Development and kinematic verification of a finite element model for the lumbar spine: application to disc degeneration

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.

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.

Computed tomography osteoabsorptiometry for imaging of degenerative disc disease

Background

Lower back pain is a common condition with significant morbidity and economic impact. The pathophysiology is poorly understood but is in part attributable to degenerative disc disease (DDD). The healthy intervertebral disc ensures spine functionality by transferring the perceived load to the caudally adjacent vertebrae. The exposure to recurring mechanical load is mirrored in the mineralization pattern of the subchondral bone plate (SBP), where increased bone density is a sign of repetitive localized high stress. Computed tomography -osteoabsorptiometry (CT-OAM) is a technique based on conventional CT scans that displays the mineral density distribution in the SBP as a surface-color map. The objective of this study was to measure and analyze the SBP mineral density patterns of healthy lumbar intervertebral disc (IVDs) and those suffering DDD using CT-OAM densitograms. These findings should provide in vitro insight into the long-term morphological properties of the IVD and how these differ in the state of disc degeneration.

Methods

The CT-data sets of spines from 17 healthy individuals and 18 patients displaying DDD in the lumbar spine were acquired. Individual vertebrae of both cohorts were 3D reconstructed, processed using image analysis software, and compared to one another. Maximum intensity projection of the subchondral mineralization provided surface densitograms of the SBP. The relative calcium concentration, the local maxima of mineralization, and a mean surface projection of level-defined SBPs were calculated from the densitogram and statistically compared.

Results

The inferior SBP, adjacent to degenerating disc, display an 18-41 % higher relative calcium concentration than their healthy counterparts. In the opposing superior SBPs the relative calcium content is significantly increased. Whereas it is reasonably consistent for L1-L3 (L1: 132 %, L2: 127 %, L3: 120 %), the increase grows in caudal direction (L4: 131 %, L5: 148 %, S1: 152 %). Furthermore, a change in the areal distribution of excessive mineralization can be differentiated between healthy and diseased motion segments.

Conclusions

The acquired data provide in vitro proof of the mechanical and anatomical properties of the SBP in relation to the state of disc degeneration. In conjunction with the diagnostic use of CT-osteoabsorptiometry, our data provide a basis for a non-invasive and sensitive technique that correlates with disc functionality. This could be promising in various cases, from early identification of early stages of DDD, tracking disease progression, and assessing the repercussions of surgical procedures or experimental therapies.

Computational Modeling Intervertebral Disc Pathophysiology: A Review

Lower back pain is a medical condition of epidemic proportion, and the degeneration of the intervertebral disc has been identified as a major contributor. The etiology of intervertebral disc (IVD) degeneration is multifactorial, depending on age, cell-mediated molecular degradation processes and genetics, which is accelerated by traumatic or gradual mechanical factors. The complexity of such intertwined biochemical and mechanical processes leading to degeneration makes it difficult to quantitatively identify cause–effect relationships through experiments. Computational modeling of the IVD is a powerful investigative tool since it offers the opportunity to vary, observe and isolate the effects of a wide range of phenomena involved in the degenerative process of discs. This review aims at discussing the main findings of finite element models of IVD pathophysiology with a special focus on the different factors contributing to physical changes typical of degenerative phenomena. Models presented are subdivided into those addressing role of nutritional supply, progressive biochemical alterations stemming from an imbalance between anabolic and catabolic processes, aging and those considering mechanical factors as the primary source that induces morphological change within the disc. Limitations of the current models, as well as opportunities for future computational modeling work are also discussed.

Development of a Three-Dimensional Finite Element Model of Thoracolumbar Kyphotic Deformity following Vertebral Column Decancellation

Background

Vertebral column decancellation (VCD) is a new spinal osteotomy technique to correct thoracolumbar kyphotic deformity (TLKD). Relevant biomechanical research is needed to evaluate the safety of the technique and the fixation system. We aimed to develop an accurate finite element (FE) model of the spine with TLKD following VCD and to provide a reliable model for further biomechanical analysis.

Methods

A male TLKD patient who had been treated with VCD on L2 and instrumented from T10 to L4 was a volunteer for this study. The CT scanning images of the postoperative spine were used for model development. The FE model, simulating the spine from T1 to the sacrum, includes vertebrae, intervertebral discs, spinal ligaments, pedicle screws, and rods. The model consists of 509580 nodes and 445722 hexahedrons. The ranges of motion (ROM) under different loading conditions were calculated for validation. The stresses acting on rods, screws, and vertebrae were calculated.

Results

The movement trend, peak stress, and ROM calculated by the current FE model are consistent with previous studies. The FE model in this study is able to simulate the mechanical response of the spine during different motions with different loading conditions. Under axial compression, the rod was the part bearing the peak stress. During flexion, the stress was concentrated on proximal pedicle screws. Under extension and lateral bending, an osteotomized L1 vertebra bore the greatest stress on the model. During tests, ligament disruption and unit deletion were not found, indicating an absence of fracture and fixation breakage.

Discussion

A subject-specific FE model of the spine following VCD is developed and validated. It can provide a reliable and accurate digital platform for biomechanical analysis and surgical planning.

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.

