Finite element analyses of human vertebral bodies embedded in polymethylmethalcrylate or loaded via the hyperelastic intervertebral disc models provide equivalent predictions of experimental strength

Impact of extracellular matrix and collagen network properties on the cervical intervertebral disc response to physiological loads: A parametric study

Current intervertebral disc finite element models are hard to validate since they describe multi-physical phenomena and contain a huge number of material properties. This work aims to simplify numerical validation/identification studies by prioritizing the sensitivity of intervertebral disc behavior to mechanical properties. A 3D fiber-reinforced hyperelastic model of a C6-C7 intervertebral disc is used to carry out the parametric study. 10 parameters describing the extracellular matrix and the collagen network behaviors are included in the parametric study. The influence of varying these parameters on the disc response is estimated during physiological movements of the head, including compression, lateral bending, flexion, and axial rotation. The obtained results highlight the high sensitivity of the disc behavior to the stiffness of the annulus fibrosus extracellular matrix for all the studied loads with a relative increase in the disc apparent stiffness by 67% for compression and by 57% for axial rotation when the annulus stiffness increases from 0.4 to 2 MPa. It is also shown that varying collagen network orientation, stiffness, and stiffening in the studied configuration range have a noticeable effect on rotational motions with a relative apparent stiffness difference reaching 6.8%, 10%, and 22%, respectively, in lateral bending. However, the collagen orientation does not affect disc response to axial load.

Predicting the effective compressive modulus of human cancellous bone using the convolutional neural network method

The efficient prediction of biomechanical properties of bone plays an important role in the assessment of bone quality. However, the present techniques are either of low accuracy or of high complexity for the clinical application. The present study aims to investigate the predictive ability of the evolving convolutional neural network (CNN) technique in predicting the effective compressive modulus of porous bone structures. The T11/T12/L1 segments of thirty-five female cadavers were scanned using the HR-pQCT scanner and the images obtained from it were used to generate 10896 2 D bone samples, in which only the cancellous bony parts were processed and investigated. The corresponding 10896 heterogeneous finite-element (FE) models were generated, and then a CNN model was constructed and trained using the predictions of the FE analysis as the ground truths. Then the remaining 260 bone samples generated from the initial HR-pQCT images were used to test the predictive power of the CNN model. The results show that the coefficient of the determinant (R²) from the linear correlation between the CNN and FE predicted elastic modulus is 0.95, which is much higher than that from the correlation between the BMD and the FE predictions (R² = 0.65). Furthermore, the 95th and 50th percentiles of relative prediction error are below 0.28 and 0.09, respectively. In the conclusion, the CNN model can efficiently predict the effective compressive modulus of human cancellous bone and can be used as a promising and clinically applicable method to evaluate the mechanical quality of porous bone.

The Influence of Axial Compression on the Cellular and Mechanical Function of Spinal Tissues; Emphasis on the Nucleus Pulposus and Annulus Fibrosus: A Review

In light of the correlation between chronic back pain and intervertebral disc (IVD) degeneration, this literature review seeks to illustrate the importance of the hydraulic response across the nucleus pulposus (NP)-annulus fibrosus (AF) interface, by synthesizing current information regarding injurious biomechanics of the spine, stemming from axial compression. Damage to vertebrae, endplates (EPs), the NP, and the AF, can all arise from axial compression, depending on the segment's posture, the manner in which it is loaded, and the physiological state of tissue. Therefore, this movement pattern was selected to illustrate the importance of the bracing effect of a pressurized NP on the AF, and how injuries interrupting support to the AF may contribute to IVD degeneration.

Multiscale Validation of Multiple Human Body Model Functional Spinal Units

A validation comparing five human body model (HBM) lumbar spines is carried out across two load cases, with the objective to use and apply HBMs in high strain rate applications such as car occupant simulation. The first load case consists of an individual intervertebral disc (IVD) loaded in compression at a strain rate of 1/s by a material testing machine. The second load case is a lumbar functional spine unit (FSU) loaded in compression using a drop tower setup, producing strain rates of up to 48/s. The IVD simulations were found to have a better agreement with the experiments than the FSU simulations, and the ranking of which HBMs matched best to the experiment differed by load case. These observations suggest the need for more hierarchical validations of the lumbar spine for increasing the utility of HBMs in high strain rate loading scenarios.

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.

