An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies

Comparative FEM study on intervertebral disc modeling: Holzapfel-Gasser-Ogden vs. structural rebars

Introduction: Numerical modeling of the intervertebral disc (IVD) is challenging due to its complex and heterogeneous structure, requiring careful selection of constitutive models and material properties. A critical aspect of such modeling is the representation of annulus fibers, which significantly impact IVD biomechanics. This study presents a comparative analysis of different methods for fiber reinforcement in the annulus fibrosus of a finite element (FE) model of the human IVD. Methods: We utilized a reconstructed L4-L5 IVD geometry to compare three fiber modeling approaches: the anisotropic Holzapfel-Gasser-Ogden (HGO) model (HGO fiber model) and two sets of structural rebar elements with linear-elastic (linear rebar model) and hyperelastic (nonlinear rebar model) material definitions, respectively. Prior to calibration, we conducted a sensitivity analysis to identify the most important model parameters to be calibrated and improve the efficiency of the calibration. Calibration was performed using a genetic algorithm and in vitro range of motion (RoM) data from a published study with eight specimens tested under four loading scenarios. For validation, intradiscal pressure (IDP) measurements from the same study were used, along with additional RoM data from a separate publication involving five specimens subjected to four different loading conditions. Results: The sensitivity analysis revealed that most parameters, except for the Poisson ratio of the annulus fibers and C01 from the nucleus, significantly affected the RoM and IDP outcomes. Upon calibration, the HGO fiber model demonstrated the highest accuracy (R2 = 0.95), followed by the linear (R2 = 0.89) and nonlinear rebar models (R2 = 0.87). During the validation phase, the HGO fiber model maintained its high accuracy (RoM R2 = 0.85; IDP R2 = 0.87), while the linear and nonlinear rebar models had lower validation scores (RoM R2 = 0.71 and 0.69; IDP R2 = 0.86 and 0.8, respectively). Discussion: The results of the study demonstrate a successful calibration process that established good agreement with experimental data. Based on our findings, the HGO fiber model appears to be a more suitable option for accurate IVD FE modeling considering its higher fidelity in simulation results and computational efficiency.

Simulation of cancer progression in bone by a virtual thermal flux with a case study on lumbar vertebrae with multiple myeloma

BACKGROUND

Two main problems examining the mechanism of cancer progression in the tissues using the computational models are lack of enough knowledge on the effective factors for such events in vivo environments and lack of specific parameters in the available computational models to simulate such complicated reactions.

METHODS

In this study, it was tried to simulate the progression of cancerous lesions in the bone tissues by an independent parameter from the anatomical and physiological characteristics of the tissues, so to degrade the orthotropic mechanical properties of the bone tissues, a virtual temperature was determined to be used by a well-known framework for simulation of damages in the composite materials. First, the reliability of the FE model to simulate hyperelastic response in the intervertebral discs (IVDs) and progressive failure in the bony components were verified by simulation of some In-Vitro tests, available in the literature. Then, the progression of the osteolytic damage was simulated in a clinical case with multiple myeloma in the lumbar vertebrae.

RESULTS

The FE model could simulate stress-shielding and diffusion of lesion in the posterior elements of the damaged vertebra which led to spinal stenosis. The load carrying shares associated with the anterior half and the posterior half of the examined vertebral body and the posterior elements were estimated equal to 41 %, 47 % and 12 %, respectively for the intact condition, that changed to 14 %, 16 % and 70 %, when lesion occupied one third of the vertebral body.

CONCLUSION

Correlation of the FE results with the deformation shapes, observed in the MRIs for the clinical case study, indicated appropriateness of the procedure, proposed for simulation of the progressive osteolytic damage in the vertebral segments. The future studies may follow simulation of tumor growth for various metastatic tissues using the method, established here.

Assessment of a fully-parametric thoraco-lumbar spine model generator with articulated ribcage

The present paper describes a novel user-friendly fully-parametric thoraco-lumbar spine CAD model generator including the ribcage, based on 22 independent parameters (1 posterior vertebral body height per vertebra + 4 sagittal alignment parameters, namely pelvic incidence, sacral slope, L1-L5 lumbar lordosis, and T1-T12 thoracic kyphosis). Reliable third-order polynomial regression equations were implemented in Solidworks to analytically calculate 56 morphological dependent parameters and to automatically generate the spine CAD model based on primitive geometrical features. A standard spine CAD model, representing the case-study of an average healthy adult, was then created and positively assessed in terms of spinal anatomy, ribcage morphology, and sagittal profile. The immediate translation from CAD to FEM for relevant biomechanical analyses was successfully demonstrated, first, importing the CAD model into Abaqus, and then, iteratively calibrating the constitutive parameters of one lumbar and three thoracic FSUs, with particular interest on the hyperelastic material properties of the IVD, and the spinal and costo-vertebral ligaments. The credibility of the resulting lumbo-sacral and thoracic spine FEM with/without ribcage were assessed and validated throughout comparison with extensive in vitro and in vivo data both in terms of kinematics (range of motion) and dynamics (intradiscal pressure) either collected under pure bending moments and complex loading conditions (bending moments + axial compressive force).

Effects of dynamic and rigid implantation on biomechanical characteristics of different sagittal alignment lumbar after single- or double-level spinal fixations: a finite-element modeling study

BACKGROUND

Although it is critical to understand the accelerated degeneration of adjacent segments after fusion, the biomechanical properties of the spine have not been thoroughly studied after various fusion techniques. This study investigates whether four Roussouly's sagittal alignment morphotypes have different biomechanical characteristics after different single- or double-level spinal fixations.

METHODS

The parametric finite element (FE) models of Roussouly's type (1-4) were developed based on the radiological data of 625 Chinese community population. The four Roussouly's type models were reassembled into four fusion models: single-level L4-5 Coflex fixation model, single-level L4-5 Fusion (pedicle screw fixation) model, double-level Coflex (L4-5) + Fusion (L5-S1) model, and double-level Fusion (L4-5) + Fusion (L4-5) model. A pure moment of 7.5 Nm was applied to simulate the physiological activities of flexion, extension, lateral bending and axial rotation.

