Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus

Direct measurements of collagen fiber recruitment in the posterior pole of the eye

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial to understanding their functions in bearing loads and maintaining tissue integrity. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 μm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9º vs. 0.6º and 3.1º vs. 2.7º. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue. STATEMENT OF SIGNIFICANCE: Peripapillary sclera (PPS) and lamina cribrosa (LC) collagen recruitment behaviors are central to the nonlinear mechanical behavior of the posterior pole of the eye. How PPS and LC collagen fibers recruit under stretch is crucial to develop constitutive models of the tissues but remains unclear. We used image-based stretch testing to characterize PPS and LC collagen fiber bundle recruitment under local stretch. We found that fiber-level stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers at a low stretch, but at 10% bundle stretch the two curves crossed with 75% bundles recruited. We also found that PPS and LC fibers had different uncrimping rates and non-zero waviness's when recruited.

Type 2 diabetes impairs annulus fibrosus fiber deformation and rotation under disc compression in the University of California Davis type 2 diabetes mellitus (UCD-T2DM) rat model

Understanding the biomechanical behavior of the intervertebral disc is crucial for studying disease mechanisms and developing tissue engineering strategies for managing disc degeneration. We used synchrotron small-angle X-ray scattering to investigate how changes to collagen behavior contribute to alterations in the disc's ability to resist compression. Coccygeal motion segments from 6-month-old lean Sprague-Dawley rats ( n = 7 ) and diabetic obese University of California Davis type 2 diabetes mellitus (UCD-T2DM) rats ( n = 6 , diabetic for 68 ± 7 days) were compressed during simultaneous synchrotron scanning to measure collagen strain at the nanoscale (beamline 7.3.3 of the Advanced Light Source). After compression, the annulus fibrosus was assayed for nonenzymatic cross-links. In discs from lean rats, resistance to compression involved two main energy-dissipation mechanisms at the nanoscale: (1) rotation of the two groups of collagen fibrils forming the annulus fibrosus and (2) straightening (uncrimping) and stretching of the collagen fibrils. In discs from diabetic rats, both mechanisms were significantly impaired. Specifically, diabetes reduced fibril rotation by 31% and reduced collagen fibril strain by 30% (compared to lean discs). The stiffening of collagen fibrils in the discs from diabetic rats was consistent with a 31% higher concentration of nonenzymatic cross-links and with evidence of earlier onset plastic deformations such as fibril sliding and fibril-matrix delamination. These findings suggest that fibril reorientation, stretching, and straightening are key deformation mechanisms that facilitate whole-disc compression, and that type 2 diabetes impairs these efficient and low-energy elastic deformation mechanisms, thereby altering whole-disc behavior and inducing the earlier onset of plastic deformation.

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 direct fiber approach to model sclera collagen architecture and biomechanics

Sclera collagen fiber microstructure and mechanical behavior are central to eye physiology and pathology. They are also complex, and are therefore often studied using modeling. Most models of sclera, however, have been built within a conventional continuum framework. In this framework, collagen fibers are incorporated as statistical distributions of fiber characteristics such as the orientation of a family of fibers. The conventional continuum approach, while proven successful for describing the macroscale behavior of the sclera, does not account for the sclera fibers are long, interwoven and interact with one another. Hence, by not considering these potentially crucial characteristics, the conventional approach has only a limited ability to capture and describe sclera structure and mechanics at smaller, fiber-level, scales. Recent advances in the tools for characterizing sclera microarchitecture and mechanics bring to the forefront the need to develop more advanced modeling techniques that can incorporate and take advantage of the newly available highly detailed information. Our goal was to create a new computational modeling approach that can represent the sclera fibrous microstructure more accurately than with the conventional continuum approach, while still capturing its macroscale behavior. In this manuscript we introduce the new modeling approach, that we call direct fiber modeling, in which the collagen architecture is built explicitly by long, continuous, interwoven fibers. The fibers are embedded in a continuum matrix representing the non-fibrous tissue components. We demonstrate the approach by doing direct fiber modeling of a rectangular patch of posterior sclera. The model integrated fiber orientations obtained by polarized light microscopy from coronal and sagittal cryosections of pig and sheep. The fibers were modeled using a Mooney-Rivlin model, and the matrix using a Neo-Hookean model. The fiber parameters were determined by inversely matching experimental equi-biaxial tensile data from the literature. After reconstruction, the direct fiber model orientations agreed well with the microscopy data both in the coronal plane (adjusted R2 = 0.8234) and in the sagittal plane (adjusted R2 = 0.8495) of the sclera. With the estimated fiber properties (C10 = 5746.9 MPa; C01 = -5002.6 MPa, matrix shear modulus 200 kPa), the model's stress-strain curves simultaneously fit the experimental data in radial and circumferential directions (adjusted R2's 0.9971 and 0.9508, respectively). The estimated fiber elastic modulus at 2.16% strain was 5.45 GPa, in reasonable agreement with the literature. During stretch, the model exhibited stresses and strains at sub-fiber level, with interactions among individual fibers which are not accounted for by the conventional continuum methods. Our results demonstrate that direct fiber models can simultaneously describe the macroscale mechanics and microarchitecture of the sclera, and therefore that the approach can provide unique insight into tissue behavior questions inaccessible with continuum approaches.

Textile Design of an Intervertebral Disc Replacement Device from Silk Yarn

Low back pain is often due to degeneration of the intervertebral discs (IVD). It is one of the most common age- and work-related problems in today's society. Current treatments are not able to efficiently restore the full function of the IVD. Therefore, the aim of the present work was to reconstruct the two parts of the intervertebral disc-the annulus fibrosus (AF) and the nucleus pulposus (NP)-in such a way that the natural structural features were mimicked by a textile design. Silk was selected as the biomaterial for realization of a textile IVD because of its cytocompatibility, biodegradability, high strength, stiffness, and toughness, both in tension and compression. Therefore, an embroidered structure made of silk yarn was developed that reproduces the alternating fiber structure of +30° and -30° fiber orientation found in the AF and mimics its lamellar structure. The developed embroidered ribbons showed a tensile strength that corresponded to that of the natural AF. Fiber additive manufacturing with 1 mm silk staple fibers was used to replicate the fiber network of the NP and generate an open porous textile 3D structure that may serve as a reinforcement structure for the gel-like NP.

