Noninvasive prediction of vertebral body compressive strength using nonlinear finite element method and an image based technique

Applying a homogeneous pressure distribution to the upper vertebral endplate: Validation of a new loading system, pilot application to human vertebral bodies, and finite element predictions of DIC measured displacements and strains

Image-based personalized Finite Element Models (pFEM) could detect alterations in physiological deformation of human vertebral bodies, but their accuracy has been seldom reported. Meaningful validation experiments should allow vertebral endplate deformability and ensure well-controlled boundary conditions. This study aimed to (i) validate a new loading system to apply a homogeneous pressure on the vertebral endplate during vertebral body compression regardless of endplate deformation; (ii) perform a pilot study on human vertebral bodies measuring surface displacements and strains with Digital Image Correlation (DIC); (iii) determine the accuracy of pFEM of the vertebral bodies. Homogeneous pressure application was achieved by pressurizing a fluid silicone encased in a rubber silicone film acting on the cranial endplate. The loading system was validated by comparing DIC-measured longitudinal strains and lower-end contact pressures, measured on three homogeneous pseudovertebrae of constant transversal section at 2.0 kN, against theoretically calculated values. Longitudinal strains and contact pressures were rather homogeneous, and their mean values close to theoretical calculations (5% underestimation). DIC measurements of surface longitudinal and circumferential displacements and strains were obtained on three human vertebral bodies at 2.0 kN. Complete displacement and strain maps were achieved for anterolateral aspects with random errors ≤0.2 μm and ≤30 μstrain, respectively. Venous plexus and double curvatures limited the completeness and accuracy of DIC data in posterior aspects. pFEM of vertebral bodies, including cortical bone mapping, were built from computed tomography images. In anterolateral aspects, pFEM accuracy of the three vertebrae was: (i) comparable to literature in terms of longitudinal displacements (R2>0.8); (ii) extended to circumferential displacements (pooled data: R2>0.9) and longitudinal strains (zero median error, 95% error: <27%). Circumferential strains were overestimated (median error: 39%). The new methods presented may permit to study how physiological and pathologic conditions influence the ability of vertebral endplates/bodies to sustain loads.

Biomechanical CT-computed bone strength predicts the risk of subsequent vertebral fracture

Following primary fractures and percutaneous kyphoplasty (PKP), patients have a high risk of incurring a subsequent vertebral fracture (SVF). Given that SVF is a consequence of mechanical deterioration of the vertebra, we sought to examine whether vertebral strength derived from QCT-based finite element analysis (i.e., BCT) can predict the risk of SVF. Sixty-six patients who underwent PKP were categorized into two groups: control or non-SVF group (age: 70 ± 7 years; n = 40) and SVF group (age: 69 ± 8 years; n = 26). BCT was performed on L4 or L3 vertebrae to noninvasively measure vertebral strength. Vertebral strength was also estimated based upon the geometry and material properties of the vertebra. Additionally, trabecular volumetric bone mineral density (vBMD) and L1 Hounsfield unit (HU) were measured. t-Test, χ² test or Mann Whitney U test were used to compare differences in these parameters between the two groups. The predictive abilities of BCT strength and other measured parameters were evaluated using the receiver operating characteristic (ROC) analysis. Results showed no significant difference in either vBMD or L1 HU between the control and SVF groups (p > 0.05), whereas BCT-computed and estimated vertebral strength values were significantly reduced by 33 % and 24 % for the SVF group relative to the non-SVF group, respectively. ROC curve indicated that BCT strength had the largest area under the curve, compared to other parameters. These results suggest that BCT-computed vertebral strength may serve as a surrogate for assessing risk of SVF.

Biomechanical analysis of vertebral wedge deformity in elderly women with quantitative CT-based finite element analysis

BACKGROUND

To explore the vertebral deformity angle (VD angle) of 1^st lumbar vertebral body (L1) in elderly women, investigate the influence of VD on vertebral stiffness (VS) by biomechanical analysis using quantitative computed tomography-based finite element analysis (QCT-FEA).