RESULTS

Both single-level and double-level spinal fixation had the greatest effect on lumbar range of motion, disc pressure, and annulus fibrosis stress in flexion, followed by lateral bending, extension, and axial rotation. In all models, the upper adjacent segment was the most influenced by the implantation and bore the most compensation from the fixed segment. For Type 2 lumbar, the L4-L5 Coflex effectively reduced the disc pressure and annulus fibrosis stress in adjacent segments compared to the L4-L5 Fusion. Similarly, the L4-L5 Coflex offered considerable advantages in preserving the biomechanical properties of adjacent segments for Type 1 lumbar. For Type 4 lumbar, the L4-L5 Coflex did not have superiority over the L4-L5 Fusion, resulting in a greater increase in range of motion at adjacent segments in flexion and extension. The difference between the two fixations was not apparent in Type 3 lumbar. Compared to the single-level Fusion, the changes in motion and mechanics of the lumbar increased after both the double-level Coflex + Fusion and Fusion + Fusion fixations, while the differences between two double-level fixation methods on adjacent segments of the four lumbar models were similar to that of the single-level fixation.

CONCLUSION

Type 3 and Type 4 lumbar have good compensatory ability and therefore allow for a wider range of surgical options, whereas surgical options for small lordotic Type 1 and Type 2 lumbar are more limited and severe.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson's ratio. The effective Poisson's ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson's ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

A Review of Finite Element Modeling for Anterior Cervical Discectomy and Fusion

The cervical spine poses many complex challenges that require complex solutions. Anterior cervical discectomy and fusion (ACDF) has been one such technique often employed to address such issues. In order to address the problems with ACDF and assess the modifications that have been made to the technique over time, finite element analyses (FEA) have proven to be an effective tool. The variations of cervical spine FEA models that have been produced over the past couple of decades, particularly more recent representations of more complex geometries, have not yet been identified and characterized in any literature. Our objective was to present material property models and cervical spine models for various simulation purposes. The outlining and refinement of the FEA process will yield more reliable outcomes and provide a stable basis for the modeling protocols of the cervical spine.

Biomechanical and clinical studies on lumbar spine fusion surgery: a review

Low back pain is associated with degenerative disc diseases of the spine. Surgical treatment includes fusion and non-fusion types. The gold standard is fusion surgery, wherein the affected vertebral segment is fused. The common complication of fusion surgery is adjacent segment degeneration (ASD). The ASD often leads to revision surgery, calling for a further fusion of adjacent segments. The existing designs of nonfusion type implants are associated with clinical problems such as subsidence, difficulty in implantation, and the requirement of revision surgeries. Various surgical approaches have been adopted by the surgeons to insert the spinal implants into the affected segment. Over the years, extensive biomechanical investigations have been reported on various surgical approaches and prostheses to predict the outcomes of lumbar spine implantations. Computer models have been proven to be very effective in identifying the best prosthesis and surgical procedure. The objective of the study was to review the literature on biomechanical studies for the treatment of lumbar spinal degenerative diseases. A critical review of the clinical and biomechanical studies on fusion spine surgeries was undertaken. The important modeling parameters, challenges, and limitations of the current studies were identified, showing the future research directions.

Contribution of Shape Features to Intradiscal Pressure and Facets Contact Pressure in L4/L5 FSUs: An In-Silico Study

Finite element models (FEMs) of the spine commonly use a limited number of simplified geometries. Nevertheless, the geometric features of the spine are important in determining its FEM outcomes. The link between a spinal segment's shape and its biomechanical response has been studied, but the co-variances of the shape features have been omitted. We used a principal component (PCA)-based statistical shape modelling (SSM) approach to investigate the contribution of shape features to the intradiscal pressure (IDP) and the facets contact pressure (FCP) in a cohort of synthetic L4/L5 functional spinal units under axial compression. We quantified the uncertainty in the FEM results, and the contribution of individual shape modes to these results. This parameterisation approach is able to capture the variability in the correlated anatomical features in a real population and sample plausible synthetic geometries. The first shape mode ([Formula: see text]) explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP (17%) and FCP (11%). The largest geometric variation in ([Formula: see text]) was in the annulus-nucleus ratio.

Reproducing Morphological Features Of Intervertebral Disc Using Finite Element Modeling To Predict The Course Of Cervical Spine Dorsopathy

Study objective — To evaluate how morphological features of intervertebral disc would affect the outcomes of finite element modeling of axial load in the cervical spine, C3-C5, in order to predict the risk of occurrence and course of dorsopathies. Material and Methods — Three-dimensional models of the cervical spine vertebrae were generated from the computed tomography data of a volunteer (24 years old male without detected pathology of his neck). Intervertebral disc models were developed in two configurations. For each model, we performed a finite element investigation of the stress-strain state with the same loading conditions. The load-displacement curves were compared with the experimental data generated from the results of previously conducted in vitro experiments. Results — The maximum and mean displacement values for the isotropic model were 1.15 mm and 0.73 ± 0.45 mm, respectively. For anisotropic model, maximum and mean displacement values were 0.86 mm and 0.47 ± 0.24 mm, correspondingly. Predicted displacement values for both models matched the experimental data fairly well. Stress profiles of intervertebral discs and stress diagrams of facet joints were calculated. Conclusion — The proposed geometric and constitutive configurations of the intervertebral disc take into account specific morphological features at low computational costs, thereby facilitating the modeling of degenerative disc changes.

Lumbar Intervertebral Disc Herniation: Annular Closure Devices and Key Design Requirements

Lumbar disc herniation is one of the most common degenerative spinal conditions resulting in lower back pain and sciatica. Surgical treatment options include microdiscectomy, lumbar fusion, total disc replacement, and other minimally invasive approaches. At present, microdiscectomy procedures are the most used technique; however, the annulus fibrosus is left with a defect that without treatment may contribute to high reherniation rates and changes in the biomechanics of the lumbar spine. This paper aims to review current commercially available products that mechanically close the annulus including the AnchorKnot® suture-passing device and the Barricaid® annular closure device. Previous studies and reviews have focused mainly on a biomimetic biomaterials approach and have described some mechanical and biological requirements for an active annular repair/regeneration strategy but are still far away from clinical implementation. Therefore, in this paper we aim to create a design specification for a mechanical annular closure strategy by identifying the most important mechanical and biological design parameters, including consideration of material selection, preclinical testing requirements, and requirements for clinical implementation.

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.

Biomechanical analysis of the cervical spine segment as a method for studying the functional and dynamic anatomy of the human neck

BACKGROUND

Traditionally, dynamic and functional anatomy, in particular the dynamic anatomy of the neck, is studied on cadaveric material. However, the development of in vivo visualization technologies and in silico modeling has made it possible to expand these possibilities. Despite significant progress in the study of dynamic and functional anatomy of the neck by means of in silico methods, the issues of validating the developed models and taking into account the pronounced nonlinearity of soft tissues as well as local anisotropy remain open. The aim of this study was to develop a virtual dynamic anatomical model of the human neck and reproduce the dynamic processes in the cervical spine from this model using the finite element method.

