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

Global and local identifiability analysis of a nonlinear biphasic constitutive model in confined compression

Application of biomechanical models relies on model parameters estimated from experimental data. Parameter non-identifiability, when the same model output can be produced by many sets of parameter values, introduces severe errors yet has received relatively little attention in biomechanics and is subtle enough to remain unnoticed in the absence of deliberate verification. The present work develops a global identifiability analysis method in which cluster analysis and singular value decomposition are applied to vectors of parameter-output variable correlation coefficients. This method provides a visual representation of which specific experimental design elements are beneficial or harmful in terms of parameter identifiability, supporting the correction of deficiencies in the test protocol prior to testing physical specimens. The method was applied to a representative nonlinear biphasic model for cartilaginous tissue, demonstrating that confined compression data does not provide identifiability for the biphasic model parameters. This result was confirmed by two independent analyses: local analysis of the Hessian of a sum-of-squares error cost function and observation of the behaviour of two optimization algorithms. Therefore, confined compression data are insufficient for the calibration of general-purpose biphasic models. Identifiability analysis by these or other methods is strongly recommended when planning future experiments.

Finite element model reveals the involvement of cartilage endplate in quasi-static biomechanics of intervertebral disc degeneration

Background and objective

The intrinsic link between the compositional and structural attributes and the biomechanical functionality is evident in intervertebral discs. However, it remains unclear from a biomechanical perspective whether cartilage endplate (CEP) degeneration exacerbates intervertebral disc degeneration.

Methods

This study developed and quantitatively validated four biphasic swelling-based finite element models. We then applied four quasi-static tests and simulated daily loading scenarios to examine the effects of CEP degradation.

Results

Under free-swelling conditions, short-term responses were prevalent, with CEP performance changes not significantly impacting response proportionality. The creep test results showed the more than 50 % of the strain was attributed to long-term responses. Stress-relaxation testing indicated that all responses increased with disc degeneration, yet CEP degeneration's impact was minimal. Daily load analyses revealed that disc degeneration significantly reduces nucleus pulposus pressure and disc height, whereas CEP degeneration marginally increases nucleus pressure and slightly decreases disc height.

Conclusions

Glycosaminoglycan content and CEP permeability are critical to the fluid-dependent viscoelastic response of intervertebral discs. Our findings suggest that CEP contributes to disc degeneration under daily loading conditions.

Contact between leaked cement and adjacent vertebral endplate induces a greater risk of adjacent vertebral fracture with vertebral bone cement augmentation biomechanically

BACKGROUND CONTEXT

Adjacent vertebral fracture (AVF) is a frequently observed complication after percutaneous vertebroplasty in patients with osteoporotic vertebral compressive fracture (OVCF). Studies have demonstrated that intervertebral cement leakage (ICL) can increase the incidence of AVF, but others have reached opposite conclusions. The stress concentration initially increases the risk of AVF, and dispersive concentrated stress is the main biomechanical function of the intervertebral disc (IVD).

PURPOSE

This study was designed to validate the hypothesis that direct contact between the leaked cement and adjacent bony endplate (BEP) can inhibit this biomechanical function, trigger adjacent vertebral stress concentration and increase the risk of AVF.

STUDY DESIGN

A retrospective study and corresponding numerical mechanical simulations.

PATIENT SAMPLE

Clinical data from 97 OVCF patients treated by bone cement augmentation operations were reviewed in this study.

OUTCOME MEASURES

Clinical assessments involved measuring ICL and cement-BEP contact status in patients with and without AVF. Numerical simulations were conducted to compute stress values in adjacent vertebral body's BEP and cancellous bone under various body positions.

MATERIALS AND METHODS

Radiographic and demographic data of 97 OVCF patients (with an average follow-up period of 11.5 months) treated using bone cement augmentation operation were reviewed in the present study. The patients were divided into 2 groups: those with AVF and those without AVF. Bone cement leakage status was judged via 2 different methods: with or without IVD cement leakage and with and without adjacent vertebral endplate contact. The data from patients with and without AVF were compared, and the independent risk factors were identified through regression analysis. Patients without IVD cement leakage, with IVD cement leakage but without adjacent vertebral endplate cement contact, and with direct adjacent vertebral endplate cement contact were simulated using a previously constructed and validated lumbar finite element model, and the biomechanical indicators related to the AVF were computed and recorded in these surgical models.

RESULTS

Radiographic analysis revealed that the incidence of AVF was numerically higher, but was not significantly higher in patients with IVD cement leakage. In contrast, patients with direct adjacent vertebral endplate cement contact had a significantly greater incidence of AVF, which has also been proven to be an independent risk factor for AVF. In addition, numerical mechanical simulations revealed an obvious stress concentration tendency (the higher maximum equivalent stress value) in the adjacent vertebral body in the model with endplate cement contact.

CONCLUSION

Direct adjacent vertebral endplate cement contact induces a greater risk of AVF through deterioration of the local biomechanical environment. Cement injection, therefore, should be terminated when IVD cement leakage occurs to reduce adjacent vertebral endplate cement contact and reduce the resulting risk of AVF biomechanics.

Biomechanics of annulus fibrosus: Elastic fiber simplification and degenerative impact on damage initiation and propagation

This study addresses three primary objectives related to lumbar intervertebral disc (IVD) biomechanics under ramping quasi-static loading conditions. First, we explore the conditions justifying the simplification of axisymmetric elastic fiber families into single fiber bundles through discretized strain energy functions. Simulations reveal that a concentration factor exceeding 10 allows for a consistent deviation below 10% between simplified and non-simplified responses. Second, we investigate the impact of elastic fibers on the physiological stiffness in IVDs, revealing minimal influence on biological motions but significant effects on degeneration. Lastly, we examine the initiation and progression of annulus fibrosus (AF) damage. Our findings confirm the validity of simplifying elastic fiber families and underscore the necessity of considering elastic fiber damage in biomechanical studies of AF tissues. Elastic fibers contribute to increased biaxial stretch stiffness, and their damage significantly affects the loading capacity of the inner AF. Additionally, degeneration significantly alters the susceptibility to damage in the AF, with specific regions exhibiting higher vulnerability. Damage tends to extend circumferentially and radially, emphasizing the regional variations in collagen and elastic fiber properties. This study offers useful insights for refining biomechanical models, paving the way for a more comprehensive understanding of IVD responses and potential clinical implications.

Geometric determinants of the mechanical behavior of image-based finite element models of the intervertebral disc

The intervertebral disc is an important structure for load transfer through the spine. Its injury and degeneration have been linked to pain and spinal fractures. Disc injury and spine fractures are associated with high stresses; however, these stresses cannot be measured, necessitating the use of finite element (FE) models. These models should include the disc's complex structure, as changes in disc geometry have been linked to altered mechanical behavior. However, image-based models using disc-specific structures have yet to be established. This study describes a multiphasic FE modeling approach for noninvasive estimates of subject-specific intervertebral disc mechanical behavior based on medical imaging. The models (n = 22) were used to study the influence of disc geometry on the predicted global mechanical response (moments and forces), internal local disc stresses, and tractions at the interface between the disc and the bone. Disc geometry was found to have a strong influence on the predicted moments and forces on the disc (R2 = 0.69-0.93), while assumptions regarding the side curvature (bulge) of the disc had only a minor effect. Strong variability in the predicted internal disc stresses and tractions was observed between the models (mean absolute differences of 5.1%-27.7%). Disc height had a systematic influence on the internal disc stresses and tractions at the disc-to-bone interface. The influence of disc geometry on mechanics highlights the importance of disc-specific modeling to estimate disc injury risk, loading on the adjacent vertebral bodies, and the mechanical environment present in disc tissues.

