The effect of fluid loss on the viscoelastic behavior of the lumbar intervertebral disc in compression

Biomechanical effects of S1 sacroiliac screws versus S2 sacroiliac screws on sacroiliac screws combined with a lumbar iliac fixation in the treatment of vertical sacral fractures: a biomechanical finite element analysis

OBJECTIVE

To examine the impact of sacroiliac screw position and length on the biomechanical properties of triangular osteosynthesis in treating unilateral vertical sacral fractures and provide a clinical reference.

METHODS

Unilateral Denis type II sacral fractures were modelled using finite elements to represent Tile C pelvic ring injuries. Six sacroiliac screws were used with iliolumbar fixation patterns to fix the sacral fractures, and the sacral stability, maximum pressure, and stress distribution were compared among the internal fixation modalities.

RESULTS

The best vertical stability of the internal fixation model was achieved when the S1 segment was fixed with lengthened sacroiliac screws, followed by when the S1 segment was fixed using normal sacroiliac screws. There was no significant difference in vertical stability between the S1 + S2 dual-segment fixation model and the S1-segment fixation model. The maximum pressure under a vertical force of 600 N showed a trend of L5LS1 < L5NS1 < L5LS12 < L5LS2 < L5NS2 < L5NS12.

CONCLUSIONS

In unilateral vertical sacral fractures (Denis II) treated with triangular osteosynthesis using triangular jointing combined with unilateral iliolumbar + sacroiliac screw fixation, the use of a single lengthened sacroiliac screw for the S1 segment is recommended to achieve the best vertical stability of the sacrum with less maximum compression on the internal fixation components. If it is not possible to apply a lengthened sacroiliac screw, the use of a normal sacroiliac screw for the S1 segment is recommended. Adding an S2 screw does not significantly increase the vertical stability of the sacrum.

Biomechanical comparison of four triangular osteosynthesis fixations for unilateral vertical sacral fractures

To compare the stability and biomechanical characteristics of four commonly used triangular osteosynthesis techniques to treat unilateral vertical sacral fractures and provide a clinical application reference. Finite element models of Tile C-type pelvic ring injury (unilateral Denis II sacral fracture) were produced. In four models, sacral fractures were fixed with a combination of unilateral L5, unilateral L4, and L5 iliac lumbar fixation with lengthened or normal sacroiliac screws. The biomechanical properties of the four fixation models were measured and compared under bipedal stance and lumbar rotation. The fixation stability of the model with the lengthened sacroiliac screw was excellent, and the fracture end was stable. The stability of fixation using unilateral L4 and L5 segments was close to that of unilateral L5 segment fixation. Triangular osteosynthesis transverse stabilization devices using lengthened sacroiliac screws can increase the vertical stability of the sacrum after internal fixation and increase the stability of the fracture. When triangular osteosynthesis lumbar fixation segments were selected, simultaneous fixation of L4 and L5 segments versus only L5 segments did not significantly enhance the vertical stability of the sacrum or the stability of the fracture end.

Biomechanical Effect of Disc Height on the Components of the Lumbar Column at the Same Axial Load: A Finite-Element Study

Intervertebral discs are fibrocartilage structures, which play a role in buffering the compression applied to the vertebral bodies evenly while permitting limited movements. According to several previous studies, degenerative changes in the intervertebral disc could be accelerated by factors, such as aging, the female sex, obesity, and smoking. As degenerative change progresses, the disc height could be reduced due to the dehydration of the nucleus pulposus. This study aimed to quantitatively analyze the pressure that each structure of the spine receives according to the change in the disc height and predict the physiological effect of disc height on the spine. We analyzed the biomechanical effect on spinal structures when the disc height was decreased using a finite-element method investigation of the lumbar spine. Using a 3D FE model, the degree and distribution of von-Mises stress according to the disc height change were measured by applying the load of four different motions to the lumbar spine. The height was changed by dividing the anterior and posterior parts of the disc, and analysis was performed in the following four motions: flexion, extension, lateral bending, and axial rotation. Except for a few circumstances, the stress applied to the structure generally increased as the disc height decreased. Such a phenomenon was more pronounced when the direction in which the force was concentrated coincided with the portion where the disc height decreased. This study demonstrated that the degree of stress applied to the spinal structure generally increases as the disc height decreases. The increase in stress was more prominent when the part where the disc height was decreased and the part where the moment was additionally applied coincided. Disc height reduction could accelerate degenerative changes in the spine. Therefore, eliminating the controllable risk factors that cause disc height reduction may be beneficial for spinal health.

