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. Author manuscript; available in PMC: 2022 Oct 1.
Published in final edited form as: Comput Biol Med. 2021 Sep 9;137:104833. doi: 10.1016/j.compbiomed.2021.104833

Single-Level Subject-Specific Finite Element Model Can Predict Fracture Outcomes in Three-Level Spine Segments Under Different Loading Rates

Asghar Rezaei 1,2, Maryam Tilton 1,2, Yong Li 1,2, Michael J Yaszemski 1,2, Lichun Lu 1,2,*
PMCID: PMC8783600  NIHMSID: NIHMS1741179  PMID: 34534795

Abstract

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%).

Keywords: Vertebral fracture, QCT/FEA, material characterization, vertebral augmentation

Introduction

Osteoporosis-related vertebral compression fracture can occur under normal physiological activities [1]. Vertebral compression fracture, due to osteoporosis or metastasis, may lead to significant pain, neurologic deficit, and eventually inability to perform normal daily activities [2, 3]. Areal bone mineral density obtained by dual x-ray absorptiometry (DXA/BMD) is the current clinical standard measure for fracture risk assessments in osteoporotic bones [4]. However, DXA/BMD is a 2D measurement of a 3D structure and, therefore, is only moderately correlated with fracture strength. Vertebral fracture can also result from bone metastasis. Osteolytic metastasis in vertebral bodies change the bony tissue into a soft material, making the structure prone to fracture [5]. Although, DXA/BMD can moderately assess fracture risks in osteoporotic bones, it may not be effective for fracture risk assessments in metastatic bones. This is because DXA/BMD cannot account for osteolytic lesion size, shape, and location.

Vertebral fracture can also occur under different loading rates from high-energy traumas such as falls, to low-energy traumas under normal physiological activities [6]. Changes in loading rates could result in different structural (such as fracture forces) and material properties (such as elastic moduli) [7, 8], making fracture assessments more challenging. Although many studies investigated the material properties of the bone under a constant testing speed [9–12], a limited number of previous studies suggested the rate-dependency of the bone material properties such as elastic modulus [13, 14]. There is still insufficient information on the extent to which loading rate affects material properties of the bone. Also, most previous experimental studies characterized the elastic moduli of the coupon samples from cortical or trabecular bones, not the entire vertebral bodies [10].

Percutaneous vertebroplasty is a technique in which an augmenting material, such as poly (methyl methacrylate) (PMMA) and poly(propylene fumarate) (PPF), is injected percutaneously through a needle into a weakened vertebral body to increase the load bearing capacity of the bone [15, 16]. This procedure can be performed prophylactically for fracture preventions [17].

One of the primary goals of therapy is to identify patients at risk of vertebral fracture. Quantitative computed tomography-based finite element analysis (QCT/FEA) is a promising computational technique for fracture risk assessment for both osteoporotic and metastatic vertebrae [18–21]. The performance of the QCT/FEA technique depends on different factors such as material characteristics [22, 23]. Specifically, elastic modulus of the bone affects predicted fracture outcomes [24]. Elastic modulus of the bone depends on mineral density of the bone [25] which can be formulated as aρb or a + bρ where ρ is bone density, a and b are constant material parameters. Previous studies have proposed a wide range of a and b values for different anatomical sites and locations [26]. Such variation in reported material parameters is partly contributed to the use of different methods for testing and acquiring data. Other contributing factors on the performance of the QCT/FEA technique are boundary conditions and loading scenarios. The spinal load is distributed on the vertebral bodies through intervertebral disks (IVDs). Previous studies have developed single- or multi-vertebral FEA models to predict fracture outcomes [12, 27, 28]. These models have been validated against mechanical testing on the same single- or multiple-level vertebrae. While multi-vertebral FEA models provide more realistic boundary conditions, complexity and computational cost of such models might be barriers for their clinical applications. Therefore, it is of scientific interest to find out how well single-level FEA models can predict experimentally-measured fracture outcomes of multi-level vertebrae that include IVDs.

In the current study, we have developed a QCT/FEA technique to predict fracture strength of intact, defect, and augmented vertebral bodies at two loading rates of 5 mm/min, representing a physiologic loading condition, and 12,000 mm/min, representing a high-energy trauma (Fig. 1a–b). Therefore, the aims of the current study were threefold: (1) characterize elastic modulus of each vertebra in order to assess the effect of loading rate on the elastic modulus using an inverse QCT/FEA (Fig. 1c–d), (2) predict vertebral fracture strength of the specimens tested at different speeds, and (3) assess the efficacy of a single vertebral model to estimate the fracture strength of spine segments that include IVDs. Additionally, sex, age, and quality of IVDs were considered as potential explanatory variables along with QCT/FEA to predict fracture strength.