Biomechanical evaluation of a novel repair strategy for intervertebral disc herniation in an ovine lumbar spine model

Following herniation of the intervertebral disc, there is a need for advanced surgical strategies to protect the diseased tissue from further herniation and to minimize further degeneration. Accordingly, a novel tissue engineered implant for annulus fibrosus (AF) repair was fabricated via three-dimensional fiber deposition and evaluated in a large animal model. Specifically, lumbar spine kinetics were assessed for eight (n = 8) cadaveric ovine lumbar spines in three pure moment loading settings (flexion-extension, lateral bending, and axial rotation) and three clinical conditions (intact, with a defect in the AF, and with the defect treated using the AF repair implant). In ex vivo testing, seven of the fifteen evaluated biomechanical measures were significantly altered by the defect. In each of these cases, the treated spine more closely approximated the intact biomechanics and four of these cases were also significantly different to the defect. The same spinal kinetics were also assessed in a preliminary in vivo study of three (n = 3) ovine lumbar spines 12 weeks post-implantation. Similar to the ex vivo results, functional efficacy of the treatment was demonstrated as compared to the defect model at 12 weeks post-implantation. These promising results motivate a future large animal study cohort which will establish statistical power of these results further elucidate the observed outcomes, and provide a platform for clinical translation of this novel AF repair patch strategy. Ultimately, the developed approach to AF repair holds the potential to maintain the long-term biomechanical function of the spine and prevent symptomatic re-herniation.

A Novel Testing Method to Quantify Mechanical Properties of the Intact Annulus Fibrosus Ring From Rat-Tail Intervertebral Discs

The annulus fibrosus is the ring-like exterior of the intervertebral disc which is composed of concentrically organized layers of collagen fibre bundles. The mechanical properties of the annulus have been studied extensively; however, tests are typically performed on extracted fragments or multilayered samples of the annulus and not on the annulus as a whole. The purpose of this study was two-fold: 1) to develop a novel testing technique to measure the mechanical properties of the intact, isolated annulus; and 2) to perform a preliminary analysis of the rate-dependency of these mechanical properties. Twenty-nine whole annulus ring samples were dissected from 11 skeletally mature Sprague Dawley rat tails and underwent a tensile failure test at either 2%/s (n=16) or 20%/s (n=13). Force and displacement were sampled at 100Hz and were subsequently normalized to stress and strain. Various mechanical properties were derived from the stress-strain curves and statistically compared between the rates. All mechanical variables, with the exception of initial failure stress, were found to be unaffected by rate. Interestingly, initial failure stress was higher for samples tested at the slower rate compared to the higher rate which is atypical for viscoelastic tissues. Although in general rate did not appear to impact the annulus ring response to tensile loading, this novel, intact annular ring testing technique provides an alternative way to quantify mechanical properties of the annulus.

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.

Effect of overload on changes in mechanical and structural properties of the annulus fibrosus of the intervertebral disc

The research focussed on analysing structural and mechanical properties in the intervertebral disc (IVD), caused by long-term cyclic loading. Spinal motion segments were divided into two groups: the control (C), and the group in which it was analysed the impact of posterior column in the load-bearing system of the spine-specimens with intact posterior column (IPC) and without posterior column (WPC). To evaluate the structural and mechanical changes, the specimens were tested with simulation of 100,000 compression-flexion load cycles after which it was performed macroscopic analysis. Mechanical properties of the annulus fibrosis (AF) from the anterior and posterior regions of the IVD were tested at the uniaxial tension test. The stiffness coefficient values were statistically 32% higher in the WPC group (110 N/mm) than in the IPC (79 N/mm). The dynamics of increase in this parameter does not correspond with the course of decrease in height loss. WPC segments revealed clear structural changes that mainly involve the posterior regions of the IVD (bulging and delamination with the effect of separation of collagen fibre bundles). Pathological changes also caused decreases in the value of stress in the AF. The greatest changes in the stress value about group C (7.43 ± 4.49 MPa) were observed in the front part of the fibrous ring, where this value was for IPC 4.49 ± 4.78 MPa and WPC 2.56 ± 1.01 MPa. The research indicates that the applied load model allows simulating damage that occurs in pathological IVD. And the posterior column's presence affects this change's dynamics, structural and mechanical properties of AF.

Development of a flexible instrumented lumbar spine finite element model and comparison with in-vitro experiments

Surgical corrections of degenerative lumbar scoliosis and sagittal malalignment are associated with significant complications, such as rod fractures and pseudarthrosis, particularly in the lumbosacral junction. Finite element studies can provide relevant insights to improve performance of spinal implants. The aim of the present study was to present the development of non-instrumented and instrumented Finite Element Models (FEMs) of the lumbopelvic spine and to compare numerical results with experimental data available in the literature. The lumbo-pelvic spine FEM was based on a CT-scan from an asymptomatic volunteer representing the 50th percentile male. In a first step a calibration of mechanical properties was performed in order to obtain a quantitative agreement between numerical results and experimental data for defect stages of spinal segments. Then, FEM results were compared in terms of range of motion and strains in rods to in-vitro experimental data from the literature for flexible non-instrumented and instrumented lumbar spines. Numerical results from the calibration process were consistent with experimental data, especially in flexion. A positive agreement was obtained between FEM and experimental results for the lumbar and sacroiliac segments. Instrumented FEMs predicted the same trends as experimental in-vitro studies. The instrumentation configuration consisting of double rods and an interbody cage at L5-S1 maximally reduced range of motion and strains in main rods and thus had the lowest risk of pseudarthrosis and rod fracture. The developed FEMs were found to be consistent with published experimental results; therefore they can be used for further post-operative complication investigations.

Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter-lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

Electrospun biodegradable poly(ε-caprolactone) membranes for annulus fibrosus repair: Long-term material stability and mechanical competence

BACKGROUND

Electrospun (ES) poly(ɛ-caprolactone) (PCL) is widely used to provide critical mechanical support in tissue engineering and regenerative medicine applications. Therefore, there is a clear need for understanding the change in the mechanical response of the membranes as the material degrades in physiological conditions.

STUDY DESIGN

ES membranes with fiber diameters from 1.6 to 6.7 μm were exposed to in vitro conditions at 37°C in Dulbecco's modified Eagle's medium (DMEM) or dry for up to 6 months.

METHODS

During this period, the mechanical properties were assessed using cyclic mechanical loading, and material properties such as crystallinity and ester bond degradation were measured.

RESULTS

No significant difference was found for any parameters between samples kept dry and in DMEM. The increase in crystallinity was linear with time, while the ester bond degradation showed an inverse logarithmic correlation with time. All samples showed an increase in modulus with exposure time for the first loading cycle. Modulus changes for the consecutive loading cycles showed a nonlinear relationship to the exposure time that depended on membrane type and maximum strain. In addition, the recovered elastic range showed an expected increase with the maximum strain reached. The mechanical response of ES membranes was compared to experimental tensile properties of the human annulus fibrosus tissue and an in silico model of the intervertebral disk. The modulus of the tested membranes was at the lower range of the values found in literature, while the elastically recoverable strain after preconditioning for all membrane types lies within the desired strain range for this application.

CONCLUSION

The long-term assessment under application-specific conditions allowed to establish the mechanical competence of the electrospun PCL membranes. It can be concluded that with the use of appropriate fixation, the membranes can be used to create a seal on the damaged AF.

