Effects of nonlinear strain-dependent permeability and rate of compression on the stress behavior of articular cartilage

Effect of uncertainties in musculoskeletal modeling inputs on sensitivity of knee joint finite element simulations

Musculoskeletal finite element modeling is used to estimate mechanical responses of knee joint tissues but involves uncertainties in muscle activations, marker locations, cartilage stiffness, maximum isometric forces, and gait parameter personalization. This study investigates how these uncertainties affect cartilage mechanical responses in knee joint finite element models during walking. We selected three subjects and constructed five musculoskeletal models for each, representing different variations of modeling assumptions, along with a reference model using conventional assumptions. We then ran finite element simulations of knee joints using both personalized gait inputs (motion and loading boundary conditions) and non-personalized gait inputs from literature. Our results demonstrated that varying modeling assumptions, such as optimization function for muscle activation patterns, knee marker position, knee cartilage stiffness, and maximum isometric force, produced highly subject-specific effects. Differences between the reference and altered models ranged from 3% to 30% in musculoskeletal modeling and from 1% to 61% in finite element modeling results. The largest effects occurred with non-personalized gait data, resulting in up to 6- and 2-fold changes in musculoskeletal and finite element modeling results, respectively. This study highlights the sensitivity of knee mechanics to different modeling assumptions and underscores the importance of applying personalized gait parameters for accurate finite element simulations.

Influence of articular cartilage sample geometry on mechanical response and properties using finite element simulation

Mechanical testing of articular cartilage yields highly variable results, posing challenges for tissue characterization. Many factors cause variability, one is sample geometry. Using in-situ phase-contrast enhanced synchrotron micro-tomographs of cartilage samples while tested in unconfined compression (stress relaxation) our group found high variability in the mechanical response. Since all samples originated from a single bovine knee, they were assumed to share mechanical properties. Microscale tomography images showed geometric irregularities in samples that were not accounted for in the often assumed intended cylindrical shape. We aimed to determine the influence of sample shape on mechanical response in unconfined compression and how sample geometry affects identified mechanical properties. Using a parametric FE model incorporating geometric irregularities in a Design of Experiments approach, results were analysed with 2-way ANOVA. Furthermore, a material parameter fitting was done with multiple segmented sample-specific finite element models simultaneously to assess the influence of sample geometry on material parameters. Results revealed that the average inclined sample surface (4°) caused a 15 % decrease in reaction forces compared to the intended cylinder. Fitting multiple sample-specific geometries simultaneously altered material parameters between -70 to +159 % compared to the average model. Strikingly, initial fibril stiffness and permeability increased by 137 % and 159 %, while the root-mean-square error of the fit was reduced by ∼2/3 compared to using parameters from a cylindrical shape model. In conclusion, minor variability in sample geometry affects property characterization and can account for some of the inter-sample variability in the mechanical data for cartilage.

Ion-Induced Swelling Behavior of Articular Cartilage due to Non-Newtonian Flow and Its Effects on Fluid Pressure and Solid Displacement

In this study, we examine the behavior of articular cartilage equilibrated in a salt (NaCl) solution during non-Newtonian fluid flow that follows an Ostwald-de Waele model. A linearly elastic and isotropic rectangular strip of cartilage is considered for analysis. A continuum theory of mixtures has been employed to develop a coupled system of partial differential equations for the solid displacement and the fluid pressure by considering the important factor of the ion concentration by assuming the cartilage as a deformable porous media. The coupled system of partial differential equations is solved using the numerical method named method of lines. In most cases, shear-thinning fluid is compared to the shear-thickening fluid to magnify the difference. Graphical results show that shear-thickening fluids bring more solid deformation and shows less fluid pressure in comparison to the shear-thinning fluids.

Osteoarthritis year in review 2023: Imaging

PURPOSE

This narrative review summarizes the original research in the field of in vivo osteoarthritis (OA) imaging between 1 January 2022 and 1 April 2023.

METHODS

A PubMed search was conducted using the following several terms pertaining to OA imaging, including but not limited to "Osteoarthritis / OA", "Magnetic resonance imaging / MRI", "X-ray" "Computed tomography / CT", "artificial intelligence /AI", "deep learning", "machine learning". This review is organized by topics including the anatomical structure of interest and modality, AI, challenges of OA imaging in the context of clinical trials, and imaging biomarkers in clinical trials and interventional studies. Ex vivo and animal studies were excluded from this review.

RESULTS

Two hundred and forty-nine publications were relevant to in vivo human OA imaging. Among the articles included, the knee joint (61%) and MRI (42%) were the predominant anatomical area and imaging modalities studied. Marked heterogeneity of structural tissue damage in OA knees was reported, a finding of potential relevance to clinical trial inclusion. The use of AI continues to rise rapidly to be applied in various aspect of OA imaging research but a lack of generalizability beyond highly standardized datasets limit interpretation and wide-spread application. No pharmacologic clinical trials using imaging data as outcome measures have been published in the period of interest.

CONCLUSIONS

Recent advances in OA imaging continue to heavily weigh on the use of AI. MRI remains the most important modality with a growing role in outcome prediction and classification.

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.

The effects of gravity and compression on interstitial fluid transport in the lower limb

Edema in the limbs can arise from pathologies such as elevated capillary pressures due to failure of venous valves, elevated capillary permeability from local inflammation, and insufficient fluid clearance by the lymphatic system. The most common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy. To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of a lower limb that includes the effects of gravity. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due to lymphatic clearance, and movement through the interstitial space due to both gravity and gradients in interstitial fluid pressure (IFP). From dimensional analysis and numerical solutions of the governing equations we have identified several parameter groups that determine the essential length and time scales involved. We find that gravity can have dramatic effects on the fluid balance in the limb with the possibility that a positive feedback loop can develop that facilitates chronic edema. This process involves localized tissue swelling which increases the hydraulic conductivity, thus allowing the movement of interstitial fluid vertically throughout the limb due to gravity and causing further swelling. The presence of a compression wrap can interrupt this feedback loop. We find that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema development and treatment in a gravity dependent limb.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

