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.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

BACKGROUND

Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases.

OBJECTIVE

Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues.

METHOD

Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed.

RESULTS

A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions.

CONCLUSIONS

The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

Nonlinear stress-dependent recovery behavior of the intervertebral disc

The intervertebral disc exhibits complex mechanics due to its heterogeneous structure, inherent viscoelasticity, and interstitial fluid-matrix interactions. Sufficient fluid flow into the disc during low loading periods is important for maintaining mechanics and nutrient transport. However, there is a lack of knowledge on the effect of loading magnitude on time-dependent recovery behavior and the relative contribution of multiple recovery mechanisms during recovery. In most studies that have evaluated disc recovery behavior, a single load condition has been considered, making it difficult to compare findings across studies. Hence, the objective of this study was to quantify unloaded disc recovery behavior after compressive creep loading under a wide range of physiologically relevant stresses (0.2-2 MPa). First, the repeatability of disc recovery behavior was assessed. Once repeatable recovery behavior was confirmed, each motion segment was subject to three cycles of creep-recovery loading, where each cycle consisted of a 24-h creep at a pre-assigned load (100, 200, 300, 600, 900, or 1200 N), followed by an 18-h recovery period at a nominal load (10 N). Results showed that disc recovery behavior was strongly influenced by the magnitude of loading. The magnitude of instantaneous and time-dependent recovery deformations increased nonlinearly with an increase in compressive stress during creep. In conclusion, this study highlights that elastic deformation, intrinsic viscoelasticity, and poroelasticity all have substantial contributions to disc height recovery during low loading periods. However, their relative contributions to disc height recovery largely depend on the magnitude of loading. While loading history does not influence the contribution of the short-term recovery, the contribution of long-term recovery is highly sensitive to loading magnitude.

Application of Finite Element Analysis for Investigation of Intervertebral Disc Degeneration: from Laboratory to Clinic

Due to the ethical concern and inability to detect inner stress distributions of intervertebral disc (IVD), traditional methods for investigation of intervertebral disc degeneration (IVDD) have significant limitations. Many researchers have demonstrated that finite element analysis (FEA) is an effective tool for the research of IVDD. However, the specific application of FEA for investigation of IVDD has not been systematically elucidated before. In the present review, we summarize the current finite element models (FEM) used for the investigation of IVDD, including the poroelastic nonlinear FEM, diffusive-reactive theory model and cell-activity coupled mechano-electrochemical theory model. We further elaborate the use of FEA for the research of IVDD pathogenesis especially for nutrition and biomechanics associated etiology, and the biological, biomechanical and clinical influences of IVDD. In addition, the application of FEA for evaluation and exploration of various treatments for IVDD is also elucidated. We conclude that FEA is an excellent technique for research of IVDD, which could be used to explore the etiology, biology and biomechanics of IVDD. In the future, FEA may help us to achieve the goal of individualized precision therapy.

Substantial vertebral body osteophytes protect against severe vertebral fractures in compression

Recent findings suggest that vertebral osteophytes increase the resistance of the spine to compression. However, the role of vertebral osteophytes on the biomechanical response of the spine under fast dynamic compression, up to failure, is unclear. Seventeen human spine specimens composed of three vertebrae (from T5-T7 to T11-L1) and their surrounding soft tissues were harvested from nine cadavers, aged 77 to 92 years. Specimens were imaged using quantitative computer tomography (QCT) for medical observation, classification of the intervertebral disc degeneration (Thomson grade) and measurement of the vertebral trabecular density (VTD), height and cross-sectional area. Specimens were divided into two groups (with (n = 9) or without (n = 8) substantial vertebral body osteophytes) and compressed axially at a dynamic displacement rate of 1 m/s, up to failure. Normalized force-displacement curves, videos and QCT images allowed characterizing failure parameters (force, displacement and energy at failure) and fracture patterns. Results were analyzed using chi-squared tests for sampling distributions and linear regression for correlations between VTD and failure parameters. Specimens with substantial vertebral body osteophytes present higher stiffness (2.7 times on average) and force at failure (1.8 times on average) than other segments. The presence of osteophytes significantly influences the location, pattern and type of fracture. VTD was a good predictor of the dynamic force and energy at failure for specimens without substantial osteophytes. This study also showed that vertebral body osteophytes provide a protective mechanism to the underlying vertebra against severe compression fractures.

Association between Measures of Vertebral Endplate Morphology and Lumbar Intervertebral Disc Degeneration

Purpose

The aim of this study was to evaluate the association between vertebral endplate morphology and the degree of lumbar intervertebral disc degeneration via magnetic resonance imaging (MRI).

Methods

In total, 150 patients who met the inclusion criteria and were 20–60 years of age were retrospectively evaluated. Patients were evaluated for the presence of intervertebral disc degeneration or herniation, and the degree of degeneration was assessed at all lumbar levels. Vertebral endplate morphology was evaluated based on the endplate sagittal diameter, endplate sagittal concave angle (ECA), and endplate sagittal concave depth (ECD) on sagittal MRI. The association between intervertebral disc degeneration or herniation and endplate morphological measurements was analysed.

