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.     

Elastic fibers in the anulus fibrosus of the dog intervertebral disc

A light microscopic investigation of the anulus fibrosus in cervical intervertebral discs of the dog was conducted to ascertain the arrangement and distribution of elastic fibers. Elastic fibers were observed in all lamellae of the anulus fibrosus. However, collagenous fibers were the predominant type of connective tissue fiber, and elastic fibers were randomly dispersed among them. Intralamellar (collagenous and elastic) fibers were vertically and obliquely oriented in both superficial and deep lamellae of the anulus fibrosus. All intralamellar fibers were densely and regularly arranged in superficial lamellae, but they were more loosely organized in deep lamellae. A narrow border of interlamellar, elastic fibers was observed between broader, contiguous lamellae in the superficial zone of the anulus fibrosus. Interlamellar elastic fibers wer vertically and obliquely arranged in superficial lamellae; however, they were radially oriented in deep lamellae. The deepest lamella of the anulus fibrosus consisted of a loose, three-dimensional network of intermeshing collagenous and elastic fibers. These observations suggest that elastic fibers are integral components of the articular and shock absorption mechanisms of the anulus fibrosus, and the cervical intervertebral disc of the dog is a suitable model for experimental investigation of the role of elastic fibers in intervertebral disc herniation.     

Glycosaminoglycans of cat invertebral disc

The glycosaminoglycan contents of samples from cat intervertebral discs were examined by using cetylpyridinium chloride salt elution techniques. The values obtained related to the region of the vertebral column from which they were derived, to the area of the disc, and to water content. In wet tissue there was a significant difference between regions of the vertebral column and between areas of the disc and findings agreed with previous histological reports. The greater part of the glycosaminoglycans present consisted of chondroitin sulphate and dermatan sulphate with smaller amounts of hyaluronic acid; little keratan sulphate was found. The maximum amounts of chondroitin sulphate and dermatan sulphate occurred in the 0.5m-magnesium chloride fractions usually, but moved towards higher molar concentrations in samples derived from some sites, particularly in the lumbar region. Mean values for the water content of the areas of the disc were: nucleus pulposus, 82.4%; inner anulus, 65.6%; outer anulus, 50.5%. The water content was directly related to the amounts of chondroitin sulphate and dermatan sulphate.     

缺氧诱导因子-1α和血管内皮生长因子在突出腰椎间盘中的表达及意义

目的探讨缺氧诱导因子-1α（hypoxia—induciblefactor-1α,HIF-1α）和血管内皮生长因子（vascular endothelial growth factor,VEGF）在突出腰椎间盘组织中的表达及意义。方法采用链霉亲和素-过氧化物酶复合物（SABC）免疫组化方法,测定40例腰椎间盘突出症患者椎间盘组织中HIF-1α和VEGF的表达情况。结果退变椎间盘组织中HIF-1α和VEGF呈高表达,HIF-1α和VEGF在髓核的表达显著高于纤维环;纤维环破裂型显著高于纤维环完整型;各组中HIF-1α和VEGF的表达均高度相关。结论HIF-1α和VEGF共同参与了椎间盘退变;HIF-1α可能通过上调VEGF的表达来促进椎间盘组织中新生血管的形成,进而延缓椎间盘退变的发生。     

