An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies

ISSLS prize winner: integrating theoretical and experimental methods for functional tissue engineering of the annulus fibrosus

STUDY DESIGN

Integrating theoretical and experimental approaches for annulus fibrosus (AF) functional tissue engineering.

OBJECTIVE

Apply a hyperelastic constitutive model to characterize the evolution of engineered AF via scalar model parameters. Validate the model and predict the response of engineered constructs to physiologic loading scenarios.

SUMMARY OF BACKGROUND DATA

There is need for a tissue engineered replacement for degenerate AF. When evaluating engineered replacements for load-bearing tissues, it is necessary to evaluate mechanical function with respect to the native tissue, including nonlinearity and anisotropy.

METHODS

Aligned nanofibrous poly-epsilon-caprolactone scaffolds with prescribed fiber angles were seeded with bovine AF cells and analyzed over 8 weeks, using experimental (mechanical testing, biochemistry, histology) and theoretical methods (a hyperelastic fiber-reinforced constitutive model).

RESULTS

The linear region modulus for phi = 0 degrees constructs increased by approximately 25 MPa, and for phi = 90 degrees by approximately 2 MPa from 1 day to 8 weeks in culture. Infiltration and proliferation of AF cells into the scaffold and abundant deposition of s-GAG and aligned collagen was observed. The constitutive model had excellent fits to experimental data to yield matrix and fiber parameters that increased with time in culture. Correlations were observed between biochemical measures and model parameters. The model was successfully validated and used to simulate time-varying responses of engineered AF under shear and biaxial loading.

CONCLUSION

AF cells seeded on nanofibrous scaffolds elaborated an organized, anisotropic AF-like extracellular matrix, resulting in improved mechanical properties. A hyperelastic fiber-reinforced constitutive model characterized the functional evolution of engineered AF constructs, and was used to simulate physiologically relevant loading configurations. Model predictions demonstrated that fibers resist shear even when the shearing direction does not coincide with the fiber direction. Further, the model suggested that the native AF fiber architecture is uniquely designed to support shear stresses encountered under multiple loading configurations.

Effect of an artificial disc on lumbar spine biomechanics: a probabilistic finite element study

The effects of different parameters on the mechanical behaviour of the lumbar spine were in most cases determined deterministically with only one uncertain parameter varied at a time while the others were kept fixed. Thus most parameter combinations were disregarded. The aim of the study was to determine in a probabilistic finite element study how intervertebral rotation, intradiscal pressure, and contact force in the facet joints are affected by the input parameters implant position, implant ball radius, presence of scar tissue, and gap size in the facet joints. An osseoligamentous finite element model of the lumbar spine ranging from L3 vertebra to L5/S1 intervertebral disc was used. An artificial disc with a fixed center of rotation was inserted at level L4/L5. The model was loaded with pure moments of 7.5 Nm to simulate flexion, extension, lateral bending, and axial torsion. In a probabilistic study the implant position in anterior-posterior (ap) and in lateral direction, the radius of the implant ball, and the gap size of the facet joint were varied. After implanting an artificial disc, scar tissue may develop, replacing the anterior longitudinal ligament. Thus presence and absence of scar tissue were also simulated. For each loading case studied, intervertebral rotations, intradiscal pressures and contact forces in the facet joints were calculated for 1,000 randomized input parameter combinations in order to determine the probable range of these output parameters. Intervertebral rotation at implant level varies strongly for different combinations of the input parameters. It is mainly affected by gap size, ap-position and implant ball radius for flexion, by scar tissue and implant ball radius for extension and lateral bending, and by gap size and implant ball radius for axial torsion. For extension, intervertebral rotation at implant level varied between 1.4 degrees and 7.5 degrees . Intradiscal pressure in the adjacent discs is only slightly affected by all input parameters. Contact forces in the facet joints at implant level vary strongly for the different combinations of the input parameters. For flexion, forces are 0 in 63% of the cases, but for small gap sizes and large implant ball radii they reach values of up to 533 N. Similar results are found for extension with a maximum predicted force of 560 N. Here the forces are mainly influenced by gap size, implant ball radius and scar tissue. The forces vary between 0 and 300 N for lateral bending and between 0 and 200 N for axial torsion. The parameters that have the greatest effect in both loading cases are the same as those for extension. Intervertebral rotation and contact force in the facet joints depend strongly on the input parameters studied. The probabilistic study shows a large variation of the results and likelihood of certain values. Clinical studies will be required to show whether or not there is a strong correlation of parameter combinations that cause high facet joint forces and low back pain after total disc replacement.

