Substructuring and poroelastic modelling of the intervertebral disc

We proposed a substructure technique to predict the time-dependant response of biological tissue within the framework of a finite element resolution. Theoretical considerations in poroelasticity preceded the calculation of the sub-structured poroelastic matrix. The transient response was obtained using an exponential fitting method. We computed the creep response of an MRI 3D reconstructed L₅–S₁ intervertebral disc of a scoliotic spine. The FE model was reduced from 10,000 degrees of freedom for the full 3D disc to only 40 degrees of freedom for the sub-structured model defined by 10 nodes attached to junction nodes located on both lower and upper surfaces of the disc. Comparisons of displacement fields were made between the full poroelastic FE model and the sub-structured model in three different loading conditions: compression, offset compression and torsion. Discrepancies in displacement were lower than 10% for the first time steps when time-dependant events were significant. The substructuring technique provided an exact solution in quasi-static behavior after pressure relaxation. Couplings between vertical and transversal displacements predicted by the reference FE model were well stored by the sub-structured model despite the drastic reduction of degrees of freedom. Finally, we demonstrated that substructuring was very efficient to reduce the size of numerical models while respecting the time-dependant behavior of the structure. This result highlighted the potential interest of substructure techniques in large-scale models of musculoskeletal structures.     

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.     

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.     

Fluid flow and convective transport of solutes within the intervertebral disc

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc.An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa.Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.     

Influence of fixed charge density magnitude and distribution on the intervertebral disc: applications of a poroelastic and chemical electric (PEACE) model

A 3-dimensional formulation for a poroelastic and chemical electric (PEACE) model is presented and applied to an intervertebral disc slice in a 1-dimensional validation problem and a 2-dimensional plane stress problem. The model was used to investigate the influence of fixed charge density magnitude and distribution on this slice of disc material. Results indicated that the mechanical, chemical, and electrical behaviors were all strongly influenced by the amount as well as the distribution of fixed charges in the matrix. Without any other changes in material properties, alterations in the fixed charge density (proteoglycan content) from a healthy to a degenerated distribution will cause an increase in solid matrix stresses and can affect whether the tissue imbibes or exudes fluid under different loading conditions. Disc tissue with a degenerated fixed charge density distribution exhibited greater solid matrix stresses and decreased streaming potential, all of which have implications for disc nutrition, disc biomechanics, and tissue remodeling. It was also seen that application of an electrical potential across the disc can induce fluid transport.     

Connective tissue growth factor expression in human intervertebral disc: implications for angiogenesis in intervertebral disc degeneration

Intervertebral disc (IVD) degeneration is strongly associated with chronic low back pain, one of the most common causes of morbidity in the West. While normal healthy IVD is avascular, angiogenesis is a constant feature of IVD degeneration and has been shown to be associated with in-growth of nerves. Connective tissue growth factor (CTGF) plays a pivotal role in angiogenesis. To investigate the expression of CTGF in both normal and degenerated IVD, 21 IVDs were obtained from patients at surgery or postmortem examination and grouped according to the severity of histological degeneration. The immunohistochemical expression of CTGF was correlated with the degree of degeneration. CD31 immunohistochemistry was used to correlate IVD degeneration with vasculature. Our results showed that CTGF is expressed in non-degenerated and degenerated human IVDs and increased expression of CTGF is associated with degenerated discs, particularly within areas of neovascularization. We suggest that CTGF may play a role in angiogenesis in the human degenerated IVD.     

Degeneration of the intervertebral disc

The intervertebral disc is a cartilaginous structure that resembles articular cartilage in its biochemistry, but morphologically it is clearly different. It shows degenerative and ageing changes earlier than does any other connective tissue in the body. It is believed to be important clinically because there is an association of disc degeneration with back pain. Current treatments are predominantly conservative or, less commonly, surgical; in many cases there is no clear diagnosis and therapy is considered inadequate. New developments, such as genetic and biological approaches, may allow better diagnosis and treatments in the future.     

Effect of intervertebral disc degeneration on disc cell viability: a numerical investigation

Degeneration of the intervertebral disc may be initiated and supported by impairment of the nutrition processes of the disc cells. The effects of degenerative changes on cell nutrition are, however, only partially understood. In this work, a finite volume model was used to investigate the effect of endplate calcification, water loss, reduction of disc height and cyclic mechanical loading on the sustainability of the disc cell population. Oxygen, lactate and glucose diffusion, production and consumption were modelled with non-linear coupled partial differential equations. Oxygen and glucose consumption and lactate production were expressed as a function of local oxygen concentration, pH and cell density. The cell viability criteria were based on local glucose concentration and pH. Considering a disc with normal water content, cell death was initiated in the centre of the nucleus for oxygen, glucose, and lactate diffusivities in the cartilaginous endplate below 20% of the physiological values. The initial cell population could not be sustained even in the non-calcified endplates when a reduction of diffusion inside the disc due to water loss was modelled. Alterations in the disc shape such as height loss, which shortens the transport route between the nutrient sources and the cells, and cyclic mechanical loads, could enhance cell nutrition processes.     

