A biochemical/biophysical 3D FE intervertebral disc model

Biphasic Properties of PVAH (Polyvinyl Alcohol Hydrogel) Reflecting Biomechanical Behavior of the Nucleus Pulposus of the Human Intervertebral Disc

PVAH is a mixture of solid and fluid, but its mechanical behavior has usually been described using solid material models. The purpose of this study was to obtain material properties that can reflect the mechanical behavior of polyvinyl alcohol hydrogel (PVAH) using finite element analysis, a biphasic continuum model, and to optimize the composition ratio of PVAH to replace the nucleus pulposus (NP) of the human intervertebral disc. Six types of PVAH specimens (3, 5, 7, 10, 15, 20 wt%) were prepared, then unconfined compression experiments were performed to acquire their material properties using the Holmes–Mow biphasic model. With an increasing weight percentage of PVA in PVAH, the Young’s modulus increased while the permeability parameter decreased. The Young’s modulus and permeability parameter were similar to those of the NP at 15 wt% and 20 wt%. The range of motion, facet joint force, and NP pressures measured from dynamic motional analysis of the lumbar segments with the NP model also exhibited similar values to those with 15~20 wt% PVAH models. Considering the structural stability and pain of the lumbar segments, it appears that 20 wt% PVAH is most suitable for replacing the NP.

Linear and Nonlinear Biphasic Mechanical Properties of Goat IVDs Under Different Swelling Conditions in Confined Compression

To define technical specifications for artificial substitutes, it is necessary to model their mechanical behaviour. Here we studied the linear and nonlinear biphasic models for Nucleus Pulposus (NP) and Annulus Fibrosus (AF). The associated material parameters were obtained using confined compression stress relaxation tests on goat intervertebral disc (IVD) samples. The first parameter, aggregate modulus H_A0, which essentially describes load-bearing capacity of the solid phase, was larger for AF (H_A0 = 0.53 ± 0.06 MPa) than for NP (H_A0 = 0.26 ± 0.04 MPa). For hydraulic permeability, which quantifies the ability to transmit interstitial fluid, it was the opposite (k₀ = (0.20 ± 0.07) × 10^-15 m⁴/Ns for AF and k₀ = (0.67 ± 0.08)×10^-15 m⁴/Ns for NP). The values of nonlinearity coefficients, nonlinear stiffening coefficient β and non-dimensional nonlinear permeability coefficient M, reflected that these tissues had nonlinear elastic behaviour and permeability. Also, investigating the effect of swelling conditions in sample preparation showed that for both AF and NP, confined-swollen samples had higher aggregate modulus and lower permeability values compared to the free-swollen ones. The quantitative description of the nonlinear properties of AF and NP provided a better understanding of IVD behaviour as well as technical specifications for their artificial substitutes.

Biomechanical Investigation Between Rigid and Semirigid Posterolateral Fixation During Daily Activities: Geometrically Parametric Poroelastic Finite Element Analyses

While spinal fusion using rigid rods remains the gold standard treatment modality for various lumbar degenerative conditions, its adverse effects, including accelerated adjacent segment disease (ASD), are well known. In order to better understand the performance of semirigid constructs using polyetheretherketone (PEEK) in fixation surgeries, the objective of this study was to analyze the biomechanical performance of PEEK versus Ti rods using a geometrically patient-specific poroelastic finite element (FE) analyses. Ten subject-specific preoperative models were developed, and the validity of the models was evaluated with previous studies. Furthermore, FE models of those lumbar spines were regenerated based on postoperation images for posterolateral fixation at the L4–L5 level. Biomechanical responses for instrumented and adjacent intervertebral discs (IVDs) were analyzed and compared subjected to static and cyclic loading. The preoperative model results were well comparable with previous FE studies. The PEEK construct demonstrated a slightly increased range of motion (ROM) at the instrumented level, but decreased ROM at adjacent levels, as compared with the Ti. However, no significant changes were detected during axial rotation. During cyclic loading, disc height loss, fluid loss, axial stress, and collagen fiber strain in the adjacent IVDs were higher for the Ti construct when compared with the intact and PEEK models. Increased ROM, experienced stress in AF, and fiber strain at adjacent levels were observed for the Ti rod group compared with the intact and PEEK rod group, which can indicate the risk of ASD for rigid fixation. Similar to the aforementioned pattern, disc height loss and fluid loss were significantly higher at adjacent levels in the Ti rod group after cycling loading which alter the fluid–solid interaction of the adjacent IVDs. This phenomenon debilitates the damping quality, which results in disc disability in absorbing stress. Such finding may suggest the advantage of using a semirigid fixation system to decrease the chance of ASD.