Finite element analysis of cancellous bone failure in the vertebral body of healthy and osteoporotic subjects

The aim of this work is to assess the fracture risk prediction of the cancellous bone in the body of a lumbar vertebra when the mechanical parameters of the bone, i.e. stiffness, porosity, and strength anisotropy, of elderly and osteoporotic subjects are considered. For this purpose, a non-linear three-dimensional continuum-based finite element model of the lumbar functional spinal unit L4—L5 was created and strength analyses of the spongy tissue of the vertebral body were carried out. A fabric-dependent strength criterion, which accounts for the micro-architecture of the cancellous bone, based on histomorphometric analyses was used. The strength analyses have shown that the cancellous bone of none of the subject types undergoes failure under loading applied during normal daily life like axial compression; however, bone failure occurs for the osteoporotic segment, subjected to a combination of the compression preloading and moments in the sagittal or in the frontal plane, which are conditions that may not be considered to occur ‘daily’. In particular, critical stress conditions are met because of the high porosity values in the horizontal direction within the cancellous bone. The computational approach presented in the paper can potentially predict the material fracture risk of the cancellous bone in the vertebral body and it may be usefully employed to draw failure maps representing, for a given micro-architecture of the spongy tissue, the critical loading conditions (forces and moments) that may lead to such a risk. This approach could be further developed in order to assess the effectiveness of biomedical devices within an engineering approach to the clinical problem of the spinal diseases.

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.

Quality of motion considerations in numerical analysis of motion restoring implants of the spine

BACKGROUND

Motion restoring implants function in a dynamic environment that encompasses the full range of spinal kinematics. Accurate assessment of the in situ performance of these devices using numerical techniques requires model verification and validation against the well-established nonlinear quality of motion of the spine, as opposed to the previous norm of matching kinematic endpoint metrics such as range of motion and intervertebral disc pressure measurements at a single kinematic reference point.

METHODS

Experimental data was obtained during cadaveric testing of nine three-functional spinal unit (L3-S1) lumbar spine segments. Each specimen was tested from 8 Nm of applied flexion moment to 6 Nm of applied extension moment with an applied 400 N compressive follower preload. A nonlinear kinematic curve representing the spinal quality of motion (applied moment versus angular rotation) for the index finite element model was constructed and compared to the kinematic responses of the experimental specimens. The effect of spinal soft tissue structure mechanical behaviors on the fidelity of the model's quality of motion to experimental data was assessed by iteratively modifying the material representations of annulus fibrosus, nucleus pulposus, and ligaments.

FINDINGS

The present work demonstrated that for this model, the annulus fibrosus played a small role in the nonlinear quality of motion of the model, whereas changes in ligament representations had a large effect, as validated against the full kinematic range of motion. An anisotropic continuum representation of the annulus fibrosus was used, along with nonlinear fabric representations of the ligaments and a hyperelastic representation of the nucleus pulposus.

INTERPRETATION

Our results suggest that improvements in current methodologies broadly used in numerical simulations of the lumbar spine are needed to fully describe the highly nonlinear motion of the spine.

Effect of position and height of a mobile core type artificial disc on the biomechanical behaviour of the lumbar spine

The extent of natural disc removal and the implant position and height of an artificial disc with a mobile core were studied for their effects on intersegmental rotation, intradiscal pressure, and facet joint force. A validated finite element model of the lumbar spine was used. The model was loaded with the upper body weight, a follower load, and muscle forces to simulate standing, flexion, extension, lateral bending, and axial rotation. The implant position was varied up to 2 mm in an anterior and posterior direction and up to 3 mm in a lateral direction. Three different implant heights were simulated. The effect of removing the lateral parts of the annulus was also studied. The implant position and height markedly affect intersegmental rotation and facet joint forces but have hardly any influence on intradiscal pressure in the adjacent discs.