METHODS

Two hundred seventy eight participants were recruited, and underwent QCT scan. Measured VD angles of L1, and constructed QCT-FEA models of L1 with the minimum (0.59°), median (5.79°) and maximum (11.15°) VD angles, respectively. Loads in two directions were applied on the upper edge of L1 with a force of 700 N, and vertebral stiffness (VS) was defined as the ratio of 700 N and displacement at the superior reference point: (1) perpendicular to the upper edge of L1 (defined as VS-U); (2) perpendicular to the lower edge of L1(defined as VS-L).

RESULTS

Age was very weak positively correlated with VD angle, moderate negatively correlated with vBMD, and moderate negatively correlated with VS (P < 0.05). VS-U was significantly different among three VD angles, so was VS-L (P < 0.001). VS-U was higher than VS-L in 5.79° and 11.15° VD angles (P < 0.05), however no difference in 0.59° VD angles (P > 0.10).

CONCLUSIONS

VD angle of L1 was slightly increased with age and not correlated with vBMD, and VS was moderate negatively correlated with age, showing that the vertebral body was more likely to fracture with aging. VS-U and VS-L were gradually decreased with the increase of VD angle, and VS-L was lower than VS-U with the increase of VD angle, which showed that vertebral body was more prone to fracture when the load was perpendicular to the lower edge of the vertebral body as the VD angle increasing.

Single-level subject-specific finite element model can predict fracture outcomes in three-level spine segments under different loading rates

Osteoporosis-related vertebral compression fracture can occur under normal physiological activities. Bone metastasis is another source of vertebral fracture. Different loading rates, either high-energy traumas such as falls or low-energy traumas under normal physiological activities, can result in different fracture outcomes. The aim of the current study was to develop a quantitative computed tomography-based finite element analysis (QCT/FEA) technique for single vertebral bodies to predict fracture strength of three-level spine segments. Developed QCT/FEA technique was also used to characterize vertebral elastic moduli at two loading rates of 5 mm/min, representing a physiologic loading condition, and 12000 mm/min, representing a high-energy trauma. To this end, a cohort of human spine segments divided into three groups of intact, defect, and augmented were mechanically tested to fracture; then, experimental stiffness and fracture strength values were measured. Outcomes of this study showed no significant difference between the elastic modulus equations at the two testing speeds. Areal bone mineral density measured by dual x-ray absorptiometry (DXA/BMD) explained only 53% variability (R² = 0.53) in fracture strength outcomes. However, QCT/FEA could explain 70% of the variability (R² = 0.70) in experimentally measured fracture strength values. Adding disk degeneration grading, testing speed, and sex to QCT/FEA-estimated fracture strength values further increased the performance of our statistical model by 14% (adjusted R² of 0.84 between the prediction and experimental fracture forces). In summary, our results indicated that a single-vertebra model, which is computationally less expensive and more time efficient, is capable of estimating fracture outcomes with acceptable performance (range: 70-84%).

Experimental testing and biomechanical CT analysis of Chinese cadaveric vertebrae with different modeling approaches

Osteoporosis is characterized by reduced bone strength predisposing to an increased risk of fracture. Biomechanical computed tomography (BCT), predicting bone strength via CT-based finite element analysis (FEA), is now clinically available in the USA for diagnosing osteoporosis or assessing fracture risk. However, it has not been previously validated using a cohort of only Chinese subjects. Additionally, the effect of various modeling approaches on BCT outcomes remains elusive. To address these issues, we performed DXA and QCT scanning, compression testing, and BCT analyses on thirteen vertebrae derived from Chinese donors. Three BCT models were created (voxBCT and tetBCT: voxel-based and tetrahedral element-based FE models generated by a commercial software; matBCT: tetrahedral element-based FE model generated by a custom MATLAB program). BCT-computed outcomes were compared with experimental measures or between different BCT models. Results showed that, DXA-measured areal bone mineral density (aBMD) showed weak correlations with experimentally-measured vertebral stiffness (R² = 0.28) and strength (R² = 0.34). Compared to DXA-aBMD, BCT-computed stiffness provided improved correlations with experimentally-measured stiffness (voxBCT: R² = 0.82; tetBCT: R² = 0.77; matBCT: R² = 0.76) and strength (voxBCT: R² = 0.55; tetBCT: R² = 0.57; matBCT: R² = 0.53); BCT-computed mechanical parameters (stiffness, stress and strain) of the three different models were highly correlated with each other, with coefficient of determination (R²) values of 0.89-0.98. These results, based on a cohort of Chinese vertebral cadavers, suggest that BCT is superior over aBMD to consistently predict vertebral mechanical characteristics, regardless of the modeling approaches of choice.