Computational Challenges in Tissue Engineering for the Spine

This paper deals with a brief review of the recent developments in computational modelling applied to innovative treatments of spine diseases. Additionally, it provides a perspective on the research directions expected for the forthcoming years. The spine is composed of distinct and complex tissues that require specific modelling approaches. With the advent of additive manufacturing and increasing computational power, patient-specific treatments have moved from being a research trend to a reality in clinical practice, but there are many issues to be addressed before such approaches become universal. Here, it is identified that the major setback resides in validation of these computational techniques prior to approval by regulatory agencies. Nevertheless, there are very promising indicators in terms of optimised scaffold modelling for both disc arthroplasty and vertebroplasty, powered by a decisive contribution from imaging methods.

Multiscale Regulation of the Intervertebral Disc: Achievements in Experimental, In Silico, and Regenerative Research

Intervertebral disc (IVD) degeneration is a major risk factor of low back pain. It is defined by a progressive loss of the IVD structure and functionality, leading to severe impairments with restricted treatment options due to the highly demanding mechanical exposure of the IVD. Degenerative changes in the IVD usually increase with age but at an accelerated rate in some individuals. To understand the initiation and progression of this disease, it is crucial to identify key top-down and bottom-up regulations' processes, across the cell, tissue, and organ levels, in health and disease. Owing to unremitting investigation of experimental research, the comprehension of detailed cell signaling pathways and their effect on matrix turnover significantly rose. Likewise, in silico research substantially contributed to a holistic understanding of spatiotemporal effects and complex, multifactorial interactions within the IVD. Together with important achievements in the research of biomaterials, manifold promising approaches for regenerative treatment options were presented over the last years. This review provides an integrative analysis of the current knowledge about (1) the multiscale function and regulation of the IVD in health and disease, (2) the possible regenerative strategies, and (3) the in silico models that shall eventually support the development of advanced therapies.

Application of Simulation Methods in Cervical Spine Dynamics

Neck injury is one of the most frequent spine injuries due to the complex structure of the cervical spine. The high incidence of neck injuries in collision accidents can bring a heavy economic burden to the society. Therefore, knowing the potential mechanisms of cervical spine injury and dysfunction is significant for improving its prevention and treatment. The research on cervical spine dynamics mainly concerns the fields of automobile safety, aeronautics, and astronautics. Numerical simulation methods are beneficial to better understand the stresses and strains developed in soft tissues with investigators and have been roundly used in cervical biomechanics. In this article, the simulation methods for the development and application of cervical spine dynamic problems in the recent years have been reviewed. The study focused mainly on multibody and finite element models. The structure, material properties, and application fields, especially the whiplash injury, were analyzed in detail. It has been shown that simulation methods have made remarkable progress in the research of cervical dynamic injury mechanisms, and some suggestions on the research of cervical dynamics in the future have been proposed.

A biomechanical investigation of thoracolumbar burst fracture under vertical impact loads using finite element method

BACKGROUND

A sudden vertical impact load on spine can cause spinal burst fracture, especially in the thoracolumbar junction region. This study aimed at investigating the mechanism of spinal burst fracture under different energy vertical impact loads, producing the failure risk region to understand burst fracture, reducing nervous system damage and guiding clinical treatment.

METHODS

A nonlinear finite element model of T12-L1 motion segment was created to analyze the response of the vertical impact load. A rigid ball was used to impact the segment vertically to simulate the vertical impact load in practice. There were three different mass balls to represent the different loads: low energy, intermediate energy and high energy (respectively 13 J, 30 J and 56 J). The results of impact force, vertical displacement, stress, intradiscal pressure and contact force were obtained during the process.

FINDINGS

At low energy condition, the rigid ball rebounded rapidly. At intermediate energy condition, fractures were initiated in vertebral foramen and left rear regions on the superior cortical bone near the superior endplate of L1. At high energy condition, burst fracture occurred and a part of L1 was isolated from the model.

