A chemo-mechanical model for osmo-inelastic effects in the annulus fibrosus

Poisson function and volume ratio of soft anisotropic materials under large deformations

Accurate transverse deformation measurements are required for the estimation of the Poisson function and volume ratio. In this study, pure silicone and soft composite specimens were subjected to uniaxial tension, and the digital image correlation method was used to measure longitudinal and in- and out-of-plane transverse stretches. To minimize the effects of measurement errors on parameter estimation, the measured transverse stretches were defined in terms of the longitudinal stretch using a new formulation based on Poisson's ratios and two stretch-dependent parameters. From this formulation, Poisson functions and volume ratio for soft materials under large deformations were obtained. The results showed that pure silicone can be considered isotropic and nearly incompressible under large deformations, as expected. In contrast, Poisson's ratio of silicone reinforced with extensible fabric can exceed classical bounds, including negative value (auxetic behavior). The incompressibility assumption can be employed for describing the stress-stretch curve of pure silicone, while volume ratios are required for soft composites. Data of human skin, aortic wall, and annulus fibrosus from the literature were selected and analyzed. Except for the aortic wall, which can be considered nearly incompressible, the studied soft tissues must be regarded as compressible. All tissues presented anisotropic behavior.

Strain rate-dependent failure mechanics of the intervertebral disc under tension/compression and constitutive analysis

BACKGROUND

The intervertebral disc exhibits not only strain rate dependence (viscoelasticity), but also significant asymmetry under tensile and compressive loads, which is of great significance for understanding the mechanism of lumbar disc injury under physiological loads.

OBJECTIVE

In this study, the strain rate sensitive and tension-compression asymmetry of the intervertebral disc were analyzed by experiments and constitutive equation.

METHOD

The Sheep intervertebral disc samples were divided into three groups, in order to test the strain rate sensitive mechanical behavior, and the internal displacement as well as pressure distribution.

RESULTS

The tensile stiffness is one order of magnitude smaller than the compression stiffness, and the logarithm of the elastic modulus is approximately linear with the logarithm of the strain rate, showing obvious tension-compression asymmetry and rate-related characteristics. In addition, the sensitivity to the strain rate is the same under these two loading conditions. The stress-strain curves of unloading and loading usually do not coincide, and form a Mullins effect hysteresis loop. The radial displacement distribution is opposite between the anterior and posterior region, which is consistent with the stress distribution. By introducing the damage factor into ZWT constitutive equation, the rate-dependent viscoelastic and weakening behavior of the intervertebral disc can be well described.

Overloading effect on the osmo-viscoelastic and recovery behavior of the intervertebral disc

In vitro studies investigating the effect of high physiological compressive loads on the intervertebral disc mechanics as well as on its recovery are rare. Moreover, the osmolarity effect on the disc viscoelastic behavior following an overloading is far from being studied. This study aims to determine whether a compressive loading-unloading cycle exceeding physiological limits could be detrimental to the cervical disc, and to examine the chemo-mechanical dependence of this overloading effect. Cervical functional spine units were subjected to a compressive loading-unloading cycle at a high physiological level (displacement of 2.5 mm). The overloading effect on the disc viscoelastic behavior was evaluated through two relaxation tests conducted before and after cyclic loading. Afterward, the disc was unloaded in a saline bath during a rest period, and its recovery response was assessed by a third relaxation test. The chemo-mechanical coupling in the disc response was further examined by repeating this protocol with three different saline concentrations in the external fluid bath. It was found that overloading significantly alters the disc viscoelastic response, with changes statistically dependent on osmolarity conditions. The applied hyper-physiological compressive cycle does not cause damage since the disc recovers its original viscoelastic behavior following a rest period. Osmotic loading only influences the loading-unloading response; specifically, increasing fluid osmolarity leads to a decrease in disc relaxation after the applied cycle. However, the disc recovery is not impacted by the osmolarity of the external fluid.

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.

Auxeticity as a Mechanobiological Tool to Create Meta-Biomaterials

Mechanical and morphological design parameters, such as stiffness or porosity, play important roles in creating orthopedic implants and bone substitutes. However, we have only a limited understanding of how the microarchitecture of porous scaffolds contributes to bone regeneration. Meta-biomaterials are increasingly used to precisely engineer the internal geometry of porous scaffolds and independently tailor their mechanical properties (e.g., stiffness and Poisson's ratio). This is motivated by the rare or unprecedented properties of meta-biomaterials, such as negative Poisson's ratios (i.e., auxeticity). It is, however, not clear how these unusual properties can modulate the interactions of meta-biomaterials with living cells and whether they can facilitate bone tissue engineering under static and dynamic cell culture and mechanical loading conditions. Here, we review the recent studies investigating the effects of the Poisson's ratio on the performance of meta-biomaterials with an emphasis on the relevant mechanobiological aspects. We also highlight the state-of-the-art additive manufacturing techniques employed to create meta-biomaterials, particularly at the micrometer scale. Finally, we provide future perspectives, particularly for the design of the next generation of meta-biomaterials featuring dynamic properties (e.g., those made through 4D printing).