Single lamellar mechanics of the human lumbar anulus fibrosus

The mechanical behavior of the entire anulus fibrosus is determined essentially by the tensile properties of its lamellae, their fiber orientations, and the regional variation of these quantities. Corresponding data are rare in the literature. The paper deals with an in vitro study of single lamellar anulus lamellae and aims to determine (i) their tensile response and regional variation, and (ii) the orientation of lamellar collagen fibers and their regional variation. Fresh human body-disc-body units (L1–L2, n=11) from cadavers were cut midsagittally producing two hemidisc units. One hemidisc was used for the preparation of single lamellar anulus specimens for tensile testing, while the other one was used for the investigation of the lamellar fiber orientation. Single lamellar anulus specimens with adjacent bone fragments were isolated from four anatomical regions: superficial and deep lamellae (3.9±0.21 mm, mean ± SD, apart from the outer boundary surface of the anulus fibrosus) at ventro-lateral and dorsal positions. The specimens underwent cyclic uniaxial tensile tests at three different strain rates in 0.15 mol/l NaCl solution at 37°C, whereby the lamellar fiber direction was aligned with the load axis. For the characterization of the tensile behavior three moduli were calculated: E_low (0–0.1 MPa), E_medium (0.1–0.5 MPa) and E_high (0.5–1 MPa). Additionally, specimens were tested with the load axis transverse to the fiber direction. From the second hemidisc fiber angles with respect to the horizontal plane were determined photogrammetrically from images taken at six circumferential positions from ventral to dorsal and at three depth levels. Tensile moduli along the fiber direction were in the range of 28–78 MPa (regional mean values). Superficial lamellae have larger E_medium (p=0.017) and E_high (p=0.012) than internal lamellae, and the mean value of superficial lamellae is about three times higher than that of deep lamellae. Tensile moduli of ventro-lateral lamellae do not differ significantly from the tensile moduli of dorsal lamellae, and E_low is generally indifferent with respect to the anatomical region. Tensile moduli transverse to the fiber direction were about two orders of magnitude smaller (0.22±0.2 MPa, mean ± SD, n=5). Tensile properties are not correlated significantly with donor age. Only small viscoelastic effects were observed. The regional variation of lamellar fiber angle is described appropriately by a regression line ||=23.2+0.130× (r²=0.55, p<0.001), where is the polar angle associated with the circumferential position. The single anulus lamella may be seen as the elementary structural unit of the anulus fibrosus, and exhibits marked anisotropy and distinct regional variation of tensile properties and fiber angles. These features must be considered for appropriate physical and numerical modeling of the anulus fibrosus.     

Analysis of nonlinear coupled diffusion of oxygen and lactic acid in intervertebral discs

The transport of oxygen and lactate (i.e., lactic acid) in the human intervertebral disc was investigated accounting for the measured coupling between species via the pH level in the tissue. Uncoupled cases were also analyzed to identify the extent of the effect of such coupling on the solute gradients across the disc. Moreover, nonlinear lactic production rate versus lactic concentration and oxygen consumption rate versus oxygen concentration were considered. The nonlinear coupled diffusion equations were solved using an in-house finite element program and an axisymmetric model of the disc with distinct nucleus and anulus regions. A pseudotransient approach with a backward integration scheme was employed to improve convergence. Coupled simulations influenced the oxygen concentration and lactic acid concentration throughout the disc, in particular the gradient of concentrations along the disc mid-height to the nucleus-anulus boundary where the solutes reached their most critical values; minimum for the oxygen tension and maximum for the lactate. Results suggest that for realistic estimates of nutrient and metabolite gradients across the disc, it could be important to take into account the coupling between the rates of synthesis and overall local metabolite/nutrient concentration.     

The micromechanical environment of intervertebral disc cells determined by a finite deformation,anisotropic, and biphasic finite element model

Cellular response to mechanical loading varies between the anatomic zones of the intervertebral disc. This difference may be related to differences in the structure and mechanics of both cells and extracellular matrix, which are expected to cause differences in the physical stimuli (such as pressure, stress, and strain) in the cellular micromechanical environment. In this study, a finite element model was developed that was capable of describing the cell micromechanical environment in the intervertebral disc. The model was capable of describing a number of important mechanical phenomena: flow-dependent viscoelasticity using the biphasic theory for soft tissues; finite deformation effects using a hyperelastic constitutive law for the solid phase; and material anisotropy by including a fiber-reinforced continuum law in the hyperelastic strain energy function. To construct accurate finite element meshes, the in situ geometry of IVD cells were measured experimentally using laser scanning confocal microscopy and three-dimensional reconstruction techniques. The model predicted that the cellular micromechanical environment varies dramatically between the anatomic zones, with larger cellular strains predicted in the anisotropic anulus fibrosus and transition zone compared to the isotropic nucleus pulposus. These results suggest that deformation related stimuli may dominate for anulus fibrosus and transition zone cells, while hydrostatic pressurization may dominate in the nucleus pulposus. Furthermore, the model predicted that micromechanical environment is strongly influenced by cell geometry, suggesting that the geometry of IVD cells in situ may be an adaptation to reduce cellular strains during tissue loading.     

