Microscale investigation of the anisotropic swelling of cartilage tissue and cells in response to hypo-osmotic challenges.

Tissue swelling represents an early sign of osteoarthritis, reflecting osmolarity changes from iso- to hypo-osmotic in the diseased joints. Increased tissue hydration may drive cell swelling. The opposing cartilages in a joint may swell differently, thereby predisposing the more swollen cartilage and cells to mechanical injuries. However, our understanding of the tissue-cell interdependence in osmotically loaded joints is limited as tissue and cell swellings have been studied separately. Here, we measured tissue and cell responses of opposing patellar (PAT) and femoral groove (FG) cartilages in lapine knees exposed to an extreme hypo-osmotic challenge. We found that the tissue matrix and most cells swelled during the hypo-osmotic challenge, but to a different extent (tissue: <3%, cells: 11%-15%). Swelling-induced tissue strains were anisotropic, showing 2%-4% stretch and 1%-2% compression along the first and third principal directions, respectively. These strains were amplified by 5-8 times in the cells. Interestingly, the first principal strains of tissue and cells occurred in different directions (60-61° for tissue vs. 8-13° for cells), suggesting different mechanisms causing volume expansion in the tissue and the cells. Instead of the continuous swelling observed in the tissue matrix, >88% of cells underwent regulatory volume decrease to return to their pre-osmotic challenge volumes. Cell shapes changed in the early phase of swelling but stayed constant thereafter. Kinematic changes to tissue and cells were larger for PAT cartilage than for FG cartilage. We conclude that the swelling-induced deformation of tissue and cells is anisotropic. Cells actively restored volume independent of the surrounding tissues and seemed to prioritize volume restoration over shape restoration. Our findings shed light on tissue-cell interdependence in changing osmotic environments that is crucial for cell mechano-transduction in swollen/diseased tissues.

Dynamic Deformation Calculation of Articular Cartilage and Cells Using Resonance-Driven Laser Scanning Microscopy.

The deformation of articular cartilage and its cells at the micro-scale during dynamic activities such as gait has high mechanoregulatory importance. Measuring the cellular geometries during such dynamics has been limited by the rate of microscopic image acquisition. The introduction of resonating mirrors for image rasterization (resonant scanning), rather than the conventional servo control (galvano scanning), has significantly improved the scanning rate by more than 100×. However, the high scanning rate comes at the cost of image quality, thereby posing challenges in image processing. Here, resonance-driven 3-D laser microscopy is used to observe the transient, micro-scale deformation of articular cartilage and its cells under osmotic challenge conditions. Custom image segmentation and deformable registration software were implemented for analysis of the resonance-scanned microscopy data. The software exhibited robust and accurate performance on the osmotic swelling measurements, as well as quantitative validation testing. The resonance-scanning protocol and developed analysis software allow for simultaneous strain calculation of both the local tissue and cells, and are thus a valuable tool for real-time probing of the cell-matrix interactions that are highly relevant in the fields of orthopedic biomechanics, cell mechanobiology, and functional tissue engineering.

The intrinsic quality of proteoglycans, but not collagen fibres, degrades in osteoarthritic cartilage.

