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

Iris stromal cell nuclei deform to more elongated shapes during pharmacologically-induced miosis and mydriasis

Nuclear shape alteration in ocular tissues, which can be used as a metric for overall cell deformation, may also lead to changes in gene expression and protein synthesis that could affect the biomechanics of the tissue extracellular matrix. The biomechanics of iris tissue is of particular interest in the study of primary angle-closure glaucoma. As the first step towards understanding the mutual role of the biomechanics and deformation of the iris on the activity of its constituent stromal cells, we conducted an ex-vivo study in freshly excised porcine eyes. Iris deformation was achieved by activating the constituent smooth muscles of the iris. Pupillary responses were initiated by inducing miosis and mydriasis, and the irides were placed in a fixative, bisected, and sliced into thin sections in a nasal and temporal horizontal orientation. The tissue sections were stained with DAPI for nucleus, and z-stacks were acquired using confocal microscopy. Images were analyzed to determine the nuclear aspect ratio (NAR) using both three-dimensional (3D) reconstructions of the nuclear surfaces as well as projections of the same 3D reconstruction into flat two-dimensional (2D) shapes. We observed that regardless of the calculation method (i.e., one that employed 3D surface reconstructions versus one that employed 2D projected images) the NAR increased in both the miosis group and the mydriasis group. Three-dimensional quantifications showed that NAR increased from 2.52 ± 0.96 in control group to 2.80 ± 0.81 and 2.74 ± 0.94 in the mydriasis and miosis groups, respectively. Notwithstanding the relative convenience in calculating the NAR using the 2D projected images, the 3D reconstructions were found to generate more physiologically realistic values and, thus, can be used in the development of future computational models to study primary angle-closure glaucoma. Since the iris undergoes large deformations in response to ambient light, this study suggests that the iris stromal cells are subjected to a biomechanically active micro-environment during their in-vivo physiological function.

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.

Mechanobiological model for simulation of injured cartilage degradation via pro-inflammatory cytokines and mechanical stimulus

Post-traumatic osteoarthritis (PTOA) is associated with cartilage degradation, ultimately leading to disability and decrease of quality of life. Two key mechanisms have been suggested to occur in PTOA: tissue inflammation and abnormal biomechanical loading. Both mechanisms have been suggested to result in loss of cartilage proteoglycans, the source of tissue fixed charge density (FCD). In order to predict the simultaneous effect of these degrading mechanisms on FCD content, a computational model has been developed. We simulated spatial and temporal changes of FCD content in injured cartilage using a novel finite element model that incorporates (1) diffusion of the pro-inflammatory cytokine interleukin-1 into tissue, and (2) the effect of excessive levels of shear strain near chondral defects during physiologically relevant loading. Cytokine-induced biochemical cartilage explant degradation occurs near the sides, top, and lesion, consistent with the literature. In turn, biomechanically-driven FCD loss is predicted near the lesion, in accordance with experimental findings: regions near lesions showed significantly more FCD depletion compared to regions away from lesions (p<0.01). Combined biochemical and biomechanical degradation is found near the free surfaces and especially near the lesion, and the corresponding bulk FCD loss agrees with experiments. We suggest that the presence of lesions plays a role in cytokine diffusion-driven degradation, and also predisposes cartilage for further biomechanical degradation. Models considering both these cartilage degradation pathways concomitantly are promising in silico tools for predicting disease progression, recognizing lesions at high risk, simulating treatments, and ultimately optimizing treatments to postpone the development of PTOA.

Post-traumatic osteoarthritis is a musculoskeletal disorder where inflammatory processes and abnormal joint loading predispose articular cartilage to degradation after a mechanical injury. Since inflamed and injured cartilage cannot be reversed back to healthy state, prevention of osteoarthritis progression is advisable, a prestigious goal where computational models could serve as tools. The current literature is short of computational models combining both biochemical and biomechanical aspects of osteoarthritis. Thus, here we implemented inflammation of living cartilage tissue followed by biochemical perturbations of tissue homeostasis and shear strain-induced biomechanical degradation in novel cell-to-tissue-level finite element models. The models presented in this paper and enriched by our experimental findings/previous literature provide profound new mechanobiological insights and predictions about cartilage degradation in injured and inflamed tissue under physiologically relevant mechanical loading. We suggest that mechanobiological computational models could be applied as in silico analysis tools that provide clinicians information of the personalized progression of post-traumatic osteoarthritis and decision-making guidance for treatment of the disease.

Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Overall Strategy

Recent explorations of knee biomechanics have benefited from computational modeling, specifically leveraging advancements in finite element analysis and rigid body dynamics of joint and tissue mechanics. A large number of models have emerged with different levels of fidelity in anatomical and mechanical representation. Adapted modeling and simulation processes vary widely, based on justifiable choices in relation to anticipated use of the model. However, there are situations where modelers' decisions seem to be subjective, arbitrary, and difficult to rationalize. Regardless of the basis, these decisions form the "art" of modeling, which impact the conclusions of simulation-based studies on knee function. These decisions may also hinder the reproducibility of models and simulations, impeding their broader use in areas such as clinical decision making and personalized medicine. This document summarizes an ongoing project that aims to capture the modeling and simulation workflow in its entirety-operation procedures, deviations, models, by-products of modeling, simulation results, and comparative evaluations of case studies and applications. The ultimate goal of the project is to delineate the art of a cohort of knee modeling teams through a publicly accessible, transparent approach and begin to unravel the complex array of factors that may lead to a lack of reproducibility. This manuscript outlines our approach along with progress made so far. Potential implications on reproducibility, on science, engineering, and training of modeling and simulation, on modeling standards, and on regulatory affairs are also noted.

Use of Computational Modeling to Study Joint Degeneration: A Review

Osteoarthritis (OA), a degenerative joint disease, is the most common chronic condition of the joints, which cannot be prevented effectively. Computational modeling of joint degradation allows to estimate the patient-specific progression of OA, which can aid clinicians to estimate the most suitable time window for surgical intervention in osteoarthritic patients. This paper gives an overview of the different approaches used to model different aspects of joint degeneration, thereby focusing mostly on the knee joint. The paper starts by discussing how OA affects the different components of the joint and how these are accounted for in the models. Subsequently, it discusses the different modeling approaches that can be used to answer questions related to OA etiology, progression and treatment. These models are ordered based on their underlying assumptions and technologies: musculoskeletal models, Finite Element models, (gene) regulatory models, multiscale models and data-driven models (artificial intelligence/machine learning). Finally, it is concluded that in the future, efforts should be made to integrate the different modeling techniques into a more robust computational framework that should not only be efficient to predict OA progression but also easily allow a patient’s individualized risk assessment as screening tool for use in clinical practice.

Chondrocyte viability is lost during high-rate impact loading by transfer of amplified strain, but not stress, to pericellular and cellular regions

OBJECTIVE

Deleterious impact loading to cartilage initiates post-traumatic osteoarthritis (OA). While cytokine and enzyme levels regulate disease progression, specific mechanical cues that elucidate cellular OA origins merit further investigation. We defined the dominant pericellular and cellular strain/stress transfer mechanisms following bulk-tissue injury associated with cell death.

METHOD

Using an in vitro model, we investigated rate-dependent loading and spatial localization of cell viability in acute indentation and time-course studies. Atomic force microscopy (AFM) and magnetic resonance imaging (MRI) confirmed depth-wise changes in cartilage micro-/macro-mechanics and structure post-indentation. To understand the transfer of loading to cartilage domains, we computationally modeled full-field strain and stress measures in interstitial matrix, pericellular and cellular regions.

RESULTS

Chondrocyte viability decreased following rapid impact (80%/s) vs slow loading (0.1%/s) or unloaded controls. Viability was lost immediately during impact within regions near the indenter-tissue contact but did not change over 7 days of tissue culture. AFM studies revealed a loss of stiffness following 80%/s loading, and MRI studies confirmed an increased tensile and shear strain, but not relaxometry. Image-based patterns of chondrocyte viability closely matched computational estimates of amplified maximum principal and shear strain in interstitial matrix, pericellular and cellular regions.