Streaming potential of human lumbar anulus fibrosus is anisotropic and affected by disc degeneration.

The streaming potential responses of non-degenerate and degenerate human anulus fibrosus were measured in a one-dimensional permeation configuration under static and dynamic loading conditions. The goal of this study was to investigate the influence of the changes in tissue structure and composition on the electrokinetic behavior of intervertebral disc tissues. It was found that the static streaming potential of the anulus fibrosus depended on the degenerative grade of the discs (p = 0.0001) and on the specimen orientation in which the fluid flows (p = 0.0001). For a statically applied pressure of 0.07 MPa, the ratio of streaming potential to applied pressure ranged from 5.3 to 6.9 mV/MPa and was largest for Grade I tissue with axial orientation and lowest for Grade III tissue with circumferential orientation. The dynamic streaming potential responses of anulus fibrosus were sensitive to the degeneration of the disc: the total harmonic distortion factor increased by 108%, from 3.92 +/- 0.66% (mean +/- SD) for Grade I specimens to 8.15 +/- 3.05% for Grades II and III specimens. The alteration of streaming potential reflects the changes in tissue composition and structure with degeneration. To our knowledge, this is the first reported data for the streaming potential of human intervertebral disc tissues. Knowledge of the streaming potential response of the intervertebral disc provides an understanding of potentially important signal transduction mechanisms in the disc and of the etiology of intervertebral disc degeneration.     

Physical signals and solute transport in human intervertebral disc during compressive stress relaxation: 3D finite element analysis

A 3D finite element model for charged hydrated soft tissues containing charged/uncharged solutes was developed based on the multi-phasic mechano-electrochemical mixture theory (Lai et al., J. Biomech. Eng. 113 (1991), 245-258; Gu et al., J. Biomech. Eng. 120 (1998), 169-180). This model was applied to analyze the mechanical, chemical and electrical signals within the human intervertebral disc during an unconfined compressive stress relaxation test. The effects of tissue composition [e.g., water content and fixed charge density (FCD)] on the physical signals and the transport rate of fluid, ions and nutrients were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization was more pronounced at the center (nucleus) region of the disc while the effective (von Mises) stress was higher at the outer (annulus) region. Parametric analyses revealed that the decrease in initial tissue water content (0.7-0.8) increased the peak stress and relaxation time due to the reduction of permeability, causing greater fluid pressurization effect. The electrical signals within the disc were more sensitive to FCD than tissue porosity, and mechanical loading affected the large solute (e.g., growth factor) transport significantly, but not for small solute (e.g., glucose). Moreover, this study confirmed that the interstitial fluid pressurization plays an important role in the load support mechanism of IVD by sharing more than 40% of the total load during disc compression. This study is important for understanding disc biomechanics, disc nutrition and disc mechanobiology.     

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.     

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.     