The Role of Biological Fusion and Anterior Column Support in a Long Lumbopelvic Spinal Fixation and Its Effect on the S1 Screw-An In Silico Biomechanics Analysis

STUDY DESIGN

Finite element analysis.

OBJECTIVE

The aim of this study was to determine the role of biological fusion and anterior column support in a long lumbopelvic spinal fixation.

SUMMARY OF BACKGROUND DATA

Retrospective studies have shown that adding anterior column support is not sensitive to construct failure, highlighting that posterior fusion quality may be a more important factor.

METHODS

Finite element models were created to match the average spinal-pelvic parameters of two patient cohorts reported in the literature: major failure and nonfailure. A moment load was applied at the T10 superior endplate to simulate gravimetric loading in a standing position. Effects of three factors on the biomechanical behavior of a fused spine were evaluated: sagittal alignment; posterior fusion versus no fusion; and anterior support at L4-S1 versus no anterior support.

RESULTS

Sagittal balance of the major failure group was positively correlated with 15% higher translation, 14% higher rotation, and 16% higher stress than in the nonfailure group. Simulated posterior fusion-only decreased motion by 32% and 29%, and alleviated rod stress by 15% and 5% and S1 screw stress by 26% and 35%, respectively, in major failure and non-failure groups. The addition of anterior fusion without posterior fusion did not help with rod stress alleviation but dramatically decreased S1 screw stress (by 57% and 41%), respectively. With both posterior fusion and anterior support, screw stress at the S1 was decreased by additional 30% and 6%, respectively.

CONCLUSION

The spinopelvic parameters of the major failure group produced increased gravity load, resulting in increased stresses in comparison to the nonfailure group. Simulated posterior "solid" fusion in the lumbar region helped reduce stresses in both major failure and nonfailure patients. Anterior column support was an important factor in reducing S1 screw stress, with or without posterior fusion, and should be considered for patients with poor alignment.Level of Evidence: N/A.

Comprehensive Evaluation of Accessory Rod Position, Rod Material and Diameter, Use of Cross-connectors, and Anterior Column Support in a Pedicle Subtraction Osteotomy Model: Part I: Effects on Apical Rod Strain: An In Vitro and In Silico Biomechanical Study

STUDY DESIGN

In silico finite element study.

OBJECTIVE

The aim of this study was to evaluate the effect of six construct factors on apical rod strain in an in silico pedicle subtraction osteotomy (PSO) model: traditional inline and alternative Ames-Deviren-Gupta (ADG) multi-rod techniques, number of accessory rods (three- vs. four-rod), rod material (cobalt-chrome [CoCr] or stainless steel [SS] vs. titanium [Ti]), rod diameter (5.5 vs. 6.35 mm), and use of cross-connectors (CC), or anterior column support (ACS).

SUMMARY OF BACKGROUND DATA

Rod fracture following lumbar PSO is frequently reported. Clinicians may modulate reconstructs with multiple rods, rod position, rod material and diameter, and with CC or ACS to reduce mechanical demand or rod contouring. A comprehensive evaluation of these features on rod strain is lacking.

METHODS

A finite element model (T12-S1) with intervertebral discs and ligaments was created and validated with cadaveric motion data. Apical rod strain of primary and accessory rods was collected for 96 constructs across all six construct factors, and normalized to the Ti two-rod control.

RESULTS

Regardless of construct features, CoCr and SS material reduced strain across all rods by 49.1% and 38.1%, respectively; increasing rod diameter from 5.5 mm to 6.35 mm rods reduced strain by 32.0%. Use of CC or lumbosacral ACS minimally affected apical rod strain (<2% difference from constructs without CC or ACS). Compared to the ADG technique, traditional inline reconstruction reduced primary rod strain by 32.2%; however, ADG primary rod required 14.2° less rod contouring. The inline technique produced asymmetrical loading between left and right rods, only when three rods were used.

CONCLUSION

The number of rods and position of accessory rods affected strain distribution on posterior fixation. Increasing rod diameter and using CoCr rods was most effective in reducing rod strain. Neither CC nor lumbosacral ACS affected apical rod strain.

LEVEL OF EVIDENCE

N/A.

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.

Interlamellar matrix governs human annulus fibrosus multiaxial behavior

Establishing accurate structure–property relationships for intervertebral disc annulus fibrosus tissue is a fundamental task for a reliable computer simulation of the human spine but needs excessive theoretical-numerical-experimental works. The difficulty emanates from multiaxiality and anisotropy of the tissue response along with regional dependency of a complex hierarchic structure interacting with the surrounding environment. We present a new and simple hybrid microstructure-based experimental/modeling strategy allowing adaptation of animal disc model to human one. The trans-species strategy requires solely the basic knowledge of the uniaxial circumferential response of two different animal disc regions to predict the multiaxial response of any human disc region. This work demonstrates for the first time the determining role of the interlamellar matrix connecting the fibers-reinforced lamellae in the disc multiaxial response. Our approach shows encouraging multiaxial predictive capabilities making it a promising tool for human spine long-term prediction.

The role of sagittal alignment in predicting major failure of lumbopelvic instrumentation: a biomechanical validation of lumbopelvic failure classification

STUDY DESIGN

Finite element analysis.

OBJECTIVES

To biomechanically validate the classification of lumbopelvic fixation failure using an in silico model. Even though major failure of lumbopelvic constructs has occurred more often in patients with suboptimal lumbar lordosis and sagittal balance, there has been no biomechanical validation of this classification.

METHODS

Finite element models (T10-pelvis) were created to match the average spinal-pelvic parameters of two cohorts of patients reported in Cho et al. (J Neurosurg Spine 19:445-453, 2013): major failure group (defined as rod breakage between L4 and S1, failure of S1 screws and prominence of iliac screws requiring removal) and non-failure group. A moment was applied at the T10 superior endplate to simulate gravimetric loading in a standing position.

RESULTS

Due to differences in the alignment of spinopelvic parameters between normal and failed spines in the presence of a fixed gravity line, the major failure cohort in this study observed a 20% higher load and 18% greater instability. As a result, the rod and screw stress in the major failure cohort increased by 20% and 42%, respectively, in comparison to the non-failure cohort.

CONCLUSIONS

The greater mechanical demand on the posterior rods in the lower lumbar spine in the major failure cohort further emphasizes the importance of proper sagittal alignment. This finite element analysis validates the classification of lumbopelvic fixation failure.