CONCLUSION

Rapid indentation worsens chondrocyte death and degrades cartilage matrix stiffness in indentation regions. Cell death at high strain rates may be driven by elevated tensile strains, but not matrix stress. Strain amplification beyond critical thresholds in the pericellular matrix and cells may define a point of origin for early damage in post-traumatic OA.

Crash Injury Analysis of Knee Joint Considering Pedestrian Safety

Background:

Lower extremity injuries are frequently observed in car-to-pedestrian accidents and due to the bumper height of most cars, knee joint is one of the most damaged body parts in car-to-pedestrian collisions.

Objective:

The aim of this paper is first to provide an accurate Finite Element model of the knee joint and second to investigate lower limb impact biomechanics in car-to-pedestrian accidents and to predict the effect of parameters such as collision speed and height due to the car speed and bumper height on knee joint injuries, especially in soft tissues such as ligaments, cartilages and menisci.

Materials and Methods:

In this analytical study, a 3D finite element (FE) model of human body knee joint is developed based on human anatomy. The model consists of femur, tibia, menisci, articular cartilages and ligaments. Material properties of bones and soft tissues were assumed to be elastic, homogenous and isotropic.

Results:

FE model is used to perform injury reconstructions and predict the damages by using physical parameters such as Von-Mises stress and equivalent elastic strain of tissues.

Conclusion:

The results of simulations first show that the most vulnerable part of the knee is MCL ligament and second the effect of speed and height of the impact on knee joint. In the critical member, MCL, the damage increased in higher speeds but as an exception, smaller damages took place in menisci due to the increased distance of two bones in the higher speed.

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.

Perspectives on Sharing Models and Related Resources in Computational Biomechanics Research

The role of computational modeling for biomechanics research and related clinical care will be increasingly prominent. The biomechanics community has been developing computational models routinely for exploration of the mechanics and mechanobiology of diverse biological structures. As a result, a large array of models, data, and discipline-specific simulation software has emerged to support endeavors in computational biomechanics. Sharing computational models and related data and simulation software has first become a utilitarian interest, and now, it is a necessity. Exchange of models, in support of knowledge exchange provided by scholarly publishing, has important implications. Specifically, model sharing can facilitate assessment of reproducibility in computational biomechanics and can provide an opportunity for repurposing and reuse, and a venue for medical training. The community's desire to investigate biological and biomechanical phenomena crossing multiple systems, scales, and physical domains, also motivates sharing of modeling resources as blending of models developed by domain experts will be a required step for comprehensive simulation studies as well as the enhancement of their rigor and reproducibility. The goal of this paper is to understand current perspectives in the biomechanics community for the sharing of computational models and related resources. Opinions on opportunities, challenges, and pathways to model sharing, particularly as part of the scholarly publishing workflow, were sought. A group of journal editors and a handful of investigators active in computational biomechanics were approached to collect short opinion pieces as a part of a larger effort of the IEEE EMBS Computational Biology and the Physiome Technical Committee to address model reproducibility through publications. A synthesis of these opinion pieces indicates that the community recognizes the necessity and usefulness of model sharing. There is a strong will to facilitate model sharing, and there are corresponding initiatives by the scientific journals. Outside the publishing enterprise, infrastructure to facilitate model sharing in biomechanics exists, and simulation software developers are interested in accommodating the community's needs for sharing of modeling resources. Encouragement for the use of standardized markups, concerns related to quality assurance, acknowledgement of increased burden, and importance of stewardship of resources are noted. In the short-term, it is advisable that the community builds upon recent strategies and experiments with new pathways for continued demonstration of model sharing, its promotion, and its utility. Nonetheless, the need for a long-term strategy to unify approaches in sharing computational models and related resources is acknowledged. Development of a sustainable platform supported by a culture of open model sharing will likely evolve through continued and inclusive discussions bringing all stakeholders at the table, e.g., by possibly establishing a consortium.