Results

In MRI, superior endplates ( ie, inferior endplates of the superior vertebra) were concave and inferior endplates ( ie, superior endplates of the inferior vertebra) were flat at all disc levels. A decrease in ECD and an increase in ECA were detected at all lumbar levels as disc degeneration increased ( P < .05). At the L4-L5 and L5-S1 levels, a decrease in ECD and an increase in ECA were detected in the group with herniated lumbar discs ( P < .05). There was no association between lumbar disc degeneration or herniation and endplate sagittal diameter at lumbar intervertebral levels ( P > .05). At all levels, ECD of women was significantly lesser than that of men and ECA of women was significantly greater than that of men ( P < .05).

Conclusions

There is an association between vertebral endplate morphology and lumbar intervertebral disc degeneration. Vertebral endplates at the degenerated disc level become flat; the severity of this flattening is correlated with the degree of disc degeneration.

Lumbar spine endplate fractures: Biomechanical evaluation and clinical considerations through experimental induction of injury

Lumbar endplate fractures were investigated in different experimental scenarios, however the biomechanical effect of segmental alignment was not outlined. The objectives of this study were to quantify effects of spinal orientation on lumbar spine injuries during single-cycle compressive loads and understand lumbar spine endplate injury tolerance. Twenty lumbar motion segments were compressed to failure. Two methods were used in the preparation of the lumbar motion segments. Group 1 (n = 7) preparation maintained pre-test sagittal lordosis, whereas Group 2 (n = 13) specimens had a free-rotational end condition for the cranial vertebra, allowing sagittal rotation of the cranial vertebra to create parallel endplates. Five Group 1 specimens experienced posterior vertebral body fracture prior to endplate fracture, whereas two sustained endplate fracture only. Group 2 specimens sustained isolated endplate fractures. Group 2 fractures occurred at approximately 41% of the axial force required for Group 1 fracture (p < 0.05). Imaging and specimen dissection indicate endplate injury consistently took place within the confines of the endplate boundaries, away from the vertebral periphery. These findings indicate that spinal alignment during compressive loading influences the resulting injury pattern. This investigation identified the specific mechanical conditions under which an endplate breach will take place. Development of endplate injuries has significant clinical implication as previous research identified internal disc disruption (IDD) and degenerative disc disease (DDD) as long-term consequences of the axial load-shift that occurs following a breach of the endplate. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1084-1091, 2016.

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.

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.

The intravertebral distribution of bone density: correspondence to intervertebral disc health and implications for vertebral strength

This study's goal was to determine associations among the intravertebral heterogeneity in bone density, bone strength, and intervertebral disc (IVD) health. Results indicated that predictions of vertebral strength can benefit from considering the magnitude of the density heterogeneity and the congruence between the spatial distribution of density and IVD health.

INTRODUCTION

This study aims to determine associations among the intravertebral heterogeneity in bone density, bone strength, and IVD health

METHODS

Regional measurements of bone density were performed throughout 30 L1 vertebral bodies using micro-computed tomography (μCT) and quantitative computed tomography (QCT). The magnitude of the intravertebral heterogeneity in density was defined as the interquartile range and quartile coefficient of variation in regional densities. The spatial distribution of density was quantified using ratios of regional densities representing different anatomical zones (e.g., anterior to posterior regional densities). Cluster analysis was used to identify groups of vertebrae with similar spatial distributions of density. Vertebral strength was measured in compression. IVD health was assessed using two scoring systems.

RESULTS

QCT- and μCT-based measures of the magnitude of the intravertebral heterogeneity in density were strongly correlated with each other (p < 0.005). Accounting for the interquartile range in regional densities improved predictions of vertebral strength as compared to predictions based only on mean density (R (2) = 0.59 vs. 0.43; F-test p-value = 0.018). Specifically, after adjustment for mean density, vertebral bodies with greater heterogeneity in density exhibited higher strength. No single spatial distribution of density was associated with high vertebral strength. Analyses of IVD scores suggested that the health of the adjacent IVDs may modulate the effect of a particular spatial distribution of density on vertebral strength.

CONCLUSIONS

Noninvasive measurements of the intravertebral distribution of bone density, in conjunction with assessments of IVD health, can aid in predictions of bone strength and in elucidating biomechanical mechanisms of vertebral fracture.

