An Experimentally Validated Mathematical Model of Axial Spinal Compression to Visualize Vertebral Compression Fracture

Summary

Here, we provide a predictive model of VCFs to support surgical intervention. Biomechanical fracture patterns of human and porcine cadaveric vertebrae under compression loading were used to verify an FEA model, providing a resource for better visualizing vertebral fracture and supporting using porcine samples in spine research.

Abstract

The finite element analysis (FEA) model established in this study predicts the mechanical behavior of a vertebral body under pure compression loading. Four human and four porcine cadaveric spines were used in the region from T9-T12 (human) and T12-T14 (porcine) to derive biomechanical failure data under pure axial compression. By implementing the data from these axial crush experiments and combining them with computed tomography (CT)-derived three-dimensional (3D) reconstructions of vertebrae, this new model mathematically predicts the behavior of the spine in vertebral compression fractures (VCFs). The development of an accurate mathematical model has the potential to aid surgical intervention of VCFs during vertebroplasty, kyphoplasty, and potentially additional techniques by accurately representing biomechanical behavior. It can be adapted for osteoporosis, fusion, and implant biomechanics cases to improve surgical accuracy. Understanding the vertebral fracture pattern is essential in surgical pre-planning and understanding prior and future risks. The presented method may serve as an additional resource for studying and treating VCF and further supports the use of porcine specimens in spine research.

Introduction

Vertebral Compression Fractures (VCFs) are biomechanical failures of the anterior vertebral body in response to axial compressive load^1,2. There are 1-1.5 million patients experiencing VCFs in the US each year, with notable risk factors including osteoporosis, advanced age, and female sex^3,4,5. Patients with VCFs can experience pain, disability, altered pulmonary or respiratory function, secondary vertebral fracture, and increased mortality risk^6,7. Preferred clinical management includes physical therapy, rehabilitation, and pain management¹. Surgical intervention for VCF treatment includes vertebroplasty and kyphoplasty, the Osseo-Fix Spinal Fracture Reduction System, internal bracing, and anterior and posterior decompression and stabilization^2,8,9. Clinical diagnosis of VCF may involve magnetic resonance imaging (MRI), CT, positron emission tomography (PET), and single-photon emission computed tomography (SPECT)¹⁰-however, additional visualization and simulation of vertebral fracture may circumvent limitations of these imaging modalities. This paper aims to outline a finite element method of VCF, validated by physical compression experiments, that allows for accurate modeling and visualization of fracture biomechanics.

Finite element analysis (FEA) is a widely used engineering method to simulate and mathematically predict an object's response to physical conditions¹¹. While numerous studies of VCF utilize FEA^12,13,14, many of these studies include CT-derived modeling from living patients and would benefit from a side-by-side validation of the vertebra's response in actual physical compression fracture. This study outlines not only the FEA process but also the protocol for the physical simulation of axial compression fracture.

FEA has been used in surgical pre-planning in a variety of clinical settings, including colorectal repair, oral and maxillofacial procedures, and orthopedic reconstruction^15,16,17. FEA provides a virtual 3D recreation of a site or organ, which may facilitate anatomic understanding of a unique patient's surgical needs. A finite element model can recreate the size, shape, orientation, and behavior of a physical object in response to loads or external pressures, which is useful in optimizing surgical techniques.

This study aims to describe this additional model to help optimize the visualization of VCF, which may augment treatment by vertebroplasty and balloon kyphoplasty. The method described may be beneficial in standardizing the research performed in biomechanical fracture experiments and offers advantages over traditional protocols related to cost, time, and sample selection. This method also provides support for previously constructed mathematical models of compression fractures that utilized medical imaging and finite element analysis^12,13,14,18. Supplemental visualization of the VCF morphology can provide a tool to optimize treatment. This study proposes a mathematical model that predicts VCF under axial compression loading, supported by physical experimental testing, in human and porcine specimens.

Protocol

All experiments were performed in accordance with relevant human research ethics and animal care guidelines at the University of Illinois College of Medicine.

1. Sample preparation

NOTE: VCFs are extensively described for the thoracolumbar region, as most wedge compression fractures occur in the mid-thoracic area¹⁹. For this reason, thoracic vertebrae T9-T12 from humans and T12-14 from porcine were used for these experiments (Table 1).