Fig. 1:

Fig. 1:

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Experimentally validated QCT/FEA study on metastatic spine. (a) cadaveric biomechanical experiments on three-level spinal segments with IVDs; (b) associated QCT images for different study groups including intact, defected, and PPF-augmented; (c) representative load-displacement curve from in-vitro experiments; and (d) representative computational model with voxel-based FE mesh mimicking the middle vertebral body of the associated experimental model.

To create computational models, we employed QCT imaging and experimental data from a cohort of spine segments, including intact, defect, and augmented specimens, fractured at two different loading rates [7] Besides intact, our QCT/FEA models also included defect, and augmented vertebral bodies to assess the prediction performance of our computational models for metastatic and augmented vertebral bodies.

Materials and Methods

In-vitro experiment

Details of the experimental procedure can be found in the previous publication [7]. In summary, total of 28 cadaveric spinal segments were prepared for compression-type biomechanical testing (Fig. 1a). This study used three-level spinal segments which was approved by the Bio-specimens Sub-committee of the Institutional review Board. The middle vertebrae were mainly consisted of T6, T9, T12, or L3 in the spinal segments. Specimens were randomly assigned to the study groups including intact, simulated lesion defect, and augmented by PPF. PPF polymer, which is a biodegradable and injectable biomaterial making it a suitable candidate for bone repair applications, was synthesized in our lab as per previously explained protocols [29] and used for augmentation purposes.

Clinically relevant defects were created in the middle vertebra body of the defect and augmented groups’ specimens by drilling anteriorly using a cylindrical diamond saw. The size of the drill bit was chosen based on both the height and diameter of the middle vertebrae in each specimen such that disruption of the endplates was avoided. The superior and inferior vertebrae were potted into PMMA up-to the IVDs. Prior to the biomechanical experiments, all the specimens were scanned using dual X-ray absorptiometry (DXA) imaging to measure the areal bone mineral densities (DXA/BMD). For the augmented groups, PPF solution was then poured into the simulated defect space. Prior to testing, specimens were stored at −20 °C and thawed at room temperature. Additionally, quantitative computed tomography (QCT) was performed on all the specimens after augmentation and prior to testing using Siemens Somatom Definition Scanner (Siemens Healthcare GmbH, Germany) at 120 kVP and 200 mAs (Fig. 1b). Collected image stacks were used for 3D reconstruction of the biomechanical constructs in Mimics software (Materialise, Ann Arbor, MI).

During the biomechanical experiments, a compression-type loading scenario under two different testing speeds was performed: 0.083 mm/s (5 mm/min) or 200 mm/s (12000 mm/min) to mimic pathologic fractures and traumatic fractures, respectively. Out of 28 samples, 12 specimens were tested under slow-speed testing while the rest of the specimens were allocated to the fast-speed testing group. The mechanical setup included a ball attached to the ram of the machine; and the center of the middle vertebral body was aligned with the axis of the MTS ram by adjusting the movable x-y stage (Fig. 1a). The bottom fixture was equipped with a six-channel load cell (Interface Inc., Scottsdale, AZ). For each trial, recorded data included three forces, three moments, and displacement of the ram; and the primary data, in this study, were the compressive force-displacement curves, which were used to obtain two biomechanical parameters. The first parameter was the stiffness, K, calculated as the slope of the linear region of the force-displacement curve as shown in Fig. 1c, which was later used for elastic modulus characterization in the QCT/FEA model development process (Fig. 1d). The second parameter was the compressive fracture force (i.e., fracture strength), defined as the maximum compressive force followed by a reduction in the force-displacement curve. After mechanical testing, the superior and inferior IVDs were graded for disk degenerations according to the Adams grading system.

Computational Approach

While mechanical testing was performed on three-level spine segments, their QCT/FEA models included only the middle vertebral bodies and potting PMMAs (Fig. 1d) for simplicity and reduction of the computational time and cost. Our QCT/FEA method included reconstructing a 3D geometry from QCT imaging data of spine segments, generating a 3D mesh, and assigning density-dependent material properties using Mimics software Ver. 22.0 (Materialise, Ann Arbor, MI). ICEM CFD 2019 R3 (ANSYS, Canonsburg, PA) was used to assemble parts and convert 8-node to 20-node voxel elements. Ansys APDL 2019 R3 (ANSYS, Canonsburg, PA) was used to apply proper boundary and load conditions, and eventually run the models.