The function of articular cartilage as a load-bearing connective tissue is derived primarily from a balanced interaction between the swelling proteoglycan (PG) matrix and tension-resistant collagen fibrous network. Such balance is compromised during joint disease such as osteoarthritis (OA) due to degradation to PGs and/or collagens. While the PG degradation is generally thought to be related to a loss of protein abundance, the collagenous degradation is more complex as it can be caused independently by a decrease of collagen content, disorganisation of fibrous structure and softening of individual collagen fibrils. A comprehensive understanding of the initial trajectories of degradation of PGs and collagen network can improve our chance of finding potential therapeutic solutions for OA. Here, we developed geometrically, structurally, and compositionally realistic and sample-specific Finite Element (FE) models under the framework of multiphasic mixture theory, from which the elastic moduli of collagen fibres and the PG load-bearing quality in healthy and diseased cartilages were estimated by numerical optimisation of the multi-step indentation stress relaxation force-time curves. We found the intrinsic quality of collagen fibres, measured by their elastic moduli, to stay constant for healthy and diseased cartilages. Combining with previous findings which show unaltered collagen content during early stages of OA, our results suggest the disorganisation of collagen fibrous network as the first form of collagenous degradation in osteoarthritic cartilage. We also found that PG degradation involves not only a loss of protein abundance, but also the quality of the remaining PGs in generating sufficient osmotic pressure for load bearing. This study sheds light on the mechanism of OA pathogenesis and highlights the restoration of collageneous organisation in cartilage as key medical intervention for OA. STATEMENT OF SIGNIFICANCE: Collagen network in articular cartilage consists of individual fibres that are organised into depth-dependent structure specialised for joint load-bearing and lubrication. During osteoarthritis, the collagen network undergoes mechanical degradation, but it is unclear if a loss of content, disorganisation of fibrous structure, or softening of individual fibres causes this degeneration. Using mechanical indentation, Finite Element modelling, and numerical optimisation methods, we determined that individual fibres did not soften in early disease stage. Together with previous findings showing unaltered collagen content, our results pinpoint the disorganisation of collagen structure as the main culprit for early collagenous degradation in osteoarthritic cartilage. Thus, early restoration in cartilage of collagen organisation, instead of individual fibre quality, may be key to slow osteoarthritis development.

Effect of cells on spatial quantification of proteoglycans in articular cartilage of small animals.

OBJECTIVE: Histochemical characterization of proteoglycan content in articular cartilage is important for the understanding of osteoarthritis pathogenesis. However, cartilage cells may interfere with the measurement of matrix proteoglycan content in small animal models (e.g. mice and rats) due to the high cell volume fraction (38%) in mice compared to human tissue (~1%). We investigated whether excluding the cells from image analysis affects the histochemically measured proteoglycan content of rat knee joint cartilage and assessed the effectiveness of a deep learning algorithm-based tool named U-Net in cell segmentation. DESIGN: Histological sections were stained with Safranin-O, after which optical densities were measured using digital densitometry to estimate proteoglycan content. U-Net was trained with 600 annotated Safranin-O cartilage images for exclusion of cells from the cartilage extracellular matrix. Optical densities of the ECM with and without cells were compared as a function of normalized tissue depth. RESULTS: U-Net cell segmentation was accurate, with the measured cell area fraction following largely that of ground-truth images (average difference: 4.3%). Cell area fraction varied as a function of tissue depth and took up 8-21% of the tissue area. The exclusion of cells from the analysis led to an increase in the analyzed depth-dependent optical density of cartilage by approximately 0.6-1.8% (p < 0.01). CONCLUSIONS: Although the effect of cells on the analyzed proteoglycan content is small, it should be considered for improved sensitivity, especially at the onset of the disease during which cells may proliferate in small animals.

The Protective Function of Directed Asymmetry in the Pericellular Matrix Enveloping Chondrocytes.

The specialized pericellular matrix (PCM) surrounding chondrocytes within articular cartilage is critical to the tissue's health and longevity. Growing evidence suggests that PCM alterations are ubiquitous across all trajectories of osteoarthritis, a crippling and prevalent joint disease. The PCM geometry is of particular interest as it influences the cellular mechanical environment. Observations of asymmetrical PCM thickness have been reported, but a quantified characterization is lacking. To this end, a novel microscopy protocol was developed and applied to acquire images of the PCM surrounding live cells. Morphometric analysis indicated a statistical bias towards thicker PCM on the inferior cellular surface. The mechanical effects of this bias were investigated with multiscale modelling, which revealed potentially damaging, high tensile strains in the direction perpendicular to the membrane and localized on the inferior surface. These strains varied substantially between PCM asymmetry cases. Simulations with a thicker inferior PCM, representative of the observed geometry, resulted in strain magnitudes approximately half of those calculated for a symmetric geometry, and a third of those with a thin inferior PCM. This strain attenuation suggests that synthesis of a thicker inferior PCM may be a protective adaptation. PCM asymmetry may thus be important in cartilage development, pathology, and engineering.

Chondrocyte Deformations Under Mild Dynamic Loading Conditions.

