Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Geometric determinants of the mechanical behavior of image-based finite element models of the intervertebral disc

The intervertebral disc is an important structure for load transfer through the spine. Its injury and degeneration have been linked to pain and spinal fractures. Disc injury and spine fractures are associated with high stresses; however, these stresses cannot be measured, necessitating the use of finite element (FE) models. These models should include the disc's complex structure, as changes in disc geometry have been linked to altered mechanical behavior. However, image-based models using disc-specific structures have yet to be established. This study describes a multiphasic FE modeling approach for noninvasive estimates of subject-specific intervertebral disc mechanical behavior based on medical imaging. The models (n = 22) were used to study the influence of disc geometry on the predicted global mechanical response (moments and forces), internal local disc stresses, and tractions at the interface between the disc and the bone. Disc geometry was found to have a strong influence on the predicted moments and forces on the disc (R2 = 0.69-0.93), while assumptions regarding the side curvature (bulge) of the disc had only a minor effect. Strong variability in the predicted internal disc stresses and tractions was observed between the models (mean absolute differences of 5.1%-27.7%). Disc height had a systematic influence on the internal disc stresses and tractions at the disc-to-bone interface. The influence of disc geometry on mechanics highlights the importance of disc-specific modeling to estimate disc injury risk, loading on the adjacent vertebral bodies, and the mechanical environment present in disc tissues.

A biomechanical investigation of lumbar interbody fusion techniques

The anterior, posterior, transforaminal, and circumferential lumbar interbody fusions (ALIF, PLIF, TLIF, CLIF/360) are used to treat spondylolisthesis, trauma, and degenerative pathologies. This study aims to investigate the biomechanical effects of the lumbar interbody fusion techniques on the spine. A validated T12-sacrum lumbar spine finite-element model was used to simulate surgical fusion of L4-L5 segment using ALIF, PLIF with one and two cages, TLIF with unilateral and bilateral fixation, and CLIF/360. The models were simulated under pure-moment and combined (moment and compression) loadings to investigate the effect of different lumbar interbody fusion techniques on range of motion, forces transferred through the vertebral bodies, disc pressures, and endplate stresses. The range of motion of the lumbar spine was decreased the most for fusions with bilateral posterior instrumentations (TLIF, PLIF, and CLIF/360). The increase in forces transmitted through the vertebrae and increase in disc pressures were directly proportional to the range of motion. The discs superior to fusion were under higher pressure, which was attributed to adjacent segment degeneration in the superior discs. The increase in endplate stresses was directly proportional to the cross-sectional area and was greater in caudal endplates at the fusion level, which was attributed to cage subsidence. The response of the models was in line with overall clinical observations from the patients and can be further used for future studies, which aim to investigate the effect of geometrical and material variations in the spine. The model results will assist surgeons in making informed decisions when selecting fusion procedures based on biomechanical effects.

Conventional finite element models estimate the strength of metastatic human vertebrae despite alterations of the bone's tissue and structure

INTRODUCTION

Pathologic vertebral fractures are a major clinical concern in the management of cancer patients with metastatic spine disease. These fractures are a direct consequence of the effect of bone metastases on the anatomy and structure of the vertebral bone. The goals of this study were twofold. First, we evaluated the effect of lytic, blastic and mixed (both lytic and blastic) metastases on the bone structure, on its material properties, and on the overall vertebral strength. Second, we tested the ability of bone mineral content (BMC) measurements and standard FE methodologies to predict the strength of real metastatic vertebral bodies.

METHODS

Fifty-seven vertebral bodies from eleven cadaver spines containing lytic, blastic, and mixed metastatic lesions from donors with breast, esophageal, kidney, lung, or prostate cancer were scanned using micro-computed tomography (μCT). Based on radiographic review, twelve vertebrae were selected for nanoindentation testing, while the remaining forty-five vertebrae were used for assessing their compressive strength. The μCT reconstruction was exploited to measure the vertebral BMC and to establish two finite element models. 1) a micro finite element (μFE) model derived at an image resolution of 24.5 μm and 2) homogenized FE (hFE) model derived at a resolution of 0.98 mm. Statistical analyses were conducted to measure the effect of the bone metastases on BV/TV, indentation modulus (E_it), ratio of plastic/total work (W_Pl/W_tot), and in vitro vertebral strength (F_exp). The predictive value of BMC, μFE stiffness, and hFE strength were evaluated against the in vitro measurements.

