An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs

The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4 | 5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.

A quadriphasic mechanical model of the human dermis

The present study investigates the multiphasic nature of the mechanical behavior of human dermis. Motivated by experimental observations and by consideration of its composition, a quadriphasic model of the dermis is proposed, distinguishing solid matrix components, interstitial fluid and charged constituents moving within the fluid, i.e., anions and cations. Compression and tensile experiments with and without change of osmolarity of the bath are performed to characterize the chemo-mechanical coupling in the dermis. Model parameters are determined through inverse analysis. The computations predict a dominant role of the permeability in the determination of the temporal evolution of the mechanical response of the tissue. In line with the previous studies on other tissues, the analysis shows that an ideal model based on Donnan's equilibrium overestimates the osmotic pressure in skin for the case of very dilute solutions. The quadriphasic model is applied to predict changes in dermal cell environment and therefore alterations in what is called the "mechanome," associated with skin stretch. The simulations indicate that skin deformation causes a variation in several local variables, including in particular the electric field associated with a deformation-induced non-homogeneous distribution of fixed charges.

Radial matrix constraint influences tissue contraction and promotes maturation of bi-layered skin equivalents

Human skin equivalents (HSEs) serve as important tools for mechanistic studies with human skin cells, drug discovery, pre-clinical applications in the field of tissue engineering and for skin transplantation on skin defects. Besides the cellular and extracellular matrix (ECM) components used for HSEs, physical constraints applied on the scaffold during HSEs maturation influence tissue organization, functionality, and homogeneity. In this study, we introduce a 3D-printed culture insert that exposes bi-layered HSEs to a static radial constraint through matrix adhesion. We examine the effect of various diameters of the ring-shaped culture insert on the HSE's characteristics and compare them to state-of-the-art unconstrained and planar constrained HSEs. We show that radial matrix constraint of HSEs regulates tissue contraction, promotes fibroblast and matrix organization that is similar to human skin in vivo and improves keratinocyte differentiation, epidermal stratification, and basement membrane formation depending on the culture insert diameter. Together, these data demonstrate that the degree of HSE's contraction is an important design consideration in skin tissue engineering. Therefore, this study can help to mimic various in vivo skin conditions and to increase the control of relevant tissue properties.

Multiscale mechanical analysis of the elastic modulus of skin

The mechanical properties of the skin determine tissue function and regulate dermal cell behavior. Yet measuring these properties remains challenging, as evidenced by the large range of elastic moduli reported in the literature-from below one kPa to hundreds of MPa. Here, we reconcile these disparate results by dedicated experiments at both tissue and cellular length scales and by computational models considering the multiscale and multiphasic tissue structure. At the macroscopic tissue length scale, the collective behavior of the collagen fiber network under tension provides functional tissue stiffness, and its properties determine the corresponding elastic modulus (100-200 kPa). The compliant microscale environment (0.1-10 kPa), probed by atomic force microscopy, arises from the ground matrix without engaging the collagen fiber network. Our analysis indicates that indentation-based elasticity measurements, although probing tissue properties at the cell-relevant length scale, do not assess the deformation mechanisms activated by dermal cells when exerting traction forces on the extracellular matrix. Using dermal-equivalent collagen hydrogels, we demonstrate that indentation measurements of tissue stiffness do not correlate with the behavior of embedded dermal fibroblasts. These results provide a deeper understanding of tissue mechanics across length scales with important implications for skin mechanobiology and tissue engineering. STATEMENT OF SIGNIFICANCE: Measuring the mechanical properties of the skin is essential for understanding dermal cell mechanobiology and designing tissue-engineered skin substitutes. However, previous results reported for the elastic modulus of skin vary by six orders of magnitude. We show that two distinct deformation mechanisms, related to the tension-compression nonlinearity of the collagen fiber network, can explain the large variations in elastic moduli. Furthermore, we show that microscale indentation, which is frequently used to assess the stiffness perceived by cells, fails to engage the fiber network, and therefore cannot predict the behavior of dermal fibroblasts in stiffness-tunable fibrous hydrogels. This has important implications for how to measure and interpret the mechanical properties of soft tissues across length scales.

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.

