Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition

Sensitivity of cartilage mechanical behaviour to spatial variations in material properties

Articular cartilage tissue exhibits a spatial dependence in material properties that govern mechanical behaviour. A mathematical model of cartilage tissue under one dimensional confined compression testing is developed for normal tissue that takes account of these variations in material properties. Modifications to the model representative of a selection of mechanisms driving osteoarthritic cartilage are proposed, allowing application of the model to both physiological and pathophysiological, osteoarthritic tissue. Incorporating spatial variations into the model requires the specification of more parameters than are required in the absence of these variations. A global sensitivity analysis of these parameters is implemented to identify the dominant mechanisms of mechanical response, in normal and osteoarthritic cartilage tissue, to both static and dynamic loading. The most sensitive parameters differ between dynamic and static mechanics of the cartilage, and also differ between physiological and osteoarthritic pathophysiological cartilage. As a consequence changes in cartilage mechanics in response to alterations in cartilage structure are predicted to be contingent on the nature of loading and the health, or otherwise, of the cartilage. In particular the mechanical response of cartilage, especially deformation, is predicted to be much more sensitive to cartilage stiffness in the superficial zone given the onset of osteoarthritic changes to material properties, such as superficial zone increases in permeability and reductions in fixed charge. In turn this indicates that any degenerative changes in the stiffness associated with the superficial cartilage collagen mesh are amplified if other elements of osteoarthritic disease are present, which provides a suggested mechanism-based explanation for observations that the range of mechanical parameters representative of normal and osteoarthritic tissue can overlap substantially.

Unveiling interactions between intervertebral disc morphologies and mechanical behavior through personalized finite element modeling

Introduction: Intervertebral Disc (IVD) Degeneration (IDD) is a significant health concern, potentially influenced by mechanotransduction. However, the relationship between the IVD phenotypes and mechanical behavior has not been thoroughly explored in local morphologies where IDD originates. This work unveils the interplays among morphological and mechanical features potentially relevant to IDD through Abaqus UMAT simulations. Methods: A groundbreaking automated method is introduced to transform a calibrated, structured IVD finite element (FE) model into 169 patient-personalized (PP) models through a mesh morphing process. Our approach accurately replicates the real shapes of the patient's Annulus Fibrosus (AF) and Nucleus Pulposus (NP) while maintaining the same topology for all models. Using segmented magnetic resonance images from the former project MySpine, 169 models with structured hexahedral meshes were created employing the Bayesian Coherent Point Drift++ technique, generating a unique cohort of PP FE models under the Disc4All initiative. Machine learning methods, including Linear Regression, Support Vector Regression, and eXtreme Gradient Boosting Regression, were used to explore correlations between IVD morphology and mechanics. Results: We achieved PP models with AF and NP similarity scores of 92.06\% and 92.10\% compared to the segmented images. The models maintained good quality and integrity of the mesh. The cartilage endplate (CEP) shape was represented at the IVD-vertebra interfaces, ensuring personalized meshes. Validation of the constitutive model against literature data showed a minor relative error of 5.20%. Discussion: Analysis revealed the influential impact of local morphologies on indirect mechanotransduction responses, highlighting the roles of heights, sagittal areas, and volumes. While the maximum principal stress was influenced by morphologies such as heights, the disc's ellipticity influenced the minimum principal stress. Results suggest the CEPs are not influenced by their local morphologies but by those of the AF and NP. The generated free-access repository of individual disc characteristics is anticipated to be a valuable resource for the scientific community with a broad application spectrum.

Depth-Dependent Strain Model (1D) for Anisotropic Fibrils in Articular Cartilage

The mechanical response of articular cartilage (AC) under compression is anisotropic and depth-dependent. AC is osmotically active, and its intrinsic osmotic swelling pressure is balanced by its collagen fibril network. This mechanism requires the collagen fibers to be under a state of tensile pre-strain. A simple mathematical model is used to explain the depth-dependent strain calculations observed in articular cartilage under 1D axial compression (perpendicular to the articular surface). The collagen fibers are under pre-strain, influenced by proteoglycan concentration (fixed charged density, FCD) and collagen stiffness against swelling stress. The stiffness is introduced in our model as an anisotropic modulus that varies with fibril orientation through tissue depth. The collagen fibers are stiffer to stretching parallel to their length than perpendicular to it; when combined with depth-varying FCD, the model successfully predicts how tissue strains decrease with depth during compression. In summary, this model highlights that the mechanical properties of cartilage depend not only on proteoglycan concentration but also on the intrinsic properties of the pre-strained collagen network. These properties are essential for the proper functioning of articular cartilage.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Knee joint biomechanics and cartilage damage prediction during landing: A hybrid MD-FE-musculoskeletal modeling

Understanding the mechanics behind knee joint injuries and providing appropriate treatment is crucial for improving physical function, quality of life, and employability. In this study, we used a hybrid molecular dynamics-finite element-musculoskeletal model to determine the level of loads the knee can withstand when landing from different heights (20, 40, 60 cm), including the height at which cartilage damage occurs. The model was driven by kinematics-kinetics data of asymptomatic subjects at the peak loading instance of drop landing. Our analysis revealed that as landing height increased, the forces on the knee joint also increased, particularly in the vastus muscles and medial gastrocnemius. The patellar tendon experienced more stress than other ligaments, and the medial plateau supported most of the tibial cartilage contact forces and stresses. The load was mostly transmitted through cartilage-cartilage interaction and increased with landing height. The critical height of 126 cm, at which cartilage damage was initiated, was determined by extrapolating the collected data using an iterative approach. Damage initiation and propagation were mainly located in the superficial layers of the tibiofemoral and patellofemoral cartilage. Finally, this study provides valuable insights into the mechanisms of landing-associated cartilage damage and could help limit joint injuries and improve training programs.

Characterizing site-specific mechanical properties of knee cartilage with indentation-relaxation maps and machine learning

Knee cartilage experiences site-specific focal lesion and degeneration, which is likely associated with tissue inhomogeneity and nonuniform mechanical stimuli in the joint, for which a complete picture remains to be depicted. The present study aimed to develop a methodology to quantify knee cartilage inhomogeneity using porcine knee specimens. Automated indentation-relaxation and needle probing were performed on fully intact cartilage to obtain data that essentially represent continuous distributions of cartilage properties in the knee. Machine learning was then introduced to approximate the tissue inhomogeneity with several regions via clusters of indentation locations, and finite element modeling was used to obtain poromechanical properties for each region using indentation-relaxation and thickness data. Significant region dependence was established from the full time-dependent mechanical response. Seventeen regions, or clusters, were found to best approximate the site-specific poromechanical properties of articular cartilage for femoral groove, lateral and medial condyles and tibial plateaus, after up to eight clusters were tested for each of the five cartilage sections. The region partitions recommended, and tissue properties acquired would facilitate implementation of tissue inhomogeneity in future applications, e.g., contact modeling of the knee joint. The results obtained from 14 porcine knees revealed interesting region differences, for example, the two condyles have the same effective stiffness when responding to slowly applied mechanical loadings but substantially lower stiffness in the medial condyle when responding to fast loadings. This mechanical behavior may be associated with the fact that medial femoral cartilage is more prone to focal lesions than the lateral one.