Dynamic deformation of chondrocytes are associated with cell mechanotransduction and thus may offer a new understanding of the mechanobiology of articular cartilage. Despite extensive research on chondrocyte deformations for static conditions, work for dynamic conditions remains rare. However, it is these dynamic conditions that articular cartilage in joints are exposed to everyday, and that seem to promote biological signaling in chondrocytes. Therefore, the objective of this study was to develop an experimental technique to determine the in situ deformations of chondrocytes when the cartilage is dynamically compressed. We hypothesized that dynamic deformations of chondrocytes vastly differ from those observed under steady-state static strain conditions. Real-time chondrocyte geometry was reconstructed at 10, 15, and 20% compression during ramp compressions with 20% ultimate strain, applied at a strain rate of 0.2% s-1, followed by stress relaxation. Dynamic compressive chondrocyte deformations were non-linear as a function of nominal strain, with large deformations in the early and small deformations in the late part of compression. Early compression (up to about 10%) was associated with chondrocyte volume loss, while late compression (> ~ 10%) was associated with cell deformation but minimal volume loss. Force continued to decrease for 5 min in the stress-relaxation phase, while chondrocyte shape/volume remained unaltered after the first minute of stress-relaxation.

Three-dimensional micro-scale strain mapping in living biological soft tissues.

Non-invasive characterization of the mechanical micro-environment surrounding cells in biological tissues at multiple length scales is important for the understanding of the role of mechanics in regulating the biosynthesis and phenotype of cells. However, there is a lack of imaging methods that allow for characterization of the cell micro-environment in three-dimensional (3D) space. The aims of this study were (i) to develop a multi-photon laser microscopy protocol capable of imprinting 3D grid lines onto living tissue at a high spatial resolution, and (ii) to develop image processing software capable of analyzing the resulting microscopic images and performing high resolution 3D strain analyses. Using articular cartilage as the biological tissue of interest, we present a novel two-photon excitation imaging technique for measuring the internal 3D kinematics in intact cartilage at sub-micrometer resolution, spanning length scales from the tissue to the cell level. Using custom image processing software, we provide accurate and robust 3D micro-strain analysis that allows for detailed qualitative and quantitative assessment of the 3D tissue kinematics. This novel technique preserves tissue structural integrity post-scanning, therefore allowing for multiple strain measurements at different time points in the same specimen. The proposed technique is versatile and opens doors for experimental and theoretical investigations on the relationship between tissue deformation and cell biosynthesis. Studies of this nature may enhance our understanding of the mechanisms underlying cell mechano-transduction, and thus, adaptation and degeneration of soft connective tissues. STATEMENT OF SIGNIFICANCE: We presented a novel two-photon excitation imaging technique for measuring the internal 3D kinematics in intact cartilage at sub-micrometer resolution, spanning from tissue length scale to cellular length scale. Using a custom image processing software (lsmgridtrack), we provide accurate and robust micro-strain analysis that allowed for detailed qualitative and quantitative assessment of the 3D tissue kinematics. The approach presented here can also be applied to other biological tissues such as meniscus and annulus fibrosus, as well as tissue-engineered tissues for the characterization of their mechanical properties. This imaging technique opens doors for experimental and theoretical investigation on the relationship between tissue deformation and cell biosynthesis. Studies of this nature may enhance our understanding of the mechanisms underlying cell mechano-transduction, and thus, adaptation and degeneration of soft connective tissues.

The potential for intercellular mechanical interaction: simulations of single chondrocyte versus anatomically based distribution.