Osmosis and viscoelasticity both contribute to time-dependent behaviour of the intervertebral disc under compressive load: A caprine in vitro study

The mechanical behaviour of the intervertebral disc highly depends on the content and transport of interstitial fluid. It is unknown, however, to what extent the time-dependent behaviour can be attributed to osmosis. Here we investigate the effect of both mechanical and osmotic loading on water content, nucleus pressure and disc height. Eight goat intervertebral discs, immersed in physiological saline, were subjected to a compressive force with a pressure needle inserted in the nucleus. The loading protocol was: 10 N (6 h); 150 N (42 h); 10 N (24 h). Half-way the 150 N-phase (24 h), we eliminated the osmotic gradient by adding 26% poly-ethylene glycol to the surrounding fluid. For 62 additional discs, we determined the water content of both nucleus and annulus after 6, 24, 48, or 72 h. The compressive load was initially counterbalanced by the hydrostatic pressure in the nucleus. The load forced 4.3% of the water out of the nucleus, which reduced nucleus pressure by 44(±6)%. Reduction of the osmotic gradient disturbed the equilibrium disc height, and a significant loss of annulus water content was found. Remarkably, pressure and water content of the nucleus pulposus remained unchanged. This shows that annulus water content is important in the response to axial loading. After unloading, in the absence of an osmotic gradient, there was substantial viscoelastic recovery of 53(±11)% of the disc height, without a change in water content. However, for restoration of the nucleus pressure and for full restoration of disc height, restoration of the osmotic gradient was needed.     

Construction of tissue-engineered composite intervertebral disc and preliminary morphological and biochemical evaluation

The aim of this study was to construct tissue-engineered composite intervertebral disc (IVD) consisting of demineralized bone matrix gelatin (DBMG) and collagenII/hyaluronate/chondroitin-6-sulfate (CII/HyA–CS) scaffolds seeded with anulus fibrosus (AF) and nucleus pulposus (NP) cells, respectively. The cell-scaffold hybrids were implanted in the subcutaneous space of the dorsum of athymic mice and harvested at 4, 8, and 12 weeks. At each time point, the gross and histological morphology and biochemical properties were evaluated. Our results are as following: the gross morphology and histology of the composite resembled those of native IVD. Morphological studies revealed progressive tissue formation and junction integration between AF and NP regions. Biochemical composition detection indicated that the content of DNA, proteoglycan and hydroxyproline increased with time, and were similar to native tissue at 12 weeks. All these results demonstrated the feasibility of creating a tissue-engineered composite IVD with similar morphological and biochemical properties to the native tissue.     

Changes with age and the effect of recombinant human BMP-2 on proteoglycan and collagen gene expression in rabbit anulus fibrosus cells

In order to compare the difference between young and old intervertebral disc cells and theirresponsiveness to recombinant human bone morphogenetic protein-2 (rhBMP-2),disc cells were isolatedfrom the anulus fibrosus (AF) and transition zones of lumbar discs from eight old and eight young NewZealand white rabbits.Compared with the ceils from the young rabbits,cells from old rabbits respond less torhBMP-2 treatment with respect to sulfated-glycosaminoglycan (sGAG) synthesis and aggrecan geneexpression.But in collagen Ⅰ and collagen Ⅱ gene expressions,there are no significant differences betweenthe old and the young.When comparing sGAG content,aggrecan,and collagen Ⅱ gene expression of the oldAF cells after rhBMP-2 treatment with that of the young AF cells without rhBMP-2 treatment,the old AFcells with rhBMP-2 treatment have a greater capacity to synthesize sGAG bound in the cells and to releasesGAG in the media,as well as to express aggrecan and collagen Ⅱ gene.It can be concluded that old AF cellsafter rhBMP-2 treatment have a greater capacity to synthesize sGAG and express aggrecan and collagen Ⅱ ascompared to young AF cells without rhBMP-2 treatment.Thus rhBMP-2 can reverse the decline in theanabolic capacity of the disc cells with ageing.So it seems that rhBMP-2 has potential for use as an agent toretard a key component of disc degeneration and loss of disc matrix.     

On the relationship between the microstructure of bone and its mechanical stiffness.