A Finite Element Algorithm for Large Deformation Biphasic Frictional Contact Between Porous-Permeable Hydrated Soft Tissues

The frictional response of porous and permeable hydrated biological tissues such as articular cartilage is significantly dependent on interstitial fluid pressurization. To model this response, it is common to represent such tissues as biphasic materials, consisting of a binary mixture of a porous solid matrix and an interstitial fluid. However, no computational algorithms currently exist in either commercial or open-source software that can model frictional contact between such materials. Therefore, this study formulates and implements a finite element algorithm for large deformation biphasic frictional contact in the open-source finite element software FEBio. This algorithm relies on a local form of a biphasic friction model that has been previously validated against experiments, and implements the model into our recently-developed surface-to-surface (STS) contact algorithm. Contact constraints, including those specific to pressurized porous media, are enforced with the penalty method regularized with an active-passive augmented Lagrangian scheme. Numerical difficulties specific to challenging finite deformation biphasic contact problems are overcome with novel smoothing schemes for fluid pressures and Lagrange multipliers. Implementation accuracy is verified against semi-analytical solutions for biphasic frictional contact, with extensive validation performed using canonical cartilage friction experiments from prior literature. Essential details of the formulation are provided in this paper, and the source code of this biphasic frictional contact algorithm is made available to the general public.

Biphasic Properties of PVAH (Polyvinyl Alcohol Hydrogel) Reflecting Biomechanical Behavior of the Nucleus Pulposus of the Human Intervertebral Disc

PVAH is a mixture of solid and fluid, but its mechanical behavior has usually been described using solid material models. The purpose of this study was to obtain material properties that can reflect the mechanical behavior of polyvinyl alcohol hydrogel (PVAH) using finite element analysis, a biphasic continuum model, and to optimize the composition ratio of PVAH to replace the nucleus pulposus (NP) of the human intervertebral disc. Six types of PVAH specimens (3, 5, 7, 10, 15, 20 wt%) were prepared, then unconfined compression experiments were performed to acquire their material properties using the Holmes–Mow biphasic model. With an increasing weight percentage of PVA in PVAH, the Young’s modulus increased while the permeability parameter decreased. The Young’s modulus and permeability parameter were similar to those of the NP at 15 wt% and 20 wt%. The range of motion, facet joint force, and NP pressures measured from dynamic motional analysis of the lumbar segments with the NP model also exhibited similar values to those with 15~20 wt% PVAH models. Considering the structural stability and pain of the lumbar segments, it appears that 20 wt% PVAH is most suitable for replacing the NP.

Comparative tribology II-Measurable biphasic tissue properties have predictable impacts on cartilage rehydration and lubricity

Healthy articular cartilage supports load bearing and frictional properties unmatched among biological tissues and man-made bearing materials. Balancing fluid exudation and recovery under loaded and articulated conditions is essential to the tissue's biological and mechanical longevity. Our prior tribological investigations, which leveraged the convergent stationary contact area (cSCA) configuration, revealed that sliding alone can modulate cartilage interstitial fluid pressurization and the recovery and maintenance of lubrication under load through a mechanism termed 'tribological rehydration.' Our recent comparative assessment of tribological rehydration revealed remarkably consistent sliding speed-dependent fluid recovery and lubrication behaviors across femoral condyle cartilage from five mammalian species (equine/horse, bovine/cow, porcine/pig, ovine/sheep, and caprine/goat). In the present study, we identified and characterized key predictive relationships among tissue properties, sliding-induced tribological rehydration, and the modulation/recovery of lubrication within healthy articular cartilage. Using correlational analysis, we linked observed speed-dependent tribological rehydration behaviors to cartilage's geometry and biphasic properties (tensile and compressive moduli, and permeability). Together, these findings demonstrate that easily measurable biphasic tissue characteristics (e.g., bulk tissue material properties, compressive strain magnitude, and strain rates) can be used to predict cartilage's rehydration and lubricating abilities, and ultimately its function in vivo. STATEMENT OF SIGNIFICANCE: In healthy cartilage, articulation recovers fluid lost to static loading thereby sustaining tissue lubricity. Osteoarthritis causes changes to cartilage composition, stiffness, and permeability associated with faster fluid exudation and presumably poorer frictional outcomes. Yet, the relationship between mechanical properties and fluid recovery during articulation/sliding remains unclear. Through innovative, high-speed benchtop sliding and indentation experiments, we found that cartilage's tissue properties regulate its exudation/hydration under slow sliding speeds but have minimal effect at high sliding speeds. In fact, cartilage rehydration appears insensitive to permeability and stiffness under high fluid load support conditions. This new understanding of the balance of cartilage exudation and rehydration during activity, based upon comparative tribology studies, may improve prevention and rehabilitation strategies for joint injuries and osteoarthritis.

The Relationship Between Proteoglycan Loss, Overloading-Induced Collagen Damage, and Cyclic Loading in Articular Cartilage

OBJECTIVE

The interaction between proteoglycan loss and collagen damage in articular cartilage and the effect of mechanical loading on this interaction remain unknown. The aim of this study was to answer the following questions: (1) Is proteoglycan loss dependent on the amount of collagen damage and does it depend on whether this collagen damage is superficial or internal? (2) Does repeated loading further increase the already enhanced proteoglycan loss in cartilage with collagen damage?

DESIGN

Fifty-six bovine osteochondral plugs were equilibrated in phosphate-buffered saline for 24 hours, mechanically tested in compression for 8 hours, and kept in phosphate-buffered saline for another 48 hours. The mechanical tests included an overloading step to induce collagen damage, creep steps to determine tissue stiffness, and cyclic loading to induce convection. Proteoglycan release was measured before and after mechanical loading, as well as 48 hours post-loading. Collagen damage was scored histologically.

RESULTS

Histology revealed different collagen damage grades after the application of mechanical overloading. After 48 hours in phosphate-buffered saline postloading, proteoglycan loss increased linearly with the amount of total collagen damage and was dependent on the presence but not the amount of internal collagen damage. In samples without collagen damage, repeated loading also resulted in increased proteoglycan loss. However, repeated loading did not further enhance the proteoglycan loss induced by damaged collagen.

