In-situ measurements of chondrocyte deformation under transient loading

Computational Modeling of Developing Cartilage Using Experimentally Derived Geometries and Compressive Moduli

During chondrogenesis, tissue organization changes dramatically. We previously showed that the compressive moduli of chondrocytes increase concomitantly with extracellular matrix (ECM) stiffness, suggesting cells were remodeling to adapt to the surrounding environment. Due to the difficulty in analyzing the mechanical response of cells in situ, we sought to create an in silico model that would enable us to investigate why cell and ECM stiffness increased in tandem. The goal of this study was to establish a methodology to segment, quantify, and generate mechanical models of developing cartilage to explore how variations in geometry and material properties affect strain distributions. Multicellular geometries from embryonic day E16.5 and postnatal day P3 murine cartilage were imaged in three-dimensional (3D) using confocal microscopy. Image stacks were processed using matlab to create geometries for finite element analysis using ANSYS. The geometries based on confocal images and isolated, single cell models were compressed 5% and the equivalent von Mises strain of cells and ECM were compared. Our simulations indicated that cells had similar strains at both time points, suggesting that the stiffness and organization of cartilage changes during development to maintain a constant strain profile within cells. In contrast, the ECM at P3 took on more strain than at E16.5. The isolated, single-cell geometries underestimated both cell and ECM strain and were not able to capture the similarity in cell strain at both time points. We expect this experimental and computational pipeline will facilitate studies investigating other model systems to implement physiologically derived geometries.

Effects of Inflammation on Multiscale Biomechanical Properties of Cartilaginous Cells and Tissues

Cells within cartilaginous tissues are mechanosensitive and thus require mechanical loading for regulation of tissue homeostasis and metabolism. Mechanical loading plays critical roles in cell differentiation, proliferation, biosynthesis, and homeostasis. Inflammation is an important event occurring during multiple processes, such as aging, injury, and disease. Inflammation has significant effects on biological processes as well as mechanical function of cells and tissues. These effects are highly dependent on cell/tissue type, timing, and magnitude. In this review, we summarize key findings pertaining to effects of inflammation on multiscale mechanical properties at subcellular, cellular, and tissue level in cartilaginous tissues, including alterations in mechanotransduction and mechanosensitivity. The emphasis is on articular cartilage and the intervertebral disc, which are impacted by inflammatory insults during degenerative conditions such as osteoarthritis, joint pain, and back pain. To recapitulate the pro-inflammatory cascades that occur in vivo, different inflammatory stimuli have been used for in vitro and in situ studies, including tumor necrosis factor (TNF), various interleukins (IL), and lipopolysaccharide (LPS). Therefore, this review will focus on the effects of these stimuli because they are the best studied pro-inflammatory cytokines in cartilaginous tissues. Understanding the current state of the field of inflammation and cell/tissue biomechanics may potentially identify future directions for novel and translational therapeutics with multiscale biomechanical considerations.

Regional variations in growth plate chondrocyte deformation as predicted by three-dimensional multi-scale simulations

The physis, or growth plate, is a complex disc-shaped cartilage structure that is responsible for longitudinal bone growth. In this study, a multi-scale computational approach was undertaken to better understand how physiological loads are experienced by chondrocytes embedded inside chondrons when subjected to moderate strain under instantaneous compressive loading of the growth plate. Models of representative samples of compressed bone/growth-plate/bone from a 0.67 mm thick 4-month old bovine proximal tibial physis were subjected to a prescribed displacement equal to 20% of the growth plate thickness. At the macroscale level, the applied compressive deformation resulted in an overall compressive strain across the proliferative-hypertrophic zone of 17%. The microscale model predicted that chondrocytes sustained compressive height strains of 12% and 6% in the proliferative and hypertrophic zones, respectively, in the interior regions of the plate. This pattern was reversed within the outer 300 μm region at the free surface where cells were compressed by 10% in the proliferative and 26% in the hypertrophic zones, in agreement with experimental observations. This work provides a new approach to study growth plate behavior under compression and illustrates the need for combining computational and experimental methods to better understand the chondrocyte mechanics in the growth plate cartilage. While the current model is relevant to fast dynamic events, such as heel strike in walking, we believe this approach provides new insight into the mechanical factors that regulate bone growth at the cell level and provides a basis for developing models to help interpret experimental results at varying time scales.