INTERPRETATION

The fracture occurred on the L1 segment only at the intermediate energy and high energy. The strength of vertebral body under low and intermediate energy was enough to support the impact. The burst fracture pattern at high energy was also observed in clinical practice. The findings may explain the mechanism of burst fracture.

Mapping of Intervertebral Disk Annulus Fibrosus Compressive Properties Is Sensitive to Specimen Boundary Conditions

Predicting the mechanical behavior of the intervertebral disk (IVD) in health and in disease requires accurate spatial mapping of its compressive mechanical properties. Previous studies confirmed that residual strains in the annulus fibrosus (AF) of the IVD, which result from nonuniform extracellular matrix deposition in response to in vivo loads, vary by anatomical regions (anterior, posterior, and lateral) and zones (inner, middle, and outer). We hypothesized that as the AF is composed of a nonlinear, anisotropic, viscoelastic material, the state of residual strain in the transverse plane would influence the apparent values of axial compressive properties. To test this hypothesis, axial creep indentation tests were performed, using a 1.6 mm spherical probe, at nine different anatomical locations on bovine caudal AFs in both the intact (residual strain present) and strain relieved states. The results showed a shift toward increased spatial homogeneity in all measured parameters, particularly instantaneous strain. This shift was not observed in control AFs, which were tested twice in the intact state. Our results confirm that time-dependent axial compressive properties of the AF are sensitive to the state of residual strain in the transverse plane, to a degree that is likely to affect whole disk behavior.

Numerical Prediction of the Mechanical Failure of the Intervertebral Disc under Complex Loading Conditions

Finite element modeling has been widely used to simulate the mechanical behavior of the intervertebral disc. Previous models have been generally limited to the prediction of the disc behavior under simple loading conditions, thus neglecting its response to complex loads, which may induce its failure. The aim of this study was to generate a finite element model of the ovine lumbar intervertebral disc, in which the annulus was characterized by an anisotropic hyperelastic formulation, and to use it to define which mechanical condition was unsafe for the disc. Based on published in vitro results, numerical analyses under combined flexion, lateral bending, and axial rotation with a magnitude double that of the physiological ones were performed. The simulations showed that flexion was the most unsafe load and an axial tensile stress greater than 10 MPa can cause disc failure. The numerical model here presented can be used to predict the failure of the disc under all loading conditions, which may support indications about the degree of safety of specific motions and daily activities, such as weight lifting.

Effect of Interbody Fusion on the Remaining Discs of the Lumbar Spine in Subjects with Disc Degeneration

OBJECTIVE

To study effects (stress loads) of lumbar fusion on the remaining segments (adjacent or not) of the lumbar spine in the setting of degenerated adjacent discs.

METHODS

A lumbar spine finite element model was built and validated. The full model of the lumbar spine was a parametric finite element model of segments L 1-5 . Numerous hypothetical combinations of one-level lumbar spine fusion and one-level disc degeneration were created. These models were subjected to 10 Nm flexion and extension moments and the stresses on the endplates and consequently on the intervertebral lumbar discs measured. These values were compared to the stresses on healthy lumbar spine discs under the same load and fusion scenarios.

RESULTS

Increased stress at endplates was observed only in the settings of L4-5 fusion and L3-4 disc degeneration (8% stress elevation at L2,3 in flexion or extension, and 25% elevation at L3,4 in flexion only). All other combinations showed less endplate stress than did the control model. For fusion at L3-4 and degeneration at L4-5 , the stresses in the endplates at the adjacent level inferior to the fused disc decreased for both loading disc height reductions. Stresses in flexion decreased after fusion by 29.5% and 25.8% for degeneration I and II, respectively. Results for extension were similar. For fusion at L2-3 and degeneration at L4-5 , stresses in the endplates decreased more markedly at the degenerated (30%), than at the fused level (14%) in the presence of 25% disc height reduction and 10 Nm flexion, whereas in extension stresses decreased more at the fused (24.3%) than the degenerated level (5.86%). For fusion at L3-4 and degeneration at L2-3 , there were no increases in endplate stress in any scenario. For fusion at L4-5 and degeneration at L3-4 , progression of degeneration from I to II had a significant effect only in flexion. A dramatic increase in stress was noted in the endplates of the degenerated disc (L3-4 ) in flexion for degeneration II.

