Intervertebral disc creep behavior assessment through an open source finite element solver

Automatic generation of subject-specific finite element models of the spine from magnetic resonance images

The generation of subject-specific finite element models of the spine is generally a time-consuming process based on computed tomography (CT) images, where scanning exposes subjects to harmful radiation. In this study, a method is presented for the automatic generation of spine finite element models using images from a single magnetic resonance (MR) sequence. The thoracic and lumbar spine of eight adult volunteers was imaged using a 3D multi-echo-gradient-echo sagittal MR sequence. A deep-learning method was used to generate synthetic CT images from the MR images. A pre-trained deep-learning network was used for the automatic segmentation of vertebrae from the synthetic CT images. Another deep-learning network was trained for the automatic segmentation of intervertebral discs from the MR images. The automatic segmentations were validated against manual segmentations for two subjects, one with scoliosis, and another with a spine implant. A template mesh of the spine was registered to the segmentations in three steps using a Bayesian coherent point drift algorithm. First, rigid registration was applied on the complete spine. Second, non-rigid registration was used for the individual discs and vertebrae. Third, the complete spine was non-rigidly registered to the individually registered discs and vertebrae. Comparison of the automatic and manual segmentations led to dice-scores of 0.93-0.96 for all vertebrae and discs. The lowest dice-score was in the disc at the height of the implant where artifacts led to under-segmentation. The mean distance between the morphed meshes and the segmentations was below 1 mm. In conclusion, the presented method can be used to automatically generate accurate subject-specific spine models.

Biomechanical consequences of the intervertebral disc centre of rotation kinematics during lateral bending and axial rotation

The location of the instantaneous centre of rotation (ICR) of a lumbar unit has a considerable clinical importance as a spinal health estimator. Consequently, many studies have been conducted to measure or estimate the ICR during rotations in the three anatomical planes; however the results reported are widely scattered. Even if some inter-subjects variability is to be expected, such inconsistencies are likely explained by the differences in methods and experiments. Therefore, in this paper we seek to model three behaviours of the ICR during lateral bending and axial rotation based on results published in the literature. In order to assess the metabolic and mechanical sensibility to the assumption made on the ICR kinematics, we used a previously validated three dimensional non-linear poroelastic model of a porcine intervertebral disc to simulate physiological lateral and axial rotations. The impact of the geometry was also briefly investigated by considering a 11[Formula: see text] wedge angle. From our simulations, it appears that the hypothesis made on the ICR location does not significantly affect the critical nutrients concentrations but gives disparate predictions of the intradiscal pressure at the centre of the disc (variation up to 0.7 MPa) and of the displacement fields (variation up to 0.4 mm). On the contrary, the wedge angle does not influence the estimated intradiscal pressure but leads to minimal oxygen concentration decreased up to 33% and increased maximal lactate concentration up to 13%. While we can not settle on which definition of the ICR is more accurate, this work suggests that patient-specific modeling of the ICR is required and brings new insights that can be useful for the development of new tools or the design of surgical material such as total lumbar disc prostheses.

Impact of extracellular matrix and collagen network properties on the cervical intervertebral disc response to physiological loads: A parametric study

Current intervertebral disc finite element models are hard to validate since they describe multi-physical phenomena and contain a huge number of material properties. This work aims to simplify numerical validation/identification studies by prioritizing the sensitivity of intervertebral disc behavior to mechanical properties. A 3D fiber-reinforced hyperelastic model of a C6-C7 intervertebral disc is used to carry out the parametric study. 10 parameters describing the extracellular matrix and the collagen network behaviors are included in the parametric study. The influence of varying these parameters on the disc response is estimated during physiological movements of the head, including compression, lateral bending, flexion, and axial rotation. The obtained results highlight the high sensitivity of the disc behavior to the stiffness of the annulus fibrosus extracellular matrix for all the studied loads with a relative increase in the disc apparent stiffness by 67% for compression and by 57% for axial rotation when the annulus stiffness increases from 0.4 to 2 MPa. It is also shown that varying collagen network orientation, stiffness, and stiffening in the studied configuration range have a noticeable effect on rotational motions with a relative apparent stiffness difference reaching 6.8%, 10%, and 22%, respectively, in lateral bending. However, the collagen orientation does not affect disc response to axial load.

