Endplate Deformation Research Articles

Initial stiffness of connection joining I-beam to concrete-filled multicellular steel tube wall

Concrete-filled multicellular steel tube (CF-MCST) wall is widely used in China in recent years. In the companion paper, the moment capacity of the connection joining an I-beam to a CF-MCST wall was studied. Realizing that the insight into the connection's stiffness would greatly benefit performing a fine structural analysis, this paper aims to propose a theoretical approach for approximating the rotational stiffness of the connection. Finite Element (FE) model is first established for analysis, which is validated by using the experimental results extracted from previous studies. In order to attain the stiffness resulting from the endplate and the wall individually, an additional companion FE model is employed, where the endplate's deformation is negligible by using an extreme great value for the Young's modulus of the endplate and the connection's rotation is therefore mainly attributed to the wall's local deformation near the connection. For the stiffness accounting for the deformation of the endplate, the stiffness accounting for the local deformation of the wall, and the connection's stiffness, parametric study is then performed via the validated FE models whose geometrical parameters falling into the range conventionally taken in the engineering. Based on the FE analysis results, the abstracted mechanical model is proposed, resulting in semi-empirical formulas where partial parameters are identified by the means of regression analysis. It is found that enlarging the geometrical parameters would improve the connection's stiffness. Among the parameters, the beam height has the most significant effects on the connection's stiffness. Accordingly, increasing the beam height first is suggested for the aim of enhancing the connection's stiffness. The comparison of the results obtained via the FE analyses and that obtained via the proposed theoretical approach shows a good agreement, and the error is <10% regarding the connection's stiffness.

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

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

Arrangement of Belleville Springs on Endplates Combined with Optimal Cross-Sectional Shape in PEMFC Stack Using Equivalent Beam Modeling and FEA

A set of Belleville springs integrated into an endplate plays a key role in a proton exchange membrane fuel cell (PEMFC) stack, which makes the applied assembly force smoother, resulting from the absorbed vibration and thermal expansion. The appropriate arrangement of Belleville springs is important in PEMFC stack design. The aim of this study is to establish an equivalent beam model to optimize the numbers and positions of Belleville springs to minimize endplate deformation. Based on this, a finite element analysis (FEA) model of the PEMFC stack is proposed to further optimize the cross-sectional shape of the endplate. For the endplate with two, three and four groups of Belleville springs, its optimal positions correspond to 0.17lin, 0.27lin and 0.5lin (lin is the equal distance between steel belts). In addition, the low thickness should be 2/3 of the high thickness of the curved endplate for a uniform contact pressure distribution as well as the high-volume-specific power. However, the curvature radius of the endplate arc is negative to the uniformity of the contact pressure distribution, and particularly the internal cells of the PEMFC stack. This study provides a design direction for endplates combined with Belleville springs in large fuel cell stacks clamped with steel belts.

The Effect of Connections on The Global Response of Built-up Cold-formed Steel Beams with Corrugated Webs

The objective of this&nbsp;paper is to quantify the slippage and rotation in the connections of a double fixed corrugated web beam. Two types of connections between the component parts of the built-up beam were used, i.e.&nbsp;MIG brazing and spot welding,&nbsp;which offer different rigidities and bearing capacities for the built-up beams. Experimental tests were conducted on three MIG brazed and two spot welded specimens, respectively. The test setup consisted of&nbsp;a six-point bending configuration which is equivalent to a uniform distributed load applied to&nbsp;the beam. The load was applied from a 500kN actuator through a leverage system that&nbsp;allowed the distribution of the force. An out-of-plane structure prevented&nbsp;the beam from lateral torsional buckling. The testing exhibited&nbsp;relatively large slippage and deformation in the bolted connections and in the supporting device, respectively. However,&nbsp;the high rigidity of the beam maintained the mid-span&nbsp;deflection in the serviceability limit state limits. The built-up corrugated web beams made of cold-formed steel profiles represent an efficient and suitable structural solution for buildings. Nevertheless, experimental research due to inevitable slippage and the endplate deformation must be performed to characterize the connection.