Minimum design requirements for a poroelastic mimic of articular cartilage

The exceptional functional performance of articular cartilage (load-bearing and lubrication) is attributed to its poroelastic structure and resulting interstitial fluid pressure. Despite this, there remains no engineered cartilage repair material capable of achieving physiologically relevant poroelasticity. In this work we develop in silico models to guide the design approach for poroelastic mimics of articular cartilage. We implement the constitutive models in FEBio, a PDE solver for multiphasic mechanics problems in biological and soft materials. We investigate the influence of strain rate, boundary conditions at the contact interface, and fiber modulus on the reaction force and load sharing between the solid and fluid phases. The results agree with the existing literature that when fibers are incorporated the fraction of load supported by fluid pressure is greatly amplified and increases with the fiber modulus. This result demonstrates that a stiff fibrous phase is a primary design requirement for poroelastic mimics of articular cartilage. The poroelastic model is fit to experimental stress-relaxation data from bovine and porcine cartilage to determine if sufficient design constraints have been identified. In addition, we fit experimental data from FiHy™, an engineered material which is claimed to be poroelastic. The fiber-reinforced poroelastic model was able to capture the primary physics of these materials and demonstrates that FiHy™ is beginning to approach a cartilage-like poroelastic response. We also develop a fiber-reinforced poroelastic model with a bonded interface (rigid contact) to fit stress relaxation data from an osteochondral explant and FiHy™ + bone substitute. The model fit quality is similar for both the chondral and osteochondral configurations and clearly captures the first order physics. Based on this, we propose that physiological poroelastic mimics of articular cartilage should be developed under a fiber-reinforced poroelastic framework.

Optimization of In Situ Indentation Protocol to Map the Mechanical Properties of Articular Cartilage

Tissue engineering aims at developing complex composite scaffolds for articular cartilage repair. These scaffolds must exhibit a mechanical behavior similar to the whole osteochondral unit. In situ spherical indentation allows us to map the mechanical behavior of articular cartilage, avoiding removal of the underlying bone tissue. Little is known about the impact of grid spacing, indenter diameter, and induced deformation on the cartilage response to indentation. We investigated the impact of grid spacing (range: a to 3a, where a is the radius of the contact area between cartilage and indenter), indenter diameter (range: 1 to 8 mm), and deformation induced by indentation (constant indentation depth versus constant nominal deformation) on cartilage response. The bias induced by indentations performed in adjacent grid points was minimized with a 3a grid spacing. The cartilage response was indenter-dependent for diameters ranging between 1 and 6 mm with a nominal deformation of 15%. No significant differences were found using 6 mm and 8 mm indenters. Six mm and 8 mm indenters were used to map human articular cartilage with a grid spacing equal to 3a. Instantaneous elastic modulus E₀ was calculated for constant indentation depth and constant nominal deformation. E₀ value distribution did not change significantly by switching the two indenters, while dispersion decreased by 5-6% when a constant nominal deformation was applied. Such an approach was able to discriminate changes in tissue response due to doubling the indentation rate. The proposed procedure seems to reduce data dispersion and properly determine cartilage mechanical properties to be compared with those of complex composite scaffolds.

Multi-fidelity surrogate modeling through hybrid machine learning for biomechanical and finite element analysis of soft tissues

Biomechanical simulation enables medical researchers to study complex mechano-biological conditions, although for soft tissue modeling, it may apply highly nonlinear multi-physics theories commonly implemented by expensive finite element (FE) solvers. This is a significantly time-consuming process on a regular computer and completely inefficient in urgent situations. One remedy is to first generate a dataset of the possible inputs and outputs of the solver in order to then train an efficient machine learning (ML) model, i.e., the supervised ML-based surrogate, replacing the expensive solver to speed up the simulation. But it still requires a large number of expensive numerical samples. In this regard, we propose a hybrid ML (HML) method that uses a reduced-order model defined by the simplification of the complex multi-physics equations to produce a dataset of the low-fidelity (LF) results. The surrogate then has this efficient numerical model and an ML model that should increase the fidelity of its outputs to the level of high-fidelity (HF) results. Based on our empirical tests via a group of diverse training and numerical modeling conditions, the proposed method can improve training convergence for very limited training samples. In particular, while considerable time gains comparing to the HF numerical models are observed, training of the HML models is also significantly more efficient than the purely ML-based surrogates. From this, we conclude that this non-destructive HML implementation may increase the accuracy and efficiency of surrogate modeling of soft tissues with complex multi-physics properties in small data regimes.

Material properties and strain distribution patterns of bovine growth plate cartilage vary with anatomic location and depth

The aim of this study was to assess the bulk material properties and depth-dependent strain distribution of bovine growth plate cartilage. We hypothesized that both moduli and strain distribution are highly depth-, orientation-, and location-dependent. Bovine proximal tibiae (1-month-old) were sliced along the sagittal and coronal planes to create ∼ 4 mm2 samples. Digital image correlation (DIC) was combined with stress relaxation tests for evaluation of bulk modulus (tangent and equilibrium) and depth-dependent strain distribution. A subset of samples was imaged after Col-F staining as well as histological staining (Safranin-O/Fast Green) to evaluate zonal organization and matrix composition. The mean tangent modulus was 4.25 ± 2.46 MPa while the equilibrium modulus was 0.86 ± 0.46 MPa. No significant differences in moduli were found with respect to orientation (sagittal vs coronal face), but sagittal location within the joint was a significant predictor for tangent modulus. Overall moduli values decreased from the periphery to the midline of the joint. Depth-dependent cellular organization, determined by cell density and shape, was highly variable. This heterogeneity may be a biological toughening mechanism. Peak normalized strains were observed most often in the hypertrophic zone. Modulus was significantly lower in the hypertrophic zone as compared to the resting and proliferative zones. This study is the first to evaluate moduli and strain distribution in intact growth plates as a function of depth, orientation, and anatomic location. Future work with growth plate tissue engineering should consider the location- and depth-dependent nature of the native tissue mechanical properties when designing mimetic constructs.

Biomechanical Characteristics of the Knee Joint during Gait in Obese versus Normal Subjects

Knee osteoarthritis (OA) is a growing source of pain and disability. Obesity is the most important avoidable risk factor underlying knee OA. The processes by which obesity impacts osteoarthritis are of tremendous interest to osteoarthritis researchers and physicians, where the joint mechanical load is one of the pathways generally thought to cause or intensify the disease process. In the current work, we developed a hybrid framework that simultaneously incorporates a detailed finite element model of the knee joint within a musculoskeletal model to compute lower extremity muscle forces and knee joint stresses in normal-weight (N) and obese (OB) subjects during the stance phase gait. This model accounts for the synergy between the active musculature and passive structures. In comparing OB subjects and normal ones, forces significantly increased in all muscle groups at most instances of stance. Mainly, much higher activation was computed with lateral hamstrings and medial gastrocnemius. Cartilage contact average pressure was mostly supported by the medial plateau and increased by 22%, with a larger portion of the load transmitted via menisci. This medial compartment experienced larger relative movement and cartilage stresses in the normal subjects and continued to do so with a higher level in the obese subjects. Finally, the developed bioengineering frame and the examined parameters during this investigation might be useful clinically in evaluating the initiation and propagation of knee OA.