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

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

Osteoarthritis as a disease of the cartilage pericellular matrix

Osteoarthritis is a painful joint disease characterized by progressive degeneration of the articular cartilage as well as associated changes to the subchondral bone, synovium, and surrounding joint tissues. While the effects of osteoarthritis on the cartilage extracellular matrix (ECM) have been well recognized, it is now becoming apparent that in many cases, the onset of the disease may be initially reflected in the matrix region immediately surrounding the chondrocytes, termed the pericellular matrix (PCM). Growing evidence suggests that the PCM - which along with the enclosed chondrocytes are termed the "chondron" - acts as a critical transducer or "filter" of biochemical and biomechanical signals for the chondrocyte, serving to help regulate the homeostatic balance of chondrocyte metabolic activity in response to environmental signals. Indeed, it appears that alterations in PCM properties and cell-matrix interactions, secondary to genetic, epigenetic, metabolic, or biomechanical stimuli, could in fact serve as initiating or progressive factors for osteoarthritis. Here, we discuss recent advances in the understanding of the role of the PCM, with an emphasis on the reciprocity of changes that occur in this matrix region with disease, as well as how alterations in PCM properties could serve as a driver of ECM-based diseases such as osteoarthritis. Further study of the structure, function, and composition of the PCM in normal and diseased conditions may provide new insights into the understanding of the pathogenesis of osteoarthritis, and presumably new therapeutic approaches for this disease.

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.

Commentary on the integration of model sharing and reproducibility analysis to scholarly publishing workflow in computational biomechanics

OBJECTIVE

The overall goal of this paper is to demonstrate that dissemination of models and analyses for assessing the reproducibility of simulation results can be incorporated in the scientific review process in biomechanics.

METHODS

As part of a special issue on model sharing and reproducibility in the IEEE Transactions on Biomedical Engineering, two manuscripts on computational biomechanics were submitted: Rajagopal et al., IEEE Trans. Biomed. Eng., 2016 and Schmitz and Piovesan, IEEE Trans. Biomed. Eng., 2016. Models used in these studies were shared with the scientific reviewers and the public. In addition to the standard review of the manuscripts, the reviewers downloaded the models and performed simulations that reproduced results reported in the studies.

RESULTS

There was general agreement between simulation results of the authors and those of the reviewers. Discrepancies were resolved during the necessary revisions. The manuscripts and instructions for download and simulation were updated in response to the reviewers' feedback; changes that may otherwise have been missed if explicit model sharing and simulation reproducibility analysis was not conducted in the review process. Increased burden on the authors and the reviewers, to facilitate model sharing and to repeat simulations, were noted.

CONCLUSION

When the authors of computational biomechanics studies provide access to models and data, the scientific reviewers can download and thoroughly explore the model, perform simulations, and evaluate simulation reproducibility beyond the traditional manuscript-only review process.

SIGNIFICANCE

Model sharing and reproducibility analysis in scholarly publishing will result in a more rigorous review process, which will enhance the quality of modeling and simulation studies and inform future users of computational models.

Open Knee: Open Source Modeling and Simulation in Knee Biomechanics

Virtual representations of the knee joint can provide clinicians, scientists, and engineers the tools to explore mechanical functions of the knee and its tissue structures in health and disease. Modeling and simulation approaches such as finite element analysis also provide the possibility to understand the influence of surgical procedures and implants on joint stresses and tissue deformations. A large number of knee joint models are described in the biomechanics literature. However, freely accessible, customizable, and easy-to-use models are scarce. Availability of such models can accelerate clinical translation of simulations, where labor-intensive reproduction of model development steps can be avoided. Interested parties can immediately utilize readily available models for scientific discovery and clinical care. Motivated by this gap, this study aims to describe an open source and freely available finite element representation of the tibiofemoral joint, namely Open Knee, which includes the detailed anatomical representation of the joint's major tissue structures and their nonlinear mechanical properties and interactions. Three use cases illustrate customization potential of the model, its predictive capacity, and its scientific and clinical utility: prediction of joint movements during passive flexion, examining the role of meniscectomy on contact mechanics and joint movements, and understanding anterior cruciate ligament mechanics. A summary of scientific and clinically directed studies conducted by other investigators are also provided. The utilization of this open source model by groups other than its developers emphasizes the premise of model sharing as an accelerator of simulation-based medicine. Finally, the imminent need to develop next-generation knee models is noted. These are anticipated to incorporate individualized anatomy and tissue properties supported by specimen-specific joint mechanics data for evaluation, all acquired in vitro from varying age groups and pathological states.