Effect of different attributes of the mimic human lumbar spine biomechanics material structure change by finite element analysis

In this study, we compared stress changes and quantity effect relationships from 3D finite element models of normal and degenerative lumbar segments. We further defined the mechanisms causing alterations in mechanical stability the control of normal and degenerative lumbar segments using traditional Chinese medicine. The characteristics of the stress change and the quantity effect relationships of the three-dimensional finite element model of normal and degenerative lumbar segments were compared. The mechanism(s) leading to changes in mechanical stability and the intervention and balance between normal and degenerative lumbar segments of the traditional Chinese medicine was analyzed. The change trend of stress and strain was compared with the three dimensional finite element model under different motion states of normal lumbar vertebrae. A 3D-FEM of degenerative lumbar segments L4 ~ 5 of the human spine was established to simulate the physiological and pathological changes of the lumbar spine in response to flexion, extension, lateral bending and torsion. The stress changes in the normal and degenerative lumbar vertebrae were assessed through external force interventions and the response to TCM. Stress in the degenerative lumbar vertebrae changed according the external load. Stress and strain were compared in the FEM model under a range of motion states. Components of the human lumbar vertebrae including the cortical vertebrae, cancellous bone, endplates, fibrous rings, and facet articular processes were investigated. The elastic modulus of the nerve roots and the posterior marginal structures of the vertebral body increased with lumbar degeneration. Under stress trends in normal lumbar and different degrees of degenerative lumbar structures including cortical bone, loose bone, terminal plate, fiber ring, nucleus, small articular processes, nerve roots and posterior structures. In normal lumbar spine, 20%, 50%, 70% lumbar degeneration, 106 different lumbar anterior flexion 30 and posterior extension with different external forces showed that ANOVA F was between 3.623 and 11.381 and P changed between 0.001 and 0.05.It is clear that in the lumbar movement segments under different pressure intervention, the changes in the degree of degeneration are significantly different from each constituent structure, among which the trend of expected change between the constituent structures of the lumbar anterior flexion 30 is particularly obvious. The stress distribution in the intervertebral discs were influenced by TCM, and the space in the spinal canal enlarged so that nerve root stress decreased, vertebral body stress increased, and facet processes and pedicle stress in the posterior regions exceeded those of the anterior flexion position. The internal stress of the intervertebral disc increased in the flexion compared to the extension position, gradually increasing from top to bottom. The stress concentration point of the degenerative lumbar disc is significantly greater than the stress in the normal lumbar disc stress distribution area, and increases with the degree of degeneration. Compared with the load capacity of normal lumbar and mild (15% reduction), moderate (40% reduction) lumbar disc protrusion model in bending, extension, axial rotation, lateral bending, the results found that the load transmission of lumbar disc degeneration model to different degrees has also changed, so its compression stiffness, strain distribution and size are also different. TCM can improve and treat lumbar disc disease through its ability to regulate the mechanical environment of degenerative lumbar vertebrae. Compared to the FEM models of the lumbar vertebrae, lumbar degenerative changes could be assessed in response to alterations in the biomechanical environment. These findings provide a scientific basis for the popularization and application of TCM to prevent and treat spinal degenerative disease.

Biomechanical study of transsacral-transiliac screw fixation versus lumbopelvic fixation and bilateral triangular fixation for "H"- and "U"-type sacrum fractures with traumatic spondylopelvic dissociation: a finite element analysis study

Objective

To compare the biomechanical stability of transsacral-transiliac screw fixation and lumbopelvic fixation for “H”- and “U”-type sacrum fractures with traumatic spondylopelvic dissociation.