Multiscale cartilage biomechanics: technical challenges in realizing a high-throughput modelling and simulation workflow

Understanding the mechanical environment of articular cartilage and chondrocytes is of the utmost importance in evaluating tissue damage which is often related to failure of the fibre architecture and mechanical injury to the cells. This knowledge also has significant implications for understanding the mechanobiological response in healthy and diseased cartilage and can drive the development of intervention strategies, ranging from the design of tissue-engineered constructs to the establishment of rehabilitation protocols. Spanning multiple spatial scales, a wide range of biomechanical factors dictate this mechanical environment. Computational modelling and simulation provide descriptive and predictive tools to identify multiscale interactions, and can lead towards a greater comprehension of healthy and diseased cartilage function, possibly in an individualized manner. Cartilage and chondrocyte mechanics can be examined in silico, through post-processing or feed-forward approaches. First, joint-tissue level simulations, typically using the finite-element method, solve boundary value problems representing the joint articulation and underlying tissue, which can differentiate the role of compartmental joint loading in cartilage contact mechanics and macroscale cartilage field mechanics. Subsequently, tissue-cell scale simulations, driven by the macroscale cartilage mechanical field information, can predict chondrocyte deformation metrics along with the mechanics of the surrounding pericellular and extracellular matrices. A high-throughput modelling and simulation framework is necessary to develop models representative of regional and population-wide variations in cartilage and chondrocyte anatomy and mechanical properties, and to conduct large-scale analysis accommodating a multitude of loading scenarios. However, realization of such a framework is a daunting task, with technical difficulties hindering the processes of model development, scale coupling, simulation and interpretation of the results. This study aims to summarize various strategies to address the technical challenges of post-processing-based simulations of cartilage and chondrocyte mechanics with the ultimate goal of establishing the foundations of a high-throughput multiscale analysis framework. At the joint-tissue scale, rapid development of regional models of articular contact is possible by automating the process of generating parametric representations of cartilage boundaries and depth-dependent zonal delineation with associated constitutive relationships. At the tissue-cell scale, models descriptive of multicellular and fibrillar architecture of cartilage zones can also be generated in an automated fashion. Through post-processing, scripts can extract biphasic mechanical metrics at a desired point in the cartilage to assign loading and boundary conditions to models at the lower spatial scale of cells. Cell deformation metrics can be extracted from simulation results to provide a simplified description of individual chondrocyte responses. Simulations at the tissue-cell scale can be parallelized owing to the loosely coupled nature of the feed-forward approach. Verification studies illustrated the necessity of a second-order data passing scheme between scales and evaluated the role that the microscale representative volume size plays in appropriately predicting the mechanical response of the chondrocytes. The tools summarized in this study collectively provide a framework for high-throughput exploration of cartilage biomechanics, which includes minimally supervised model generation, and prediction of multiscale biomechanical metrics across a range of spatial scales, from joint regions and cartilage zones, down to that of the chondrocytes.

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

Computational analyses have been used to study the biomechanical microenvironment of the chondrocyte that cannot be assessed by in vitro experimental studies; yet all computational studies thus far have focused on the effect of zonal location (superficial, middle, and deep) on the mechanical microenvironment of chondrocytes. The aim of this paper was to study the effect of both zonal and radial locations on the biomechanical microenvironment of chondrocytes in inhomogeneous cartilage under unconfined stress relaxation. A biphasic multiscale approach was employed and nine chondrocytes in different locations were studied. Hyperelastic biphasic theory and depth-dependent aggregate modulus and permeability of articular cartilage were included in the models. It was found that both zonal and radial locations affected the biomechanical stresses and strains of the chondrocytes. Chondrocytes in the mid-radial location had increased volume during the early stage of the loading process. Maximum principal shear stress at the interface between the chondrocyte and the extracellular matrix (ECM) increased with depth, yet that at the ECM-pericellular matrix (PCM) interface had an inverse trend. Fluid pressure decreased with depth, while the fluid pressure difference between the top and bottom boundaries of the microscale model increased with depth. Regardless of location, fluid was exchanged between the chondrocyte, PCM, and ECM. These findings suggested that even under simple compressive loading conditions, the biomechanical microenvironment of the chondrocytes, PCM and ECM was spatially dependent. The current study provides new insight on chondrocyte biomechanics.