CONCLUSION

Proteoglycan loss is enhanced by collagen damage and it depends on the presence of internal collagen damage. Cyclic loading stimulates proteoglycan loss in healthy cartilage but does not lead to additional loss in cartilage with damaged collagen.

Effects of solvent osmolarity and viscosity on cartilage energy dissipation under high-frequency loading

Articular cartilage is a spatially heterogeneous, dissipative biological hydrogel with a high fluid volume fraction. Although energy dissipation is important in the context of delaying cartilage damage, the dynamic behavior of articular cartilage equilibrated in media of varied osmolarity and viscosity is not widely understood. This study investigated the mechanical behaviors of cartilage when equilibrated to media of varying osmolarity and viscosity. Dynamic moduli and phase shift were measured at both low (1 Hz) and high (75-300 Hz) frequency, with cartilage samples compressed to varied offset strain levels. Increasing solution osmolarity and viscosity both independently resulted in larger energy dissipation and decreased dynamic modulus of cartilage at both low and high frequency. Mechanical property alterations induced by varying osmolarity are likely due to the change in permeability and fluid volume fraction within the tissue. The effects of solution viscosity are likely due to frictional interactions at the solid-fluid interface, affecting energy dissipation. These findings highlight the significance of interstitial fluid on the energy dissipation capabilities of the tissue, which can influence the onset of cartilage damage.

The Influence of Running on Lower Limb Cartilage: A Systematic Review and Meta-analysis

BACKGROUND

Running is a popular activity practiced worldwide. It is important to understand how running affects joint health to provide recommendations to sports medicine practitioners and runners.

OBJECTIVE

Our aim was to summarize the influence of running on lower limb cartilage morphology and composition using quantitative magnetic resonance imaging (MRI).

METHODS

Prospective repeated-measures studies evaluating cartilage using MRI before and after running were included. Data sources included Pubmed, Embase, CINAHL, SportDiscus, Web of Science, and Cochrane Central Registry of Controlled Trials. Qualitative analyses considered the number and methodological quality ratings of studies based on the QualSyst tool, and recommendations were based on the strength of evidence (strong, moderate, limited, or very limited). Quantitative analysis involved meta-analyses, for which effect sizes were calculated as Hedge's g standardized mean differences.

RESULTS

We included 43 articles, assessing seven outcomes (lesions, volume, thickness, glycosaminoglycan content, and T1ρ, T2, and T2* relaxation times). Nineteen articles were rated as high quality, 24 were rated as moderate quality, and none were rated as low quality. Qualitative analyses suggest that running may cause an immediate reduction in knee cartilage volume, thickness, as well as T1ρ and T2 relaxation times immediately; however, these changes did not persist. Meta-analyses revealed a small and moderate decrease immediately following a single running bout in T2 relaxation time in the medial femur and tibia, respectively. Qualitative analyses indicated that the influence of repeated exposure to running on cartilage morphology and composition was limited. Despite conflicting evidence regarding pre-existing knee cartilage lesions, moderate evidence suggests that running does not lead to the formation of new lesions. Repeated running exposure did not cause changes to foot and ankle cartilage thickness or composition.

CONCLUSIONS

Changes to lower limb cartilage following running are transient. Immediate changes to cartilage morphology and composition, which likely reflect natural fluid dynamics, do not persist and were generally not significant when pooled statistically. Results suggest that cartilage recovers well from a single running bout and adapts to repeated exposure. Given that moderate evidence indicates that running does not lead to new lesions, future trials should focus on clinical populations, such as those with osteoarthritis.

TRIAL REGISTRATION

Not applicable.

The effect of highly inhomogeneous biphasic properties on mechanical behaviour of articular cartilage

BACKGROUND AND OBJECTIVE

Investigating the biomechanics of cartilage could help to understand the unique load-bearing property of the cartilage and optimize the scaffold design in tissue-engineering. It is important to model the cartilage as a highly inhomogeneous fibril-reinforced biphasic material to represent its complex composition and structure. The depth-dependent and strain-dependent properties of the cartilage would also play an important role in its mechanical behaviour. However, the differences in representing the cartilage as a highly inhomogeneous model or as simplified models still remain unclear. Hence, in this study, a highly inhomogeneous fibril-reinforced biphasic cartilage model considering both the depth-dependent and strain-dependent properties was constructed; the effect of highly inhomogeneous properties on the mechanical behaviour of articular cartilage was investigated.

METHODS

A finite element model of the cartilage was developed based on a flat-ended indentation test. Compressive forces were applied to four various inhomogeneous layered models through a porous indenter (Model 1: nine layers with strain-dependent permeability; Model 2: three layers with strain-dependent permeability; Model 3: single layer with strain-dependent permeability; Model 4: nine layers with constant permeability).

RESULTS

Models 1 and 2 provided similar results with less than 3% difference in the peak effective stress, contact pressure, fluid pressure as well as fluid support ratio. However, Model 1 to Model 3 differed in stress and strain distribution patterns along depth over prolonged loads, which may provide an important insight into the highly inhomogeneous depth-dependent properties of cartilage. In addition, Model 1 with strain-dependent permeability demonstrated an enhanced capability on fluid pressurisation as compared with Model 4 which had constant permeability.

CONCLUSIONS

A highly inhomogeneous fibril-reinforced biphasic model considering both depth-dependent and strain-dependent properties was developed in this study, in order to illustrate the effect of highly inhomogeneous properties on the mechanical behaviour of the articular cartilage. The number of layers in the models with depth-dependent properties should be selected according to the research questions and clinical demands. The model with strain-dependent permeability offers an enhanced capability on fluid pressurisation. In future studies, the proposed model could be adopted in cell-models to provide more in-depth information or in tissue-engineering to optimize the depth-dependent scaffold structure.

