Remedy for fictive negative pressures in biphasic finite element models of the intervertebral disc during unloading

Previous biphasic finite element studies investigated the temporal response of a spinal segment under rather simplified loading conditions with no attention to unloading and recovery phases. Employment of existing constitutive relations in porous media yields rather large suction-type pore pressures in the disc as the load suddenly disappears. Such negative pressures are absent in vivo and are hence fictive. The aim of this study was to search for remedies to avoid the computation of negative pressures upon unloading. Partial saturation for the disc or a rest load (RL) higher than 400 N totally eliminated the negative pressures. Decreasing the voids ratio (VR) also led to a reduced negative pressure. When defining a partial saturated disc or using a lower VR in combination with a boundary pressure of 0.25 MPa and a RL of 350 N, no negative pressure was calculated. It appears that the constraint of full saturation and a high mobile fluid fraction of the disc tissues along with inadequate tissue properties are the likely causes of negative pressures during unloading.     

Numerical analysis of the influence of nucleus pulposus removal on the biomechanical behavior of a lumbar motion segment

Nucleus replacement was deemed to have therapeutic potential for patients with intervertebral disc herniation. However, whether a patient would benefit from nucleus replacement is technically unclear. This study aimed to investigate the influence of nucleus pulposus (NP) removal on the biomechanical behavior of a lumbar motion segment and to further explore a computational method of biomechanical characteristics of NP removal, which can evaluate the mechanical stability of pulposus replacement. We, respectively, reconstructed three types of models for a mildly herniated disc and three types of models for a severely herniated disc based on a L4–L5 segment finite element model with computed tomography image data from a healthy adult. First, the NP was removed from the herniated disc models, and the biomechanical behavior of NP removal was simulated. Second, the NP cavities were filled with an experimental material (Poisson's ratio = 0.3; elastic modulus = 3 MPa), and the biomechanical behavior of pulposus replacement was simulated. The simulations were carried out under the five loadings of axial compression, flexion, lateral bending, extension, and axial rotation. The changes of the four biomechanical characteristics, i.e. the rotation degree, the maximum stress in the annulus fibrosus (AF), joint facet contact forces, and the maximum disc deformation, were computed for all models. Experimental results showed that the rotation range, the maximum AF stress, and joint facet contact forces increased, and the maximum disc deformation decreased after NP removal, while they changed in the opposite way after the nucleus cavities were filled with the experimental material.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4–L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion–extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion–extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Finite elements/Taguchi method based procedure for the identification of the geometrical parameters significantly affecting the biomechanical behavior of a lumbar disc

The aim of this work is to show a quick and simple procedure able to identify the geometrical parameters of the intervertebral disc that strongly affect the behavior of the FEM model. First, we allocated a selection criterion for the minimum number of geometrical parameters that describe, with a good degree of approximation, a healthy human vertebra. Next, we carried out a sensitivity analysis using the ‘Taguchi orthogonal array’ to arrive at a quick identification of the parameters that strongly affect the behavior of the Fem model.     

PTEN promotes intervertebral disc degeneration by regulating nucleus pulposus cell behaviors

Intervertebral disc degeneration (IDD) is induced by multiple factors including increased apoptosis, decreased survival, and reduced extracellular matrix (ECM) synthesis in the nucleus pulposus (NP) cells. The tumor suppressor phosphatase and tensin homolog deleted from chromosome 10 (PTEN) is the only known lipid phosphatase counteracting the PI3K/AKT pathway. Loss of PTEN leads to activated PI3K/AKT signaling, which plays a key role in a variety of cancers. However, the role of PTEN/PI3K/AKT signaling nexus in IDD remains unknown. Here, we report that PTEN is overexpressed in degenerative NP, which correlates with inactivated AKT. Using the PTEN knockdown approach by lentivirus‐mediated short interfering RNA gene transfer technique, we report that PTEN decreases survival but induces apoptosis and senescence of NP cells. PTEN also inhibits expression and production of ECM components including collagen II, aggrecan, and proteoglycan. Furthermore, PTEN modulates the expression of ECM regulatory molecules SOX‐9 and matrix metalloproteinase‐3 (MMP‐3). Using small‐molecule AKT inhibitor GDC‐0068, we confirm that PTEN regulates NP cell behaviors through its direct targeting of PI3K/AKT. These findings demonstrate for the first time that PTEN/PI3K/AKT signaling axis plays an important role in the pathogenesis of IDD. Targeting PTEN using gene therapy may represent a promising therapeutic approach against disc degenerative diseases.     

