Biomechanical effects of spinal cord compression due to ossification of posterior longitudinal ligament and ligamentum flavum: A finite element analysis

Finite Element Analysis for Degenerative Cervical Myelopathy: Scoping Review of the Current Findings and Design Approaches, Including Recommendations on the Choice of Material Properties

BACKGROUND

Degenerative cervical myelopathy (DCM) is a slow-motion spinal cord injury caused via chronic mechanical loading by spinal degenerative changes. A range of different degenerative changes can occur. Finite element analysis (FEA) can predict the distribution of mechanical stress and strain on the spinal cord to help understand the implications of any mechanical loading. One of the critical assumptions for FEA is the behavior of each anatomical element under loading (ie, its material properties).

OBJECTIVE

This scoping review aims to undertake a structured process to select the most appropriate material properties for use in DCM FEA. In doing so, it also provides an overview of existing modeling approaches in spinal cord disease and clinical insights into DCM.

METHODS

We conducted a scoping review using qualitative synthesis. Observational studies that discussed the use of FEA models involving the spinal cord in either health or disease (including DCM) were eligible for inclusion in the review. We followed the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) guidelines. The MEDLINE and Embase databases were searched to September 1, 2021. This was supplemented with citation searching to retrieve the literature used to define material properties. Duplicate title and abstract screening and data extraction were performed. The quality of evidence was appraised using the quality assessment tool we developed, adapted from the Newcastle-Ottawa Scale, and shortlisted with respect to DCM material properties, with a final recommendation provided. A qualitative synthesis of the literature is presented according to the Synthesis Without Meta-Analysis reporting guidelines.

RESULTS

A total of 60 papers were included: 41 (68%) "FEA articles" and 19 (32%) "source articles." Most FEA articles (33/41, 80%) modeled the gray matter and white matter separately, with models typically based on tabulated data or, less frequently, a hyperelastic Ogden variant or linear elastic function. Of the 19 source articles, 14 (74%) were identified as describing the material properties of the spinal cord, of which 3 (21%) were considered most relevant to DCM. Of the 41 FEA articles, 15 (37%) focused on DCM, of which 9 (60%) focused on ossification of the posterior longitudinal ligament. Our aggregated results of DCM FEA indicate that spinal cord loading is influenced by the pattern of degenerative changes, with decompression alone (eg, laminectomy) sufficient to address this as opposed to decompression combined with other procedures (eg, laminectomy and fusion).

CONCLUSIONS

FEA is a promising technique for exploring the pathobiology of DCM and informing clinical care. This review describes a structured approach to help future investigators deploy FEA for DCM. However, there are limitations to these recommendations and wider uncertainties. It is likely that these will need to be overcome to support the clinical translation of FEA to DCM.

Effect of Different Types of Ossification of the Posterior Longitudinal Ligament on the Dynamic Biomechanical Response of the Spinal Cord: A Finite Element Analysis

Ossification of the posterior longitudinal ligament (OPLL) has been identified as an important cause of cervical myelopathy. However, the biomechanical mechanism between the OPLL type and the clinical characteristics of myelopathy remains unclear. The aim of this study was to evaluate the effect of different types of OPLL on the dynamic biomechanical response of the spinal cord. A three-dimensional finite element model of the fluid-structure interaction of the cervical spine with spinal cord was established and validated. The spinal cord stress and strain, cervical range of motion (ROM) in different types of OPLL models were predicted during dynamic flexion and extension activity. Different types of OPLL models showed varying degrees of increase in stress and strain under the process of flexion and extension, and there was a surge toward the end of extension. Larger spinal cord stress was observed in segmental OPLL. For continuous and mixed types of OPLL, the adjacent segments of OPLL showed a dramatic increase in ROM, while the ROM of affected segments was limited. As a dynamic factor, flexion and extension of the cervical spine play an amplifying role in OPLL-related myelopathy, while appropriate spine motion is safe and permitted. Segmental OPLL patients are more concerned about the spinal cord injury induced by large stress, and patients with continuous OPLL should be noted to progressive injuries of adjacent level.