MATERIALS AND METHODS

Reverse engineering was used to generate a dynamic anatomical model of the neck from CT data (both male, 24 and 22 years old). Two segments of the cervical spine (C3-C5, C2-T1) were isolated from the resulting model for finite element analysis. Finite element mesh generation and contact interactions were performed using the HyperMesh software (Altair Engineering Inc, Troy, Michigan, USA). The anisotropic hyperelastic Holzapfel-Gasser-Ogden model was used to describe the material behavior of the fibrous rings of the disc. Material modeling and finite element analysis were performed using Abaqus CAE 6.14 software (Simulia, Johnston, Rhode Island, USA).

RESULTS

A technique for creating a virtual dynamic anatomical model of the neck was elaborated and implemented. The model includes 79 major anatomical structures of the neck segmented from radiological data. A finite element analysis of the cervical spine was performed. The results of finite element analysis of the C3-C5 segment under axial load were compared with in vitro data. The proposed model shows nonlinear deformation of the disc under static loading; the model predicted displacement values agree well with the experimental ones. The displacement of the С3-С5 central vertebra with an axial load of 800 N reaches a value of 0.65 mm. For the segment C2-T1, data on intradiscal pressure, stress plots and displacements during flexion were obtained. The maximum stress value of 10.036 MPa is observed in the C3-C4 disc.

CONCLUSION

Simulation results using the proposed methodology are in good agreement with experimental data. The generated biomechanical models allow describing dynamic phenomena in the cervical spine and obtaining a wide range of quantitative properties of anatomical objects, which are otherwise inaccessible to classical methods for studying dynamic and functional anatomy.

Influence of nucleotomy on the load sharing in the spinal facet joint under the loading scenarios of different human postures

One-in-five people suffer from chronic low back pain (LBP). The incidence of this disease has doubled since 1950s and affects not only the elderly, but also the young population. However, the mechanism of LBP is still unknown. A possible location where the LBP may develop is the facet joint and it has been revealed that the intervertebral disc (IVD) nucleotomy may be a trigger for LBP. The aim of the present study was to investigate the influence of IVD nucleotomy on the load sharing in the spinal facet joint under the loading scenarios of different postures. Finite element (FE) models of the intact and nucleotomised L4 - L5 spinal segments were generated from the clinical CT images. Seven human postures, including upright, 5° extension, 5° flexion, ± 6° lateral bending and ± 2° axial rotation, were simulated. The resultant forces in the fact joint were compared between the intact and the nucleotomised cases. It was revealed that the IVD nucleotomy significantly increased the forces in the facet joints under the loading scenarios of upright, 5° extension and 5° flexion. The IVD nucleotomy increased the force in the ipsilateral facet joint but decreased the force on the contralateral side under the loading scenarios of ± 2° axial rotation. However, the IVD nucleotomy made little influence on the resultant forces in both facet joints in the postures of ± 6° lateral bending. In conclusion, the IVD nucleotomy can cause an increase in the overall force in the facet joint, and thus may serve as a possible explanation for the LBP and a main contributing factor for the pain complaints.

Calibration and validation of a novel hybrid model of the lumbosacral spine in ArtiSynth-The passive structures

In computational biomechanics, two separate types of models have been used predominantly to enhance the understanding of the mechanisms of action of the lumbosacral spine (LSS): Finite element (FE) and musculoskeletal multibody (MB) models. To combine advantages of both models, hybrid FE-MB models are an increasingly used alternative. The aim of this paper is to develop, calibrate, and validate a novel passive hybrid FE-MB open-access simulation model of a ligamentous LSS using ArtiSynth. Based on anatomical data from the Male Visible Human Project, the LSS model is constructed from the L1-S1 rigid vertebrae interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, and facet joints. A mesh convergence study, sensitivity analyses, and systematic calibration were conducted with the hybrid functional spinal unit (FSU) L4/5. The predicted mechanical responses of the FSU L4/5, the lumbar spine (L1-L5), and the LSS were validated against literature data from in vivo and in vitro measurements and in silico models. Spinal mechanical responses considered when loaded with pure moments and combined loading modes were total and intervertebral range of motions, instantaneous axes and centers of rotation, facet joint contact forces, intradiscal pressures, disc bulges, and stiffnesses. Undesirable correlations with the FE mesh were minimized, the number of crisscrossed collagen fiber rings was reduced to five, and the individual influences of specific anatomical structures were adjusted to in vitro range of motions. Including intervertebral motion couplings for axial rotation and nonlinear stiffening under increasing axial compression, the predicted kinematic and structural mechanics responses were consistent with the comparative data. The results demonstrate that the hybrid simulation model is robust and efficient in reproducing valid mechanical responses to provide a starting point for upcoming optimizations and extensions, such as with active skeletal muscles.

Computational Challenges in Tissue Engineering for the Spine

This paper deals with a brief review of the recent developments in computational modelling applied to innovative treatments of spine diseases. Additionally, it provides a perspective on the research directions expected for the forthcoming years. The spine is composed of distinct and complex tissues that require specific modelling approaches. With the advent of additive manufacturing and increasing computational power, patient-specific treatments have moved from being a research trend to a reality in clinical practice, but there are many issues to be addressed before such approaches become universal. Here, it is identified that the major setback resides in validation of these computational techniques prior to approval by regulatory agencies. Nevertheless, there are very promising indicators in terms of optimised scaffold modelling for both disc arthroplasty and vertebroplasty, powered by a decisive contribution from imaging methods.

The Effect of Degeneration on Internal Strains and the Mechanism of Failure in Human Intervertebral Discs Analyzed Using Digital Volume Correlation (DVC) and Ultra-High Field MRI

The intervertebral disc (IVD) plays a main role in absorbing and transmitting loads within the spinal column. Degeneration alters the structural integrity of the IVDs and causes pain, especially in the lumbar region. The objective of this study was to investigate non-invasively the effect of degeneration on human 3D lumbar IVD strains (n = 8) and the mechanism of spinal failure (n = 10) under pure axial compression using digital volume correlation (DVC) and 9.4 Tesla magnetic resonance imaging (MRI). Degenerate IVDs had higher (p < 0.05) axial strains (58% higher), maximum 3D compressive strains (43% higher), and maximum 3D shear strains (41% higher), in comparison to the non-degenerate IVDs, particularly in the lateral and posterior annulus. In both degenerate and non-degenerate IVDs, peak tensile and shear strains were observed close to the endplates. Inward bulging of the inner annulus was observed in all degenerate IVDs causing an increase in the AF compressive, tensile, and shear strains at the site of inward bulge, which may predispose it to circumferential tears (delamination). The endplate is the spine's “weak link” in pure axial compression, and the mechanism of human vertebral fracture is associated with disc degeneration. In non-degenerate IVDs the locations of failure were close to the endplate centroid, whereas in degenerate IVDs they were in peripheral regions. These findings advance the state of knowledge on mechanical changes during degeneration of the IVD, which help reduce the risk of injury, optimize treatments, and improve spinal implant designs. Additionally, these new data can be used to validate computational models.