Material property calibration is more important than element size and number of different materials on the finite element modelling of vertebral bodies: A Taguchi study

Finite element (FE) modelling of a vertebral body (VB) is considered challenging due to the many parameters involved such as element size and type, and material properties. Previous studies have reported how these parameters affect the mechanical behaviour of a VB model; however, most studies just compared results without any specific statistical tool to quantify their influence. The Taguchi Method (TM) has been successfully used in manufacturing and biomechanics to evaluate process parameters and to determine optimum set-up conditions. This study aimed to evaluate the influence of the main finite element modelling parameters on the mechanical behaviour of a VB model using the Taguchi Method. A FE model was developed based on a C2 juvenile porcine vertebral body and three of the most commonly used modelling parameters were evaluated using TM in terms of the change in the predicted stiffness in comparison to experimental values: element size, number of different material properties for VB (based on grey-scale bins) and calibration factor for grey-scale to density to Young's Modulus equation. The influence of the combined factors was also assessed. The Taguchi analysis showed that the three factors are independent. The calibration factor is the main contributor, accounting for 97% of the predicted stiffness, with the value of 0.03 most closely aligning the numerical and experimental results. Element size accounted for 2% of the predicted stiffness, with 0.75 mm being the optimal, while the number of grey-scale bins influenced the results by less than 1%. Our findings indicate that the calibration factor is the main modelling parameter, with the element size and number of bins accounting for less than 3% of the predicted stiffness. Therefore, calibration of material properties should be done based on a large number of samples to ensure reliable results.

A Novel Modelling Methodology Which Predicts the Structural Behaviour of Vertebral Bodies under Axial Impact Loading: A Finite Element and DIC Study

Cervical spine injuries (CSIs) arising from collisions are uncommon in contact sports, such as rugby union, but their consequences can be devastating. Several FE modelling approaches are available in the literature, but a fully calibrated and validated FE modelling framework for cervical spines under compressive dynamic-impact loading is still lacking and material properties are not adequately calibrated for such events. This study aimed to develop and validate a methodology for specimen-specific FE modelling of vertebral bodies under impact loading. Thirty-five (n = 35) individual vertebral bodies (VBs) were dissected from porcine spine segments, potted in bone cement and μCT scanned. A speckle pattern was applied to the anterior faces of the bones to allow digital image correlation (DIC), which monitored the surface displacements. Twenty-seven (n = 27) VBs were quasi-statically compressively tested to a load up to 10 kN from the cranial side. Specimen-specific FE models were developed for fourteen (n = 14) of the samples in this group. The material properties were optimised based on the experimental load-displacement data using a specimen-specific factor (kGSstatic) to calibrate a density to Young’s modulus relationship. The average calibration factor arising from this group was calculated (K¯GSstatic) and applied to a control group of thirteen (n = 13) samples. The resulting VB stiffnesses was compared to experimental findings. The final eight (n = 8) VBs were subjected to an impact load applied via a falling mass of 7.4kg at a velocity of 3.1ms⁻¹. Surface displacements and strains were acquired from the anterior VB surface via DIC, and the impact load was monitored with two load cells. Specimen-specific FE models were created for this dynamic group and material properties were assigned again based on the density–Young’s modulus relationship previously validated for static experiments, supplemented with an additional factor (KGSdynamic). The optimised conversion factor for quasi-static loading, K¯GSstatic, had an average of 0.033. Using this factor, the validation models presented an average numerical stiffness value 3.72% greater than the experimental one. From the dynamic loading experiments, the value for KGSdynamic was found to be 0.14, 4.2 times greater than K¯GSstatic. The average numerical stiffness was 2.3% greater than in the experiments. Almost all models presented similar stiffness variations and regions of maximum displacement to those observed via DIC. The developed FE modelling methodology allowed the creation of models which predicted both static and dynamic behaviour of VBs. Deformation patterns on the VB surfaces were acquired from the FE models and compared to DIC data, achieving high agreement. This methodology is now validated to be fully applied to create whole cervical spine models to simulate axial impact scenarios replicating rugby collision events.