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.

Fabrication of a novel 3D scaffold for cartilage tissue repair: In-vitro and in-vivo study

Self-repairing is not an advanced ability of articular cartilage. Tissue engineering has provided a novel way for reconstructing cartilage using natural polymers because of their biocompatibility and bio-functionality. The purpose of cartilage tissue engineering is to design a scaffold with proper pore structure and similar biological and mechanical properties to the native tissue. In this study, porous scaffolds prepared from gelatin, chitosan and silk fibroin were blended with varying ratios. Between the blends of chitosan (C), gelatin (G) and silk fibroin (S), the scaffold with the weight per volume ratio of 2:2:3 (w/v) showed the most favorable and higher certain properties than the other blends. The CGS 2:2:3 scaffold showed the best pore size that is between 100 μm and 300 μm. The water absorption and degradation rate of the CGS 2:2:3 scaffold were found suitable for cartilage tissue engineering. Cell culture study using human chondrocytes showed good cell adhesion and proliferation. To further study the effect of this scaffold on the living tissue, 36 rabbits were randomly assigned to CGS 2:2:3 scaffold with and without seeded chondrocytes and control groups. Hematoxylin and Eosin (H&E), Masson's trichrome (MT), and safranin O (SO) staining showed 65 ± 9.1% new cartilage tissue present in the defect filled with cell-seeded scaffold and most of the cartilaginous tissue was hyaline cartilage, while the control group showed no new cartilage tissue.

Elastic, Dynamic Viscoelastic and Model-Derived Fibril-Reinforced Poroelastic Mechanical Properties of Normal and Osteoarthritic Human Femoral Condyle Cartilage

Osteoarthritis (OA) degrades articular cartilage and weakens its function. Modern fibril-reinforced poroelastic (FRPE) computational models can distinguish the mechanical properties of main cartilage constituents, namely collagen, proteoglycans, and fluid, thus, they can precisely characterize the complex mechanical behavior of the tissue. However, these properties are not known for human femoral condyle cartilage. Therefore, we aimed to characterize them from human subjects undergoing knee replacement and from deceased donors without known OA. Multi-step stress-relaxation measurements coupled with sample-specific finite element analyses were conducted to obtain the FRPE material properties. Samples were graded using OARSI scoring to determine the severity of histopathological cartilage degradation. The results suggest that alterations in the FRPE properties are not evident in the moderate stages of cartilage degradation (OARSI 2-3) as compared with normal tissue (OARSI 0-1). Drastic deterioration of the FRPE properties was observed in severely degraded cartilage (OARSI 4). We also found that the FRPE properties of femoral condyle cartilage related to the collagen network (initial fibril-network modulus) and proteoglycan matrix (non-fibrillar matrix modulus) were greater compared to tibial and patellar cartilage in OA. These findings may inform cartilage tissue-engineering efforts and help to improve the accuracy of cartilage representations in computational knee joint models.

Articular and Artificial Cartilage, Characteristics, Properties and Testing Approaches-A Review

The design and manufacture of artificial tissue for knee joints have been highlighted recently among researchers which necessitates an apt approach for its assessment. Even though most re-searches have focused on specific mechanical or tribological tests, other aspects have remained underexplored. In this review, elemental keys for design and testing artificial cartilage are dis-cussed and advanced methods addressed. Articular cartilage structure, its compositions in load-bearing and tribological properties of hydrogels, mechanical properties, test approaches and wear mechanisms are discussed. Bilayer hydrogels as a niche in tissue artificialization are presented, and recent gaps are assessed.

A Robust Multiscale and Multiphasic Structure-Based Modeling Framework for the Intervertebral Disc

A comprehensive understanding of multiscale and multiphasic intervertebral disc mechanics is crucial for designing advanced tissue engineered structures aiming to recapitulate native tissue behavior. The bovine caudal disc is a commonly used human disc analog due to its availability, large disc height and area, and similarities in biochemical and mechanical properties to the human disc. Because of challenges in directly measuring subtissue-level mechanics, such as in situ fiber mechanics, finite element models have been widely employed in spinal biomechanics research. However, many previous models use homogenization theory and describe each model element as a homogenized combination of fibers and the extrafibrillar matrix while ignoring the role of water content or osmotic behavior. Thus, these models are limited in their ability in investigating subtissue-level mechanics and stress-bearing mechanisms through fluid pressure. The objective of this study was to develop and validate a structure-based bovine caudal disc model, and to evaluate multiscale and multiphasic intervertebral disc mechanics under different loading conditions and with degeneration. The structure-based model was developed based on native disc structure, where fibers and matrix in the annulus fibrosus were described as distinct materials occupying separate volumes. Model parameters were directly obtained from experimental studies without calibration. Under the multiscale validation framework, the model was validated across the joint-, tissue-, and subtissue-levels. Our model accurately predicted multiscale disc responses for 15 of 16 cases, emphasizing the accuracy of the model, as well as the effectiveness and robustness of the multiscale structure-based modeling-validation framework. The model also demonstrated the rim as a weak link for disc failure, highlighting the importance of keeping the cartilage endplate intact when evaluating disc failure mechanisms in vitro. Importantly, results from this study elucidated important fluid-based load-bearing mechanisms and fiber-matrix interactions that are important for understanding disease progression and regeneration in intervertebral discs. In conclusion, the methods presented in this study can be used in conjunction with experimental work to simultaneously investigate disc joint-, tissue-, and subtissue-level mechanics with degeneration, disease, and injury.

A backward pre-stressing algorithm for efficient finite element implementation of in vivo material and geometrical parameters into fibril-reinforced mixture models of articular cartilage

Classical continuum mechanics has been widely used for implementation of the material models of articular cartilage (AC) mainly with the aid of the finite element (FE) method, which, in many cases, considers the stress-free configuration as the initial configuration. On the contrary, the AC experimental tests typically begin with the pre-stressed state of both material and geometrical properties. Indeed, imposing the initial pre-stress onto AC models with the in vivo values as the initial state would result in nonphysiologically expansion of the FE mesh due to the soft nature of AC. This change in the model configuration can also affect the material behavior kinematically in the mixture models of cartilage due to the intrinsic compressibility of the tissue. Although several different fixed-point backward algorithms, as the most straightforward pre-stressing methods, have already been developed to incorporate these initial conditions into FE models iteratively, such methods focused merely on the geometrical parameters, and they omitted the material variations of the anisotropic mixture models of AC. To address this issue, we propose an efficient algorithm generalizing the backward schemes to restore stress-free conditions by optimizing both the involving variables, and we hypothesize that it can affect the results considerably. To this end, a comparative simulation was implemented on an advanced and validated multiphasic model by the new and conventional algorithms. The results are in support of the hypothesis, as in our illustrative general AC model, the material parameters experienced a maximum error of 16% comparing to the initial in vivo data when the older algorithm was employed, and it led to a maximum variation of 44% in the recorded stresses comparing to the results of the new method. We conclude that our methodology enhanced the model fidelity, and it is applicable in most of the existing FE solvers for future mixture studies with accurate stress distributions.

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.