Depth and strain rate-dependent mechanical response of chondrocytes in reserve zone cartilage subjected to compressive loading

The role of the growth plate reserve zone is not well understood. It has been proposed to serve as a source of stem cells and to produce morphogens that control the alignment of clones in preparation for the transition into the proliferative zone. We hypothesized that if such a role exists, there are likely to be mechanoregulatory stimuli in cellular response through the depth of the reserve zone. A poroelastic multiscale finite element model of bone/growth-plate/bone was developed for examining the reserve zone cell transient response when compressed to 5% of the cartilage thickness at strain rates of 0.18%/s, 5%/s, 50%/s, and 200%/s. Chondrocyte maximum principal strains, height-, width-, and membrane-strains were found to be highly dependent on reserve zone tissue depth and strain rate. Cell-level strains and fluid transmembrane outflow from the cell were influenced by the permeability of the calcified cartilage between subchondral bone plate and reserve zone and by the applied strain rate. Cell strain levels in the lower reserve zone were less sensitive to epiphyseal permeability than in the upper reserve zone. In contrast, the intracellular fluid pressures were relatively uniform with reserve zone tissue depth and less sensitive to epiphyseal permeability. Fluid shear stress, induced by fluid flow over the cell surface, provided mechanoregulatory signals potentially sufficient to stimulate reserve zone chondrocytes near the subchondral bone plate interface. These results suggest that the strain rate and tissue depth dependence of cell-level strains and cell surface fluid shear stress may provide mechanoregulatory cues in the reserve zone.

Characterization of breast tissue permeability for detection of vascular breast tumors: An in vitro study

The biological tissue could be considered as a porous matrix filled with the interstitial fluid. The tumoral tissue has a different permeability from the healthy tissue. With regard to this knowledge, the main objective of the present study is to study the tissue permeability as a diagnostic parameter for the detection of breast cancer. To this end, the healthy and the cancerous specimens of the breast tissue are taken from 17 female cases. All cancerous tumors are in the vascular phase of the growth. The samples undergo a uniaxial compression test by a robotic system while the strain rate is set to remain unchanged. Using the stress and the strain rate data, the strain-dependent permeability is determined, which is an exponential function of the strain level. The permeability function is identified by the initial permeability at the zero compressive strain and a material constant. Results show that the initial permeability of the healthy breast tissue is significantly different from the corresponding value for the cancerous tissue. For all cancerous samples, the permeability is less than the healthy tissue samples; as 40-70% reduction in the initial permeability is observed compared to the healthy breast tissue. The evaluation of the permeability between the healthy and the cancerous specimens is accompanied by the biopsy reports and observing structural images of the specimens using environmental scanning electron microscope. Based on the results, the permeability is suggested to have a diagnostic application for the detection of vascular breast tumors.

Control of Dissipation Sources: A Central Aspect for Enhancing the Mechanical and Mechanobiological Performances of Hydrogels

Development of mechanically durable and biologically inductive hydrogels is a major challenge for load-bearing applications such as engineered cartilage. Dissipative capacity of articular cartilage is central to its functional behavior when submitted to loading. While fluid frictional drag is playing a significant role in this phenomenon, the flow-dependent source of dissipation is mostly overlooked in the design of hydrogel scaffolds. Herein, we propose an original strategy based on the combination of fluidic and polymeric dissipation sources to simultaneously enhance hydrogel mechanical and mechanobiological performances. The nondestructive dissipation processes were carefully designed by hybrid cross-linking of the hydrogel network and low permeability of the porous structure. It was found that intrachain and pore water distribution in the porous hydrogels improves the mechanical properties in high water fractions. In contrast to widely reported tough hydrogels presenting limited load support capability at low strain values, we obtained stiff and dissipative hydrogels with unique fatigue behavior. We showed that the fatigue resistance capability is not a function of morphology, dissipation level, and stiffness of the viscoelastic hydrogels but rather depends on the origin of the dissipation. Moreover, the preserved dissipation source under mechanical stimulation maintained a mechanoinductive niche for enhancing chondrogenesis owing to fluid frictional drag contribution. The proposed strategy can be widely used to design functional scaffolds in high loading demands for enduring physiological stimuli and generating regulatory cues to cells.

The effects of dynamic compressive loading on human mesenchymal stem cell osteogenesis in the stiff layer of a bilayer hydrogel

Bilayer hydrogels with a soft cartilage-like layer and a stiff bone-like layer embedded with human mesenchymal stem cells (hMSCs) are promising for osteochondral tissue engineering. The goals of this work were to evaluate the effects of dynamic compressive loading (2.5% applied strain, 1 Hz) on osteogenesis in the stiff layer and spatially map local mechanical responses (strain, stress, hydrostatic pressure, and fluid velocity). A bilayer hydrogel was fabricated from soft (24 kPa) and stiff (124 kPa) poly (ethylene glycol) hydrogels. With hMSCs embedded in the stiff layer, osteogenesis was delayed under loading evident by lower OSX and OPN expressions, alkaline phosphatase activity, and collagen content. At Day 28, mineral deposits were present throughout the stiff layer without loading but localized centrally and near the interface under loading. Local strains mapped by particle tracking showed substantial equivalent strain (~1.5%) transferring to the stiff layer. When hMSCs were cultured in stiff single-layer hydrogels subjected to similar strains, mineralization was inhibited. Finite element analysis revealed that hydrostatic pressures ≥~600 Pa correlated to regions lacking mineralization in both hydrogels. Fluid velocities were low (~1-10 nm/s) in the hydrogels with no apparent correlation to mineralization. Mineralization was recovered by inhibiting ERK1/2, indicating cell-mediated inhibition. These findings suggest that high strains (~1.5%) combined with higher hydrostatic pressures negatively impact osteogenesis, but in a manner that depends on the magnitude of each mechanical response. This work highlights the importance of local mechanical responses in mediating osteogenesis of hMSCs in bilayer hydrogels being studied for osteochondral tissue engineering.

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.