Recent Advances in Coupled MBS and FEM Models of the Spine—A Review

How back pain is related to intervertebral disc degeneration, spinal loading or sports-related overuse remains an unanswered question of biomechanics. Coupled MBS and FEM simulations can provide a holistic view of the spine by considering both the overall kinematics and kinetics of the spine and the inner stress distribution of flexible components. We reviewed studies that included MBS and FEM co-simulations of the spine. Thereby, we classified the studies into unidirectional and bidirectional co-simulation, according to their data exchange methods. Several studies have demonstrated that using unidirectional co-simulation models provides useful insights into spinal biomechanics, although synchronizing the two distinct models remains a key challenge, often requiring extensive manual intervention. The use of a bidirectional co-simulation features an iterative, automated process with a constant data exchange between integrated subsystems. It reduces manual corrections of vertebra positions or reaction forces and enables detailed modeling of dynamic load cases. Bidirectional co-simulations are thus a promising new research approach for improved spine modeling, as a main challenge in spinal biomechanics is the nonlinear deformation of the intervertebral discs. Future studies will likely include the automated implementation of patient-specific bidirectional co-simulation models using hyper- or poroelastic intervertebral disc FEM models and muscle forces examined by an optimization algorithm in MBS. Applications range from clinical diagnosis to biomechanical analysis of overload situations in sports and injury prediction.

Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.

Activation of Nrf2 in fibroblasts promotes a skin aging phenotype via an Nrf2-miRNA-collagen axis

Aging is associated with progressive skin fragility and a tendency to tear, which can lead to severe clinical complications. The transcription factor NRF2 is a key regulator of the cellular antioxidant response, and pharmacological NRF2 activation is a promising strategy for the prevention of age-related diseases. Using a combination of molecular and cellular biology, histology, imaging and biomechanical studies we show, however, that constitutive genetic activation of Nrf2 in fibroblasts of mice suppresses collagen and elastin expression, resulting in reduced skin strength as seen in aged mice. Mechanistically, the "aging matrisome" results in part from direct Nrf2-mediated overexpression of a network of microRNAs that target mRNAs of major skin collagens and other matrix components. Bioinformatics and functional studies revealed high NRF2 activity in aged human fibroblasts in 3D skin equivalents and human skin biopsies, highlighting the translational relevance of the functional mouse data. Together, these results identify activated NRF2 as a promoter of age-related molecular and biomechanical skin features.

Multiscale modelling for investigating the long-term time-dependent biphasic behaviour of the articular cartilage in the natural hip joint

A better understanding of the time-dependent biomechanical behaviour of the biphasic hip articular cartilage (AC) under physiological loadings is important to understand the onset of joint pathology and guide the clinical treatment. Current computational studies for the biphasic hip AC were usually limited to short-term duration or using elaborate loading. The present study aimed to develop a multiscale computational modelling to investigate the long-term biphasic behaviour of the hip AC under physiological loadings over multiple gait cycles. Two-scale computational modelling including a musculoskeletal model and a finite element model of the natural hip was created. These two models were then combined and used to investigate the biphasic behaviour of hip AC over 80 gait cycles. The results showed that the interstitial fluid pressure in the AC supported over 89% of the loading during gait. When the contact area was located at the AC centre, the contact pressure and fluid pressure increased over time from the first cycle to the 80th cycle, while when the contact area approached the edge, these pressures decreased first dramatically and then slowly over time. The peak stresses and strains in the solid matrix of the AC remained at a low level and increased over time from the first cycle to the 80th cycle. This study demonstrated that the long-term temporal variations of the biphasic behaviour of hip AC under physiological loadings are significant. The methodology has potentially important implications in the biomechanical studies of human cartilage and supporting the development of cartilage substitution.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

Torque- and Muscle-Driven Flexion Induce Disparate Risks of In Vitro Herniation: A Multiscale and Multiphasic Structure-Based Finite Element Study

