Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc

The present numerical study aims to investigate the disc nutrition and factors affecting it by evaluating the concentrations of oxygen, glucose and lactic acid in the disc while accounting for the coupling between these species via the pH level in the tissue and the nonlinear concentration-consumption (for glucose and oxygen) and concentration-production (for lactate) relations. The effects of changes in the endplate exchange area (EA) adjacent to the nucleus or the inner annulus for the transport of nutrients and in the disc geometry as well as tissue diffusivities under static compression loading on species concentrations are also studied. Moreover, alterations in solute diffusion following a central endplate fracture are investigated. An axisymmetric geometry with four distinct regions is considered. Supply sources are assumed at the outer annulus periphery and disc endplates. Coupling between different solutes, pH level, endplate disruptions (calcifications and fractures) and mechanical loads substantially influenced the distribution of nutrients throughout the disc as well as the magnitude and location of critical concentrations; maximum for the lactic acid and minimum for oxygen and glucose. In cases with loss of endplate permeability and/or disruptions therein, as well as changes in geometry and fall in diffusivity associated with fluid expression, the nutrient concentrations could fall to levels inadequate to maintain cellular activity or viability, thus initiating or accelerating disc degeneration.     

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.     

Disc mechanics with trans-endplate partial nucleotomy are not fully restored following cyclic compressive loading and unloaded recovery

Mechanical function of the intervertebral disc is maintained through the interaction between the hydrated nucleus pulposus, the surrounding annulus fibrosus, and the superior and inferior endplates. In disc degeneration the normal transfer of load between disc substructures is compromised. The objective of this study was to explore the mechanical role of the nucleus pulposus in support of axial compressive loads over time. This was achieved by measuring the elastic slow ramp and viscoelastic stress-relaxation mechanical behaviors of cadaveric sheep motion segments before and after partial nucleotomy through the endplate (keeping the annulus fibrosus intact). Mechanics were evaluated at five conditions: Intact, intact after 10,000 cycles of compression, acutely after nucleotomy, following nucleotomy and 10,000 cycles of compression, and following unloaded recovery. Radiographs and magnetic resonance images were obtained to examine structure. Only the short time constant of the stress relaxation was altered due to nucleotomy. In contrast, cyclic loading resulted in significant and large changes to both the stiffness and stress relaxation behaviors. Moreover, the nucleotomy had little to no effect on the disc mechanics after cyclic loading, as there were no significant differences comparing mechanics after cyclic loading with or without the nucleotomy. Following unloaded recovery the mechanical changes that had occurred as a consequence of cyclic loading were restored, leaving only a sustained change in the short time constant due to the trans-endplate nucleotomy. Thus the swelling and redistribution of the remaining nucleus pulposus was not able to fully restore mechanical behaviors. This study reveals insights into the role of the nucleus pulposus in disc function, and provides new information toward the potential role of altered nucleus pulpous function in the degenerative cascade.     

Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus.

Accurate tissue stress predictions for the annulus fibrosus are essential for understanding the factors that cause or contribute to disc degeneration and mechanical failure. Current computational models used to predict in vivo disc stresses utilize material laws for annular tissue that are not rigorously validated against experimental data. Consequently, predictions of disc stress resulting from physical activities may be inaccurate and therefore unreliable as a basis for defining mechanical-biologic injury criteria. To address this need we present a model for the annulus as an isotropic ground substance reinforced with two families of collagen fibers, and an approach for determining the material constants by simultaneous consideration of multiple experimental data sets. Two strain energy functions for the annulus are proposed and used in the theory to derive the constitutive equations relating the stress to pure stretch deformations. These equations are applied to four distinct experimental protocols and the material constants are determined from a simultaneous, nonlinear regression analysis. Good agreement between theory and experiment is achieved when the invariants are included within multiple, separate exponentials in the strain energy function.     

Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc

Degenerate intervertebral discs exhibit both material and structural changes. Structural defects (lesions) develop in the anulus fibrosus with age. While degeneration has been simulated in numerous previous studies, the effects of structural lesions on disc mechanics are not well known. In this study, a finite element model (FEM) of the L4/5 intervertebral disc was developed in order to study the effects of anular lesions and loss of hydrostatic pressure in the nucleus pulposus on the disc mechanics. Models were developed to simulate both healthy and degenerate discs. Degeneration was simulated with either rim, radial or circumferential anular lesions and by equating nucleus pressure to zero. The anulus fibrosus ground substance was represented as a nonlinear incompressible material using a second-order polynomial, hyperelastic strain energy equation. Hyperelastic material parameters were derived from experimentation on sheep discs. Endplates were assumed to be rigid, and annulus lamellae were assumed to be vertical in the unloaded state. Loading conditions corresponding to physiological ranges of rotational motion were applied to the models and peak rotation moments compared between models. Loss of nucleus pulposus pressure had a much greater effect on the disc mechanics than the presence of anular lesions. This indicated that the development of anular lesions alone (prior to degeneration of the nucleus) has minimal effect on disc mechanics, but that disc stiffness is significantly reduced by the loss of hydrostatic pressure in the nucleus. With the degeneration of the nucleus, the outer innervated anulus or surrounding osteo-ligamentous anatomy may therefore experience increased strains.     

Preparation of Intact Bovine Tail Intervertebral Discs for Organ Culture

The intervertebral disc (IVD) is the joint of the spine connecting vertebra to vertebra. It functions to transmit loading of the spine and give flexibility to the spine. It composes of three compartments: the innermost nucleus pulposus (NP) encompassing by the annulus fibrosus (AF), and two cartilaginous endplates connecting the NP and AF to the vertebral body on both sides. Discogenic pain possibly caused by degenerative intervertebral disc disease (DDD) and disc herniations has been identified as a major problem in our modern society. To study possible mechanisms of IVD degeneration, in vitro organ culture systems with live disc cells are highly appealing. The in vitro culture of intact bovine coccygeal IVDs has advanced to a relevant model system, which allows the study of mechano-biological aspects in a well-controlled physiological and mechanical environment. Bovine tail IVDs can be obtained relatively easy in higher numbers and are very similar to the human lumbar IVDs with respect to cell density, cell population and dimensions. However, previous bovine caudal IVD harvesting techniques retaining cartilaginous endplates and bony endplates failed after 1-2 days of culture since the nutrition pathways were obviously blocked by clotted blood. IVDs are the biggest avascular organs, thus, the nutrients to the cells in the NP are solely dependent on diffusion via the capillary buds from the adjacent vertebral body. Presence of bone debris and clotted blood on the endplate surfaces can hinder nutrient diffusion into the center of the disc and compromise cell viability. Our group established a relatively quick protocol to "crack"-out the IVDs from the tail with a low risk for contamination. We are able to permeabilize the freshly-cut bony endplate surfaces by using a surgical jet lavage system, which removes the blood clots and cutting debris and very efficiently reopens the nutrition diffusion pathway to the center of the IVD. The presence of growth plates on both sides of the vertebral bone has to be avoided and to be removed prior to culture. In this video, we outline the crucial steps during preparation and demonstrate the key to a successful organ culture maintaining high cell viability for 14 days under free swelling culture. The culture time could be extended when appropriate mechanical environment can be maintained by using mechanical loading bioreactor. The technique demonstrated here can be extended to other animal species such as porcine, ovine and leporine caudal and lumbar IVD isolation.     

Effect of endplate calcification and mechanical deformation on the distribution of glucose in intervertebral disc: a 3D finite element study

The intervertebral disc (IVD) is avascular, receiving nutrition from surrounding vasculature. Theoretical modelling can supplement experimental results to understand nutrition to IVD more clearly. A new, 3D finite element model of the IVD was developed to investigate effects of endplate calcification and mechanical deformation on glucose distributions in IVD. The model included anatomical disc geometry, non-linear coupling of cellular metabolism with pH and oxygen concentration and strain-dependent properties of the extracellular matrix. Calcification was simulated by reducing endplate permeability (～79%). Mechanical loading was applied based on in vivo disc deformation during the transition from supine to standing positions. Three static strain conditions were considered: supine, standing and weight-bearing standing. Minimum glucose concentrations decreased 45% with endplate calcification, whereas disc deformation led to a 4.8-63% decrease, depending on the endplate condition (i.e. normal vs. calcified). Furthermore, calcification more strongly affected glucose concentrations in the nucleus compared to the annulus fibrous region. This study provides important insight into nutrient distributions in IVD under mechanical deformation.     