CONCLUSIONS

Stresses are greater in flexion at the endplates of L3-4 and in flexion and extension at L2-3 in the presence of L3-4 disc disease and L4-5 fusion than in the control group. In all other combinations of fusion and disc disease, endplate stress was less for all levels tested than in the control model.

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.

Moderately Degenerated Human Intervertebral Disks Exhibit a Less Geometrically Specific Collagen Fiber Orientation Distribution

STUDY DESIGN

Collagen fiber orientation analysis in moderately degenerated human cadaveric annulus fibrosus (AF) tissue samples.

OBJECTIVE

Little is known about the changes in tissue architecture during early degeneration of intervertebral disks (IVDs). As collagen organization strongly affects the disk function, the objective of this study was to quantify the AF collagen orientation and its spatial distribution in moderately degenerated IVDs (Pfirrmann grade III).

METHODS

AF tissue samples were dissected from four circumferential (anterior, left and right lateral, and posterior) and two radial (outer and inner) locations. Cryosections were imaged using Second Harmonic Generation microscopy, and the collagen fiber orientations per location were determined utilizing a fiber-tracking image analysis algorithm. Also, the proportionality between the fibers aligned in the primary direction versus other oriented fibers was determined.

RESULTS

Mean collagen fiber angles ranged between 21 and 31 degrees for outer and 15 to 19 degrees for inner AF samples. Mean collagen orientations at circumferential locations were only significantly different from each other at inner anterior and lateral location. Similarly, fiber angles between the outer and inner AF were not significantly different except at the posterior location. Fiber orientation proportionality did not show large variations. Except for a significant difference in outer AF proportionality between posterior and lateral positions, no other differences were observed.

CONCLUSION

The results of this study provide the first quantitative evidence that the collagen fiber orientation of moderately degenerated disks exhibits a spatial rather than homogeneous distribution and typical collagen orientation gradients characterizing healthy IVDs are only partially retained.

A database of lumbar spinal mechanical behavior for validation of spinal analytical models

Data from two experimental studies with eight specimens each of spinal motion segments and/or intervertebral discs are presented in a form that can be used for comparison with finite element model predictions. The data include the effect of compressive preload (0, 250 and 500N) with quasistatic cyclic loading (0.0115Hz) and the effect of loading frequency (1, 0.1, 0.01 and 0.001Hz) with a physiological compressive preload (mean 642N). Specimens were tested with displacements in each of six degrees of freedom (three translations and three rotations) about defined anatomical axes. The three forces and three moments in the corresponding axis system were recorded during each test. Linearized stiffness matrices were calculated that could be used in multi-segmental biomechanical models of the spine and these matrices were analyzed to determine whether off-diagonal terms and symmetry assumptions should be included. These databases of lumbar spinal mechanical behavior under physiological conditions quantify behaviors that should be present in finite element model simulations. The addition of more specimens to identify sources of variability associated with physical dimensions, degeneration, and other variables would be beneficial. Supplementary data provide the recorded data and Matlab® codes for reading files. Linearized stiffness matrices derived from the tests at different preloads revealed few significant unexpected off-diagonal terms and little evidence of significant matrix asymmetry.

An Anisotropic Multiphysics Model for Intervertebral Disk

Intervertebral disk (IVD) is the largest avascular structure in human body, consisting of three types of charged hydrated soft tissues. Its mechanical behavior is nonlinear and anisotropic, due mainly to nonlinear interactions among different constituents within tissues. In this study, a more realistic anisotropic multiphysics model was developed based on the continuum mixture theory and employed to characterize the couplings of multiple physical fields in the IVD. Numerical simulations demonstrate that this model is capable of systematically predicting the mechanical and electrochemical signals within the disk under various loading conditions, which is essential in understanding the mechanobiology of IVD.

A computational spinal motion segment model incorporating a matrix composition-based model of the intervertebral disc

The extracellular matrix of the intervertebral disc is subjected to changes with age and degeneration, affecting the biomechanical behaviour of the spine. In this study, a finite element model of a generic spinal motion segment that links spinal biomechanics and intervertebral disc biochemical composition was developed. The local mechanical properties of the tissue were described by the local matrix composition, i.e. fixed charge density, amount of water and collagen and their organisation. The constitutive properties of the biochemical constituents were determined by fitting numerical responses to experimental measurements derived from literature. This general multi-scale model of the disc provides the possibility to evaluate the relation between local disc biochemical composition and spinal biomechanics.