The intervertebral disc is a complex structure that experiences multiaxial stresses regularly. Disc failure through herniation is a common cause of lower back pain, which causes reduced mobility and debilitating pain, resulting in heavy socioeconomic burdens. Unfortunately, herniation etiology is not well understood, partially due to challenges in replicating herniation in vitro. Previous studies suggest that flexion elevated risks of herniation. Thus, the objective of this study was to use a multiscale and multiphasic finite element model to evaluate the risk of failure under torque- or muscle-driven flexion. Models were developed to represent torque-driven flexion with the instantaneous center of rotation (ICR) located on the disc, and the more physiologically representative muscle-driven flexion with the ICR located anterior of the disc. Model predictions highlighted disparate disc mechanics regarding bulk deformation, stress-bearing mechanisms, and intradiscal stress-strain distributions. Specifically, failure was predicted to initiate at the bone-disc boundary under torque-driven flexion, which may explain why endplate junction failure, instead of herniation, has been the more common failure mode observed in vitro. By contrast, failure was predicted to initiate in the posterolateral annulus fibrosus under muscle-driven flexion, resulting in consistent herniation. Our findings also suggested that muscle-driven flexion combined with axial compression could be sufficient for provoking herniation in vitro and in silico. In conclusion, this study provided a computational framework for designing in vitro testing protocols that can advance the assessment of disc failure behavior and the performance of engineered disc implants.

Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology

Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.

Saline-polyethylene glycol blends preserve in vitro annulus fibrosus hydration and mechanics: An experimental and finite-element analysis

Precise control of tissue water content is essential for ensuring accurate, repeatable, and physiologically relevant measurements of tissue mechanics and biochemical composition. While previous studies have found that saline and polyethylene glycol (PEG) blends were effective at controlling tendon and ligament hydration levels, this work has yet to be extended to the annulus fibrosus (AF). Thus, the first objective of this study was to determine and validate an optimal buffer solution for targeting and maintaining hydration levels of tissue-level AF specimens in vitro. This was accomplished by measuring the transient swelling behavior of bovine AF specimens in phosphate-buffered saline (PBS) and PEG buffers across a wide range of concentrations. Sub-failure, failure, and post-failure mechanics were measured to determine the relationship between changes in tissue hydration and tensile mechanical response. The effect of each buffer solution on tissue composition was also assessed. The second objective of this study was to assess the feasibility and effectiveness of using multi-phasic finite element models to investigate tissue swelling and mechanical responses in different external buffer solutions. A solution containing 6.25%w/v PBS and 6.25%w/v PEG effectively maintained tissue-level AF specimen hydration at fresh-frozen levels after 18 h in solution. Modulus, failure stress, failure strain, and post-failure toughness of specimens soaked in this solution for 18 h closely matched those of fresh-frozen specimens. In contrast, specimens soaked in 0.9%w/v PBS swelled over 100% after 18 h and exhibited significantly diminished sub-failure and failure properties compared to fresh-frozen controls. The increased cross-sectional area with swelling contributed to but was not sufficient to explain the diminished mechanics of PBS-soaked specimens, suggesting additional sub-tissue scale mechanisms. Computational simulations of these specimens generally agreed with experimental results, highlighting the feasibility and importance of including a fluid-phase description when models aim to provide accurate predictions of biological tissue responses. As numerous previous studies suggest that tissue hydration plays a central role in maintaining proper mechanical and biological function, robust methods for controlling hydration levels are essential as the field advances in probing the relationship between tissue hydration, aging, injury, and disease.

Assessment of the viscoelastic mechanical properties of the porcine optic nerve head using micromechanical testing and finite element modeling

Optic nerve head (ONH) biomechanics is centrally involved in the pathogenesis of glaucoma, a blinding ocular condition often characterized by elevation and fluctuation of the intraocular pressure and resulting loads on the ONH. Further, tissue viscoelasticity is expected to strongly influence the mechanical response of the ONH to mechanical loading, yet the viscoelastic mechanical properties of the ONH remain unknown. To determine these properties, we conducted micromechanical testing on porcine ONH tissue samples, coupled with finite element modeling based on a mixture model consisting of a biphasic material with a viscoelastic solid matrix. Our results provide a detailed description of the viscoelastic properties of the porcine ONH at each of its four anatomical quadrants (i.e., nasal, superior, temporal, and inferior). We showed that the ONH's viscoelastic mechanical response can be explained by a dual mechanism of fluid flow and solid matrix viscoelasticity, as is common in other soft tissues. We obtained porcine ONH properties as follows: matrix Young's modulus E=1.895[1.056,2.391] kPa (median [min., max.]), Poisson's ratio ν=0.142[0.060,0.312], kinetic time-constant τ=214[89,921] sec, and hydraulic permeability k=3.854×10^-1[3.457×10^-2,9.994×10^-1] mm⁴/(N.sec). These values can be used to design and fabricate physiologically appropriate ex vivo test environments (e.g., 3D cell culture) to further understand glaucoma pathophysiology. STATEMENT OF SIGNIFICANCE: Optic nerve head (ONH) biomechanics is an important aspect of the pathogenesis of glaucoma, the leading cause of irreversible blindness. The ONH experiences time-varying loads, yet the viscoelastic behavior of this tissue has not been characterized. Here, we measure the time-dependent response of the ONH in porcine eyes and use mechanical modeling to provide time-dependent mechanical properties of the ONH. This information allows us to identify time-varying stimuli in vivo which have timescales matching the characteristic response times of the ONH, and can also be used to design and fabricate ex vivo 3D cultures to study glaucoma pathophysiology in a physiologically relevant environment, enabling the discovery of new generations of glaucoma medications focusing on neuroprotection.