Removing the lateral parts of the annulus increases intersegmental rotation and facet joint force mainly for lateral bending and axial rotation. The calculated translation of the mobile implant core is about 1 mm at most, and thus its effect is often overestimated. Great care should be taken to choose the optimal implant height and to insert the implant in the best position for each individual patient.

Mechanics of oriented electrospun nanofibrous scaffolds for annulus fibrosus tissue engineering

Engineering a functional replacement for the annulus fibrosus (AF) of the intervertebral disc is contingent upon recapitulation of AF structure, composition, and mechanical properties. In this study, we propose a new paradigm for AF tissue engineering that focuses on the reconstitution of anatomic fiber architecture and uses constitutive modeling to evaluate construct function. A modified electrospinning technique was utilized to generate aligned nanofibrous polymer scaffolds for engineering the basic functional unit of the AF, a single lamella. Scaffolds were tested in uniaxial tension at multiple fiber orientations, demonstrating a nonlinear dependence of modulus on fiber angle that mimicked the nonlinearity and anisotropy of native AF. A homogenization model previously applied to native AF successfully described scaffold mechanical response, and parametric studies demonstrated that nonfibrillar matrix, along with fiber connectivity, are key contributors to tensile mechanics for engineered AF. We demonstrated that AF cells orient themselves along the aligned scaffolds and deposit matrix that contributes to construct mechanics under loading conditions relevant to the in vivo environment. The homogenization model was applied to cell-seeded constructs and provided quantitative measures for the evolution of matrix and interfibrillar interactions. Finally, the model demonstrated that at fiber angles of the AF (28 degrees -44 degrees ), engineered material behaved much like native tissue, suggesting that engineered constructs replicate the physiologic behavior of the single AF lamella. Constitutive modeling provides a powerful tool for analysis of engineered AF neo-tissue and native AF tissue alike, highlighting key mechanical design criteria for functional AF tissue engineering.

A bimodular polyconvex anisotropic strain energy function for articular cartilage

A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex "strong interaction terms" for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson's ratios, as well as axial stress-axial strain responses, in tension and compression for finite deformations.

Application of a calibration method provides more realistic results for a finite element model of a lumbar spinal segment

BACKGROUND

An important step in finite element modeling is the process of validation to derive clinical relevant data. It can be assumed that defect states of a finite element model, which have not been validated before, may predict wrong results. The purpose of this study was to show the differences in accuracy between a calibrated and a non-calibrated finite element model of a lumbar spinal segment for different clinical defects.

METHODS

For this study, two geometrically identical finite element models were used. An in vitro experiment was designed, deriving data for the calibration. Frequently used material properties were obtained from the literature and transferred into the non-calibrated model. Both models were validated on three clinical defects: bilateral hemifacetectomy, nucleotomy and interspinous defects, whereas in vitro range of motion data served as control points. Predictability and accuracy of the calibrated and non-calibrated finite element model were evaluated and compared.

FINDINGS

Both finite element models could mimic the intact situation with a good agreement. In the defects, the calibrated model predicted motion behavior with excellent agreement, whereas the non-calibrated model diverged greatly.

INTERPRETATION

Investigating the biomechanical performance of implants and load distribution of different spinal structures by numerical analysis requires not only good agreement with the intact segment, but also with the defect states, which are initiated prior to implant insertion. Because of more realistic results the calibration method may be recommended, however, it is more time consuming.

Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading

STUDY DESIGN

Finite element study.

OBJECTIVE

To investigate intradiscal pressure, shear strain between anulus and adjacent endplates, and fiber strain in the anulus under pure and combined moments.

SUMMARY OF BACKGROUND DATA

Concerning anulus failures such as fissures and disc prolapses, the mechanical response of the intervertebral disc during combined load situations is still not well understood.

METHODS

A 3-dimensional, nonlinear finite element model of a lumbar spinal segment L4-L5 was used. Pure unconstraint moments of 7.5 Nm in all anatomic planes with and without an axial preload of 500 N were applied to the upper vertebral body. The load direction was incrementally changed with an angle of 15 degrees between the 3 anatomic planes to realize not only moments in the principle motion planes but also moment combinations.

RESULTS

Intradiscal pressure was highest in flexion and lowest in lateral bending. Load combinations did not increase the pressure. A combination of lateral bending plus flexion or lateral bending plus extension strongly increased the maximum shear strains. Lateral bending plus axial rotation yielded the highest increase in fiber strains, followed by axial rotation plus flexion or axial rotation plus extension. The highest shear and fiber strains were both located posterolaterally. An additional axial preload tended to increase the pressure, the shear, and fiber strains essentially for all load scenarios.