1. Obtain four cadaveric human spines.
2. Obtain four commercially available cadaveric porcine spines.
3. Identify vertebrae T9-12 and T12-14 for the human and porcine spines, respectively. Ensure there are a total of sixteen human vertebrae and twelve porcine vertebrae.
4. Using a round-tip bone saw and dissection scalpel, dissect the identified vertebrae and remove soft tissue, muscle ligaments, and intervertebral discs.
5. Perform CT scans for each spinal vertebra with the specifications listed in Table 2.
6. Using dissection tools, remove posterior elements of the vertebrae (spinous process, transverse process, facet joints, lamina, and pedicles), following the curvature between the pedicle and vertebral body, such that only the body remains (Supplementary Figure 1).
7. Polish the superior and inferior surfaces of each vertebral body to ensure a planar surface for compression. Remove soft tissue debris and remaining tissue on the vertebral superior and inferior surfaces with a standard scalpel and forceps.
8. Obtain 15 and 12 cortical cores from the upper and lower facets of the vertebrae for human and porcine specimens, respectively. Obtain cortical cores using an oscillating bone saw to remove a 1 cm x 1 cm sample of cortical bone and use a standard scalpel to remove the remaining cancellous bone.
9. Perform density test on samples by weighing each cortical core within a volume-measured pipe to determine scaling (Supplementary Figure 2).
10. In preparation for compression experiments, use the CT images to create a 3D-printed plastic polymer guide of the vertebral body lower profile (Supplementary Figure 3).
11. Using a laser cutter machine, create four holes to define sagittal and coronal planes through the center of mass.

2. Creating a 3D model mesh from radiographic imaging (Supplementary Figure 4)

1. Open the MIMICS (image processing software) software.
2. Import the CT images previously obtained in step 1.5. Click File > New Project Wizard > Import DICOM File.
3. Create a new Threshold by selecting New under the Masks tab and apply the default settings selected for Bone (CT).
4. Rename the new mask appropriately (e.g., Human Spine 1, T9).
5. Click Control + Select the new mask, select Calculate 3D > Optimal Quality > Calculate. The 3D model will appear in the lower right quadrant.
6. Select File > Export > 3-matic > Select 3D Object, which contains the named file.
7. Select Fix > Smooth > Select 3D object > Apply at Smooth Factor 0.5.
8. Select Fix > Fix Wizard > Follow Advice. Continue to click Follow Advice until the # detected prompt appears green. This step optimizes edges, shells, and overlapping triangles.
9. Select Design > Create Analytical Primitive > Create Datum Plane.
10. Select points and Apply for Points 1-3 of the Datum Plane. The average cranial and caudal surfaces defined the transverse plane parallel with the superior and inferior endplates. The sagittal plane is defined as perpendicular to the transverse plane, passing through the center of mass from the anterior to posterior direction of the vertebrae following the spinous process.
11. In the lefthand toolbar, change the surface mesh from Smooth Shaded to Filled with Triangle Edges.
12. Select Remesh > Uniform Remesh > Set Triangle Edge Length to 1.0 mm > Apply.
13. Select Remesh > Create Volume Mesh > Apply.
14. Save *.INP file.

3. Assigning material properties to the volume mesh (Supplementary Figure 5)

1. Export the file back into the image processing software.
2. Convert CT grayscale values to real density values using mineral calibration as previously outlined, using density values obtained in step 1.9^20,21.
   NOTE: The resulting values for the Young modulus (E), the yield strain (εy), and the Poisson Coefficient (ν) are shown below. The Young modulus is calculated as a function of the apparent density and assumed ratio ρ_app/ρ_ash equal to 0.6.
   
3. Under FEA, select Material Assignment.
4. Assign values for Young's modulus, yield strain, and Poisson Coefficient as determined above. The minimum grayscale value limits the density to 0.01 g/cm³ to avoid unobtainable negative density values.
5. Click Export > Abaqus > Select File> Add > Check boxes for Single Output File and Create Assembly > Select OK.
6. Open Abaqus CAE > Right click > Properties > Start folder.
7. Right click > New > Rich Text Format > Rename and convert from .txt to .m
8. Open the new file in MATLAB > in Editor, assign post-yield behavior as perfectly plastic, as described by the following equation, with constraint (σ):
   