The biomechanical effect of different types of ossification of the ligamentum flavum on the spinal cord during cervical dynamic activities

Ossification of the ligamentum flavum (OLF) is thought to be an influential etiology of myelopathy, as thickened ligamentum flavum causes the stenosis of the vertebral canal, which could subsequently compress the spinal cord. Unfortunately, there was little information available on the effects of cervical OLF on spinal cord compression, such as the relationship between the progression of cervical OLF and nervous system symptoms during dynamic cervical spine activities. In this research, a finite element model of C1-C7 including the spinal cord featured by dynamic fluid-structure interaction was reconstructed and utilized to analyze how different types of cervical OLF affect principal strain and stress distribution in spinal cord during spinal activities towards six directions. For patients with cervical OLF, cervical extension induces higher stress within the spinal cord among all directions. From the perspective of biomechanics, extension leads to stress concentration in the lateral corticospinal tracts or the posterior of gray matter. Low energy damage to the spinal cord would be caused by the high and fluctuating stresses during cervical movements to the affected side for patients with unilateral OLF at lower grades.

Finite element modeling of the human cervical spinal cord and its applications: A systematic review

Background Context

Finite element modeling (FEM) is an established tool to analyze the biomechanics of complex systems. Advances in computational techniques have led to the increasing use of spinal cord FEMs to study cervical spinal cord pathology. There is considerable variability in the creation of cervical spinal cord FEMs and to date there has been no systematic review of the technique. The aim of this study was to review the uses, techniques, limitations, and applications of FEMs of the human cervical spinal cord.

Methods

A literature search was performed through PubMed and Scopus using the words finite element analysis, spinal cord, and biomechanics. Studies were selected based on the following inclusion criteria: (1) use of human spinal cord modeling at the cervical level; (2) model the cervical spinal cord with or without the osteoligamentous spine; and (3) the study should describe an application of the spinal cord FEM.

Results

Our search resulted in 369 total publications, 49 underwent reviews of the abstract and full text, and 23 were included in the study. Spinal cord FEMs are used to study spinal cord injury and trauma, pathologic processes, and spine surgery. Considerable variation exists in the derivation of spinal cord geometries, mathematical models, and material properties. Less than 50% of the FEMs incorporate the dura mater, cerebrospinal fluid, nerve roots, and denticulate ligaments. Von Mises stress, and strain of the spinal cord are the most common outputs studied. FEM offers the opportunity for dynamic simulation, but this has been used in only four studies.

Conclusions

Spinal cord FEM provides unique insight into the stress and strain of the cervical spinal cord in various pathological conditions and allows for the simulation of surgical procedures. Standardization of modeling parameters, anatomical structures and inclusion of patient-specific data are necessary to improve the clinical translation.

Effects of cervical rotatory manipulation on the cervical spinal cord complex with ossification of the posterior longitudinal ligament in the vertebral canal: A finite element study

Background: There are few studies focusing on biomechanism of spinal cord injury according to the ossification of the posterior longitudinal ligament (OPLL) during cervical rotatory manipulation (CRM). This study aimed to explore the biomechanical effects of CRM on the spinal cord, dura matter and nerve roots with OPLL in the cervical vertebral canal. Methods: Three validated FE models of the craniocervical spine and spinal cord complex were constructed by adding mild, moderate, and severe OPLL to the healthy FE model, respectively. We simulated the static compression of the spinal cord by OPLL and the dynamic compression during CRM in the flexion position. The stress distribution of the spinal cord complex was investigated. Results: The cervical spinal cord experienced higher von Mises stress under static compression by the severe OPLL. A higher von Mises stress was observed on the spinal cord in the moderate and severe OPLL models during CRM. The dura matter and nerve roots had a higher von Mises stress in all three models during CRM. Conclusion: The results show a high risk in performing CRM in the flexion position on patients with OPLL, in that different occupying ratios in the vertebral canal due to OPLL could significantly increase the stress on the spinal cord complex.