Osmo-inelastic response of the intervertebral disc annulus fibrosus tissue

The aim of this article is to provide some insights on the osmo-inelastic response under stretching of annulus fibrosus of the intervertebral disc. Circumferentially oriented specimens of square cross section, extracted from different regions of bovine cervical discs (ventral-lateral and dorsal-lateral), are tested under different strain-rates and saline concentrations within normal range of strains. An accurate optical strain measuring technique, based upon digital image correlation, is used in order to determine the full-field displacements in the lamellae and fibers planes of the layered soft tissue. Annulus stress-stretch relationships are measured along with full-field transversal strains in the two planes. The mechanical response is found hysteretic, rate-dependent and osmolarity-dependent with a Poisson's ratio higher than 0.5 in the fibers plane and negative (auxeticity) in the lamellae plane. While the stiffness presents a regional-dependency due to variations in collagen fibers content/orientation, the strain-rate sensitivity of the response is found independent on the region. A significant osmotic effect is found on both the auxetic response in the lamellae plane and the stiffness rate-sensitivity. These local experimental observations will result in more accurate chemo-mechanical modeling of the disc annulus and a clearer multi-scale understanding of the disc intervertebral function.

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.

Interlamellar-induced time-dependent response of intervertebral disc annulus: A microstructure-based chemo-viscoelastic model

The annulus fibrosus of the intervertebral disc exhibits an unusual transversal behavior for which a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency has not yet been developed, and it is hence the aim of the present contribution. A physically-based model is proposed by introducing a free energy function that takes into account the actual disc annulus structure in relation with the surrounding biochemical environment. The response is assumed to be dominated by the viscoelastic contribution of the extracellular matrix, the elastic contribution of the oriented collagen fibers and the osmo-induced volumetric contribution of the internal fluid content variation. The regional dependence of the disc annulus response due to variation in fibers content/orientation allows a micromechanical treatment of the soft tissue. A finite element model of the annulus specimen is designed while taking into consideration the 'interlamellar' ground substance zone between lamellae of the layered soft tissue. The kinetics is designed using full-field strain measurements performed on specimens extracted from two disc annulus regions and tested under different osmotic conditions. The time-dependency of the tissue response is reported on stress-free volumetric changes, on hysteretic stress and transversal strains during quasi-static stretching at different strain-rates and on their temporal changes during an interrupted stretching. Considering the effective contributions of the internal fluid transfer and the extracellular matrix viscosity, the microstructure-based chemo-mechanical model is found able to successfully reproduce the significant features of the macro-response and the unusual transversal behavior including the strong regional dependency from inner to outer parts of the disc: Poisson's ratio lesser than 0 (auxetic) in lamellae plane, higher than 0.5 in fibers plane, and their temporal changes towards usual values (between 0 and 0.5) at chemo-mechanical equilibrium. The underlying time-dependent mechanisms occurring in the tissue are analyzed via the local numerical fields and important insights about the effective role of the interlamellar zone are revealed for the different disc localizations. STATEMENT OF SIGNIFICANCE: The structural complexity of the annulus fibrosus has only been appreciated through recent experimental contributions and a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency of the unusual transversal behavior has not yet been developed. Here, a microstructure-based chemo-viscoelastic model is developed to highlight the interlamellar-induced time-dependent response by means of a two-scale strategy. The model provides important insights about the origin of the time-dependent phenomena in disc annulus along with regional dependency, essential for understanding disc functionality.

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.

Mechanics of pulmonary airways: Linking structure to function through constitutive modeling, biochemistry, and histology

Breathing involves fluid-solid interactions in the lung; however, the lack of experimental data inhibits combining the mechanics of air flow to airway deformation, challenging the understanding of how biomaterial constituents contribute to tissue response. As such, lung mechanics research is increasingly focused on exploring the relationship between structure and function. To address these needs, we characterize mechanical properties of porcine airways using uniaxial tensile experiments, accounting for bronchial orientation- and location- dependency. Structurally-reinforced constitutive models are developed to incorporate the role of collagen and elastin fibers embedded within the extrafibrillar matrix. The strain-energy function combines a matrix description (evaluating six models: compressible NeoHookean, unconstrained Ogden, uncoupled Mooney-Rivlin, incompressible Ogden, incompressible Demiray and incompressible NeoHookean), superimposed with non-linear fibers (evaluating two models: exponential and polynomial). The best constitutive formulation representative of all bronchial regions is determined based on curve-fit results to experimental data, accounting for uniqueness and sensitivity. Glycosaminoglycan and collagen composition, alongside tissue architecture, indicate fiber form to be primarily responsible for observed airway anisotropy and heterogeneous mechanical behavior. To the authors' best knowledge, this study is the first to formulate a structurally-motivated constitutive model, augmented with biochemical analysis and microstructural observations, to investigate the mechanical function of proximal and distal bronchi. Our systematic pulmonary tissue characterization provides a necessary foundation for understanding pulmonary mechanics; furthermore, these results enable clinical translation through simulations of airway obstruction in disease, fluid-structure interaction insights during breathing, and potentially, predictive capabilities for medical interventions. STATEMENT OF SIGNIFICANCE: The advancement of pulmonary research relies on investigating the biomechanical response of the bronchial tree. Experiments demonstrating the non-linear, heterogeneous, and anisotropic material behavior of porcine airways are used to develop a structural constitutive model representative of proximal and distal bronchial behavior. Calibrated material parameters exhibit regional variation in biomaterial properties, initially hypothesized to originate from tissue constituents. Further exploration through biochemical and histological analysis indicates mechanical function is primarily governed by microstructural form. The results of this study can be directly used in finite element and fluid-structure interaction models to enable physiologically relevant and more accurate computational simulations aimed to help diagnose and monitor pulmonary disease.

A Validated, Subject-Specific Finite Element Model for Predictions of Rotator Cuff Tear Propagation

Rotator cuff tears are a significant clinical problem previously investigated by unvalidated computational models that either use simplified geometry or isotropic elastic material properties to represent the tendon. The objective of this study was to develop an experimentally validated, finite element model of supraspinatus tendon using specimen-specific geometry and inhomogeneous material properties to predict strains in intact supraspinatus tendon. Three-dimensional tendon surface strains were determined at 60°, 70°, and 90° of glenohumeral abduction for articular and bursal surfaces of supraspinatus tendon during cyclic loading to serve as validation data. A finite element model was developed using the tendon geometry and inhomogeneous material properties to predict surface strains for loading conditions mimicking experimental loading conditions. Experimental strains were directly compared with computational model predictions to validate the model. Overall, the model successfully predicted magnitudes of strains that were within the experimental repeatability of 3% strain of experimental measures on both surfaces of the tendon. Model predictions and experiments showed the largest strains to be located on the articular surface (~8% strain) between the middle and anterior edge of the tendon. Importantly, the reference configuration chosen to calculate strains had a significant effect on strain calculations, and therefore must be defined with an innovative optimization algorithm. This study establishes a rigorously validated, specimen-specific computational model using novel surface strain measurements for use in investigating the function of the supraspinatus tendon and to ultimately predict the propagation of supraspinatus tendon tears based on the tendon's mechanical environment.