The Importance of Controlled Mismatch of Biomechanical Compliances of Implantable Scaffolds and Native Tissue for Articular Cartilage Regeneration

Scaffolds for articular cartilage repair have to be optimally biodegradable with simultaneous promotion of hyaline cartilage formation under rather complex biomechanical and physiological conditions. It has been generally accepted that scaffold structure and composition would be the best when it mimics the structure of native cartilage. However, a reparative construct mimicking the mature native tissue in a healing tissue site presents a biological mismatch of reparative stimuli. In this work, we studied a new recombinant human type III collagen-polylactide (rhCol-PLA) scaffolds. The rhCol-PLA scaffolds were assessed for their relative performance in simulated synovial fluids of 1 and 4 mg/mL sodium hyaluronate with application of model-free analysis with Biomaterials Enhanced Simulation Test (BEST). Pure PLA scaffold was used as a control. The BEST results were compared to the results of a prior in vivo study with rhCol-PLA. Collectively the data indicated that a successful articular cartilage repair require lower stiffness of the scaffold compared to surrounding cartilage yet matching the strain compliance both in static and dynamic conditions. This ensures an optimal combination of load transfer and effective oscillatory nutrients supply to the cells. The results encourage further development of intelligent scaffold structures for optimal articular cartilage repair rather than simply trying to imitate the respective original tissue.

Computational Investigation on the Biomechanical Responses of the Osteocytes to the Compressive Stimulus: A Poroelastic Model

Osteocytes, the major type of bone cells embedded in the bone matrix and surrounded by the lacunar and canalicular system, can serve as biomechanosensors and biomechanotranducers of the bone. Theoretical analytical methods have been employed to investigate the biomechanical responses of osteocytes in vivo; the poroelastic properties have not been taken into consideration in the three-dimensional (3D) finite element model. In this study, a 3D poroelastic idealized finite element model was developed and was used to predict biomechanical behaviours (maximal principal strain, pore pressure, and fluid velocity) of the osteocyte-lacunar-canalicular system under 150-, 1000-, 3000-, and 5000-microstrain compressive loads, respectively, representing disuse, physiological, overuse, and pathological overload loading stimuli. The highest local strain, pore pressure, and fluid velocity were found to be highest at the proximal region of cell processes. These data suggest that the strain, pore pressure, and fluid velocity of the osteocyte-lacunar-canalicular system increase with the global loading and that the poroelastic material property affects the biomechanical responses to the compressive stimulus. This new model can be used to predict the mechanobiological behaviours of osteocytes under the four different compressive loadings and may provide an insight into the mechanisms of mechanosensation and mechanotransduction of the bone.

Real-time observation of fluid flows in tissue during stress relaxation using Raman spectroscopy

This paper outlines a technique to measure fluid levels in articular cartilage tissue during an unconfined stress relaxation test. A time series of Raman spectrum were recorded during relaxation and the changes in the specific Raman spectral bands assigned to water and protein were monitored to determine the fluid content of the tissue. After 1000s unconfined compression the fluid content of the tissue is reduced by an average of 3.9%±1.7%. The reduction in fluid content during compression varies between samples but does not significantly increase with increasing strain. Further development of this technique will allow mapping of fluid distribution and flows during dynamic testing making it a powerful tool to understand the role of interstitial fluid in the functional performance of cartilage.

Diffusion tensor imaging of articular cartilage at 3T correlates with histology and biomechanics in a mechanical injury model

PURPOSE

We establish a mechanical injury model for articular cartilage to assess the sensitivity of diffusion tensor imaging (DTI) in detecting cartilage damage early in time. Mechanical injury provides a more realistic model of cartilage degradation compared with commonly used enzymatic degradation.

METHODS

Nine cartilage-on-bone samples were obtained from patients undergoing knee replacement. The 3 Tesla DTI (0.18 × 0.18 × 1 mm3 ) was performed before, 1 week, and 2 weeks after (zero, mild, and severe) injury, with a clinical radial spin-echo DTI (RAISED) sequence used in our hospital. We performed stress-relaxation tests and used a quasilinear-viscoelastic (QLV) model to characterize cartilage mechanical properties. Serial histology sections were dyed with Safranin-O and given an OARSI grade. We then correlated the changes in DTI parameters with the changes in QLV-parameters and OARSI grades.

RESULTS

After severe injury the mean diffusivity increased after 1 and 2 weeks, whereas the fractional anisotropy decreased after 2 weeks (P < 0.05). The QLV-parameters and OARSI grades of the severe injury group differed from the baseline with statistical significance. The changes in mean diffusivity across all the samples correlated with the changes in the OARSI grade (r = 0.72) and QLV-parameters (r = -0.75).

CONCLUSION

DTI is sensitive in tracking early changes after mechanical injury, and its changes correlate with changes in biomechanics and histology. Magn Reson Med 78:69-78, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Quantifying Cartilage Biomechanical Properties Using a Linearized Frequency-Domain Method

Articular cartilage function relies on its unique mechanical behavior. Cartilage mechanics have been described by several analytic models, whose parameters are usually estimated by fitting their constitutive equations to stress-relaxation data. This procedure can be long and is prone to experimental and fitting errors. Τhis study describes a novel methodology for estimating the biomechanical properties of cartilage samples based on their linearized frequency response, derived by applying a series of small-amplitude harmonic displacements superimposed to a bias strain. The proposed methodology, denoted as linearized frequency-domain method (LFM), was demonstrated by quantifying the effects of collagenase and hyaluronidase on cartilage, where it provided robust cartilage parameter estimates that overall agreed well with estimates obtained by stress-relaxation analysis. LFM was also applied to unveil the strain-dependent nature of porcine cartilage biomechanical parameters. Results showed that increasing the bias strain from 5% to 15% caused a significant decrease in cartilage permeability but did not have significant effect on the compression modulus and the Poisson's ratio. Apart from cartilage, LFM can potentially quantify the strain-dependent nature of tissues and biomaterials, thereby enhance tissue-level understanding on organ physiology and pathology, lead to better computational tissue models, and guide tissue engineering research.