Biomechanical Investigation Between Rigid and Semirigid Posterolateral Fixation During Daily Activities: Geometrically Parametric Poroelastic Finite Element Analyses

While spinal fusion using rigid rods remains the gold standard treatment modality for various lumbar degenerative conditions, its adverse effects, including accelerated adjacent segment disease (ASD), are well known. In order to better understand the performance of semirigid constructs using polyetheretherketone (PEEK) in fixation surgeries, the objective of this study was to analyze the biomechanical performance of PEEK versus Ti rods using a geometrically patient-specific poroelastic finite element (FE) analyses. Ten subject-specific preoperative models were developed, and the validity of the models was evaluated with previous studies. Furthermore, FE models of those lumbar spines were regenerated based on postoperation images for posterolateral fixation at the L4–L5 level. Biomechanical responses for instrumented and adjacent intervertebral discs (IVDs) were analyzed and compared subjected to static and cyclic loading. The preoperative model results were well comparable with previous FE studies. The PEEK construct demonstrated a slightly increased range of motion (ROM) at the instrumented level, but decreased ROM at adjacent levels, as compared with the Ti. However, no significant changes were detected during axial rotation. During cyclic loading, disc height loss, fluid loss, axial stress, and collagen fiber strain in the adjacent IVDs were higher for the Ti construct when compared with the intact and PEEK models. Increased ROM, experienced stress in AF, and fiber strain at adjacent levels were observed for the Ti rod group compared with the intact and PEEK rod group, which can indicate the risk of ASD for rigid fixation. Similar to the aforementioned pattern, disc height loss and fluid loss were significantly higher at adjacent levels in the Ti rod group after cycling loading which alter the fluid–solid interaction of the adjacent IVDs. This phenomenon debilitates the damping quality, which results in disc disability in absorbing stress. Such finding may suggest the advantage of using a semirigid fixation system to decrease the chance of ASD.

[Research progress in creep characteristics of lumbar intervertebral disc]

Objective

To summarize the research progress in creep characteristics of lumbar intervertebral disc.

Methods

The relevant literature at home and abroad was systematically searched. Then, the concept and structural basis of lumbar disc creep, the description of creep characteristics, and the latest progress of its influencing factors were summarized and analyzed.

Results

The intervertebral disc is viscoelastic. After loading, the deformation increases with time. However, the degree of increase is not linear with time. That is creep, which plays an important role in buffering the load generated by human activities and absorbing energy in order to maintain stable movement of the spine. Both experimental and simulation studies can well describe the creep behavior of intervertebral disc. Various models including standard linear solid model and corresponding constitutive equations can quantify and compare the creep characteristics, which can be obviously changed by the degeneration of intervertebral disc and the mode of loading stress.

Conclusion

Creep is an important mechanical properties of intervertebral discs, and an in-depth understanding of the creep characteristics of lumbar intervertebral discs is of great guiding significance for the intervention and treatment of low back pain.

Numerical implementation of an osmo-poro-visco-hyperelastic finite element solver: application to the intervertebral disc

This work deals with the finite element (FE) implementation of a biphasic poroelastic formulation specifically developed to address the intricate behaviour of the Intervertebral Disc (IVD) and other highly hydrated soft tissues. This formulation is implemented in custom FE solver V-Biomech, being the validation performed with a lumbar IVD model, which was compared against the analogous FE model of Williams et al. and the experiments of Tyrrell et al. Good agreement with these benchmarks was achieved, meaning that V-Biomech and its novel poroelastic formulation are a viable alternative for simulation of biphasic soft tissues.

The response surface method-genetic algorithm for identification of the lumbar intervertebral disc material parameters

Long-term compressive load on the lumbar intervertebral disc (IVD) might lead to lumbar IVD herniation. Exploring the material parameters of normal and degenerative enucleated IVDs is the basis for studying their mechanical behavior. According to the inverse analysis principle of the parameter estimation, an optimization method was proposed to identify the parameters of the porous material of the lumbar IVD based on finite element inverse analysis. The poroelastic finite element models were established in line with the compression creep experiment. The material parameters were combined by Box-Behnken design (BBD), and the response surface (RS) models were constructed using a quadratic polynomial with cross terms and optimized by genetic algorithm (GA). The results showed that the simulation result of the best material parameter combination had a good agreement with the experiment. Compared with the normal lumbar IVD, the elastic modulus and permeability decreased, and Poisson's ratio increased for the enucleated disk, resulting in a significant difference in mechanical properties. The algorithm used in this study can reduce the parameter identification error compared with only the RS method, and decrease the number of finite element simulations compared with only the GA.