Fiber engagement accounts for geometry-dependent annulus fibrosus mechanics: A multiscale, Structure-Based Finite Element Study

A comprehensive understanding of biological tissue mechanics is crucial for designing engineered tissues that aim to recapitulate native tissue behavior. Tensile mechanics of many fiber-reinforced tissues have been shown to depend on specimen geometry, which makes it challenging to compare data between studies. In this study, a validated multiscale, structure-based finite element model was used to evaluate the effect of specimen geometry on multiscale annulus fibrosus tensile mechanics through a fiber engagement analysis. The relationships between specimen geometry and modulus, Poisson's ratio, tissue stress-strain distributions, and fiber reorientation behaviors were investigated at both tissue and sub-tissue levels. It was observed that annulus fibrosus tissue level tensile properties and stress transmission mechanisms were dependent on specimen geometry. The model also demonstrated that the contribution of fiber-matrix interactions to tissue mechanical response was specimen size- and orientation-dependent. The results of this study reinforce the benefits of structure-based finite element modeling in studies investigating multiscale tissue mechanics. This approach also provides guidelines for developing optimal combined computational-experimental study designs for investigating fiber-reinforced biological tissue mechanics. Additionally, findings from this study help explain the geometry dependence of annulus fibrosus tensile mechanics previously reported in the literature, providing a more fundamental and comprehensive understanding of tissue mechanical behavior. In conclusion, the methods presented here can be used in conjunction with experimental tissue level data to simultaneously investigate tissue and sub-tissue scale mechanics, which is important as the field of soft tissue biomechanics advances toward studies that focus on diminishing length scales.

Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand

Quantification of lumbar spine load transfer is important for understanding low back pain, especially among persons with a lower limb amputation. Computational modeling provides a helpful solution for obtaining estimates of in vivo loads. A multiscale model was constructed by combining musculoskeletal and finite element (FE) models of the lumbar spine to determine tissue loading during daily activities. Three-dimensional kinematic and ground reaction force data were collected from participants with ([Formula: see text]) and without ([Formula: see text]) a unilateral transtibial amputation (TTA) during 5 sit-to-stand trials. We estimated tissue-level load transfer from the multiscale model by controlling the FE model with intervertebral kinematics and muscle forces predicted by the musculoskeletal model. Annulus fibrosis stress, intradiscal pressure (IDP), and facet contact forces were calculated using the FE model. Differences in whole-body kinematics, muscle forces, and tissue-level loads were found between participant groups. Notably, participants with TTA had greater axial rotation toward their intact limb ([Formula: see text]), greater abdominal muscle activity ([Formula: see text]), and greater overall tissue loading throughout sit-to-stand ([Formula: see text]) compared to able-bodied participants. Both normalized (to upright standing) and absolute estimates of L4-L5 IDP were close to in vivo values reported in the literature. The multiscale model can be used to estimate the distribution of loads within different lumbar spine tissue structures and can be adapted for use with different activities, populations, and spinal geometries.

Combined Effects of Graded Foraminotomy and Annular Defect on Biomechanics after Percutaneous Endoscopic Lumbar Decompression: A Finite Element Study

Percutaneous endoscopic technology has been widely used in the treatment of lumbar disc stenosis and herniation. However, the quantitative influence of percutaneous endoscopic lumbar decompression on spinal biomechanics of the L5–S1 lumbosacral segment remains poorly understood. Hence, the objective of this study is to investigate the combined effects on the biomechanics of different grades of foraminotomy and annular defect for the L5–S1 segment. A 3D, nonlinear, detailed finite element model of L4–S1 was established and validated. Changes in biomechanical responses upon stimulation to the intact spine during different degrees of resection were analyzed. Measurements included intervertebral rotation, intradiscal pressure, and the strain of disc structure under flexion, extension, left/right lateral bending, and left/right axial rotation under pure bending moments and physiological loads. Compared with the intact model, under prefollower load, annular defect slightly decreased intervertebral rotation by −5.0% in extension and 2.2% in right axial rotation and significantly increased the mean strain of the exposed disc by 237.7% in all loading cases. For right axial rotation, unilateral total foraminotomy with an annular detect increased intervertebral rotation by 29.5% and intradiscal pressure by 57.6% under pure bending moment while the maximum corresponding values were 9.8% and 6.6% when the degree of foraminotomy was below 75%, respectively. These results indicate that percutaneous endoscopic lumbar foraminotomy highly maintains spinal stability, even if the effect of annular detect is taken into account, when the unilateral facet is not totally removed. Patients should avoid excessive extension and axial rotation after surgery on L5–S1. The postoperative open annular defect may substantially increase the risk of recurrent disc herniation.

Finite element models can reproduce the effect of nucleotomy on the multi-axial compliance of human intervertebral discs

Finite element (FE) models can unravel the link between intervertebral disc (IVD) degeneration and its mechanical behaviour. Nucleotomy may provide the data required for model verification. Three human IVDs were scanned with MRI and tested in multiple loading scenarios, prior and post nucleotomy. The resulting data was used to generate, calibrate, and verify the FE models. Nucleotomy increased the experimental range of motion by 26%, a result reproduced by the FE simulation within a 5% error. This work demonstrates the ability of FE models to reproduce the mechanical compliance of human IVDs prior and post nucleotomy.

Historical Review of Combined Experimental and Computational Approaches for Investigating Annulus Fibrosus Mechanics

Intervertebral disc research has sought to develop a deeper understanding of spine biomechanics, the complex relationship between disc health and back pain, and the mechanisms of spinal injury and repair. To do so, many researchers have focused on characterizing tissue-level properties of the disc, where the roles of tissue subcomponents can be more systematically investigated. Unfortunately, experimental challenges often limit the ability to measure important disc tissue- and subtissue-level behaviors, including fiber-matrix interactions, transient nutrient and electrolyte transport, and damage propagation. Numerous theoretical and numerical modeling frameworks have been introduced to explain, complement, guide, and optimize experimental research efforts. The synergy of experimental and computational work has significantly advanced the field, and these two aspects have continued to develop independently and jointly. Meanwhile, the relationship between experimental and computational work has become increasingly complex and interdependent. This has made it difficult to interpret and compare results between experimental and computational studies, as well as between solely computational studies. This paper seeks to explore issues of model translatability, robustness, and efficient study design, and to propose and motivate potential future directions for experimental, computational, and combined tissue-level investigations of the intervertebral disc.