A combined numerical and experimental technique for estimation of the forces and moments in the lumbar intervertebral disc

Evaluation of the loads on lumbar intervertebral discs (IVD) is critically important since it is closely related to spine biomechanics, pathology and prosthesis design. Non-invasive estimation of the loads in the discs remains a challenge. In this study, we proposed a new technique to estimate in vivo loads in the IVD using a subject-specific finite element (FE) model of the disc and the kinematics of the disc endplates as input boundary conditions. The technique was validated by comparing the forces and moments in the discs calculated from the FE analyses to the in vitro experiment measurements of three corresponding lumbar discs. The results showed that the forces and moments could be estimated within an average error of 20%. Therefore, this technique can be a promising tool for non-invasive estimation of the loads in the discs and may be extended to be used on living subjects.     

The influence of different magnitudes and methods of applying preload on fusion and disc replacement constructs in the lumbar spine: a finite element analysis

In a finite element (FE) analysis of the lumbar spine, different preload application methods that are used in biomechanical studies may yield diverging results. To investigate how the biomechanical behaviour of a spinal implant is affected by the method of applying the preload, hybrid-controlled FE analysis was used to evaluate the biomechanical behaviour of the lumbar spine under different preload application methods. The FE models of anterior lumbar interbody fusion (ALIF) and artificial disc replacement (ADR) were tested under three different loading conditions: a 150 N pressure preload (PP) and 150 and 400 N follower loads (FLs). This study analysed the resulting range of motion (ROM), facet contact force (FCF), inlay contact pressure (ICP) and stress distribution of adjacent discs. The FE results indicated that the ROM of both surgical constructs was related to the preload application method and magnitude; differences in the ROM were within 7% for the ALIF model and 32% for the ADR model. Following the application of the FL and after increasing the FL magnitude, the FCF of the ADR model gradually increased, reaching 45% at the implanted level in torsion. The maximum ICP gradually decreased by 34.1% in torsion and 28.4% in lateral bending. This study concluded that the preload magnitude and application method affect the biomechanical behaviour of the lumbar spine. For the ADR, remarkable alteration was observed while increasing the FL magnitude, particularly in the ROM, FCF and ICP. However, for the ALIF, PP and FL methods had no remarkable alteration in terms of ROM and adjacent disc stress.     

Characterization of Krt19CreERT allele for targeting the nucleus pulposus cells in the postnatal mouse intervertebral disc

Intervertebral disc degeneration and associated back pain are relatively common but sparsely understood conditions, affecting over 70% of the population during some point of life. Disc degeneration is often associated with a loss of nucleus pulposus (NP) cells. Genetic mouse models offer convenient avenues to understand the cellular and molecular regulation of the disc during its formation, growth, maintenance, and aging. However, due to the lack of inducible driver lines to precisely target NP cells in the postnatal mouse disc, progress in this area of research has been moderate. NP cells are known to express cytokeratin 19 (Krt19), and tamoxifen (Tam)-inducible Krt19^CreERT allele is available. The current study describes the characterization of Krt19^CreERT allele to specifically and efficiently target NP cells in neonatal, skeletally mature, middle-aged, and aged mice using two independent fluorescent reporter lines. The efficiency of recombination at all ages was validated by immunostaining for KRT19. Results show that following Tam induction, Krt19^CreERT specifically drives recombination of NP cells in the spine of neonatal and aged mice, while no recombination was detected in the surrounding tissues. Knee joints from skeletally mature Tam-treated Krt19^CreERT/+; R26^tdTOM mouse show the absence of recombination in all tissues and cells of the knee joint. Thus, this study provides evidence for the use of Krt19^CreERT allele for genetic characterization of NP cells at different stages of the mouse life.     