Computational studies of chondrocyte mechanics, and cell mechanics in general, have typically been performed using single cell models embedded in an extracellular matrix construct. The assumption of a single cell microstructural model may not capture intercellular interactions or accurately reflect the macroscale mechanics of cartilage when higher cell concentrations are considered, as may be the case in many instances. Hence, the goal of this study was to compare cell-level response of single and eleven cell biphasic finite element models, where the latter provided an anatomically based cellular distribution representative of the actual number of cells for a commonly used [Formula: see text] edge cubic representative volume in the middle zone of cartilage. Single cell representations incorporated a centered single cell model and eleven location-corrected single cell models, the latter to delineate the role of cell placement in the representative volume element. A stress relaxation test at 10% compressive strain was adopted for all simulations. During transient response, volume- averaged chondrocyte mechanics demonstrated marked differences (up to 60% and typically greater than 10%) for the centered single versus the eleven cell models, yet steady-state loading was similar. Cell location played a marked role, due to inhomogeneity of the displacement and fluid pressure fields at the macroscopic scale. When the single cell representation was corrected for cell location, the transient response was consistent, while steady-state differences on the order of 1-4% were realized, which may be attributed to intercellular mechanical interactions. Anatomical representations of the superficial and deep zones, where cells reside in close proximity, may exhibit greater intercellular interactions, but these have yet to be explored.

In vivo Sarcomere Lengths and Sarcomere Elongations Are Not Uniform across an Intact Muscle.

Sarcomere lengths have been a crucial outcome measure for understanding and explaining basic muscle properties and muscle function. Sarcomere lengths for a given muscle are typically measured at a single spot, often in the mid-belly of the muscle, and at a given muscle length. It is then assumed implicitly that the sarcomere length measured at this single spot represents the sarcomere lengths at other locations within the muscle, and force-length, force-velocity, and power-velocity properties of muscles are often implied based on these single sarcomere length measurements. Although, intuitively appealing, this assumption is yet to be supported by systematic evidence. The objective of this study was to measure sarcomere lengths at defined locations along and across an intact muscle, at different muscle lengths. Using second harmonic generation (SHG) imaging technique, sarcomere patterns in passive mouse tibialis anterior (TA) were imaged in a non-contact manner at five selected locations ("proximal," "distal," "middle," "medial," and "lateral" TA sites) and at three different lengths encompassing the anatomical range of motion of the TA. We showed that sarcomere lengths varied substantially within small regions of the muscle and also for different sites across the entire TA. Also, sarcomere elongations with muscle lengthening were non-uniform across the muscle, with the highest sarcomere stretches occurring near the myotendinous junction. We conclude that muscle mechanics derived from sarcomere length measured from a small region of a muscle may not well-represent the sarcomere length and associated functional properties of the entire muscle.

High-fat high-sucrose diet leads to dynamic structural and inflammatory alterations in the rat vastus lateralis muscle.

The influence of obesity on muscle integrity is not well understood. The purpose of this study was to quantify structural and molecular changes in the rat vastus lateralis (VL) muscle as a function of a 12-week obesity induction period and a subsequent adaptation period (additional 16-weeks). Male Sprague-Dawley rats consumed a high-fat, high-sucrose (DIO, n = 40) diet, or a chow control-diet (n = 14). At 12-weeks, DIO rats were grouped as prone (DIO-P, top 33% of weight change) or resistant (DIO-R, bottom 33%). Animals were euthanized at 12- or 28-weeks on the diet. At sacrifice, body composition was determined and VL muscles were collected. Intramuscular fat, fibrosis, and CD68+ cells were quantified histologically and relevant molecular markers were evaluated using RT-qPCR. At 12- and 28-weeks post-obesity induction, DIO-P rats had more mass and body fat than DIO-R and chow rats (p < 0.05). DIO-P and DIO-R rats had similar losses in muscle mass, which were greater than those in chow rats (p < 0.05). mRNA levels for MAFbx/atrogin-1 were reduced in DIO-P and DIO-R rats at 12- and 28-weeks compared to chow rats (p < 0.05), while expression of MuRF1 was similar to chow values. DIO-P rats demonstrated increased mRNA levels for pro-inflammatory mediators, inflammatory cells, and fibrosis compared to DIO-R and chow animals, despite having similar levels of intramuscular fat. The down-regulation of MAFbx/atrogin-1 may suggest onset of degenerative changes in VL muscle integrity of obese rats. DIO-R animals exhibited fewer inflammatory changes compared to DIO-P animals, suggesting a protective effect of obesity resistance on local inflammation. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:2069-2078, 2016.

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.

Automated generation of tissue-specific three-dimensional finite element meshes containing ellipsoidal cellular inclusions.