A Microstructure-Based Mechanistic Approach to Detect Degeneration Effects on Potential Damage Zones and Morphology of Young and Old Human Intervertebral Discs

There is an increasing demand to develop predictive medicine through the creation of predictive models and digital twins of the different body organs. To obtain accurate predictions, real local microstructure, morphology changes and their accompanying physiological degenerative effects must be taken into account. In this article, we present a numerical model to estimate the long-term aging effect on the human intervertebral disc response by means of a microstructure-based mechanistic approach. It allows to monitor in-silico the variations in disc geometry and local mechanical fields induced by age-dependent long-term microstructure changes. Both lamellar and interlamellar zones of the disc annulus fibrosus are constitutively represented by considering the main underlying microstructure features in terms of proteoglycans network viscoelasticity, collagen network elasticity (along with content and orientation) and chemical-induced fluid transfer. With age, a noticeable increase in shear strain is especially observed in the posterior and lateral posterior regions of the annulus which is in correlation with the high vulnerability of elderly people to back problems and posterior disc hernia. Important insights about the relation between age-dependent microstructure features, disc mechanics and disc damage are revealed using the present approach. These numerical observations are hardly obtainable using current experimental technologies which makes our numerical tool useful for patient-specific long-term predictions.

Elastic Fibers in the Intervertebral Disc: From Form to Function and toward Regeneration

Despite extensive efforts over the past 40 years, there is still a significant gap in knowledge of the characteristics of elastic fibers in the intervertebral disc (IVD). More studies are required to clarify the potential contribution of elastic fibers to the IVD (healthy and diseased) function and recommend critical areas for future investigations. On the other hand, current IVD in-vitro models are not true reflections of the complex biological IVD tissue and the role of elastic fibers has often been ignored in developing relevant tissue-engineered scaffolds and realistic computational models. This has affected the progress of IVD studies (tissue engineering solutions, biomechanics, fundamental biology) and translation into clinical practice. Motivated by the current gap, the current review paper presents a comprehensive study (from the early 1980s to 2022) that explores the current understanding of structural (multi-scale hierarchy), biological (development and aging, elastin content, and cell-fiber interaction), and biomechanical properties of the IVD elastic fibers, and provides new insights into future investigations in this domain.

Modeling multiaxial damage regional variation in human annulus fibrosus

In the present article, a fully three-dimensional human annulus fibrosus model is developed by considering the regional variation of the complex structural organization of collagen network at different scales to predict the regional anisotropic multiaxial damage of the intervertebral disc. The model parameters are identified using experimental data considering as elementary structural unit, the single annulus lamellae stretched till failure along the micro-sized collagen fibers. The multi-layered lamellar/inter-lamellar annulus model is constructed by considering the effective interactions between adjacent layers and the chemical-induced volumetric strain. The regional dependent model predictions are analyzed under various loading modes and compared to experimental data when available. The stretching along the circumferential and radial directions till failure serves to check the predictive capacities of the annulus model. Model results under simple shear, biaxial stretching and plane-strain compression are further presented and discussed. Finally, a full disc model is constructed using the regional annulus model and simulations are presented to assess the most likely failed areas under disc axial compression. STATEMENT OF SIGNIFICANCE: The damage in annulus soft tissues is a complex multiscale phenomenon due to a complex structural arrangement of collagen network at different scales of hierarchical organization. A fully three-dimensional constitutive representation that considers the regional variation of the structural complexity to estimate annulus multiaxial mechanics till failure has not yet been developed. Here, a model is developed to predict deformation-induced damage and failure of annulus under multiaxial loading histories considering as time-dependent physical process both chemical-induced volumetric effects and damage accumulation. After model identification using single lamellae extracted from different disc regions, the model predictability is verified for various multiaxial elementary loading modes representative of the spine movement. The heterogeneous mechanics of a full human disc model is finally presented.