3D finite element analysis of nutrient distributions and cell viability in the intervertebral disc: effects of deformation and degeneration

The intervertebral disc (IVD) receives important nutrients, such as glucose, from surrounding blood vessels. Poor nutritional supply is believed to play a key role in disc degeneration. Several investigators have presented finite element models of the IVD to investigate disc nutrition; however, none has predicted nutrient levels and cell viability in the disc with a realistic 3D geometry and tissue properties coupled to mechanical deformation. Understanding how degeneration and loading affect nutrition and cell viability is necessary for elucidating the mechanisms of disc degeneration and low back pain. The objective of this study was to analyze the effects of disc degeneration and static deformation on glucose distributions and cell viability in the IVD using finite element analysis. A realistic 3D finite element model of the IVD was developed based on mechano-electrochemical mixture theory. In the model, the cellular metabolic activities and viability were related to nutrient concentrations, and transport properties of nutrients were dependent on tissue deformation. The effects of disc degeneration and mechanical compression on glucose concentrations and cell density distributions in the IVD were investigated. To examine effects of disc degeneration, tissue properties were altered to reflect those of degenerated tissue, including reduced water content, fixed charge density, height, and endplate permeability. Two mechanical loading conditions were also investigated: a reference (undeformed) case and a 10% static deformation case. In general, nutrient levels decreased moving away from the nutritional supply at the disc periphery. Minimum glucose levels were at the interface between the nucleus and annulus regions of the disc. Deformation caused a 6.2% decrease in the minimum glucose concentration in the normal IVD, while degeneration resulted in an 80% decrease. Although cell density was not affected in the undeformed normal disc, there was a decrease in cell viability in the degenerated case, in which averaged cell density fell 11% compared with the normal case. This effect was further exacerbated by deformation of the degenerated IVD. Both deformation and disc degeneration altered the glucose distribution in the IVD. For the degenerated case, glucose levels fell below levels necessary for maintaining cell viability, and cell density decreased. This study provides important insight into nutrition-related mechanisms of disc degeneration. Moreover, our model may serve as a powerful tool in the development of new treatments for low back pain.     

Statistical factorial analysis on the material property sensitivity of the mechanical responses of the C4-C6 under compression, anterior and posterior shear

A systematic approach using factorial analysis was conducted on the C4-C6 finite element model to analyse the influence of six spinal components (cortical shell, vertebral body, posterior elements, endplate, disc annulus and disc nucleus) on the internal stresses and external biomechanical responses under compression, anterior and posterior shear. Results indicated that the material properties variation of the disc annulus has a significant influence on both the external biomechanical responses and internal stress of the disc annulus and its neighboring hard bones. The study reveals for the first time, the significant influence of the cancellous bone under compression, while variation in the cortical shell modulus has a high influence under anterior and posterior shear. The study also reveals that the effects of interaction between two main components are insignificant.     

几种椎间盘退变动物模型的建立和应用

椎间盘退变是一种年龄相关的退行性疾病,是引起下腰痛的主要因素,严重影响病人的生活质量,并显著增加家庭的经济负担。目前,缺少椎间盘退变的有效干预和治疗手段,部分原因是其发病机制尚未阐明。椎间盘退变动物模型的构建对于阐明该疾病的病理机制至关重要。椎间盘退变是一个复杂的过程,受机械应力、结构损伤、生物化学与基因表达等多种因素的影响。本文总结了应用异常机械应力、结构损伤、生物化学或化学诱导和基因敲除等方式构建的椎间盘退变动物模型。生物力学是维持椎间盘稳态的重要因素,异常的机械应力会导致椎间盘退变。同时,椎间盘退变常伴随结构性损伤,椎间盘结构破坏也会导致椎间盘发生退变。此外,生物化学或化学诱导和关键基因敲除也会导致椎间盘退变。本文按照造成异常机械应力的因素将机械应力模型分为加压模型和失稳模型;按照椎间盘结构将结构损伤模型分为髓核与纤维环损伤模型和软骨终板损伤模型。总结了生物化学或化学诱导模型以及新型的基因敲除模型。讨论了不同类型椎间盘退变动物模型的可能应用和局限性。     