A recent study of bone structure shows that the plate-shaped carbonate apatite crystals in individual lamellae are arranged in layers across the lamellae, and that the orientation of these layers are different in alternate lamellae. Based on these findings, a new micromechanical model for the Young's modulus of bone is proposed, which accounts for the anisotropy and geometrical characteristics of the material. The model incorporates the platelet-like geometry of the basic reinforcing unit, the presence of alternating thin and thick lamellae, and the orientations of the crystal platelets in the lamellae. The thin and thick lamellae are modeled as orthotropic composite layers made up of thin rectangular apatite platelets within a collagen matrix, and classical orthotropic elasticity theory is used to calculate the Young's modulus of the lamellae. Bone is viewed as an assembly of such orthotropic lamellae bent into cylindrical structures, and having a constant, alternating angle between successive lamellae. The micromechanical model employs a modified rule-of-mixtures to account for the two types of lamellae. The model provides a curve similar to the published experimental data on the angular dependence of Young's modulus, including a local maximum at an angle between 0 and 90 degrees. A rigorous testing of the model awaits additional experimental data.     

缺氧诱导因子-1α和葡萄糖转运蛋白-1在不同月龄大鼠椎间盘中的表达

目的检测缺氧诱导因子-1α(hypoxia-inducible factor-1α,HIF-1α)和葡萄糖转运蛋白-1(glucose transporter-1,GLUT-1)在不同月龄大鼠椎间盘纤维环组织中的表达及其相关性,探讨HIF-1α及GLUT-1在椎间盘退变过程中的作用。方法取Wistar大鼠50只,分别以1,3,6,12,18个月龄分为5组。采用免疫组化法及Western blot法检测各组椎间盘中HIF-1α和GLUT-1表达情况。结果随着大鼠月龄的增长,其椎间盘纤维环组织中HIF-1α和GLUT-1的表达也发生变化,由低月龄组(1-3月龄)至成年组(6-12月龄)HIF-1α和GLUT-1表达逐渐减少,而老年组(18月龄)二者表达显著增加。且这种变化有显著统计学意义(P0.01)。纤维环中HIF-1α和GLUT-1的蛋白表达呈正相关。结论HIF-1α、GLUT-1表达水平的变化与椎间盘退变的发生关系密切相关,HIF-1α可以通过上调GLUT-1等相关因子并延缓椎间盘退变,可能作为椎间盘退变治疗研究的切入点。     

Computational study of the role of fluid content and flow on the lumbar disc response in cyclic compression: Replication of in vitro and in vivo conditions

The intervertebral disc viscoelastic response is governed primarily by its fluid content and flow. In vivo measurements demonstrate that the disc volume, fluid content, height and nucleus pressure completely recover during resting even after diurnal loading with twice longer duration (16 vs. 8 h). In view of much longer periods required for the recovery of disc height and pressure in vitro, concerns have been raised on the fluid inflow through the endplates that might be hampered by clogged blood vessels post mortem. This in silico study aimed to identify fluid-flow dependent response of discs and conditions essential to replicate in vitro and in vivo observations.An osmo-poroelastic finite element model of the human lumbar L4-L5 disc-bone unit was used. Simulating earlier in vitro experiments on bovine discs, the loading protocol started with 8 h preload at 0.06 MPa followed by 30 high/low compression loading cycles each lasting 7.5 min at 0.5/0.06 MPa, respectively. Three different endplate configurations were investigated: free in- and outflow, no inflow and closed endplates with no flow. Additionally, the preload magnitude was increased from 0.06 MPa to 0.28 MPa and 0.50 MPa, or the initial nucleus hydration was reduced from 83% to 50%.For 0.06 MPa preload, the model with no inflow best matched in vitro trends. The model with free inflow increased segment height and nucleus pressure while the model with no fluid inflow resulted in a relatively small recovery in segment height and a rather constant nucleus pressure during unloading periods.Results highlight an excessive mobile fluid content as well as a restricted fluid inflow through endplates as likely causes of the discrepancies between in vivo and in vitro studies. To replicate in vivo conditions in vitro and in silico, disc hydration level should be controlled by adequate selection of preload magnitude/period and/or mobile fluid porosity.     

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.