9. Click Run to perform the function.

4. Finite element analysis

1. Select Module > Step > Create > Dynamic, Explicit > Continue > Ok.
2. Select Module > Load > Boundary Condition Manager > Step: Initial > Displacement/Rotation > Continue.
3. Select the inferior boundary of the mesh and select Done.
4. Select Module > Mesh > Select Part > Assign Element Type > Done > 3D Stress > Select Yes for Element deletion.
5. Select Module > Load > Boundary Condition Manager > Create > Step-1 > ensure category is Mechanical > Continue.
6. Select the superior boundary of the mesh and select Done.
7. Select Module > Interaction > Reference Point > Assign to Mesh.
8. Select Constraint Manager > Create > Rigid Body > Tie and select superior boundary of mesh > Assign Reference Point > Done. Find the controlled point location using the follower load technique, where the follower load is tangent to the curve of the spine, ensuring that the controlled point is located at 10% of the width of the vertebral body along the sagittal plane from the center of mass projection from the upper plate (Supplementary Figure 6)²².
9. Select Module > Load > Boundary Condition Manager > Create > assign load at the reference point.
10. Within Edit Boundary Condition, select Create Amplitude > Continue > assign displacement rate of 3 mm/min.
11. Select Module > Property > Material Manager > Create > Mechanical > Elasticity > Elastic > assign input data (Table 3).
12. Select Mechanical > Plasticity > Plastic.
13. Select Module > Step > Field Output Requests Manager > Created > Failure/Fracture > select Compressive Damage and State/Field/User/Time > STATUS.
14. Select Module > Job > Job Manager > Results > Visualization > DAMAGE > Frame Selector > increase load using Step Slider.
15. Document the point of failure previously defined.

5. Experimental testing

1. Configure the upper loading plate to the MTS connector, allowing free rotation of up to 5°.
2. Place the vertebral body on the lower compression plate.
3. Trace the silhouette of the vertebral body to ensure that the center of loading is aligned with 10% of the width of the vertebral body from the center of mass in the sagittal direction.
4. Place the vertebral body lower profile onto the outline, oriented by the 3D-printed polymer piece described in steps 1.10 and 1.11.
5. Orient data tracking equipment to capture motion changes and fix the digital marker on the loading plate.
6. Obtain pre-compression photos of the vertebral bodies in all views. Orient the video capture device.
7. Using the materials test systems (MTS) machine, apply an axial load of a quasistatic displacement rate of 3 mm/min, where failure is set as ⅓ of the vertebra height. The MTS machine automatically outputs the load (N) for each experiment.
8. Use the coordinates of three digitized features on the scale to calculate the displacement from the center marker.
9. Use the coordinates of four digitized points of the sagittal and coronal planes to calculate the upper surface (Supplementary Figure 7).
10. Obtain post-compression photos of the vertebral bodies in all views.

6. Data analysis

1. The MTS collects the load and extension values to compute the load-displacement curve. From both FEA and experimental compression, utilize stiffness and strength values to perform statistical analysis.
   NOTE: Stiffness is the slope in its linear trajectory, and strength is the highest point of elastic response. Finally, the failure pattern is defined by identifying any fracture along the compression load from finite elements with a nonzero plastic strain.
2. Perform all statistical analysis using appropriate data analysis software.

Results

From the 12 porcine vertebrae, the load-displacement curves obtained for all specimens are depicted in Figure 1, where all experimental data curves showed similar patterns. Results show an average vertebral stiffness and strength of 9.54 ±1.1 kN/mm (range 6.73-13.63 kN/mm) and 10.2 ± 0.86 kN (range 8.1-13 kN). Video analysis of the experimental compression tests demonstrated a common failure pattern across specimens. The failure pattern consisted of three fracture lines. The first two fracture lines emerged in the posterolateral surface of the body, where the failure propagated vertically from the top to the bottom end plate. The third fracture line consisted of a transverse midline split, generally occurring in the superior part of the body. As a result, there was peeling on the anterior surface. The fracture propagation in oblique directions formed triangular lines in the anterior wall, producing the desired anterior wedge fractures. The fracture separated the anterior cortical shell from the top and the bottom surface. A demonstration of this fracture pattern is shown in Supplementary Figure 8.

From the 16 human vertebrae, compression yielded load-displacement curves presented in Figure 2, where most vertebrae demonstrated similar patterns. The outlier, spine #3, appeared to be more osteoporotic, fragile, and flat, with an average of 79.6% and 58.4% of error on the stiffness and strength value. Excluding spine #3, the average stiffness obtained for the human vertebrae is 5.83 ± 1.2 kN/mm (range 3.6-9.5 kN/mm). The peak load varied between 2.53 kN and 6.23 kN (average 3.54 ± 0.6 kN). The stiffness and peak load values depended on the vertebra level (from T9 to T12). Unlike the porcine specimens, the human vertebrae mostly demonstrated a fracture line in the anterior wall. The failure line was distributed laterally and resulted in a separation of the cortical anterior shell from the top and/or bottom surface. A representative depiction of human vertebrae following axial compression is shown in Supplementary Figure 9.