QCT image stacks were imported into Mimics where a manual frame-by-frame segmentation of the FE model components. Therefore, the models included the middle vertebral body as well as the top and bottom PMMAs. Voxel volume or hexahedral meshes with a 1:1 ratio (FE voxel: CT voxel) were used in the models and each voxel was assigned a Hounsfield unit (HU) value calculated from the QCT image voxel. The size of each element was 1.37×1.37×1.2 mm in all the models. During imaging, a QCT calibration phantom comprising of five solid rods from known materials (Mindways Inc., Austin, TX) was placed under each segment to convert HUs to the equivalent K2HPO4 density which was equal to ash density (ρash). This process has been explained in detail in previous works [30]. To assign density and material properties, the range of HU values (from −1024 to 3075) was divided into 309 bins, representing a distribution of grey scale values in each spine segment. Similar loading and boundary conditions as the in-vitro experiment setup were implemented in the FE models. In short, the bottom PMMA was fully constrained in all directions, while the top PMMA was free about the three rotational degrees of freedom and allowed to translate along the z-axis using an MPC boundary condition. In our QCT/FEA modeling, elastic moduli of 2,500 MPa [28] and 2,000 MPa [31] were assigned to PMMA and PPF, respectively. The Poisson’s ratio values were kept constant at 0.3 for the bone and 0.4 for the polymers.

QCT/FEA optimization approach

First, as previously explained in details [30], inverse QCT/FEA approach was used to characterize the elastic properties of the vertebra. In this approach, an arbitrary set of material constants (a and b) was initially chosen as input for the elastic modulus of the vertebra; then the model was run and the QCT/FEA-predicted stiffness was compared with the experimentally-measured value (Fig. 1c). This process was repeated using the Nelder-Mead simplex optimization algorithm [32] in MATLAB (MathWorks, Natick, MA). To this end, an objective function was defined as the difference between experimentally measured and estimated stiffness values in accordance to previous report [30]. The material constants in the models were changed iteratively to minimize the objective function. When the change in the objective function for two consecutive iterations was less than an acceptable tolerance, the optimization process was stopped, and the last set of material coefficients was reported as the optimal coefficients. This led to an optimal match between the QCT/FEA-estimated stiffness values and the experimental values. Next, for fracture strength estimations, subject-specific density-elastic equations (from Table S1) were used to represent the elastic modulus of each model as suggested by a previous study [33]. Bone damage was also assessed for each individual element using a von Mises strain criterion. In other words, at each step, elements with equivalent von Mises strain exceeding the yield stain εy = 0.0081ρ−1.42 were assigned an elastic modulus of 0.01 MPa [34]. Force-displacement data were recorded for each vertebral model and fracture strength was calculated as the maximum force in the force-displacement curve. At the fast speed, two of the models were removed from the study, as they did not reach to maximum force at or under 14 mm which was the maximum displacement assigned for mechanical testing. It was decided to not continue the analysis for these two models to avoid excessive distortion of the elements.

Statistical analysis

In this study, JMP Pro version 14.1.0 (SAS Institute Inc., NC, USA) was used for statistical analyses. The outcomes of the experimental portion of the study were the measured stiffness and fracture strength. Univariate linear regression analysis was performed to evaluate the discrepancy between the QCT/FEA-predicted maximum compressive forces and experimentally measured vertebral strength. Coefficient of determination was also calculated for univariate regression lines. In addition, multivariate linear regression analyses were performed to explain measured fracture strength values using QCT/FEA-estimated fracture forces along with other explanatory variables. In the multivariate analysis, the explanatory variables including QCT/FEA-predicted outcomes, testing speed, sex, group, as well as disk degeneration grading were added simultaneously to predict experimentally measured outcomes. Next, backward elimination was performed by removing one variable at a time from the model (starting from the most insignificant) until all the insignificant variables were removed from the model [34]. For multivariate analyses, adjusted R2 values were calculated and reported. One-way ANOVA was used to compare differences between the study groups (i.e., intact, defect, and augmented) with regards to stiffness and fracture force. Additionally, unpaired T-test was employed to compare differences between the two testing speeds in terms of stiffness and fracture force when the three study groups were combined.