Investigation of the assembly for high-power proton exchange membrane fuel cell stacks through an efficient equivalent model

A high-power proton exchange membrane fuel cell (PEMFC) stack usually composes many cells, which induce high difficulty in evaluating its mechanical state of stack assembly. A methodology based on composite model and material property equivalent is developed to predict the mechanical state in PEMFC stack. In this methodology, the stack system is modeled based on a finite element model (FEM), in which bipolar plate (BPP) and membrane exchange assembly (MEA) are combined into a composite component. Experiments with stamped BPP are carried out to validate the FEM of the stack, and both the predicted clamping force and endplates deformation of FEM have a great agreement with the experimental results. Based on the methodology, it is found that more uniform pressure distribution can be generated when high-stiffness endplates are applied and cell number of the stack increases. The cells approaching to mid-stack have more uniform pressure. The pressure distribution of the stack is very sensitive to the compression ratio. High compression ratios leads to large endplate deformation, which increases the average pressure deviation between simulated value and design value, and also increases non-uniformity of pressure distribution. This methodology offers the possibility of evaluating the mechanical state of high-power fuel cell stack and greatly improves the computational efficiency.

Endplate Deformation Due to Open and Strutted Intervertebral Devices.

There is an absence of work on vertebral endplate response to peripheral loading following disc removal and interbody placement. Endplate deflection into the interbody space may impart beneficial strain on the developing fusion mass, influencing bone formation and remodeling. The aim of this study was to verify endplate deformation due to peripheral loading using a custom transducer and to investigate whether endplate motion is inhibited by implant design. A total of 14 porcine (L4, L5) vertebrae were assigned to open or strutted implant designs. A custom transducer was placed on the endplate while 500 N was applied to the implant at 1 Hz for 500 cycles. Endplate motion was acquired for each time point and averaged among specimens of the same design. The rates and magnitudes of endplate deformation were compared between implant designs using unpaired t tests. Peripheral loading of both implant designs resulted in endplate deflection into the interbody space. The open implant design demonstrated an increased rate and magnitude of endplate deformation when compared with strutted implants. Interbody cage design directly influences the dynamic motion of the vertebral endplate during cyclic loading. A larger, faster deflection of the endplate could increase the strain rate, duration, and magnitude on the developing interbody fusion mass. These parameters of dynamic strain have been correlated with increased bone formation and remodeling. Unimpeded endplate deformation in an open cage design could impart a strain pattern on the developing fusion mass that increases bone formation and remodeling, ultimately leading to a faster and stronger fusion.

Age and sex analysis of the modic changes in the vertebrae

&lt;p class="abstract"&gt;&lt;strong&gt;Background:&lt;/strong&gt; Modic changes are common bone marrow and end plate changes that appear on magnetic resonance imaging of the lumbar spine. These changes are clinically associated with back pain and are generally classified into three types. In this study, we aimed to determine the frequency of patients with end plate deformities according to age and sex in their vertebrae.&lt;/p&gt;&lt;p class="abstract"&gt;&lt;strong&gt;Methods:&lt;/strong&gt; The study was performed on 100 patients (50 females, 50 males) who were admitted to Konya Education Research Hospital and thoracic region bone structures screened with MRI. &lt;/p&gt;&lt;p class="abstract"&gt;&lt;strong&gt;Results:&lt;/strong&gt; Modic changes were observed most at L4-L5 levels.&lt;/p&gt;&lt;p class="abstract"&gt;&lt;strong&gt;Conclusions:&lt;/strong&gt; We believe that the results obtained in our study will be beneficial in the surgeon, radiology and anatomy training.&lt;/p&gt;

Flush Endplate Connections in Fire: Time-Dependent Behavior of Tension Bolts

Steel connections play a crucial role in maintaining the integrity and stability of steel building frames especially when exposed to fire temperatures. The behavior of flush endplate connections in fire is shown to be governed by tension bolt failure as bolts lose their strength and stiffness more rapidly at higher temperatures. As a result, the ability to predict the development of stresses in tension bolts of flush endplate connections at different stages of fire is of special importance. One of the factors influencing bolt stresses in fire is the thermal creep or time-dependent inelastic response of steel to elevated temperatures. Therefore, time- and temperature-dependent behavior of tension bolts of flush endplate connections in fire is the focus of this study. Stress-time histories in tension bolts are obtained by explicit consideration of thermal creep of steel in FE models of flush endplate connections at elevated temperatures. To better understand the effect of thermal creep on tension bolt behavior, the correlation between time-dependent rotational deformation of flush endplate connections and bolt stresses is also investigated. Further, the isochronous representation is utilized to study the rotational deformation and the tension bolt stresses under various applied moments ranging from 50% to 95% of the moment capacity and fire temperatures ranging from 450°C to 600°C with 25°C increment. Through such representation, it is indicated that the connection behavior is not only dependent on bolt strength degradation and applied moment, but also affected by the time duration of applied moments and temperatures. Also, with the inclusion of thermal creep of steel, the connection experiences higher rotation and excessive endplate deformation with stress relaxation leading to top tension bolt failure at earlier stages of fire. More specifically, for time exposure greater than or equal to 60 min, the failure temperature of the connection decreases from 600°C to around 550°C. Therefore, neglecting thermal creep of structural steel may result in an unsafe prediction of the overall response of flush endplate connections in fire.