CONCLUSIONS

Combined moments seem to lead to higher stresses in the disc, especially posterolaterally. This region might be more susceptible to disc failure and prolapses. These results may help clinicians better understand the mechanical causes of disc prolapses and may also be valuable in developing preventive clinical strategies and postoperative treatments.

Quantifying the contributions of structure to annulus fibrosus mechanical function using a nonlinear, anisotropic, hyperelastic model

The annulus fibrosus of the intervertebral disc is comprised of concentric lamella of oriented collagen fibers embedded in a hydrated proteoglycan matrix with smaller amounts of minor collagens, elastin, and small proteoglycans. Its structure and composition enable the disc to withstand complex loads and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of the annulus fibrosus constituent structures to mechanical function remain unclear. Therefore, the objective of this study was to use a structurally motivated, anisotropic, nonlinear strain energy model of annulus fibrosus to determine the relative contributions of its structural components to tissue mechanical behavior. A nonlinear, orthotropic hyperelastic model was developed for the annulus fibrosus. Terms to describe fibers, matrix, and interactions between annulus fibrosus structures (shear and normal to the fiber directions) were explicitly included. The contributions of these structures were analyzed by including or removing terms and determining the effect on the fit to multidimensional experimental data. Correlation between experimental and model-predicted stress, a Bland-Altman analysis of bias and standard deviation of residuals, and the contribution of structural terms to overall tissue stress were calculated. Both shear and normal interaction terms were necessary to accurately model multidimensional behavior. Inclusion of shear interactions more accurately described annulus fibrosus nonlinearity. Fiber stretch and shear interactions dominated contributions to circumferential direction stress, while normal and shear interactions dominated axial stress. The results suggest that interactions between fibers and matrix, perhaps facilitated by crosslinks, elastin, or minor collagens, augment traditional (i.e., fiber-uncrimping) models of nonlinearity.

Comparison of the effects of bilateral posterior dynamic and rigid fixation devices on the loads in the lumbar spine: a finite element analysis

A bilateral dynamic stabilization device is assumed to alter favorable the movement and load transmission of a spinal segment without the intention of fusion of that segment. Little is known about the effect of a posterior dynamic fixation device on the mechanical behavior of the lumbar spine. Muscle forces were disregarded in the few biomechanical studies published. The aim of this study was to determine how the spinal loads are affected by a bilateral posterior dynamic implant compared to a rigid fixator which does not claim to maintain mobility. A paired monosegmental posterior dynamic implant was inserted at level L3/L4 in a validated finite element model of the lumbar spine. Both a healthy and a slightly degenerated disc were assumed at implant level. Distraction of the bridged segment was also simulated. For comparison, a monosegmental rigid fixation device as well as the effect of implant stiffness on intersegmental rotation were studied. The model was loaded with the upper body weight and muscle forces to simulate the four loading cases standing, 30 degrees flexion, 20 degrees extension, and 10 degrees axial rotation. Intersegmental rotations, intradiscal pressure and facet joint forces were calculated at implant level and at the adjacent level above the implant. Implant forces were also determined. Compared to an intact spine, a dynamic implant reduces intersegmental rotation at implant level, decreases intradiscal pressure in a healthy disc for extension and standing, and decreases facet joint forces at implant level. With a rigid implant, these effects are more pronounced. With a slightly degenerated disc intersegmental rotation at implant level is mildly increased for extension and axial rotation and intradiscal pressure is strongly reduced for extension. After distraction, intradiscal pressure values are markedly reduced only for the rigid implant. At the adjacent level L2/L3, a posterior implant has only a minor effect on intradiscal pressure. However, it increases facet joint forces at this level for axial rotation and extension. Posterior implants are mostly loaded in compression. Forces in the implant are generally higher in a rigid fixator than in a dynamic implant. Distraction strongly increases both axial and shear forces in the implant. A stiffness of the implant greater than 1,000 N/mm has only a minor effect on intersegmental rotation. The mechanical effects of a dynamic implant are similar to those of a rigid fixation device, except after distraction, when intradiscal pressure is considerably lower for rigid than for dynamic implants. Thus, the results of this study demonstrate that a dynamic implant does not necessarily reduce axial spinal loads compared to an un-instrumented spine.