Effect of the intervertebral disc on vertebral bone strength prediction: a finite-element study

BACKGROUND CONTEXT

Osteoporotic vertebral fractures (OVFs) are a prevalent skeletal condition in the elderly but the mechanism behind these fractures remain unclear due to the complex biomechanical interplay between spinal segments such as the vertebra and intervertebral discs (IVDs).

PURPOSE

To investigate the biomechanical influence of IVDs by (1) comparing finite element (FE)-predicted failure load with experimentally measured failure load of functional spinal units (FSUs) and (2) comparing this correlation with those of FE-predicted failure load and bone mineral density (BMD) of the single central vertebra with experimentally measured failure load.

STUDY DESIGN

A computational biomechanical analysis.

PATIENT SAMPLE

Ten thoracic FSUs consisting of a central vertebra, the adjacent IVDs, and the upper and lower halves of the adjacent vertebrae were harvested from formalin-fixed human donors (4 males, 6 females; mean age of 82±9 years).

OUTCOME MEASURES

The outcome measures included the prediction of vertebral strength and determination of BMD in FSUs and the single central vertebra and the correlation of both measures with experimentally measured vertebral strength of the FSUs.

METHODS

The FSUs underwent clinical multidetector computed tomography (MDCT) (spatial resolution: 250×250×600 μm³). BMD was determined for the FSUs from the MDCT images of the central vertebrae. FE-predicted failure load was calculated in the single central vertebra of the FSUs alone and the entire FSUs. Experimentally measured failure load of the FSUs was determined in a uniaxial biomechanical test.

RESULTS

BMD of the central vertebrae correlated significantly with experimentally measured failure load (R²=0.66, p<.02), whereas FE-predicted failure load of the central vertebra showed no significant correlation with experimentally measured failure load (p=.07). However, FE-predicted failure load of FSUs best predicted experimentally measured failure load of FSUs (R²=0.93, p<.0001).

CONCLUSIONS

This study demonstrated that routine clinical MDCT images can be an accurate and feasible tool for prediction of OVFs using patient-specific FE analysis of FSU models.

CLINICAL SIGNIFICANCE

Improved management of OVFs is essential amidst current clinical challenges. Implementation of a vertebral strength assessment tool could result in more accurate prediction of osteoporotic fracture risk and aid clinicians with better targeted early treatment strategies.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

Mechanical testing setups affect spine segment fracture outcomes

The purpose of the work presented here was to establish an experimental testing configuration that would generate a bending compression fracture in a laboratory setting. To this end, we designed and fabricated a fixture to accommodate a three level spine segment and to be able to perform mechanical testing by applying an off-centric compressive loading to create a flexion-type motion. Forces and moments occurring during testing were measured with a six-channel load cell. The initial testing configuration (Fixture A) included plates connected to the superior potted vertebral body and to the ball-socket joint of the testing system ram. Surprisingly, while all cadaveric specimens underwent a similar off-centric compressive loading, most of the specimens showed extension outcomes as opposed to the intended pure-flexion motion. The extension was due to fixture size and weight; by applying an off-centric load directly on the top plate, unintended large shear forces were generated. To resolve the issue, several modifications were made to the original fixture configuration. These modifications included the removal of the superior plates and the implementation of wedges at the superior surface of the fixture (Fixture B). A synthetic sample was used during this modification phase to minimize the number of cadaveric specimens while optimizing the process. The best outcomes were consistently observed when a 15°-wedge was used to provide flexion-type loading. Cadaveric specimens were then experimentally tested to fracture using the modified testing configuration (Fixture B). A comparison between both fixtures, A and B, revealed that almost all biomechanical parameters, including force, moment, and displacement data, were affected by the testing setup. These results suggest that fixture design and implementation for testing is of extreme importance, and can influence the fracture properties and affect the intended motion.