Expression of the two pore domain potassium channel TREK-1 in human intervertebral disc cells

Potassium channels play a major role in intracellular homeostasis and regulation of cell volume. Intervertebral disc cells respond to mechanical loading in a complex manner. Mechanical loading may play a role in disc degeneration. Lumbar intervertebral disc samples from 5 patients (average age: 47 years, range: 25-64 years) were used for this study, investigating cells from the nucleus pulposus and the annulus fibrosus duplicate samples to determine RNA expression and protein expression. Analysis of mRNA expression by RT-PCR demonstrated that TREK 1 was expressed by nucleus pulposus (n=5) and annulus fibrosus (n=5) cells. Currently, TREK-1 is the only potassium channel known to be activated by intracellular acidosis, and responds to mechanical and chemical stimuli. Whilst the precise role of potassium channels in cellular homeostasis remains to be determined, TREK-1 may be important to protect disc cells against ischaemic damage, and subsequent disc degeneration, and may also play a role in effecting mechanotransduction. Further research is required to fully elucidate the role of the TREK-1 ion channel in intervertebral disc cells.     

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.     

Failure strength of the bovine caudal disc under internal hydrostatic pressure

The structure of the disc is both complex and inhomogeneous, and it functions as a successful load-bearing organ by virtue of the integration of its various structural regions. These same features also render it impossible to assess the failure strength of the disc from isolated tissue samples, which at best can only yield material properties. This study investigated the intrinsic failure strength of the intact bovine caudal disc under a simple mode of internal hydrostatic pressure. Using a hydraulic actuator, coloured hydrogel was injected under monitored pressure into the nucleus through a hollow screw insert which passed longitudinally through one of the attached vertebrae. Failure did not involve vertebra/endplate structures. Rather, failure of the disc annulus was indicated by the simultaneous manifestation of a sudden loss of gel pressure, a flood of gel colouration appearing in the outer annulus and audible fibrous tearing. A mean hydrostatic failure pressure of 18+/-3 MPa was observed which was approximated as a thick-wall hoop stress of 45+/-7 MPa. The experiment provides a measurement of the intrinsic strength of the disc using a method of internal hydrostatic loading which avoids any disruption of the complex architecture of the annular wall. Although the disc in vivo is subjected to a much more complex pattern of loading than is achieved using simple hydrostatic pressurization, this latter mode provides a useful tool for investigating alterations in intrinsic disc strength associated with prior loading history or degeneration.     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

A Structurally and Functionally Biomimetic Biphasic Scaffold for Intervertebral Disc Tissue Engineering

Tissue engineering offers high hopes for the treatment of intervertebral disc (IVD) degeneration. Whereas scaffolds of the disc nucleus and annulus have been extensively studied, a truly biomimetic and mechanically functional biphasic scaffold using naturally occurring extracellular matrix is yet to be developed. Here, a biphasic scaffold was fabricated with collagen and glycosaminoglycans (GAGs), two of the most abundant extracellular matrix components in the IVD. Following fabrication, the scaffold was characterized and benchmarked against native disc. The biphasic scaffold was composed of a collagen-GAG co-precipitate making up the nucleus pulposus-like core, and this was encapsulated in multiple lamellae of photochemically crosslinked collagen membranes comprising the annulus fibrosus-like lamellae. On mechanical testing, the height of our engineered disc recovered by ~82-89% in an annulus-independent manner, when compared with the 99% recovery exhibited by native disc. The annulus-independent nature of disc height recovery suggests that the fluid replacement function of the engineered nucleus pulposus core might mimic this hitherto unique feature of native disc. Biphasic scaffolds comprised of 10 annulus fibrosus-like lamellae had the best overall mechanical performance among the various designs owing to their similarity to native disc in most aspects, including elastic compliance during creep and recovery, and viscous compliance during recovery. However, the dynamic mechanical performance (including dynamic stiffness and damping factor) of all the biphasic scaffolds was similar to that of the native discs. This study contributes to the rationalized design and development of a biomimetic and mechanically viable biphasic scaffold for IVD tissue engineering.     