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.

Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

The importance of intervertebral disc material model on the prediction of mechanical function of the cervical spine

BACKGROUND

Linear elastic, hyperelastic, and multiphasic material constitutive models are frequently used for spinal intervertebral disc simulations. While the characteristics of each model are known, their effect on spine mechanical response requires a careful investigation. The use of advanced material models may not be applicable when material constants are not available, model convergence is unlikely, and computational time is a concern. On the other hand, poor estimations of tissue's mechanical response are likely if the spine model is oversimplified. In this study, discrepancies in load response introduced by material models will be investigated.

METHODS

Three fiber-reinforced C2-C3 disc models were developed with linear elastic, hyperelastic, and biphasic behaviors. Three different loading modes were investigated: compression, flexion and extension in quasi-static and dynamic conditions. The deformed disc height, disc fluid pressure, range of motion, and stresses were compared.

RESULTS

Results indicated that the intervertebral disc material model has a strong effect on load-sharing and disc height change when compression and flexion were applied. The predicted mechanical response of three models under extension had less discrepancy than its counterparts under flexion and compression. The fluid-solid interaction showed more relevance in dynamic than quasi-static loading conditions. The fiber-reinforced linear elastic and hyperelastic material models underestimated the load-sharing of the intervertebral disc annular collagen fibers.

CONCLUSION

This study confirmed the central role of the disc fluid pressure in spinal load-sharing and highlighted loading conditions where linear elastic and hyperelastic models predicted energy distribution different than that of the biphasic model.

Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes

Probing mechanical properties of cells has been identified as a means to infer information on their current state, e.g. with respect to diseases or differentiation. Oocytes have gained particular interest, since mechanical parameters are considered potential indicators of the success of in vitro fertilisation procedures. Established tests provide the structural response of the oocyte resulting from the material properties of the cell's components and their disposition. Based on dedicated experiments and numerical simulations, we here provide novel insights on the origin of this response. In particular, polarised light microscopy is used to characterise the anisotropy of the zona pellucida, the outermost layer of the oocyte composed of glycoproteins. This information is combined with data on volumetric changes and the force measured in relaxation/cyclic, compression/indentation experiments to calibrate a multi-phasic hyper-viscoelastic model through inverse finite element analysis. These simulations capture the oocyte's overall force response, the distinct volume changes observed in the zona pellucida, and the structural alterations interpreted as a realignment of the glycoproteins with applied load. The analysis reveals the presence of two distinct timescales, roughly separated by three orders of magnitude, and associated with a rapid outflow of fluid across the external boundaries and a long-term, progressive relaxation of the glycoproteins, respectively. The new results allow breaking the overall response down into the contributions from fluid transport and the mechanical properties of the zona pellucida and ooplasm. In addition to the gain in fundamental knowledge, the outcome of this study may therefore serve an improved interpretation of the data obtained with current methods for mechanical oocyte characterisation.

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.

A biphasic multilayer computational model of human skin

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin’s histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

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.

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

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

Effect of aggrecan degradation on the nanomechanics of hyaluronan in extra-fibrillar matrix of annulus fibrosus: A molecular dynamics investigation