Tenascin in the human intervertebral disc: alterations with aging and disc degeneration

Our objective for this study was to determine the presence and distribution of tenascin in the human intervertebral disc. The tenascins are a family of extracellular matrix proteins with repeated structural domains homologous to epidermal growth factor, fibronectin type III and the fibrinogens. Little is known about the presence of this protein in the disc. Ten normal human discs donated from subjects newborn to 15 years old, 10 control discs from adult donors aged 24-41 years, and 11 surgical disc specimens from patients aged 26-76 years were examined for immunolocalization of tenascin. In young discs, tenascin was localized throughout the annulus; in the nucleus, localization was confined to pericellular matrix. In adult control and degenerating disc specimens, tenascin in the annulus was localized primarily in pericellular matrix regions encircling either single cells or clusters of disc cells; in rare instances localization was more diffuse in the intraterritorial matrix. In young, healthy disc, tenascin was abundant throughout the annulus. In contrast, degenerating discs in adults showed a localization restricted to the pericellular, and rarely, more restricted intraterritorial matrix. These observations indicate that changes in the amount and distribution of tenascin may have a role in disc aging and degeneration, possibly by modulating fibronectin-disc-cell interactions, and causing alterations in the shape of disc cells.     

Accelerated cellular senescence in degenerate intervertebral discs: a possible role in the pathogenesis of intervertebral disc degeneration

Current evidence implicates intervertebral disc degeneration as a major cause of low back pain, although its pathogenesis is poorly understood. Numerous characteristic features of disc degeneration mimic those seen during ageing but appear to occur at an accelerated rate. We hypothesised that this is due to accelerated cellular senescence, which causes fundamental changes in the ability of disc cells to maintain the intervertebral disc (IVD) matrix, thus leading to IVD degeneration. Cells isolated from non-degenerate and degenerate human tissue were assessed for mean telomere length, senescence-associated β-galactosidase (SA-β-gal), and replicative potential. Expression of P16 ^INK4A (increased in cellular senescence) was also investigated in IVD tissue by means of immunohistochemistry. RNA from tissue and cultured cells was used for real-time polymerase chain reaction analysis for matrix metalloproteinase-13, ADAMTS 5 (a disintegrin and metalloprotease with thrombospondin motifs 5), and P16 ^INK4A . Mean telomere length decreased with age in cells from non-degenerate tissue and also decreased with progressive stages of degeneration. In non-degenerate discs, there was an age-related increase in cellular expression of P16 ^INK4A . Cells from degenerate discs (even from young patients) exhibited increased expression of P16 ^INK4A , increased SA-β-gal staining, and a decrease in replicative potential. Importantly, there was a positive correlation between P16 ^INK4A and matrix-degrading enzyme gene expression. Our findings indicate that disc cell senescence occurs in vivo and is accelerated in IVD degeneration. Furthermore, the senescent phenotype is associated with increased catabolism, implicating cellular senescence in the pathogenesis of IVD degeneration.     

MicroRNA in intervertebral disc degeneration

Aetiology of intervertebral disc degeneration (IDD) is complex, with genetic, developmental, biochemical and biomechanical factors contributing to the disease process. It is becoming obvious that epigenetic processes influence evolution of IDD as strongly as the genetic background. Deregulated phenotypes of nucleus pulposus cells, including differentiation, migration, proliferation and apoptosis, are involved in all stages of progression of human IDD. Non‐coding RNAs, including microRNAs, have recently been recognized as important regulators of gene expression. Research into roles of microRNAs in IDD has been very active over the past 5 years. Our review summarizes current research enlightenment towards understanding roles of microRNAs in regulating nucleus pulposus cell functions in IDD. These exciting findings support the notion that specific modulation of microRNAs may represent an attractive approach for management of IDD.     

Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression,flexion and axial rotation

A statistical factorial analysis approach was conducted on a poroelastic finite element model of a lumbar intervertebral disc to analyse the influence of six material parameters (permeabilities of annulus, nucleus, trabecular vertebral bone, cartilage endplate and Young's moduli of annulus and nucleus) on the displacement, fluid pore pressure and velocity fields. Three different loading modes were investigated: compression, flexion and axial rotation. Parameters were varied considering low and high levels in agreement with values found in the literature for both healthy and degenerated lumbar discs. Results indicated that annulus stiffness and cartilage endplate permeability have a strong effect on the overall fluid- and solid-phase responses in all loading conditions studied. Nucleus stiffness showed its main relevance in compression while annulus permeability influenced mainly the annular pressure field. This study confirms the permeability's central role in biphasic modelling and highlights for the lumbar disc which experiments of material property characterization should be performed. Moreover, such sensitivity study gives important guidelines in poroelastic material modelling and finite element disc validation.     