A numerical study of beam-to-column joints subjected to impact

Limited documentation is concerned with the behaviour of steel joints subjected to severe impulsive loading originating from incidents such as explosions or impact. In this paper, finite element simulations are used to investigate the behaviour of beam-to-column joints with bolted end-plate connections subjected to impact loading. An elastic-thermoviscoplastic material model was employed in the simulations. Good agreement was obtained between the simulations and previously reported tests in terms of both global and local behaviour. In particular, the numerical model successfully reproduced the experienced failure mode of tensile bolt fracture combined with end-plate deformation. The validated model was employed in investigations of three cases, in which the main findings are as follows: (1) reducing the end-plate thickness significantly increased the energy dissipated by the joint; (2) axial forces in the beams only marginally affected the response; and (3) including the additional inertia introduced by the presence of floor slabs may change the failure mode to premature shear failure.

Osteogenesis imperfecta in adults

A 42-year-old premenopausal woman with osteogenesis imperfecta presents to the metabolic bone clinic. She has a daughter with osteogenesis imperfecta who is seen regularly in a specialist pediatric clinic, but the patient herself hasn't had a clinical consultation in years. She has pain and stiffness in her back and is worried for her future bone health. The patient asks, "Am I going to fall apart?" She had numerous fractures in childhood, including fractures of her femur and wrist; fractured her ankles several times in her late teens; and had occasional fractures in adulthood. Her last fracture was a comminuted fracture of her humerus three years ago, when she stumbled and fell forward onto her hands and knees. The woman is hyperextensible and thinks her ankles feel weak. Her bone mineral density T scores are -2.6 at the lumbar spine and -1.9 at the total hip, and spine imaging shows several vertebral endplate deformities, but overall preservation of vertebral height. What are the available pharmacological and nonpharmacological strategies to preserve her skeletal health and function?

Biomechanics of vertebral compression fractures and clinical application

Local biomechanical factors in the etiology of vertebral compression fractures are reviewed. The vertebral body is particularly vulnerable to compression fracture when its bone mineral density (BMD) falls with age. However, the risk of fracture, and the type of fracture produced, does not depend simply on BMD. Equally important is the state of degeneration of the adjacent intervertebral discs, which largely determines how compressive forces are distributed over the vertebral body. Disc height also influences load-sharing between the vertebral body and neural arch, and hence by Wolff's Law can influence regional variations in trabecular density within the vertebral body. Vertebral deformity is not entirely attributable to trauma: it can result from the gradual accumulation of fatigue damage, and can progress by a quasi-continuous process of "creep". Cement injection techniques such as vertebroplasty and kyphoplasty are valuable in the treatment of these fractures. Both techniques can stiffen a fractured vertebral body, and kyphoplasty may contribute towards restoring its height. The presence of cement can limit endplate deformation, and thereby partially reverse the adverse changes in load-sharing which follow vertebral fracture. Cement also reduces time-dependent "creep" deformation of damaged vertebrae.

Restoration of Spinal Alignment and Disk Mechanics following Polyetheretherketone Wafer Kyphoplasty with StaXx FX

EPFs sustained during VCFs degrade the disk's ability to develop IDP under load. This inability to develop pressure in combination with residual kyphotic deformity increases the risk for adjacent vertebral fractures. We tested the hypothesis that StaXx FX reduces kyphosis and endplate deformity following vertebral compression fracture, restoring disk mechanics. Eight thoracolumbar, 5-vertebrae segments were tested. A void was selectively created in the middle vertebra. The specimens were compressed until EPF and to a grade I-II VCF. PEEK wafer kyphoplasty was then performed. The specimens were then tested in flexion-extension (±6 Nm) under 400-N preload intact, after EPF, VCF, and kyphoplasty. Endplate deformity, kyphosis, and IDP adjacent to the fractured body were measured. Vertebral body height at the point of maximal endplate deformity decreased after EPF and VCF and was partially corrected after StaXx FX, remaining less than intact (P = .047). Anterior vertebral height decreased after VCF (P = .002) and was partially restored with StaXx FX, remaining less than intact (P = .015). Vertebral kyphosis increased after VCF (P < .001) and reduced after StaXx FX, remaining greater than intact (P = .03). EPF reduced IDP in the affected disk in compression-flexion loading (P < .001), which was restored after StaXx FX (P = 1.0). IDP in the unaffected disk did not change during testing (P > .3). StaXx FX reduced endplate deformity and kyphosis, and significantly increased anterior height following VCF. Although height and kyphosis were not fully corrected, the disk's ability to pressurize under load was restored.