Biomechanical properties of novel transpedicular transdiscal screw fixation with interbody arthrodesis technique in lumbar spine: A finite element study

Purpose

The purpose of this study was to investigate finite element biomechanical properties of the novel transpedicular transdiscal (TPTD) screw fixation with interbody arthrodesis technique in lumbar spine.

Methods

An L4–L5 finite element model was established and validated. Then, two fixation models, TPTD screw system and bilateral pedicle screw system (BPSS), were established on the validated L4–L5 finite element model. The inferior surface of the L5 vertebra was set immobilised, and moment of 7.5 Nm was applied on the L4 vertebra to test the range of motion (ROM) and stress at flexion, extension, lateral bending and axial rotation.

Results

The intact model was validated for prediction accuracy by comparing two previously published studies. Both of TPTD and BPSS fixation models displayed decreased motion at L4–L5. The ROMs of six moments of flexion, extension, left lateral bending, right lateral bending, left axial rotation and right axial rotation in TPTD model were 1.92, 2.12, 1.10, 1.11, 0.90 and 0.87°, respectively; in BPSS model, they were 1.48, 0.42, 0.35, 0.38, 0.74 and 0.75°, respectively. The screws' peak stress of above six moments in TPTD model was 182.58, 272.75, 133.01, 137.36, 155.48 and 150.50 MPa, respectively; and in BPSS model, it was 103.16, 129.74, 120.28, 134.62, 180.84 and 169.76 MPa, respectively.

Conclusion

Both BPSS and TPTD can provide stable biomechanical properties for lumbar spine. The decreased ROM of flexion, extension and lateral bending was slightly more in BPSS model than in TPTD model, but TPTD model had similar ROM of axial rotation with BPSS model. The screws' peak stress of TPTD screw focused on the L4–L5 intervertebral space region, and more caution should be put at this site for the fatigue breakage.

The translational potential of this article

Our finite element study provides the biomechanical properties of novel TPTD screw fixation, and promotes this novel transpedicular transdiscal screw fixation with interbody arthrodesis technique be used clinically.

A two-step procedure for coupling development and usage of a pair of human neck models

Both finite element models and multi-body models of human head-neck complex had been widely used in neck injuries analysis, as the former could be used to generate detailed stress strain information and the later could generate dynamic responses with high efficiency. Sometimes, detailed stress and strain information were hoped to be obtained more efficiently, but current methods were not effective enough when they were used to analyze responses of human head neck complex to long duration undulate accelerations. In this paper, a two-step procedure for 'parallel' development and 'sequential' usage of a pair of human head neck models was discussed. The pair of models contained a finite element model and a multi-body model, which were developed based on the coupling 'parallel' procedure using the same bio-realistic geometry. After being validated using available data, the pair of human neck models were applied to analyze biomechanical responses of pilot's neck during arrested landing operation according to the 'sequential' procedure, because typical sustained undulate accelerations usually appeared during such processes. The results, including both kinematic and detailed biomechanical responses of human head-neck complex, were obtained with preferable efficiency. This research provided an effective way for biomechanical analysis of human head neck responses to sustained undulate accelerations.

Swelling of fiber-reinforced soft tissues is affected by fiber orientation, fiber stiffness, and lamella structure

Native and engineered fiber-reinforced tissues are composites comprised of stiff collagen fibers embedded within an extrafibrillar matrix that is capable of swelling by absorbing water molecules. Tissue swelling is important for understanding stress distributions between collagen fibers and extrafibrillar matrix, as well as for understanding mechanisms of tissue failure. The swelling behavior of fiber-reinforced tissues in the musculoskeletal system has been largely attributed to the glycosaminoglycan content. Recent work demonstrated anisotropy in the swelling response of the annulus fibrosus in the intervertebral disc. It is well known that collagen fiber orientation affects elastic behavior, but the effect of collagen fiber network on tissue swelling behavior is not well understood. In this study, we developed three series of models to evaluate the effect of collagen fiber orientation, fiber network architecture (i.e., single or multi-fiber families within a layer), and fiber stiffness on bulk tissue swelling, which was simulated by describing the extrafibrillar matrix as a triphasic material, as proposed by Lai et al. Model results were within one standard deviation of reported mean values for changes in tissue volume, width, and thickness under free swelling conditions. The predicted swelling response of single-fiber family structures was highly dependent on fiber orientation and the number of lamellae in the bulk tissue. Moreover, matrix swelling resulted in tissue to twist, which reduced fiber deformations, demonstrating a balance between fiber deformation and matrix swelling. Large changes in fiber stiffness (20 × increase) had a relatively small effect on tissue swelling (~ 2% decrease in swelling). In conclusion, fiber angle, fiber architecture (defined as single- versus multiple fiber families in a layer), and the number of layers in a single fiber family structure directly affected tissue swelling behavior, including fiber stretch, fiber reorientation, and tissue deformation. These findings support the need to develop computational models that closely mimic the native architecture in order to understand mechanisms of stress distributions and tissue failure.

On the importance of retaining stresses and strains in repositioning computational biomechanical models of the cervical spine

Human body models are created in a specific posture and often repositioned and analyzed without retaining stresses that result from repositioning. For example, repositioning a human neck model within the physiological range of motion to a head-turned posture prior to an impact results in initial stresses within the tissues distracted from their neutral position. The aim of this study was to investigate the effect of repositioning on the subsequent kinetics, kinematics, and failure modes, of a lower cervical spine motion segment, to support future research at the full neck level. Repositioning was investigated for 3 modes (tension, flexion, and extension) and 3 load cases. The model was repositioned and loaded to failure in one continuous load history (case 1), or repositioned then restarted with retained stresses and loaded to failure (case 2). In case 3, the model was repositioned and then restarted in a stress-free state, representing current repositioning methods. Not retaining the repositioning stresses and strains resulted in different kinetics, kinematics, or failure modes, depending on the mode of loading. For the motion segment model, the differences were associated with the intervertebral disc fiber reorientation and load distribution, because the disc underwent the largest deformation during repositioning. This study demonstrated that repositioning led to altered response and tissue failure, which is critical for computational models intended to predict injury at the tissue level. It is recommended that stresses and strains be included and retained for subsequent analysis when repositioning a human computational neck model.