Mechanical testing setups affect spine segment fracture outcomes

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

Bioinspirational understanding of flexural performance in hedgehog spines

In this research, the flexural performance of hedgehog spines is investigated in four ways. First, X-ray micro-computed tomography (μCT) is employed to analyze the complex internal architecture of hedgehog spines. μCT images reveal distinct structural morphology, characterized by longitudinal stringers and transverse central plates, which enhance flexural performance. Second, computer-aided design (CAD) is utilized to create and produce different three-dimensional (3D) computational models that gradually approach resemblance to hedgehog spines. Various levels of models are constructed by including and excluding key internal features of hedgehog spines, resulting in the formation of model levels from the simplest to the most realistic form. Third, finite element analysis (FEA) is exploited to simulate flexural behavior of hedgehog spines undergoing three-point bending. FEA results aim to identify and elucidate how internal structural features affect flexural stiffness and bending stress contours. Fourth, flexural analytical modeling is performed to calculate flexural shear flow and twist angle during transverse loading. The effects of the number of hedgehog outer cells, the spine wall thickness ratio and radius ratio are theoretically investigated to predict the shear stress and twist angle of the hedgehog spine structure. Results demonstrate that longitudinal stringers of the hedgehog spine significantly increase the overall flexural stiffness, while the transverse central plates provide support and rigidity to prevent spines from buckling and collapsing. Interestingly, the 3D model level that most realistically resembles the actual hedgehog spine is evidenced to have the highest specific bending stiffness, demonstrating nature's most efficient design. The findings of this study may be useful for developing hedgehog-inspired lightweight, high-stiffness, impact-tolerant structures. STATEMENT OF SIGNIFICANCE: This research has given much needed insight on the inner morphology of hedgehog spines and the structure-property relationship to the spine's flexural performance. X-ray μCT images reveal inner structural morphology, characterized by longitudinal stringers and transverse plates. Finite element analysis shows that longitudinal stringers significantly increase flexural stiffness, while the transverse plates provide support and rigidity to prevent buckling. The model that resembles the actual hedgehog spine is evidenced to have the highest specific bending stiffness, demonstrating nature's most efficient design. Analytical model studies influence on cell number, spine geometrical ratios, and further confirms nature's perfect design with lowest flexural shear flow and twist angle during transverse loading. This work paths future design for hedgehog-inspired lightweight, high-stiffness, impact-tolerant structures.

A critical review on the three-dimensional finite element modelling of the compression therapy for chronic venous insufficiency

Compression therapy is an adjuvant physical intervention providing the benefits of calibrated compression and controlled stretch and consequently is increasingly applied for the treatment of chronic venous insufficiency. However, the mechanism of the compression therapy for chronic venous insufficiency is still unclear. To elaborate the mechanism of compression therapy, in recent years, the computational modelling technique, especially the finite element modelling method, has been widely used. However, there are still many unclear issues regarding the finite element modelling of compression therapy, for example, the selection of appropriate material models, the validation of the finite element predictions, the post-processing of the results. To shed light on these unclear issues, this study provides a state-of-the-art review on the application of finite element modelling technique in the compression therapy for chronic venous insufficiency. The aims of the present study are as follows: (1) to provide guidance on the application of the finite element technique in healthcare and relevant fields, (2) to enhance the understanding of the mechanism of compression therapy and (3) to foster the collaborations among different disciplines. To achieve these aims, the following parts are reviewed: (1) the background on chronic venous insufficiency and the computational modelling approach, (2) the acquisition of medical images and the procedure for generating the finite element model, (3) the definition of material models in the finite element model, (4) the methods for validating the finite element predictions, (5) the post-processing of the finite element results and (6) future challenges in the finite element modelling of compression therapy.

Effect of parathyroid hormone on the structural, densitometric and failure behaviors of mouse tibia in the spatiotemporal space

Parathyroid hormone (PTH) is an anabolic bone drug approved by the US Food and Drug Administration (FDA) to treat osteoporosis. However, previous studies using cross-sectional designs have reported variable and sometimes contradictory results. The aim of the present study was to quantify the localized effect of PTH on the structural and densitometric behaviors of mouse tibia and their links with the global mechanical behavior of bone using a novel spatiotemporal image analysis approach and a finite element analysis technique. Twelve female C57BL/6J mice were divided into two groups: the control and PTH treated groups. The entire right tibiae were imaged using an in vivo micro-computed tomography (μCT) system eight consecutive times. Next, the in vivo longitudinal tibial μCT images were rigidly registered and divided into 10 compartments across the entire tibial space. The bone volume (BV), bone mineral content (BMC), bone tissue mineral density (TMD), and tibial endosteal and periosteal areas (TEA and TPA) were quantified in each compartment. Additionally, finite element models of all the tibiae were generated to analyze the failure behavior of the tibia. It was found that both the BMC and BV started to increase in the proximal tibial region, and then the increases extended to the entire tibial region after two weeks of treatment (p < 0.05). PTH intervention significantly reduced the TEA in most tibial compartments after two weeks of treatment, and the TPA increased in most tibial regions after four weeks of treatment (p < 0.05). Tibial failure loads significantly increased after three weeks of PTH treatment (p < 0.01). The present study provided the first evidence of the localized effect of PTH on bone structural and densitometric properties, as well as their links with the global mechanical behaviors of bone, which are important pieces of information for unveiling the mechanism of PTH intervention.