Effect of patient-specific factors on regeneration in lumbar spine at healthy disc and total disc replacement. Computer simulation

BACKGROUND AND OBJECTIVE

Degenerative diseases of the spine have a negative impact on the quality of life of patients. This study presents the results of numerical modelling of the mechanical behaviour of the lumbar spine with patient-specific conditions at physiological loads. This paper aims to numerically study the influence of degenerative changes in the spine and the presence of an endoprosthesis on the creation of conditions for tissue regeneration.

METHODS

A numerical model of the mechanical behaviour of lumbar spine at healthy and after total disc replacement under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behaviour of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid. The nutritional pathways of the intervertebral disc in cases of healthy and osteoporotic bone tissues were predicted based on the analysis of the simulation results according to the mechanobiological principles.

RESULTS

Simulation of total disc replacement showed that osseointegration of the artificial disc plates occurs only in healthy bone tissue. With total disc replacement in a patient with osteoporosis, there is an area of increased risk of bone resorption in the near-contact area, approximately 1 mm wide, around the fixators. Dynamic loads may improve the osseointegration of the implant in pathological conditions of the bone tissue.

CONCLUSIONS

The results obtained in the case of healthy spine and osteoporotic bone tissues correspond to the experimental data on biomechanics and possible methods of IVD regeneration from the position of mechanobiological principles. The results obtained with an artificial disc (with keel-type fixation) showed that the use of this type of endoprosthesis in healthy bone tissues allows to reproduce the function of the natural intervertebral disc and does not contribute to the development of neoplastic processes. In the case of an artificial disc with osteoporosis of bone tissues, there is a zone with increased risk of tissue resorption and development of neoplastic processes in the area near the contact of the implant attachment. This circumstance can be compensated by increasing the loading level.

Intraoperative capsule protection can reduce the potential risk of adjacent segment degeneration acceleration biomechanically: an in silico study

BACKGROUND

The capsule of the zygapophyseal joint plays an important role in motion segmental stability maintenance. Iatrogenic capsule injury is a common phenomenon in posterior approach lumbar interbody fusion operations, but whether this procedure will cause a higher risk of adjacent segment degeneration acceleration biomechanically has yet to be identified.

METHODS

Posterior lumbar interbody fusion (PLIF) with different grades of iatrogenic capsule injury was simulated in our calibrated and validated numerical model. By adjusting the cross-sectional area of the capsule, different grades of capsule injury were simulated. The stress distribution on the cranial motion segment was computed under different loading conditions to judge the potential risk of adjacent segment degeneration acceleration.

RESULTS

Compared to the PLIF model with an intact capsule, a stepwise increase in the stress value on the cranial motion segment can be observed with a step decrease in capsule cross-sectional areas. Moreover, compared to the difference between models with intact and slightly injured capsules, the difference in stress values was more evident between models with slight and severe iatrogenic capsule injury.

CONCLUSION

Intraoperative capsule protection can reduce the potential risk of adjacent segment degeneration acceleration biomechanically, and iatrogenic capsule damage on the cranial motion segment should be reduced to optimize patients' long-term prognosis.

A Novel Fiber-Reinforced Poroviscoelastic Bovine Intervertebral Disc Finite Element Model for Organ Culture Experiment Simulations

Intervertebral disc (IVD) degeneration and methods for repair and regeneration have commonly been studied in organ cultures with animal IVDs under compressive loading. With the recent establishment of a novel multi-axial organ culture system, accurate predictions of the global and local mechanical response of the IVD are needed for control system development and to aid in experiment planning. This study aimed to establish a finite element model of bovine IVD capable of predicting IVD behavior at physiological and detrimental load levels. A finite element model was created based on the dimensions and shape of a typical bovine IVD used in the organ culture. The nucleus pulposus (NP) was modeled as a neo-Hookean poroelastic material and the annulus fibrosus (AF) as a fiber-reinforced poroviscoelastic material. The AF consisted of 10 lamella layers and the material properties were distributed in the radial direction. The model outcome was compared to a bovine IVD in a compressive stress-relaxation experiment. A parametric study was conducted to investigate the effect of different material parameters on the overall IVD response. The model was able to capture the equilibrium response and the relaxation response at physiological and higher strain levels. Permeability and elastic stiffness of the AF fiber network affected the overall response most prominently. The established model can be used to evaluate the response of the bovine IVD at strain levels typical for organ culture experiments, to define relevant boundaries for such studies, and to aid in the development and use of new multi-axial organ culture systems.

The cranial vertebral body suffers a higher risk of adjacent vertebral fracture due to the poor biomechanical environment in patients with percutaneous vertebralplasty

BACKGROUND CONTEXT

Adjacent vertebral fracture (AVF), a frequent complication of PVP, is influenced by factors such as osteoporosis progression, increased intervertebral cement leakage (ICL), and biomechanical deterioration. Notably, the risk of AVF is notably elevated in the cranial vertebral body compared with the caudal counterpart. Despite this knowledge, the underlying pathological mechanism remains elusive.

PURPOSE

This study delves into the role of biomechanical deterioration as a pivotal factor in the heightened risk of AVF in the cranial vertebral body following PVP. By isolating this variable, we aim to unravel its prominence relative to other potential risk factors.

STUDY DESIGN

A retrospective study and corresponding numerical mechanical simulations.

PATIENT SAMPLE

Clinical data from 101 patients treated by PVP were reviewed in this study.

OUTCOME MEASURES

Clinical assessments involved measuring Hounsfield unit (HU) values of adjacent vertebral bodies as a representation of patients' bone mineral density (BMD). Additionally, the rates of ICL were compared among these patients. Numerical simulations were conducted to compute stress values in the cranial and caudal vertebral bodies under various body positions.

METHODS

In a retrospective analysis of PVP patients spanning July 2016 to August 2019, we scrutinized the HU values of adjacent vertebral bodies to discern disparities in BMD between cranial and caudal regions. Additionally, we compared ICL rates on both cranial and caudal sides. To augment our investigation, well-validated numerical models simulated the PVP procedure, enabling the computation of maximum stress values in cranial and caudal vertebral bodies across varying body positions.

RESULTS

The incidence rate of cranial AVF was significantly higher than the caudal side. No notable distinctions in HU values or ICL rates were observed between the cranial and caudal sides. The incidence of AVF showed no significant elevation in patients with ICL in either region. However, numerical simulations unveiled heightened stress values in the cranial vertebral body.

CONCLUSIONS

In patients postPVP, the cranial vertebral body faces a heightened risk of AVF, primarily attributed to biomechanical deterioration rather than lower BMD or an elevated ICL rate.

Annulus Calibration Increases the Computational Accuracy of the Lumbar Finite Element Model

STUDY DESIGN

Mechanical simulations.