Methods

Finite element models of “H”- and “U”-type sacrum fractures with traumatic spondylopelvic dissociation were created in this study. The models mimicked the standing position of a human. Fixation with transsacral-transiliac screw fixation, lumbopelvic fixation, and bilateral triangular fixation were simulated. Biomechanical tests of instability were performed, and the fracture gap displacement, anteflexion, rotation, and stress distribution after fixation were assessed.

Results

For H-type fractures, the three kinds of fixation ranked by stability were bilateral triangular fixation > lumbopelvic fixation > transsacral-transiliac screw fixation in the vertical and anteflexion directions, bilateral triangular fixation > transsacral-transiliac S1 and S2 screw fixation > lumbopelvic fixation in rotation. The largest displacements in the vertical, anteflexion, and rotational directions were 0.57234 mm, 0.37923 mm, and 0.13076 mm, respectively. For U-type fractures, these kinds of fixation ranked by stability were bilateral triangular fixation > lumbopelvic fixation > transsacral-transiliac S1 and S2 screw fixation > transsacral-transiliac S1 screw fixation in the vertical, anteflexion, and rotational directions. The largest displacements in the vertical, anteflexion, and rotational directions were 0.38296 mm, 0.33976 mm, and 0.05064 mm, respectively.

Conclusion

All these kinds of fixation met the mechanical criteria for clinical applications. The biomechanical analysis showed better bilateral balance with transsacral-transiliac screw fixation. The maximal displacement for these types of fixation was less than 1 mm. Percutaneous transsacral-transiliac screw fixation can be considered the best option among these kinds of fracture fixation.

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.

Use of a personalized hybrid biomechanical model to assess change in lumbar spine function with a TDR compared to an intact spine

Total disc replacements (TDRs) have been employed with increasing frequency in recent years with the intention of restoring natural motion to the spine and reducing adjacent level trauma. Previous assessments of the TDRs have subjectively measured patient satisfaction, evaluated sagittal range of motion via static imaging, or examined biomechanical loading in vitro. This study examined the kinematics and biomechanical loading of the lumbar spine with an intact spine compared to a TDR inserted at L5/S1 in the same spine. A validated biologically driven personalized dynamic biomechanical model was used to assess range of motion (ROM) and lumbar spine tissue forces while a subject performed a series of bending and lifting exertions representative of normal life activities. This analysis concluded that with the insertion of a TDR, forces are of much greater magnitude in all three directions of loading and are concentrated at both the endplates and the posterior element structures compared to an intact spine. A significant difference is seen between the intact spine and the TDR spine at levels above the TDR insertion level as a function of supporting an external load (lifting). While ROM within the TDR joint was larger than in the intact spine (yet within the normal ranges under the unloaded bending conditions), the differences between spines were far greater in all three planes of motion under loaded lifting conditions. At levels above the TDR insertion, larger ROM was present during the lifting conditions. Sagittal motions were often greater at the higher lumbar levels, but there appeared to be less lateral and twisting motion. Collectively, this analysis indicates that the insertion of a TDR significantly alters the function of the spine.

Degenerative anular changes induced by puncture are associated with insufficiency of disc biomechanical function

STUDY DESIGN

In vivo experiments to examine physiologic consequences and in vitro tests to determine immediate biomechanical effects of anular injury by needle puncture.

OBJECTIVE

To determine whether a relationship exists between induction of degenerative changes in anulus fibrosus (AF) and compromised disc biomechanical function according to injury size.

SUMMARY OF BACKGROUND DATA

Various studies in intervertebral disc mechanics, degeneration, and regeneration involve the creation of a defect in the anulus fibrosus (AF). However, the impact of the puncture, itself, on biomechanical function and disc health are not understood.

METHODS

For in vivo experiments, rat caudal discs subjected to percutaneous anular punctures using different gauge size hypodermic needles (18, 22, 26 g) and nonpunctured controls were examined histologically up to 4 weeks postsurgery. For in vitro biomechanical testing, healthy motion segments were isolated and their creep compression response assessed immediately after needle puncture.

RESULTS

We found that needle size-dependence of creep compression behavior paralleled the size-dependence of degenerative changes in the AF. Specifically, 18-g punctures resulted in inward bulging of the AF, lamellar disorganization, and cellular changes. These changes were not seen in 22- and 26-g punctured discs. Biomechanical tests showed that only 18-g needle punctures led to significant changes in disc mechanics. Importantly, a statistically significant association was found between needle sizes that caused biomechanical changes and induction of degenerative changes in the AF.