A comparison of porcine and human stiffness and peak values is shown in Figure 3. The concordance of experimental results was marginally lower for the human vertebrae. The average error on the stiffness and strength value were 34% and 23% for human specimens but 24% and 17% for porcine specimens. One potential source of variation is the age of the sample, as the human samples were between 61-93 years old, while all porcine specimens were between 1-2 years old. Given the age discrepancies, the integrity of the human vertebrae may be subject to influences of calcification or osteoporosis. Regarding the failure patterns, both specimens displayed the transverse fracture line in the anterior wall, causing peeling of the top and/or bottom anterior cortical shell. However, porcine specimens demonstrated additional fracture lines on the lateral sides. For both groups, the resulting tilt during the compression was not significant: in the sagittal plane, there was a maximal tilt of 1.25° and 1.73° for the porcine and human vertebral bodies, respectively.

FE modeling
The FEA prediction of the porcine body stiffness was accurate, showing an average error of 9.9% (range 1.3-18.4%). However, the recovered strength was low compared to values found from experimental testing (average of 67% of error). For the human cadaveric specimens that showed a stiffer and stronger mechanical characteristic than the others in experimental compression, the two corresponding FE models acted analogously. Errors of 3.5% and 10.6% on the stiffness and 0.3% and 18.3% on the strength values were calculated. For the rest of the human models, the resulting yield strain was consistent with the experimental one, but the stiffness was significantly higher than the actual cadavers, leading to excessive peak load values.

To optimize the results, a scaling factor was imposed on the yield strain calculation equation since the errors on the peak load for porcine bodies were similar for each vertebral level. The new value was equal to 3.1. With the same reasoning for the cadaver specimens, the Young modulus calculation was scaled by 1.85.²¹. Comparisons of the experimental versus scaled predicted displacement curves are shown in Figure 4.

The resulting stiffness and strength from numerical analyses for the porcine vertebrae were 9.6 ± 0.9 kN/mm (range 8.4-10.5 kN/mm) and 9.9 ± 0.5 kN (range 9.6-10.7 kN), respectively. This scaling provoked an increase of the stiffness average error to 28% (range 17%-42%) but a significant improvement in the peak load prediction with a final average error of 2.8%. For the human model, the final stiffness and peak load were 5.9 ± 0.6 kN/mm (range 4.6-7.2 kN/mm) and 3.2 ± 0.4 kN (range 2.5-4.1 kN), respectively. The predicted average error changed from 83.3% to 19.6% (range 7.9%-32.7%) for the stiffness and down to 5% (range 1.6%-14.5%) for the peak load. The correlation between numerical and experimental data for all these specimens is shown in Figure 5. The data shows a high coefficient of determination of 0.71, p < 0.01, and 0.88, p < 0.01 for the stiffness and the strength, which indicates a significant correlation between the modeling and the experimental data.

A qualitative comparison of the pictures from the experiments with the nonzero equivalent plastic strain location from the FEA demonstrates an analogous pattern (Figure 6). The failure pattern predicted by finite elements was comparable to the actual vertebral patterns, yielding a midline fracture, with its distribution in the anterior wall and a resulting damage location at the top anterior cortical shell.

Figure 1: Load-displacement characteristics of experimental thoracic porcine vertebrae under pure axial compression. Please click here to view a larger version of this figure.

Figure 2: Load-displacement patterns from experimental human bodies compression, excluding outlier #3, which was significantly osteoporotic. This figure has been adapted with permission from Guitteny et al.²³. Please click here to view a larger version of this figure.

Figure 3: Experimental values of porcine and human by vertebral level. (A) Stiffness. (B) Peak load. This figure has been adapted with permission from Guitteny et al.²³. Please click here to view a larger version of this figure.

Figure 4: Comparison between the experimental and predicted load-displacement curves for a vertebra after equation adjustment with scaling coefficient. (A) Porcine vertebra. (B) Human vertebra. This figure has been adapted with permission from Guitteny et al.²³. Please click here to view a larger version of this figure.

Figure 5: Predictions with FE model. (A) Stiffness and (B) strength predictions. The dashed line represents the quadrant bisector. Please click here to view a larger version of this figure.