On the Use of Biaxial Properties in Modeling Annulus as a Holzapfel-Gasser-Ogden Material

Besides the biology, stresses and strains within the tissue greatly influence the location of damage initiation and mode of failure in an intervertebral disk. Finite element models of a functional spinal unit (FSU) that incorporate reasonably accurate geometry and appropriate material properties are suitable to investigate such issues. Different material models and techniques have been used to model the anisotropic annulus fibrosus, but the abilities of these models to predict damage initiation in the annulus and to explain clinically observed phenomena are unclear. In this study, a hyperelastic anisotropic material model for the annulus with two different sets of material constants, experimentally determined using uniaxial and biaxial loading conditions, were incorporated in a 3D finite element model of a ligamentous FSU. The purpose of the study was to highlight the biomechanical differences (e.g., intradiscal pressure, motion, forces, stresses, strains, etc.) due to the dissimilarity between the two sets of material properties (uniaxial and biaxial). Based on the analyses, the biaxial constants simulations resulted in better agreements with the in vitro and in vivo data, and thus are more suitable for future damage analysis and failure prediction of the annulus under complex multiaxial loading conditions.

On the relative relevance of subject-specific geometries and degeneration-specific mechanical properties for the study of cell death in human intervertebral disk models

Capturing patient- or condition-specific intervertebral disk (IVD) properties in finite element models is outmost important in order to explore how biomechanical and biophysical processes may interact in spine diseases. However, disk degenerative changes are often modeled through equations similar to those employed for healthy organs, which might not be valid. As for the simulated effects of degenerative changes, they likely depend on specific disk geometries. Accordingly, we explored the ability of continuum tissue models to simulate disk degenerative changes. We further used the results in order to assess the interplay between these simulated changes and particular IVD morphologies, in relation to disk cell nutrition, a potentially important factor in disk tissue regulation. A protocol to derive patient-specific computational models from clinical images was applied to different spine specimens. In vitro, IVD creep tests were used to optimize poro-hyperelastic input material parameters in these models, in function of the IVD degeneration grade. The use of condition-specific tissue model parameters in the specimen-specific geometrical models was validated against independent kinematic measurements in vitro. Then, models were coupled to a transport-cell viability model in order to assess the respective effects of tissue degeneration and disk geometry on cell viability. While classic disk poro-mechanical models failed in representing known degenerative changes, additional simulation of tissue damage allowed model validation and gave degeneration-dependent material properties related to osmotic pressure and water loss, and to increased fibrosis. Surprisingly, nutrition-induced cell death was independent of the grade-dependent material properties, but was favored by increased diffusion distances in large IVDs. Our results suggest that in situ geometrical screening of IVD morphology might help to anticipate particular mechanisms of disk degeneration.

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.

Human L3L4 intervertebral disc mean 3D shape, modes of variation, and their relationship to degeneration

Intervertebral disc mechanics are affected by both disc shape and disc degeneration, which in turn each affect the other; disc mechanics additionally have a role in the etiology of disc degeneration. Finite element analysis (FEA) is a favored tool to investigate these relationships, but limited data for intervertebral disc 3D shape has forced the use of simplified or single-subject geometries, with the effect of inter-individual shape variation investigated only in specialized studies. Similarly, most data on disc shape variation with degeneration is based on 2D mid-sagittal images, which incompletely define 3D shape changes. Therefore, the objective of this study was to quantify inter-individual disc shape variation in 3D, classify this variation into independently-occurring modes using a statistical shape model, and identify correlations between disc shape and degeneration. Three-dimensional disc shapes were obtained from MRI of 13 human male cadaver L3L4 discs. An average disc shape and four major modes of shape variation (representing 90% of the variance) were identified. The first mode represented disc axial area and was significantly correlated to degeneration (R(2)=0.44), indicating larger axial area in degenerate discs. Disc height variation occurred in three distinct modes, each also involving non-height variation. The statistical shape model provides an average L3L4 disc shape for FEA that is fully defined in 3D, and makes it convenient to generate a set of shapes with which to represent aggregate inter-individual variation. Degeneration grade-specific shapes can also be generated. To facilitate application, the model is included in this paper׳s supplemental content.