In Vivo Dynamic Deformation of Articular Cartilage in Intact Joints Loaded by Controlled Muscular Contractions

When synovial joints are loaded, the articular cartilage and the cells residing in it deform. Cartilage deformation has been related to structural tissue damage, and cell deformation has been associated with cell signalling and corresponding anabolic and catabolic responses. Despite the acknowledged importance of cartilage and cell deformation, there are no dynamic data on these measures from joints of live animals using muscular load application. Research in this area has typically been done using confined and unconfined loading configurations and indentation testing. These loading conditions can be well controlled and allow for accurate measurements of cartilage and cell deformations, but they have little to do with the contact mechanics occurring in a joint where non-congruent cartilage surfaces with different material and functional properties are pressed against each other by muscular forces. The aim of this study was to measure in vivo, real time articular cartilage deformations for precisely controlled static and dynamic muscular loading conditions in the knees of mice. Fifty and 80% of the maximal knee extensor muscular force (equivalent to approximately 0.4N and 0.6N) produced average peak articular cartilage strains of 10.5±1.0% and 18.3±1.3% (Mean ± SD), respectively, during 8s contractions. A sequence of 15 repeat, isometric muscular contractions (0.5s on, 3.5s off) of 50% and 80% of maximal muscular force produced cartilage strains of 3.0±1.1% and 9.6±1.5% (Mean ± SD) on the femoral condyles of the mouse knee. Cartilage thickness recovery following mechanical compression was highly viscoelastic and took almost 50s following force removal in the static tests.

A Comprehensive Specimen-Specific Multiscale Data Set for Anatomical and Mechanical Characterization of the Tibiofemoral Joint

Understanding of tibiofemoral joint mechanics at multiple spatial scales is essential for developing effective preventive measures and treatments for both pathology and injury management. Currently, there is a distinct lack of specimen-specific biomechanical data at multiple spatial scales, e.g., joint, tissue, and cell scales. Comprehensive multiscale data may improve the understanding of the relationship between biomechanical and anatomical markers across various scales. Furthermore, specimen-specific multiscale data for the tibiofemoral joint may assist development and validation of specimen-specific computational models that may be useful for more thorough analyses of the biomechanical behavior of the joint. This study describes an aggregation of procedures for acquisition of multiscale anatomical and biomechanical data for the tibiofemoral joint. Magnetic resonance imaging was used to acquire anatomical morphology at the joint scale. A robotic testing system was used to quantify joint level biomechanical response under various loading scenarios. Tissue level material properties were obtained from the same specimen for the femoral and tibial articular cartilage, medial and lateral menisci, anterior and posterior cruciate ligaments, and medial and lateral collateral ligaments. Histology data were also obtained for all tissue types to measure specimen-specific cell scale information, e.g., cellular distribution. This study is the first of its kind to establish a comprehensive multiscale data set for a musculoskeletal joint and the presented data collection approach can be used as a general template to guide acquisition of specimen-specific comprehensive multiscale data for musculoskeletal joints.