CONCLUSION

Our findings suggest that injury sizes large enough to disrupt biomechanical function are needed to drive degenerative changes in rat caudal disc AF. Based on the data, we believe that small anular defects become sealed, allowing the disc to function normally and the AF to heal. Larger defects appear to require longer wound closure times, and may prolong the duration of impaired disc function.

Material properties in unconfined compression of human nucleus pulposus, injectable hyaluronic acid-based hydrogels and tissue engineering scaffolds

Surgical treatment for lower back pain related to degenerative disc disease commonly includes discectomy and spinal fusion. While surgical intervention may provide short-term pain relief, it results in altered biomechanics of the spine and may lead to further degenerative changes in adjacent segments. One non-fusion technique currently being investigated is nucleus pulposus (NP) support via either an injectable hydrogel or tissue engineered construct. A major challenge for either approach is to mimic the mechanical properties of native NP. Here we adopt an unconfined compression testing configuration to assess toe-region and linear-region modulus and Poisson's ratio, key functional parameters for NP replacement. Human NP, experimental biocompatible hydrogel formulations composed of hyaluronic acid (HA), PEG-g-chitosan, and gelatin, and conventional alginate and agarose gels were investigated as injectable NP replacements or tissue engineering scaffolds. Testing consisted of a stress-relaxation experiment of 5% strain increments followed by 5-min relaxation periods to a total of 25% strain. Human NP had an average linear-region modulus of 5.39 +/- 2.56 kPa and a Poisson's ratio of 0.62 +/- 0.15. The modulus and Poisson's ratio are important parameters for evaluating the design of implant materials and scaffolds. The synthetic HA-based hydrogels approximated NP well and may serve as suitable NP implant materials.

Consistent hydration of intervertebral discs during in vitro testing

Spinal specimens are commonly sprayed with saline solution during mechanical testing to ensure adequate hydration. However, potting of vertebrae inhibits physiological fluid exchange through the porous endplates during loading. This un-physiological flow regime may influence mechanical properties of intervertebral discs and therefore of the whole spinal unit. The objective of this study was to evaluate a new method of spinal specimen hydration through the vertebral body during in vitro testing in order to improve consistency of mechanical behaviour. Ovine lumbar anterior column units were prepared for testing. Half of the specimens were sprayed with Ringer's solution and wrapped in plastic foil. The remainder received an additional saline infusion into the centre of each vertebral body. Three consecutive compression steps were applied by a hydraulic testing machine. Average forces within four sectors of the relaxation curves were compared. Applying saline infusion improves the consistency of consecutive relaxation curves. Differences between consecutive relaxation curves were less than those for standard hydration. The forces at the beginning of the relaxation curve were also lower for the infusion method. The standard deviation between specimens of each group was lower for saline infusion of vertebrae. Hence, the new method leads to more consistent in vitro testing conditions.

Nucleus pulposus glycosaminoglycan content is correlated with axial mechanics in rat lumbar motion segments

The unique biochemical composition and structure of the intervertebral disc allow it to support load, permit motion, and dissipate energy. With degeneration, both the biochemical composition and mechanical behavior of the disc are drastically altered, yet quantitative relationships between the biochemical changes and overall motion segment mechanics are lacking. The objective of this study was to determine the contribution of nucleus pulposus glycosaminoglycan content, which decreases with degeneration, to mechanical function of a rat lumbar spine motion segment in axial loading. Motion segments were treated with varying doses of Chondroitinase-ABC (to degrade glycosaminoglycans) and loaded in axial cyclic compression-tension, followed by compressive creep. Nucleus glycosaminoglycan content was significantly correlated (p < 0.05) with neutral zone mechanical behavior, which occurs in low load transition between tension and compression (stiffness: r = 0.59; displacement: r = -0.59), and with creep behavior (viscous parameter eta(1): r = 0.34; short time constant tau(1): r = 0.46). These results indicate that moderate decreases in nucleus glycosaminoglycan content consistent with early human degeneration affect overall mechanical function of the disc. These decreases may expose the disc to altered internal stress and strain patterns, thus contributing through mechanical or biological mechanisms to the degenerative cascade.