Intervertebral Disc (IVD) Degeneration is one of the primary causes of low back pain among the adult population - the most significant cause being the degradation of aggrecan present in the extra-fibrillar matrix (EFM). Aggrecan degradation is closely associated with loss of water content leading to an alteration in the mechanical behaviour of the IVD. The loss in water content has a significant impact on the chemo-mechanical interplay of IVD biochemical constituents at the fundamental level. This work presents a mechanistic understanding of the effect of hydration, closely associated with aggrecan degradation, on the nanoscale mechanical behaviour of the hyaluronan present in the EFM of the Annulus Fibrosus. For this purpose, explicit three-dimensional molecular dynamics analyses of tensile and compressive tests are performed on a representative atomistic model of the hyaluronan present in the EFM. To account for the degradation of aggrecan, hydration levels are varied from 0 to 75% by weight of water. Analyses show that an increase in the hydration levels decreases the elastic modulus of hyaluronan in tension from ~4.6 GPa to ~2.1 GPa. On the other hand, the increase in hydration level increases the elastic moduli in axial compression from ~1.6 GPa in un-hydrated condition to ~6 GPa in 50% hydrated condition. But as the hydration levels increase to 75%, the elastic modulus reduces to ~3.5 GPa signifying a shift in load-bearing characteristic, from the solid hyaluronan component to the fluid component. Furthermore, analyses show a reduction in the intermolecular energy between hyaluronan and water, under axial tensile loading, indicating a nanoscale intermolecular debonding between hyaluronan and water molecules. This is attributed to the ability of hyaluronan to form stabilizing intra-molecular hydrogen bonds between adjacent residues. Compressive loading, on the other hand, causes intensive coiling of hyaluronan molecule, which traps more water through hydrogen bonding and aids in bearing compressive loads. Overall, study shows that hydration level has a strong influence on the atomistic level interactions between hyaluronan molecules and hyaluronan and water molecules in the EFM which influences the nanoscale mechanics of the Annulus Fibrosus.

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.

On the compressibility and poroelasticity of human and murine skin

A total of 37 human and 33 murine skin samples were subjected to uniaxial monotonic, cyclic, and relaxation experiments. Detailed analysis of the three-dimensional kinematic response showed that skin volume is significantly reduced as a consequence of a tensile elongation. This behavior is most pronounced in monotonic but persists in cyclic tests. The dehydration associated with volume loss depends on the osmolarity of the environment, so that tension relaxation changes as a consequence of modifying the ionic strength of the environmental bath. Similar to ex vivo observations, complementary in vivo stretching experiments on human volar forearms showed strong in-plane lateral contraction. A biphasic homogenized model is proposed which allows representing all relevant features of the observed mechanical response.

Tear resistance of soft collagenous tissues

Fracture toughness characterizes the ability of a material to maintain a certain level of strength despite the presence of a macroscopic crack. Understanding this tolerance for defects in soft collagenous tissues (SCT) has high relevance for assessing the risks of fracture after cutting, perforation or suturing. Here we investigate the peculiar toughening mechanisms of SCT through dedicated experiments and multi-scale simulations, showing that classical concepts of fracture mechanics are inadequate to quantify and explain the high defect tolerance of these materials. Our results demonstrate that SCT strength is only modestly reduced by defects as large as several millimeters. This defect tolerance is achieved despite a very narrow process zone at the crack tip and even for a network of brittle fibrils. The fracture mechanics concept of tearing energy fails in predicting failure at such defects, and its magnitude is shown to depend on the chemical potential of the liquid environment.

On incorporating osmotic prestretch/prestress in image-driven finite element simulations of cartilage

Medical imaging performed in vivo captures geometries under Donnan osmotic loading, even when the articulating joint is otherwise mechanically unloaded. Hence patient-specific finite element (FE) models constructed from such medical images of cartilage represent osmotically induced prestretched/prestressed states. When applying classical modeling approaches to patient-specific simulations of cartilage a theoretical inconsistency arises: the in-vivo imaged geometry (used to construct the model) is not an unloaded, stress-free reference configuration. Furthermore when fitting nonlinear constitutive models that include osmotic swelling (to obtain material parameters), if one assumes that experimental data-generated from osmotically loaded cartilage-begin from a stress-free reference configuration the fitted stress-stretch relationship (parameters) obtained will actually describe a different behavior. In this study we: (1) establish a practical computational method to include osmotically induced prestretch/prestress in image-driven simulations of cartilage; and (2) investigate the influence of considering the prestretched/prestressed state both when fitting fiber-reinforced, biphasic constitutive models of cartilage that include osmotic swelling and when simulating cartilage responses. Our results highlight the importance of determining the prestretched/prestressed state within cartilage induced by osmotic loading in the imaged configuration prior to solving boundary value problems of interest. With our new constitutive model and modeling methods, we aim to improve the fidelity of FE-based, patient-specific biomechanical simulations of joints and cartilage. Improved simulations can provide medical researchers with new information often unavailable in a clinical setting, information that may contribute to better insight into the pathophysiology of cartilage diseases.