Lower Thoracic Spine Pain in a 33-Year-Old Female

The patient was a 33-year-old woman with a chief complaint of midthoracic spine pain. Anterior-posterior and lateral radiographs of the thoracic spine revealed superior and inferior endplate deformities and a mild reduction of stature of the T9 vertebral body, which were suspicious for a fracture. Computed tomography scans revealed cortical irregularity of the vertebral body of T9, however, magnetic resonance imaging of the thoracic spine was negative. Given the magnetic resonance imaging findings, the smooth, well-defined cortical defect, and the absence of paraspinal hemorrhaging on the computed tomography scan, it was hypothesized that this may not have been an acute fracture. Rather, the cortical irregularity of the anterior vertebral body of T9 seen on computed tomography could have instead represented normal nutrient vascular channels. The patient was referred to an orthopaedic surgeon, who recommended conservative management by a physical therapist. J Orthop Sports Phys Ther 2010;40(8):533. doi:10....

010 Restoration of intervertebral disc mechanics after endplate deformity reduction using structural kyphoplasty

Introduction/Purpose: Recent studies suggest endplate fracture incurred during vertebral compression fracture (VCF) increases nucleus volume which alters intervertebral disc mechanics. Altered disc behavior has been theorized to increase adjacent fracture...

Translational aspects of bone quality—vertebral fractures, cortical shell, microdamage and glycation: a tribute to Pierre D. Delmas

Among vertebral deformities, the prevalence of wedge fractures is about twice that of endplate (biconcave) deformities, both of which are greater than that of crush deformities. The anterior cortex is, therefore, a site of interest for understanding mechanisms of vertebral fracture. Despite its importance to vertebral mechanics, there are limited data describing the role of cortical shell, microdamage, and bone matrix parameters in vertebral fragility. This review of literature emphasizes the translational aspects of bone quality and demonstrates that a greater understanding of bone fractures will be gained through bone quality parameters related to both cortical and cancellous compartments as well as from microdamage and bone matrix parameters. In the context of vertebral fractures, measures of cortical shell and bone matrix parameters related to the organic matrix (advanced glycation products and alpha/beta CTX ratio) are independent of BMD measurements and can therefore provide an additional estimate of fracture risk in older patients.

Differences in endplate deformation of the adjacent and augmented vertebra following cement augmentation

Vertebral cement augmentation can restore the stiffness and strength of a fractured vertebra and relieve chronic pain. Previous finite element analysis, biomechanical tests and clinical studies have indirectly associated new adjacent vertebral fractures following augmentation to altered loading. The aim of this repeated measures in situ biomechanical study was to determine the changes in the adjacent and augmented endplate deformation following cement augmentation of human cadaveric functional spine units (FSU) using micro-computed tomography (micro-CT). The surrounding soft tissue and posterior elements of 22 cadaveric human FSU were removed. FSU were assigned to two groups, control (n = 8) (loaded on day 1 and day 2) and augmented (n = 14) (loaded on day 1, augmented 20% cement fill, and loaded on day 2). The augmented group was further subdivided into a prophylactic augmentation group (n = 9), and vertebrae which spontaneously fractured during loading on day 1 (n = 5). The FSU were axially loaded (200, 1,000, 1,500-2,000 N) within a custom made radiolucent, saline filled loading device. At each loading step, FSUs were scanned using the micro-CT. Endplate heights were determined using custom software. No significant increase in endplate deformation following cement augmentation was noted for the adjacent endplate (P > 0.05). The deformation of the augmented endplate was significantly reduced following cement augmentation for both the prophylactic and fracture group (P < 0.05, P < 0.01, respectively). Endplate deformation of the controls showed no statistically significant differences between loading on day 1 and day 2. A linear relationship was noted between the applied compressive load and endplate deflection (R (2) = 0.58). Evidence of significant endplate deformation differences between unaugmented and augmented FSU, while evident for the augmented endplate, was not present for the adjacent endplate. This non-invasive micro-CT method may also be useful to investigate endplate failure, and parameters that predict vertebral failure.

