitecture and mineralization of cancellous bone in the porcine mandibular condyle

The mandibular condyle is considered a good model for developing cancellous bone because of its rapid growth and high rate of remodeling. The aim of the present study was to analyze the simultaneous changes in microarchitecture and mineralization of cancellous bone during development in a three-dimensional fashion. Eight mandibular condyles of pigs aged 8 weeks prepartum to 108 weeks postpartum were scanned using microCT with an isotropic spatial resolution of 10 microm. The number of trabeculae decreased during development, whereas both the trabecular thickness and the distance between the trabeculae increased. The bone surface to volume ratio decreased during development, possibly limiting the amount of (re)modeling. Both the mean degree of mineralization and intratrabecular differences in mineralization between the surfaces and cores of trabecular elements increased during development. The trabecular surfaces were more highly mineralized in the older condyles compared to the younger ones. Together with the observed decrease in the relative size of trabecular surface, this finding suggests a decrease in (re)modeling activity during development. In accordance with the general growth and development of the pig, it was concluded that most developmental changes in cancellous bone occur until the age of 40 weeks postpartum.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

On shear properties of trabecular bone under torsional loading: effects of bone marrow and strain rate

To further improve our understanding of trabecular bone mechanical behavior in torsion, our objective was to determine the effects of strain rate, apparent density, and presence of bone marrow on trabecular bone shear material properties. Torsion tests of cylindrical trabecular bone specimens from sheep lumbar vertebrae with and without bone marrow were conducted. The bones with marrow were divided into two groups and tested at shear strain rates of 0.002 and 0.05s(-1) measured at the specimen perimeter. The bones without marrow were divided into three groups and tested at shear strain rates of 0.002, 0.015, and 0.05s(-1). Comparing the results of bones with and without marrow tested at low (0.002s(-1)) and high (0.05s(-1)) strain rates, presence of bone marrow did not have any significant effect on trabecular bone shear modulus and strength. In specimens without marrow, power relationships were used to define shear strength and modulus as dependent variables in terms of strain rate and apparent density as independent variables. The shear strength was proportional to the apparent density raised to the 1.02 power and to the strain rate raised to the 0.13 power. The shear modulus was proportional to the apparent density raised to the 1.08 power and to the strain rate raised to the 0.07 power. This study provides further insight into the mechanism of bone failure in trauma as well as failure at the interface between bone and implants as it relates to prediction of trabecular bone shear properties.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.     

Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution

The bone remodeling process takes place at the surface of trabeculae and results in a non-uniform mineral distribution. This will affect the mechanical properties of cancellous bone, because the properties of bone tissue depend on its mineral content. We investigated how large this effect is by simulating several non-uniform mineral distributions in 3D finite element models of human trabecular bone and calculating the apparent stiffness of these models. In the ‘linear model’ we assumed a linear relation between mineral content and Young's modulus of the tissue. In the ‘exponential model’ we included an empirical exponential relation in the model. When the linear model was used the mineral distribution slightly changed the apparent stiffness, the difference varied between an 8% decrease and a 4% increase compared to the uniform model with the same BMD. The exponential model resulted in up to 20% increased apparent stiffness in the main load-bearing direction. A thin less mineralized surface layer (28 μm) and highly mineralized interstitial bone (mimicking mineralization resulting from anti-resorptive treatment) resulted in the highest stiffness. This could explain large reductions in fracture risk resulting from small increases in BMD. The non-uniform mineral distribution could also explain why bone tissue stiffness determined using nano-indentation is usually higher than finite element (FE)-determined stiffness. We conclude that the non-uniform mineral distribution in trabeculae does affect the mechanical properties of cancellous bone and that the tissue stiffness determined using FE-modeling could be improved by including detailed information about mineral distribution in trabeculae in the models.     

Nonlinear behavior of trabecular bone at small strains

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.     

Microdensitometric analysis for study of skeletal growth and aging in the living subject

Microdensitometric analysis of a radiographic image of mineralized tissue offers information on the morphologic characteristics of the specimen examined. The use of microstructure (such as individual trabecula of bone) and macrostructure (such as Harris lines of arrest) as in vivo bone markers allows for assessment of gross skeletal changes in nondestructive fashion. This technique is also applicable to the study of the interrelationship of tooth and bone. In addition, microdensitometry offers precise information on the fine structure of bone as regards the trabecular elements. This technique is applicable in determining the size and quantity of trabeculae, their persistence over long periods of time, and the factors responsible for change or lack of change in trabeculae during growth and aging.     

Physical and mechanical properties of calf lumbosacral trabecular bone.

The physical and mechanical properties of calf lumbar and sacral trabecular bone were determined and compared with those of human trabecular bone. The mean tissue density (1.66 +/- 0.12 g cm-3), equivalent mineral density (169 +/- 36 mg cm-3), apparent density (453 +/- 89 mg cm-3), ash density (194 +/- 59 mg cm-3), ash content (0.6 +/- 0.05%), compressive strength (7.1 +/- 3.0 MPa) and compressive modulus (173 +/- 97 MPa) of calf trabecular bone are similar to those of young human. There were moderate, positive linear correlations between apparent density and equivalent mineral density, ash density, and compressive strength; and between compressive strength and equivalent mineral density (R2 ranging from 0.35 to 0.48, p less than 0.001). Apparent density, ash density, and equivalent mineral density did not differ significantly in different regions. In contrast to humans, the compressive strength increased from posterior, near the facet, to the anterior vertebral body. These comparisons of physical and mechanical properties, as well as anatomical comparisons by others, indicate that the calf spine is a good model of the young non-osteoporotic human spine and thus useful for the testing of spinal instrumentation.