Effect of degenerative factors on cervical spinal cord during flexion and extension: a dynamic finite element analysis

Spinal cord injury (SCI) is a global problem that brings a heavy burden to both patients and society. Recent investigations indicated degenerative disease is taking an increasing part in SCI with the growth of the aging population. However, little insight has been gained about the effect of cervical degenerative disease on the spinal cord during dynamic activities. In this work, a dynamic fluid-structure interaction model was developed and validated to investigate the effect of anterior and posterior encroachment caused by degenerative disease on the spinal cord during normal extension and flexion. Maximum von-Mises stress and maximum principal strain were observed at the end of extension and flexion. The abnormal stress distribution caused by degenerative factors was concentrated in the descending tracts of the spinal cord. Our finding indicates that the excessive motion of the cervical spine could potentially exacerbate spinal cord injury and enlarge injury areas. Stress and strain remained low compared to extension during moderate flexion. This suggests that patients with cervical degenerative disease should avoid frequent or excessive flexion and extension which could result in motor function impairment, whereas moderate flexion is safe. Besides, encroachment caused by degenerative factors that are not significant in static imaging could also cause cord compression during normal activities.

A New Framework for Investigating the Biological Basis of Degenerative Cervical Myelopathy [AO Spine RECODE-DCM Research Priority Number 5]: Mechanical Stress, Vulnerability and Time

STUDY DESIGN

Literature Review (Narrative).

OBJECTIVE

To propose a new framework, to support the investigation and understanding of the pathobiology of DCM, AO Spine RECODE-DCM research priority number 5.

METHODS

Degenerative cervical myelopathy is a common and disabling spinal cord disorder. In this perspective, we review key knowledge gaps between the clinical phenotype and our biological models. We then propose a reappraisal of the key driving forces behind DCM and an individual's susceptibility, including the proposal of a new framework.

RESULTS

Present pathobiological and mechanistic knowledge does not adequately explain the disease phenotype; why only a subset of patients with visualized cord compression show clinical myelopathy, and the amount of cord compression only weakly correlates with disability. We propose that DCM is better represented as a function of several interacting mechanical forces, such as shear, tension and compression, alongside an individual's vulnerability to spinal cord injury, influenced by factors such as age, genetics, their cardiovascular, gastrointestinal and nervous system status, and time.

CONCLUSION

Understanding the disease pathobiology is a fundamental research priority. We believe a framework of mechanical stress, vulnerability, and time may better represent the disease as a whole. Whilst this remains theoretical, we hope that at the very least it will inspire new avenues of research that better encapsulate the full spectrum of disease.

Percutaneous Endoscopic Posterior Decompression for Therapy of Spinal Cord Compression Due to Ossification of the Ligamentum Flavum: A Long-Term Follow-up

BACKGROUND

Thoracic ossification of the ligamentum flavum (OLF) is a pathologic condition that affects ligamentation of the OLF and causes slowly progressive myeloradiculopathy. There is a trend toward performing minimally invasive surgery. In this study, we assess the long-term efficacy of percutaneous endoscopic surgical management of thoracic OLF.

METHODS

Twenty patients with thoracic myelopathy due to thoracic OLF underwent percutaneous endoscopic surgical management. We investigated clinical outcomes and neurologic improvements. Magnetic resonance imaging was performed on all patients preoperatively and postoperatively, and intramedullary signal changes were evaluated.

RESULTS

The operation time averaged at 170.4 minutes (range 110-320 minutes). The mean intraoperative blood loss was 29.6 mL (range 5-100 mL). Cerebrospinal fluid leakage occurred in 1 patient and healed well. The follow-up period ranged from 60 to 72 months. The mean score on the Japanese Orthopedic Association scale improved from (6.0 ± 1.41) preoperatively to (7.83 ± 1.40) at 1 month postoperatively to (9.67 ± 1.30) at the final follow-up (P < 0.05). At the final follow-up stage, 11 patients had excellent outcomes, 6 good, 2 fair, and 1 unchanged, according to the Hirabayashi recovery rate. No patient had postoperative deterioration in neurologic status.

CONCLUSIONS

Percutaneous endoscopic surgical management of thoracic OLF has proven to be both safe and effective for the resection of the OLF in the thoracic spine.

Biomechanical comparison of spinal cord compression types occurring in Degenerative Cervical Myelopathy

BACKGROUND

Degenerative Cervical Myelopathy results from spine degenerations narrowing the spinal canal and inducing cord compressions. Prognosis is challenging. This study aimed at simulating typical spinal cord compressions observed in patients with a realistic model to better understand pathogenesis for later prediction of patients' evolution.