RESULTS

Blastic vertebral bodies exhibit significantly higher BV/TV compared to the mixed (p = 0.0205) and lytic (p = 0.0216) vertebral bodies. No significant differences were found between lytic and mixed vertebrae (p = 0.7584). Blastic bone tissue exhibited a 5.8% lower median E_it (p< 0.001) and a 3.3% lower median W_pl/W_tot (p<0.001) compared to non-involved bone tissue. No significant differences were measured between lytic and non-involved bone tissues. F_exp ranged from 1.9 to 13.8 kN, was strongly associated with hFE strength (R²=0.78, p< 0.001) and moderately associated with BMC (R²=0.66, p< 0.001) and μFE stiffness (R²=0.66, p< 0.001), independently of the lesion type.

DISCUSSION

Our findings show that tumour-induced osteoblastic metastases lead to slightly, but significantly lower bone tissue properties compared to controls, while osteolytic lesions appear to have a negligible impact. These effects may be attributed to the lower mineralization and woven nature of bone forming in blastic lesions whilst the material properties of bone in osteolytic vertebrae appeared little changed. The moderate association between BMC- and FE-based predictions to fracture strength suggest that vertebral strength is affected by the changes of bone mass induced by the metastatic lesions, rather than altered tissue properties. In a broader context, standard hFE approaches generated from CTs at clinical resolution are robust to the lesion type when predicting vertebral strength. These findings open the door for the development of FE-based prediction tools that overcomes the limitations of BMC in accounting for shape and size of the metastatic lesions. Such tools may help clinicians to decide whether a patient needs the prophylactic fixation of an impending fracture.

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.

Isotropic Failure Criteria Are Not Appropriate for Anisotropic Fibrous Biological Tissues

The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.

Case-specific non-linear finite element models to predict failure behavior in two functional spinal units

Current finite element (FE) models predicting failure behavior comprise single vertebrae, thereby neglecting the role of the posterior elements and intervertebral discs. Therefore, this study aimed to develop a more clinically relevant, case-specific non-linear FE model of two functional spinal units able to predict failure behavior in terms of (i) the vertebra predicted to fail; (ii) deformation of the specimens; (iii) stiffness; and (iv) load to failure. For this purpose, we also studied the effect of different bone density-mechanical properties relationships (material models) on the prediction of failure behavior. Twelve two functional spinal units (T6-T8, T9-T11, T12-L2, and L3-L5) with and without artificial metastases were destructively tested in axial compression. These experiments were simulated using CT-based case-specific non-linear FE models. Bone mechanical properties were assigned using four commonly used material models. In 10 of the 11 specimens our FE model was able to correctly indicate which vertebrae failed during the experiments. However, predictions of the three-dimensional deformations of the specimens were less promising. Whereas stiffness of the whole construct could be strongly predicted (R²  = 0.637-0.688, p < 0.01), we obtained weak correlations between FE predicted and experimentally determined load to failure, as defined by the total reaction force exhibiting a drop in force (R²  = 0.219-0.247, p > 0.05). Additionally, we found that the correlation between predicted and experimental fracture loads did not strongly depend on the material model implemented, but the stiffness predictions did. In conclusion, this work showed that, in its current state, our FE models may be used to identify the weakest vertebra, but that substantial improvements are required in order to quantify in vivo failure loads. © 2018 The Authors. Journal of Orthopaedic Research® Published by Wiley Periodical, Inc. on behalf of Orthopaedic Research Society. J Orthop Res 36:3208-3218, 2018.

Development and initial validation of a novel smoothed-particle hydrodynamics-based simulation model of trabecular bone penetration by metallic implants

A novel computational model of implant migration in trabecular bone was developed using smoothed-particle hydrodynamics (SPH), and an initial validation was performed via correlation with experimental data. Six fresh-frozen human cadaveric specimens measuring 10 × 10 × 20 mm were extracted from the proximal femurs of female donors (mean age of 82 years, range 75-90, BV/TV ratios between 17.88% and 30.49%). These specimens were then penetrated under axial loading to a depth of 10 mm with 5 mm diameter cylindrical indenters bearing either flat or sharp/conical tip designs similar to blunt and self-tapping cancellous screws, assigned in a random manner. SPH models were constructed based on microCT scans (17.33 µm) of the cadaveric specimens. Two initial specimens were used for calibration of material model parameters. The remaining four specimens were then simulated in silico using identical material model parameters. Peak forces varied between 92.0 and 365.0 N in the experiments, and 115.5-352.2 N in the SPH simulations. The concordance correlation coefficient between experimental and simulated pairs was 0.888, with a 95%CI of 0.8832-0.8926, a Pearson ρ (precision) value of 0.9396, and a bias correction factor Cb (accuracy) value of 0.945. Patterns of bone compaction were qualitatively similar; both experimental and simulated flat-tipped indenters produced dense regions of compacted material adjacent to the advancing face of the indenter, while sharp-tipped indenters deposited compacted material along their peripheries. Simulations based on SPH can produce accurate predictions of trabecular bone penetration that are useful for characterizing implant performance under high-strain loading conditions. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1114-1123, 2018.