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.

Biomechanics of the C5-C6 Spinal Unit Before and After Placement of a disc prosthesis

The study consists of a biomechanical comparison between the intact C5-C6 spinal segment and the same segment implanted with the Bryan artificial disc prosthesis (Medtronic Ltd., Memphis, TN, USA), by the use of the finite element (FE) method. Our target is the prediction of the influence of prosthesis placement on the resulting mechanics of the C5-C6 spine unit. A FE model of the intact C5-C6 segment was built, employing realistic models of the vertebrae, disc and ligaments. Simulations were conducted imposing a compression preload combined to a flexion/extension moment, a pure lateral bending moment and a pure torsion moment, and the calculated results were compared to data from literature. The model was then modified to include the Bryan cervical disc prosthesis, and the simulations were repeated. The location of the instantaneous center of rotation (ICR) of C5 with respect to C6 throughout flexion/extension was calculated in both models. In general, the moment-rotation curves obtained from the disc prosthesis-implanted model were comparable to the curves obtained from the intact model, except for a slightly greater stiffness induced by the artificial disc. The position of the calculated ICRs was rather stable throughout flexion-extension and was generally confined to a small area, qualitatively matching the corresponding physiological region, in both models. These results imply that the Bryan disc prosthesis allows to correctly reproduce a physiological flexion/extension at the implanted level. The results of this study have quantified aspects that may assist in optimizing cervical disc replacement primarily from a biomechanical point of view.

Biomechanical and biochemical characterization of composite tissue-engineered intervertebral discs

Composite tissue-engineered intervertebral tissue was assembled in the shape of cylindrical disks composed of an outer shell of PGA mesh seeded with annulus fibrosus cells with an inner core of nucleus pulposus cells seeded into an alginate gel. Samples were implanted subcutaneously in athymic mice and retrieved at time points up to 16 weeks. At all retrieval times, samples maintained shape and contained regions of distinct tissue formation. Histology revealed progressive tissue formation with distinct morphological differences in tissue formation in regions seeded with annulus fibrosus and nucleus pulposus cells. Biochemical analysis indicated that DNA, proteoglycan, and collagen content in tissue-engineered discs increased with time, reaching >50% of the levels of native tissue by 16 weeks. The exception to this was the collagen content of the nucleus pulposus portion of the implants with were approximately 15% of native values. The equilibrium modulus of tissue-engineered discs was 49.0+/-13.2 kPa at 16 weeks, which was between the measured values for the modulus of annulus fibrosus and nucleus pulposus. The hydraulic permeability of tissue-engineered discs was 5.1+/-1.7x10(-14) m2/Pa at 16 weeks, which was between the measured values for the hydraulic permeability of annulus fibrosus and nucleus pulposus. These studies document the feasibility of creating composite tissue-engineered intevertebral disc implants with similar composition and mechanical properties to native tissue.

A homogenization model of the annulus fibrosus

The objective of this study was to use a homogenization model of the anisotropic mechanical behavior of annulus fibrosus (AF) to address some of the issues raised in structural finite element and fiber-reinforced strain energy models. Homogenization theory describes the effect of microstructure on macroscopic material properties by assuming the material is composed of repeating representative volume elements. We first developed the general homogenization model and then specifically prescribed the model to in-plane single lamella and multi-lamellae AF properties. We compared model predictions to experimentally measured AF properties and performed parametric studies. The predicted tensile moduli (E theta and E z) and their dependence on fiber volume fraction and fiber angle were consistent with measured values. However, the model prediction for shear modulus (G thetaz) was two orders of magnitude larger than directly measured values. The values of E theta and E z were strongly dependent on the model input for matrix modulus, much more so than the fiber modulus. These parametric analyses demonstrated the contribution of the matrix in AF load support, which may play a role when protoeglycans are decreased in disc degeneration, and will also be an important design factor in tissue engineering. We next compared the homogenization model to a 3-D structural finite element model and fiber-reinforced energy models. Similarities between the three model types provided confidence in the ability of these models to predict AF tissue mechanics. This study provides a direct comparison between the several types of AF models and will be useful for interpreting previous studies and elucidating AF structure-function relationships in disc degeneration and for functional tissue engineering.