A serial multiparametric quantitative magnetic resonance imaging study to assess proteoglycan depletion of human articular cartilage and its effects on functionality

Water, collagen, and proteoglycans determine articular cartilage functionality. If altered, susceptibility to premature degeneration is increased. This study investigated the effects of enzymatic proteoglycan depletion on cartilage functionality as assessed by advanced Magnetic Resonance Imaging (MRI) techniques under standardized loading. Lateral femoral condylar cartilage-bone samples from patients undergoing knee replacement (n = 29) were serially imaged by Proton Density-weighted and T1, T1ρ, T2, and T2* mapping sequences on a clinical 3.0 T MRI scanner (Achieva, Philips). Using pressure-controlled indentation loading, samples were imaged unloaded and quasi-statically loaded to 15.1 N and 28.6 N, and both before and after exposure to low-concentrated (LT, 0.1 mg/mL, n = 10) or high-concentrated trypsin (HT, 1.0 mg/mL, n = 10). Controls were not treated (n = 9). Responses to loading were assessed for the entire sample and regionally, i.e. sub- and peri-pistonally, and zonally, i.e. upper and lower sample halves. Trypsin effects were quantified as relative changes (Δ), analysed using appropriate statistical tests, and referenced histologically. Histological proteoglycan depletion was reflected by significant sub-pistonal decreases in T1 (p = 0.003) and T2 (p = 0.008) after HT exposure. Loading-induced changes in T1ρ and T2* were not related. In conclusion, proteoglycan depletion alters cartilage functionality and may be assessed using serial T1 and T2 mapping under loading.

Heterogeneous matrix deposition in human tissue engineered cartilage changes the local shear modulus and resistance to local construct buckling

Human tissue engineered cartilage is a promising solution for focal cartilage defects, but these constructs do not have the same local mechanical properties as native tissue. Most clinically relevant engineered cartilage constructs seed human chondrocytes onto a collagen scaffold, which buckles at low loads and strains. This buckling creates local regions of high strain that could cause cell death and damage the engineered tissue. Since human tissue engineered cartilage is commonly grown in-vivo prior to implantation, new matrix deposition could improve the local implant mechanics and prevent local tissue buckling. However, the relationship between local biochemical composition and the local mechanics or local buckling probability has never been quantified. Therefore, this study correlated the local biochemical composition of human tissue engineered cartilage constructs using Fourier transform infrared spectroscopy (FTIR) with the local shear modulus and local buckling probability. The local shear modulus and local buckling probability were obtained using a confocal elastography technique. The local shear modulus increased with increases in local aggrecan content in the interior region (inside the scaffold). A minimum amount of aggrecan was required to prevent local construct buckling at physiologic strains. Since the original scaffold was primarily composed of collagen, increases in collagen content due to new matrix deposition was minimal and had little effect on the mechanical properties. Thus, we concluded that aggrecan deposition inside the scaffold pores is the most effective way to improve the mechanical function and prevent local tissue damage in human tissue engineered cartilage constructs.

The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models

The Flory–Rehner theoretical description of the free energy in a hydrogel swelling model can be broken into two swelling components: the mixing energy and the ionic energy. Conventionally for ionized gels, the ionic energy is characterized as the main contributor to swelling and, therefore, the mixing energy is assumed negligible. However, this assumption is made at the equilibrium state and ignores the dynamics of gel swelling. Here, the influence of the mixing energy on swelling ionized gels is quantified through numerical simulations on sodium polyacrylate using a Mixed Hybrid Finite Element Method. For univalent and divalent solutions, at initial porosities greater than 0.90, the contribution of the mixing energy is negligible. However, at initial porosities less than 0.90, the total swelling pressure is significantly influenced by the mixing energy. Therefore, both ionic and mixing energies are required for the modeling of sodium polyacrylate ionized gel swelling. The numerical model results are in good agreement with the analytical solution as well as experimental swelling tests.

Cartilage mechanical tests: Evolution of current standards for cartilage repair and tissue engineering. A literature review

BACKGROUND

Repair procedures and tissue engineering are solutions available in the clinical practice for the treatment of damaged articular cartilage. Regulatory bodies defined the requirements that any products, intended to regenerate cartilage, should have to be applied. In order to verify these requirements, the Food and Drug Administration (FDA, USA) and the International Standard Organization (ISO) indicated some Standard tests, which allow evaluating, in a reproducible way, the performances of scaffolds/treatments for cartilage tissue regeneration.

METHODS

A review of the literature about cartilage mechanical characterization found 394 studies, from 1970 to date. They were classified by material (simulated/animal/human cartilage) and method (theoretical/applied; static/dynamic; standard/non-standard study), and analyzed by nation and year of publication.

FINDINGS

While Standard methods for cartilage mechanical characterization still refer to studies developed in the eighties, expertise and interest on cartilage mechanics research are evolving continuously and internationally, with studies both in vitro - on human and animal tissues - and in silico, dealing with tissue function and modelling, using static and dynamic loading conditions.

INTERPRETATION

there is a consensus on the importance of mechanical characterization that should be considered to evaluate cartilage treatments. Still, relative Standards need to be updated to describe advanced constructs and procedures for cartilage regeneration in a more exhaustive way. The use of the more complex, fibre-reinforced biphasic model, instead of the standard simple biphasic model, to describe cartilage response to loading, and the standardisation of dynamic tests can represent a first step in this direction.

Depth-dependent ratcheting strains of young and adult articular cartilages by experiments and predictions

Background

Ratcheting strain is produced due to the repeated accumulation of compressive strain in cartilage and may be a precursor to osteoarthritis. The aim of this study was to investigate the ratcheting behaviors of young and adult articular cartilages under cyclic compression by experiments and theoretical predictions.

Methods

A series of uniaxial cyclic compression tests were conducted for young and adult cartilage, and the effects of different loading conditions on their ratcheting behaviors were probed. A theoretical ratcheting model was constructed and applied to predict the ratcheting strains of young and adult cartilages with different loading conditions.

Results

Ratcheting strains of young and adult cartilages rapidly increased at the initial stage, followed by a slower increase in subsequent stages. The strain accumulation value and its rate for young cartilage were greater than them for adult cartilage. The ratcheting strains of the two groups of cartilage samples decreased with increasing stress rate, while they increased with increasing stress amplitude. As the stress amplitude increased, the gap between the ratcheting strains of young and adult cartilages increased gradually. The ratcheting strains of young and adult cartilages decreased along the cartilage depth from the surface to the deep layer. The ratcheting strains of different layers increased with the compressive cycle, and the difference among the three layers was noticeable. Additionally, the theoretical predictions agreed with the experimental data.

Conclusions

Overall, the ratcheting behavior of articular cartilage is affected by the degree of articular cartilage maturation.

Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests

It has been experimentally proposed that the discrete regions of articular cartilage, along with different subchondral bone tissues, known as the bone-cartilage unit, are biomechanically altered during osteoarthritis degeneration. However, a computational framework capturing all of the dominant changes in the multiphasic parameters has not yet been developed. This article proposes a new finite element model of the bone-cartilage unit by combining several validated, nonlinear, depth-dependent, fibril-reinforced, and swelling models, which can computationally simulate the variations in the dominant parameters during osteoarthritis degeneration by indentation and unconfined compression tests. The mentioned dominant parameters include the proteoglycan depletion, collagen fibrillar softening, permeability, and fluid fraction increase for approximately non-advanced osteoarthritis. The results depict the importance of subchondral bone tissues in fluid distribution within the bone-cartilage units by decreasing the fluid permeation and pressure (up to a maximum of 100 kPa) during osteoarthritis, supporting the notion that subchondral bones might play a role in the pathogenesis of osteoarthritis. Furthermore, the osteoarthritis composition-based studies shed light on the significant biomechanical role of the calcified cartilage, which experienced a maximum change of 70 kPa in stress, together with relative load contributions of articular cartilage constituents during osteoarthritis, in which the osmotic pressure bore around 70% of the loads after degeneration. To conclude, the new insights provided by the results reveal the significance of the multiphasic osteoarthritis simulation and demonstrate the functionality of the proposed bone-cartilage unit model.

Effects of Intrinsic Properties on Fracture Nucleation and Propagation in Swelling Hydrogels

In numerous industrial applications, the microstructure of materials is critical for performance. However, finite element models tend to average out the microstructure. Hence, finite element simulations are often unsuitable for optimisation of the microstructure. The present paper presents a modelling technique that addresses this limitation for superabsorbent polymers with a partially cross-linked surface layer. These are widely used in the industry for a variety of functions. Different designs of the cross-linked layer have different material properties, influencing the performance of the hydrogel. In this work, the effects of intrinsic properties on the fracture nucleation and propagation in cross-linked hydrogels are studied. The numerical implementation for crack propagation and nucleation is based on the framework of the extended finite element method and the enhanced local pressure model to capture the pressure difference and fluid flow between the crack and the hydrogel, and coupled with the cohesive method to achieve crack propagation without re-meshing. Two groups of numerical examples are given: (1) effects on crack propagation, and (2) effects on crack nucleation. Within each example, we studied the effects of the stiffness (shear modulus) and ultimate strength of the material separately. Simulations demonstrate that the crack behaviour is influenced by the intrinsic properties of the hydrogel, which gives numerical support for the structural design of the cross-linked hydrogel.

Towards Patient-Specific Computational Modelling of Articular Cartilage on the Basis of Advanced Multiparametric MRI Techniques

Cartilage degeneration is associated with tissue softening and represents the hallmark change of osteoarthritis. Advanced quantitative Magnetic Resonance Imaging (qMRI) techniques allow the assessment of subtle tissue changes not only of structure and morphology but also of composition. Yet, the relation between qMRI parameters on the one hand and microstructure, composition and the resulting functional tissue properties on the other hand remain to be defined. To this end, a Finite-Element framework was developed based on an anisotropic constitutive model of cartilage informed by sample-specific multiparametric qMRI maps, obtained for eight osteochondral samples on a clinical 3.0 T MRI scanner. For reference, the same samples were subjected to confined compression tests to evaluate stiffness and compressibility. Moreover, the Mankin score as an indicator of histological tissue degeneration was determined. The constitutive model was optimized against the resulting stress responses and informed solely by the sample-specific qMRI parameter maps. Thereby, the biomechanical properties of individual samples could be captured with good-to-excellent accuracy (mean R² [square of Pearson's correlation coefficient]: 0.966, range [min, max]: 0.904, 0.993; mean Ω [relative approximated error]: 33%, range [min, max]: 20%, 47%). Thus, advanced qMRI techniques may be complemented by the developed computational model of cartilage to comprehensively evaluate the functional dimension of non-invasively obtained imaging biomarkers. Thereby, cartilage degeneration can be perspectively evaluated in the context of imaging and biomechanics.

Understanding how reduced loading affects Achilles tendon mechanical properties using a fibre-reinforced poro-visco-hyper-elastic model

Understanding tendon mechanobiology is important for gaining insight into the development of tendon pathology and subsequent repair processes. The aim of this study was to investigate how experimentally observed mechanobiological adaptation of rat Achilles tendons translate to changes in constitutive mechanical properties and biomechanical behavior. In addition, we assessed the ability of the model to simulate tendon creep and stress-relaxation. A three dimensional finite element framework of rat Achilles tendon was implemented with a fibre-reinforced poro-visco-hyper-elastic constitutive model. Stress-relaxation and creep data from Achilles tendons of Sprague Dawley rats that had been subjected to both daily loading and a period of reduced loading were used to determine the constitutive properties of the tendons. Our results showed that the constitutive model captures creep and stress-relaxation data from rat Achilles tendons for both loaded and unloaded tendons with good accuracy (normalized root mean square error between model and experimental data were 0.010-0.027). Only when the model parameters were fitted to data from both mechanical tests simultaneously, were we able to also capture similar increase in elastic energy (increased stiffness) and decreased viscoelasticity in response to unloading, as was reported experimentally. Our study is the first to show that experimentally observed mechanobiological changes in tendon biomechanics, such as stiffness and viscoelasticity, can be designated to mechanical quantities in a constitutive model. Further investigation in this direction has potential to discriminate tissue components responsible for specific biomechanical response, and enable targeted treatment strategies for tendon health.

Detection of Early-Stage Degeneration in Human Articular Cartilage by Multiparametric MR Imaging Mapping of Tissue Functionality

To assess human articular cartilage tissue functionality by serial multiparametric quantitative MRI (qMRI) mapping as a function of histological degeneration. Forty-nine cartilage samples obtained during total knee replacement surgeries were placed in a standardized artificial knee joint within an MRI-compatible compressive loading device and imaged in situ and at three loading positions, i.e. unloaded, at 2.5 mm displacement (20% body weight [BW]) and at 5 mm displacement (110% BW). Using a clinical 3.0 T MRI system (Achieva, Philips), serial T1, T1ρ, T2 and T2* maps were generated for each sample and loading position. Histology (Mankin scoring) and biomechanics (Young’s modulus) served as references. Samples were dichotomized as intact (int, n = 27) or early degenerative (deg, n = 22) based on histology and analyzed using repeated-measures ANOVA and unpaired Student’s t-tests after log-transformation. For T1ρ, T2 and T2*, significant loading-induced differences were found in deg (in contrast to int) samples, while for T1 significant decreases in all zones were observed, irrespective of degeneration. In conclusion, cartilage functionality may be visualized using serial qMRI parameter mapping and the response-to-loading patterns are associated with histological degeneration. Hence, loading-induced changes in qMRI parameter maps provide promising surrogate parameters of tissue functionality and status in health and disease.

T1ρ-based fibril-reinforced poroviscoelastic constitutive relation of human articular cartilage using inverse finite element technology

Background

Mapping of T_1ρ relaxation time is a quantitative magnetic resonance (MR) method and is frequently used for analyzing microstructural and compositional changes in cartilage tissues. However, there is still a lack of study investigating the link between T_1ρ relaxation time and a feasible constitutive relation of cartilage which can be used to model complicated mechanical behaviors of cartilage accurately and properly.