Results

Experimental results

In this study, groups (intact, defect, and augmented) showed similar stiffness which was an indication of insignificant variation between study groups in terms of stiffness (p=0.29). The scatterplot presented in Fig. 2a compares the experimental stiffness between the two testing speeds when the three groups were combined. The average stiffness value at slow speed was 1724.80 N/mm, while the respective value at the fast speed was 2320.04 N/mm (showing a 35% increase). However, the difference between the two average values were statistically insignificant (p=0.19).

Fig. 2:

Fig. 2:

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Experimental outcomes: (a) experimental stiffness for the two testing speeds when study groups were combined, and (b) experimentally measured fracture strength compared between the two testing speeds.

Likewise, ANOVA was performed for the experimentally measured fracture strength as the outcome and group as well as testing speed as explanatory variables. Testing speed became significant (p=0.0408), while the group was found to be insignificant (p=0.68). Fig. 2b shows the scatterplot of the fracture strength at the two testing speeds while the three statistically similar groups were combined. The average strength values at the slow testing speed was 2075.18 N, while its counterpart at the fast testing speed was 3369.38 N (p=0.0247).

Computational results

Elastic modulus characterization

The inverse QCT/FEA process was successfully performed individually for all the specimens at the slow and fast speeds. Figs. 3a–b shows the plots of the elastic modulus verses ρash from the slow (n=12) and fast (n=16) speed testing groups, respectively. Table S1 provides the density-elastic modulus constant parameters a and b for the two groups. The average value for the constants a and b were 8303.21 (±3083.42) and 1.8941 (±0.3998) at the fast speed, and 7597.25 (±3313.10) and 2.0261(±0.5014) at the slow speed, respectively. Statistical analysis showed that a or b values were similar for intact, defect, and augmented specimens. Fig. 3c shows the elastic modulus verses ρash based on the average constant parameters, suggesting almost identical curves. We also compared the elastic moduli of the specimens (as shown in Fig. 3c) at two different densities of 0.5 g/cm3 (in a trabecular region) and 1 g/cm3 (in a cortical region) to investigate whether the differences between the elastic moduli at the two speeds were significant. Unpaired T-test showed the difference in moduli (at each density value) were statistically insignificant (p=0.57).

Fig. 3:

Fig. 3:

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Characterization of the elastic modulus through QCT/FEA approach: (a) elastic modulus vs. ρash from the slow speed testing group (n=12), (b) elastic modulus vs. ρash from the fast speed testing group (n=16), and (c) average constant elastic modulus for each testing speed vs. ρash. The study groups (i.e., intact, defect, and PPF-augmented) are color coded in each graph.

Fracture strength prediction

The study groups (intact, defect, and augmented) and the two loading rates were combined as the DXA/BMD was used to predict the fracture outcomes (Fig. 4a). DXA/BMD was found to be a significant variable (p<0.0001) but explained only 53% variability in experimentally-measured outcomes. Then, DXA/BMD was replaced by QCT/FEA to predict fracture strength in the same cohort. QCT/FEA was able to explain 70% (R2=0.7) of the variability between the experiment and FEA-prediction (p<0.0001) (Fig. 4a). Compared with DXA/BMD, QCT/FEA was able to explain about 17% more variability in the experimental fracture outcomes.

Fig. 4:

Fig. 4:

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Fracture force prediction using subject-specific QCT/FEA method: (a) correlation between the experimental fracture force and the DXA/BMD, (b) regression analysis between the experiment and QCT/FEA-prediction, and (c) multivariant regression analysis between the experimental fracture outcomes and the prediction when explanatory variables including sex, inferior intervertebral disk degeneration grading, and testing speed were added to the QCT/FEA. Note that slow speed (white markers) and fast speed (black markers) were combined in these regression analyses.

Additionally, explanatory variables including sex, age, the superior and inferior intervertebral disk degeneration gradings, group, and testing speed were added to QCT/FEA predictions to explain measured fracture strength as the outcome. Then, using backward elimination, insignificant variables were removed to include only significant explanatory variables. Through this approach, it was found that variables such as age, group (intact, defect, and augmented), and the superior disk grading were insignificant (p≥0.45). However, along with QCT/FEA (p<0.0001), other variables including testing speed (p=0.0006), the inferior disk grading (p=0.0023), and sex (p=0.0264) were found to be significant. Altogether, these significant variables were able to account for 84% of variability in the experimentally measured fracture strength in our predictive model (with the adjusted R2 of 0.84) (Fig. 4b). If divided by intact, defect, and augmented groups in the same statistical model, adjusted R2 values varied from 0.80 to 0.87.