Relationship between T1rho magnetic resonance imaging, synovial fluid biomarkers, and the biochemical and biomechanical properties of cartilage

Non-invasive techniques for quantifying early biochemical and biomechanical changes in articular cartilage may provide a means of more precisely assessing osteoarthritis (OA) progression. The goals of this study were to determine the relationship between T1rho magnetic resonance (MR) imaging relaxation times and changes in cartilage composition, cartilage mechanical properties, and synovial fluid biomarker levels and to demonstrate the application of T1rho imaging to evaluate cartilage composition in human subjects in vivo. Femoral condyles and synovial fluid were harvested from healthy and OA porcine knee joints. Sagittal T1rho relaxation MR images of the condyles were acquired. OA regions of OA joints exhibited an increase in T1rho relaxation times as compared to non-OA regions. Furthermore in these regions, cartilage sGAG content and aggregate modulus decreased, while percent degraded collagen and water content increased. In OA joints, synovial fluid concentrations of sGAG decreased and C2C concentrations increased compared to healthy joints. T1rho relaxation times were negatively correlated with cartilage and synovial fluid sGAG concentrations and aggregate modulus and positively correlated with water content and permeability. Additionally, we demonstrated the application of these in vitro findings to the study of human subjects. Specifically, we demonstrated that walking results in decreased T1rho relaxation times, consistent with water exudation and an increase in proteoglycan concentration with in vivo loading. Together, these findings demonstrate that cartilage MR imaging and synovial fluid biomarkers provide powerful non-invasive tools for characterizing changes in the biochemical and biomechanical environments of the joint.

Investigation of the Effects of Extracellular Osmotic Pressure on Morphology and Mechanical Properties of Individual Chondrocyte

It has been demonstrated that most cells of the body respond to osmotic pressure in a systematic manner. The disruption of the collagen network in the early stages of osteoarthritis causes an increase in water content of cartilage which leads to a reduction of pericellular osmolality in chondrocytes distributed within the extracellular environment. It is therefore arguable that an insight into the mechanical properties of chondrocytes under varying osmotic pressure would provide a better understanding of chondrocyte mechanotransduction and potentially contribute to knowledge on cartilage degeneration. In this present study, the chondrocyte cells were exposed to solutions with different osmolality. Changes in their dimensions and mechanical properties were measured over time. Atomic force microscopy (AFM) was used to apply load at various strain-rates and the force-time curves were logged. The thin-layer elastic model was used to extract the elastic stiffness of chondrocytes at different strain-rates and at different solution osmolality. In addition, the porohyperelastic (PHE) model was used to investigate the strain-rate-dependent responses under the loading and osmotic pressure conditions. The results revealed that the hypo-osmotic external environment increased chondrocyte dimensions and reduced Young's modulus of the cells at all strain-rates tested. In contrast, the hyper-osmotic external environment reduced dimensions and increased Young's modulus. Moreover, using the PHE model coupled with inverse FEA simulation, we established that the hydraulic permeability of chondrocytes increased with decreasing extracellular osmolality which is consistent with previous work in the literature. This could be due to a higher intracellular fluid volume fraction with lower osmolality.

Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability

Solid-interstitial fluid interaction, which depends on tissue permeability, is significant to the strain-rate-dependent mechanical behavior of humeral head (shoulder) cartilage. Due to anatomical and biomechanical similarities to that of the human shoulder, kangaroos present a suitable animal model. Therefore, indentation experiments were conducted on kangaroo shoulder cartilage tissues from low (10(-4)/s) to moderately high (10(-2)/s) strain-rates. A porohyperelastic model was developed based on the experimental characterization; and a permeability function that takes into account the effect of strain-rate on permeability (strain-rate-dependent permeability) was introduced into the model to investigate the effect of rate-dependent fluid flow on tissue response. The prediction of the model with the strain-rate-dependent permeability was compared with those of the models using constant permeability and strain-dependent permeability. Compared to the model with constant permeability, the models with strain-dependent and strain-rate-dependent permeability were able to better capture the experimental variation at all strain-rates (p < 0.05). Significant differences were not identified between models with strain-dependent and strain-rate-dependent permeability at strain-rate of 5 × 10(-3)/s (p = 0.179). However, at strain-rate of 10(-2)/s, the model with strain-rate-dependent permeability was significantly better at capturing the experimental results (p < 0.005). The findings thus revealed the significance of rate-dependent fluid flow on tissue behavior at large strain-rates, which provides insights into the mechanical deformation mechanisms of cartilage tissues.

Biomimetic Model of Articular Cartilage Based on In Vitro Experiments

Articular cartilage is a complicated material to model for a variety of reasons: its biphasic/triphasic properties, heterogeneous structure, compressibility, unique geometry, and variance between samples. However, the applications for a biomimetic, cartilage-like material are numerous and include: porous bearings, viscous dampers, robotic linkages, artificial joints, etc. This work reports experimental results on the stress-relaxation of equine articular cartilage in unconfined compression. The response is consistent with simple spring and damper systems, and gives a storage and loss moduli. This model is proposed for use in evaluating biomimetic materials, and can be incorporated into large-scale dynamic analyses to account for motion or impact. The proposed characterization is suited for high-level analysis of multi-phase materials, where separating the contribution of each phase is not desired.

Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration

The understanding of load support mechanisms in cartilage has evolved with computational models that better mimic the tissue ultrastructure. Fibril-reinforced poroelastic models can reproduce cartilage behaviour in a variety of test conditions and can be used to model tissue anisotropy as well as assess stress and pressure partitioning to the tissue constituents. The goal of this study was to examine the stress distribution in the fibrillar and non-fibrillar solid phase and pressure in the fluid phase of cartilage in axisymmetric models of a healthy and osteoarthritic hip joint. Material properties, based on values from the literature, were assigned to the fibrillar and poroelastic components of cartilage and cancellous and subchondral compact bone regions. A cyclic load representing walking was applied for 25 cycles. Contact stresses in the fibrillar and non-fibrillar solid phase supported less than 1% of the contact force and increased only minimally with load cycles. Simulated proteoglycan depletion increased stresses in the radial and tangential collagen fibrils, whereas fibrillation of the tangential fibrils resulted in increased compressive stress in the non-fibrillar component and tensile stress in the radial fibrils. However neither had an effect on fluid pressure. Subchondral sclerosis was found to have the largest effect, resulting in increased fluid pressure, non-fibrillar compressive stress, tangential fibril stress and greater cartilage consolidation. Subchondral bone stiffening may play an important role in the degenerative cascade and may adversely affect tissue repair and regeneration treatments.