METHODS

A 30% reduction in cord cross-sectional area at C5-C6 was defined as myelopathy threshold based on Degenerative Cervical Myelopathy features from literature and MRI measurements in 20 patients. Four main compression types were extracted from MRIs and simulated with a comprehensive three-dimensional finite element spine model. Median diffuse, median focal and lateral types were modelled as disk herniation while circumferential type additionally involved ligamentum flavum hypertrophy. All stresses were quantified along inferior-superior axis, compression development and across atlas-defined spinal cord regions.

FINDINGS

Anterior gray and white matter globally received the highest stress while lateral pathways were the least affected. Median diffuse compression induced the highest stresses. Circumferential type focused stresses in posterior gray matter. Along inferior-superior axis, those two types showed a peak of constraints at compression site while median focal and lateral types showed lower values but extending further.

INTERPRETATION

Median diffuse type would be the most detrimental based on stress amplitude. Anterior regions would be the most at risk, except for circumferential type where posterior regions would be equally affected. In addition to applying constraints, ischemia could be a significant component explaining the early demyelination reported in lateral pathways. Moving towards patient-specific simulations, biomechanical models could become strong predictors for degenerative changes.

A comprehensive finite element model of surgical treatment for cervical myelopathy

BACKGROUND

Cervical myelopathy is a common and debilitating chronic spinal cord dysfunction. Treatment includes anterior and/or posterior surgical intervention to decompress the spinal cord and stabilize the spine, but no consensus has been made as to the preferable surgical intervention. The objective of this study was to develop an finite element model of the healthy and myelopathic C2-T1 cervical spine and common anterior and posterior decompression techniques to determine how spinal cord stress and strain is altered in healthy and diseased states.

METHODS

A finite element model of the C2-T1 cervical spine, spinal cord, pia, dura, cerebral spinal fluid, and neural ligaments was developed and validated against in vivo human displacement data. To model cervical myelopathy, disc herniation and osteophytes were created at the C4-C6 levels. Three common surgical interventions were then incorporated at these levels.

FINDINGS

The finite element model accurately predicted healthy and myelopathic spinal cord displacement compared to motions observed in vivo. Spinal cord strain increased during extension in the cervical myelopathy finite element model. All surgical techniques affected spinal cord stress and strain. Specifically, adjacent levels had increased stress and strain, especially in the anterior cervical discectomy and fusion case.

INTERPRETATIONS

This model is the first biomechanically validated, finite element model of the healthy and myelopathic C2-T1 cervical spine and spinal cord which predicts spinal cord displacement, stress, and strain during physiologic motion. Our findings show surgical intervention can cause increased strain in the adjacent levels of the spinal cord which is particularly worse following anterior cervical discectomy and fusion.

Numerical investigation of the relative effect of disc bulging and ligamentum flavum hypertrophy on the mechanism of central cord syndrome

BACKGROUND

The pathogenesis of the central cord syndrome is still unclear. While there is a consensus on hyperextension as the main traumatic mechanism leading to this condition, there is yet to be consensus in studies regarding the pathological features of the spine (intervertebral disc bulging or ligamentum flavum hypertrophy) that could contribute to clinical manifestations.

METHODS

A comprehensive finite element model of the cervical spine segment and spinal cord was used to simulate high-speed hyperextension. Four stenotic cases were modelled to study the effect of ligamentum flavum hypertrophy and intervertebral disc bulging on the von Mises stress and strain.

FINDINGS

During hyperextension, the downward displacement of the ligamentum flavum and a reduction of the spinal canal diameter (up to 17%) led to a dynamic compression of the cord. Ligamentum flavum hypertrophy was associated with stress and strain (peak of 0.011 Mpa and 0.24, respectively) in the lateral corticospinal tracts, which is consistent with the histologic pattern of the central cord syndrome. Linear intervertebral disc bulging alone led to a higher stress in the anterior and posterior funiculi (peak 0.029 Mpa). Combined with hypertrophic ligamentum flavum, it further increased the stress and strain in the corticospinal tracts and in the posterior horn (peak of 0.023 Mpa and 0.35, respectively).

INTERPRETATION

The stenotic typology and geometry greatly influence stress and strain distribution resulting from hyperextension. Ligamentum flavum hypertrophy is a main feature leading to central cord syndrome.