Methods

Three-dimensional finite element (FE) models of ten in vitro human tibial cartilage samples were reconstructed such that each element was assigned by material-level parameters, which were determined by a corresponding T_1ρ value from MR maps. A T_1ρ-based fibril-reinforced poroviscoelastic (FRPE) constitutive relation for human cartilage was developed through an inverse FE optimization technique between the experimental and simulated indentations.

Results

A two-parameter exponential relationship was obtained between the T_1ρ and the volume fraction of the hydrated solid matrix in the T_1ρ-based FRPE constitutive relation. Compared with the common FRPE constitutive relation (i.e., without T_1ρ), the T_1ρ-based FRPE constitutive relation indicated similar indentation depth results but revealed some different local changes of the stress distribution in cartilages.

Conclusions

Our results suggested that the T_1ρ-based FRPE constitutive relation may improve the detection of changes in the heterogeneous, anisotropic, and nonlinear mechanical properties of human cartilage tissues associated with joint pathologies such as osteoarthritis (OA). Incorporating T_1ρ relaxation time will provide a more precise assessment of human cartilage based on the individual in vivo MR quantification.

The combined impact of tissue heterogeneity and fixed charge for models of cartilage: the one-dimensional biphasic swelling model revisited

Articular cartilage is a complex, anisotropic, stratified tissue with remarkable resilience and mechanical properties. It has been subject to extensive modelling as a multiphase medium, with many recent studies examining the impact of increasing detail in the representation of this tissue's fine scale structure. However, further investigation of simple models with minimal constitutive relations can nonetheless inform our understanding at the foundations of soft tissue simulation. Here, we focus on the impact of heterogeneity with regard to the volume fractions of solid and fluid within the cartilage. Once swelling pressure due to cartilage fixed charge is also present, we demonstrate that the multiphase modelling framework is substantially more complicated, and thus investigate this complexity, especially in the simple setting of a confined compression experiment. Our findings highlight the importance of locally, and thus heterogeneously, approaching pore compaction for load bearing in cartilage models, while emphasising that such effects can be represented by simple constitutive relations. In addition, simulation predictions are observed for the sensitivity of stress and displacement in the cartilage to variations in the initial state of the cartilage and thus the details of experimental protocol, once the tissue is heterogeneous. These findings are for the simplest models given only heterogeneity in volume fractions and swelling pressure, further emphasising that the complex behaviours associated with the interaction of volume fraction heterogeneity and swelling pressure are likely to persist for simulations of cartilage representations with more fine-grained structural detail of the tissue.

Maximum shear strain-based algorithm can predict proteoglycan loss in damaged articular cartilage

Post-traumatic osteoarthritis (PTOA) is a common disease, where the mechanical integrity of articular cartilage is compromised. PTOA can be a result of chondral defects formed due to injurious loading. One of the first changes around defects is proteoglycan depletion. Since there are no methods to restore injured cartilage fully back to its healthy state, preventing the onset and progression of the disease is advisable. However, this is problematic if the disease progression cannot be predicted. Thus, we developed an algorithm to predict proteoglycan loss of injured cartilage by decreasing the fixed charge density (FCD) concentration. We tested several mechanisms based on the local strains or stresses in the tissue for the FCD loss. By choosing the degeneration threshold suggested for inducing chondrocyte apoptosis and cartilage matrix damage, the algorithm driven by the maximum shear strain showed the most substantial FCD losses around the lesion. This is consistent with experimental findings in the literature. We also observed that by using coordinate system-independent strain measures and selecting the degeneration threshold in an ad hoc manner, all the resulting FCD distributions would appear qualitatively similar, i.e., the greatest FCD losses are found at the tissue adjacent to the lesion. The proposed strain-based FCD degeneration algorithm shows a great potential for predicting the progression of PTOA via biomechanical stimuli. This could allow identification of high-risk defects with an increased risk of PTOA progression.

The Effect of Charge and Mechanical Loading on Antibody Diffusion Through the Articular Surface of Cartilage

Molecular transport of osteoarthritis (OA) therapeutics within articular cartilage is influenced by many factors, such as solute charge, that have yet to be fully understood. This study characterizes how solute charge influences local diffusion and convective transport of antibodies within the heterogeneous cartilage matrix. Three fluorescently tagged solutes of varying isoelectric point (pI) (4.7–5.9) were tested in either cyclic or passive cartilage loading conditions. In each case, local diffusivities were calculated based on local fluorescence in the cartilage sample, as observed by confocal microscopy. In agreement with past research, local solute diffusivities within the heterogeneous cartilage matrix were highest around 200–275 μm from the articular surface, but 3–4 times lower at the articular surface and in the deeper zones of the tissue. Transport of all 150 kDa solutes was significantly increased by the application of mechanical loading at 1 Hz, but local transport enhancement was not significantly affected by changes in solute isoelectric point. More positively charged solutes (higher pI) had significantly higher local diffusivities 200–275 μm from the tissue surface, but no other differences were observed. This implies that there are certain regions of cartilage that are more sensitive to changes in solute charge than others, which could be useful for future development of OA therapeutics.

Imaging of nuclear magnetic resonance spin-lattice relaxation activation energy in cartilage

Samples of human and bovine cartilage have been examined using magnetic resonance imaging to determine the proton nuclear magnetic resonance spin-lattice relaxation time, T₁, as a function of depth within through the cartilage tissue. T₁ was measured at five to seven temperatures between 8 and 38°C. From this, it is shown that the T₁ relaxation time is well described by Arrhenius-type behaviour and the activation energy of the relaxation process is quantified. The activation energy within the cartilage is approximately 11 ± 2 kJ mol^-1 with this notably being less than that for both pure water (16.6 ± 0.4 kJ mol^-1) and the phosphate-buffered solution in which the cartilage was immersed (14.7 ± 1.0 kJ mol^-1). It is shown that this activation energy increases as a function of depth in the cartilage. It is known that cartilage composition varies with depth, and hence, these results have been interpreted in terms of the structure within the cartilage tissue and the association of the water with the macromolecular constituents of the cartilage.

A three-dimensional transient mixed hybrid finite element model for superabsorbent polymers with strain-dependent permeability

A hydrogel is a cross-linked polymer network with water as solvent. Industrially widely used superabsorbent polymers (SAP) are partially neutralized sodium polyacrylate hydrogels. The extremely large degree of swelling is one of the most distinctive characteristics of such hydrogels, as the volume increase can be about 30 times its original volume when exposed to physiological solution. The large deformation resulting from the swelling demands careful numerical treatment. In this work, we present a biphasic continuum-level swelling model using the mixed hybrid finite element method (MHFEM) in three dimensions. The hydraulic permeability is highly dependent on the swelling ratio, resulting in values that are orders of magnitude apart from each other. The property of the local mass conservation of MHFEM contributes to a more accurate calculation of the deformation as the permeability across the swelling gel in a transient state is highly non-uniform. We show that the proposed model is able to simulate the free swelling of a random-shaped gel and the squeezing of fluid out of a swollen gel. Finally, we make use of the proposed numerical model to study the onset of surface instability in transient swelling.