Aquaporin expression in the human intervertebral disc

The nucleus pulposus (NP) of the human intervertebral disc (IVD) is a hyperosmotic tissue that is subjected to daily dynamic compressive loads. In order to survive within this environment the resident chondrocyte-like cells must be able to control their cell volume, whilst also controlling the anabolism and catabolism of their extra-cellular matrix. Recent studies have demonstrated expression of a range of bi-directional, transmembrane water and solute transporters, named aquaporins (AQPs), within chondrocytes of articular cartilage. The aim of this study was to use immunohistochemsitry to investigate the expression of aquaporins 1, 2 and 3 within the human IVD. Results demonstrated expression of both AQP-1 and -3 by cells within the NP and inner annulus fibrosus (AF), while outer AF cells lacked expression of AQP-1 and showed very low numbers of AQP-3 immunopositive cells. Cells from all regions were negative for AQP-2. Therefore this study demonstrates similarities in the phenotype of NP cells and articular chondrocytes, which may be due to similarities in tissue osmolarity and mechanobiology. The decrease in expression of AQPs from the NP to the outer AF may signify changes in cellular phenotype in response to differences in mechanbiology, osmolarity and hydration between the gelatinous NP and the fibrous AF.     

Uridine diphosphoglucose dehydrogenase in the intervertebral disc

Synopsis Intervertebral discs of an old sheep and a young pig were examined for the presence of cells containing the enzyme uridine diphosphoglucose dehydrogenase. In the sheep, the inner anulus had a higher proportion of active cells than the outer anulus; in the pig, there was no difference. From a consideration of cell numbers, it is suggested that there is an accumulation of glycosaminoglycans in the centre of the disc rather than an increased production rate. Notochordal cells in the pig disc contain uridine diphosphoglucose dehydrogenase and are capable of producing glycosaminoglycans.     

Pathophysiology of the human intervertebral disc

Intervertebral disc degeneration is a common invalidating disorder that can affect the musculoskeletal apparatus in both younger and older ages. The chief component of the intervertebral disc is the highly organized extracellular matrix; maintenance of its organization is essential for correct spinal mechanics. The matrix components, mainly proteoglycans and collagens, undergo a slow and continuous cell-mediated turnover process that enables disc cells to adapt their environment to external stimuli. Cellular senescence and a history of chronic abnormal loading can upset this balance, leading to progressive tissue failure that results in disc degeneration. Although biological treatment approaches to disc repair are still far to come, advances in our understanding of disc biochemistry and in defining the role of genetic inheritance have provided a starting point for developing new concepts in the diagnosis, therapy and prevention of disc degeneration.     

Cell death in intervertebral disc degeneration

Degeneration of intervertebral disc (IVD) is mainly a chronic process of excessive destruction of the extracellular matrix (ECM), and also is thought to be the primary cause of low back pain. Presently, however, the underlying mechanism of IVD degeneration is still not elucidated. Cellular loss from cell death has been believed to contribute to the degradation of ECM and plays an important role in the process of IVD degeneration, but the mechanisms of cell death in degenerated IVD remain unclear. Apoptosis, a very important type of IVD cell death, has been considered to play a crucial role in the process of degeneration. Autophagy, a non-apoptosis death type of programmed cell death, has been considered extensively involved in many pathological and physiological processes, including the degenerative diseases. Thus, the research on cell death in IVD degeneration has become a new focus recently. In this review, by analyzing the available literature pertaining to cell death in IVD and discussing the inducing factors of IVD degeneration, NP cells and ECM in IVD degeneration, apoptotic signal transduction pathways involved in IVD cell death, the relationship of cell death with IVD degeneration and potential therapeutic strategy for IVD degeneration by regulating cell death, we conclude that different stimuli induce cell death in IVD via various signal transduction pathways, and that cell death may play a key role in the degenerative process of IVD. Regulation of cell death could be a potential and attractive therapeutic strategy for IVD degeneration.     

Fluid and solid mechanics in a poroelastic network induced by ultrasound

We made a theoretical analysis on the fluid and solid mechanics in a poroelastic medium induced by low-power ultrasound. Using a perturbative approach, we were able to linearize the governing equations and obtain analytical solutions. We found that ultrasound could propagate in the medium as a mechanical wave, but would dissipate due to frictional forces between the fluid and the solid phase. The amplitude of the wave depends on the ultrasonic power input. We applied this model to the problem of drug delivery to soft biological tissues by low-power ultrasound and proposed a mechanism for enhanced drug penetration. We have also found the coexistence of two acoustic waves under certain circumstances and pointed out the importance of very accurate experimental determination of the high-frequency properties of brain tissue.