A novel technique with reduced computed tomography exposure to predict vertebral compression fracture: a finite element study based on rat vertebrae

Vertebral compression fractures are a significant clinical issue with an annual incidence of approximately 750,000 cases in the USA alone. Mechanical properties of vertebrae are successfully evaluated through finite element (FE) models based on vertebrae CT. However, clinical drawbacks associated to radiation transmission encouraged to explore the possibility to use selected or reduced portions of the vertebra. The objective of our study was to develop a new procedure to predict vertebral compression fracture from sub-volumes. We reconstructed rat vertebras from micro-CT of thoracic and lumbar groups. Each vertebra was partitioned into three sub-volumes of different axial thickness. FE simulating compression tests were performed on each model to evaluate their failure load and stiffness. Using a power function, a high correlation was found for stiffness and strength. The sub-volume with three fifths thickness had a failure load of 180.7 ± 19.2 N for thoracic and of 209.5 ± 27.4 N for the lumbar vertebra. These values were not significantly different from the values found for the entire vertebra (p > 0.05). Based on our findings, failure loads and stiffnesses obtained with reduced CT scans can be successfully used to predict full vertebral failure. This sub-region analysis and power relationship suggests that one can limit radiation exposure to patients when bone characterization is needed. Graphical abstract Estimated mechanical properties in relation to the extent of the computed tomography reconstruction.

Effects of Scan Resolutions and Element Sizes on Bovine Vertebral Mechanical Parameters from Quantitative Computed Tomography-Based Finite Element Analysis

Quantitative computed tomography-based finite element analysis (QCT/FEA) has been developed to predict vertebral strength. However, QCT/FEA models may be different with scan resolutions and element sizes. The aim of this study was to explore the effects of scan resolutions and element sizes on QCT/FEA outcomes. Nine bovine vertebral bodies were scanned using the clinical CT scanner and reconstructed from datasets with the two-slice thickness, that is, 0.6 mm (PA resolution) and 1 mm (PB resolution). There were significantly linear correlations between the predicted and measured principal strains (R² > 0.7, P < 0.0001), and the predicted vertebral strength and stiffness were modestly correlated with the experimental values (R² > 0.6, P < 0.05). Two different resolutions and six different element sizes were combined in pairs, and finite element (FE) models of bovine vertebral cancellous bones in the 12 cases were obtained. It showed that the mechanical parameters of FE models with the PB resolution were similar to those with the PA resolution. The computational accuracy of FE models with the element sizes of 0.41 × 0.41 × 0.6 mm³ and 0.41 × 0.41 × 1 mm³ was higher by comparing the apparent elastic modulus and yield strength. Therefore, scan resolution and element size should be chosen optimally to improve the accuracy of QCT/FEA.

Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

BACKGROUND

Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

RESULTS

Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K2HPO4) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

CONCLUSIONS

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.

A simulation study on marrow fat effect on biomechanics of vertebra bone

Trabecular bone and bone marrow are main components of cancellous bone. Most mechanical studies for bone mainly focus on hard tissues, while if bone marrow contributes to bone biomechanics is not clear yet. This study was proposed to investigate marrow fat effect on trabecular bone biomechanics by simulation. Finite element (FE) bone models were established based on quantitative CT images at L3 lumbar spine, from which trabecular structures with and without marrow fat were investigated respectively. Auni-static compressive test was applied on the proposed models until to the appearance of fracture. Simulation results showed that trabecular models filled with marrow fat had about 3%-9% less maximum stress in volume than models with only trabeculae. However, its average stress in volume was about 9%-56% larger than those with only trabeculae. The strain energy density of the bone model with marrow fat showed a more uniformed distribution. As a conclusion, marrow fat has contributions to the bone mechanics. It can balance the stress distribution of the bone tissue, which may reduce bone deformation under a compressive loading. The mixture of trabecular structure and marrow fat would be against higher compress load before the failure point.

Specimen-specific nonlinear finite element modeling to predict vertebrae fracture loads after vertebroplasty

STUDY DESIGN

Vertebral fracture load and stiffness from a metastatic vertebral defect model were predicted using nonlinear finite element models (FEM) and validated experimentally.

OBJECTIVE

The study objective was to develop and validate an FEM-based tool for predicting polymer-augmented lytic vertebral fracture load and stiffness and the influence of metastatic filling materials.