On the modeling of an intervertebral disc using a novel large deformation multi-shell approach

The objective of this study is to develop an analytical model to predict the stresses and displacements in the lamellae of the intervertebral disc subjected to a compressive force. This is achieved by developing a model based on membrane theory combined to large deformation multishell structural behavior. Equations for longitudinal and circumferential stresses are formulated for each lamella of the anulus fibrosus. Multilamellae interaction is a statically indeterminate problem, which requires equations of compatibility of the displacements of adjacent lamellae to be resolved. The large deformation inherent to soft tissue is considered and the solution is obtained using an iterative process. Elastic interactions with a large deformation is a novelty in analytical modeling of soft tissues. This provides model realism and offers the possibility for new and in-depth investigations. Results are given for longitudinal and circumferential stresses and displacements as well as contact pressures for every lamella of the anulus fibrosus. The analytical results are compared to those of two finite element models. The results suggest that the most highly stressed zone is located on the innermost lamella. Stresses decrease through disc thickness and are at a maximum at the innermost lamella. Circumferential stress is predominant and the difference is less than 5% at any point of the anulus fibrosus when the analytical model is compared to the finite element model using coupled degrees of freedom at the lamellae interface. When compared to the finite element model using contact elements, the difference is below 11%. Contact pressures from the inside to the outside of the anulus fibrosus are shown to decrease nonlinearly. The model presented in this study has demonstrated that it is possible to analytically simulate the complex mechanical behavior of a multishell intervertebral disc subjected to compression, provided some simplifications. Further improvements are suggested to increase model realism and recommendations are given for future experimentation necessary to support both the analytical and numerical models.

A review of the combination of experimental measurements and fibril-reinforced modeling for investigation of articular cartilage and chondrocyte response to loading

The function of articular cartilage depends on its structure and composition, sensitively impaired in disease (e.g. osteoarthritis, OA). Responses of chondrocytes to tissue loading are modulated by the structure. Altered cell responses as an effect of OA may regulate cartilage mechanotransduction and cell biosynthesis. To be able to evaluate cell responses and factors affecting the onset and progression of OA, local tissue and cell stresses and strains in cartilage need to be characterized. This is extremely challenging with the presently available experimental techniques and therefore computational modeling is required. Modern models of articular cartilage are inhomogeneous and anisotropic, and they include many aspects of the real tissue structure and composition. In this paper, we provide an overview of the computational applications that have been developed for modeling the mechanics of articular cartilage at the tissue and cellular level. We concentrate on the use of fibril-reinforced models of cartilage. Furthermore, we introduce practical considerations for modeling applications, including also experimental tests that can be combined with the modeling approach. At the end, we discuss the prospects for patient-specific models when aiming to use finite element modeling analysis and evaluation of articular cartilage function, cellular responses, failure points, OA progression, and rehabilitation.

Modeling Degenerative Disk Disease in the Lumbar Spine: A Combined Experimental, Constitutive, and Computational Approach

Using a continuum approach for modeling the constitutive mechanical behavior of the intervertebral disk’s annulus fibrosus holds the potential for facilitating the correlation of morphology and biomechanics of this clinically important tissue. Implementation of a continuum representation of the disk’s tissues into computational models would yield a particularly valuable tool for investigating the effects of degenerative disease. However, to date, relevant efforts in the literature towards this goal have been limited due to the lack of a computationally tractable and implementable constitutive function. In order to address this, annular specimens harvested from a total of 15 healthy and degenerated intervertebral disks were tested under planar biaxial tension. Predictions of a strain energy function, which was previously shown to be unconditionally convex, were fit to the experimental data, and the optimized coefficients were used to modify a previously validated finite element model of the L4/L5 functional spinal unit. Optimization of material coefficients based on experimental results indicated increases in the micro-level orientation dispersion of the collagen fibers and the mechanical nonlinearity of these fibers due to degeneration. On the other hand, the finite element model predicted a progressive increase in the stress generation in annulus fibrosus due to stepwise degeneration of initially the nucleus and then the entire disk. Range of motion was predicted to initially increase with the degeneration of the nucleus and then decrease with the degeneration of the annulus in all rotational loading directions, except for axial rotation. Overall, degeneration was observed to specifically impact the functional effectiveness of the collagen fiber network of the annulus, leading to changes in the biomechanical behavior at both the tissue level and the motion-segment level.

Motion characteristics of the vertebral segments with lumbar degenerative spondylolisthesis in elderly patients

OBJECTIVE

Although some studies have reported on the kinematics of the lumbar segments with degenerative spondylolisthesis (DS), few data have been reported on the in vivo 6 degree-of-freedom kinematics of different anatomical structures of the diseased levels under physiological loading conditions. This research is to study the in vivo motion characteristics of the lumbar vertebral segments with L4 DS during weight-bearing activities.

METHODS

Nine asymptomatic volunteers (mean age 54.4) and 9 patients with L4 DS (mean age 73.4) were included. Vertebral kinematics was obtained using a combined MRI/CT and dual fluoroscopic imaging technique. During functional postures (supine, standing upright, flexion, and extension), disc heights, vertebral motion patterns and instability were compared between the two groups.

RESULTS

Although anterior disc heights were smaller in the DS group than in the normal group, the differences were only significant at standing upright. Posterior disc heights were significantly smaller in DS group than in the normal group under all postures. Different vertebral motion patterns were observed in the DS group, especially in the left-right and cranial-caudal directions during flexion and extension of the body. However, the range of motions of the both groups were much less than the reported criteria of lumbar spinal instability.

CONCLUSION

The study showed that lumbar vertebra with DS has disordered motion patterns. DS did not necessary result in vertebral instability. A restabilization process may have occurred and surgical treatment should be planned accordingly.