A three-dimensional nonlinear finite element analysis of the mechanical behavior of tissue engineered intervertebral discs under complex loads

The use of tissue-engineering method holds great promise for treating degenerative disc disease [Gan JC, Ducheyne P, Vresilovic E, Shapiro IM. J Biomed Mater Res 2000; 51(4): 596-604]. This concept typically implies that nucleus pulposus (NP) cells are seeded on a scaffold, while the NP tissue is regenerated. Such hybrid implant is inserted into the host intervertebral disc. Because the success of a tissue engineering approach depends on maintenance or restoration of the mechanical function of the intervertebral disc, it is useful to study the initial mechanical performance of the disc after implantation of the hybrid. A three-dimensional finite element model (FEM) of the L2-L3 disc-vertebrae unit has been analyzed. The model took into account the material nonlinearities and it imposed different and complex loading conditions. In this study, we validated the model by comparison of its predictions with several sets of experimental data; we determined the optimal Young's modulus as well as the failure strength for the tissue-engineered scaffold under different loading conditions; and we analyzed the effects of implanted scaffold on the mechanical behavior of the intervertebral disc. The results of this study suggest that a well-designed tissue-engineered scaffold preferably has a modulus in the range of 5-10 MPa and a compressive strength exceeding 1.67 MPa. Implanted scaffolds with such properties can then achieve the goal of restoring the disc height and distributing stress under different loading conditions.

Material Sensitivity Study on Lumbar Motion Segment (L2-L3) Under Sagittal Plane Loadings Using Probabilistic Method

OBJECTIVE

In this study, the probabilistic responses of a three-dimensional finite element L2-L3 motion segment, with and without posterior elements, tested under sagittal plane loadings, are presented. Understanding the effect of biologic uncertainties and variations on the biomechanical response provides an insight into spinal behavior under normal and degenerated conditions.

METHODS

The biologic variability of 19 spinal components (nucleus, annulus, ligament, cortical/cancellous bone, endplate, and ligaments) in the motion segment was incorporated using statistical distributions into the model. A total of 2000 runs were performed using Monte Carlo probabilistic algorithms to compute the probabilistic response.

RESULTS

This study establishes the relative importance of the spinal components in resisting the loading modes. The results show that for an intact motion segment, posterior ligaments are more dominant than intervertebral disc in resisting flexion moment. In extension, the capsular ligaments were found to be the most influential parameter. The intervertebral disc (ie, nucleus and annulus) affects the angular response of the disc body segment more than the hard tissues (ie, cortical and cancellous bone).

CONCLUSIONS

The application of the probabilistic analysis provides a new approach whereby the influences of inherent uncertainties and variations in biologic structures can be studied and the biomechanical response assessed.

Poroelastic Analysis of Lumbar Spinal Stability in Combined Compression and Anterior Shear

OBJECTIVE

A three-dimensional poroelastic finite element (FE) L2-L3 model was developed to study lumbar spinal instability and intrinsic parameters in the intervertebral disc (IVD).

METHODS

The FE model took into consideration poroelasticity of the IVD and viscoelasticity of the annulus fibers and ligaments to predict the time-dependent behavior. To simulate a holding task, the motion segment was subjected to a combined loading of constant compressive load (1600 N) and anterior shear (200 N) for 2 hours, and the role of facet joints and ligaments in the biomechanical response was investigated by removal of unilateral/bilateral facets, posterior ligaments (supraspinous and interspinous), and facets and ligaments.

RESULTS

The results show the stabilizing role of the facets and ligaments in resisting anterior shear and sagittal rotation under combined loading over time. The main pathway of fluid movement was found to permeate through the central region of the endplate, and the fluid diffusion occurred earlier at the posterior nucleus than the anterior nucleus. The fluid loss from the nucleus dictated the time-dependent motion under the sustained loading, whereas the intrinsic properties of ligaments/annulus fibers played a role only in the early stage of the loading.