How does the geometry affect the internal biomechanics of a lumbar spine bi-segment finite element model? Consequences on the validation process

Numerical modelling can provide a thorough understanding of the mechanical influence on the spinal tissues and may offer explanations to mechanically linked pathologies. Such objective might be achieved only if the models are carefully validated. Sensitivity study must be performed in order to evaluate the influence of the approximations inherent to modelling. In this study, a new geometrically accurate L3-L5 lumbar spine bi-segmental finite-element model was acquired by modifying a previously existing model. The effect of changes in bone geometry, ligament fibres distribution, nucleus position and disc height was investigated in flexion and extension by comparison of the results obtained from the model before and after the geometrical update. Additional calculations were performed in axial rotation and lateral bending in order to compare the computed ranges of motion (ROM) with experimental results. It was found that the geometrical parameters affected the stress distribution and strain energy in the zygapophysial joints, the ligaments, and the intervertebral disc, changing qualitatively and quantitatively their relative role in resisting the imposed loads. The predicted ROM were generally in good agreement with the experimental results, independently of the geometrical changes. Hence, although the model update affected its internal biomechanics, no conclusions could be drawn from the experimental data about the validation of a particular geometry. Hence the validation of the lumbar spine model should be based on the relative role of its structural components and not only on its global mobility.

Stress-driven collagen fiber remodeling in arterial walls

A stress-driven model for the relation between the collagen morphology and the loading conditions in arterial walls is proposed. We assume that the two families of collagen fibers in arterial walls are aligned along preferred directions, located between the directions of the two maximal principal stresses. For the determination of these directions an iterative finite element based procedure is developed. As an example the remodeling of a section of a human common carotid artery is simulated. We find that the predicted fiber morphology correlates well with experimental observations. Interesting outcomes of the model including local shear minimization and the possibility of axial compressions due to high blood pressure are revealed and discussed.

Validation of a clinical finite element model of the human lumbosacral spine

Very few finite element models on the lumbosacral spine have been reported because of its unique biomechanical characteristics. In addition, most of these lumbosacral spine models have been only validated with rotation at single moment values, ignoring the inherent nonlinear nature of the moment-rotation response of the spine. Because a majority of lumbar spine surgeries are performed between L4 and S1 levels, and the confidence in the stress analysis output depends on the model validation, the objective of the present study was to develop a unique finite element model of the lumbosacral junction. The clinically applicable model was validated throughout the entire nonlinear range. It was developed using computed tomography scans, subjected to flexion and extension, and left and right lateral bending loads, and quantitatively validated with cumulative variance analyses. Validation results for each loading mode and for each motion segment (L4-L5, L5-S1) and bisegment (L4-S1) are presented in the paper.

Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus

BACKGROUND

Major deficits of many finite element models of the lumbar spine are the oversimplification, assumed constellation of the material properties or the insufficiently performed calibration using experimental in vitro data. The aim of this study was, to develop a method for calibrating the two-composite structure of the annulus fibrosus, the ground substance and collagen fibers.

METHODS

For that purpose, a three-dimensional, non-linear finite element model of a denucleated intervertebral disc with the adjacent vertebral bodies (L4-L5) was created. Previously performed in vitro experiments provided experimental data for the range of motion in each load direction, needed for calibration. A method was developed to determine the individual contribution of the fibers and the ground substance for bending moments with four different magnitudes (2.5, 5.0, 7.5 and 10 Nm). For each bending moment, the stiffness of fibers was varied to approximate the Young's modulus of the ground substance in order to fulfil the required range of motion obtained from in vitro results within an accuracy of 99%.

RESULTS

Infinite material parameter combinations of collagen fibers and ground substance led to the same range of motion, which were different for each bending moment. However, there was only one combination, which was valid for all applied bending moments; and in all load direction.

INTERPRETATION

This calibration method was performed on range of motion data; however, the procedure could also be applied to other loading scenarios and measurement parameters like disc bulge, translation and intradiscal pressure.

A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage

Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile-compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.