A microstructure-based model for a full lamellar-interlamellar displacement and shear strain mapping inside human intervertebral disc core

The determinant role of the annulus fibrosus interlamellar zones in the intervertebral disc transversal and volumetric responses and hence on their corresponding three-dimensional conducts have been only revealed and appreciated recently. Their consideration in disc modeling strategies has been proven to be essential for the reproduction of correct local strain and displacement fields inside the disc especially in the unconstrained directions of the disc. In addition, these zones are known to be the starting areas of annulus fibrosus circumferential tears and disc delamination failure mode, which is often judged as one of the most dangerous disc failure modes that could evolve with time leading to disc hernia. For this latter reason, the main goal of the current contribution is to incorporate physically for the first time, the interlamellar zones, at the scale of a complete human lumbar intervertebral disc, in order to allow a correct local vision and replication of the different lamellar-interlamellar interactions and an identification of the interlamellar critical zones. By means of a fully tridimensional chemo-viscoelastic constitutive model, which we implemented into a finite element code, the physical, mechanical and chemical contribution of the interlamellar zones is added to the disc. The chemical-induced volumetric response is accounted by the model for both the interlamellar zones and the lamellae using experimentally-based fluid kinetics. Computational simulations are performed and critically discussed upon different simple and complex physiological movements. The disc core and the interlamellar zones are numerically accessed, allowing the observation of the displacement and shear strain fields that are compared to direct MRI experiments from the literature. Important conclusions about the correct lamellar-interlamellar-nucleus interactions are provided thanks to the developed model. The critical interlamellar spots with the highest delamination potentials are defined, analyzed and related to the local kinetics and microstructure.

Application of textile technology in tissue engineering: A review

One of the key elements in tissue engineering is to design and fabricate scaffolds with tissue-like properties. Among various scaffold fabrication methods, textile technology has shown its unique advantages in mimicking human tissues' properties such as hierarchical, anisotropic, and strain-stiffening properties. As essential components in textile technology, textile patterns affect the porosity, architecture, and mechanical properties of textile-based scaffolds. However, the potential of various textile patterns has not been fully explored when fabricating textile-based scaffolds, and the effect of different textile patterns on scaffold properties has not been thoroughly investigated. This review summarizes textile technology development and highlights its application in tissue engineering to facilitate the broader application of textile technology, especially various textile patterns in tissue engineering. The potential of using different textile methods such as weaving, knitting, and braiding to mimic properties of human tissues is discussed, and the effect of process parameters in these methods on fabric properties is summarized. Finally, perspectives on future directions for explorations are presented. STATEMENT OF SIGNIFICANCE: Recently, biomedical engineers have applied textile technology to fabricate scaffolds for tissue engineering applications. Various textile methods, especially weaving, knitting, and braiding, enables engineers to customize the physical, mechanical, and biological properties of scaffolds. However, most textile-based scaffolds only use simple textile patterns, and the effect of different textile patterns on scaffold properties has not been thoroughly investigated. In this review, we cover for the first time the effect of process parameters in different textile methods on fabric properties, exploring the potential of using different textile methods to mimic properties of human tissues. Previous advances in textile technology are presented, and future directions for explorations are presented, hoping to facilitate new breakthroughs of textile-based tissue engineering.

Sensitivity of Intervertebral Disc Finite Element Models to Internal Geometric and Non-geometric Parameters

Finite element models are useful for investigating internal intervertebral disc (IVD) behaviours without using disruptive experimental techniques. Simplified geometries are commonly used to reduce computational time or because internal geometries cannot be acquired from CT scans. This study aimed to (1) investigate the effect of altered geometries both at endplates and the nucleus-anulus boundary on model response, and (2) to investigate model sensitivity to material and geometric inputs, and different modelling approaches (graduated or consistent fibre bundle angles and glued or cohesive inter-lamellar contact). Six models were developed from 9.4 T MRIs of bovine IVDs. Models had two variations of endplate geometry (a simple curved profile from the centre of the disc to the periphery, and precise geometry segmented from MRIs), and three variations of NP-AF boundary (linear, curved, and segmented). Models were subjected to axial compressive loading (to 0.86 mm at a strain rate of 0.1/s) and the effect on stiffness and strain distributions, and the sensitivity to modelling approaches was investigated. The model with the most complex geometry (segmented endplates, curved NP-AF boundary) was 3.1 times stiffer than the model with the simplest geometry (curved endplates, linear NP-AF boundary), although this difference may be exaggerated since segmenting the endplates in the complex geometry models resulted in a shorter average disc height. Peak strains were close to the endplates at locations of high curvature in the segmented endplate models which were not captured in the curved endplate models. Differences were also seen in sensitivity to material properties, graduated fibre angles, cohesive rather than glued inter-lamellar contact, and NP:AF ratios. These results show that FE modellers must take care to ensure geometries are realistic so that load is distributed and passes through IVDs accurately.