CONCLUSION

The predicted results using poroelastic elements provide new insight into the IVD in providing the spinal stiffness under combined loading.

Biomechanical responses of the intervertebral joints to static and vibrational loading: a finite element study

OBJECTIVE

This study was performed to investigate the time-dependent responses of the intervertebral joint to static and vibrational loads.

DESIGN

A poroelastic finite element model was established to analyse the fluid flow, stress distribution and deformation of the intervertebral disc.

BACKGROUND

Long-term exposure to whole body vibration is highly associated with disc degeneration and low back pain. It is hypothesized that moderate vibrational loading may increase the efficiency of fluid and nutritional transport of the intervertebral disc while prolonged static and excessive vibrational loading may have deleterious effect.

METHODS

A three-dimensional finite element model was established using the actual geometry of the L4-L5 lumber motion segment. Nonlinear poroelastic properties were assigned to the intervertebral disc and cancellous bone. Static and vibrational loads were applied and the responses of fluid flow and stress distributions were analysed.

RESULTS

The finite element model showed that the loads carried by the annulus and the facets increased with time under static loading. The fluid flow and deformation of the intervertebral disc were dependent on the loading frequency.

CONCLUSION

Vibration loading may be able to enhance disc fluid exchange via the fluid pumping mechanism.

RELEVANCE

The predicted responses implied that vibrational motion may be important in facilitating fluid and metabolic transport of the intervertebral disc.

Finite element analysis in spine research

Finite element analysis is a widely accepted tool used in many industries and research activities. It allows new designs to be thoroughly 'tested' before a prototype is even manufactured, components and systems which cannot readily be experimented upon to be examined, and 'diagnostic' investigations to be undertaken. Finite element models are already making an important contribution to our understanding of the spine and its components. Models are being used to reveal the biomechanical function of the spine and its behaviour when healthy, diseased or damaged. They are also providing support in the design and application of spinal instrumentation. The spine is a very complex structure, and many of the models are simplified and idealized because of the complexity and uncertainty in the geometry, material properties and boundary conditions of these problems. This type of modelling simplification is not peculiar to spinal modelling problems. Indeed, the idealization is often a strength when there is such uncertainty and variation between one individual and another, allowing cause-effect relationships to be isolated and fully explored, and the inherent variability of experimental tests to be eliminated. This paper reviews the development of finite element analysis in spinal modelling. It shows how modelling provides a wealth of information on our physiological performance, reduces our dependence on animal and cadaveric experiments and is an invaluable complement to clinical studies. It also leads to the conclusion that, as computing power and software capabilities increase, it is quite conceivable that in the future it will be possible to generate patient-specific models that could be used for patient assessment and even pre- and inter-operative planning.

Patient-specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc--a material sensitivity study

If patient-specific finite element models of the spine could be developed, they would offer enormous opportunities in the diagnosis and management of back problems. Several generic models have been developed in the past, but there has been very little detailed examination of the sensitivity of these models' characteristics to the input parameters. This relationship must be thoroughly understood if representative patient-specific models are to be realized and used with confidence. In particular, the performance of the intervertebral discs are central to any spine model and need detailed investigation first. A generic non-linear model of an intervertebral disc was developed and subjected to compressive, flexion and torsional loading regimes. The effects of both material and geometric non-linearities were investigated for the three loading schemes and the results compared with experimental data. The basic material properties of the fibres, annulus and nucleus were then varied and the effects on the stiffness, annulus bulge and annulus stresses analysed. The results showed that the non-linear geometry assumption had a significant effect on the compression characteristics, whereas the non-linear material option did not. In contrast, the material non-linearity was more important for the flexural and torsional loading schemes. Thus, the inclusion of non-linear material and geometry analysis options in finite element models of intervertebral discs is necessary to predict in vivo load-deflection characteristics accurately. When the influence of the material properties was examined in detail, it was found that the fibre properties did not have a significant effect on the compressive stiffness of the disc but did affect the flexural and torsional stiffnesses by up to +/-20 per cent. All loading modes were sensitive to the annulus properties with stiffnesses varying by up to +/-16 per cent. The model also revealed that for a particular compressive deformation or flexural or torsional rotation, the disc bulge was not sensitive to any of the material properties over the range of properties considered. The annulus stresses did differ significantly as the material properties were varied (up to 70 per cent under a compressive load and 60 per cent during disc flexion).