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.

Finite element study of human lumbar disc nucleus replacements

Currently, there are a number of nucleus replacements under development. The important concern is how well these implants duplicate the mechanical function of the native nucleus. This finite element model study aimed to investigate the influence of different nucleus replacements on the mechanical response of the disc. Models included partial, full, over-sized, partially saturated, elastic and poroelastic solid replacements. Over-sized nucleus replacements up to 25% yielded results that were comparable to those in the intact state. Differences were much greater in cases with under-sized nucleus replacements. The effect was most pronounced for the 75% under-sized replacement that resembled the condition with a full nucleotomy. Nucleus implants with elastic properties substantially altered load transmission when 10% under-sized and over-sized replacements were considered. Compared to intact, the under-sized implants should be avoided when using biphasic materials with properties similar to the native nucleus, whereas for elastic replacements both under- and over-sized implants should not be used.

Periosteum, bone's "smart" bounding membrane, exhibits direction-dependent permeability

The periosteum serves as bone's bounding membrane, exhibits hallmarks of semipermeable epithelial barrier membranes, and contains mechanically sensitive progenitor cells capable of generating bone. The current paucity of data regarding the periosteum's permeability and bidirectional transport properties provided the impetus for the current study. In ovine femur and tibia samples, the periosteum's hydraulic permeability coefficient, k, was calculated using Darcy's Law and a custom-designed permeability tester to apply controlled, volumetric flow of phosphate-buffered saline through periosteum samples. Based on these data, ovine periosteum demonstrates mechanically responsive and directionally dependent (anisotropic) permeability properties. At baseline flow rates comparable to interstitial fluid flow (0.5 µL/s), permeability is low and does not exhibit anisotropy. In contrast, at high flow rates comparable to those prevailing during traumatic injury, femoral periosteum exhibits an order of magnitude higher permeability compared to baseline flow rates. In addition, at high flow rates permeability exhibits significant directional dependence, with permeability higher in the bone to muscle direction than vice versa. Furthermore, compared to periosteum in which the intrinsic tension (pre-stress) is maintained, free relaxation of the tibial periosteum after resection significantly increases its permeability in both flow directions. Hence, the structure and mechanical stress state of periosteum influences its role as bone's bounding membrane. During periods of homeostasis, periosteum may serve as a barrier membrane on the outer surface of bone, allowing for equal albeit low quiescent molecular communication between tissue compartments including bone and muscle. In contrast, increases in pressure and baseline flow rates within the periosteum resulting from injury, trauma, and/or disease may result in a significant increase in periosteum permeability and consequently in increased molecular communication between tissue compartments. Elucidation of the periosteum's permeability properties is key to understanding periosteal mechanobiology in bone health and healing, as well as to elucidate periosteum structure and function as a smart biomaterial that allows bidirectional and mechanically responsive fluid transport.

Recent advances in computational mechanics of the human knee joint

Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscectomies, ACL and PCL reconstructions, and joint replacements. Recently, poromechanical models accounting for fluid pressurization in soft tissues have been proposed to study the viscoelastic response of the healthy and impaired knee joints. While the constitutive modeling has been considerably advanced at the tissue level, many challenges still exist in applying a good material model to three-dimensional joint simulations. A complete model validation at the joint level seems impossible presently, because only simple data can be obtained experimentally. Therefore, model validation may be concentrated on the constitutive laws using multiple mechanical tests of the tissues. Extensive model verifications at the joint level are still crucial for the accuracy of the modeling.

Subject-specific analysis of joint contact mechanics: application to the study of osteoarthritis and surgical planning

Advances in computational mechanics, constitutive modeling, and techniques for subject-specific modeling have opened the door to patient-specific simulation of the relationships between joint mechanics and osteoarthritis (OA), as well as patient-specific preoperative planning. This article reviews the application of computational biomechanics to the simulation of joint contact mechanics as relevant to the study of OA. This review begins with background regarding OA and the mechanical causes of OA in the context of simulations of joint mechanics. The broad range of technical considerations in creating validated subject-specific whole joint models is discussed. The types of computational models available for the study of joint mechanics are reviewed. The types of constitutive models that are available for articular cartilage are reviewed, with special attention to choosing an appropriate constitutive model for the application at hand. Issues related to model generation are discussed, including acquisition of model geometry from volumetric image data and specific considerations for acquisition of computed tomography and magnetic resonance imaging data. Approaches to model validation are reviewed. The areas of parametric analysis, factorial design, and probabilistic analysis are reviewed in the context of simulations of joint contact mechanics. Following the review of technical considerations, the article details insights that have been obtained from computational models of joint mechanics for normal joints; patient populations; the study of specific aspects of joint mechanics relevant to OA, such as congruency and instability; and preoperative planning. Finally, future directions for research and application are summarized.

Is the ovine intervertebral disc a small human one? A finite element model study

The sheep is one of the most frequently used animal models for experimental intervertebral disc research questions. Although there are large differences in size between human and ovine discs, recent in vivo and in vitro studies indicate similarities in the internal disc stresses. The present finite element model study, therefore, intended to detect the parameters that, despite the different geometry, ensure mechanical comparability between both species. At first, a finite element model of the human L4-L5 lumbar intervertebral disc was developed. The predicted displacement and nucleus pressure response were validated with experimental in vivo and in vitro data. Starting with adapting the model geometry from the human to the ovine disc, several material and biochemical parameters, which might contribute to the preservation of the mechanical disc response across both species, were successively adapted to ovine properties. Replacing the geometry yielded a substantially higher disc stiffness and lower nucleus pressure compared to in vitro measurements performed on ovine discs. Additional reduction of annulus and nucleus elasticity led to an improved correlation between model predictions and measurements. Changes in the glycosaminoglycan content and endplate permeability improved the predicted pressure, but only slightly affected the displacement response. Only the combination of all parameters resulted in a good agreement between the predictions and measurements. This study demonstrated that there are profound differences between model predictions and in vitro results if an ovine simulation is run with human material properties. However, once the species-specific material properties are included, the predictions fit the in vitro results. Therefore, it seems that the human and ovine disc is functionally adapted to produce similar internal stresses, despite the large variation in geometry.