Physicochemical characterization of mineral deposits in human ligamenta flava

The aim of our study was the detailed characterization of calcium deposits in ligamenta flava. The use of microcomputed tomography allowed extending the routine medical investigations to characterize mineral grains in the microscopic scale. A possible connection between spinal stenosis and ligament mineralization was investigated. The studies were carried out on 24 surgically removed ligamentum flavum samples divided into control and stenosis groups. Physicochemical characterization of the inorganic material was performed using X-ray fluorescence, X-ray diffraction, and Fourier transform infrared spectroscopy. The minerals were present in 14 of 24 ligament samples, both in stenosis and control groups. The inorganic substance constitutes on average ~0.1% of the sample volume. The minerals are scattered in the soft tissue matrix without any regular pattern. It was confirmed that minerals possess an internal structure and consist of the organic material and small inorganic grains mixture. The physicochemical analyses show that the predominant crystalline phase was hydroxyapatite (HAP). In the stenosis group calcium pyrophosphate dehydrate (CPPD) was identified. Both structures were never present in a single sample. Two different crystal structures suggest two independent processes of mineralization. The formation of CPPD may be treated as a more intense process since CPPD minerals are characterized by bigger values of the structural parameters and higher density than HAP deposits. The formation of HAP minerals is a soft tissue degeneration process that begins, in some cases, at early age or may not occur at all. Various density and volume of mineral grains indicate that the mineralization process does not occur in a constant environment and proceeds with various speeds. The formation of minerals in ligamenta flava is not directly associated with diagnosed spinal canal stenosis.

Increased stress and strain on the spinal cord due to ossification of the posterior longitudinal ligament in the cervical spine under flexion after laminectomy

Myelopathy in the cervical spine due to cervical ossification of the posterior longitudinal ligament could be induced by static compression and/or dynamic factors. It has been suggested that dynamic factors need to be considered when planning and performing the decompression surgery on patients with the ossification of the posterior longitudinal ligament. A finite element model of the C2-C7 cervical spine in the neutral position was developed and used to generate flexion and extension of the cervical spine. The segmental ossification of the posterior longitudinal ligament on the C5 was assumed, and laminectomy was performed on C4-C6 according to a conventional surgical technique. For various occupying ratios of the ossified ligament between 20% and 60%, von-Mises stresses, maximum principal strains in the spinal cord, and cross-sectional area of the cord were investigated in the pre-operative and laminectomy models under flexion, neutral position, and extension. The results were consistent with previous experimental and computational studies in terms of stress, strain, and cross-sectional area. Flexion leads to higher stresses and strains in the cord than the neutral position and extension, even after decompression surgery. These higher stresses and strains might be generated by residual compression occurring at the segment with the ossification of the posterior longitudinal ligament. This study provides fundamental information under different neck positions regarding biomechanical characteristics of the spinal cord in cervical ossification of the posterior longitudinal ligament.

Biomechanical Behaviors in Three Types of Spinal Cord Injury Mechanisms

Clinically, spinal cord injuries (SCIs) are radiographically evaluated and diagnosed from plain radiographs, computed tomography (CT), and magnetic resonance imaging. However, it is difficult to conclude that radiographic evaluation of SCI can directly explain the fundamental mechanism of spinal cord damage. The von-Mises stress and maximum principal strain are directly associated with neurological damage in the spinal cord from a biomechanical viewpoint. In this study, the von-Mises stress and maximum principal strain in the spinal cord as well as the cord cross-sectional area (CSA) were analyzed under various magnitudes for contusion, dislocation, and distraction SCI mechanisms, using a finite-element (FE) model of the cervical spine with spinal cord including white matter, gray matter, dura mater with nerve roots, and cerebrospinal fluid (CSF). A regression analysis was performed to find correlation between peak von-Mises stress/peak maximum principal strain at the cross section of the highest reduction in CSA and corresponding reduction in CSA of the cord. Dislocation and contusion showed greater peak stress and strain values in the cord than distraction. The substantial increases in von-Mises stress as well as CSA reduction similar to or more than 30% were produced at a 60% contusion and a 60% dislocation, while the maximum principal strain was gradually increased as injury severity elevated. In addition, the CSA reduction had a strong correlation with peak von-Mises stress/peak maximum principal strain for the three injury mechanisms, which might be fundamental information in elucidating the relationship between radiographic and mechanical parameters related to SCI.