OBJECTIVE

Inadequate calibration of annuli negatively affects the computational accuracy of finite element (FE) models. Specifically, the definition of annulus average radius (AR) does not have uniformity standards. Differences between the elastic moduli in the different layers and parts of the annulus were not fully calibrated when a linear elastic material is used to define its material properties. This study aims to optimize the computational accuracy of the FE model by calibrating the annulus.

METHODS

We calibrated the annulus AR and elastic modulus in our anterior-constructed lumbar model by eliminating the difference between the computed range of motion and that measured by in vitro studies under a flexion-extension loading condition. Multi-indicator validation was performed by comparing the computed indicators with those measured in in vitro studies. The computation time required for the different models has also been recorded to evaluate the computational efficiency.

RESULTS

The difference between computed and measured ROMs was less than 1% when the annulus AR and elastic modulus were calibrated. In the model validation process, all the indicators computed by the calibrated FE model were within ±1 standard deviation of the average values obtained from in vitro studies. The maximum difference between the computed and measured values was less than 10% under nearly all loading conditions. There is no apparent variation tendency for the computational time associated with different models.

CONCLUSION

The FE model with calibrated annulus AR and regional elastic modulus has higher computational accuracy and can be used in subsequent mechanical studies.

On the identification of the ultra-structural organization of elastic fibers and their effects on the integrity of annulus fibrosus

Due to the complicated structure of the elastic fiber network in annulus fibrosus, existing in-silico studies either simplified or just overlooked its distribution pattern. Nonetheless, experimental and simulation results have proven that elastic fibers are of great importance to maintaining the structural integrity of annulus fibrosus and therefore to ensuring the load-bearing ability of intervertebral discs. Such needs call for a fine model. This work aims at developing a biphasic annulus fibrosus model by incorporating the accurate distribution pattern of collagen and elastic fibers. Both the structural parameters and intrinsic mechanical parameters were successfully identified using single lamella and inter-lamella microscopy anatomy and micromechanical testing data. The proposed model was then used to implement finite element simulations on various anterior and posterolateral multi-lamellae annulus fibrosus specimens. In general, simulation results agree well with available experimental and simulation data. On this basis, the effects of elastic fibers on the integrity of annulus fibrosus were further investigated. It was found that elastic fibers significantly influence the free swelling, radial stretching and circumferential shear performances of annulus fibrosus. Nonetheless, no significant effects were found for the circumferential stretching capability. The proposed biphasic model considers for the first time the distribution characteristics of elastic fibers at two scales, including both the principal orientations of all fiber families and the detailed distribution pattern within each family. Better understandings on the functions of collagen and elastic fibers can therefore be realized. To further enhance its prediction capability, the current model can be extended in the future by taking the fiber-matrix interaction as well as progressive damages into consideration.

A swelling-based biphasic analysis on the quasi-static biomechanical behaviors of healthy and degenerative intervertebral discs

BACKGROUND AND OBJECTIVE

The degeneration of intervertebral discs is significantly dependent of the changes in tissue composition ratio and tissue structure. Up to the present, the effects of degeneration on the quasi-static biomechanical responses of discs have not been well understood. The goal of this study is to quantitatively analyze the quasi-static responses of healthy and degenerative discs.

METHODS

Four biphasic swelling-based finite element models are developed and quantitatively validated. Four quasi-static test protocols, including the free-swelling, slow-ramp, creep and stress-relaxation, are implemented. The double Voigt and double Maxwell models are further used to extract the immediate (or residual), short-term and long-term responses of these tests.

RESULTS

Simulation results show that both the swelling-induced pressure in the nucleus pulposus and the initial modulus decrease with degeneration. In the free-swelling test of discs possessing healthy cartilage endplates, simulation results show that over 80% of the total strain is contributed by the short-term response. The long-term response is dominant for discs with degenerated permeability in cartilage endplates. For the creep test, over 50% of the deformation is contributed by the long-term response. In the stress-relaxation test, the long-term stress contribution occupies approximately 31% of total response and is independent of degeneration. Both the residual and short-term responses vary monotonically with degeneration. In addition, both the glycosaminoglycan content and permeability affect the engineering equilibrium time constants of the rheologic models, in which the determining factor is the permeability.

CONCLUSIONS

The content of glycosaminoglycan in intervertebral soft tissues and the permeability of cartilage endplates are two critical factors that affect the fluid-dependent viscoelastic responses of intervertebral discs. The component proportions of the fluid-dependent viscoelastic responses depend also strongly on test protocols. In the slow-ramp test, the glycosaminoglycan content is responsible for the changes of the initial modulus. Since existing computational models simulate disc degenerations only by altering disc height, boundary conditions and material stiffness, the current work highlights the significance of biochemical composition and cartilage endplates permeability in the biomechanical behaviors of degenerated discs.

Will the adjustment of insertional pedicle screw positions affect the risk of adjacent segment diseases biomechanically? An in-silico study

Background

The fixation-induced biomechanical deterioration will increase the risk of adjacent segment diseases (ASD) after lumbar interbody fusion with Bilateral pedicle screw (BPS) fixation. The accurate adjustment of insertional pedicle screw positions is possible, and published studies have reported its mechanical effects. However, no studies clarified that adjusting insertional screw positions would affect the postoperative biomechanical environment and the risk of ASD. The objective of this study was to identify this issue and provide theoretical references for the optimization of insertional pedicle screw position selections.

Methods

The oblique lumbar interbody fusion fixed by BPS with different insertional positions has been simulated in the L4-L5 segment of our previously constructed and validated lumbosacral model. Biomechanical indicators related to ASD have been computed and recorded under flexion, extension, bending, and axial rotation loading conditions.

Results

The change of screw insertional positions has more apparent biomechanical effects on the cranial than the caudal segment. Positive collections can be observed between the reduction of the fixation length and the alleviation of motility compensation and stress concentration on facet cartilages. By contrast, no pronounced tendency of stress distribution on the intervertebral discs can be observed with the change of screw positions.

Conclusions

Reducing the fixation stiffness by adjusting the insertional screw positions could alleviate the biomechanical deterioration and be an effective method to reduce the risk of ASD caused by BPS.

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

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

Development of a Computational Model of the Mechanical Behavior of the L4-L5 Lumbar Spine: Application to Disc Degeneration

Degenerative changes in the lumbar spine significantly reduce the quality of life of people. In order to fully understand the biomechanics of the affected spine, it is crucial to consider the biomechanical alterations caused by degeneration of the intervertebral disc (IVD). Therefore, this study is aimed at the development of a discrete element model of the mechanical behavior of the L4-L5 spinal motion segment, which covers all the degeneration grades from healthy IVD to its severe degeneration, and numerical study of the influence of the IVD degeneration on stress state and biomechanics of the spine. In order to analyze the effects of IVD degeneration on spine biomechanics, we simulated physiological loading conditions using compressive forces. The results of modeling showed that at the initial stages of degenerative changes, an increase in the amplitude and area of maximum compressive stresses in the disc is observed. At the late stages of disc degradation, a decrease in the value of intradiscal pressure and a shift in the maximum compressive stresses in the dorsal direction is observed. Such an influence of the degradation of the geometric and mechanical parameters of the tissues of the disc leads to the effect of bulging, which in turn leads to the formation of an intervertebral hernia.