Figure 6: Qualitative comparison between the experimental damage after 4.5 mm or final compression for a human T10 cadaver. (A, B) After 4.5 mm. (C-F) Final compression for a human T10 cadaver. Please click here to view a larger version of this figure.

	Dataset	Age	Sex	Vertebrae level
Human	Spine 1	93	F	T9 to T12
	Spine 2	67	M	T9 to T12
	Spine 3	61	F	T9 to T12
	Spine 4	73	F	T9 to T12
Porcine	Spine 1	About 1-2 year	-	T12 to T14
	Spine 2	About 1-2 year	-	T12 to T14
	Spine 3	About 1-2 year	-	T12 to T14
	Spine 4	About 1-2 year	-	T12 to T14

Table 1: Information about the subjects from which were extracted the vertebrae used for the compression tests. Four human cadaveric spines and four adolescent porcine spines were obtained to isolate experimental vertebrae.

X-ray Tube Current	200 mA
KVP	120 kV
Slice Thickness	max = 0.5 mm
Pixel Slice	max = 0.27 mm
Slice Width	min = 512 px
Slice Height	min = 512 px

Table 2: Specifications for the CT imaging scans, outlining values for current, KVP, thickness, pixel slice, width, and height. This table has been adapted with permission from Guitteny et al.²³.

	a	b	Number FE
Porcine	0.48	0.00046	162,799-200,758
Human	0.32	0.0003	161,213-336,620

Table 3: Constant calculated to assign the material to porcine and human cadaver models and range of FE amount of the models.

Supplementary Figure 1: Porcine specimen preparation: (A) Separation of each vertebra from the whole cadaveric spine. (B) Removal of posterior spinal elements. (C) Polishing of vertebral body to ensure planar surface. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 2: Density test including weight and volume scaling of a vertebral cortical core. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 3: Positioning of vertebral specimens within the MTS machine. (A) the laser-cut plastic polymer resting on the tracing of the vertebral body with relation to the compression plate and (B) a sheet of paper cut along the vertebral profile aligned with the setup reference points of the lower end plate and used to position the specimen. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 4: Representative definitions of spatial planes for each vertebra from 3-MATIC and MIMICS. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 5: Representative reconstruction of a vertebral body FE model. with its refined mesh and material assignment. (A) Refined mesh and (B) Material assignment. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 6: Schematic of the mechanical test performed on cadaveric vertebrae, describing actual loading to achieve a pure axial compression test. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 7: Compression testing setup. (A) OPTOTRAK camera in relation to the MTS machine and (B) three digitized point coordinates to determine axial displacement. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 8: The intact and fractured T14 vertebral body of porcine #4 in the anterior and lateral views. (A) Intact anterior view. (B) Intact lateral view. (C) Fractured anterior view. (F) Fractured lateral view. (E) Explicative scheme of fracture patterns. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Supplementary Figure 9: T10 vertebral body of the spine #4, where the anterior wall of the body demonstrates upper peeling of the cortical shell after compression. (A) Intact and (B) fractured human T10 vertebral body in the anterior view and (C) explicative scheme. This figure has been adapted with permission from Guitteny et al.²³. Please click here to download this File.

Discussion

While CT-derived FEA is a well-established tool for modeling biomechanical behavior, few studies apply mathematical modeling in conjunction with physical validation in the context of VCFs. This study demonstrates an accurate predictive mathematical model of thoracolumbar VCF, supported by experimental compression of porcine and human cadaveric spines. The model incorporates strength, stiffness, fracture pattern, load mechanics, and material properties to mathematically predict vertebra response to axial load. The morphological similarities between the porcine and the human spine are well-established and motivate the use of porcine specimens as a comparative model^24,25,26,27. Using the porcine spine provides data to support the FEA model and future comparative studies between the two models. The porcine spinal model has previously been characterized with similarities to the human in vertebral height, pedicle, spinal canal, and transverse process dimensions²⁴. However, skepticism of its analogy remains due to the nature of porcine weight-bearing, quadrupedal status, and differences in anatomy^25,26. The Yucatan minipig has been established as an appropriate model for spine facet research, but several studies note nuance in the general applicability of porcine spines due to greater analogy in the upper-middle thoracic region, but less resemblance in the lower thoracic vertebrae especially when posterior elements are removed^28,29. However, the data presented here supports the use of lower thoracic porcine samples in this particular case. The motivation for investigating this preclinical model for spine research is to support a more financially and logistically accessible resource for preclinical experiments compared to human cadaver models. A porcine cadaver can cost around $180, while a human cadaver will range from $5,000-$10,000²⁶. Overall, our data supports the growing use of porcine spines as a representative model in preclinical biomechanical evaluation, whether for surgical technique or pedicle screw evaluation^30,31.