Influence of the pericellular and extracellular matrix structural properties on chondrocyte mechanics

Understanding the mechanical factors that drive the biological responses of chondrocytes is central to our interpretation of the cascade of events that lead to osteoarthritic changes in articular cartilage. Chondrocyte mechanics is complicated by changes in tissue properties that can occur as osteoarthritis (OA) progresses and by the interaction between macro-scale, tissue level, properties, and micro-scale pericellular matrix (PCM) and local extracellular matrix (ECM) properties, both of which cannot be easily studied using in vitro systems. Our objective was to study the influence of macro- and micro-scale OA-associated structural changes on chondrocyte strains. We developed a multi-scale finite element model of articular cartilage subjected to unconfined loading, for the following three conditions: (i) normal articular cartilage, (ii) OA cartilage (where macro and micro-scale changes in collagen content, matrix modulus, and permeability were modeled), and (iii) early-stage OA cartilage (where only micro-scale changes in matrix modulus were modeled). In the macro-scale model, we found that a depth-dependent strain field was induced in both healthy and OA cartilage and that the middle and superficial zones of OA cartilage had increased tensile and compressive strains. At the micro-scale, chondrocyte shear strains were sensitive to PCM and local ECM properties. In the early-OA model, micro-scale spatial softening of PCM and ECM resulted in a substantial increase (30%) of chondrocyte shear strain, even with no structural changes in macro-scale tissue properties. Our study provides evidence that micromechanical changes at the cellular level may affect chondrocyte activities before macro-scale degradations at the tissue level become apparent. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:721-729, 2018.

A study of the damage behaviour of porcine intervertebral discs in a bioreactor environment

The intervertebral discs are cartilaginous, articulating structures that lie between vertebral bodies, allowing flexibility, transmission, modification, and also distribution of the forces to the spinal column. Disc degeneration is characterised by progressive loss of disc height and exaggerated radial bulging. Therefore, the spine becomes shorter, stiffer, and less mobile. In the last several decades, there is a strong need for a tissue engineering strategy that alleviates pain and restores spine function by directly addressing the underlying biological causes of disc degeneration. Numerous studies that are currently showing potential have been conducted on developing regenerative and reparative strategies for treating this condition. In this study, to numerically describe the anisotropic mechanical damage behaviour of discs, the pseudo-elastic damage model was applied. To experimentally picture the biomechanical response of discs and to study the damage mechanisms as well as the spinal disc herniation, a special bioreactor was evolved. The specimens were obtained from pigs aged six months. A total of eight functional spine units were taken from porcine lumbar spines (L1-L2). Firstly, the experiments were performed by using long-term cyclic uniaxial compression tests. Secondly, the mean value of experimental results with consideration of the different shapes and sizes of the samples was calculated. Afterwards, the experimental results were compared with outcomes of numerical simulations.

An Anisotropic Multiphysics Model for Intervertebral Disk

Intervertebral disk (IVD) is the largest avascular structure in human body, consisting of three types of charged hydrated soft tissues. Its mechanical behavior is nonlinear and anisotropic, due mainly to nonlinear interactions among different constituents within tissues. In this study, a more realistic anisotropic multiphysics model was developed based on the continuum mixture theory and employed to characterize the couplings of multiple physical fields in the IVD. Numerical simulations demonstrate that this model is capable of systematically predicting the mechanical and electrochemical signals within the disk under various loading conditions, which is essential in understanding the mechanobiology of IVD.

A computational spinal motion segment model incorporating a matrix composition-based model of the intervertebral disc

The extracellular matrix of the intervertebral disc is subjected to changes with age and degeneration, affecting the biomechanical behaviour of the spine. In this study, a finite element model of a generic spinal motion segment that links spinal biomechanics and intervertebral disc biochemical composition was developed. The local mechanical properties of the tissue were described by the local matrix composition, i.e. fixed charge density, amount of water and collagen and their organisation. The constitutive properties of the biochemical constituents were determined by fitting numerical responses to experimental measurements derived from literature. This general multi-scale model of the disc provides the possibility to evaluate the relation between local disc biochemical composition and spinal biomechanics.