Modeling the effect of collagen fibril alignment on ligament mechanical behavior

Ligament mechanical behavior is primarily regulated by fibrous networks of type I collagen. Although these fibrous networks are typically highly aligned, healthy and injured ligament can also exhibit disorganized collagen architecture. The objective of this study was to determine whether variations in the collagen fibril network between neighboring ligaments can predict observed differences in mechanical behavior. Ligament specimens from two regions of bovine fetlock joints, which either exhibited highly aligned or disorganized collagen fibril networks, were mechanically tested in uniaxial tension. Confocal microscopy and FiberFit software were used to quantify the collagen fibril dispersion and mean fibril orientation in the mechanically tested specimens. These two structural parameters served as inputs into an established hyperelastic constitutive model that accounts for a continuous distribution of planar fibril orientations. The ability of the model to predict differences in the mechanical behavior between neighboring ligaments was tested by (1) curve fitting the model parameters to the stress response of the ligament with highly aligned fibrils and then (2) using this model to predict the stress response of the ligament with disorganized fibrils by only changing the parameter values for fibril dispersion and mean fibril orientation. This study found that when using parameter values for fibril dispersion and mean fibril orientation based on confocal imaging data, the model strongly predicted the average stress response of ligaments with disorganized fibrils ([Formula: see text]); however, the model only successfully predicted the individual stress response of ligaments with disorganized fibrils in half the specimens tested. Model predictions became worse when parameters for fibril dispersion and mean fibril orientation were not based on confocal imaging data. These findings emphasize the importance of collagen fibril alignment in ligament mechanics and help advance a mechanistic understanding of fibrillar networks in healthy and injured ligament.

An investigation of dimensional scaling using cervical spine motion segment finite element models

The paucity of experimental data for validating computational models of different statures underscores the need for appropriate scaling methods so that models can be verified and validated using experimental data. Scaling was investigated using 50th percentile male (M50) and 5th percentile female (F05) cervical spine motion segment (C4-C5) finite element models subject to tension, flexion, and extension loading. Two approaches were undertaken: geometric scaling of the models to investigate size effects (volumetric scaling) and scaling of the force-displacement or moment-angle model results (data scaling). Three sets of scale factors were considered: global (body mass), regional (neck dimensions), and local (segment tissue dimensions). Volumetric scaling of the segment models from M50 to F05, and vice versa, produced correlations that were good or excellent in both tension and flexion (0.825-0.991); however, less agreement was found in extension (0.550-0.569). The reduced correlation in extension was attributed to variations in shape between the models leading to nonlinear effects such as different time to contact for the facet joints and posterior processes. Data scaling of the responses between the M50 and F05 models produced similar trends to volumetric scaling, with marginally greater correlations. Overall, the local tissue level and neck region level scale factors produced better correlations than the traditional global scaling. The scaling methods work well for a given subject, but are limited in applicability between subjects with different morphology, where nonlinear effects may dominate the response.

Prognostic Value of Lordosis Decrease in Radiographic Adjacent Segment Pathology After Anterior Cervical Corpectomy and Fusion

While cervical lordosis alteration is not uncommon after anterior cervical arthrodesis, its influence on radiological adjacent segment pathology (RASP) is still unclear. Biomechanical changes induced by arthrodesis may contribute to ASP onset. To investigate the correlation between cervical lordosis decrease and RASP onset after anterior cervical corpectomy and fusion (ACCF) and to determine its biomechanical effect on adjacent segments after surgery, 80 CSM patients treated with ACCF were retrospectively studied, and a baseline finite element model of the cervical spine as well as post-operation models with normal and decreased lordosis were established and validated. We found that post-operative lordosis decrease was prognostic in predicting RASP onset, with the hazard ratio of 0.45. In the FE models, ROM at the adjacent segment increased after surgery, and the increase was greater in the model with decreased lordosis. Thus, post-operative cervical lordosis change significantly correlated with RASP occurrence, and it may be of prognostic value. The biomechanical changes induced by lordosis change at the adjacent segments after corpectomy may be one of the mechanisms for this phenomenon. Restoring a well lordotic cervical spine after corpectomy may reduce RASP occurrence and be beneficial to long-term surgical outcomes.

A Novel Method for Repeatable Failure Testing of Annulus Fibrosus

Tears in the annulus fibrosus (AF) of the intervertebral disk can result in disk herniation and progressive degeneration. Understanding AF failure mechanics is important as research moves toward developing biological repair strategies for herniated disks. Unfortunately, failure mechanics of fiber-reinforced tissues, particularly tissues with fibers oriented off-axis from the applied load, is not well understood, partly due to the high variability in reported mechanical properties and a lack of standard techniques ensuring repeatable failure behavior. Therefore, the objective of this study was to investigate the effectiveness of midlength (ML) notch geometries in producing repeatable and consistent tissue failure within the gauge region of AF mechanical test specimens. Finite element models (FEMs) representing several notch geometries were created to predict the location of bulk tissue failure using a local strain-based criterion. FEM results were validated by experimentally testing a subset of the modeled specimen geometries. Mechanical testing data agreed with model predictions (∼90% agreement), validating the model's predictive power. Two of the modified dog-bone geometries (“half” and “quarter”) effectively ensured tissue failure at the ML for specimens oriented along the circumferential-radial and circumferential-axial directions. The variance of measured mechanical properties was significantly lower for notched samples that failed at the ML, suggesting that ML notch geometries result in more consistent and reliable data. In addition, the approach developed in this study provides a framework for evaluating failure properties of other fiber-reinforced tissues, such as tendons and meniscus.

Biomechanics of the human intervertebral disc: A review of testing techniques and results

Many experimental testing techniques have been adopted in order to provide an understanding of the biomechanics of the human intervertebral disc (IVD). The aim of this review article is to amalgamate results from these studies to provide readers with an overview of the studies conducted and their contribution to our current understanding of the biomechanics and function of the IVD. The overview is presented in a way that should prove useful to experimentalists and computational modellers. Mechanical properties of whole IVDs can be assessed conveniently by testing 'motion segments' comprising two vertebrae and the intervening IVD and ligaments. Neural arches should be removed if load-sharing between them and the disc is of no interest, and specimens containing more than two vertebrae are required to study 'adjacent level' effects. Mechanisms of injury (including endplate fracture and disc herniation) have been studied by applying complex loading at physiologically-relevant loading rates, whereas mechanical evaluations of surgical prostheses require slower application of standardised loading protocols. Results can be strongly influenced by the testing environment, preconditioning, loading rate, specimen age and degeneration, and spinal level. Component tissues of the disc (anulus fibrosus, nucleus pulposus, and cartilage endplates) have been studied to determine their material properties, but only the anulus has been thoroughly evaluated. Animal discs can be used as a model of human discs where uniform non-degenerate specimens are required, although differences in scale, age, and anatomy can lead to problems in interpretation.