Finite element modeling of soft tissues: material models, tissue interaction and challenges

BACKGROUND

Musculoskeletal soft tissues, such as articular cartilage, ligaments, knee meniscus and intervertebral disk, have a complex structure, which provides elasticity and capability to support and distribute the body loads. Soft tissues describe an inhomogeneous and multiphasic structure, and exhibit a nonlinear, time-dependent behavior. Their mechanical response is governed by a substance composed of protein fiber-rich and proteoglycan-rich extracellular matrix and interstitial fluid. Protein fibers (e.g. collagen) give the tissue direction dependent stiffness and strength. To investigate these complex biological systems, the use of mathematical tools is well established, alone or in combination with experimental in vitro and in vivo tests. However, the development of these models poses many challenges due to the complex structure and mechanical response of soft tissues.

METHODS

Non-systematic literature review.

FINDINGS

This paper provides a summary of different modeling strategies with associated material properties, contact interactions between articulating tissues, validation and sensitivity of soft tissues with special focus on knee joint soft tissues and intervertebral disk. Furthermore, it reviews and discusses some salient clinical findings of reported finite element simulations.

INTERPRETATION

Model studies extensively contributed to the understanding of functional biomechanics of soft tissues. Models can be effectively used to elucidate clinically relevant questions. However, users should be aware of the complexity of such tissues and of the capabilities and limitations of these approaches to adequately simulate a specific in vivo or in vitro phenomenon.

Intervertebral disc creep behavior assessment through an open source finite element solver

Degenerative Disc Disease (DDD) is one of the largest health problems faced worldwide, based on lost working time and associated costs. By means of this motivation, this work aims to evaluate a biomimetic Finite Element (FE) model of the Intervertebral Disc (IVD). Recent studies have emphasized the importance of an accurate biomechanical modeling of the IVD, as it is a highly complex multiphasic medium. Poroelastic models of the disc are mostly implemented in commercial finite element packages with limited access to the algorithms. Therefore, a novel poroelastic formulation implemented on a home-developed open source FE solver is briefly addressed throughout this paper. The combination of this formulation with biphasic osmotic swelling behavior is also taken into account. Numerical simulations were devoted to the analysis of the non-degenerated human lumbar IVD time-dependent behavior. The results of the tests performed for creep assessment were inside the scope of the experimental data, with a remarkable improvement of the numerical accuracy when compared with previously published results obtained with ABAQUS(®). In brief, this in-development open-source FE solver was validated with literature experimental data and aims to be a valuable tool to study the IVD biomechanics and DDD mechanisms.

Biomechanical behavior of a biomimetic artificial intervertebral disc

STUDY DESIGN

The biomechanical behavior of a biomimetic artificial intervertebral disc (AID) was characterized in vitro in axial compression and compared with natural disc behavior.

OBJECTIVE

To evaluate the strength and durability of a novel biomimetic AID and to demonstrate whether its axial deformation behavior is similar to that of a natural disc.

SUMMARY OF BACKGROUND DATA

Current clinically used AIDs have reasonable success rates. However, because of their nonphysiological design, spinal mechanics are altered. To avoid long-term complications, a novel biomimetic AID, with a nucleus-annulus structure and osmotic swelling properties has been developed.

METHODS

Eighteen AIDs in total were tested in axial compression. Six were loaded monotonically to determine strength. Six were tested in fatigue (600-6000 N). Another 6 were used to characterize the axial creep and dynamic behavior (0.01-10 Hz). Creep and dynamic response were also determined for 4 AIDs after fatigue loading.

RESULTS

The AIDs remained intact up to 15 kN and 10 million cycles. The creep and dynamic behavior were similar to the natural disc behavior, except for hysteresis, which was 20% to 30% higher. After fatigue, creep decreased from 4% to 1%, stiffness increased 2-fold, and hysteresis was reduced to that for a normal disc.

CONCLUSION

A strong and durable AID design was introduced. Compared with current clinical articulating AIDs, this biomimetic AID introduces the natural disc annulus-nucleus structure, resulting in axial behavior closer to that of the natural disc.