Comparison of Biomechanical Performance of Five Different Treatment Approaches for Fixing Posterior Pelvic Ring Injury

Background

A large number of pelvic injuries are seriously unstable, with mortality rates reaching 19%. Approximately 60% of pelvic injuries are related to the posterior pelvic ring. However, the selection of a fixation method for a posterior pelvic ring injury remains a challenging problem for orthopedic surgeons. The aim of the present study is to investigate the biomechanical performance of five different fixation approaches for posterior pelvic ring injury and thus provide guidance on the choice of treatment approach in a clinical setting.

Methods

A finite element (FE) model, including the L3-L5 lumbar vertebrae, sacrum, and full pelvis, was created from CT images of a healthy adult. Tile B and Tile C types of pelvic fractures were created in the model. Five different fixation methods for fixing the posterior ring injury (PRI) were simulated: TA1 (conservative treatment), TA2 (S1 screw fixation), TA3 (S1 + S2 screw fixation), TA4 (plate fixation), and TA5 (modified triangular osteosynthesis). Based on the fixation status (fixed or nonfixed) of the anterior ring and the fixation method for PRI, 20 different FE models were created. An upright standing loading scenario was simulated, and the resultant displacements at the sacroiliac joint were compared between different models.

Results

When TA5 was applied, the resultant displacements at the sacroiliac joint were the smallest (1.5 mm, 1.6 mm, 1.6 mm, and 1.7 mm) for all the injury cases. The displacements induced by TA3 and TA2 were similar to those induced by TA5. TA4 led to larger displacements at the sacroiliac joint (2.3 mm, 2.4 mm, 4.8 mm, and 4.9 mm), and TA1 was the worst case (3.1 mm, 3.2 mm, 6.3 mm, and 6.5 mm).

Conclusions

The best internal fixation method for PRI is the triangular osteosynthesis approach (TA5), followed by S1 + S2 screw fixation (TA3), S1 screw fixation (TA2), and plate fixation (TA4).

Quantifying deformations and strains in human intervertebral discs using Digital Volume Correlation combined with MRI (DVC-MRI)

Physical disruptions to intervertebral discs (IVDs) can cause mechanical changes that lead to degeneration and to low back pain which affects 75% of us in our lifetimes. Quantifying the effects of these changes on internal IVD strains may lead to better preventative strategies and treatments. Digital Volume Correlation (DVC) is a non-invasive technique that divides volumetric images into subsets, and measures strains by tracking the internal patterns within them under load. Applying DVC to MRIs may allow non-invasive strain measurements. However, DVC-MRI for strain measurements in IVDs has not been used previously. The purpose of this study was to quantify the strain and deformation errors associated with DVC-MRI for measurements in human IVDs. Eight human lumbar IVDs were MRI scanned (9.4 T) for a 'zero-strain study' (multiple unloaded scans to quantify noise within the system), and a loaded study (2 mm axial compression). Three DVC methodologies: Fast-Fourier transform (FFT), direct correlation (DC), and a combination of both FFT and DC approaches were compared with subset sizes ranging from 8 to 88 voxels to establish the optimal DVC methodology and settings which were then used in the loaded study. FFT + DC was the optimal method and a subset size of 56 voxels (2520 µm) was found to be a good compromise between errors and spatial resolution. Displacement and strain errors did not exceed 28 µm and 3000 microstrain, respectively. These findings demonstrate that DVC-MRI can quantify internal strains within IVDs non-invasively and accurately. The method has unique potential for assessing IVD strains within patients.

Material properties of human lumbar intervertebral discs across strain rates

BACKGROUND CONTEXT

The use of finite element (FE) methods to study the biomechanics of the intervertebral disc (IVD) has increased over recent decades due to their ability to quantify internal stresses and strains throughout the tissue. Their accuracy is dependent upon realistic, strain-rate dependent material properties, which are challenging to acquire.

PURPOSE

The aim of this study was to use the inverse FE technique to characterize the material properties of human lumbar IVDs across strain rates.

STUDY DESIGN

A human cadaveric experimental study coupled with an inverse finite element study.

METHODS

To predict the structural response of the IVD accurately, the material response of the constituent structures was required. Therefore, compressive experiments were conducted on 16 lumbar IVDs (39±19 years) to obtain the structural response. An FE model of each of these experiments was developed and then run through an inverse FE algorithm to obtain subject-specific constituent material properties, such that the structural response was accurate.

RESULTS

Experimentally, a log-linear relationship between IVD stiffness and strain rate was observed. The material properties obtained through the subject-specific inverse FE optimization of the annulus fibrosus (AF) fiber and AF fiber ground matrix allowed a good match between the experimental and FE response. This resulted in a Young modulus of AF fibers (-MPa) to strain rate (ε˙, /s) relationship of YMAF=31.5ln(ε˙)+435.5, and the C₁₀ parameter of the Neo-Hookean material model of the AF ground matrix was found to be strain-rate independent with an average value of 0.68 MPa.

CONCLUSIONS

These material properties can be used to improve the accuracy, and therefore predictive ability of FE models of the spine that are used in a wide range of research areas and clinical applications.

CLINICAL SIGNIFICANCE

Finite element models can be used for many applications including investigating low back pain, spinal deformities, injury biomechanics, implant design, design of protective systems, and degenerative disc disease. The accurate material properties obtained in this study will improve the predictive ability, and therefore clinical significance of these models.