Evaluation of the capability of the simulated dual energy X-ray absorptiometry-based two-dimensional finite element models for predicting vertebral failure loads

Prediction of the vertebral failure load is of great importance for the prevention and early treatment of bone fracture. However, an efficient and effective method for accurately predicting the failure load of vertebral bones is still lacking. The aim of the present study was to evaluate the capability of the simulated dual energy X-ray absorptiometry (DXA)-based finite element (FE) model for predicting vertebral failure loads. Thirteen dissected spinal segments (T11/T12/L1) were scanned using a HR-pQCT scanner and then were mechanically tested until failure. The subject-specific three-dimensional (3D) and two-dimensional (2D) FE models of T12 were generated from the HR-pQCT scanner and the simulated DXA images, respectively. Additionally, the areal bone mineral density (aBMD) and areal bone mineral content (aBMC) of T12 were calculated. The failure loads predicted by the simulated DXA-based 2D FE models were more moderately correlated with the experimental failure loads (R² = 0.66) than the aBMC (R² = 0.61) and aBMD (R² = 0.56). The 2D FE models were slightly outperformed by the HR-pQCT-based 3D FE models (R² = 0.71). The present study demonstrated that the simulated DXA-based 2D FE model has better capability for predicting the vertebral failure loads than the densitometric measurements but is outperformed by the 3D FE model. The 2D FE model is more suitable for clinical use due to the low radiation dose and low cost, but it remains to be validated by further in vitro and in vivo studies.

Correlation between vertebral bone microstructure and estimated strength in elderly women: An ex-vivo HR-pQCT study of cadaveric spine

PURPOSE

A vertebral fracture is the most common complication of osteoporosis, and various factors are involved in its occurrence. The purpose of this study was to investigate the role of trabecular and cortical bone microstructure on vertebral strength using high-resolution peripheral quantitative computed tomography (HR-pQCT).

METHODS

Three female cadaveric spines were investigated (average age: 80.3 years). The whole spine (T1-L4) was scanned by second-generation HR-pQCT at a voxel size of 60.7 μm. Bone microstructure analysis and micro finite element analysis were performed after excluding the upper and lower endplates and posterior elements of a total of 48 vertebrae. Correlations between trabecular and cortical bone microstructure parameters and estimated vertebral strength were analyzed by univariate and multivariate regression models.

RESULTS

Cortical thickness (Ct.Th) and trabecular thickness (Tb.Th) were strongly correlated with estimated failure load on univariate analysis (r = 0.89, 0.82). Trabecular volumetric bone mineral density (Tb.vBMD), bone volume fraction (BV/TV), trabecular number (Tb.N), and Ct.Th were correlated with estimated failure load on multivariate regression analysis.

CONCLUSIONS

It was suggested that, in addition to trabecular bone (Tb.vBMD, BV/TV, Tb.N), cortical bone (Ct.Th) contributed significantly to vertebral strength in elderly women.

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.

Variogram-based evaluations of DXA correlate with vertebral strength, but do not enhance the prediction compared to aBMD alone

Ancillary evaluation of spinal Dual-energy X-ray Absorptiometry (DXA) via variogram-based texture evaluation (e.g., Trabecular Bone Score) is used for improving the fracture risk assessment, despite no proven relationship with vertebral strength. The purpose of this study was thus to determine whether classical variogram-based parameters (sill variance and correlation length) evaluated from simulated DXA scans could help predicting the in vitro vertebral strength. Experimental data of thirteen human full vertebrae (i.e., with posterior elements) and twelve vertebral bodies were obtained from two existing studies. Areal bone mineral density (aBMD) was calculated from 2D projection images of the 3D HR-pQCT scan of the specimens mimicking clinical DXA scans. Stochastic predictors, sill variance and correlation length, were calculated from their experimental variogram. Vertebral strength was measured as the maximum failure load of human vertebrae and vertebral bodies from mechanical tests. Vertebral strength correlated significantly with sill variance (r = 0.727) and correlation length (r = 0.727) for the vertebral bodies, and with correlation length (r = 0.593) for full vertebrae. However, the stochastic predictors improved the strength prediction made by aBMD alone by only 11% for the vertebral bodies while no improvement was observed for the full vertebrae. Despite a correlation, classical variogram parameters such as sill variance and correlation length do not enhance the prediction of in vitro vertebral strength beyond aBMD. It remains unclear why some variogram-based evaluations of DXA improve fracture prediction without a proven relationship with vertebral strength.