The data presented in this study add to existing FEA data on VCF. A notable strength of this study is the use of four human spines, whereas similar studies in this realm typically evaluate a single human spine or sample^32,33,34. The motivation for the use of four porcine and four human samples was to evaluate the impact of anatomic variance in the compression mechanics while sustaining statistical significance in analysis. The findings of anterior vertebral collapse, stress distribution, and fracture pattern were consistent with findings in previous FEA and physical compression studies. A notable difference from previous work showed that 2 mm elements demonstrate a stronger linear correlation (r = 0.978, p < 0.0001) as compared to 3 mm elements (r = 0.866, p < 0.0001)³⁵. However, a distinguishing factor of the presented study is the use of thoracic vertebrae under pure axial compression, which is not heavily documented in the literature. Existing studies evaluate flexion and extension, fixation devices, and lumbar FEA^14,34, whereas this study is a pure axial compression experiment with a comparison to the porcine model. Additionally, existing studies utilize FEA for the evaluation of vertebroplasty and kyphoplasty mechanics^33,36. However, understanding the biomechanics of an initial fracture initiation or failure of the vertebral body may benefit not only therapeutic intervention but may eventually inform preventative and prophylactic treatment of VCFs. Though the use of pure axial compression and removal of posterior elements and soft tissue limits this study's direct clinical applicability, this method serves as a proof-of-concept tool for building a better preclinical understanding of vertebral biomechanics.

There were several procedural limitations and challenges in conducting this protocol. First, density was calculated as mass per volume, but we would potentially benefit from a more accurate DEXA scan since density values drive the foundation of material behavior. Similarly, the basis of FEA modeling would be improved with the use of micro-CT scans that would give a more accurate representation of the vertebral body. Within the software modeling itself, there are many subjective specifications that lead to material property assignment, which can be improved or more accurately modeled. The mechanical experiments also follow a simple, loose-plate attachment. The incorporation of a ball joint would allow for the rotation of the loading plate. In relation to the vertebral samples, further investigation should be performed on lumbar specimens to fully understand the thoracolumbar region. Though thoracic vertebrae were used throughout this study, understanding the mechanics of lumbar vertebrae, at least L1-L3 should be performed as well. Furthermore, the varying degrees of osteoporosis between samples impact the failure load, and further study should distinguish the nuance between bone mineral density at various locations within the cortical and trabecular regions, as the porosity is known to impact biomechanics^37,38. Finally, though the CT-derived FE models were able to recreate the same failure pattern seen in the compression experiments, they required a scaling factor of Young's modulus and yield strain equations to reduce the error found in the initial comparison. Overall, the data outlined here supports previous studies investigating the role of FEA in human VCFs^35,39,20 but additionally provides a concurrent physical validation, as well as an animal model comparison through the use of porcine cadaveric spines.

This model may serve as a foundation for mathematically derived morphological resources to aid in the surgical intervention of VCF. Furthermore, it can also be adapted for future studies examining differences in material properties, sex differences, age differences, and cases of osteoporosis. However, since samples were prepared and isolated to evaluate individual vertebral response to load, future FEA and compression studies would benefit from evaluating fracture in the context of the entire spine.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
3-MATIC	Materialise	v15.0
Abaqus/CAE	Simulia	n/a
Analytical Balance	Sigma Aldrich	OH30122634
Cadaveric porcine spines			Local butcher shop, Chicago, IL
CT machine	Siemens	SOMATOM Definition AS
Epredia Shandon Round Tip Bone Saw, Blade: 8 in. x 2.5 in. (20.3 in. 6.4 cm), standard, 11.5 in. (29.2 cm)	Fischer Scientific	40018
Fisherbrand Fine Precision Medium Tipped Tweezers/Forceps	Fischer Scientific	12-000-157
Integra Miltex Sterile Standard Scalpels	Fischer Scientific	12-460-451
Laser cutter machine/3D printer	Fusion3	F400HFR
Mimics Software	Materialise	v2.0
NDI Optotrak Certus	NextGen Ergonomics	Certus Products
Orthopedic Bone Saw	OrthopedicDrills	OTS-1
SPSS Statistics	IBM	v27
Absorbent Underpads with Waterproof Moisture Barrier, 58.4 x 61 cm, 410 mL, Blue, 200/cs	VWR INTERNATIONAL INC	56616-032