Multiparametric MRI and Computational Modelling in the Assessment of Human Articular Cartilage Properties: A Comprehensive Approach

Quantitative magnetic resonance imaging (qMRI) is a promising approach to detect early cartilage degeneration. However, there is no consensus on which cartilage component contributes to the tissue's qMRI signal properties. T1, T1ρ, and T2^⁎ maps of cartilage samples (n = 8) were generated on a clinical 3.0-T MRI system. All samples underwent histological assessment to ensure structural integrity. For cross-referencing, a discretized numerical model capturing distinct compositional and structural tissue properties, that is, fluid fraction (FF), proteoglycan (PG) and collagen (CO) content and collagen fiber orientation (CFO), was implemented. In a pixel-wise and region-specific manner (central versus peripheral region), qMRI parameter values and modelled tissue parameters were correlated and quantified in terms of Spearman's correlation coefficient ρs. Significant correlations were found between modelled compositional parameters and T1 and T2^⁎, in particular in the central region (T1: ρs ≥ 0.7 [FF, CFO], ρs ≤ −0.8 [CO, PG]; T2^⁎: ρs ≥ 0.67 [FF, CFO], ρs ≤ −0.71 [CO, PG]). For T1ρ, correlations were considerably weaker and fewer (0.16 ≤ ρs ≤ −0.15). QMRI parameters are characterized in their biophysical properties and their sensitivity and specificity profiles in a basic scientific context. Although none of these is specific towards any particular cartilage constituent, T1 and T2^⁎ reflect actual tissue compositional features more closely than T1ρ.

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.

Micrometer scale guidance of mesenchymal stem cells to form structurally oriented large-scale tissue engineered cartilage

Current clinical methods to treat articular cartilage lesions provide temporary relief of the symptoms but fail to permanently restore the damaged tissue. Tissue engineering, using mesenchymal stem cells (MSCs) combined with scaffolds and bioactive factors, is viewed as a promising method for repairing cartilage injuries. However, current tissue engineered constructs display inferior mechanical properties compared to native articular cartilage, which could be attributed to the lack of structural organization of the extracellular matrix (ECM) of these engineered constructs in comparison to the highly oriented structure of articular cartilage ECM. We previously showed that we can guide MSCs undergoing chondrogenesis to align using microscale guidance channels on the surface of a two-dimensional (2-D) collagen scaffold, which resulted in the deposition of aligned ECM within the channels and enhanced mechanical properties of the constructs. In this study, we developed a technique to roll 2-D collagen scaffolds containing MSCs within guidance channels in order to produce a large-scale, three-dimensional (3-D) tissue engineered cartilage constructs with enhanced mechanical properties compared to current constructs. After rolling the MSC-scaffold constructs into a 3-D cylindrical structure, the constructs were cultured for 21days under chondrogenic culture conditions. The microstructure architecture and mechanical properties of the constructs were evaluated using imaging and compressive testing. Histology and immunohistochemistry of the constructs showed extensive glycosaminoglycan (GAG) and collagen type II deposition. Second harmonic generation imaging and Picrosirius red staining indicated alignment of neo-collagen fibers within the guidance channels of the constructs. Mechanical testing indicated that constructs containing the guidance channels displayed enhanced compressive properties compared to control constructs without these channels. In conclusion, using a novel roll-up method, we have developed large scale MSC based tissue-engineered cartilage that shows microscale structural organization and enhanced compressive properties compared to current tissue engineered constructs.

STATEMENT OF SIGNIFICANCE

Tissue engineered cartilage constructs made with human mesenchymal stem cells (hMSCs), scaffolds and bioactive factors are a promising solution to treat cartilage defects. A major disadvantage of these constructs is their inferior mechanical properties compared to the native tissue, which is likely due to the lack of structural organization of the extracellular matrix of the engineered constructs. In this study, we developed three-dimensional (3-D) cartilage constructs from rectangular scaffold sheets containing hMSCs in micro-guidance channels and characterized their mechanical properties and metabolic requirements. The work led to a novel roll-up method to embed 2-D microscale structures in 3-D constructs. Further, micro-guidance channels incorporated within the 3-D cartilage constructs led to the production of aligned cell-produced matrix and enhanced mechanical function.

Finite Element Modeling of Avascular Tumor Growth Using a Stress-Driven Model

Tumor growth being a multistage process has been investigated from different aspects. In the present study, an attempt is made to represent a constitutive-structure-based model of avascular tumor growth in which the effects of tensile stresses caused by collagen fibers are considered. Collagen fibers as a source of anisotropy in the structure of tissue are taken into account using a continuous fiber distribution formulation. To this end, a finite element modeling is implemented in which a neo-Hookean hyperelastic material is assigned to the tumor and its surrounding host. The tumor is supplied with a growth term. The growth term includes the effect of parameters such as nutrient concentration on the tumor growth and the tumor's solid phase content in the formulation. Results of the study revealed that decrease of solid phase is indicative of decrease in growth rate and the final steady-state value of tumor's radius. Moreover, fiber distribution affects the final shape of the tumor, and it could be used to control the shape and geometry of the tumor in complex morphologies. Finally, the findings demonstrated that the exerted stresses on the tumor increase as time passes. Compression of tumor cells leads to the reduction of tumor growth rate until it gradually reaches an equilibrium radius. This finding is in accordance with experimental data. Hence, this formulation can be deployed to evaluate both the residual stresses induced by growth and the mechanical interactions with the host tissue.

T2 MR imaging vs. computational modeling of human articular cartilage tissue functionality

The detection of early stages of cartilage degeneration remains diagnostically challenging. One promising non-invasive approach is to functionally assess the tissue response to loading by serial magnetic resonance (MR) imaging in terms of T2 mapping under simultaneous mechanical loading. As yet, however, it is not clear which cartilage component contributes to the tissue functionality as assessed by quantitative T2 mapping. To this end, quantitative T2 maps of histologically intact cartilage samples (n=8) were generated using a clinical 3.0-T MR imaging system. Using displacement-controlled quasi-static indentation loading, serial T2 mapping was performed at three defined strain levels and loading-induced relative changes were determined in distinct regions-of-interest. Samples underwent conventional biomechanical testing (by unconfined compression) as well as histological assessment (by Mankin scoring) for reference purposes. Moreover, an anisotropic hyperelastic constitutive model of cartilage was implemented into a finite element (FE) code for cross-referencing. In efforts to simulate the evolution of compositional and structural intra-tissue changes under quasi-static loading, the indentation-induced changes in quantitative T2 maps were referenced to underlying changes in cartilage composition and structure. These changes were parameterized as cartilage fluid, proteoglycan and collagen content as well as collagen orientation. On a pixel-wise basis, each individual component correlation with T2 relaxation times was determined by Spearman's ρ_s and significant correlations were found between T2 relaxation times and all four tissue parameters for all indentation strain levels. Thus, the biological changes in functional MR Imaging parameters such as T2 can further be characterized to strengthen the scientific basis of functional MRI techniques with regards to their perspective clinical applications.