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).

A microstructure-based modeling approach to assess aging-sensitive mechanics of human intervertebral disc

BACKGROUND AND OBJECTIVE

The human body soft tissues are hierarchic structures interacting in a complex manner with the surrounding biochemical environment. The loss of soft tissues functionality with age leads to more vulnerability regarding to the external mechanical loadings and increases the risk of injuries. As a main example of the human body soft tissues, the intervertebral disc mechanical response evolution with age is explored. Although the age-dependence of the intervertebral disc microstructure is a well-known feature, no noticeable age effect on the disc stiffness is evidenced in the in-vitro experimental studies of the literature. So, if the disc intrinsic mechanics remains constant, how to explain the correlation of disc degeneration and disc functionality loss with age.

METHODS

A microstructure-based modeling approach was developed to assess in-silico the aging-sensitive mechanics of human intervertebral disc. The model considers the relationship between stress/volumetric macro-response and microstructure along with effective age effects acting at the lamellar and multi-lamellar scales. The stress-stretch and transversal responses of the different disc regions were computed for various age groups (13-18, 36, 58, 69 and 82 years old) and their evolution with age was studied.

RESULTS

While matching with in-vitro experimental data, the predicted stiffness was found to increase while passing from adolescent young discs to mature older discs and then to remain almost constant for the rest of life. Important age-related changes in the disc transversal behavior were also predicted affecting the flexibility of the disc, changing its volumetric behavior, and modifying its dimensions.

CONCLUSION

The developed approach was found able to bring new conclusions about age-dependent mechanical properties including regional dependency. The disc mechanics in terms of rigidity, radial and axial transversal responses were found to alter going from adolescent to middle age where the disc reaches a certain maturity. After reaching maturity, the mechanical properties undergo very slight changes until becoming almost constant with age.

Relevance of a novel external dynamic distraction device for treating back pain

Low back pain is a common, expensive, and disabling condition in industrialized countries. There is still no consensus for its ideal management. Believing in the beneficial effect of traction, we developed a novel external dynamic distraction device. The purpose of this work was to demonstrate that external distraction allows limiting the pressure exerted in standing-up position on the lower intervertebral discs. Numerical and cadaveric studies were used as complementary approaches. Firstly, we implemented the device into a numerical model of a validated musculoskeletal software (Anybody Modeling System) and we calculated the lower disc pressure while traction forces were applied. Secondly, we performed an anatomical study using a non-formalin preserved cadaver placed in a sitting position. A pressure sensor was placed in the lower discs under fluoroscopic control through a Jamshidi needle. The intradiscal pressure was then measured continuously at rest while applying a traction force of 200 N. Both numerical and cadaveric studies demonstrated a decrease in intradiscal pressures after applying a traction force with the external device. Using the numerical model, we showed that tensile forces below 500 N in total were sufficient. The application of higher forces seems useless and potentially deleterious. External dynamic distraction device is able to significantly decrease the intradiscal pressure in a sitting or standing position. However, the therapeutic effects need to be proven using clinical studies.

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.

How Osmoviscoelastic Coupling Affects Recovery of Cyclically Compressed Intervertebral Disc

STUDY DESIGN

Osmoviscoelastic behavior of cyclically loaded cervical intervertebral disc.

OBJECTIVE

The aim of this study was to evaluate in vitro the effects of physiologic compressive cyclic loading on the viscoelastic properties of cervical intervertebral disc and, examine how the osmoviscoelastic coupling affects time-dependent recovery of these properties following a long period of unloading.

SUMMARY OF BACKGROUND DATA

The human neck supports repetitive loadings during daily activities and recovery of disc mechanics is essential for normal mechanical function. However, the response of cervical intervertebral disc to cyclic loading is still not very well defined. Moreover, how loading history conditions could affect the time-dependent recovery is still unclear.

METHODS

Ten thousand cycles of compressive loading, with different magnitudes and saline concentrations of the surrounding fluid bath, are applied to 8 motion segments (composed by 2 adjacent vertebrae and the intervening disc) extracted from the cervical spines of mature sheep. Subsequently, specimens are hydrated during 18 hours of unloading. The viscoelastic disc responses, after cyclic loading and recovery phase, are characterized by relaxation tests.

RESULTS

Viscoelastic behaviors are significantly altered following large number of cyclic loads. Moreover, after 18-hour recovery period in saline solution at reference concentration (0.15 mol/L), relaxation behaviors were fully restored. Nonetheless, full recovery is not obtained whether the concentration of the surrounding fluid, that is, hypo-, iso-, or hyper-osmotic conditions.