Multiphasic modelling of bone-cement injection into vertebral cancellous bone

Percutaneous vertebroplasty represents a current procedure to effectively reinforce osteoporotic bone via the injection of bone cement. This contribution considers a continuum-mechanically based modelling approach and simulation techniques to predict the cement distributions within a vertebra during injection. To do so, experimental investigations, imaging data and image processing techniques are combined and exploited to extract necessary data from high-resolution μCT image data. The multiphasic model is based on the Theory of Porous Media, providing the theoretical basis to describe within one set of coupled equations the interaction of an elastically deformable solid skeleton, of liquid bone cement and the displacement of liquid bone marrow. The simulation results are validated against an experiment, in which bone cement was injected into a human vertebra under realistic conditions. The major advantage of this comprehensive modelling approach is the fact that one can not only predict the complex cement flow within an entire vertebra but is also capable of taking into account solid deformations in a fully coupled manner. The presented work is the first step towards the ultimate and future goal of extending this framework to a clinical tool allowing for pre-operative cement distribution predictions by means of numerical simulations.

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

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

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot.

Elastic, permeability and swelling properties of human intervertebral disc tissues: A benchmark for tissue engineering

The aim of functional tissue engineering is to repair and replace tissues that have a biomechanical function, i.e., connective orthopaedic tissues. To do this, it is necessary to have accurate benchmarks for the elastic, permeability, and swelling (i.e., biphasic-swelling) properties of native tissues. However, in the case of the intervertebral disc, the biphasic-swelling properties of individual tissues reported in the literature exhibit great variation and even span several orders of magnitude. This variation is probably caused by differences in the testing protocols and the constitutive models used to analyze the data. Therefore, the objective of this study was to measure the human lumbar disc annulus fibrosus (AF), nucleus pulposus (NP), and cartilaginous endplates (CEP) biphasic-swelling properties using a consistent experimental protocol and analyses. The testing protocol was composed of a swelling period followed by multiple confined compression ramps. To analyze the confined compression data, the tissues were modeled using a biphasic-swelling model, which augments the standard biphasic model through the addition of a deformation-dependent osmotic pressure term. This model allows considering the swelling deformations and the contribution of osmotic pressure in the analysis of the experimental data. The swelling stretch was not different between the disc regions (AF: 1.28±0.16; NP: 1.73±0.74; CEP: 1.29±0.26), with a total average of 1.42. The aggregate modulus (Ha) of the extra-fibrillar matrix was higher in the CEP (390kPa) compared to the NP (100kPa) or AF (30kPa). The permeability was very different across tissue regions, with the AF permeability (64 E(-16)m(4)/Ns) higher than the NP and CEP (~5.5 E(-16)m(4)/Ns). Additionally, a normalized time-constant (3000s) for the stress relaxation was similar for all the disc tissues. The properties measured in this study are important as benchmarks for tissue engineering and for modeling the disc's mechanical behavior and transport.

Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent

The mechanical behavior of the annulus fibrosus (AF) of the intervertebral disc can be modeled as a mixture of fibers, extra-fibrillar matrix (EFM), ions, and fluid. However, the properties of the EFM have not been measured directly. We measured mechanical properties of the human EFM at several locations, determined the effect of age and degeneration, and evaluated whether changes in EFM properties correspond to AF compositional changes. EFM mechanical properties were measured using a method that combines osmotic loading and confined compression. AF samples were dissected from several locations, and mechanical properties were correlated with age, degeneration, and composition. EFM modulus was found to range between 10 and 50 kPa, increasing nonlinearly with compression magnitude and being highest in the AF outer-anterior region. EFM properties were not correlated with composition or degeneration. However, the EFM modulus, its relative contribution to tissue modulus, and model parameters were correlated with age. These measurements will result in more accurate predictions of deformations in the intervertebral disc. Additionally, parameters such as permeability and diffusivity used for biotransport analysis of glucose and other solutes depend on EFM deformation. Consequently, the accuracy of biotransport simulations will be greatly improved.