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 multi-scale finite element model for investigation of chondrocyte mechanics in normal and medial meniscectomy human knee joint during walking

Mechanical signals experienced by chondrocytes (articular cartilage cells) modulate cell synthesis and cartilage health. Multi-scale modeling can be used to study how forces are transferred from joint surfaces through tissues to chondrocytes. Therefore, estimation of chondrocyte behavior during certain physical activities, such as walking, could provide information about how cells respond to normal and abnormal loading in joints. In this study, a 3D multi-scale model was developed for evaluating chondrocyte and surrounding peri- and extracellular matrix responses during gait loading within healthy and medial meniscectomy knee joints. The knee joint geometry was based on MRI, whereas the input used for gait loading was obtained from the literature. Femoral and tibial cartilages were modeled as fibril-reinforced poroviscoelastic materials, whereas menisci were considered as transversely isotropic. Fluid pressures in the chondrocyte and cartilage tissue increased up to 2MPa (an increase of 30%) in the meniscectomy joint compared to the normal, healthy joint. The elevated level of fluid pressure was observed during the entire stance phase of gait. A medial meniscectomy caused substantially larger (up to 60%) changes in maximum principal strains in the chondrocyte compared to those in the peri- or extracellular matrices. Chondrocyte volume or morphology did not change substantially due to a medial meniscectomy. Current findings suggest that during walking chondrocyte deformations are not substantially altered due to a medial meniscectomy, while abnormal joint loading exposes chondrocytes to elevated levels of fluid pressure and maximum principal strains (compared to strains in the peri- or extracellular matrices). These might contribute to cell viability and the onset of osteoarthritis.

Using information metrics and molecular communication to detect cellular tissue deformation

Calcium-signaling-based molecular communication has been proposed as one form of communication for short range transmission between nanomachines. This form of communication is naturally found within cellular tissues, where Ca(2+) ions propagate and diffuse between cells. However, the naturally flexible structure of cells usually leads to the cells dynamically changing shape under strain. Since the interconnected cells form the tissue, a change in shape of one cell will change the shape of the neighboring cells and the tissue as a whole. This will in turn dramatically impair the communication channel between the nanomachines. We propose a process for nanomachines utilizing Ca(2+) based molecular communication to infer and detect the state of the tissue, which we term the Molecular Nanonetwork Inference Process. The process employs a threshold based classifier that identifies its threshold boundaries based on a training process. The inference/detection mechanism allows the destination nanomachine to determine: i) the type of tissue deformation; ii) the amount of tissue deformation; iii) the amount of Ca(2+) concentration emitted from the source nanomachine; and iv) its distance from the destination nanomachines. We evaluate the use of three information metrics: mutual information, mutual information with generalized entropy and information distance. Our analysis, which is conducted on two different topologies, finds that mutual information with generalized entropy provides the most accurate inferencing/detection process, enabling the classifier to obtain 80% of accuracy on average.

The structure and function of the pericellular matrix of articular cartilage

Chondrocytes in articular cartilage are surrounded by a narrow pericellular matrix (PCM) that is both biochemically and biomechanically distinct from the extracellular matrix (ECM) of the tissue. While the PCM was first observed nearly a century ago, its role is still under investigation. In support of early hypotheses regarding its function, increasing evidence indicates that the PCM serves as a transducer of biochemical and biomechanical signals to the chondrocyte. Work over the past two decades has established that the PCM in adult tissue is defined biochemically by several molecular components, including type VI collagen and perlecan. On the other hand, the biomechanical properties of this structure have only recently been measured. Techniques such as micropipette aspiration, in situ imaging, computational modeling, and atomic force microscopy have determined that the PCM exhibits distinct mechanical properties as compared to the ECM, and that these properties are influenced by specific PCM components as well as disease state. Importantly, the unique relationships among the mechanical properties of the chondrocyte, PCM, and ECM in different zones of cartilage suggest that this region significantly influences the stress-strain environment of the chondrocyte. In this review, we discuss recent advances in the measurement of PCM mechanical properties and structure that further increase our understanding of PCM function. Taken together, these studies suggest that the PCM plays a critical role in controlling the mechanical environment and mechanobiology of cells in cartilage and other cartilaginous tissues, such as the meniscus or intervertebral disc.

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.

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.

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.

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.

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.