Calibration of hyperelastic material properties of the human lumbar intervertebral disc under fast dynamic compressive loads

Under fast dynamic loading conditions (e.g. high-energy impact), the load rate dependency of the intervertebral disc (IVD) material properties may play a crucial role in the biomechanics of spinal trauma. However, most finite element models (FEM) of dynamic spinal trauma uses material properties derived from quasi-static experiments, thus neglecting this load rate dependency. The aim of this study was to identify hyperelastic material properties that ensure a more biofidelic simulation of the IVD under a fast dynamic compressive load. A hyperelastic material law based on a first-order Mooney-Rivlin formulation was implemented in a detailed FEM of a L2-L3 functional spinal unit (FSU) to represent the mechanical behavior of the IVD. Bony structures were modeled using an elasto-plastic Johnson-Cook material law that simulates bone fracture while ligaments were governed by a viscoelastic material law. To mimic experimental studies performed in fast dynamic compression, a compressive loading velocity of 1 m/s was applied to the superior half of L2, while the inferior half of L3 was fixed. An exploratory technique was used to simulate dynamic compression of the FSU using 34 sets of hyperelastic material constants randomly selected using an optimal Latin hypercube algorithm and a set of material constants derived from quasi-static experiments. Selection or rejection of the sets of material constants was based on compressive stiffness and failure parameters criteria measured experimentally. The two simulations performed with calibrated hyperelastic constants resulted in nonlinear load-displacement curves with compressive stiffness (7335 and 7079 N/mm), load (12,488 and 12,473 N), displacement (1.95 and 2.09 mm) and energy at failure (13.5 and 14.7 J) in agreement with experimental results (6551 ± 2017 N/mm, 12,411 ± 829 N, 2.1 ± 0.2 mm and 13.0 ± 1.5 J respectively). The fracture pattern and location also agreed with experimental results. The simulation performed with constants derived from quasi-static experiments showed a failure energy (13.2 J) and a fracture pattern and location in agreement with experimental results, but a compressive stiffness (1580 N/mm), a failure load (5976 N) and a displacement to failure (4.8 mm) outside the experimental corridors. The proposed method offers an innovative way to calibrate the hyperelastic material properties of the IVD and to offer a more realistic simulation of the FSU in fast dynamic compression.     

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.     

The role of the nucleus pulposus in neutral zone human lumbar intervertebral disc mechanics

To study the effect of denucleation on the mechanical behavior of the human lumbar intervertebral disc through a 2mm incision, two groups of six human cadaver lumbar spinal units were tested in axial compression, axial rotation, lateral bending and flexion/extension after incremental steps of "partial" denucleation. Neutral zone, range of motion, stiffness, intradiscal pressure and energy dissipation were measured; the results showed that the contribution of the nucleus pulposus to the mechanical behavior of the intervertebral disc was more dominant through the neutral zone than at the farther limits of applied loads and moments.     

Effect of annular incision type on the change in biomechanical properties in a herniated lumbar intervertebral disc

The technique used to incise the disc during discectomy may play a role in the subsequent healing and change in biomechanical stiffness of the disc. Several techniques of lumbar disc annulotomy have been described in clinical reports. The purpose of this paper was to study the influence of annulotomy technique on motion segment stiffness using a finite element model. Four incision methods (square, circular, cross, and slit) were compared. The analyses showed that each of the annular incisions produced increase in motions under axial moment loadings with circular incision producing the largest change in the corresponding rotational motion. Under shear loading mode, cross and slit-type annular incisions produced slightly larger changes in the principal motions of the disc than square and circular incisions. All other incision types considered in the current study produced negligibly small increase in motion under rest of the loading conditions. In addition to annulotomy, when nucleotomy was also included in the analyses, once again cross and slit incisions produced larger change in motion under shear loading mode as compared to the other two incision types. A comparison between the four types of annular incisions showed that cross incision produced an increase in motion larger than those produced by the other three incisions under flexion/extension and lateral moment loading and both shear force loadings. Circular incision produced the largest increase in motion under axial moment load in comparison to those produced by square, cross, and slit incisions. Sagittal plane symmetry was influenced by the incision injury to the motion segment leading to coupled motions as well as increased facet loads. From the study it can be concluded that the increase inflexibility of the disc due to annulotomy depends on the type of annulotomy and the annulotomy also produce asymmetrical deformations leading to increased facet loading.     

Thermal analysis of the human intervertebral disc

Intervertebral disc (IVD) degeneration is one of the most common musculuskeletal disorders affecting western society. Degeneration alters the morphology and the mechanical properties of the discs. According to previous reports, DSC proved to be a suitable method for the demonstration of thermal consequences of local as well as global conformational changes in the structure of the human intervertebral discs. In the present study, a wide spectrum of degenerated IVD was examined by DSC. The results suggest that definitive differences exist between the stages of disc degeneration in calorimetric measures.     