Effect of age and cytoskeletal elements on the indentation-dependent mechanical properties of chondrocytes

Articular cartilage chondrocytes are responsible for the synthesis, maintenance, and turnover of the extracellular matrix, metabolic processes that contribute to the mechanical properties of these cells. Here, we systematically evaluated the effect of age and cytoskeletal disruptors on the mechanical properties of chondrocytes as a function of deformation. We quantified the indentation-dependent mechanical properties of chondrocytes isolated from neonatal (1-day), adult (5-year) and geriatric (12-year) bovine knees using atomic force microscopy (AFM). We also measured the contribution of the actin and intermediate filaments to the indentation-dependent mechanical properties of chondrocytes. By integrating AFM with confocal fluorescent microscopy, we monitored cytoskeletal and biomechanical deformation in transgenic cells (GFP-vimentin and mCherry-actin) under compression. We found that the elastic modulus of chondrocytes in all age groups decreased with increased indentation (15-2000 nm). The elastic modulus of adult chondrocytes was significantly greater than neonatal cells at indentations greater than 500 nm. Viscoelastic moduli (instantaneous and equilibrium) were comparable in all age groups examined; however, the intrinsic viscosity was lower in geriatric chondrocytes than neonatal. Disrupting the actin or the intermediate filament structures altered the mechanical properties of chondrocytes by decreasing the elastic modulus and viscoelastic properties, resulting in a dramatic loss of indentation-dependent response with treatment. Actin and vimentin cytoskeletal structures were monitored using confocal fluorescent microscopy in transgenic cells treated with disruptors, and both treatments had a profound disruptive effect on the actin filaments. Here we show that disrupting the structure of intermediate filaments indirectly altered the configuration of the actin cytoskeleton. These findings underscore the importance of the cytoskeletal elements in the overall mechanical response of chondrocytes, indicating that intermediate filament integrity is key to the non-linear elastic properties of chondrocytes. This study improves our understanding of the mechanical properties of articular cartilage at the single cell level.

Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

A Finite Element Model of Cell-Matrix Interactions to Study the Differential Effect of Scaffold Composition on Chondrogenic Response to Mechanical Stimulation

Mechanically induced cell deformations have been shown to influence chondrocyte response in 3D culture. However, the relationship between the mechanical stimulation and cell response is not yet fully understood. In this study a finite element model was developed to investigate cell-matrix interactions under unconfined compression conditions, using a tissue engineered encapsulating hydrogel seeded with chondrocytes. Model predictions of stress and strain distributions within the cell and on the cell boundary were shown to exhibit space-dependent responses that varied with scaffold mechanical properties, the presence of a pericellular matrix (PCM), and the cell size. The simulations predicted that when the cells were initially encapsulated into the hydrogel scaffolds, the cell size hardly affected the magnitude of the stresses and strains that were reaching the encapsulated cells. However, with the inclusion of a PCM layer, larger cells experienced enhanced stresses and strains resulting from the mechanical stimulation. It was also noted that the PCM had a stress shielding effect on the cells in that the peak stresses experienced within the cells during loading were significantly reduced. On the other hand, the PCM caused the stresses at the cell-matrix interface to increase. Based on the model predictions, the PCM modified the spatial stress distribution within and around the encapsulated cells by redirecting the maximum stresses from the periphery of the cells to the cell nucleus. In a tissue engineered cartilage exposed to mechanical loading, the formation of a neo-PCM by encapsulated chondrocytes appears to protect them from initially excessive mechanical loading. Predictive models can thus shed important insight into how chondrocytes remodel their local environment in order to redistribute mechanical signals in tissue engineered constructs.

Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading

The aim was to assess the role of the composition changes in the pericellular matrix (PCM) for the chondrocyte deformation. For that, a three-dimensional finite element model with depth-dependent collagen density, fluid fraction, fixed charge density and collagen architecture, including parallel planes representing the split-lines, was created to model the extracellular matrix (ECM). The PCM was constructed similarly as the ECM, but the collagen fibrils were oriented parallel to the chondrocyte surfaces. The chondrocytes were modelled as poroelastic with swelling properties. Deformation behaviour of the cells was studied under 15% static compression. Due to the depth-dependent structure and composition of cartilage, axial cell strains were highly depth-dependent. An increase in the collagen content and fluid fraction in the PCMs increased the lateral cell strains, while an increase in the fixed charge density induced an inverse behaviour. Axial cell strains were only slightly affected by the changes in PCM composition. We conclude that the PCM composition plays a significant role in the deformation behaviour of chondrocytes, possibly modulating cartilage development, adaptation and degeneration. The development of cartilage repair materials could benefit from this information.

Pericellular Matrix Mechanics in the Anulus Fibrosus Predicted by a Three-Dimensional Finite Element Model and In Situ Morphology

Anulus fibrosus (AF) cells have been demonstrated to exhibit dramatic differences in morphology and biologic responses to different types of mechanical stimuli. AF cells may reside as single cell, paired or multiple cells in a contiguous pericellular matrix (PCM), whose structure and properties are expected to have a significant influence on the mechanical stimuli that these cells may experience during physiologic loading of the spine, as well as in tissue degeneration and regeneration. In this study, a computational model was developed to predict the micromechanical stimuli, such as stress and strain, fluid pressure and flow, of cells and their surrounding PCM in the AF tissue using three-dimensional (3D) finite element models based on in situ morphology. 3D solid geometries of cell-PCM regions were registered from serial confocal images obtained from mature rat AF tissues by custom codes. Distinct cell-matrix units were modeled with a custom 3D biphasic finite element code (COMSOL Multiphysics), and simulated to experience uni-axial tensile strain along the local collagen fiber direction. AF cells were predicted to experience higher volumetric strain with a strain amplification ratio (relative to that in the extracellular matrix) of ~ 3.1 - 3.8 at equilibrium, as compared to the PCM domains (1.3 - 1.9). The strain concentrations were generally found at the cell/PCM interface and stress concentration at the PCM/ECM interface. Increased numbers of cells within a contiguous PCM was associated with an apparent increase of strain levels and decreased rate of fluid pressurization in the cell, with magnitudes dependent on the cell size, shape and relative position inside the PCM. These studies provide spatio-temporal information on micromechanics of AF cells in understanding the mechanotransduction in the intervertebral disc.

Two-dimensional strain fields on the cross-section of the human patellofemoral joint under physiological loading

The objective of this study was to provide a detailed experimental assessment of the two-dimensional cartilage strain distribution on the cross-section of the human patellofemoral joint (PFJ) subjected to physiological load magnitudes and rates. The medial side of six human PFJs sectioned along their mid-sagittal plane was loaded up to the equivalent of two body weights on a whole joint, and strain measurements obtained from digital image correlation are reported at 0.5s. Normal strains tangential to the articular surface and shear strains in the plane of the cross-section showed consistent patterns among all specimens, whereas normal strains perpendicular to the articular surface exhibited some variability that may be attributed to subject-specific variations in material properties through the depth of the articular layers. Elevated tensile and compressive principal normal strains were observed near the articular surface, around the center of the contact region, with additional locations of elevated compressive strains occurring at the bone-cartilage interface. Under an average contact stress of approximately 3.3MPa, the peak compressive principal normal strains for the patella and femur averaged -0.158+/-0.072 and -0.118+/-0.051, respectively, magnitudes that are significantly greater than the relative changes in cartilage thickness, -0.090+/-0.030 and -0.072+/-0.038 (p<0.005). These experimental results provide a detailed description of the manner by which human PFJ articular layers deform in situ under physiological load conditions.

The dynamic mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions under cyclic compressive loading