A PARAMETRIC INVESTIGATION OF THE EFFECTS OF CERVICAL DISC PROSTHESES WITH UPWARD AND DOWNWARD NUCLEI ON SPINE BIOMECHANICS

This work aimed at investigating the influence of Baguera and Discocerv cervical disc prostheses, with mobile downward center of rotation (COR) and fixed upward COR, respectively, on the biomechanical behavior of C4–C6 cervical spine. For this purpose, using computed tomography (CT) data, a parametric nonlinear finite element (FE) model of intact C4–C6 spinal segments was developed, and an artificial disc was implanted at C5–C6 level. To assess the influence of implants on the biomechanics of cervical spine, the FE models were analyzed in flexion, extension, lateral bending, and axial rotation, and the results were presented in the range of motion (ROM) curves, and torsional stiffness. Results of this study, in agreement with the literature, suggested that both Baguera and Discocerv implants might be able to preserve the motion, and limit the alteration of the biomechanics of adjacent levels. Except for the possible confliction of adjacent vertebrae at the implanted level with Baguera implant in lateral bending, results of this study also indicated that the movability and downward COR of Baguera disc prosthesis caused ROMs of the implanted segment to be more similar to the intact model than Discocerv implant. Moreover, the upward COR of Discocerv implant may result in over-distraction on facets in the maximal flexion, with the ratio of 1.22 versus 1.36, and consequently facet syndrome during extension for Bageura and Discocerv disc prostheses, respectively.

Design Requirements for Annulus Fibrosus Repair: Review of Forces, Displacements, and Material Properties of the Intervertebral Disk and a Summary of Candidate Hydrogels for Repair

There is currently a lack of clinically available solutions to restore functionality to the intervertebral disk (IVD) following herniation injury to the annulus fibrosus (AF). Microdiscectomy is a commonly performed surgical procedure to alleviate pain caused by herniation; however, AF defects remain and can lead to accelerated degeneration and painful conditions. Currently available AF closure techniques do not restore mechanical functionality or promote tissue regeneration, and have risk of reherniation. This review determined quantitative design requirements for AF repair materials and summarized currently available hydrogels capable of meeting these design requirements by using a series of systematic PubMed database searches to yield 1500+ papers that were screened and analyzed for relevance to human lumbar in vivo measurements, motion segment behaviors, and tissue level properties. We propose a testing paradigm involving screening tests as well as more involved in situ and in vivo validation tests to efficiently identify promising biomaterials for AF repair. We suggest that successful materials must have high adhesion strength (∼0.2 MPa), match as many AF material properties as possible (e.g., approximately 1 MPa, 0. 3 MPa, and 30 MPa for compressive, shear, and tensile moduli, respectively), and have high tensile failure strain (∼65%) to advance to in situ and in vivo validation tests. While many biomaterials exist for AF repair, few undergo extensive mechanical characterization. A few hydrogels show promise for AF repair since they can match at least one material property of the AF while also adhering to AF tissue and are capable of easy implantation during surgical procedures to warrant additional optimization and validation.

A comparative study on dynamic stiffness in typical finite element model and multi-body model of C6-C7 cervical spine segment

In contrast to numerous researches on static or quasi-static stiffness of cervical spine segments, very few investigations on their dynamic stiffness were published. Currently, scale factors and estimated coefficients were usually used in multi-body models for including viscoelastic properties and damping effects, meanwhile viscoelastic properties of some tissues were unavailable for establishing finite element models. Because dynamic stiffness of cervical spine segments in these models were difficult to validate because of lacking in experimental data, we tried to gain some insights on current modeling methods through studying dynamic stiffness differences between these models. A finite element model and a multi-body model of C6-C7 segment were developed through using available material data and typical modeling technologies. These two models were validated with quasi-static response data of the C6-C7 cervical spine segment. Dynamic stiffness differences were investigated through controlling motions of C6 vertebrae at different rates and then comparing their reaction forces or moments. Validation results showed that both the finite element model and the multi-body model could generate reasonable responses under quasi-static loads, but the finite element segment model exhibited more nonlinear characters. Dynamic response investigations indicated that dynamic stiffness of this finite element model might be underestimated because of the absence of dynamic stiffen effect and damping effects of annulus fibrous, while representation of these effects also need to be improved in current multi-body model. Copyright © 2015 John Wiley & Sons, Ltd.

Lamellar and fibre bundle mechanics of the annulus fibrosus in bovine intervertebral disc

The intervertebral disc is a multicomposite structure, with an outer fibrous ring, the annulus fibrosus, retaining a gel-like core, the nucleus pulposus. The disc presents complex mechanical behaviour, and it is of high importance for spine biomechanics. Advances in multiscale modelling and disc repair raised a need for new quantitative data on the finest details of annulus fibrosus mechanics. In this work we explored inter-lamella and inter-bundle behaviour of the outer annulus using micromechanical testing and second harmonic generation microscopy. Twenty-one intervertebral discs were dissected from cow tails; the nucleus and inner annulus were excised to leave a ring of outer annulus, which was tested in circumferential loading while imaging the tissue's collagen fibres network with sub-micron resolution. Custom software was developed to determine local tissue strains through image analysis. Inter-bundle linear and shear strains were 5.5 and 2.8 times higher than intra-bundle strains. Bundles tended to remain parallel while rotating under loading, with large slipping between them. Inter-lamella linear strain was almost 3 times the intra-lamella one, but no slipping was observed at the junction between lamellae. This study confirms that outer annulus straining is mainly due to bundles slipping and rotating. Further development of disc multiscale modelling and repair techniques should take into account this modular behaviour of the lamella, rather than considering it as a homogeneous fibre-reinforced matrix.

STATEMENT OF SIGNIFICANCE

The intervertebral disc is an organ tucked between each couple of vertebrae in the spine. It is composed by an outer fibrous layer retaining a gel-like core. This organ undergoes severe and repeated loading during everyday life activities, since it is the compliant component that gives the spine its flexibility. Its properties are affected by pathologies such as disc degeneration, a major cause of back pain. In this article we explored the micromechanical behaviour of the disc's outer layer using second harmonic generation, a technique which allowed us to visualize, with unprecedented detail, how bundles of collagen fibres slide relative to each other when loaded. Our results will help further the development of new multiscale numerical models and repairing techniques.

Effective modulus of the human intervertebral disc and its effect on vertebral bone stress

The mechanism of vertebral wedge fractures remains unclear and may relate to typical variations in the mechanical behavior of the intervertebral disc. To gain insight, we tested 16 individual whole discs (between levels T8 and L5) from nine cadavers (mean±SD: 66±16 years), loaded in compression at different rates (0.05-20.0% strain/s), to measure a homogenized "effective" linear elastic modulus of the entire disc. The measured effective modulus, and average disc height, were then input and varied parametrically in micro-CT-based finite element models (60-μm element size, up to 80 million elements each) of six T9 human vertebrae that were virtually loaded to 3° of moderate forward-flexion via a homogenized disc. Across all specimens and loading rates, the measured effective modulus of the disc ranged from 5.8 to 42.7MPa and was significantly higher for higher rates of loading (p<0.002); average disc height ranged from 2.9 to 9.3mm. The parametric finite element analysis indicated that, as disc modulus increased and disc height decreased across these ranges, the vertebral bone stresses increased but their spatial distribution was largely unchanged: most of the highest stresses occurred in the central trabecular bone and endplates, and not anteriorly. Taken together with the literature, our findings suggest that the effective modulus of the human intervertebral disc should rarely exceed 100MPa and that typical variations in disc effective modulus (and less so, height) minimally influence the spatial distribution but can appreciably influence the magnitude of stress within the vertebral body.