To assess the contribution of each significant variable in our statistical model, the variables were removed one-by-one (from the largest p-value to the smallest) and the adjusted R2 were calculated. Table 1 shows the contribution of these variables in explaining measured fracture strength outcomes. The results showed that QCT/FEA-predicted values explained 70% of the fracture outcomes. Specifically, the testing speed contributed about 6% when added to QCT/FEA and addition of inferior disk grading had 5% contribution (while combined with QCT/FEA and testing speed). Finally, sex improved the R2 value by only about 3% while added to the other significant variables.

Table 1:

Contributions of explanatory variables (represented by R2) in predicting vertebral fracture strength along with their statistical equations.

Explanatory variables R2
QCT/FEA + Testing speed + Inferior disk grade (IDG) + Sex 0.84
1.18(QCT/FEA) + 515.1(Speed)* + 708.8(IDG) + 338.9(Sex)** + 1935.1
QCT/FEA + Testing speed + Inferior disk grade 0.81
1.25(QCT/FEA) + 484.4(Speed)* + 538.8(IDG) −1394.2
QCT/FEA + Testing speed 0.76
1.14(QCT/FEA) + 459.7(Speed)* +731.5
QCT/FEA 0.70
1.21(QCT/FEA)
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*

Speed is 1 for fast speed and 0 for slow speed.

**

Sex is 1 for male and −1 for female

Discussion

In the current study, a QCT/FEA technique was developed to assess vertebral fracture strength at two different loading rates while the specimens were divided into three groups of intact, defect, and PPF-augmented. Using inverse QCT/FEA, the ash density-elastic relation was determined for each individual model (total of 28 subject-specific QCT/FEA models) and optimal material parameters were calculated. While DXA/BMD moderately correlated with measured outcomes, the QCT/FEA accounted for 70% variability between experimentally measured fracture strength and the prediction. Our computational modeling performance in predicting fracture forces was improved by adding speed of testing, sex, and IVDs’ quality to the QCT/FEA, explaining 14% more variability (R2= 0.84) in the fracture outcomes. However, there was no significant difference between the slow and fast groups with regards to the density-elastic modulus equations.

Previous studies validated their single vertebral computational models using data from mechanical testing on single vertebrae. Those studies ignored the effect of IVDs on the fracture outcomes. In this study, biomechanical data were used from a cohort of three-level segments, each of which included superior and inferior IVDs as well as three vertebral bodies. In order to develop less expensive computational models, only the middle vertebrae were included in the modeling. Specifically, one of the main aims of the study was to assess the performance of a single vertebral model to estimate the fracture strength in the presence of IVDs. The single vertebral QCT/FEA models with added factor of testing speed accounted for 76% variability in fracture outcomes. This is an acceptable performance for a single vertebral model, capable of explaining fracture outcomes in three-level spine segments. Additionally, including the disk quality gradings (to QCT/FEA and testing speed) further improved the performance of our statistical model by about 5%, leading to an R2 of 0.81. The results of the current study suggest the application of single vertebral QCT/FEA models for fracture predictions, and that IVDs grading can significantly increase predictive ability of the single vertebral modeling.

Average (or cohort-specific) material constants obtained through inverse QCT/FEA and the described optimization method were similar to previously published reports [23]. However, the range of density-elastic equations obtained from individual models were large at both slow and fast testing speeds, even though all the specimens were mechanically tested and computationally assessed using the same protocols. This suggests involvement of other contributing factors that can affect elastic moduli of the bone such as microstructure.

Loading rate has been previously reported as an important factor affecting the elastic modulus of the bone [13, 14]. However, our study found that the density-elastic modulus of the vertebra at the fast speed was only slightly larger than that of slow speed. For instance, this difference at the density of 1 g/cm3 was about 9%. Our statistical analysis also showed insignificance of the loading rates based on the two implemented testing speeds. One reason for such discrepancy between the present study and previous published reports [13, 14] is that those studies performed the mechanical characterizations on coupon samples dissected from trabecular regions. Moreover, it is still not clear how much increase in the strain rate would lead to significant differences in elastic modulus. As opposed to previous studies, proposed inverse QCT/FEA method was performed on the entire vertebral body and not the trabecular coupons alone. In addition, 35% difference between the measured stiffness values at the two testing speed groups was still insignificant, which might partly explain the insignificance of loading rate in the reported density-elastic moduli of the vertebrae.