Numerical investigation of the effect of bone cement porosity on osteoporotic femoral augmentation

Femoroplasty is the injection of bone cement into the proximal femur, enhances the bone load capacity, and is typically applied to osteoporotic femora. To minimize the required injected volume of bone cement and maximize the load capacity enhancement, an optimization problem must be solved, where the modulus of elasticity of the augmented bone is a key element. This paper, through the numerical investigation of a fall on the greater trochanter of an osteoporotic femur, compares different ways to calculate this modulus and introduces an approach, based on the concept of bone cement porosity, which provides results statistically similar to those obtained with other considerations. Based on this approach, the present paper quantifies the correlation between degree of osteoporosis and optimum volume of bone cement. It concludes with an exhaustive search that reveals the effect of the bone cement porosity on the optimum volume of PMMA, for various combinations of the frontal and transverse angles of the fall on the greater trochanter.

A REVIEW ON BIOMECHANICAL ASPECTS OF VERTEBROPLASTY AND KYPHOPLASTY USING FINITE ELEMENT MODELING-BASED METHODS

The vertebroplasty (VP) and kyphoplasty (KP) are two minimally invasive surgeries using cement augmentation to treat the osteoporotic vertebrae in elderlies in order to relieve pain and prevent the continuation of microfractures. Biomechanists have always tried to assess the mechanical behavior of vertebrae after cement augmentation by using both the experimental and theoretical methods such as finite element modeling (FEM).

In this study, 31 related articles using FEM in analyzing the VP and KP have been reviewed. This study included two main categories of spinal load distribution and tension in vertebrae after the VP and KP operations. This could be obtained by conducting FEM on the whole spine or other sectors of it such as intervertebral disc (IVD) or end plates (EPs). This study also referred to articles predicting the probability of adjacent fractures following VP and KP. The most common software employed in FEM was ABAQUS, applied for static and dynamic loads’ analyses.

It was found that most of the reviewed articles adopted reverse engineering techniques by converting 2D computed tomography (CT) scan images into 3D reconstructed models. The material properties were generally taken from the literature. In more than 80% of studies, the model geometry was based on CT data of the spine. Almost 45% of the studies have attempted to compare the simulated vertebra after augmentation with experimental results taken from the literature (5% of the reviewed articles) or their own experimental tests (40% of the reviewed articles).

Effect of the In Vitro Boundary Conditions on the Surface Strain Experienced by the Vertebral Body in the Elastic Regime

The vertebral strength and strain can be assessed in vitro by both using isolated vertebrae and sets of three adjacent vertebrae (the central one is loaded through the disks). Our goal was to elucidate if testing single-vertebra-specimens in the elastic regime provides different surface strains to three-vertebrae-segments. Twelve three-vertebrae sets were extracted from thoracolumbar human spines. To measure the principal strains, the central vertebra of each segment was prepared with eight strain-gauges. The sets were tested mechanically, allowing comparison of the surface strains between the two boundary conditions: first when the same vertebra was loaded through the disks (three-vertebrae-segment) and then with the endplates embedded in cement (single-vertebra). They were all subjected to four nondestructive tests (compression, traction, torsion clockwise, and counterclockwise). The magnitude of principal strains differed significantly between the two boundary conditions. For axial loading, the largest principal strains (along vertebral axis) were significantly higher when the same vertebra was tested isolated compared to the three-vertebrae-segment. Conversely, circumferential strains decreased significantly in the single vertebrae compared to the three-vertebrae-segment, with some variations exceeding 100% of the strain magnitude, including changes from tension to compression. For torsion, the differences between boundary conditions were smaller. This study shows that, in the elastic regime, when the vertebra is loaded through a cement pot, the surface strains differ from when it is loaded through the disks. Therefore, when single vertebrae are tested, surface strain should be taken with caution.

Three-dimensional multifractal analysis of trabecular bone under clinical computed tomography

PURPOSE

An adequate understanding of bone structural properties is critical for predicting fragility conditions caused by diseases such as osteoporosis, and in gauging the success of fracture prevention treatments. In this work we aim to develop multiresolution image analysis techniques to extrapolate high-resolution images predictive power to images taken in clinical conditions.

