Biomechanical response of the pubic symphysis in lateral pelvic impacts: a finite element study

Automotive side impacts are a leading cause of injuries to the pubic symphysis, yet the mechanisms of those injuries have not been clearly established. Previous mechanical testing of isolated symphyses revealed increased joint laxity following drop tower lateral impacts to isolated pelvic bone structures, which suggested that the joints were damaged by excessive stresses and/or deformations during the impact tests. In the present study, a finite element (FE) model of a female pelvis including a previously validated symphysis sub-model was developed from computed tomography data. The full pelvis model was validated against measured force-time impact responses from drop tower experiments and then used to study the biomechanical response of the symphysis during the experimental impacts. The FE models predicted that the joint underwent a combination of lateral compression, posterior bending, anterior/posterior and superior/inferior shear that exceeded normal physiological levels prior to the onset of bony fractures. Large strains occurred concurrently within the pubic ligaments. Removal of the contralateral constraints to better approximate the boundary conditions of a seated motor vehicle occupant reduced cortical stresses and deformations of the pubic symphysis; however, ligament strains, compressive and shear stresses in the interpubic disc, as well as posterior bending of the joint structure remained as potential sources of joint damage during automotive side impacts.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

A simple model for the function of proteoglycans and collagen in the response to compression of the intervertebral disc.

The nucleus pulposus of the intervertebral disc exerts a pressure which enables it to support axial compression when contained by the annulus fibrosus. The disc was modelled as a thick-walled cylindrical pressure vessel in which the nucleus was contained radially by the annulus. As a result, the stress in the annulus had radial (compressive) as well as tangential (tensile) components. The radial stress at a given point in the annulus was considered to be balanced by the internal pressure which is expected to arise from the attraction of water by proteoglycans. There was a reasonable agreement between the calculated radial stress distribution and published results on the distribution of water within the annulus. As the internal pressure is expected to be isotropic, the annulus was expected to contribute to the axial resistance to compression of the disc; this contribution would be equal, in magnitude, to the radial stress. Predictions of the pressure distribution within the annulus were similar to published experimental measurements made in the radial and axial directions. The tangential stress within the annulus was considered to arise from the restoring stress in its strained collagen fibrils.     

Predictive equations to estimate spinal loads in symmetric lifting tasks

Response surface methodology is used to establish robust and user-friendly predictive equations that relate responses of a complex detailed trunk finite element biomechanical model to its input variables during sagittal symmetric static lifting activities. Four input variables (thorax flexion angle, lumbar/pelvis ratio, load magnitude, and load position) and four model responses (L4–L5 and L5–S1 disc compression and anterior–posterior shear forces) are considered. Full factorial design of experiments accounting for all combinations of input levels is employed. Quadratic predictive equations for the spinal loads at the L4–S1 disc mid-heights are obtained by regression analysis with adequate goodness-of-fit (R²>98%, p<0.05, and low root-mean-squared-error values compared with the range of predicted spine loads). Results indicate that intradiscal pressure values at the L4–L5 disc estimated based on the predictive equations are in close agreement with available in vivo data measured under similar loadings and postures. Combinations of input (posture and loading) variable levels that yield spine loads beyond the tolerance compression limit of 3400 N are identified using contour plots. Ergonomists and bioengineers, faced with the dilemma of using either complex but more accurate models on one hand or less accurate but simple models on the other hand, have thereby easy-to-use predictive equations that quantifies spinal loads and risk of injury under different occupational tasks of interest.     

Numerical analysis of the influence of nucleus pulposus removal on the biomechanical behavior of a lumbar motion segment

Nucleus replacement was deemed to have therapeutic potential for patients with intervertebral disc herniation. However, whether a patient would benefit from nucleus replacement is technically unclear. This study aimed to investigate the influence of nucleus pulposus (NP) removal on the biomechanical behavior of a lumbar motion segment and to further explore a computational method of biomechanical characteristics of NP removal, which can evaluate the mechanical stability of pulposus replacement. We, respectively, reconstructed three types of models for a mildly herniated disc and three types of models for a severely herniated disc based on a L4–L5 segment finite element model with computed tomography image data from a healthy adult. First, the NP was removed from the herniated disc models, and the biomechanical behavior of NP removal was simulated. Second, the NP cavities were filled with an experimental material (Poisson's ratio = 0.3; elastic modulus = 3 MPa), and the biomechanical behavior of pulposus replacement was simulated. The simulations were carried out under the five loadings of axial compression, flexion, lateral bending, extension, and axial rotation. The changes of the four biomechanical characteristics, i.e. the rotation degree, the maximum stress in the annulus fibrosus (AF), joint facet contact forces, and the maximum disc deformation, were computed for all models. Experimental results showed that the rotation range, the maximum AF stress, and joint facet contact forces increased, and the maximum disc deformation decreased after NP removal, while they changed in the opposite way after the nucleus cavities were filled with the experimental material.     

Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression,flexion and axial rotation

A statistical factorial analysis approach was conducted on a poroelastic finite element model of a lumbar intervertebral disc to analyse the influence of six material parameters (permeabilities of annulus, nucleus, trabecular vertebral bone, cartilage endplate and Young's moduli of annulus and nucleus) on the displacement, fluid pore pressure and velocity fields. Three different loading modes were investigated: compression, flexion and axial rotation. Parameters were varied considering low and high levels in agreement with values found in the literature for both healthy and degenerated lumbar discs. Results indicated that annulus stiffness and cartilage endplate permeability have a strong effect on the overall fluid- and solid-phase responses in all loading conditions studied. Nucleus stiffness showed its main relevance in compression while annulus permeability influenced mainly the annular pressure field. This study confirms the permeability's central role in biphasic modelling and highlights for the lumbar disc which experiments of material property characterization should be performed. Moreover, such sensitivity study gives important guidelines in poroelastic material modelling and finite element disc validation.     

Stepwise reduction of functional spinal structures increase disc bulge and surface strains

Previous studies postulated that an axial compression of lumbar intervertebral discs causes a complex strain pattern on the annulus. This pattern is not fully understood, since most studies measured only the uniaxial ultimate tensile strain of the annulus. The aim of this study was to investigate surface strains and their relation to disc bulging. This work was extended to study some defects that are relevant for the intermediate process of finite element modeling. Six specimens (L2-3) with a median age of 51 years were utilized for this in vitro study. Specimens were loaded with pure moments (2.5-7.5Nm) in the principal directions. The anatomy was subsequently reduced in three steps: (1) ligamentous and bony posterior structures, (2) anterior and posterior ligaments and (3) nucleus. Measured were ranges of motion, three-dimensional disc bulging and surface strains of the outer annulus. Lateral bending showed the largest axial strains (9.7%) for intact specimens, which increased to 15.1% after the removal of posterior structures. Disc bulging was largest in flexion with 1.56mm, which increased to 2.06mm after step (1). Defect (2) caused that flexion yielded the largest axial strains with 22.6% and 2.17mm of bulging. We could also determine a constriction effect of these ligaments. Nucleotomy did not essentially increase anterior disc bulging in flexion, but inward disc bulging increased by 0.55mm, in extension. Due to the increase in the complexity of finite element models, it is difficult to obtain data from the literature for validation purposes. This study presents new data, which assist in the development of such models.     

Biomechanical comparison of the effects of anterior,posterior and transforaminal lumbar interbody fusion on vibration characteristics of the human lumbar spine

Previous studies have compared the effects of different interbody fusion approaches on biomechanical responses of the lumbar spine to static loadings. However, very few have dealt with the whole body vibration (WBV) condition that is typically present in vehicles. This study was designed to determine the biomechanical differences among anterior, posterior and transforaminal lumbar interbody fusion (ALIF, PLIF and TLIF) under vertical WBV. A previously developed and validated finite element (FE) model of the intact L1–sacrum human lumbar spine was modified to simulate ALIF, PLIF and TLIF with bilateral pedicle screw fixation at L4–L5. Comparative studies on dynamic responses to the axial cyclic loading in these developed models were conducted. The results showed that at the fused L4–L5 level, dynamic responses of the von-Mises stress in L4 inferior and L5 superior endplates for the ALIF, PLIF and TLIF models were increased compared with the intact model. The endplate stresses in the TLIF model were lower than in the ALIF and PLIF models, but the TLIF generated greater stresses in the screws and rods compared with the ALIF and PLIF. At other levels, a decrease in dynamic responses of the disc bulge, annulus stress and intradiscal pressure was observed in all the fusion models compared with the intact one, but there was no obvious difference in these dynamic responses among the ALIF, PLIF and TLIF models. These findings might be useful in understanding vibration characteristics of the whole lumbar spine after different types of fusion surgery.     

Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study

A simple finite element model of the L₅-S₁ intervertebral disc body has been constructed; it is circular and symmetrical about the sagittal plane. The annulus fibrosus of the model was idealized as an inhomogeneous composite of an isotropic ground substance, reinforced by helically oriented collagen fibres so that the model has six different structural components namely: cortical bone, cancellous bone, cartilaginous endplates, nucleus pulposus, ground substance and collagen fibres. A sensitivity analysis of the material properties of each structural component was carried out by varying those properties for one structural component at a time and evaluating the changes in the biomechanical response to compressive displacements. Experimentally available relations between the applied compressive force and the vertical displacements, the nucleus pulposus pressure increase and the disc lateral bulge were used to evaluate the biomechanical responses for each set of material properties. Results showed that both the Poisson's ratio and the Young's modulus of the ground substance play an important role in the prediction of the biomechanical response.     

Relationship Between Structure and Mechanical Function of the Tissues of the Intervertebral Joint

This paper reviews our current understanding of the relationshipbetween the structures and properties of the tissues of thespine and their mechanical functions. Emphasis is on the humanlumbar spine. Vertebrae consist of a core of cancellous bone(low density) surrounded by a shell of cortical bone (high stiffness);as a result they have high stiffness but low mass. The intervertebraldisc is able to withstand compression because of the swellingpressure exerted by the nucleus pulposus which is constrained,radially, by the annulus fibrosus. Thus the disc acts as a thick-walledpressure vessel. Collagen fibers within the annulus providereinforcement during compression, bending and torsion of thedisc. Collagen fibers also provide tensile reinforcement andprevent tears spreading across ligaments. The ligamenta flavacontain elastic fibers (low stiffness and low strength) withcollagen fibers (high stiffness and high strength). In the unstretchedligamenta flava, the collagen fibers have almost random orientationsbut they become aligned as the ligament is stretched. This structureenables the high extensibility of elastic fibers to be exploitedbut protects them from damage at high strains. The structureof the interspinous ligament suggests that its main functionis to attach the thoracolumbar fascia to the posterior spine.Thus the fascia is maintained in tension when stretched by theabdominal muscles. This and other observations indicate theimportance of muscles for maintaining the stability of the spinalcolumn.     

Nonlinear gross response analysis of a lumbar motion segment in combined sagittal loadings

A 3-D nonlinear mathematical model is used to analyze the mechanical response of a lumbar L2-3 motion segment including the posterior elements when subjected to combined sagittal plane loads. The loadings consist of axial compression force, anterior and posterior shear forces, and flexion and extension moments. The facet articulation is modelled as a general moving contact problem and the ligaments as a collection of uniaxial elements. The disk nucleus is considered as an inviscid fluid and the annulus as a composite of collagenous fibers embedded in a matrix of ground substance. The presence of axial compression force reduces the segmental stiffness in flexion whereas a reverse trend is predicted in extension. In the presence of axial compression with and without sagittal shear force, flexion considerably increases the intradiscal pressure while extension reduces it. In other words, under an identical compression force, disk pressure is predicted to be noticeably larger in flexion than in extension. The segmental mechanical response in extension loadings is markedly influenced by the changes in the relative geometry of the articular surfaces at the lower regions. Finally, the deformation of the bony structures plays a significant role in the segmental mechanics under relatively large loads.     

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.     

An anisotropic multiphysics damage model with application to annulus fibrosus

An anisotropic multiphysics damage model is developed to characterize the couplings among multiple physical fields within soft tissues and the tissue damage based on thermodynamic principles. This anisotropic multiphysics damage model integrates the continuum mixture theory and a continuum damage model, and the anisotropic damage is considered by evolution of internal damage variables governing the anisotropic mechanical behaviors of tissues. The energy dissipation associated with the transport of fluid and ions is generally related to tissue damage. The anisotropic multiphysics damage model is applied to simulate a case of annulus fibrosus (AF) damage in an isolated intervertebral disc under compression, to understand the damage initiation and propagation. It is found that, for this case (with 1000 N/s of compression rate and neglected ground matrix damage), the damage initiated in the outer and middle posterior regions of AF at about 700 N of axial compression. The region-dependent yield stretch ratio predicted by this model is consistent with experimental findings. A sensitive study on the damage parameters is also presented. This study provides an additional insight into AF damage in the isolated disc under mechanical compression.     