CONCLUSION

Cyclic loading effects and full recovery of viscoelastic behavior after hydration at iso-osmotic condition (0.15 mol/L) are governed by osmotic attraction of fluid content in the disc due to imbalance between the external load and the swelling pressure of the disc. After removal of the load, the disc recovers its viscoelastic properties following period of rest. Nevertheless, the viscoelastic recovery is a chemically activated process and its dependency on saline concentration is governed by fluid flow due to imbalance of ions between the disc tissues and the surrounding fluid.

LEVEL OF EVIDENCE

3.

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.

How pre-strain affects the chemo-torsional response of the intervertebral disc

BACKGROUND

The role of the axial pre-strain on the torsional response of the intervertebral disc remains largely undefined. Moreover, the chemo-mechanical interactions in disc tissues are still unclear and corresponding data are rare in the literature. The paper deals with an in-vitro study of the pre-strain effect on the chemical sensitivity of the disc torsional response.

METHODS

Fifteen non-frozen 'motion segments' (two vertebrae and the intervening soft tissues) were extracted from the cervical spines of mature sheep. The motion segments were loaded in torsion at various saline concentrations and axial pre-strain levels in order to modulate the intradiscal pressure. After preconditioning with successive low-strain compressions at a magnitude of 0.1 mm (10 cycles at 0.05 mm/s), the motion segment was subjected to a cyclic torsion until a twisting level of 2 deg. at 0.05 deg./s while a constant axial pre-strain (in compression or in tension) is maintained, the saline concentration of the surrounding fluid bath being changed from hypo-osmotic condition to hyper-osmotic condition.

FINDINGS

Analysis of variance shows that the saline concentration influences the torsional response only when the motion segments are pre-compressed (p < .001) with significant differences between hypo-osmotic condition and hyper-osmotic condition.

INTERPRETATION

The combination of a compressive pre-strain with twisting amplifies the nucleus hydrostatic pressure on the annulus and the annulus collagen fibers tensions. The proteoglycans density increases with the compressive pre-strain and leads to higher chemical imbalances, which would explain the increase in chemical sensitivity of the disc torsional response.

The use of auxetic materials in tissue engineering

A number of biological tissues have been reported as behaving in an auxetic manner, defined by a negative Poisson's ratio. This describes the deformation of tissue which expands in the axial and the transverse directions simultaneously while under uniaxial tension; and contracts axially and transversely upon uniaxial compression. The discovery of auxetic behaviour within biological tissues has implications for the recreation of the auxetic loading environment within tissue engineering. Tissue engineers strive to recreate the natural properties of biological tissue and in order to recreate the unique loading environment of cells from auxetic tissue, an auxetic scaffold is required. A number of studies have used a variety of auxetic scaffolds within tissue engineering. Investigation into the effect of auxetic micro-environments created by auxetic scaffolds on cellular behaviour has demonstrated an increased cellular proliferation and enhanced differentiation. Here, we discuss studies which have identified auxetic behaviour within biological tissues, and where cells have been cultured within auxetic scaffolds, bringing together current knowledge of the potential use of auxetic materials in tissue engineering applications and biomedical devices.

Effect of intervertebral disc degeneration on mechanical and electric signals at the interface between disc and vertebra

Intervertebral disc (IVD) degeneration is significantly correlated with the changes in structure and material properties of adjacent vertebral bone, possibly through mechanical and electrical interactions. However, the mechanisms underlying the alteration of the mechanical and electrical environment at the disc-vertebra interface related with disc degeneration have not been well studied. The objective of this study was to numerically investigate the long-term distributions of mechanical and electrical signals on the disc-vertebra interface with disc degeneration. A three-dimensional finite element model of a human lumbar IVD was used to study the mechanical and electric signals at the interface between disc and vertebral body. The disc degeneration was simulated by reducing the nutrition levels on the nucleus pulposus (NP)-vertebra interface and on the annulus fibrosus (AF) periphery to 30% and 60% of its normal values, respectively. In the simulation, the total external mechanical load applied to the disc-vertebra segment was assumed unchanged during disc degeneration. The simulation results showed that the compressive stress of solid matrix changed by up to ~37 kPa on the NP-vertebra interface, while it increased by up to ~32 kPa on the AF-vertebra interface. The shear stress increased by up to ~37 kPa with disc degeneration. The absolute value of the electric potential on the disc-vertebra interface of the disc slightly decreased with the disc degeneration (~0.5 mV). The knowledge of these spatial and temporal variations of the mechanical stresses and electric potential on the disc-vertebra interface is important for understanding the vertebrae adaptation and remodeling during disc degeneration.

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.