Effects of fusion-bone stiffness on the mechanical behavior of the lumbar spine after vertebral body replacement

BACKGROUND

Implants for vertebral body replacement are often inserted together with an additional stabilizing implant, e.g. an internal fixation device. During implantation bone grafts or milled bone is normally added to the anterior implant. Little is known about the stiffening effect of this fusion-bone mass on the mechanical behavior of the corresponding bone region, including the load distribution between the different parts.

METHODS

A three-dimensional finite element model of the lumbar spine was created with a vertebral body replacement at L3, a paired internal fixation device between L2 and L4, and left anterolateral fusion bone. The elastic modulus of fusion bone was varied in discrete steps between 0 MPa and 10,000 MPa. The model was loaded to simulate standing, 20 degrees flexion, 15 degrees extension and 6 degrees axial rotation in the lumbar spine.

FINDINGS

The elastic modulus of fusion bone has a considerable effect on the compressive force on vertebral body replacement and fusion bone for all loading cases studied. For extension, it also affects intersegmental rotation, the force in the erector spinae muscle, the compressive force on the internal fixator and intradiscal pressure in the adjacent discs. The elastic modulus most strongly affects the different parameters at values between 0 MPa and 500 MPa.

INTERPRETATION

Adding bone mass during vertebral body replacement reduces the loads on the ventral implant for all loading cases studied but extension when the fusion-bone stiffens. This protects the implant from fatigue. The load on the fusion bone increases with increasing elastic modulus. Thus bone grafts should be used whenever possible.

Finite element study of a novel intervertebral disc substitute

STUDY DESIGN

A new type of composite device with a similar structure to a natural lumbar intervertebral disc was modeled, and its mechanical interaction with a L3-L5 lumbar spine segment was studied by a finite element analysis.

OBJECTIVE

To identify the influence of the prosthesis on the biomechanical changes induced in a L3-L4 lumbar spine segment model after having substituted the physiologic L4-L5 intervertebral disc by the implant.

SUMMARY OF BACKGROUND DATA

In our societies, the large number of back pain cases highly motivates the investigation of intervertebral disc prostheses. Postoperative complications induced by spinal fusion showed that the mechanical properties of the novel components and its interactivity with the rest of the spine are a critical point.

METHODS

The prosthesis replaced the L4-L5 intervertebral disc within a previously developed L3-L5 lumbar spine segment physiologic model. The effect of loads in compression, flexion, extension, and axial rotation was simulated, and two types of vertebrae-implant contact were compared to the physiologic model.

RESULTS

Models with disc substitute are much stiffer than the physiologic model. In case of perfect contact with the adjacent vertebrae, the implant behaves like a physiologic intervertebral disc and respects the surrounding motion segment biomechanics. Although no traumatic loads were calculated within the adjacent vertebrae, bone remodeling would be expected in the trabecular bone.

CONCLUSION

By using numerical methods, this study allows prediction of the static mechanical behavior of a new device within a lumbar spine structure, which appears very useful for preclinical study.

Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method

Compared to a healthy intervertebral disc, the geometry and the material properties of the involved tissues are altered in a degenerated disc. It is not completely understood how this affects the mechanical behaviour of a motion segment. In order to study the influence of disc degeneration on motion segment mechanics a three-dimensional, nonlinear finite element model of the L3/L4 functional unit was used. Different grades of disc degeneration were simulated by varying disc height and bulk modulus of the nucleus pulposus. The model was loaded with pure moments of 10Nm in the three main anatomic planes. The finite element model predicted the same trends for intersegmental rotation and intradiscal pressure as described in the literature for in vitro studies. A comparison between calculated intersegmental rotation and experimental data showed a mean difference of 1.9 degrees while the mean standard deviation was 2.5 degrees . A mildly degenerated disc increases intersegmental rotation for all loading cases. With further increasing disc degeneration intersegmental rotation is decreased. For axial rotation the decrease takes place in the final stage. Intradiscal pressure is lower while facet joint force and maximum von Mises stress in the annulus are higher in a degenerated compared to a healthy disc.