Therapeutic potential of melatonin in the intervertebral disc degeneration through inhibiting the ferroptosis of nucleus pulpous cells

Ferroptosis, a novel type of cell death mediated by the iron-dependent lipid peroxidation, contributes to the pathogenesis of the intervertebral disc degeneration (IDD). Increasing evidence demonstrated that melatonin (MLT) displayed the therapeutic potential to prevent the development of IDD. Current mechanistic study aims to explore whether the downregulation of ferroptosis contributes to the therapeutic capability of MLT in IDD. Current studies demonstrated that conditioned medium (CM) from the lipopolysaccharide (LPS)-stimulated macrophages caused a series of changes about IDD, including increased intracellular oxidative stress (increased reactive oxygen species and malondialdehyde levels, but decreased glutathione levels), upregulated expression of inflammation-associated factors (IL-1β, COX-2 and iNOS), increased expression of key matrix catabolic molecules (MMP-13, ADAMTS4 and ADAMTS5), reduced the expression of major matrix anabolic molecules (COL2A1 and ACAN), and increased ferroptosis (downregulated GPX4 and SLC7A11 levels, but upregulated ACSL4 and LPCAT3 levels) in nucleus pulposus (NP) cells. MLT could alleviate CM-induced NP cell injury in a dose-dependent manner. Moreover, the data substantiated that intercellular iron overload was involved in CM-induced ferroptosis in NP cells, and MLT treatment alleviated intercellular iron overload and protected NP cells against ferroptosis, and those protective effects of MLT in NP cells further attenuated with erastin and enhanced with ferrostatin-1(Fer-1). This study demonstrated that CM from the LPS-stimulated RAW264.7 macrophages promoted the NP cell injury. MLT alleviated the CM-induced NP cell injury partly through inhibiting ferroptosis. The findings support the role of ferroptosis in the pathogenesis of IDD, and suggest that MLT may serve as a potential therapeutic approach for clinical treatment of IDD.     

Finite element simulations of the active stress in the imaginal disc of the Drosophila Melanogaster

During the larval stages of development, the imaginal disc of Drosphila Melanogaster is composed by a monolayer of epithelial cells, which undergo a strain actively produced by the cells themselves. The well-organized collective contraction produces a stress field that seemingly has a double morphogenetic role: it orchestrates the cellular organization towards the macroscopic shape emergence while simultaneously providing a local information on the organ size. Here we perform numerical simulations of such a mechanical control on morphogenesis at a continuum level, using a three-dimensional finite model that accounts for the active cell contraction. The numerical model is able to reproduce the (few) known qualitative characteristics of the tensional patterns within the imaginal disc of the fruit fly. The computed stress components slightly deviate from planarity, thus confirming the previous theoretical assumptions of a nonlinear elastic analytical model, and enforcing the hypothesis that the spatial variation of the mechanical stress may act as a size regulating signal that locally scales with the global dimension of the domain.     

Finite element assessment of block-augmented total knee arthroplasty

Loosening and migration of tibial prostheses have been identified as causes of early total knee replacement (TKR) failure. The problem is made more complex when defects occur in the proximal tibia compromising fixation and alignment. Clinical studies using metal augments have shown these to be an alternative to other means of defect treatment. Finite element (FE) analysis can be used to identify regions that may be prone to loosening and migration. In the current work, 3D FE models of TKR uncontained type-2 defects treated with block augments have been constructed and analysed. It has been shown that a metal augment is the most suitable. The use of bone cement (PMMA) to fill proximal defects is not considered suitable as stresses carried by the cement block exceed those of the fatigue limit of bone cement. It has been shown that the stresses in the proximal cancellous bone of block-augmented models are significantly below levels likely to cause damage due to overloading. Furthermore, the use of stem extensions has been shown to reduce the cancellous bone stresses in the proximal region thus increasing the likelihood of bone resorption. Given this, it is recommended that stem extensions are not required unless necessary to mitigate some other problem.     