Large residual strains are present in the intervertebral disc annulus fibrosus in the unloaded state

The intervertebral disc annulus fibrosus (AF) is subjected to high circumferential tensile stresses resulting from nucleus pulposus pressurisation under axial compression. In other pressure containing tissues, such as blood vessel walls, residual compressive stresses along the inside surface of the tissues without pressurisation reduce peak tensile stresses under pressurisation. This study hypothesised that similar patterns of residual stress exist in the annulus fibrosus. Accurate characterisation of residual stresses is essential for both the incorporation of nonlinear material descriptions into models of the disc as well as the design of effective annulus repair strategies. By imaging nine bovine caudal discs before and after the release of residual stresses via incision, we measured a mean residual stretch of 0.86 ± 0.13 at the inner AF and 1.02 ± 0.08 at the outer AF. These stretch values were used to calculate a gradient of residual stress ranging from -230 ± 22 kPa of compression at the inner AF to 54 ± 0.2 kPa of tension at the outer AF. Material models of AF have assumed that the AF was in a stress free reference state when there are no external loads. However, this study documents that there are large residual stresses in the AF even without external loads. The release of residual tension in the outer AF by herniation, needle injection or incisions makes closure difficult and may accelerate degeneration of the surrounding tissue. Retention of these residual stresses may be essential to maintaining disc mechanical function and to producing viable AF repair techniques.

Design of next generation total disk replacements

To improve the treatments for low back pain, new designs of total disk replacement have been proposed. The question is how well these designs can act as a functional replacement of the intervertebral disk. Four finite element models were made, for four different design concepts, to determine how well they can mimic the physiological intervertebral disk mechanical function. The four designs were a homogenous elastomer, a multi-stiffness elastomer, an elastomer with fiber jacket, and a hydrogel with fiber jacket. The best material properties of the four models were determined by optimizing the model behavior to match the behavior of the intervertebral disk in flexion-extension, axial rotation, and lateral bending. It was shown that neither a homogeneous elastomer nor a multi-stiffness elastomer could mimic the non-linear behavior within the physiological range of motion. Including a fiber jacket around an elastomer allowed for physiological motion in all degrees of freedom. Replacing the elastomer by a hydrogel yielded similar good behavior. Mimicking the non-linear behavior of the intervertebral disk, in the physiological range of motion is essential in maintaining and restoring spinal motion and in protecting surrounding tissues like the facet joints or adjacent segments. This was accomplished with designs mimicking the function of the annulus fibrosus.

Biomechanics of intervertebral disk degeneration

Degenerative changes in the material properties of nucleus pulposus and anulus fibrosus promote changes in viscoelastic properties of the whole disc. Volume, pressure and hydration loss in the nucleus pulposus, disk height decreases and fissures in the anulus fibrosus, are some of the signs of the degenerative cascade that advances with age and affect, among others, spinal function and its stability. Much remains to be learned about how these changes affect the function of the motion segment and relate to symptoms such as low back pain and altered spinal biomechanics.

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential-axial and the radial-axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber-matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure-function, and to quantify the effect of degeneration. The biaxial stress-strain response was described well by the model (R (2) > 0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young's modulus, provided an explanation for the low values in previously published axial direction Young's modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.

Comparison of four methods to simulate swelling in poroelastic finite element models of intervertebral discs

Osmotic phenomena influence the intervertebral disc biomechanics. Their simulation is challenging and can be undertaken at different levels of complexity. Four distinct approaches to simulate the osmotic behaviour of the intervertebral disc (a fixed boundary pore pressure model, a fixed osmotic pressure gradient model in the whole disc or only in the nucleus pulposus, and a swelling model with strain-dependent osmotic pressure) were analysed. Predictions were compared using a 3D poroelastic finite element model of a L4-L5 spinal unit under three different loading conditions: free swelling for 8 h and two daily loading cycles: (i) 200 N compression for 8 h followed by 500 N compression for 16 h; (ii) 500 N for 8 h followed by 1000 N for 16 h. Overall, all swelling models calculated comparable results, with differences decreasing under greater loads. Results predicted with the fixed boundary pore pressure and the fixed osmotic pressure in the whole disc models were nearly identical. The boundary pore pressure model, however, cannot simulate differential osmotic pressures in disc regions. The swelling model offered the best potential to provide more accurate results, conditional upon availability of reliable values for the required coefficients and material properties. Possible fields of application include mechanobiology investigations and crack opening and propagation. However, the other approaches are a good compromise between the ease of implementation and the reliability of results, especially when considering higher loads or when the focus is on global results such as spinal kinematics.