Neutral proteinases of the human intervertebral disc

Disc tissue consisting of pooled annuli fibrosus and nuclei pulposus from the cadaver of an adolescent aged 19 years was extracted with 4.0 M Gu-HCl. Proteins of low buoyant density (p less than or equal to 1.38 g/ml) containing the disc enzymes and inhibitors were separated from proteoglycans of high buoyant density (p greater than or equal to 1.50 g/ml) by density gradient ultracentrifugation. Sephadex G-75F gel chromatography followed by trypsin affinity chromatography was then used to resolve disc proteolytic and trypsin inhibitory activities. The results obtained were strongly suggestive of the presence of a high molecular weight zymogen which upon activation generated a population of smaller molecular weight proteinases. The disc proteinases obtained by this process showed similar properties in terms of: their pH optima (7.4-7.6); their inhibition patterns by class-specific proteinase inhibitors; their variation of activity as a function of NaCl and lysine concentrations; and the hydrodynamic size of their proteoglycan degradation products. The activated disc neutral proteinase demonstrated many characteristics in common with plasmin; however, unlike the latter, the disc proteinases also showed some calcium dependence.     

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.     

Dynamic compressive properties of human lumbar intervertebral joints: a comparison between fresh and thawed specimens

A comparison between the dynamic compressive properties of human lumbar intervertebral joints when fresh and after a period of deep frozen storage was made. Physiologically relevant loads of -750 +/- 250 N were applied in axial compression with the joint constrained against bending, over a frequency range of 0.01-10 Hz. Frozen storage was found not to affect the compressive stiffness or hysteresis of the seven joints. The magnitude of the observed changes in mean values were small, less than 1% decrease in the compressive stiffness and less than 1% increase in hysteresis after deep frozen storage.     

Nucleus pulposus related lncRNA and mRNA expression profiles in intervertebral disc degeneration

In the present study, we aimed to have a comprehensive understanding of nucleus pulposus related long noncoding RNA (lncRNA) and mRNA expression profiles in intervertebral disc degeneration (IDD). In total, 2418 mRNAs and 528 lncRNAs were found to be differentially expressed in the IDD group compared with the Control group. Combining microarray datasets and sequencing data, 5 overlapping DEMs and 7 overlapping DELs were identified. NF-κB signaling pathway, PI3K-Akt signaling pathway and Wnt/β-catenin signaling pathway were strongly linked with enriched GO terms and KEGG pathways. The ceRNA network suggested that lnc-TMEM44-AS1-hsa-miR-206-HDAC4 may be one crucial axis in IDD. PPI network analysis was constructed with 309 nodes and 129 edges. And the highest connectivity degrees were ALB, APOB and CCL2. This study suggested that specific lncRNAs and ceRNA axes may be crucial in the development of IDD. It provides a new perspective for delaying IDD process and enhancing intervertebral disc repair.     

A mechanical model for the human intervertebral disc

Stress relaxation experiments were performed on specimens from a human intervertebral disc. Specimens were made from the nucleus pulposus and from the external lamellae of the anulus fibrosus in two different orientations. Tests were run with varying moisture content so as to develop a relaxation master curve. A model was developed based on the experimental data. It was found that the short term master curve for the lamellae of the anulus and nucleus are similar, whereas the long term rubbery plateau is different between the lamellae and the nucleus. It was also established that the master curves for different lamellae and the nucleus were shifted relative to each other in the time domain due to changes in water content. The average relaxation modulus of the whole disc was obtained by averaging the properties between the anulus and nucleus. This model was then used for studies of Schmorl's nodes, of degenerated discs and for circumstances in which hydration is considered to be important.     

Ex vivo measurement of lumbar intervertebral disc pressure using fibre-Bragg gratings

Methods were developed to measure intervertebral disc pressure using optical fibre-Bragg gratings (FBGs). The FBG sensor was calibrated for hydrostatic pressure in a purpose-built apparatus and the average sensitivity was determined to be -5.7 +/- 0.085 pm/MPa (mean +/- SD). The average coefficient of determination (r(2)) for the calibration data was 0.99, and the average hysteresis of the sensor was 2.13% of full scale. The FBG was used to measure intradiscal pressure response to compressive load in five lumbar functional spine units. The pressure measured by the FBG sensor varied linearly with applied compressive load with coefficients of determination ranging from 0.84 to 0.97. The FBG sensor's sensitivity to compressive load ranged from 0.702 +/- 0.043 kPa/N (mean +/- SD) in a L1-L2 specimen, to 1.07 +/- 0.069 kPa/N in a L4-L5 specimen. These measurements agree with those of previous studies in lumbar spines. Two strain gauge pressure sensors were also used to measure intradiscal pressure response to compressive load. The measured pressure sensitivity to load ranged from 0.251 kPa/N (L4-L5) to 0.850 kPa/N (L2-L3). The average difference in pressure sensitivity to load between Sensors 1 and 2 was 12.9% of the value for Sensor 1, with a range from 1.1% to 20.4%, which suggests that disc pressure was not purely hydrostatic. This may have contributed to the difference between the responses of the FBG and strain gauge sensors.     

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.     

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.     

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.