The statistical significance observed between the experiment and prediction after integration of sex as an explanatory factor indicates that QCT/FEA was not able to completely account for sex during the modeling. This finding is similar to a previously published study that used rigidity analysis and found the significance after addition of sex to the computationally-predicted vertebral fracture strength [36]. This finding could potentially suggest that there are other contributing factors (such as trabecular bone microstructure and morphology) which cannot be easily detected using QCT imaging which could explain the sex differences in fracture outcomes.

Although many previous studies have employed QCT/FEA to predict vertebral fractures [36, 37], little is known on the predictive ability of this technique under different loading rates, in particular, at high loading speed that the effect of inertia may affect the FEA outcomes. Majority of previous studies have used implicit solvers for fracture analysis as the inertial forces are ignorable [33, 39, 40], with only few studies that have employed explicit solvers [41, 42]. Similarly, in this study, the effect of inertial force was ignored, and an implicit finite element solver was employed to investigate the fracture strength of the spinal segments. Using subject-specific density-elastic modulus equations, the implicit solver was able to show an acceptable performance with an R2 of 0.7. Speed also improved the prediction performance of the QCT/FEA by 6%, this suggests the possibility of using an implicit solver for estimating vertebral fracture forces at different loading rates (as high as 12,000 mm/min).

This study was limited by a small cadaveric sample size, which potentially resulted in lower prediction power in term of statistical analysis, especially the multivariate regression analysis. This limitation applies to many cadaveric studies, as performing cadaveric biomechanical studies with large sample size are difficult, time intensive, and costly. The large variation in the experimentally measured outcomes were from a relatively small sample size. When assigning the cadaveric specimens to different groups, we included same range of vertebral bodies in all the study groups, this resulted in having range of vertebrae size as small as T6 to as large as L3. Additionally, each group included specimens from both sexes that partly contributed the large differences in the experimental outcomes. Also, larger sample size might have helped to find a significant difference between the two elastic modulus equations at the two testing speeds. Despite this limitation, we believe the current investigation provides invaluable information on the use of single vertebral-level QCT/FEA to estimate experimentally measured fracture outcomes at different loading rates. Although, in this study, the loading speed of 12000 mm/min considered as a high-energy trauma, it is unclear what traumatic events could generate this loading rate as our understanding on this matter is still limited. In the statistical analysis, only the inferior-IVD grading (along with the QCT/FEA and testing speed) remained a significant explanatory variable. In future studies, a larger cohort should be utilized to assess the effects of inferior-IVD on the biomechanical outcomes. Finally, the current study was limited by using individualized density-elastic modulus relationships, which are not possible to obtain without performing in-vitro experiment.

Conclusion

This study presented a subject-specific QCT/FEA method to predict fracture outcomes in different vertebra cases including intact, simulated metastatic, and PPF-augmented when undergoing either physiologically-relevant loading condition (5 mm/min) or high-energy trauma (12000 mm/min). In summary, our results indicated that single-vertebra model, which is computationally less expensive and more time efficient, is capable of estimating fracture outcomes with acceptable accuracy (range: 70–84%). It was found that addition of variables such as testing speed, sex, and IVDs’ quality to the QCT/FEA (which was based on single-vertebral models) further improves the prediction. Based on the outcomes of the present study, there are other contributing factors, which are not readily captured in the QCT/FEA method, that can affect elastic moduli prediction; trabecular bone microstructure is an example of those factors. Overall, present study provided new knowledge on fracture outcome prediction in metastatic and augmented cases; such a subject-specific QCT/FEA approach could potentially assist with identifying patients at risk of vertebral fracture.

Supplementary Material

1

A single-vertebral model is capable of estimating fracture outcomes in a three-level spine segment

QCT/FEA technique, alone, accounted for 70% variability between experimentally measured fracture strength and the prediction

Adding disk degeneration grading can significantly increase predictive ability of the single vertebral modeling

The loading rates of 5 mm/min and 12000 mm/min did not change the density-elastic modulus equations significantly

Acknowledgement

This work was supported by National Institutes of Health grant (R01AR56212) and the Eagles 5th District Cancer Telethon Funds for Cancer Research. MT was supported by National Institute of Health grant (T32AR56950) for Musculoskeletal Research Training. Biostatistics services were supported by NIH grant TL1-TR000137 from the National Center for Advancing Translational Science (NCATS), NIH, United States.

Footnotes

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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