METHODS

We performed multifractal analysis (MFA) on a set of 17 ex vivo human vertebrae clinical CT scans. The vertebrae failure loads (FFailure) were experimentally measured. We combined bone mineral density (BMD) with different multifractal dimensions, and BMD with multiresolution statistics (e.g., skewness, kurtosis) of MFA curves, to obtain linear models to predict FFailure. Furthermore we obtained short- and long-term precisions from simulated in vivo scans, using a clinical CT scanner. Ground-truth data - high-resolution images - were obtained with a High-Resolution Peripheral Quantitative Computed Tomography (HRpQCT) scanner.

RESULTS

At the same level of detail, BMD combined with traditional multifractal descriptors (Lipschitz-Hölder exponents), and BMD with monofractal features showed similar prediction powers in predicting FFailure (87%, adj. R² ). However, at different levels of details, the prediction power of BMD with multifractal features raises to 92% (adj. R2) of FFailure. Our main finding is that a simpler but slightly less accurate model, combining BMD and the skewness of the resulting multifractal curves, predicts 90% (adj. R2) of FFailure.

CONCLUSIONS

Compared to monofractal and standard bone measures, multifractal analysis captured key insights in the conditions leading to FFailure. Instead of raw multifractal descriptors, the statistics of multifractal curves can be used in several other contexts, facilitating further research.

Mechanical assessment of the effects of metastatic lytic defect on the structural response of human thoracolumbar spine

To investigate the effects of a clinical lytic defect on the structural response of human thoracolumbar functional spinal unit. A novel CT-compatible mechanical test system was used to image the deformation of a T12-L1 motion segment and measure the change in strain response under compressive loads ranging from 50 to 750 N. A lytic lesion (LM) with cortex involvement (33% by volume) was introduced to the upper vertebral body and the CT experiments were repeated. Finite element models, established from the CT volumes, were used to investigate the defect's effects on the structural response and the state of principal and shear stresses within the affected and adjacent vertebrae. The lytic lesion resulted in severe loss of the vertebral structural competence, resulting in significant, non-linear, and asymmetric increase in the experimentally measured strains and computed stresses within both vertebrae (p < 0.01). At the cortex, the tensile strains were significantly increased, while compressive strains significantly decreased, (p < 0.05). Both the vertebral bone and cortex regions adjacent to the defect showed significant increase in computed compressive, tensile, and shear stresses (p < 0.01). Changes in stress and strain distribution within the affected and adjacent vertebral bone and the experimentally observed bulging and buckling of the vertebral cortices suggested that initiation of catastrophic vertebral failure may occur under load magnitudes encountered in daily living. Although the effect of LM on the global deformation of the spine was well-predicted, our results show that FE predictions of local strain changes must be carefully assessed for clinical relevance. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1808-1819, 2016.

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.

The Initial Slope of the Variogram, Foundation of the Trabecular Bone Score, Is Not or Is Poorly Associated With Vertebral Strength

Trabecular bone score (TBS) rests on the textural analysis of dual-energy X-ray absorptiometry (DXA) to reflect the decay in trabecular structure characterizing osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible because prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly owing to an unrealistic setup and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings were used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation ("full vertebra"); 2) via the classical endplate embedding ("vertebral body"); or 3) via a ball joint to induce anterior wedge failure ("vertebral section"). High-resolution peripheral quantitative computed tomography (HR-pQCT) scans acquired from prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (F(exp)) and apparent failure stress (σexp) was assessed, and their relative contribution to a multilinear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with F(exp) and σexp , except for the "vertebral body" case (r(2) = 0.396, p = 0.028). Aside from the "vertebra section" setup where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing setup, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk.

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

Vertebral compression fractures are becoming increasingly common. Patient-specific nonlinear finite element (FE) models have shown promise in predicting yield strength and damage pattern but have not been experimentally validated for clinically relevant vertebral fractures, which involve loading through intervertebral discs with varying degrees of degeneration up to large compressive strains. Therefore, stepwise axial compression was applied in vitro on segments and performed in silico on their FE equivalents using a nonlocal damage-plastic model including densification at large compression for bone and a time-independent hyperelastic model for the disc. The ability of the nonlinear FE models to predict the failure pattern in large compression was evaluated for three boundary conditions: healthy and degenerated intervertebral discs and embedded endplates. Bone compaction and fracture patterns were predicted using the local volume change as an indicator and the best correspondence was obtained for the healthy intervertebral discs. These preliminary results show that nonlinear finite element models enable prediction of bone localisation and compaction. To the best of our knowledge, this is the first study to predict the collapse of osteoporotic vertebral bodies up to large compression using realistic loading via the intervertebral discs.