The Effect of Antibody Size and Mechanical Loading on Solute Diffusion Through the Articular Surface of Cartilage

Because of the heterogeneous nature of articular cartilage tissue, penetration of potential therapeutic molecules for osteoarthritis (OA) through the articular surface (AS) is complex, with many factors that affect transport of these solutes within the tissue. Therefore, the goal of this study is to investigate how the size of antibody (Ab) variants, as well as application of cyclic mechanical loading, affects solute transport within healthy cartilage tissue. Penetration of fluorescently tagged solutes was quantified using confocal microscopy. For all the solutes tested, fluorescence curves were obtained through the articular surface. On average, diffusivities for the solutes of sizes 200 kDa, 150 kDa, 50 kDa, and 25 kDa were 3.3, 3.4, 5.1, and 6.0 μm2/s from 0 to 100 μm from the articular surface. Diffusivities went up to a maximum of 16.5, 18.5, 20.5, and 23.4 μm2/s for the 200 kDa, 150 kDa, 50 kDa, and 25 kDa molecules, respectively, from 225 to 325 μm from the surface. Overall, the effect of loading was very significant, with maximal transport enhancement for each solute ranging from 2.2 to 3.4-fold near 275 μm. Ultimately, solutes of this size do not diffuse uniformly nor are convected uniformly, through the depth of the cartilage tissue. This research potentially holds great clinical significance to discover ways of further optimizing transport into cartilage and leads to effective antibody-based treatments for OA.

A mathematical model of tissue-engineered cartilage development under cyclic compressive loading

In this work a coupled model of solute transport and uptake, cell proliferation, extracellular matrix synthesis and remodeling of mechanical properties accounting for the impact of mechanical loading is presented as an advancement of a previously validated coupled model for free-swelling tissue-engineered cartilage cultures. Tissue-engineering constructs were modeled as biphasic with a linear elastic solid, and relevant intrinsic mechanical stimuli in the constructs were determined by numerical simulation for use as inputs of the coupled model. The mechanical dependent formulations were derived from a calibration and parametrization dataset and validated by comparison of normalized ratios of cell counts, total glycosaminoglycans and collagen after 24-h continuous cyclic unconfined compression from another dataset. The model successfully fit the calibration dataset and predicted the results from the validation dataset with good agreement, with average relative errors up to 3.1 and 4.3 %, respectively. Temporal and spatial patterns determined for other model outputs were consistent with reported studies. The results suggest that the model describes the interaction between the simultaneous factors involved in in vitro tissue-engineered cartilage culture under dynamic loading. This approach could also be attractive for optimization of culture protocols, namely through the application to longer culture times and other types of mechanical stimuli.

Effect of crosslinking in cartilage-like collagen microstructures

The mechanical performance of biological tissues is underpinned by a complex and finely balanced structure. Central to this is collagen, the most abundant protein in our bodies, which plays a dominant role in the functioning of tissues, and also in disease. Based on the collagen meshwork of articular cartilage, we have developed a bottom-up spring-node model of collagen and examined the effect of fibril connectivity, implemented by crosslinking, on mechanical behaviour. Although changing individual crosslink stiffness within an order of magnitude had no significant effect on modelling predictions, the density of crosslinks in a meshwork had a substantial impact on its behaviour. Highly crosslinked meshworks maintained a 'normal' configuration under loading, with stronger resistance to deformation and improved recovery relative to sparsely crosslinked meshwork. Stress on individual fibrils, however, was higher in highly crosslinked meshworks. Meshworks with low numbers of crosslinks reconfigured to disease-like states upon deformation and recovery. The importance of collagen interconnectivity may provide insight into the role of ultrastructure and its mechanics in the initiation, and early stages, of diseases such as osteoarthritis.

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.

The effect of loading rate on the development of early damage in articular cartilage

Experimental reports suggest that cartilage damage depends on strain magnitude. Additionally, because of its poro-viscoelastic nature, strain magnitude in cartilage can depend on strain rate. The present study explores whether cartilage damage may develop dependent on strain rate, even when the presented damage numerical model is strain-dependent but not strain-rate-dependent. So far no experiments have been distinguished whether rate-dependent cartilage damage occurs in the collagen or in the non-fibrillar network. Thus, this research presents a finite element analysis model where, among others, collagen and non-fibrillar matrix are incorporated as well as a strain-dependent damage mechanism for these components. Collagen and non-fibrillar matrix stiffness decrease when a given strain is reached until complete failure upon reaching a maximum strain. With such model, indentation experiments at increasing strain rates were simulated on cartilage plugs and damage development was monitored over time. Collagen damage increased with increasing strain rate from 21 to 42 %. In contrast, damage in the non-fibrillar matrix decreased with increasing strain rates from 72 to 34 %. Damage started to develop at a depth of approximately 20 % of the sample height, and this was more pronounced for the slow and modest loading rates. However, the most severe damage at the end of the compression step occurred at the surface for the plugs subjected to 120 mm/min strain rate. In conclusion, the present study confirms that the location and magnitude of damage in cartilage may be strongly dependent on strain rate, even when damage occurs solely through a strain-dependent damage mechanism.

Relative contribution of articular cartilage's constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.

Polymers in Cartilage Defect Repair of the Knee: Current Status and Future Prospects

Cartilage defects in the knee are often seen in young and active patients. There is a need for effective joint preserving treatments in patients suffering from cartilage defects, as untreated defects often lead to osteoarthritis. Within the last two decades, tissue engineering based techniques using a wide variety of polymers, cell sources, and signaling molecules have been evaluated. We start this review with basic background information on cartilage structure, its intrinsic repair, and an overview of the cartilage repair treatments from a historical perspective. Next, we thoroughly discuss polymer construct components and their current use in commercially available constructs. Finally, we provide an in-depth discussion about construct considerations such as degradation rates, cell sources, mechanical properties, joint homeostasis, and non-degradable/hybrid resurfacing techniques. As future prospects in cartilage repair, we foresee developments in three areas: first, further optimization of degradable scaffolds towards more biomimetic grafts and improved joint environment. Second, we predict that patient-specific non-degradable resurfacing implants will become increasingly applied and will provide a feasible treatment for older patients or failed regenerative treatments. Third, we foresee an increase of interest in hybrid construct, which combines degradable with non-degradable materials.

An overview of multiphase cartilage mechanical modelling and its role in understanding function and pathology

There is a long history of mathematical and computational modelling with the objective of understanding the mechanisms governing cartilage׳s remarkable mechanical performance. Nonetheless, despite sophisticated modelling development, simulations of cartilage have consistently lagged behind structural knowledge and thus the relationship between structure and function in cartilage is not fully understood. However, in the most recent generation of studies, there is an emerging confluence between our structural knowledge and the structure represented in cartilage modelling. This raises the prospect of further refinement in our understanding of cartilage function and also the initiation of an engineering-level understanding for how structural degradation and ageing relates to cartilage dysfunction and pathology, as well as informing the potential design of prospective interventions. Aimed at researchers entering the field of cartilage modelling, we thus review the basic principles of cartilage models, discussing the underlying physics and assumptions in relatively simple settings, whilst presenting the derivation of relatively parsimonious multiphase cartilage models consistent with our discussions. We proceed to consider modern developments that start aligning the structure captured in the models with observed complexities. This emphasises the challenges associated with constitutive relations, boundary conditions, parameter estimation and validation in cartilage modelling programmes. Consequently, we further detail how both experimental interrogations and modelling developments can be utilised to investigate and reduce such difficulties before summarising how cartilage modelling initiatives may improve our understanding of cartilage ageing, pathology and intervention.