Biomechanical effects of fusion levels on the risk of proximal junctional failure and kyphosis in lumbar spinal fusion surgery

BACKGROUND

Spinal fusion surgery is a widely used surgical procedure for sagittal realignment. Clinical studies have reported that spinal fusion may cause proximal junctional kyphosis and failure with disc failure, vertebral fracture, and/or failure at the implant-bone interface. However, the biomechanical injury mechanisms of proximal junctional kyphosis and failure remain unclear.

METHODS

A finite element model of the thoracolumbar spine was used. Nine fusion models with pedicle screw systems implanted at the L2-L3, L3-L4, L4-L5, L5-S1, L2-L4, L3-L5, L4-S1, L2-L5, and L3-S1 levels were developed based on the respective surgical protocols. The developed models simulated flexion-extension using hybrid testing protocol.

FINDINGS

When spinal fusion was performed at more distal levels, particularly at the L5-S1 level, the following biomechanical properties increased during flexion-extension: range of motion, stress on the annulus fibrosus fibers and vertebra at the adjacent motion segment, and the magnitude of axial forces on the pedicle screw at the uppermost instrumented vertebra.

INTERPRETATIONS

The results of this study demonstrate that more distal fusion levels, particularly in spinal fusion including the L5-S1 level, lead to greater increases in the risk of proximal junctional kyphosis and failure, as evidenced by larger ranges of motion, higher stresses on fibers of the annulus fibrosus and vertebra at the adjacent segment, and higher axial forces on the screw at the uppermost instrumented vertebra in flexion-extension. Therefore, fusion levels should be carefully selected to avoid proximal junctional kyphosis and failure.

A computational model to describe the regional interlamellar shear of the annulus fibrosus

Interlamellar shear may play an important role in the homeostasis and degeneration of the intervertebral disk. Accurately modeling the shear behavior of the interlamellar compartment would enhance the study of its mechanobiology. In this study, physical experiments were utilized to describe interlamellar shear and define a constitutive model, which was implemented into a finite element analysis. Ovine annulus fibrosus (AF) specimens from three locations within the intervertebral disk (lateral, outer anterior, and inner anterior) were subjected to in vitro mechanical shear testing. The local shear stress-stretch relationship was described for the lamellae and across the interlamellar layer of the AF. A hyperelastic constitutive model was defined for interlamellar and lamellar materials at each location tested. The constitutive models were incorporated into a finite element model of a block of AF, which modeled the interlamellar and lamellar layers using a continuum description. The global shear behavior of the AF was compared between the finite element model and physical experiments. The shear moduli at the initial and final regions of the stress-strain curve were greater within the lamellae than across the interlamellar layer. The difference between interlamellar and lamellar shear was greater at the outer anterior AF than at the inner anterior region. The finite element model was shown to accurately predict the global shear behavior or the AF. Future studies incorporating finite element analysis of the interlamellar compartment may be useful for predicting its physiological mechanical behavior to inform the study of its mechanobiology.

Biomechanical analysis of two-step traction therapy in the lumbar spine

Traction therapy is one of the most common conservative treatments for low back pain. However, the effects of traction therapy on lumbar spine biomechanics are not well known. We investigated biomechanical effects of two-step traction therapy, which consists of global axial traction and local decompression, on the lumbar spine using a validated three-dimensional finite element model of the lumbar spine. One-third of body weight was applied on the center of the L1 vertebra toward the superior direction for the first axial traction. Anterior translation of the L4 vertebra was considered as the second local decompression. The lordosis angle between the superior planes of the L1 vertebra and sacrum was 44.6° at baseline, 35.2° with global axial traction, and 46.4° with local decompression. The fibers of annulus fibrosus in the posterior region, and intertransverse and posterior longitudinal ligaments experienced stress primarily during global axial traction, these stresses decreased during local decompression. A combination of global axial traction and local decompression would be helpful for reducing tensile stress on the fibers of the annulus fibrosus and ligaments, and intradiscal pressure in traction therapy. This study could be used to develop a safer and more effective type of traction therapy.

A coupled fiber-matrix model demonstrates highly inhomogeneous microstructural interactions in soft tissues under tensile load

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

Quantification of continuous in vivo flexion-extension kinematics and intervertebral strains

PURPOSE

Healthy subjects performed lumbar flexion and were assessed by video fluoroscopy to measure the in vivo kinematics of the lower lumbar motion segments.

METHODS

Fifteen healthy subjects (8 male, 7 female, 28 ± 10 years) performed lumbar flexion and extension back to neutral while their vertebrae were imaged. The sagittal plane vertebral margins of L3-S1 were identified. Lumbar angle, segmental margin strains, axial displacements, anterior-posterior (A-P) translations, and segmental rotations over the course of flexion were measured.

RESULTS

L4-L5 had the largest posterior margin Green strain (65%). Each segment displayed more axial displacement than A-P translation. Peak vertebral angulation occurred at approximately 75% of peak flexion during the extension phase.

CONCLUSION

L4-L5 exhibited the largest anterior and posterior margin strains (29 and 65%, respectively). Strains in the disc during in vivo lumbar flexion are due to both angular rotation and linear translation.

Influence of biochemical composition on endplate cartilage tensile properties in the human lumbar spine

Endplate cartilage integrity is critical to spine health and is presumably impaired by deterioration in biochemical composition. Yet, quantitative relationships between endplate biochemical composition and biomechanical properties are unavailable. Using endplate cartilage harvested from human lumbar spines (six donors, ages 51-67 years) we showed that endplate biochemical composition has a significant influence on its equilibrium tensile properties and that the presence of endplate damage associates with a diminished composition-function relationship. We found that the equilibrium tensile modulus (5.9 ± 5.7 MPa) correlated significantly with collagen content (559 ± 147 µg/mg dry weight, r(2)  = 0.35) and with the collagen/GAG ratio (6.0 ± 2.1, r(2)  = 0.58). Accounting for the damage status of the adjacent cartilage improved the latter correlation (r(2)  = 0.77) and indicated that samples with adjacent damage such as fissures and avulsions had a diminished modulus-collagen/GAG relationship (p = 0.02). Quasi-linear viscoelastic relaxation properties (C, t1 , and t2 ) did not correlate with biochemical composition. We conclude that reduced matrix quantity decreases the equilibrium tensile modulus of human endplate cartilage and that characteristics of biochemical composition that are independent of matrix quantity, that is, characteristics related to matrix quality, may also be important.