Poroelastic Modeling of Highly Hydrated Collagen Hydrogels: Experimental Results vs. Numerical Simulation With Custom and Commercial Finite Element Solvers

This study presents a comparison between the performances of two Finite Element (FE) solvers for the modeling of the poroelastic behavior of highly hydrated collagen hydrogels. Characterization of collagen hydrogels has been a widespread challenge since this is one of the most used natural biomaterials for Tissue Engineering (TE) applications. V-Biomech® is a free custom FE solver oriented to soft tissue modeling, while Abaqus® is a general-purpose commercial FE package which is widely used for biomechanics computational modeling. Poroelastic simulations with both solvers were compared to two experimental protocols performed by Busby et al. (2013) and Chandran and Barocas (2004), also using different implementations of the frequently used Neo-Hookean hyperelastic model. The average differences between solvers outputs were under 5% throughout the different tests and hydrogel properties. Thus, differences were small enough to be considered negligible and within the variability found experimentally from one sample to another. This work demonstrates that constitutive modeling of soft tissues, such as collagen hydrogels can be achieved with either V-Biomech or Abaqus standard options (without user-subroutine), which is important for the biomechanics and biomaterials research community. V-Biomech has shown its potential for the validation of biomechanical characterization of soft tissues, while Abaqus' versatility is useful for the modeling and analysis of TE applications where other complex phenomena may also need to be captured.

Numerical Prediction of the Mechanical Failure of the Intervertebral Disc under Complex Loading Conditions

Finite element modeling has been widely used to simulate the mechanical behavior of the intervertebral disc. Previous models have been generally limited to the prediction of the disc behavior under simple loading conditions, thus neglecting its response to complex loads, which may induce its failure. The aim of this study was to generate a finite element model of the ovine lumbar intervertebral disc, in which the annulus was characterized by an anisotropic hyperelastic formulation, and to use it to define which mechanical condition was unsafe for the disc. Based on published in vitro results, numerical analyses under combined flexion, lateral bending, and axial rotation with a magnitude double that of the physiological ones were performed. The simulations showed that flexion was the most unsafe load and an axial tensile stress greater than 10 MPa can cause disc failure. The numerical model here presented can be used to predict the failure of the disc under all loading conditions, which may support indications about the degree of safety of specific motions and daily activities, such as weight lifting.

Combined numerical and experimental biomechanical characterization of soft collagen hydrogel substrate

This work presents a combined experimental-numerical framework for the biomechanical characterization of highly hydrated collagen hydrogels, namely with 0.20, 0.30 and 0.40% (by weight) of collagen concentration. Collagen is the most abundant protein in the extracellular matrix of animals and humans. Its intrinsic biocompatibility makes collagen a promising substrate for embedding cells within a highly hydrated environment mimicking natural soft tissues. Cell behaviour is greatly influenced by the mechanical properties of the surrounding matrix, but the biomechanical characterization of collagen hydrogels has been challenging up to now, since they present non-linear poro-viscoelastic properties. Combining the stiffness outcomes from rheological experiments with relevant literature data on collagen permeability, poroelastic finite element (FE) models were developed. Comparison between experimental confined compression tests available in the literature and analogous FE stress relaxation curves showed a close agreement throughout the tests. This framework allowed establishing that the dynamic shear modulus of the collagen hydrogels is between 0.0097 ± 0.018 kPa for the 0.20% concentration and 0.0601 ± 0.044 kPa for the 0.40% concentration. The Poisson's ratio values for such conditions lie within the range of 0.495-0.485 for 0.20% and 0.480-0.470 for 0.40%, respectively, showing that rheology is sensitive enough to detect these small changes in collagen concentration and thus allowing to link rheology results with the confined compression tests. In conclusion, this integrated approach allows for accurate constitutive modelling of collagen hydrogels. This framework sets the grounds for the characterization of related hydrogels and to the use of this collagen parameterization in more complex multiscale models.

A database of lumbar spinal mechanical behavior for validation of spinal analytical models

Data from two experimental studies with eight specimens each of spinal motion segments and/or intervertebral discs are presented in a form that can be used for comparison with finite element model predictions. The data include the effect of compressive preload (0, 250 and 500N) with quasistatic cyclic loading (0.0115Hz) and the effect of loading frequency (1, 0.1, 0.01 and 0.001Hz) with a physiological compressive preload (mean 642N). Specimens were tested with displacements in each of six degrees of freedom (three translations and three rotations) about defined anatomical axes. The three forces and three moments in the corresponding axis system were recorded during each test. Linearized stiffness matrices were calculated that could be used in multi-segmental biomechanical models of the spine and these matrices were analyzed to determine whether off-diagonal terms and symmetry assumptions should be included. These databases of lumbar spinal mechanical behavior under physiological conditions quantify behaviors that should be present in finite element model simulations. The addition of more specimens to identify sources of variability associated with physical dimensions, degeneration, and other variables would be beneficial. Supplementary data provide the recorded data and Matlab® codes for reading files. Linearized stiffness matrices derived from the tests at different preloads revealed few significant unexpected off-diagonal terms and little evidence of significant matrix asymmetry.