Deterioration of the fixation segment's stress distribution and the strength reduction of screw holding position together cause screw loosening in ALSR fixed OLIF patients with poor BMD

The vertebral body's Hounsfield unit (HU) value can credibly reflect patients' bone mineral density (BMD). Given that poor bone-screw integration initially triggers screw loosening and regional differences in BMD and strength in the vertebral body exist, HU in screw holding planes should better predict screw loosening. According to the stress shielding effect, the stress distribution changes in the fixation segment with BMD reduction should be related to screw loosening, but this has not been identified. We retrospectively collected the radiographic and demographic data of 56 patients treated by single-level oblique lumbar interbody fusion (OLIF) with anterior lateral single rod (ALSR) screw fixation. BMD was identified by measuring HU values in vertebral bodies and screw holding planes. Regression analyses identified independent risk factors for cranial and caudal screw loosening separately. Meanwhile, OLIF with ALSR fixation was numerically simulated; the elastic modulus of bony structures was adjusted to simulate different grades of BMD reduction. Stress distribution changes were judged by computing stress distribution in screws, bone-screw interfaces, and cancellous bones in the fixation segment. The results showed that HU reduction in vertebral bodies and screw holding planes were independent risk factors for screw loosening. The predictive performance of screw holding plane HU is better than the mean HU of vertebral bodies. Cranial screws suffer a higher risk of screw loosening, but HU was not significantly different between cranial and caudal sides. The poor BMD led to stress concentrations on both the screw and bone-screw interfaces. Biomechanical deterioration was more severe in the cranial screws than in the caudal screws. Additionally, lower stress can also be observed in fixation segments' cancellous bone. Therefore, a higher proportion of ALSR load transmission triggers stress concentration on the screw and bone-screw interfaces in patients with poor BMD. This, together with decreased bony strength in the screw holding position, contributes to screw loosening in osteoporotic patients biomechanically. The trajectory optimization of ALSR screws based on preoperative HU measurement and regular anti-osteoporosis therapy may effectively reduce the risk of screw loosening.

Detailed mechanical characterization of the transition zone: New insight into the integration between the annulus and nucleus of the intervertebral disc

The Nucleus Pulposus (NP) and Annulus Fibrous (AF) are two primary regions of the intervertebral disc (IVD). The interface between the AF and NP, where the gradual transition in structure and type of fibers are observed, is known as the Transition Zone (TZ). Recent structural studies have shown that the TZ contains organized fibers that appear to connect the NP to the AF. However, the mechanical characteristics of the TZ are yet to be explored. The current study aimed to investigate the mechanical properties of the TZ at the anterolateral (AL) and posterolateral (PL) regions in both radial and circumferential directions of loading using ovine IVDs (N = 28). Young's and toe moduli, maximum stress, failure strain, strain at maximum stress, and toughness were calculated mechanical parameters. The findings from this study revealed that the mechanical properties of the TZ, including young's modulus (p = 0.001), failure strain (p < 0.001), strain at maximum stress (p = 0.002), toughness (p = 0.027), and toe modulus (p = 0.005), were significantly lower for the PL compared to the AL region. Maximum stress was not significantly different between the PL and AL regions (p = 0.164). We found that maximum stress (p = 0.002), failure strain (p < 0.001), and toughness (p = 0.001) were significantly different in different loading directions. No significant differences for modulus (young's; p = 0.169 and toe; p = 0.352) and strain at maximum stress (p = 0.727) were found between the radial and circumferential loading directions. STATEMENT OF SIGNIFICANCE: To date there has not been a study that has investigated the mechanical characterization of the annulus (AF)-nucleus (NP) interface (transition zone; TZ) in the intervertebral disc (IVD), nor is it known whether the posterolateral (PL) and anterolateral (AL) regions of the TZ exhibit different mechanical properties. Accordingly, the TZ mechanical properties have been rarely used in the development of computational IVD models and relevant tissue-engineered scaffolds. The current research reported the mechanical properties of the TZ region and revealed that its mechanical properties were significantly lower for the PL compared to the AL region. These new findings enhance our knowledge about the nature of AF-NP integration and may help to develop more realistic tissue-engineered or computational IVD models.

The Mismatch Between Bony Endplates and Grafted Bone Increases Screw Loosening Risk for OLIF Patients With ALSR Fixation Biomechanically

The mismatch between bony endplates (BEPs) and grafted bone (GB) triggers several complications biomechanically. However, no published study has identified whether this factor increases the risk of screw loosening by deteriorating the local stress levels. This study aimed to illustrate the biomechanical effects of the mismatch between BEP and GB and the related risk of screw loosening. In this study, radiographic and demographic data of 56 patients treated by single segment oblique lumbar interbody fusion (OLIF) with anterior lateral single rod (ALSR) fixation were collected retrospectively, and the match sufficiency between BEP and GB was measured and presented as the grafted bony occupancy rate (GBOR). Data in patients with and without screw loosening were compared; regression analyses identified independent risk factors. OLIF with different GBORs was simulated in a previously constructed and validated lumbosacral model, and biomechanical indicators related to screw loosening were computed in surgical models. The radiographic review and numerical simulations showed that the coronal plane’s GBOR was significantly lower in screw loosening patients both in the cranial and caudal vertebral bodies; the decrease in the coronal plane’s GBOR has been proven to be an independent risk factor for screw loosening. In addition, numerical mechanical simulations showed that the poor match between BEP and GB will lead to stress concentration on both screws and bone-screw interfaces. Therefore, we can conclude that the mismatch between the BEP and GB will increase the risk of screw loosening by deteriorating local stress levels, and the increase in the GBOR by modifying the OLIF cage’s design may be an effective method to optimize the patient’s prognosis.

Low-Modulus PMMA Has the Potential to Reduce Stresses on Endplates after Cement Discoplasty

Cement discoplasty has been developed to treat patients with advanced intervertebral disc degeneration. In discoplasty, poly(methylmethacrylate) (PMMA) bone cement is injected into the disc, leading to reduced pain and certain spinal alignment correction. Standard PMMA-cements have much higher elastic modulus than the surrounding vertebral bone, which may lead to a propensity for adjacent fractures. A PMMA-cement with lower modulus might be biomechanically beneficial. In this study, PMMA-cements with lower modulus were obtained using previously established methods. A commercial PMMA-cement (V-steady^®, G21 srl) was used as control, and as base cement. The low-modulus PMMA-cements were modified by 12 vol% (LA12), 16 vol% (LA16) and 20 vol% (LA20) linoleic acid (LA). After storage in 37 °C PBS from 24 h up to 8 weeks, specimens were tested in compression to obtain the material properties. A lower E-modulus was obtained with increasing amount of LA. However, with storage time, the E-modulus increased. Standard and low-modulus PMMA discoplasty were compared in a previously developed and validated computational lumbar spine model. All discoplasty models showed the same trend, namely a substantial reduction in range of motion (ROM), compared to the healthy model. The V-steady model had the largest ROM-reduction (77%), and the LA20 model had the smallest (45%). The average stress at the endplate was higher for all discoplasty models than for the healthy model, but the stresses were reduced for cements with higher amounts of LA. The study indicates that low-modulus PMMA is promising for discoplasty from a mechanical viewpoint. However, validation experiments are needed, and the clinical setting needs to be further considered.

FEBio finite element model of a pediatric cervical spine

OBJECTIVE

The underlying biomechanical differences between the pediatric and adult cervical spine are incompletely understood. Computational spine modeling can address that knowledge gap. Using a computational method known as finite element modeling, the authors describe the creation and evaluation of a complete pediatric cervical spine model.