Altered disc pressure profile after an osteoporotic vertebral fracture is a risk factor for adjacent vertebral body fracture

This study investigated the effect of endplate deformity after an osteoporotic vertebral fracture in increasing the risk for adjacent vertebral fractures. Eight human lower thoracic or thoracolumbar specimens, each consisting of five vertebrae were used. To selectively fracture one of the endplates of the middle VB of each specimen a void was created under the target endplate and the specimen was flexed and compressed until failure. The fractured vertebra was subjected to spinal extension under 150 N preload that restored the anterior wall height and vertebral kyphosis, while the fractured endplate remained significantly depressed. The VB was filled with cement to stabilize the fracture, after complete evacuation of its trabecular content to ensure similar cement distribution under both the endplates. Specimens were tested in flexion-extension under 400 N preload while pressure in the discs and strain at the anterior wall of the adjacent vertebrae were recorded. Disc pressure in the intact specimens increased during flexion by 26 +/- 14%. After cementation, disc pressure increased during flexion by 15 +/- 11% in the discs with un-fractured endplates, while decreased by 19 +/- 26.7% in the discs with the fractured endplates. During flexion, the compressive strain at the anterior wall of the vertebra next to the fractured endplate increased by 94 +/- 23% compared to intact status (p < 0.05), while it did not significantly change at the vertebra next to the un-fractured endplate (18.2 +/- 7.1%, p > 0.05). Subsequent flexion with compression to failure resulted in adjacent fracture close to the fractured endplate in six specimens and in a non-adjacent fracture in one specimen, while one specimen had no adjacent fractures. Depression of the fractured endplate alters the pressure profile of the damaged disc resulting in increased compressive loading of the anterior wall of adjacent vertebra that predisposes it to wedge fracture. This data suggests that correction of endplate deformity may play a role in reducing the risk of adjacent fractures.

Determination of vertebral endplate deformation under load using micro-computed tomography

Endplate strength plays an important role in preventing vertebral failure of normal vertebrae and in cases where surgical intervention has replaced the disc with an implant or has altered the vertebral loading. We have developed a non-contact method based on the principles of image guided failure analysis, mechanical testing, and micro-computed tomography analysis, which allows for in vitro quantification of endplate deformation under axial load. The method allows for the implementation of a repeated measures experimental design, each specimen acting as its own control. Our methodology was validated using cadaveric functional spine units, loaded stepwise from 200 N to a maximum of 2000 N. The loading protocol was repeated over two days, allowing time for recovery of the disc mechanical properties. We found no meaningful difference in measured force, stiffness, and endplate deformation between day 1 and day 2. The mean fiducial registration error was less than 0.015 mm for all three axes. Endplate deformation could be reproducibly estimated. The root mean squared error was 0.03 mm, which is the effective precision of the method. Using this micro-CT based method, the effect of interbody implants, grafts, disc replacement strategies, and surgical procedures such as nucleotomy and vertebral cement augmentation on endplate mechanical behaviour can be ascertained.

Vertebral endplate deformation before and after vertebral augmentation with polymethylmethacrylate (PMMA) determined by micro-CT

Vertebral endplate deformation before and after vertebral augmentation with polymethylmethacrylate (PMMA) determined by micro-CT

Thoracolumbar spine mechanics contrasted under compression and shear loading

The mechanical properties of the human spine have been studied extensively in compression, but there remains a lack of fundamental data in shear. The overall goal of this study was to contrast the mechanics of the thoracolumbar functional spinal unit (FSU) under compression and shear-type loads by evaluating endplate deformation, disc pressures, and kinematics between the different loading types. Eleven T12-L1 and one L1-L2 human FSUs were tested. Compression loads consisted of pure compression, extension–compression, flexion–compression, lateral left and right compression applied individually to a maximum of 500 N. Shear loading consisted of posterior, anterior, left, and right shear to a maximum of 500 N. Intervertebral motions, disc pressure, and vertebral body deformations were recorded for all loads. The deformations were measured using strain gauge rosettes at three points on the inferior vertebral body and one on the superior endplate of the inferior vertebra. The disc pressures and endplate deformations measured were significantly less in shear loading compared to compression and did not change significantly with the type of compression load. Vertebral rim strains were generally greater under shear loading compared with compression. The mechanics of load transfer in compression was the production of high disc pressures which were not linearly correlated with the central endplate deformation. In shear, the mechanism appears to be via the annulus fibrosus without the development of significant disc pressure. These differences between compression and shear loading may have implications for injury mechanisms in the thoracolumbar spine.