Finite element analysis provides a means of describing cellular mechanics in tissue, which can be useful in understanding and predicting physiological and pathological changes. Many prior studies have been limited to simulations of models containing single cells, which may not accurately describe the influence of mechanical interactions between cells. It is desirable to generate models that more accurately reflect the cellular organisation in tissue in order to evaluate the mechanical function of cells. However, as the model geometry becomes more complicated, manual model generation can become laborious. This can be prohibitive if a large number of distinct cell-scale models are required, for example, in multiscale modelling or probabilistic analysis. Therefore, a method was developed to automatically generate tissue-specific cellular models of arbitrary complexity, with minimal user intervention. This was achieved through a set of scripts, which are capable of generating both sample-specific models, with explicitly defined geometry, and tissue-specific models, with geometry derived implicitly from normal statistical distributions. Models are meshed with tetrahedral (TET) elements of variable size to sufficiently discretise model geometries at different spatial scales while reducing model complexity. The ability of TET meshes to appropriately simulate the biphasic mechanical response of a single-cell model is established against that of a corresponding hexahedral mesh for an illustrative use case. To further demonstrate the flexibility of this tool, an explicit model was developed from three-dimensional confocal laser scanning image data, and a set of models were generated from a statistical cellular distribution of the articular femoral cartilage. The tools presented herein are free and openly accessible to the community at large.

Extracellular matrix integrity affects the mechanical behaviour of in-situ chondrocytes under compression.

Cartilage lesions change the microenvironment of cells and may accelerate cartilage degradation through catabolic responses from chondrocytes. In this study, we investigated the effects of structural integrity of the extracellular matrix (ECM) on chondrocytes by comparing the mechanics of cells surrounded by an intact ECM with cells close to a cartilage lesion using experimental and numerical methods. Experimentally, 15% nominal compression was applied to bovine cartilage tissues using a light-transmissible compression system. Target cells in the intact ECM and near lesions were imaged by dual-photon microscopy. Changes in cell morphology (N(cell)=32 for both ECM conditions) were quantified. A two-scale (tissue level and cell level) Finite Element (FE) model was also developed. A 15% nominal compression was applied to a non-linear, biphasic tissue model with the corresponding cell level models studied at different radial locations from the centre of the sample in the transient phase and at steady state. We studied the Green-Lagrange strains in the tissue and cells. Experimental and theoretical results indicated that cells near lesions deform less axially than chondrocytes in the intact ECM at steady state. However, cells near lesions experienced large tensile strains in the principal height direction, which are likely associated with non-uniform tissue radial bulging. Previous experiments showed that tensile strains of high magnitude cause an up-regulation of digestive enzyme gene expressions. Therefore, we propose that cartilage degradation near tissue lesions may be due to the large tensile strains in the principal height direction applied to cells, thus leading to an up-regulation of catabolic factors.

The biomechanical relevance of anterior rotator cuff cable tears in a cadaveric shoulder model.

BACKGROUND: Anterior tears of the supraspinatus tendon are more likely to be clinically relevant than posterior tears of the supraspinatus. We hypothesized that anterior tears of the supraspinatus tendon involving the rotator cuff cable insertion are associated with greater tear gapping, decreased tendon stiffness, and increased regional tendon strain under physiologic loading conditions compared with equivalently sized tears of the rotator cuff crescent. METHODS: Twelve human cadaveric shoulders were randomized to undergo simulation of equivalently sized supraspinatus tears of either the anterior rotator cuff cable (n = 6) or the adjacent rotator cuff crescent (n = 6). For each specimen, the supraspinatus tendon was cyclically loaded from 10 N to 180 N, and a custom three-dimensional optical system was used to track markers on the surface of the tendon. Tear gap distance, stiffness, and regional strains of the supraspinatus tendon were calculated. RESULTS: The tear gap distance of large cable tears (median gap distance, 5.2 mm) was significantly greater than that of large crescent tears (median gap distance, 1.3 mm) (p = 0.002), the stiffness of tendons with a small (p = 0.002) or large (p = 0.002) cable tear was significantly greater than that of tendons with equivalently sized crescent tears, and regional strains across the supraspinatus were significantly increased in magnitude and altered in distribution by tears involving the anterior insertion of the rotator cuff cable. CONCLUSIONS: These findings support our hypothesis that the rotator cuff cable, which is in the most anterior 8 to 12 mm of the supraspinatus tendon immediately posterior to the bicipital groove, is the primary load-bearing structure within the supraspinatus for force transmission to the proximal part of the humerus. Conversely, in the presence of an intact rotator cuff cable, the rotator cuff crescent insertion is relatively stress-shielded and plays a significantly lesser role in supraspinatus force transmission. CLINICAL RELEVANCE: Clinicians should consider early repair of rotator cuff cable tears, which may need surgical intervention to address their biomechanical pathology. In contrast, surgical treatment may be more safely delayed for rotator cuff crescent tears.

Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes.

Understanding the mechanical behaviour of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue-level deformations drive cell-level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular-scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of first- and second-order data passing to predict chondrocyte mechanics by analysing cartilage deformations obtained for varying complexity of loading scenarios. A tissue-scale model with a sub-region incorporating representation of chondron size and distribution served as control. The post-processing approach first required solution of a homogeneous tissue-level model, results of which were used to drive a separate cell-level model (same characteristics as the sub-region of control model). The first-order data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, for example, change in aspect ratio. The second-order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries was considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, for example, mass exchange rate. Nonetheless, employing higher order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.

A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation.

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.

Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations.

Cells of the musculoskeletal system are known to respond to mechanical loading and chondrocytes within the cartilage are not an exception. However, understanding how joint level loads relate to cell level deformations, e.g. in the cartilage, is not a straightforward task. In this study, a multi-scale analysis pipeline was implemented to post-process the results of a macro-scale finite element (FE) tibiofemoral joint model to provide joint mechanics based displacement boundary conditions to micro-scale cellular FE models of the cartilage, for the purpose of characterizing chondrocyte deformations in relation to tibiofemoral joint loading. It was possible to identify the load distribution within the knee among its tissue structures and ultimately within the cartilage among its extracellular matrix, pericellular environment and resident chondrocytes. Various cellular deformation metrics (aspect ratio change, volumetric strain, cellular effective strain and maximum shear strain) were calculated. To illustrate further utility of this multi-scale modeling pipeline, two micro-scale cartilage constructs were considered: an idealized single cell at the centroid of a 100×100×100 µm block commonly used in past research studies, and an anatomically based (11 cell model of the same volume) representation of the middle zone of tibiofemoral cartilage. In both cases, chondrocytes experienced amplified deformations compared to those at the macro-scale, predicted by simulating one body weight compressive loading on the tibiofemoral joint. In the 11 cell case, all cells experienced less deformation than the single cell case, and also exhibited a larger variance in deformation compared to other cells residing in the same block. The coupling method proved to be highly scalable due to micro-scale model independence that allowed for exploitation of distributed memory computing architecture. The method's generalized nature also allows for substitution of any macro-scale and/or micro-scale model providing application for other multi-scale continuum mechanics problems.

Angiogenesis in a microvascular construct for transplantation depends on the method of chamber circulation.

Effective tissue prevascularization depends on new vessel growth and subsequent progression of neovessels into a stable microcirculation. Isolated microvessel fragments in a collagen-based microvascular construct (MVC) spontaneously undergo angiogenesis in static conditions in vitro but form a new microcirculation only when implanted in vivo. We have designed a bioreactor, the dynamic in vitro perfusion (DIP) chamber, to culture MVCs in vitro with perfusion. By altering bioreactor circulation, microvessel fragments in the DIP chamber either maintained stable, nonsprouting, patent vessel morphologies or sprouted endothelial neovessels that extended out into the surrounding collagen matrix (i.e., angiogenesis), yielding networks of neovessels within the MVC. Neovessels formed in regions of the construct predicted by simulation models to have the steepest gradients in oxygen levels and expressed hypoxia inducible factor-1alpha. By altering circulation conditions in the DIP chamber, we can control, possibly by modulating hypoxic stress, prevascularizing activity in vitro.