Multiscale composite model of fiber-reinforced tissues with direct representation of sub-tissue properties

In many fiber-reinforced tissues, collagen fibers are embedded within a glycosaminoglycan-rich extrafibrillar matrix. Knowledge of the structure-function relationship between the sub-tissue properties and bulk tissue mechanics is important for understanding tissue failure mechanics and developing biological repair strategies. Difficulties in directly measuring sub-tissue properties led to a growing interest in employing finite element modeling approaches. However, most models are homogeneous and are therefore not sufficient for investigating multiscale tissue mechanics, such as stress distributions between sub-tissue structures. To address this limitation, we developed a structure-based model informed by the native annulus fibrosus structure, where fibers and the matrix were described as distinct materials occupying separate volumes. A multiscale framework was applied such that the model was calibrated at the sub-tissue scale using single-lamellar uniaxial mechanical test data, while validated at the bulk scale by predicting tissue multiaxial mechanics for uniaxial tension, biaxial tension, and simple shear (13 cases). Structure-based model validation results were compared to experimental observations and homogeneous models. While homogeneous models only accurately predicted bulk tissue mechanics for one case, structure-based models accurately predicted bulk tissue mechanics for 12 of 13 cases, demonstrating accuracy and robustness. Additionally, six of eight structure-based model parameters were directly linked to tissue physical properties, further broadening its future applicability. In conclusion, the structure-based model provides a powerful multiscale modeling approach for simultaneously investigating the structure-function relationship at the sub-tissue and bulk tissue scale, which is important for studying multiscale tissue mechanics with degeneration, disease, or injury.

Synchrotron tomography of intervertebral disc deformation quantified by digital volume correlation reveals microstructural influence on strain patterns

The intervertebral disc (IVD) has a complex and multiscale extracellular matrix structure which provides unique mechanical properties to withstand physiological loading. Low back pain has been linked to degeneration of the disc but reparative treatments are not currently available. Characterising the disc's 3D microstructure and its response in a physiologically relevant loading environment is required to improve understanding of degeneration and to develop new reparative treatments. In this study, techniques for imaging the native IVD, measuring internal deformation and mapping volumetric strain were applied to an in situ compressed ex vivo rat lumbar spine segment. Synchrotron X-ray micro-tomography (synchrotron CT) was used to resolve IVD structures at microscale resolution. These image data enabled 3D quantification of collagen bundle orientation and measurement of local displacement in the annulus fibrosus between sequential scans using digital volume correlation (DVC). The volumetric strain mapped from synchrotron CT provided a detailed insight into the micromechanics of native IVD tissue. The DVC findings showed that there was no slipping at lamella boundaries, and local strain patterns were of a similar distribution to the previously reported elastic network with some heterogeneous areas and maximum strain direction aligned with bundle orientation, suggesting bundle stretching and sliding. This method has the potential to bridge the gap between measures of macro-mechanical properties and the local 3D micro-mechanical environment experienced by cells. This is the first evaluation of strain at the micro scale level in the intact IVD and provides a quantitative framework for future IVD degeneration mechanics studies and testing of tissue engineered IVD replacements. STATEMENT OF SIGNIFICANCE: Synchrotron in-line phase contrast X-ray tomography provided the first visualisation of native intact intervertebral disc microstructural deformation in 3D. For two annulus fibrosus volumes of interest, collagen bundle orientation was quantified and local displacement mapped as strain. Direct evidence of microstructural influence on strain patterns could be seen such as no slipping at lamellae boundaries and maximum strain direction aligned with collagen bundle orientation. Although disc elastic structures were not directly observed, the strain patterns had a similar distribution to the previously reported elastic network. This study presents technical advances and is a basis for future X-ray microscopy, structural quantification and digital volume correlation strain analysis of soft tissue.

Biomechanical effects of posterior pedicle fixation techniques on the adjacent segment for the treatment of thoracolumbar burst fractures: a biomechanical analysis

Posterior pedicle fixation technique is a common method for treating thoracolumbar burst fractures, but the effect of different fixation techniques on the postoperative spinal mechanical properties has not been clearly defined, especially on adjacent segments. A finite element model of T10-L2 with moderate T12 vertebra burst fracture was constructed to investigate biomechanical behavior of three posterior pedicle screw fixation techniques. Compared with traditional short-segment 4 pedicle screw fixation (TS-4) and intermediate long-segment 6 pedicle screw fixation (IL-6), mono-segment 4 pedicle screw fixation (MS-4) provides a safer surgical selection to prevent the secondary degeneration of adjacent segments in the long-term.

The Path to Deliver the Most Realistic Follower Load for a Lumbar Spine in Standing Posture: A Finite Element Study

A spine is proven to be subjected to a follower load which is a compressive load of physiologic magnitude acting on the whole spine. The path of the follower load approximates the tangent to the curve of the spine in in vivo neutral standing posture. However, the specific path location of the follower load is still unclear. The aim of this study is to find out the most realistic location of the follower load path (FLP) for a lumbar spine in standing. A three-dimensional (3D) nonlinear finite element model (FEM) of lumbosacral vertebrae (L1-S1) with consideration of the calibrated material properties was established and validated by comparing with the experimental data. We show that the shape of the lumbosacral spine is strongly affected by the location of FLP. An evident nonlinear relationship between the FLP location and the kinematic response of the L1-S1 lumbosacral spine exists. The FLP at about 4 and 3 mm posterior to the curve connecting the center of the vertebral bodies delivers the most realistic location in standing for healthy people and patients having low back pains (LPBs), respectively. Moreover, the “sweeping” method introduced in this study can be applicable to all individualized FEM to determine the location of FLP.

Validation of an In Vivo Medical Image-Based Young Human Lumbar Spine Finite Element Model

Mathematical models of the human spine can be used to investigate spinal biomechanics without the difficulties, limitations, and ethical concerns associated with physical experimentation. Validation of such models is necessary to ensure that the modeled system behavior accurately represents the physics of the actual system. The goal of this work was to validate a medical image-based nonlinear lumbosacral spine finite element model of a healthy 20-yr-old female subject under physiological moments. Range of motion (ROM), facet joint forces (FJF), and intradiscal pressure (IDP) were compared with experimental values and validated finite element models from the literature. The finite element model presented in this work was in good agreement with published experimental studies and finite element models under pure moments. For applied moments of 7.5 N·m, the ROM in flexion–extension, axial rotation, and lateral bending were 39 deg, 16 deg, and 28 deg, respectively. Excellent agreement was observed between the finite element model and experimental data for IDP under pure compressive loading. The predicted FJFs were lower than those of the experimental results and validated finite element models for extension and torsion, likely due to the nondegenerate properties chosen for the intervertebral disks and morphology of the young female spine. This work is the first to validate a computational lumbar spine model of a young female subject. This model will serve as a valuable tool for predicting orthopedic spinal injuries, studying the effect of intervertebral disk replacements using advanced biomaterials, and investigating soft tissue degeneration.