Periostin is expressed by cells of the human and sand rat intervertebral discs

Abstract

Periostin, a matricellular protein in the fasciclin family, is expressed in tissues subjected to constant mechanical stress. Periostin modulates cell-to-extracellular matrix interactions and can bind to collagen, fibronectin, tenascin-C and several integrins. Our objective was to evaluate whether periostin is expressed in the human intervertebral disc. Immunohistochemical localization of periostin was carried out in tissue of human lumbar discs and lumbar discs of the sand rat (Psammomys obesus). Human discs also were examined for periostin gene expression. Immunohistochemical localization demonstrated periostin in the cytoplasm of annulus and nucleus cells, and occasionally in the surrounding pericellular and interterritorial extracellular matrix. Periostin distribution in the human disc was distinctive. Outer annulus contained the highest proportion of periostin-positive cells (88.8%), whereas inner annulus contained only 61.4%. The nucleus pulposus contained the fewest periostin-positive cells (18.5%). There was a significant negative correlation between the percentage of cells positive for periostin in the inner annulus and subject age. Periostin gene expression in the human disc also was confirmed using molecular microarray analysis. Because work by others has shown that periostin plays an important role in the biomechanical properties of other connective tissues (skin, tendon, heart valves), future research is needed to elucidate the role of periostin in disc, loading, aging and degeneration.     

Effect of disc degeneration on the muscle recruitment pattern in upright posture: a computational analysis

Based on the sensor driving control mechanism model, the effect of disc degeneration on the trunk muscle recruitment (TMR) pattern was analysed in erect standing posture. A previously developed computational model was used for this analysis, with modifications incorporating the T12-L1 motion segment and additional muscle fascicles. To generate disc degeneration at three different levels (L3–L4, L4–L5, or L5–S1), the material properties of the ground matrix of the annulus and bulk modulus of the nucleus were reduced. The finite element method combined with an optimization technique was applied to calculate the muscle forces. Minimization of deviations in the averaged tensile stress in the annulus fibres at the outermost layer in the five discs was selected for muscle force calculations. The results indicated that the disc degeneration noticeably increased the activation of the superficial muscle (IT and R) even though there was no clear change in the longissimus thoracis. Unlike some of the superficial muscles, activation in the deep muscles (multifidus (ML, MS, MT), LL and Q) was decreased. The change in TMR pattern generated an intervertebral disc angle difference and nucleus pressure increased in the upper level. These differences are expected to be functional in that they reduce the stress at the degenerated disc by changing the muscle activation, which slows down the progress of disc degeneration.     

Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus

Intervertebral disc degeneration results in disorganization of the laminate structure of the annulus that may arise from mechanical microfailure. Failure mechanisms in the annulus were investigated using composite lamination theory and other analyses to calculate stresses in annulus layers, interlaminar shear stress, and the region of stress concentration around a fiber break. Scanning electron microscopy (SEM) was used to evaluate failure patterns in the annulus and evaluate novel structural features of the disc tissue. Stress concentrations in the annulus due to an isolated fiber break were localized to approximately 5 microm away from the break, and only considered a likely cause of annulus fibrosus failure (i.e., radial tears in the annulus) under extreme loading conditions or when collagen damage occurs over a relatively large region. Interlaminar shear stresses were calculated to be relatively large, to increase with layer thickness (as reported with degeneration), and were considered to be associated with propagation of circumferential tears in the annulus. SEM analysis of intervertebral disc annulus fibrosus tissue demonstrated a clear laminate structure, delamination, matrix cracking, and fiber failure. Novel structural features noted with SEM also included the presence of small tubules that appear to run along the length of collagen fibers in the annulus and a distinct collagenous structure representative of a pericellular matrix in the nucleus region.