The internal mechanics of the intervertebral disc under cyclic loading

The mechanics of the intervertebral disc (IVD) under cyclic loading are investigated via a one-dimensional poroelastic model and experiment. The poroelastic model, based on that of Biot (J. Appl. Phys. 12 (1941) 155; J. Appl. Mech. 23 (1956) 91), includes a power-law relation between porosity and permeability, and a linear relation between the osmotic potential and solidity. The model was fitted to experimental data of the unconfined IVD undergoing 5 cyclic loads of 20 min compression by an applied stress of 1MPa, followed by 40 min expansion. To obtain a good agreement between experiment and theory, the initial elastic deformation of the IVD, possibly associated with the bulging of the IVD into the vertebral bodies or laterally, was removed from the experimental data. Many combinations of the permeability-porosity relationship with the initial osmotic potential (pi(i)) were investigated, and the best-fit parameters for the aggregate modulus (H(A)) and initial permeability (k(i)) were determined. The values of H(A) and k(i) were compared to literature values, and agreed well especially in the context of the adopted high-stress testing regime, and the strain related permeability in the model.

Discography

Discography is a diagnostic tool that has been used for many years. Although controversial, it provides a physiologic test for evaluation of a disc with a volumetric, manometric, radiographic, and pain-provocative challenge. Although it has a controversial past, when the anatomy and pathophysiology are considered particularly in relation to intradiscal pressure and applied loads (that correlate with daily activities of the patient), the interpretation of the results of discography become more objective and reproducible. As with any procedure, indications for patient selection are an important step in successful outcomes. The equipment and technique used for performing discography using a manometry system are described in this article, as are a review of complications and outcomes. Discography is a safe, accurate, reproducible, objective diagnostic tool when tested for volume, pressure, fluoroscopic changes, and pain provocation.

Viscoelastic finite-element analysis of a lumbar motion segment in combined compression and sagittal flexion. Effect of loading rate

STUDY DESIGN

A study using a validated viscoelastic finite-element model of a L2-L3 motion segment to identify the load sharing among the passive elements at different loading rates.

OBJECTIVE

To enhance understanding concerning the role of the loading rate (i.e., speed of lifting and lowering during manual material handling tasks) on the load sharing and safety margin of spinal structures.

SUMMARY OF BACKGROUND DATA

Industrial epidemiologic studies have shown that jobs requiring a higher speed of trunk motion contribute to a higher risk of industrial low back disorders. Consideration of the dynamic loading characteristics, such as lifting at different speeds, requires modeling of the viscoelastic behavior of passive tissues. Detailed systematic analysis of loading rate effects has been lacking in the literature.

METHODS

Complex flexion movement was simulated by applying compression and shear loads at the top of the upper vertebra while its sagittal flexion angle was prescribed without constraining any translations. The lower vertebra was fixed at the bottom. The load reached its maximum values of 2000 N compression and 200 N anterior shear while L2 was flexed to 10 degrees of flexion in the three different durations of 0.3, 1, and 3 seconds to represent fast, medium, and slow movements, respectively. The resisted bending moment, gross load-displacement response of the motion segment, forces in facet joints and ligaments, stresses and strains in anulus fibrosus, and intradiscal pressure were compared across different rates.

RESULTS

The distribution of stress and strain was markedly affected by the loading rate. The higher loading rate increased the peak intradiscal pressure (12.4%), bending moment (20.7%), total ligament forces (11.4%), posterior longitudinal ligament stress (15.7%), and anulus fiber stress at the posterolateral innermost region (17.9%), despite the 15.4% reduction in their strain.

CONCLUSIONS

Consideration of the time-dependent material properties of passive elements is essential to improving understanding of motion segment responses to dynamic loading conditions. Higher loading rate markedly reduces the safety margin of passive spinal elements. When the dynamic tolerance limits of tissues are available, the results provide bases for the guidelines of safe dynamic activities in clinics or industry.