The Mechanical Role of the Radial Fiber Network Within the Annulus Fibrosus of the Lumbar Intervertebral Disc: A Finite Elements Study

The annulus fibrosus (AF) of the intervertebral disc (IVD) consists of a set of concentric layers composed of a primary circumferential collagen fibers arranged in an alternating oblique orientation. Moreover, there exists an additional secondary set of radial translamellar collagen fibers which connects the concentric layers, creating an interconnected fiber network. The aim of this study was to investigate the mechanical role of the radial fiber network. Toward that goal, a three-dimensional (3D) finite element model of the L3–L4 spinal segment was generated and calibrated to axial compression and pure moment loading. The AF model explicitly recognizes the two heterogeneous networks of fibers. The presence of radial fibers demonstrated a pronounced effect on the local disc responses under lateral bending, flexion, and extension modes. In these modes, the radial fibers were in a tensile state in the disc region that subjected to compression. In addition, the circumferential fibers, on the opposite side of the IVD, were also under tension. The local stress in the matrix was decreased in up to 9% in the radial fibers presence. This implies an active fiber network acting collectively to reduce the stresses and strains in the AF lamellae. Moreover, a reduction of 26.6% in the matrix sideways expansion was seen in the presence of the radial fibers near the neutral bending axis of the disc. The proposed biomechanical model provided a new insight into the mechanical role of the radial collagen fibers in the AF structure. This model can assist in the design of future IVD substitutes.

Stand-alone lumbar cage subsidence: A biomechanical sensitivity study of cage design and placement

BACKGROUND AND OBJECTIVE

Spinal degeneration and instability are commonly treated with interbody fusion cages either alone or supplemented with posterior instrumentation with the aim to immobilise the segment and restore intervertebral height. The purpose of this work is to establish a tool which may help to understand the effects of intervertebral cage design and placement on the biomechanical response of a patient-specific model to help reducing post-surgical complications such as subsidence and segment instability.

METHODS

A 3D lumbar functional spinal unit (FSU) finite element model was created and a parametric model of an interbody cage was designed and introduced in the FSU. A Drucker-Prager Cap plasticity formulation was used to predict plastic strains and bone failure in the vertebrae. The effect of varying cage size, cross-sectional area, apparent stiffness and positioning was evaluated under 500 N preload followed by 7.5 Nm multidirectional rotation and the results were compared with the intact model.

RESULTS

The most influential cage parameters on the FSU were size, curvature congruence with the endplates and cage placement. Segmental stiffness was higher when increasing the cross-sectional cage area in all loading directions and when the cage was anteriorly placed in all directions but extension. In general, the facet joint forces were reduced by increasing segmental stiffness. However, these forces were higher than in the intact model in most of the cases due to the displacement of the instantaneous centre of rotation. The highest plastic deformations took place at the caudal vertebra under flexion and increased for cages with greater stiffness. Thus, wider cages and a more anteriorly placement would increase the volume of failed bone and, therefore, the risk of subsidence.

CONCLUSIONS

Cage geometry plays a crucial role in the success of lumbar surgery. General considerations such as larger cages may be applied as a guideline, but parameters such as curvature or cage placement should be determined for each specific patient. This model provides a proof-of-concept of a tool for the preoperative evaluation of lumbar surgical outcomes.

Integrating MRI-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc

Intervertebral disc degeneration is a common disease that is often related to impaired mechanical function, herniations and chronic back pain. The degenerative process induces alterations of the disc's shape, composition and structure that can be visualized in vivo using magnetic resonance imaging (MRI). Numerical tools such as finite element analysis (FEA) have the potential to relate MRI-based information to the altered mechanical behavior of the disc. However, in terms of geometry, composition and fiber architecture, current FE models rely on observations made on healthy discs and might therefore not be well suited to study the degeneration process. To address the issue, we propose a new, more realistic FE methodology based on diffusion tensor imaging (DTI). For this study, a human disc joint was imaged in a high-field MR scanner with proton-density weighted (PD) and DTI sequences. The PD image was segmented and an anatomy-specific mesh was generated. Assuming accordance between local principal diffusion direction and local mean collagen fiber alignment, corresponding fiber angles were assigned to each element. Those element-wise fiber directions and PD intensities allowed the homogenized model to smoothly account for composition and fibrous structure of the disc. The disc's in vitro mechanical behavior was quantified under tension, compression, flexion, extension, lateral bending and rotation. The six resulting load-displacement curves could be replicated by the FE model, which supports our approach as a first proof of concept towards patient-specific disc modeling.

The Effect of Muscle Direction on the Predictions of Finite Element Model of Human Lumbar Spine

The normal physiological loads from muscles experienced by the spine are largely unknown due to a lack of data. The aim of this study is to investigate the effects of varying muscle directions on the outcomes predicted from finite element models of human lumbar spine. A nonlinear finite element model of L3–L5 was employed. The force of the erector spinae muscle, the force of the rectus abdominis muscle, follower loads, and upper body weight were applied. The model was fixed in a neural standing position and the direction of the force of the erector spinae muscle and rectus abdominis muscle was varied in three directions. The intradiscal pressure, reaction moments, and intervertebral rotations were calculated. The intradiscal pressure of L4-L5 was 0.56–0.57 MPa, which agrees with the in vivo pressure of 0.5 MPa from the literatures. The models with the erector spinae muscle loaded in anterior-oblique direction showed the smallest reaction moments (less than 0.6 Nm) and intervertebral rotations of L3-L4 and L4-L5 (less than 0.2 degrees). In comparison with loading in the vertical direction and posterior-oblique direction, the erector spinae muscle loaded in the anterior-oblique direction required lower external force or moment to keep the lumbar spine in the neutral position.

Visualising the 3D microstructure of stained and native intervertebral discs using X-ray microtomography

Intervertebral disc degeneration (IVDD) is linked to low back pain. Microstructural changes during degeneration have previously been imaged using 2D sectioning techniques and 3D methods which are limited to small specimens and prone to inducing artefacts from sample preparation. This study explores micro computed X-ray tomography (microCT) methods with the aim of resolving IVD 3D microstructure whilst minimising sample preparation artefacts. Low X-ray absorption contrast in non-mineralised tissue can be enhanced using staining and phase contrast techniques. A step-wise approach, including comparing three stains, was used to develop microCT for bovine tail IVD using laboratory and synchrotron sources. Staining successfully contrasted collagenous structures; however not all regions were stained and the procedure induced macroscopic structural changes. Phase contrast microCT of chemically fixed yet unstained samples resolved the nucleus pulposus, annulus fibrosus and constituent lamellae, and finer structures including collagen bundles and cross-bridges. Using the same imaging methods native tissue scans were of slightly lower contrast but free from sample processing artefacts. In the future these methods may be used to characterise structural remodelling in soft (non-calcified) tissues and to conduct in situ studies of native loaded tissues and constructs to characterise their 3D mechanical properties.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