METHODS

Using a thin-slice CT scan of the cervical spine from a 5-year-old boy, a 3D model was created for finite element analysis. The material properties and boundary and loading conditions were created and model analysis performed using open-source software. Because the precise material properties of the pediatric cervical spine are not known, a published parametric approach of scaling adult properties by 50%, 25%, and 10% was used. Each scaled finite element model (FEM) underwent two types of simulations for pediatric cadaver testing (axial tension and cardinal ranges of motion [ROMs]) to assess axial stiffness, ROM, and facet joint force (FJF). The authors evaluated the axial stiffness and flexion-extension ROM predicted by the model using previously published experimental measurements obtained from pediatric cadaveric tissues.

RESULTS

In the axial tension simulation, the model with 50% adult ligamentous and annulus material properties predicted an axial stiffness of 49 N/mm, which corresponded with previously published data from similarly aged cadavers (46.1 ± 9.6 N/mm). In the flexion-extension simulation, the same 50% model predicted an ROM that was within the range of the similarly aged cohort of cadavers. The subaxial FJFs predicted by the model in extension, lateral bending, and axial rotation were in the range of 1-4 N and, as expected, tended to increase as the ligament and disc material properties decreased.

CONCLUSIONS

A pediatric cervical spine FEM was created that accurately predicts axial tension and flexion-extension ROM when ligamentous and annulus material properties are reduced to 50% of published adult properties. This model shows promise for use in surgical simulation procedures and as a normal comparison for disease-specific FEMs.

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.

Magnetic Resonance Imaging-based biomechanical simulation of cartilage: A systematic review

MRI-based mathematical and computational modeling studies can contribute to a better understanding of the mechanisms governing cartilage's mechanical performance and cartilage disease. In addition, distinct modeling of cartilage is needed to optimize artificial cartilage production. These studies have opened up the prospect of further deepening our understanding of cartilage function. Furthermore, these studies reveal the initiation of an engineering-level approach to how cartilage disease affects material properties and cartilage function. Aimed at researchers in the field of MRI-based cartilage simulation, research articles pertinent to MRI-based cartilage modeling were identified, reviewed, and summarized systematically. Various MRI applications for cartilage modeling are highlighted, and the limitations of different constitutive models used are addressed. In addition, the clinical application of simulations and studied diseases are discussed. The paper's quality, based on the developed questionnaire, was assessed, and out of 79 reviewed papers, 34 papers were determined as high-quality. Due to the lack of the best constitutive models for various clinical conditions, researchers may consider the effect of constitutive material models on the cartilage disease simulation. In the future, research groups may incorporate various aspects of machine learning into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification, such as gait analysis.

Saline-polyethylene glycol blends preserve in vitro annulus fibrosus hydration and mechanics: An experimental and finite-element analysis

Precise control of tissue water content is essential for ensuring accurate, repeatable, and physiologically relevant measurements of tissue mechanics and biochemical composition. While previous studies have found that saline and polyethylene glycol (PEG) blends were effective at controlling tendon and ligament hydration levels, this work has yet to be extended to the annulus fibrosus (AF). Thus, the first objective of this study was to determine and validate an optimal buffer solution for targeting and maintaining hydration levels of tissue-level AF specimens in vitro. This was accomplished by measuring the transient swelling behavior of bovine AF specimens in phosphate-buffered saline (PBS) and PEG buffers across a wide range of concentrations. Sub-failure, failure, and post-failure mechanics were measured to determine the relationship between changes in tissue hydration and tensile mechanical response. The effect of each buffer solution on tissue composition was also assessed. The second objective of this study was to assess the feasibility and effectiveness of using multi-phasic finite element models to investigate tissue swelling and mechanical responses in different external buffer solutions. A solution containing 6.25%w/v PBS and 6.25%w/v PEG effectively maintained tissue-level AF specimen hydration at fresh-frozen levels after 18 h in solution. Modulus, failure stress, failure strain, and post-failure toughness of specimens soaked in this solution for 18 h closely matched those of fresh-frozen specimens. In contrast, specimens soaked in 0.9%w/v PBS swelled over 100% after 18 h and exhibited significantly diminished sub-failure and failure properties compared to fresh-frozen controls. The increased cross-sectional area with swelling contributed to but was not sufficient to explain the diminished mechanics of PBS-soaked specimens, suggesting additional sub-tissue scale mechanisms. Computational simulations of these specimens generally agreed with experimental results, highlighting the feasibility and importance of including a fluid-phase description when models aim to provide accurate predictions of biological tissue responses. As numerous previous studies suggest that tissue hydration plays a central role in maintaining proper mechanical and biological function, robust methods for controlling hydration levels are essential as the field advances in probing the relationship between tissue hydration, aging, injury, and disease.

Sensitivity of Intervertebral Disc Finite Element Models to Internal Geometric and Non-geometric Parameters

Finite element models are useful for investigating internal intervertebral disc (IVD) behaviours without using disruptive experimental techniques. Simplified geometries are commonly used to reduce computational time or because internal geometries cannot be acquired from CT scans. This study aimed to (1) investigate the effect of altered geometries both at endplates and the nucleus-anulus boundary on model response, and (2) to investigate model sensitivity to material and geometric inputs, and different modelling approaches (graduated or consistent fibre bundle angles and glued or cohesive inter-lamellar contact). Six models were developed from 9.4 T MRIs of bovine IVDs. Models had two variations of endplate geometry (a simple curved profile from the centre of the disc to the periphery, and precise geometry segmented from MRIs), and three variations of NP-AF boundary (linear, curved, and segmented). Models were subjected to axial compressive loading (to 0.86 mm at a strain rate of 0.1/s) and the effect on stiffness and strain distributions, and the sensitivity to modelling approaches was investigated. The model with the most complex geometry (segmented endplates, curved NP-AF boundary) was 3.1 times stiffer than the model with the simplest geometry (curved endplates, linear NP-AF boundary), although this difference may be exaggerated since segmenting the endplates in the complex geometry models resulted in a shorter average disc height. Peak strains were close to the endplates at locations of high curvature in the segmented endplate models which were not captured in the curved endplate models. Differences were also seen in sensitivity to material properties, graduated fibre angles, cohesive rather than glued inter-lamellar contact, and NP:AF ratios. These results show that FE modellers must take care to ensure geometries are realistic so that load is distributed and passes through IVDs accurately.

Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter-lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

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.

Biomechanical effects of laminectomies in the human lumbar spine: a finite element study

BACKGROUND CONTEXT

Previous studies have analyzed the effect of laminectomy on intervertebral disc (IVD), facet-joint-forces (FJF), and range of motion (ROM), while only two have specifically reported stresses at the pars interarticularis (PI) with posterior element resection. These studies have been performed utilizing a single subject, questioning their applications to a broader population.

PURPOSE

We investigate the effect of graded PI resection in a three-dimensional manner on PI stress to provide surgical guidelines for avoidance of iatrogenic instability following lumbar laminectomy. Additionally, quantified FJF and IVD stresses can provide further insight into the development of adjacent segment disease.

STUDY DESIGN

Biomechanical finite element (FE) method investigation of the lumbar spine.