Damage Identification on Vertebral Bodies During Compressive Loading Using Digital Image Correlation

MINI: Identifying fracture is important for understanding vertebral mechanics. Isolated cadaveric thoracolumbar vertebrae were compressed, and surface strains were measured using digital image correlation. Fracture locations from video analysis were qualitatively similar to the locations of high compressive strains and local damage occurred before the maximum force was reached.

STUDY DESIGN

Ex vivo compression experiments on isolated cadaveric vertebrae.

OBJECTIVE

To qualitatively compare the fracture locations identified in video analysis with the locations of high compressive strain measured with digital image correlation (DIC) on vertebral bodies and to evaluate the timing of local damage to the cortical shell relative to the global yield force.

SUMMARY OF BACKGROUND DATA

In previous ex vivo experiments, cortical bone fracture has been identified using various methods including acoustic emission sensors, strain gages, video analysis, or force signals. These methods are, however, limited in their ability to detect the location and timing of fracture. We propose use of DIC, a noncontact optical technique that measures surface displacement, to quantify variables related to damage.

METHODS

Isolated thoracolumbar human cadaveric vertebral bodies (n = 6) were tested in compression to failure at a quasi-static rate, and the force applied was measured using a load cell. The surface displacement and strain were measured using DIC. Video analysis was performed to identify fractures.

RESULTS

The location of fractures identified in the video corresponded well with the locations of high compressive strain on the bone. Before reaching the global yield force, more than 10% of the DIC measurements reached a minimum principal strain of 1.0%, a previously reported threshold for cortical bone damage.

CONCLUSION

DIC measurements provide an objective measure that can be used to identify the location and timing of fractures during ex vivo vertebral experiments. This is important for understanding fracture mechanics and for validating vertebral computational models that incorporate failure.

LEVEL OF EVIDENCE

N /A.

Regional analysis of age-related local bone loss in the spine of a healthy population using 3D voxel-based modeling

Local variations in bone loss may be of great importance to individually predict osteoporotic fractures but are neglected by current densitometry techniques. The purpose of this study was to evaluate regional variations of normal bone loss at the spine among different age groups using voxel-based morphometry. Non-contrast MDCT scans of 16 patients under the age of 40 (mean age 26years) without spinal pathology were identified as a reference cohort, where each thoracolumbar vertebra was assessed individually. For comparison, 38 patients >40years were grouped by decades in 4 cohorts of 10 patients each, except the youngest, including 8 patients only. All spines were automatically detected, segmented and non-rigidly registered for spatially normalized vertebral bodies. Afterwards, statistical and T-score mapping was performed to highlight local density differences in comparison to the reference cohort. The calculated statistical maps of significantly affected density regions (ADR) started to highlight small local changes of volumetric bone mineral density (vBMD) distribution within the vertebra of L5 (ADR: 7.9%) in the fifties cohort. Regions near the endplates were most affected. The effect dramatically increased in the sixties cohort, where bone loss was most prominent from T12 to L2. In the seventies cohort, around 50% of voxels in T10 to L5 showed significantly decreased vBMD. In conclusion, ADR and local T-score maps of the spine showed age-related local variations in a healthy population, corresponding to known areas of fracture origination and increased fracture incidence. It thus might provide a powerful tool in diagnosis of osteoporosis.

Is bone density associated with intervertebral disc pressure in healthy and degenerated discs?

The coupling of the intervertebral disc (IVD) and vertebra as a biomechanical unit suggests that changes in the distribution of pressure within the IVD (intradiscal pressure, IDP) as a result of disc degeneration can influence the distribution of bone density within the vertebra, and vice versa. The goal of this study was to assess the correspondence between IDP and bone density in the adjacent vertebrae, with emphasis on how this correspondence differs between healthy and degenerated IVDs. Bone density of the endplates and subchondral bone in regions adjacent to the anterior and posterior annulus fibrosus (aAF and pAF, respectively) and nucleus pulposus (NP) was measured via quantitative computed tomography (QCT) in 61 spine segments (T7-9, T9-11, T10-12; 71±14years). IDP was measured in the aAF, NP, and pAF regions in 26 of the spine segments (68±16years) while they were tested in flexed (5°) or erect postures. Disc degeneration was assessed by multiple grading schemes. No correlation was found between bone density and IDP in either posture (p>0.104). Regional variations in IDP and, to a greater extent bone density, were found to change with advancing degeneration: both IDP (p=0.045) and bone density (p=0.024) decreased in the NP region relative to the aAF region. The finding of only a modest correspondence between degeneration-associated changes in IDP and bone density may arise from complexity in how IDP relates to mechanical force transmission through the endplate and from limitations of the available IVD grading schemes in estimating the mechanical behavior of the IVD.