Impact of poroelasticity of intraluminal thrombus on wall stress of abdominal aortic aneurysms

Background

The predictions of stress fields in Abdominal Aortic Aneurysm (AAA) depend on constitutive descriptions of the aneurysm wall and the Intra-luminal Thrombus (ILT). ILT is a porous diluted structure (biphasic solid–fluid material) and its impact on AAA biomechanics is controversially discussed in the literature. Specifically, pressure measurements showed that the ILT cannot protect the wall from the arterial pressure, while other (numerical and experimental) studies showed that at the same time it reduces the stress in the wall.

Method

To explore this phenomenon further a poroelastic description of the ILT was integrated in Finite Element (FE) Models of the AAA. The AAA model was loaded by a pressure step and a cyclic pressure wave and their transition into wall tension was investigated. To this end ILT’s permeability was varied within a microstructurally motivated range.

Results

The two-phase model verified that the ILT transmits the entire mean arterial pressure to the wall while, at the same time, it significantly reduces the stress in the wall. The predicted mean stress in the AAA wall was insensitive to the permeability of the ILT and coincided with the results of AAA models using a single-phase ILT description.

Conclusion

At steady state, the biphasic ILT behaves like a single-phase material in an AAA model. Consequently, computational efficient FE single-phase models, as they have been exclusively used in the past, accurately predict the wall stress in AAA models.

Contrast-Enhanced Micro-Computed Tomography in Evaluation of Spontaneous Repair of Equine Cartilage

OBJECTIVE

Contrast-enhanced computed tomography (CECT) has been introduced for the evaluation of cartilage integrity. Furthermore, CECT enables imaging of the structure and density of subchondral bone. In this laboratory study, we investigate the potential of microCECT to simultaneously image cartilage and subchondral bone for the evaluation of tissue healing.

DESIGN

Osteochondral lesions (Ø = 6 mm) were surgically created in equine intercarpal joints (n = 7). After spontaneous healing for 12 months, the horses were sacrificed and osteochondral plugs (Ø = 14 mm), including the repair cartilage and adjacent intact tissue, were harvested. The nonfibrillar and fibrillar moduli and the permeability of cartilage were determined using indentation testing. Contrast agent diffusion into the samples was imaged for 36 hours using high-resolution CT. Results from CECT, mechanical testing, and microscopic analyses were compared and correlated.

RESULTS

The contrast agent diffusion coefficient showed a significant (P < 0.05) difference between the repair and adjacent intact tissue. MicroCECT revealed altered (P < 0.05) bone volume fraction, mineral density, and microstructure of subchondral bone at the repair site. The contrast agent diffusion coefficient correlated with the moduli of the nonfibrillar matrix (R = -0.662, P = 0.010), collagen fibril parallelism index (R = -0.588, P = 0.035), and glycosaminoglycan content (R = -0.503, P = 0.067). The repair cartilage was mechanically and structurally different from adjacent intact tissue (P < 0.05).

CONCLUSIONS

MicroCECT enabled simultaneous quantitative evaluation of subchondral bone and monitoring of cartilage repair, distinguishing quantitatively the repair site from the adjacent intact tissue. As the only technique able to simultaneously image cartilage and determine subchondral bone mineral density and microstructure, CECT has potential clinical value.

Cartilage-like mechanical properties of poly (ethylene glycol)-diacrylate hydrogels

Hydrogels prepared from poly-(ethylene glycol) (PEG) have been used in a variety of studies of cartilage tissue engineering. Such hydrogels may also be useful as a tunable mechanical material for cartilage repair. Previous studies have characterized the chemical and mechanical properties of PEG-based hydrogels, as modulated by precursor molecular weight and concentration. Cartilage mechanical properties vary substantially, with maturation, with depth from the articular surface, in health and disease, and in compression and tension. We hypothesized that PEG hydrogels could mimic a broad range of the compressive and tensile mechanical properties of articular cartilage. The objective of this study was to characterize the mechanical properties of PEG hydrogels over a broad range and with reference to articular cartilage. In particular, we assessed the effects of PEG precursor molecular weight (508 Da, 3.4 kDa, 6 kDa, and 10 kDa) and concentration (10-40%) on swelling property, equilibrium confined compressive modulus (H(A0)), compressive dynamic stiffness, and hydraulic permeability (k(p0)) of PEG hydrogels in static/dynamic confined compression tests, and equilibrium tensile modulus (E(ten)) in tension tests. As molecular weight of PEG decreased and concentration increased, hydrogels exhibited a decrease in swelling ratio (31.5-2.2), an increase in H(A0) (0.01-2.46 MPa) and E(ten) (0.02-3.5 MPa), an increase in dynamic compressive stiffness (0.055-42.9 MPa), and a decrease in k(p0) (1.2 × 10(-15) to 8.5 × 10(-15) m(2)/(Pa s)). The frequency-dependence of dynamic compressive stiffness amplitude and phase, as well as the strain-dependence of permeability, were typical of the time- and strain-dependent mechanical behavior of articular cartilage. H(A0) and E(ten) were positively correlated with the final PEG concentration, accounting for swelling. These results indicate that PEG hydrogels can be prepared to mimic many of the static and dynamic mechanical properties of articular cartilage.

A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion

A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.

Finite element implementation of mechanochemical phenomena in neutral deformable porous media under finite deformation

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http:∕∕mrl.sci.utah.edu∕software).