METHODS

FE models of the lumbar spine of three subjects were created using the open-source finite element software, FEBio. Single-level laminectomy, two-level laminectomy, and ventral-to-dorsal PI resection simulations were performed with varying degrees of PI resection from 0% to 75% of the native PI. These models were taken through cardinal ROM under standard loading conditions and PI stresses, FJF, IVD stresses, and ROM were analyzed.

RESULTS

The three types of laminectomy simulated in this study showed a nonlinear increase in PI stress with increased bone resection. Axial rotation generated the most stress at the PI followed by flexion, extension and lateral bending. At 75% bone resection all three types of laminectomy produced PI stresses that were near the ultimate strength of human cortical bone during axial rotation. FJF decreased with increased bone resection for the three laminectomies simulated. This was most notable in axial rotation followed by extension and lateral bending. IVD stresses varied greatly between the nonsurgical models and likewise the effect of laminectomy on IVD stresses varied between subjects. ROM was mostly unaffected by the laminectomies performed in this study.

CONCLUSIONS

Regarding the risk of iatrogenic spondylolisthesis, the combined results are sufficient evidence to suggest surgeons should be particularly cautious when PI resection exceeds 50% bone resection for all laminectomies included in this study. Lastly, the effects seen in FJF and IVD stresses indicate the degree to which the remainder of the spine must experience compensatory biomechanical changes as a result of the surgical intervention.

Febio finite element models of the human cervical spine

Finite element (FE) analysis has proven to be useful when studying the biomechanics of the cervical spine. Although many FE studies of the cervical spine have been published, they typically develop their models using commercial software, making the sharing of models between researchers difficult. They also often model only one part of the cervical spine. The goal of this study was to develop and evaluate three FE models of the adult cervical spine using open-source software and to freely provide these models to the scientific community. The models were created from computed tomography scans of 26-, 59-, and 64-year old female subjects. These models were evaluated against previously published experimental and FE data. Despite the fact that all three models were assigned identical material properties and boundary conditions, there was notable variation in their biomechanical behavior. It was therefore apparent that these differences were the result of morphological differences between the models.

Trabecular Architecture and Mechanical Heterogeneity Effects on Vertebral Body Strength

PURPOSE OF REVIEW

We aimed to synthesize the recent work on the intra-vertebral heterogeneity in density, trabecular architecture and mechanical properties, its implications for fracture risk, its association with degeneration of the intervertebral discs, and its implications for implant design.

RECENT FINDINGS

As compared to the peripheral regions of the centrum, the central region of the vertebral body exhibits lower density and more sparse microstructure. As compared to the anterior region, the posterior region shows higher density. These variations are more pronounced in vertebrae from older persons and in those adjacent to degenerated discs. Mixed results have been reported in regard to variation along the superior-inferior axis and to relationships between the heterogeneity in density and vertebral strength and fracture risk. These discrepancies highlight that, first, despite the large amount of study of the intra-vertebral heterogeneity in microstructure, direct study of that in mechanical properties has lagged, and second, more measurements of vertebral loading are needed to understand how the heterogeneity affects distributions of stress and strain in the vertebra. These future areas of study are relevant not only to the question of spine fractures but also to the design and selection of implants for spine fusion and disc replacement. The intra-vertebral heterogeneity in microstructure and mechanical properties may be a product of mechanical adaptation as well as a key determinant of the ability of the vertebral body to withstand a given type of loading.

Alterations in the Geometry, Fiber Orientation, and Mechanical Behavior of the Lumbar Intervertebral Disc by Nucleus Swelling

Soft tissues observed in clinical medical images are often prestrained in tension by internal pressure or tissue hydration. For a native disc, nucleus swelling occurs in equilibrium with osmotic pressure induced by the high concentration of proteoglycan in the nucleus. The objective of this computational study was to investigate the effects of nucleus swelling on disc geometry, fiber orientation, and mechanical behavior by comparing those of prestrained and zero-pressure (unswelled) discs. Thermoelastic analysis techniques were repurposed in order to determine the zero-pressure disc geometry which, when pressurized, matches the prestrained disc geometry observed in clinical images. The zero-pressure geometry was then used in simulations to approximately represent a degenerated disc, which loses the ability of nucleus swelling but has not undergone distinct soft tissue remodeling/disruption. Our simulation results demonstrated that the loss of nucleus swelling caused a slight change in the disc geometry and fiber orientation, but a distinct deterioration in the resistance to intervertebral rotations including sagittal bending, lateral bending, and axial torsion. Different from rotational loading, in compression (with a displacement of 0.45 mm applied), a much larger stiffness (3.02 KN/mm) and a greater intradiscal pressure (IDP) (0.61 MPa) were measured in the zero-pressure disc, compared to the prestrained disc (1.41 KN/mm and 0.52 MPa). This computational study could be useful to understand mechanisms of disc degeneration, and guide the future design of disc tissue engineering material and biomimic disc implants.

Historical Review of Combined Experimental and Computational Approaches for Investigating Annulus Fibrosus Mechanics

Intervertebral disc research has sought to develop a deeper understanding of spine biomechanics, the complex relationship between disc health and back pain, and the mechanisms of spinal injury and repair. To do so, many researchers have focused on characterizing tissue-level properties of the disc, where the roles of tissue subcomponents can be more systematically investigated. Unfortunately, experimental challenges often limit the ability to measure important disc tissue- and subtissue-level behaviors, including fiber-matrix interactions, transient nutrient and electrolyte transport, and damage propagation. Numerous theoretical and numerical modeling frameworks have been introduced to explain, complement, guide, and optimize experimental research efforts. The synergy of experimental and computational work has significantly advanced the field, and these two aspects have continued to develop independently and jointly. Meanwhile, the relationship between experimental and computational work has become increasingly complex and interdependent. This has made it difficult to interpret and compare results between experimental and computational studies, as well as between solely computational studies. This paper seeks to explore issues of model translatability, robustness, and efficient study design, and to propose and motivate potential future directions for experimental, computational, and combined tissue-level investigations of the intervertebral disc.

Intervertebral disc swelling maintains strain homeostasis throughout the annulus fibrosus: A finite element analysis of healthy and degenerated discs

Tissues in the intervertebral disc have a large capacity to absorb water, partially due to the high glycosaminoglycan (GAG) content, which decreases linearly from the nucleus pulposus (NP) in the center to the outer annulus. Our recent work showed that fiber network and GAG distribution contributes to development of residual stresses and strains that were compressive in the inner annulus to tensile in the outer annulus. GAG loss in the inner annulus, as observed with early to moderate degeneration, reduced swelling capacity and circumferential-direction stress by over 50%. However, our previous model was not capable of evaluating interactions between the NP and annulus fibrosus (AF) during swelling. In this study, we evaluated the effect of degeneration (GAG content or swelling capacity) on residual stress development throughout the disc. Simulations of moderate to severe degeneration showed a 40% decrease in NP swelling capacity, with a 25% decrease in AF and cartilaginous endplate swelling. Together, these changes in tissue swelling resulted in a decrease in NP pressure (healthy = 0.21 MPa; severe degeneration = 0.03 MPa) that was comparable to observations in human discs. There was a 60% decrease in circumferential-direction residual deformations with early degeneration. Radial-direction stretch switched from compressive to tensile with degeneration, which may increase the risk for tears or delamination. Degeneration had a significant impact on residual stress/stretch and fiber stretch in the posterior AF, which is important for understanding herniation risk. In conclusion, degenerative changes in disc geometry and intradiscal deformations was recreated by only altering NP and AF GAG composition. Since most computational models simulate degeneration by altering material stiffness, this work highlights the importance of directly simulating biochemical composition and distribution to study disc biomechanics with degeneration. STATEMENT OF SIGNIFICANCE: Tissues in the intervertebral disc have a large swelling capacity, due to its high glycosaminoglycan content. Our recent work demonstrated the importance of fiber network and glycosaminoglycan distribution residual stresses and strains development. In this study, we evaluated the effect of swelling on intradiscal deformations between the nucleus pulposus and annulus fibrosus. We also investigated the effect of degenerative glycosaminoglycan loss on swelling-based intradiscal deformations of the intact disc and its subcomponents. Decreases in nucleus glycosaminoglycan content resulted in morphological changes observed with degenerated discs and may help to explain mechanisms behind the increases in annular tears and mechanical dysfunction with degeneration.