Anisotropic elasto-damage constitutive model for the biomechanical analysis of tendons

The aim of this work is to investigate the instantaneous mechanical response of tendons by the use of an anisotropic elasto-damage constitutive model. This study addresses the analysis of the mechanical behaviour of healthy tendons during physiological loading and to degeneration phenomena. These are correlated with aging or traumatic events such as chronic or acute overloading during sporting activities. Histo-morphometric considerations suggest the adoption of a transversally isotropic constitutive model that describes the anisotropy of the material. The non-linearity of its overall mechanical response is taken into account by using a hyperelastic approach and also evaluates softening behaviour related to damage phenomena. The values of the parameters adopted within the analytical model are estimated both for human tendons previously subjected to cyclical loading and for specimens not subjected to cyclical loading. The results obtained by adopting this analytical model are compared with the experimental data in order to evaluate the capability of the model to describe the mechanical response of the tissue.

Role of facet curvature for accurate vertebral facet load analysis

The curvature of vertebral facet joints may play an important role in the study of load-bearing characteristics and clinical interventions such as graded facetectomy. In previously-published finite element simulations of this procedure, the curvature was either neglected or approximated with a varying degree of accuracy. Here we study the effect of the curvature in three different load situations by using a numerical model which is able to represent the actual curvature without any loss of accuracy. The results show that previously-used approximations of the curvature lead to good results in the analysis of sagittal moment/rotation. However, for sagittal shear-force/displacement and for the contact stress distribution, previous results deviate significantly from our results. These findings are supported through related convergence studies. Hence we can conclude that in order to obtain reliable results for the analysis of sagittal shear-force/displacement and the contact stress distribution in the facet joint, the curvature must not be neglected. This is of particular importance for the numerical simulation of the spine, which may lead to improved diagnostics, effective surgical planning and intervention. The proposed method may represent a more reliable basis for optimizing the biomedical engineering design for tissue engineering or, for example, for spinal implants.

Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus

Intervertebral disc degeneration results in disorganization of the laminate structure of the annulus that may arise from mechanical microfailure. Failure mechanisms in the annulus were investigated using composite lamination theory and other analyses to calculate stresses in annulus layers, interlaminar shear stress, and the region of stress concentration around a fiber break. Scanning electron microscopy (SEM) was used to evaluate failure patterns in the annulus and evaluate novel structural features of the disc tissue. Stress concentrations in the annulus due to an isolated fiber break were localized to approximately 5 microm away from the break, and only considered a likely cause of annulus fibrosus failure (i.e., radial tears in the annulus) under extreme loading conditions or when collagen damage occurs over a relatively large region. Interlaminar shear stresses were calculated to be relatively large, to increase with layer thickness (as reported with degeneration), and were considered to be associated with propagation of circumferential tears in the annulus. SEM analysis of intervertebral disc annulus fibrosus tissue demonstrated a clear laminate structure, delamination, matrix cracking, and fiber failure. Novel structural features noted with SEM also included the presence of small tubules that appear to run along the length of collagen fibers in the annulus and a distinct collagenous structure representative of a pericellular matrix in the nucleus region.

A finite element model of the L4–L5 spinal motion segment: biomechanical compatibility of an interspinous device

The biomechanical compatibility of an interspinous device, used for the "dynamic stabilization" of a diseased spinal motion segment, was investigated. The behaviour of an implant made of titanium based alloy (Ti6Al4V) and that of an implant made of a super-elastic alloy (Ni-Ti) have been compared. The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitable constitutive laws have been adopted for the annulus fibrosus and for the metal alloys. The model was aimed at simulating the healthy, the nucleotomized and the treated L4-L5 lumbar segment, subjected to compressive force and flexion-extension as well as lateral flexion moments. The computational model has shown that both the implants were able to achieve their main design purpose, which is to diminish the forces acting on the apophyseal joints. Nevertheless, the Ni-Ti implant has shown a more physiological flexural stiffness with respect to the Ti6Al4V implant, which exhibited an excessive stiffness and permanent strains (plastic strains), even under physiological loads. The computational models presented in this paper seems to be a promising tool able to predict the effectiveness of a biomedical device and to select the materials to be used for the implant manufacturing, within an engineering approach to the clinical problem of the spinal diseases.