SUMMARY OF BACKGROUND DATA

Percutaneous vertebroplasty has the potential to reduce vertebral fracture risk affected with lytic metastases by providing mechanical stabilization. However, it has been shown that the mismatch in mechanical properties between poly(methyl-methacrylate) (PMMA) and bone induces secondary fractures and intervertebral disc degeneration. A biodegradable copolymer, poly(propylene fumarate-co-caprolactone) (P(PF-co-CL)), has been shown to possess the appropriate mechanical properties for bone defect repair.

METHODS

Simulated metastatic lytic defects were created in 40 cadaveric vertebral bodies, which were randomized into 4 groups: intact vertebral body (intact), simulated defect without treatment (negative), defect treated with P(PF-co-CL) (copolymer), and defect treated with PMMA (PMMA). Spines were imaged with quantitative computed tomography (QCT), and QCT/FEM-subject-specific, nonlinear models were created. Predicted fracture loads and stiffness were identified and compared with experimentally measured values using Pearson correlation analysis and paired t test.

RESULTS

There was no significant difference between the measured and predicted fracture loads and stiffness for each group. Predicted fracture loads were larger for PMMA augmentation (3960 N [1371 N]) than that for the copolymer, negative and intact groups (3484 N [1497 N], 3237 N [1744 N], and 1747 N [702 N]). A similar trend was observed in the predicted stiffness. Moreover, predicted and experimental fracture loads were strongly correlated (R=0.78), whereas stiffness showed moderate correlation (R=0.39).

CONCLUSION

QCT/FEM was successful for predicting fracture loads of metastatic, polymer-augmented vertebral bodies. Overall, we have demonstrated that QCT/FEM may be a useful tool for predicting in situ vertebral fracture load resulting from vertebroplasty.

LEVEL OF EVIDENCE

N/A.

Effect of specimen-specific anisotropic material properties in quantitative computed tomography-based finite element analysis of the vertebra

Intra- and inter-specimen variations in trabecular anisotropy are often ignored in quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra. The material properties are typically estimated solely from local variations in bone mineral density (BMD), and a fixed representation of elastic anisotropy ("generic anisotropy") is assumed. This study evaluated the effect of incorporating specimen-specific, trabecular anisotropy on QCT-based FE predictions of vertebral stiffness and deformation patterns. Orthotropic material properties estimated from microcomputed tomography data ("specimen-specific anisotropy"), were assigned to a large, columnar region of the L1 centrum (n = 12), and generic-anisotropic material properties were assigned to the remainder of the vertebral body. Results were compared to FE analyses in which generic-anisotropic properties were used throughout. FE analyses were also performed on only the columnar regions. For the columnar regions, the axial stiffnesses obtained from the two categories of material properties were uncorrelated with each other (p = 0.604), and the distributions of minimum principal strain were distinctly different (p ≤ 0.022). In contrast, for the whole vertebral bodies in both axial and flexural loading, the stiffnesses obtained using the two categories of material properties were highly correlated (R2 > 0.82, p < 0.001) with, and were no different (p > 0.359) from, each other. Only moderate variations in strain distributions were observed between the two categories of material properties. The contrasting results for the columns versus vertebrae indicate a large contribution of the peripheral regions of the vertebral body to the mechanical behavior of this bone. In companion analyses on the effect of the degree of anisotropy (DA), the axial stiffnesses of the trabecular column (p < 0.001) and vertebra (p = 0.007) increased with increasing DA. These findings demonstrate the need for accurate modeling of the peripheral regions of the vertebral body in analyses of the mechanical behavior of the vertebra.

QCT-based finite element models predict human vertebral strength in vitro significantly better than simulated DEXA

SUMMARY

While dual energy X-ray absorptiometry (DXA) is considered the gold standard to evaluate fracture risk in vivo, in the present study, the quantitative computed tomography (QCT)-based finite element modeling has been found to provide a quantitative and significantly improved prediction of vertebral strength in vitro. This technique might be used in vivo considering however the much larger doses of radiation needed for QCT.

INTRODUCTION

Vertebral fracture is a common medical problem in osteoporotic individuals. Bone mineral density (BMD) is the gold standard measure to evaluate fracture risk in vivo. QCT-based finite element (FE) modeling is an engineering method to predict vertebral strength. The aim of this study was to compare the ability of FE and clinical diagnostic tools to predict vertebral strength in vitro using an improved testing protocol.