Human Disc Nucleotomy Alters Annulus Fibrosus Mechanics at Both Reference and Compressed Loads

Nucleotomy is a common surgical procedure and is also performed in ex vivo mechanical testing to model decreased nucleus pulposus (NP) pressurization that occurs with degeneration. Here, we implement novel and noninvasive methods using magnetic resonance imaging (MRI) to study internal 3D annulus fibrosus (AF) deformations after partial nucleotomy and during axial compression by evaluating changes in internal AF deformation at reference loads (50 N) and physiological compressive loads (∼10% strain). One particular advantage of this methodology is that the full 3D disc deformation state, inclusive of both in-plane and out-of-plane deformations, can be quantified through the use of a high-resolution volumetric MR scan sequence and advanced image registration. Intact grade II L3-L4 cadaveric human discs before and after nucleotomy were subjected to identical mechanical testing and imaging protocols. Internal disc deformation fields were calculated by registering MR images captured in each loading state (reference and compressed) and each condition (intact and nucleotomy). Comparisons were drawn between the resulting three deformation states (intact at compressed load, nucleotomy at reference load, nucleotomy at compressed load) with regard to the magnitude of internal strain and direction of internal displacements. Under compressed load, internal AF axial strains averaged -18.5% when intact and -22.5% after nucleotomy. Deformation orientations were significantly altered by nucleotomy and load magnitude. For example, deformations of intact discs oriented in-plane, whereas deformations after nucleotomy oriented axially. For intact discs, in-plane components of displacements under compressive loads oriented radially outward and circumferentially. After nucleotomy, in-plane displacements were oriented radially inward under reference load and were not significantly different from the intact state at compressed loads. Re-establishment of outward displacements after nucleotomy indicates increased axial loading restores the characteristics of internal pressurization. Results may have implications for the recurrence of pain, design of novel therapeutics, or progression of disc degeneration.

Lumbar model generator: a tool for the automated generation of a parametric scalable model of the lumbar spine

Low back pain is a major cause of disability and requires the development of new devices to treat pathologies and improve prognosis following surgery. Understanding the effects of new devices on the biomechanics of the spine is crucial in the development of new effective and functional devices. The aim of this study was to develop a preliminary parametric, scalable and anatomically accurate finite-element model of the lumbar spine allowing for the evaluation of the performance of spinal devices. The principal anatomical surfaces of the lumbar spine were first identified, and then accurately fitted from a previous model supplied by S14 Implants (Bordeaux, France). Finally, the reconstructed model was defined according to 17 parameters which are used to scale the model according to patient dimensions. The developed model, available as a toolbox named the lumbar model generator, enables generating a population of models using subject-specific dimensions obtained from data scans or averaged dimensions evaluated from the correlation analysis. This toolbox allows patient-specific assessment, taking into account individual morphological variation. The models have applications in the design process of new devices, evaluating the biomechanics of the spine and helping clinicians when deciding on treatment strategies.

Disentangling geometrical, viscoelastic and hyperelastic effects in force-displacement relationships of folded biological tissues

Drosophila wing discs show a remarkable variability when subject to mechanical perturbation. We developed a stretching bench that allows accurate measurements of instantaneous and time-dependent material behaviour of the disc as a whole, while determining the exact three-dimensional structure of the disc during stretching. Our experiments reveal force relaxation dynamics on timescales that are significant for development, along with a surprisingly nonlinear force-displacement relationship. Concurrently our imaging indicates that the disc is a highly heterogeneous tissue with a complex geometry. Using image-based 3D finite element modelling we are able to identify the contributions of size, shape and materials parameters to the measured force-displacement relations. In particular, we find that simulating the stretching of a disc with stiffness patterns in the extra-cellular matrix (ECM) recapitulates the experimentally found stretched geometries. In our simulations, linear hyperelasticity explains the measured nonlinearity to a surprising extent. To fully match the experimental force-displacement curves, we use an exponentially elastic material, which, when coupled to material relaxation also explains time-dependent experiments. Our simulations predict that as the disc develops, two counteracting effects, namely the discs foldedness and the hardening of the ECM lead to force-relative displacement curves that are nearly conserved during development.

A growth-based model for the prediction of fiber angle distribution in the intervertebral disc annulus fibrosus

There is a growing interest in the development of patient-specific finite element models of the human lumbar spine for both the assessment of injury risk and the development of treatment strategies. A current challenge in implementing these models is that the outer annulus fibrosus of the disc is composed of concentric sheets of aligned collagen fibers, the helical angles of which vary spatially. In finite element models, fiber angle is typically assumed to be constant, based on average experimental measurements from a small number of locations. The present study hypothesized that the full spatial distribution of fiber angles in the annulus fibrosus may be predicted for any disc geometry by assuming growth from a thin cylinder with constant fiber angle. This hypothesis was tested by developing an analytical model of disc growth and calibrating it with fiber angle measurements of adult bovine caudal discs. The calibrated model was then run on a representative human lumbar disc geometry. The model was able to accurately predict fiber angle distributions in both the experimental bovine caudal disc measurements and literature-reported human lumbar disc measurements. Despite its theoretical basis in development, the model requires only mature state geometry, making it practical for implementation in patient-specific finite element analyses, in which disc geometry is obtained from clinical imaging.

Relative Nucleus Pulposus Area and Position Alters Disc Joint Mechanics

Aging and degeneration of the intervertebral disc are noted by changes in tissue composition and geometry, including a decrease in nucleus pulposus (NP) area. The NP centroid is positioned slightly posterior of the disc's centroid, but the effect of NP size and location on disc joint mechanics is not well understood. We evaluated the effect of NP size and centroid location on disc joint mechanics under dual-loading modalities (i.e., compression in combination with axial rotation or bending). A finite element model was developed to vary the relative NP area (NP:Disc area ratio range = 0.21 - 0.60). We also evaluated the effect of NP position by shifting the NP centroid anteriorly and posteriorly. Our results showed that compressive stiffness and average first principal strains increased with NP size. Under axial compression, stresses are distributed from the NP to the annulus, and stresses were redistributed towards the NP with axial rotation. Moreover, peak stresses were greater for discs with a smaller NP area. NP centroid location had a greater impact on intradiscal pressure during flexion and extension, where peak pressures in the posterior annulus under extension was greater for discs with a more posteriorly situated NP. In conclusion, the findings from this study highlight the importance of closely mimicking NP size and location in computational models that aim to understand stress/strain distribution during complex loading and for developing repair strategies that aim to recapitulate the mechanical behavior of healthy discs.