Cyclic mechanical loading of articular cartilage results in a complex biomechanical environment at the scale of the chondrocytes that strongly affects cellular metabolic activity. Under dynamic loading conditions, the quantitative relationships between macroscopic loading characteristics and solid and fluid mechanical variables in the local cellular environment are not well understood. In this study, an axisymmetric multiscale model of linear biphasic cell-matrix interactions in articular cartilage was developed to investigate the cellular microenvironment in an explant subjected to cyclic confined compressive loading. The model was based on the displacement-velocity-pressure (u-v-p) mixed-penalty weighted residual formulation of linear biphasic theory that was implemented in the COMSOL MULTIPHYSICS software package. The microscale cartilage environment was represented as a three-zone biphasic region consisting of a spherical chondrocyte with encapsulating pericellular matrix (PCM) that was embedded in a cylindrical extracellular matrix (ECM) subjected to cyclic confined compressive loading boundary conditions. Biphasic material properties for the chondrocyte and the PCM were chosen based on previous in vitro micropipette aspiration studies of cells or chondrons isolated from normal or osteoarthritic cartilage. Simulations performed at four loading frequencies in the range 0.01-1.0 Hz supported the hypothesized dual role of the PCM as both a protective layer for the cell and a mechanical transducer of strain. Time varying biphasic variables at the cellular scale were strongly dependent on relative magnitudes of the loading period, and the characteristic gel diffusion times for the ECM, the PCM, and the chondrocyte. The multiscale simulations also indicated that axial strain was significantly amplified in the range 0.01-1.0 Hz, with a decrease in amplification factor and frequency insensitivity at the higher frequencies. Simulations of matrix degradation due to osteoarthritis indicated that strain amplification factors were more significantly altered when loss of matrix stiffness was exclusive to the PCM. The findings of this study demonstrate the complex dependence of dynamic mechanics in the local cellular environment of cartilage on macroscopic loading features and material properties of the ECM and the chondron.

Physiologic deformational loading does not counteract the catabolic effects of interleukin-1 in long-term culture of chondrocyte-seeded agarose constructs

An interplay of mechanical and chemical factors is integral to cartilage maintenance and/or degeneration. Interleukin-1 (IL-1) is a pro-inflammatory cytokine that is present at elevated concentrations in osteoarthritic joints and initiates the rapid degradation of cartilage when cultured in vitro. Several short-term studies have suggested that applied dynamic deformational loading may have a protective effect against the catabolic actions of IL-1. In the current study, we examine whether the long-term (42 days) application of dynamic deformational loading on chondrocyte-seeded agarose constructs can mitigate these catabolic effects. Three studies were carried out using two IL-1 isoforms (IL-1alpha and IL-1beta) in chemically defined medium supplemented with a broad range of cytokine concentrations and durations. Physiologic loading was unable to counteract the long-term catabolic effects of IL-1 under any of the conditions tested, and in some cases led to further degeneration over unloaded controls.

Transfer of macroscale tissue strain to microscale cell regions in the deformed meniscus

Cells within fibrocartilaginous tissues, including chondrocytes and fibroblasts of the meniscus, ligament, and tendon, regulate cell biosynthesis in response to local mechanical stimuli. The processes by which an applied mechanical load is transferred through the extracellular matrix to the environment of a cell are not fully understood. To better understand the role of mechanics in controlling cell phenotype and biosynthetic activity, this study was conducted to measure strain at different length scales in tissue of the fibrocartilaginous meniscus of the knee joint, and to define a quantitative parameter that describes the strain transferred from the far-field tissue to a microenvironment surrounding a cell. Experiments were performed to apply a controlled uniaxial tensile deformation to explants of porcine meniscus containing live cells. Using texture correlation analyses of confocal microscopy images, two-dimensional Lagrangian and principal strains were measured at length scales representative of the tissue (macroscale) and microenvironment in the region of a cell (microscale) to yield a strain transfer ratio as a measure of median microscale to macroscale strain. The data demonstrate that principal strains at the microscale are coupled to and amplified from macroscale principal strains for a majority of cell microenvironments located across diverse microstructural regions, with average strain transfer ratios of 1.6 and 2.9 for the maximum and minimum principal strains, respectively. Lagrangian strain components calculated along the experimental axes of applied deformations exhibited considerable spatial heterogeneity and intersample variability, and suggest the existence of both strain amplification and attenuation. This feature is consistent with an in-plane rotation of the principal strain axes relative to the experimental axes at the microscale that may result from fiber sliding, fiber twisting, and fiber-matrix interactions that are believed to be important for regulating deformation in other fibrocartilaginous tissues. The findings for consistent amplification of macroscale to microscale principal strains suggest a coordinated pattern of strain transfer from applied deformation to the microscale environment of a cell that is largely independent of these microstructural features in the fibrocartilaginous meniscus.