Effect of an interspinous implant on loads in the lumbar spine / Einfluss eines interspinösen Implantats auf die Belastungen der Lendenwirbelsäule

Interspinous process implants are increasingly used to treat canal stenoses. Little information exists about the effects of implant height and stiffness on the biomechanical behavior of the lumbar spine. Therefore, a three-dimensional nonlinear finite element model of the osseoligamentous lumbar spine (L1 to L5) was created with a slightly degenerated disc at L3/L4. An interspinous implant was inserted at that segment. Implants with different heights and stiffnesses were studied. The model was loaded with the upper body weight and muscle forces to simulate walking and 25 degrees extension. Implant forces are influenced strongly by the height and negligibly by the elastic modulus of the implant. Intersegmental rotation at implant level is markedly reduced, while intradiscal pressure is slightly increased. Implant size and stiffness have only a minor effect on intradiscal pressure. The maximum von Mises stress in the vertebral arch is strongly increased by the implant.

Single lamellar mechanics of the human lumbar anulus fibrosus

The mechanical behavior of the entire anulus fibrosus is determined essentially by the tensile properties of its lamellae, their fiber orientations, and the regional variation of these quantities. Corresponding data are rare in the literature. The paper deals with an in vitro study of single lamellar anulus lamellae and aims to determine (i) their tensile response and regional variation, and (ii) the orientation of lamellar collagen fibers and their regional variation. Fresh human body-disc-body units (L1-L2, n=11) from cadavers were cut midsagittally producing two hemidisc units. One hemidisc was used for the preparation of single lamellar anulus specimens for tensile testing, while the other one was used for the investigation of the lamellar fiber orientation. Single lamellar anulus specimens with adjacent bone fragments were isolated from four anatomical regions: superficial and deep lamellae (3.9+/-0.21 mm, mean +/- SD, apart from the outer boundary surface of the anulus fibrosus) at ventro-lateral and dorsal positions. The specimens underwent cyclic uniaxial tensile tests at three different strain rates in 0.15 mol/l NaCl solution at 37 degrees C, whereby the lamellar fiber direction was aligned with the load axis. For the characterization of the tensile behavior three moduli were calculated: E(low) (0-0.1 MPa), E(medium) (0.1-0.5 MPa) and E(high) (0.5-1 MPa). Additionally, specimens were tested with the load axis transverse to the fiber direction. From the second hemidisc fiber angles with respect to the horizontal plane were determined photogrammetrically from images taken at six circumferential positions from ventral to dorsal and at three depth levels. Tensile moduli along the fiber direction were in the range of 28-78 MPa (regional mean values). Superficial lamellae have larger E(medium) (p=0.017) and E(high) (p=0.012) than internal lamellae, and the mean value of superficial lamellae is about three times higher than that of deep lamellae. Tensile moduli of ventro-lateral lamellae do not differ significantly from the tensile moduli of dorsal lamellae, and E(low) is generally indifferent with respect to the anatomical region. Tensile moduli transverse to the fiber direction were about two orders of magnitude smaller (0.22+/-0.2 MPa, mean +/- SD, n=5). Tensile properties are not correlated significantly with donor age. Only small viscoelastic effects were observed. The regional variation of lamellar fiber angle phi is described appropriately by a regression line |phi|=23.2 + 0.130 x alpha (r(2)=0.55, p<0.001), where alpha is the polar angle associated with the circumferential position. The single anulus lamella may be seen as the elementary structural unit of the anulus fibrosus, and exhibits marked anisotropy and distinct regional variation of tensile properties and fiber angles. These features must be considered for appropriate physical and numerical modeling of the anulus fibrosus.

Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus

The physical properties of the annulus fibrosus are critical to the intervertebral disc's biomechanical function; alterations with degeneration and aging can contribute directly to joint dysfunction and pain. A constitutive model that links the mechanical structure of the annulus to its material properties is important for many bioengineering purposes. To this end, we developed a strain energy function with separate terms to represent the matrix, the fibers, and the interactions between the constituents. Additionally, we measured the tensile and compressive stress-strain response of the annulus in the circumferential direction. We simultaneously applied the strain energy function to these new data and to data from a wide range of experimental protocols reported in the literature. By choosing experimental protocols that use an unloaded reference configuration, we developed a comprehensive formulation for the multiaxial annular elastic behavior. As a partial validation, this formulation predicted experimental results that were not included in model parameter specification. We anticipate that this constitutive formulation will be useful for computational simulations of the disc's biomechanical response and for elucidating structure-function relationships of the annulus fibrosus.