Effect of posterior decompression extent on biomechanical parameters of the spinal cord in cervical ossification of the posterior longitudinal ligament

Ossification of the posterior longitudinal ligament is a common cause of the cervical myelopathy due to compression of the spinal cord. Patients with ossification of the posterior longitudinal ligament usually require the decompression surgery, and there is a need to better understand the optimal surgical extent with which sufficient decompression without excessive posterior shifting can be achieved. However, few quantitative studies have clarified this optimal extent for decompression of cervical ossification of the posterior longitudinal ligament. We used finite element modeling of the cervical spine and spinal cord to investigate the effect of posterior decompression extent for continuous-type cervical ossification of the posterior longitudinal ligament on changes in stress, strain, and posterior shifting that occur with three different surgical methods (laminectomy, laminoplasty, and hemilaminectomy). As posterior decompression extended, stress and strain in the spinal cord decreased and posterior shifting of the cord increased. The location of the decompression extent also influenced shifting. Laminectomy and laminoplasty were very similar in terms of decompression results, and both were superior to hemilaminectomy in all parameters tested. Decompression to the extents of C3-C6 and C3-C7 of laminectomy and laminoplasty could be considered sufficient with respect to decompression itself. Our findings provide fundamental information regarding the treatment of cervical ossification of the posterior longitudinal ligament and can be applied to patient-specific surgical planning.

Influence of sagittal and axial types of ossification of posterior longitudinal ligament on mechanical stress in cervical spinal cord: A finite element analysis

BACKGROUND

There are few studies focusing on the prediction of stress distribution according to the types of ossification of the posterior longitudinal ligament, which can be fundamental information associated with clinical aspects such as the relationship between stress level and neurological symptom severity. In this study, the influence of sagittal and axial types of ossification of the posterior longitudinal ligament on mechanical stress in the cervical spinal cord was investigated.

METHODS

A three-dimensional finite element model of the cervical spine with spinal cord was developed and validated. The von Mises stresses in the cord and the reduction in cross-sectional areas and volume of the cord were investigated for various axial and sagittal types according to the occupying ratio of ossification of the posterior longitudinal ligament in the spinal canal.

FINDINGS

The influence of axial type was less than that of the sagittal type, even though the central type showed higher maximum stresses in the cord, especially for the continuous type. With a 60% occupying ratio of ossification of the posterior longitudinal ligament, the maximum stress was significantly high and the cross-sectional area of the spinal cord was reduced by more than 30% of the intact area regardless of sagittal or axial types. Finally, a higher level of sagittal extension would increase the peak cord tissue stress, which would be related to the neurological dysfunction and tissue damage.

INTERPRETATION

Quantitative investigation of biomechanical characteristics such as mechanical stress may provide fundamental information for pre-operative planning of treatment for ossification of the posterior longitudinal ligament.

Uniaxial cyclic stretch promotes osteogenic differentiation and synthesis of BMP2 in the C3H10T1/2 cells with BMP2 gene variant of rs2273073 (T/G)

Ossification of the posterior longitudinal ligament of the cervical spine (OPLL) is characterized by the replacement of ligament tissues with ectopic bone formation, and this result is strongly affected by genetic and local factors. Two single nucleotide polymorphisms (SNPs) of rs2273073 (T/G) and rs235768 (A/T) of bone morphogenetic protein 2 (BMP2) gene which are associated with OPLL have been reported in our previous report. In this study, we confirmed the connection in 18 case samples analysis of BMP2 gene in OPLL patients; additionally, it was also shown from the OPLL patients with ligament tissues that enchondral ossification and expression of BMP2 were significantly higher compared with the non-OPLL patients by histological examination, immunohistochemistry and Western blotting analysis. To investigate the underlying mechanism, we studied the effect of SNPs in cell model. The C3H10T1/2 cells with different BMP2 gene variants were constructed and then subjected to uniaxial cyclic stretch (0.5 Hz, 10% stretch). In the presence of mechanical stress, the expression of BMP2 protein in C3H10T1/2 cells transfected by BMP2 (rs2273073 (T/G)) and BMP2 (rs2273073 (T/G), rs235768 (A/T)) were significantly higher than the corresponding static groups (P<0.05). In conclusion, these results suggested that BMP2 gene variant of rs2273073 (T/G) could not only increase cell susceptibility to bone transformation similar to pre-OPLL change, but also increase the sensibility to mechanical stress which might play an important role during the progression of OPLL.