Annulus fibrosus functional extrafibrillar and fibrous mechanical behaviour: experimental and computational characterisation

The development of current surgical treatments for intervertebral disc damage could benefit from virtual environment accounting for population variations. For such models to be reliable, a relevant description of the mechanical properties of the different tissues and their role in the functional mechanics of the disc is of major importance. The aims of this work were first to assess the physiological hoop strain in the annulus fibrosus in fresh conditions (n = 5) in order to extract a functional behaviour of the extrafibrillar matrix; then to reverse-engineer the annulus fibrosus fibrillar behaviour (n = 6). This was achieved by performing both direct and global controlled calibration of material parameters, accounting for the whole process of experimental design and in silico model methodology. Direct-controlled models are specimen-specific models representing controlled experimental conditions that can be replicated and directly comparing measurements. Validation was performed on another six specimens and a sensitivity study was performed. Hoop strains were measured as 17 ± 3% after 10 min relaxation and 21 ± 4% after 20-25 min relaxation, with no significant difference between the two measurements. The extrafibrillar matrix functional moduli were measured as 1.5 ± 0.7 MPa. Fibre-related material parameters showed large variability, with a variance above 0.28. Direct-controlled calibration and validation provides confidence that the model development methodology can capture the measurable variation within the population of tested specimens.

A novel finite element model of the ovine lumbar intervertebral disc with anisotropic hyperelastic material properties

The Ovine spine is an accepted model to investigate the biomechanical behaviour of the human lumbar one. Indeed, the use of animal models for in vitro studies is necessary to investigate the mechanical behaviour of biological tissue, but needs to be reduced for ethical and social reasons. The aim of this study was to create a finite element model of the lumbar intervertebral disc of the sheep that may help to refine the understanding of parallel in vitro experiments and that can be used to predict when mechanical failure occurs. Anisotropic hyperelastic material properties were assigned to the annulus fibrosus and factorial optimization analyses were performed to find out the optimal parameters of the ground substance and of the collagen fibers. For the ground substance of the annulus fibrosus the investigation was based on experimental data taken from the literature, while for the collagen fibers tensile tests on annulus specimens were conducted. Flexibility analysis in flexion-extension, lateral bending and axial rotation were conducted. Different material properties for the anterior, lateral and posterior regions of the annulus were found. The posterior part resulted the stiffest region in compression whereas the anterior one the stiffest region in tension. Since the flexibility outcomes were in a good agreement with the literature data, we considered this model suitable to be used in conjunction with in vitro and in vivo tests to investigate the mechanical behaviour of the ovine lumbar disc.

Effect of Graded Facetectomy on Lumbar Biomechanics

Facetectomy is an important intervention for spinal stenosis but may lead to spinal instability. Biomechanical knowledge for facetectomy can be beneficial when deciding whether fusion is necessary. Therefore, the aim of this study was to investigate the biomechanical effect of different grades of facetectomy. A three-dimensional nonlinear finite element model of L3–L5 was constructed. The mobility of the model and the intradiscal pressure (IDP) of L4-L5 for standing were inside the data from the literature. The effect of graded facetectomy on intervertebral rotation, IDP, facet joint forces, and maximum von Mises equivalent stresses in the annuli was analyzed under flexion, extension, left/right lateral bending, and left/right axial rotation. Compared with the intact model, under extension, unilateral facetectomy increased the range of intervertebral rotation (IVR) by 11.7% and IDP by 10.7%, while the bilateral facetectomy increased IVR by 40.7% and IDP by 23.6%. Under axial rotation, the unilateral facetectomy and the bilateral facetectomy increased the IVR by 101.3% and 354.3%, respectively, when turned to the right and by 1.1% and 265.3%, respectively, when turned to the left. The results conclude that, after unilateral and bilateral facetectomy, care must be taken when placing the spine into extension and axial rotation posture from the biomechanical point of view.

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.

The effects of muscle weakness on degenerative spondylolisthesis: A finite element study

BACKGROUND

Whether muscle weakness is a cause, or result, of degenerative spondylolisthesis is not currently well understood. Little biomechanical evidence is available to offer an explanation for the mechanism behind exercise therapy. Therefore, the aim of this study is to investigate the effects of back muscle weakness on degenerative spondylolisthesis and to tease out the biomechanical mechanism of exercise therapy.

METHODS

A nonlinear 3-D finite element model of L3-L5 was constructed. Forces representing global back muscles and global abdominal muscles, follower loads and an upper body weight were applied. The force of the global back muscles was reduced to 75%, 50% and 25% to simulate different degrees of back muscle weakness. An additional boundary condition which represented the loads from other muscles after exercise therapy was set up to keep the spine in a neutral standing position. Shear forces, intradiscal pressure, facet joint forces and von Mises equivalent stresses in the annuli were calculated.

FINDINGS

The intervertebral rotations of L3-L4 and L4-L5 were within the range of in vitro experimental data. The calculated intradiscal pressure of L4-L5 for standing was 0.57MPa, which is similar to previous in vivo data. With the back muscles were reduced to 75%, 50% and 25% force, the shear force moved increasingly in a ventral direction. Due to the additional stabilizing force and moment provided by boundary conditions, the shear force varied less than 15%.

INTERPRETATION

Reducing the force of global back muscles might lead to, or aggravate, degenerative spondylolisthesis with forward slipping from biomechanical point of view. Exercise therapy may improve the spinal biomechanical environment. However, the intrinsic correlation between back muscle weakness and degenerative spondylolisthesis needs more clinical in vivo study and biomechanical analysis.

Prediction of clinically relevant initiation and progression of tears within annulus fibrosus

Internal disc disruption and annular tears are some of the causes of back and leg pain. It is difficult to observe location of internal damage and its distribution and propagation in cadaveric experiments or via imaging in clinical scenarios. Finite element analysis is useful for understanding the effects of different loading conditions on the location of initiation and propagation of tears in the annulus. In this study, a hyperelastic anisotropic material model in conjunction with biaxial properties was used for modelling annulus fibrosus material under a variety of loading conditions. The loading conditions considered included compression, flexion, extension, and their combinations. Tsai-Wu criterion was used to evaluate the damage, considering strength anisotropy and asymmetry. Damage predictions based on this criterion are in better agreement with available experimental studies and clinical observations, as compared to other approaches. Therefore, the use of Tsai-Wu criterion is suggested as an appropriate mechanical parameter to quantify damage, its initiation locations, and its distribution in annulus fibrosus under different loading conditions. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:113-122, 2017.