Finite element simulation and clinical follow-up of lumbar spine biomechanics with dynamic fixations

Arthrodesis is a recommended treatment in advanced stages of degenerative disc disease. Despite dynamic fixations were designed to prevent abnormal motions with better physiological load transmission, improving lumbar pain and reducing stress on adjacent segments, contradictory results have been obtained. This study was designed to compare differences in the biomechanical behaviour between the healthy lumbar spine and the spine with DYNESYS and DIAM fixation, respectively, at L4-L5 level. Behaviour under flexion, extension, lateral bending and axial rotation are compared using healthy lumbar spine as reference. Three 3D finite element models of lumbar spine (healthy, DYNESYS and DIAM implemented, respectively) were developed, together a clinical follow-up of 58 patients operated on for degenerative disc disease. DYNESYS produced higher variations of motion with a maximum value for lateral bending, decreasing intradiscal pressure and facet joint forces at instrumented level, whereas screw insertion zones concentrated stress. DIAM increased movement during flexion, decreased it in another three movements, and produced stress concentration at the apophyses at instrumented level. Dynamic systems, used as single systems without vertebral fusion, could be a good alternative to degenerative disc disease for grade II and grade III of Pfirrmann.

Effects of Different Angles of the Traction Table on Lumbar Spine Ligaments: A Finite Element Study

Background

The traction bed is a noninvasive device for treating lower back pain caused by herniated intervertebral discs. In this study, we investigated the impact of the traction bed on the lower back as a means of increasing the disc height and creating a gap between facet joints.

Methods

Computed tomography (CT) images were obtained from a female volunteer and a three-dimensional (3D) model was created using software package MIMICs 17.0. Afterwards, the 3D model was analyzed in an analytical software (Abaqus 6.14). The study was conducted under the following traction loads: 25%, 45%, 55%, and 85% of the whole body weight in different angles.

Results

Results indicated that the loading angle in the L3–4 area had 36.8%, 57.4%, 55.32%, 49.8%, and 52.15% effect on the anterior longitudinal ligament, posterior longitudinal ligament, intertransverse ligament, interspinous ligament, and supraspinous ligament, respectively. The respective values for the L4–5 area were 32.3%, 10.6%, 53.4%, 56.58%, and 57.35%. Also, the body weight had 63.2%, 42.6%, 44.68%, 50.2%, and 47.85% effect on the anterior longitudinal ligament, posterior longitudinal ligament, intertransverse ligament, interspinous ligament, and supraspinous ligament, respectively. The respective values for the L4–5 area were 67.7%, 89.4%, 46.6%, 43.42% and 42.65%. The authenticity of results was checked by comparing with the experimental data.

Conclusions

The results show that traction beds are highly effective for disc movement and lower back pain relief. Also, an optimal angle for traction can be obtained in a 3D model analysis using CT or magnetic resonance imaging images. The optimal angle would be different for different patients and thus should be determined based on the decreased height of the intervertebral disc, weight and height of patients.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

A predictive mechanical model for evaluating vertebral fracture probability in lumbar spine under different osteoporotic drug therapies

Osteoporotic vertebral fractures represent a major cause of disability, loss of quality of life and even mortality among the elderly population. Decisions on drug therapy are based on the assessment of risk factors for fracture from bone mineral density (BMD) measurements. A previously developed model, based on the Damage and Fracture Mechanics, was applied for the evaluation of the mechanical magnitudes involved in the fracture process from clinical BMD measurements. BMD evolution in untreated patients and in patients with seven different treatments was analyzed from clinical studies in order to compare the variation in the risk of fracture. The predictive model was applied in a finite element simulation of the whole lumbar spine, obtaining detailed maps of damage and fracture probability, identifying high-risk local zones at vertebral body. For every vertebra, strontium ranelate exhibits the highest decrease, whereas minimum decrease is achieved with oral ibandronate. All the treatments manifest similar trends for every vertebra. Conversely, for the natural BMD evolution, as bone stiffness decreases, the mechanical damage and fracture probability show a significant increase (as it occurs in the natural history of BMD). Vertebral walls and external areas of vertebral end plates are the zones at greatest risk, in coincidence with the typical locations of osteoporotic fractures, characterized by a vertebral crushing due to the collapse of vertebral walls. This methodology could be applied for an individual patient, in order to obtain the trends corresponding to different treatments, in identifying at-risk individuals in early stages of osteoporosis and might be helpful for treatment decisions.

Theory of MRI contrast in the annulus fibrosus of the intervertebral disc

OBJECTIVE

Here we develop a three-dimensional analytic model for MR image contrast of collagen lamellae in the annulus fibrosus of the intervertebral disc of the spine, based on the dependence of the MRI signal on collagen fiber orientation.

MATERIALS AND METHODS

High-resolution MRI scans were performed at 1.5 and 7 T on intact whole disc specimens from ovine, bovine, and human spines. An analytic model that approximates the three-dimensional curvature of the disc lamellae was developed to explain inter-lamellar contrast and intensity variations in the annulus. The model is based on the known anisotropic dipolar relaxation of water in tissues with ordered collagen.

RESULTS

Simulated MRI data were generated that reproduced many features of the actual MRI data. The calculated inter-lamellar image contrast demonstrated a strong dependence on the collagen fiber angle and on the circumferential location within the annulus.

CONCLUSION

This analytic model may be useful for interpreting MR images of the disc and for predicting experimental conditions that will optimize MR image contrast in the annulus fibrosus.