Quantitative comparison of ligament formulation and pre-strain in finite element analysis of the human lumbar spine

Data has been published that quantifies the nonlinear, anisotropic material behaviour and pre-strain behaviour of the anterior longitudinal, supraspinous (SSL), and interspinous ligaments of the human lumbar spine. Additionally, data has been published on localized material properties of the SSL. These results have been incrementally incorporated into a previously validated finite element model of the human lumbar spine. Results suggest that the effects of increased ligament model fidelity on bone strain energy were moderate and the effects on disc pressure were slight, and do not justify a change in modelling strategy for most clinical applications. There were significant effects on the ligament stresses of the ligaments that were directly modified, suggesting that these phenomena should be included in FE models where ligament stresses are the desired metric.     

Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R² = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.     

Immunolocalization of MMP-19 in the human intervertebral disc: implications for disc aging and degeneration

Matrix metalloproteinases (MMPs) degrade components of the extracellular matrix of the disc, but the presence of MMP-19 has not been explored. In other tissues, MMP-19 is known to act in proteolysis of the insulin-like growth factor (IGF) binding protein-3, thereby exposing this protein to make it available to influence cell behavior. MMP-19 also has been shown to inhibit capillary-like formation and thus play a role in the avascular nature of the disc. Using immunohistochemistry, normal discs from six subjects aged newborn through 10 years and 20 disc specimens from control donors or surgical patients aged 15-76 (mean age 40.2 years) were examined for immunolocalization of MMP-19; six Thompson grade I discs, five Thompson grade II, eight Thompson grade III, five Thompson grade IV, and one Thompson grade V discs were analyzed. The results indicate that in discs from young subjects, MMP-19 was uniformly localized in the outer annulus. In discs from adult donors and surgical patients, outer and inner annulus cells only occasionally showed MMP-19 localization. The greatest expression of MMP-19 was observed in young discs, and little expression was seen in older or degenerating discs. Because MMP-19 has been shown to regulate IGF-mediated proliferation in other tissues, its decline in the aging/degenerating disc may contribute to the age-related decrease in disc cell numbers.     

Alterations of bovine nucleus pulposus cells with aging

Aging is one of the major etiological factors driving intervertebral disc (IVD) degeneration, the main cause of low back pain. The nucleus pulposus (NP) includes a heterogeneous cell population, which is still poorly characterized. Here, we aimed to uncover main alterations in NP cells with aging. For that, bovine coccygeal discs from young (12 months) and old (10–16 years old) animals were dissected and primary NP cells were isolated. Gene expression and proteomics of fresh NP cells were performed. NP cells were labelled with propidium iodide and analysed by flow cytometry for the expression of CD29, CD44, CD45, CD146, GD2, Tie2, CD34 and Stro-1. Morphological cell features were also dissected by imaging flow cytometry. Elder NP cells (up-regulated bIL-6 and bMMP1 gene expression) presented lower percentages of CD29+, CD44+, CD45+ and Tie2+ cells compared with young NP cells (upregulated bIL-8, bCOL2A1 and bACAN gene expression), while GD2, CD146, Stro-1 and CD34 expression were maintained with age. NP cellulome showed an upregulation of proteins related to endoplasmic reticulum (ER) and melanosome independently of age, whereas proteins upregulated in elder NP cells were also associated with glycosylation and disulfide bonds. Flow cytometry analysis of NP cells disclosed the existence of 4 subpopulations with distinct auto-fluorescence and size with different dynamics along aging. Regarding cell morphology, aging increases NP cell area, diameter and vesicles. These results contribute to a better understanding of NP cells aging and highlighting potential anti-aging targets that can help to mitigate age-related disc disease.     

Statistical factorial analysis approach for parameter calibration on material nonlinearity of intervertebral disc finite element model

In the biomechanics field, material parameters calibration is significant for finite element (FE) model to ensure a legit estimation of biomechanical response. Determining an appropriate combination of calibration factors is challenging as each constitutive component responds differently. This study proposes a statistical factorial analysis approach using L₁₆(4⁵) orthogonal array to evaluate material nonlinearity and applicable calibration factor of the intervertebral disc FE model in pure moment. The calibrated model exhibits improved agreement to the experimental findings for all directions. Appropriate combination of calibration parameter reduces the estimation gap to the experimental findings, ensuring agreeable biomechanical responses.