Residual strains in the intervertebral disc annulus fibrosus suggest complex tissue remodeling in response to in-vivo loading

The annulus fibrosus (AF) of the intervertebral disc (IVD) serves the dual roles of containing hydrostatic pressure from the inner nucleus pulposus (NP) and allowing flexible connection between adjacent vertebral bodies. Previous work has indicated that in the unloaded state, the AF is under a state of residual circumferential strain that, on average, is comparable to that which is believed to reduce peak stresses in other pressure containing organs. The complex in-vivo loading of the IVD, however, led us to hypothesize that variations with anatomical region should also exist. Residual strains were measured by imaging bovine caudal IVDs at both macro and micro scales in both the intact state (under residual strain) and opened into anterior, posterior, and lateral quadrants (residual strains relieved). Calculation of macro scale residual strains using changes in lamellar arc length and thickness confirmed circumferential tension (anterior: 0.63±2.1%, lateral: 8.3±1.5%, posterior: 4.4±2.1%) and radial compression (anterior: 12.4±5.8%, lateral: 11.120±2.8%, posterior: 4.8±4.2%) around the outer zone of the AF. The inner zone, however, had residual circumferential strains ranging from 28.7±3.4% compression in the anterior region to 3.4±3% tension in the posterior region, with radial strains of 9.7±5.5% tension and 0.2±4.4% compression respectively. This pattern of residual circumferential strain was corroborated at the microscale by comparing the crimp period of collagen fiber bundles in the intact and open states. The results of this study point toward a complex pattern of residual strains in the AF, which develop in response to stresses from both NP pressurization and bending movements.

Biomechanical analysis of press-extension technique on degenerative lumbar with disc herniation and staggered facet joint

This study investigates the effect of a new Chinese massage technique named “press-extension” on degenerative lumbar with disc herniation and facet joint dislocation, and provides a biomechanical explanation of this massage technique. Self-developed biomechanical software was used to establish a normal L1–S1 lumbar 3D FE model, which integrated the spine CT and MRI data-based anatomical structure. Then graphic technique is utilized to build a degenerative lumbar FE model with disc herniation and facet joint dislocation. According to the actual press-extension experiments, mechanic parameters are collected to set boundary condition for FE analysis. The result demonstrated that press-extension techniques bring the annuli fibrosi obvious induction effect, making the central nucleus pulposus forward close, increasing the pressure in front part. Study concludes that finite element modelling for lumbar spine is suitable for the analysis of press-extension technique impact on lumbar intervertebral disc biomechanics, to provide the basis for the disease mechanism of intervertebral disc herniation using press-extension technique.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Accuracy of finite element analyses of CT scans in predictions of vertebral failure patterns under axial compression and anterior flexion

Finite element (FE) models built from quantitative computed tomography (QCT) scans can provide patient-specific estimates of bone strength and fracture risk in the spine. While prior studies demonstrate accurate QCT-based FE predictions of vertebral stiffness and strength, the accuracy of the predicted failure patterns, i.e., the locations where failure occurs within the vertebra and the way in which the vertebra deforms as failure progresses, is less clear. This study used digital volume correlation (DVC) analyses of time-lapse micro-computed tomography (μCT) images acquired during mechanical testing (compression and anterior flexion) of thoracic spine segments (T7-T9, n=28) to measure displacements occurring throughout the T8 vertebral body at the ultimate point. These displacements were compared to those simulated by QCT-based FE analyses of T8. We hypothesized that the FE predictions would be more accurate when the boundary conditions are based on measurements of pressure distributions within intervertebral discs of similar level of disc degeneration vs. boundary conditions representing rigid platens. The FE simulations captured some of the general, qualitative features of the failure patterns; however, displacement errors ranged 12-279%. Contrary to our hypothesis, no differences in displacement errors were found when using boundary conditions representing measurements of disc pressure vs. rigid platens. The smallest displacement errors were obtained using boundary conditions that were measured directly by DVC at the T8 endplates. These findings indicate that further work is needed to develop methods of identifying physiological loading conditions for the vertebral body, for the purpose of achieving robust, patient-specific FE analyses of failure mechanisms.