METHODS

Thirty-seven vertebral sections were scanned with QCT and high resolution peripheral QCT (HR-pQCT). Bone mineral content (BMC), total BMD (tBMD), areal BMD from lateral (aBMD-lat), and anterior-posterior (aBMD-ap) projections were evaluated for both resolutions. Wedge-shaped fractures were then induced in each specimen with a novel testing setup. Nonlinear homogenized FE models (hFE) and linear micro-FE (μFE) were generated from QCT and HR-pQCT images, respectively. For experiments and models, both structural properties (stiffness, ultimate load) and material properties (apparent modulus and strength) were computed and compared.

RESULTS

Both hFE and μFE models predicted material properties better than structural ones and predicted strength significantly better than aBMD computed from QCT and HR-pQCT (hFE: R² = 0.79, μFE: R² = 0.88, aBMD-ap: R² = 0.48-0.47, aBMD-lat: R² = 0.41-0.43). Moreover, the hFE provided reasonable quantitative estimations of the experimental mechanical properties without fitting the model parameters.

CONCLUSIONS

The QCT-based hFE method provides a quantitative and significantly improved prediction of vertebral strength in vitro when compared to simulated DXA. This superior predictive power needs to be verified for loading conditions that simulate even more the in vivo case for human vertebrae.

A new material mapping procedure for quantitative computed tomography-based, continuum finite element analyses of the vertebra

Inaccuracies in the estimation of material properties and errors in the assignment of these properties into finite element models limit the reliability, accuracy, and precision of quantitative computed tomography (QCT)-based finite element analyses of the vertebra. In this work, a new mesh-independent, material mapping procedure was developed to improve the quality of predictions of vertebral mechanical behavior from QCT-based finite element models. In this procedure, an intermediate step, called the material block model, was introduced to determine the distribution of material properties based on bone mineral density, and these properties were then mapped onto the finite element mesh. A sensitivity study was first conducted on a calibration phantom to understand the influence of the size of the material blocks on the computed bone mineral density. It was observed that varying the material block size produced only marginal changes in the predictions of mineral density. Finite element (FE) analyses were then conducted on a square column-shaped region of the vertebra and also on the entire vertebra in order to study the effect of material block size on the FE-derived outcomes. The predicted values of stiffness for the column and the vertebra decreased with decreasing block size. When these results were compared to those of a mesh convergence analysis, it was found that the influence of element size on vertebral stiffness was less than that of the material block size. This mapping procedure allows the material properties in a finite element study to be determined based on the block size required for an accurate representation of the material field, while the size of the finite elements can be selected independently and based on the required numerical accuracy of the finite element solution. The mesh-independent, material mapping procedure developed in this study could be particularly helpful in improving the accuracy of finite element analyses of vertebroplasty and spine metastases, as these analyses typically require mesh refinement at the interfaces between distinct materials. Moreover, the mapping procedure is not specific to the vertebra and could thus be applied to many other anatomic sites.

Biomechanics of vertebral fractures and the vertebral fracture cascade

Vertebral fractures (VFxs) are the most common osteoporotic fracture, and are a strong risk factor for future fracture. The presence of a VFx greatly increases the risk of sustaining subsequent VFxs-a phenomenon often referred to as the "vertebral fracture cascade." VFxs do not occur uniformly along the spine, but occur more often at the mid-thoracic and thoracolumbar regions than elsewhere. It is likely that both the vertebral fracture cascade and the bimodal distribution of VFx along the spine are attributable to biomechanical factors. VFxs occur when the forces applied to the vertebral body exceed its strength. Loading on the spine is primarily determined by a person's height, weight, muscle forces, and the task or movement performed, but can also be affected by other factors, such as spinal curvature and invertebral disk deterioration. Vertebral strength is determined mainly by bone size, shape, and bone mineral density, and secondarily by bone microarchitecture, collagen characteristics, and microdamage. Better understanding of VFx etiology is hampered by the fact that most VFxs do not come to clinical attention; therefore, the factors and activities that cause VFxs remain ill defined, including possible differences in the etiology of acute fractures versus those of slow onset. Additional research is needed to elucidate the precise mechanical, morphologic, and biological mechanisms that underlie VFx to improve strategies for assessing VFx risk and preventing the vertebral fracture cascade.