Quantitative analysis and comparative regional investigation of the extracellular matrix of the porcine temporomandibular joint disc.

Characterization of the extracellular matrix of the temporomandibular joint (TMJ) disc is crucial to advancing efforts in tissue engineering the disc. However, the current literature is incomplete and often contradictory in its attempts to describe the nature of the TMJ disc matrix. The aim of this study was to identify the variation of key matrix components along the three axes of the porcine disc using ELISAs to quantify these matrix components, immunohistochemistry to identify their regional distribution, and SEM to examine collagen fiber diameter and orientation. The overall GAG content of the TMJ disc (including the dermatan sulfate proteoglycans) was 5.3+/-1.2% of the dry weight. Chondroitin sulfate, which comprised 74% of this total GAG content, was 4.4, 8.2, and 164 times more abundant than dermatan sulfate proteoglycan, keratan sulfate, and hyaluronic acid, respectively. In general, these GAGs were most concentrated in the intermediate zone of the TMJ disc, appearing in dense clusters, and least concentrated in the posterior band. Additionally, chondroitin sulfate was more abundant medially than laterally. Collagen II was discovered in trace amounts, with higher relative amounts in the intermediate zone. Collagen fibers were observed to run primarily in a ring-like fashion around the periphery of the disc and anteroposteriorly through the intermediate zone, with a mean fiber diameter of 18+/-9 mum. Characterization studies of the TMJ disc, including prior biomechanical and cell studies along with the current study of the extracellular matrix, collectively reveal a distinct character of the intermediate zone of the disc compared to its anterior and posterior bands.     

An accurate finite element model of the cervical spine under quasi-static loading

Cervical disc injury due to impact has been observed in clinical and biomechanical investigations; however, there is a lack of data that helps to elucidate the mechanisms of disc injury during these collisions. Therefore, it is necessary to understand the behavior of the cervical spine under different types of loading situations. A three dimensional finite element (FE) model for the multi-level cervical spine segment (C0-C7) was developed using computed tomography (CT) data and applied to study the internal stresses and strains of the intervertebral discs under quasi-static loading conditions. The intervertebral discs were treated as nonlinear, anisotropic and incompressible subjected to large deformations. The model accuracy was validated by comparing it with previously published experimental and numerical results for different movements. It was shown that the use of a fiber reinforced model to describe the behavior of the annulus of the discs would predict higher maximum shear strains than an isotropic one, being therefore important the use of complex constitutive models in order to be able to detect the appearance of injured zones, since those strains and stresses are supposed to be related with damage to soft tissues. Several movements were analyzed: flexion, extension and axial rotation, obtaining that the maximum shear stresses in the disc were higher for a flexo-extension movement.     

Mechanical response of a simple finite element model of the intervertebral disc under complex loading

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disc was constructed. The bodies and disc were modeled by three substructures; one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when non- axisymmetric loads were imposed on the model. The response of the model to compression, shear, torsion and bending loads applied to the superior vertebral body was examined to determine the effects of disc geometry and material properties on response. Comparisons of model responses with experimentally measured responses were made to estimate material property values for which model behaviors are in agreement with measured behaviors.     

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.     

Influence of cervical disc degeneration after posterior surgical techniques in combined flexion-extension--a nonlinear analytical study

Laminectomy and facetectomy are surgical techniques used for decompression of the cervical spinal stenosis. Recent in vitro and finite element studies have shown significant cervical spinal instability after performing these surgical techniques. However, the influence of degenerated cervical disk on the biomechanical responses of the cervical spine after these surgical techniques remains unknown. Therefore, a three-dimensional nonlinear finite element model of the human cervical spine (C2-C7) was created. Two types of disk degeneration grades were simulated. For each grade of disk degeneration, the intact as well as the two surgically altered models simulating C5 laminectomy with or without C5-C6 total facetectomies were exercised under flexion and extension. Intersegmental rotational motions, internal disk annulus, cancellous and cortical bone stresses were obtained and compared to the normal intact model. Results showed that the cervical rotational motion decreases with progressive disk degeneration. Decreases in the rotational motion due to disk degeneration were accompanied by higher cancellous and cortical bone stress. The surgically altered model showed significant increases in the rotational motions after laminectomies and facetectomies when compared to the intact model. However, the percentage increases in the rotational motions after various surgical techniques were reduced with progressive disk degeneration.