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.

A Reactive Inelasticity Theoretical Framework for Modeling Viscoelasticity, Plastic Deformation, and Damage in Fibrous Soft Tissue

Fibrous soft tissues are biopolymeric materials that are made of extracellular proteins, such as different types of collagen and proteoglycans, and have a high water content. These tissues have nonlinear, anisotropic, and inelastic mechanical behaviors that are often categorized into viscoelastic behavior, plastic deformation, and damage. While tissue's elastic and viscoelastic mechanical properties have been measured for decades, there is no comprehensive theoretical framework for modeling inelastic behaviors of these tissues that is based on their structure. To model the three major inelastic mechanical behaviors of tissue's fibrous matrix, we formulated a structurally inspired continuum mechanics framework based on the energy of molecular bonds that break and reform in response to external loading (reactive bonds). In this framework, we employed the theory of internal state variables (ISV) and kinetics of molecular bonds. The number fraction of bonds, their reference deformation gradient, and damage parameter were used as state variables that allowed for consistent modeling of all three of the inelastic behaviors of tissue by using the same sets of constitutive relations. Several numerical examples are provided that address practical problems in tissue mechanics, including the difference between plastic deformation and damage. This model can be used to identify relationships between tissue's mechanical response to external loading and its biopolymeric structure.

FEBio finite element models of the human lumbar spine

Finite element analysis has proven to be a viable method for assessing many structure-function relationships in the human lumbar spine. Several validated models of the spine have been published, but they typically rely on commercial packages and are difficult to share between labs. The goal of this study is to present the development of the first open-access models of the human lumbar spine in FEBio. This modeling framework currently targets three deficient areas in the field of lumbar spine modeling: 1) open-access models, 2) accessibility for multiple meshing schemes, and 3) options to include advanced hyperelastic and biphasic constitutive models.

Effect of collagen fibre orientation on intervertebral disc torsion mechanics

The intervertebral disc is a complex fibro-cartilaginous material, consisting of a pressurized nucleus pulposus surrounded by the annulus fibrosus, which has an angle-ply structure. Disc injury and degeneration are noted by significant changes in tissue structure and function, which significantly alters stress distribution and disc joint stiffness. Differences in fibre orientation are thought to contribute to changes in disc torsion mechanics. Therefore, the objective of this study was to evaluate the effect of collagen fibre orientation on internal disc mechanics under compression combined with axial rotation. We developed and validated a finite element model (FEM) to delineate changes in disc mechanics due to fibre orientation from differences in material properties. FEM simulations were performed with fibres oriented at [Formula: see text] throughout the disc (uniform by region and fibre layer). The initial model was validated by published experimental results for two load conditions, including [Formula: see text] axial compression and [Formula: see text] axial rotation. Once validated, fibre orientation was rotated by [Formula: see text] or [Formula: see text] towards the horizontal plane, resulting in a decrease in disc joint torsional stiffness. Furthermore, we observed that axial rotation caused a sinusoidal change in disc height and radial bulge, which may be beneficial for nutrient transport. In conclusion, including anatomically relevant fibre angles in disc joint FEMs is important for understanding stress distribution throughout the disc and will be important for understanding potential causes for disc injury. Future models will include regional differences in fibre orientation to better represent the fibre architecture of the native disc.

Residual strains in the intervertebral disc annulus fibrosus suggest complex tissue remodeling in response to in-vivo loading

The annulus fibrosus (AF) of the intervertebral disc (IVD) serves the dual roles of containing hydrostatic pressure from the inner nucleus pulposus (NP) and allowing flexible connection between adjacent vertebral bodies. Previous work has indicated that in the unloaded state, the AF is under a state of residual circumferential strain that, on average, is comparable to that which is believed to reduce peak stresses in other pressure containing organs. The complex in-vivo loading of the IVD, however, led us to hypothesize that variations with anatomical region should also exist. Residual strains were measured by imaging bovine caudal IVDs at both macro and micro scales in both the intact state (under residual strain) and opened into anterior, posterior, and lateral quadrants (residual strains relieved). Calculation of macro scale residual strains using changes in lamellar arc length and thickness confirmed circumferential tension (anterior: 0.63±2.1%, lateral: 8.3±1.5%, posterior: 4.4±2.1%) and radial compression (anterior: 12.4±5.8%, lateral: 11.120±2.8%, posterior: 4.8±4.2%) around the outer zone of the AF. The inner zone, however, had residual circumferential strains ranging from 28.7±3.4% compression in the anterior region to 3.4±3% tension in the posterior region, with radial strains of 9.7±5.5% tension and 0.2±4.4% compression respectively. This pattern of residual circumferential strain was corroborated at the microscale by comparing the crimp period of collagen fiber bundles in the intact and open states. The results of this study point toward a complex pattern of residual strains in the AF, which develop in response to stresses from both NP pressurization and bending movements.

Computer simulation of lumbar flexion shows shear of the facet capsular ligament

BACKGROUND CONTEXT

The lumbar facet capsular ligament (FCL) is a posterior spinal ligament with a complex structure and kinematic profile. The FCL has a curved geometry, multiple attachment sites, and preferentially aligned collagen fiber bundles on the posterior surface that are innervated with mechanoreceptive nerve endings. Spinal flexion induces three-dimensional (3D) deformations, requiring the FCL to maintain significant tensile and shear loads. Previous works aimed to study 3D facet joint kinematics during flexion, but to our knowledge none have reported localized FCL surface deformations likely created by this complex structure.

PURPOSE

The purpose of this study was to elucidate local deformations of both the posterior and anterior surfaces of the lumbar FCL to understand the distribution and magnitude of in-plane and through-plane deformations, including the prevalence of shear.

STUDY DESIGN/SETTING

The FCL anterior and posterior surface deformations were quantified through creation of a finite element model simulating facet joint flexion using a realistic geometry, physiological kinematics, and fitted constitutive material.

METHODS

Geometry was obtained from the micro-CT data of a healthy L3-L4 facet joint capsule (n=1); kinematics were extracted from sagittal plane fluoroscopic data of healthy volunteers (n=10) performing flexion; and average material properties were determined from planar biaxial extension tests of L4-L5 FCLs (n=6). All analyses were performed with the non-linear finite element solver, FEBio. A grid of equally spaced 3×3 nodes on the posterior surface identified regional differences within the strain fields and was used to create comparisons against previously published experimental data. This study was funded by the National Institutes of Health and the authors have no disclosures.

RESULTS

Inhomogeneous in-plane and through-plane shear deformations were prominent through the middle body of the FCL on both surfaces. Anterior surface deformations were more pronounced because of the small width of the joint space, whereas posterior surface deformations were more diffuse because the larger area increased deformability. We speculate these areas of large deformation may provide this proprioceptive system with an excellent measure of spinal motion.

CONCLUSIONS

We found that in-plane and through-plane shear deformations are widely present in finite element simulations of a lumbar FCL during flexion. Importantly, we conclude that future studies of the FCL must consider the effects of both shear and tensile deformations.