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

Degenerative Disc Disease (DDD) is one of the largest health problems faced worldwide, based on lost working time and associated costs. By means of this motivation, this work aims to evaluate a biomimetic Finite Element (FE) model of the Intervertebral Disc (IVD). Recent studies have emphasized the importance of an accurate biomechanical modeling of the IVD, as it is a highly complex multiphasic medium. Poroelastic models of the disc are mostly implemented in commercial finite element packages with limited access to the algorithms. Therefore, a novel poroelastic formulation implemented on a home-developed open source FE solver is briefly addressed throughout this paper. The combination of this formulation with biphasic osmotic swelling behavior is also taken into account. Numerical simulations were devoted to the analysis of the non-degenerated human lumbar IVD time-dependent behavior. The results of the tests performed for creep assessment were inside the scope of the experimental data, with a remarkable improvement of the numerical accuracy when compared with previously published results obtained with ABAQUS(®). In brief, this in-development open-source FE solver was validated with literature experimental data and aims to be a valuable tool to study the IVD biomechanics and DDD mechanisms.

What have we learned from finite element model studies of lumbar intervertebral discs in the past four decades?

Finite element analysis is a powerful tool routinely used to study complex biological systems. For the last four decades, the lumbar intervertebral disc has been the focus of many such investigations. To understand the disc functional biomechanics, a precise knowledge of the disc mechanical, structural and biochemical environments at the microscopic and macroscopic levels is essential. In response to this need, finite element model studies have proven themselves as reliable and robust tools when combined with in vitro and in vivo measurements. This paper aims to review and discuss some salient findings of reported finite element simulations of lumbar intervertebral discs with special focus on their relevance and implications in disc functional biomechanics. Towards this goal, the earlier investigations are presented, discussed and summarized separately in three distinct groups of elastic, multi-phasic transient and transport model studies. The disc overall response as well as the relative role of its constituents are markedly influenced by loading rate, magnitude, combinations/preloads and posture. The nucleus fluid content and pressurizing capacity affect the disc compliance, annulus strains and failure sites/modes. Biodynamics of the disc is affected by not only the excitation characteristics but also preloads, existing mass and nucleus condition. The role of fluid pressurization and collagen fiber stiffening diminish with time during diurnal loading. The endplates permeability influences the time-dependent response of the disc in both loaded and unloaded recovery phases. The transport of solutes is substantially influenced by the disc size, tissue diffusivity and endplates permeability.

In vitro electro-mechanical characterization of human knee articular cartilage of different degeneration levels: a comparison with ICRS and Mankin scores

In the present study, the electro-mechanical properties of human knee articular cartilage were measured in vitro. An arthroscopic measurement tool was used to measure streaming potential integral (SPI), after which creep indentation tests were performed. Additionally, degradation level of the tissue was determined in accordance with the International Cartilage Repair Society (ICRS score), and hematoxylin/eosin and safranin O staining were performed to determine the Mankin score. Mechanical test results were evaluated both analytically and by means of a finite-element-optimized parameter identification procedure. The SPI was then correlated with poroelastic E modulus (r=0.563, p<0.008, n=22), natural logarithm of hydraulic permeability (r=0.374, p<0.095, n=22) and cartilage degeneration scores (ICRS and Mankin) (r=-0.749, p<0.000, n=22 and r=-0.409, p<0.059, n=22 respectively).

IONIC OSMOTIC EFFECTS INCREASE FLUID FLOW DURING PERMEATION TESTS

Fluid flow is essential for the transport of metabolites to, from and within the intervertebral disc (IVD). By applying quadriphasic mixture theory experimentally, this study relates fluid flow within the bovine nucleus pulposus (NP) to the applied fluid pressure gradients and fixed charge and mobile ion concentration gradients. 24 plugs of NP tissue (diameter 10 mm, height 1020 ± 122 μm (mean ± SD)), orientated in the axial direction, were harvested from bovine tail discs. The plugs were permeated with either; 0 M NaCl , 0.15 M NaCl or 3 M NaCl solutions by subjecting them to 30, 45 and 60 kPa fluid pressure gradients applied in a random sequence. The hypertonic solution was assumed to render all non-fluid pressure gradients negligible, whilst the hypotonic solution was assumed to render the mobile ion concentration gradient negligible. The effects of these gradients on fluid flow were expressed as a percentage of the applied fluid pressure. Fluid velocity was significantly increased through the tissue in the isotonic case compared to the hypertonic case by up to 55% of the applied fluid pressure. The fixed charges accounted for between 26% and 43% and the mobile ion gradient responsible for 12–26% of this increased fluid flow. These results highlight the importance of using a constitutive equation for permeability that includes mobile ions and fixed charges as separate phases when modeling cartilaginous tissue in order to better describe fluid flow, and thus convective transfer of metabolites, within the tissue.