Effect of Degeneration on Fluid-Solid Interaction within Intervertebral Disk Under Cyclic Loading - A Meta-Model Analysis of Finite Element Simulations

The risk of low back pain resulted from cyclic loadings is greater than that resulted from prolonged static postures. Disk degeneration results in degradation of disk solid structures and decrease of water contents, which is caused by activation of matrix digestive enzymes. The mechanical responses resulted from internal solid-fluid interactions of degenerative disks to cyclic loadings are not well studied yet. The fluid-solid interactions in disks can be evaluated by mathematical models, especially the poroelastic finite element (FE) models. We developed a robust disk poroelastic FE model to analyze the effect of degeneration on solid-fluid interactions within disk subjected to cyclic loadings at different loading frequencies. A backward analysis combined with in vitro experiments was used to find the elastic modulus and hydraulic permeability of intact and enzyme-induced degenerated porcine disks. The results showed that the averaged peak-to-peak disk deformations during the in vitro cyclic tests were well fitted with limited FE simulations and a quadratic response surface regression for both disk groups. The results showed that higher loading frequency increased the intradiscal pressure, decreased the total fluid loss, and slightly increased the maximum axial stress within solid matrix. Enzyme-induced degeneration decreased the intradiscal pressure and total fluid loss, and barely changed the maximum axial stress within solid matrix. The increase of intradiscal pressure and total fluid loss with loading frequency was less sensitive after the frequency elevated to 0.1 Hz for the enzyme-induced degenerated disk. Based on this study, it is found that enzyme-induced degeneration decreases energy attenuation capability of disk, but less change the strength of disk.

Long-Term Creep Behavior of the Intervertebral Disk: Comparison between Bioreactor Data and Numerical Results

The loaded disk culture system is an intervertebral disk (IVD)-oriented bioreactor developed by the VU Medical Center (VUmc, Amsterdam, The Netherlands), which has the capacity of maintaining up to 12 IVDs in culture, for approximately 3 weeks after extraction. Using this system, eight goat IVDs were provided with the essential nutrients and submitted to compression tests without losing their biomechanical and physiological properties, for 22 days. Based on previous reports (Paul et al., 2012, 2013; Detiger et al., 2013), four of these IVDs were kept in physiological condition (control) and the other four were previously injected with chondroitinase ABC (CABC), in order to promote degenerative disk disease (DDD). The loading profile intercalated 16 h of activity loading with 8 h of loading recovery to express the standard circadian variations. The displacement behavior of these eight IVDs along the first 2 days of the experiment was numerically reproduced, using an IVD osmo-poro-hyper-viscoelastic and fiber-reinforced finite element (FE) model. The simulations were run on a custom FE solver (Castro et al., 2014). The analysis of the experimental results allowed concluding that the effect of the CABC injection was only significant in two of the four IVDs. The four control IVDs showed no signs of degeneration, as expected. In what concerns to the numerical simulations, the IVD FE model was able to reproduce the generic behavior of the two groups of goat IVDs (control and injected). However, some discrepancies were still noticed on the comparison between the injected IVDs and the numerical simulations, namely on the recovery periods. This may be justified by the complexity of the pathways for DDD, associated with the multiplicity of physiological responses to each direct or indirect stimulus. Nevertheless, one could conclude that ligaments, muscles, and IVD covering membranes could be added to the FE model, in order to improve its accuracy and properly describe the recovery periods.

Finite element simulation of an artificial intervertebral disk using fiber reinforced laminated composite model

Degeneration of intervertebral disk (IVD) has been increased in recent years. The lumbar herniation can be cured using conservative and surgical procedures. Surgery is considered after failure of conservative treatment. Partial discectomy, fusion, and total disk replacement (TDR) are also common surgical treatments for degenerative disk disease. However, due to limitations and disadvantages of the current treatments, many studies have been carried out to approach the best design of mimicking natural disk. Recently, a new method of TDRs has been introduced using nature deformation of IVD by reinforced fibers of annulus fibrosis. Nonetheless, owing to limitations of experimental works on the human body, numerical studies of IVD may help to understand load transfer and biomechanical properties within the disks with reinforced fibers. In this study, a three-dimensional (3D) finite element model of the L2-L3 disk vertebrae unit with 12 vertical fibers embedded into annulus fibrosis was constructed. The IVD was subjected to compressive force, bending moment, and axial torsion. The most important parameters of disk failures were compared to that of experimental data. The results showed that the addition of reinforced fibers into the disk invokes a significant decrease of stress in the nucleus and annulus. The findings of this study may have implications not only for developing IVDs with reinforced fibers but also for the application of fiber reinforced IVD in orthopedics surgeries as a suitable implant.