A Hybrid Biphasic Mixture Formulation for Modeling Dynamics in Porous Deformable Biological Tissues

The primary aim of this study is to establish the theoretical foundations for a solid-fluid biphasic mixture domain that can accommodate inertial effects and a viscous interstitial fluid, which can interface with a dynamic viscous fluid domain. Most mixture formulations consist of constituents that are either all intrinsically incompressible or compressible, thereby introducing inherent limitations. In particular, mixtures with intrinsically incompressible constituents can only model wave propagation in the porous solid matrix, whereas those with compressible constituents require internal variables, and related evolution equations, to distinguish the compressibility of the solid and fluid under hydrostatic pressure. In this study, we propose a hybrid framework for a biphasic mixture where the skeleton of the porous solid is intrinsically incompressible but the interstitial fluid is compressible. We define a state variable as a measure of the fluid volumetric strain. Within an isothermal framework, the Clausius-Duhem inequality shows that a function of state arises for the fluid pressure as a function of this strain measure. We derive jump conditions across hybrid biphasic interfaces, which are suitable for modeling hydrated biological tissues. We then illustrate this framework using confined compression and dilatational wave propagation analyses. The governing equations for this hybrid biphasic framework reduce to those of the classical biphasic theory whenever the bulk modulus of the fluid is set to infinity and inertia terms and viscous fluid effects are neglected. The availability of this novel framework facilitates the implementation of finite element solvers for fluid-structure interactions at interfaces between viscous fluids and porous-deformable biphasic domains, which can include fluid exchanges across those interfaces.

A Hybrid Reactive Multiphasic Mixture With a Compressible Fluid Solvent

Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.

On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics

This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius-Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.

Finite Element Implementation of Biphasic-Fluid Structure Interactions in febio

In biomechanics, solid-fluid mixtures have commonly been used to model the response of hydrated biological tissues. In cartilage mechanics, this type of mixture, where the fluid and solid constituents are both assumed to be intrinsically incompressible, is often called a biphasic material. Various physiological processes involve the interaction of a viscous fluid with a porous-hydrated tissue, as encountered in synovial joint lubrication, cardiovascular mechanics, and respiratory mechanics. The objective of this study was to implement a finite element solver in the open-source software febio that models dynamic interactions between a viscous fluid and a biphasic domain, accommodating finite deformations of both domains as well as fluid exchanges between them. For compatibility with our recent implementation of solvers for computational fluid dynamics (CFD) and fluid-structure interactions (FSI), where the fluid is slightly compressible, this study employs a novel hybrid biphasic formulation where the porous skeleton is intrinsically incompressible but the fluid is also slightly compressible. The resulting biphasic-FSI (BFSI) implementation is verified against published analytical and numerical benchmark problems, as well as novel analytical solutions derived for the purposes of this study. An illustration of this BFSI solver is presented for two-dimensional (2D) airflow through a simulated face mask under five cycles of breathing, showing that masks significantly reduce air dispersion compared to the no-mask control analysis. In addition, we model three-dimensional (3D) blood flow in a bifurcated carotid artery assuming porous arterial walls and verify that mass is conserved across all fluid-permeable boundaries. The successful formulation and implementation of this BFSI solver offers enhanced multiphysics modeling capabilities that are accessible via an open-source software platform.

Attachment of cartilage wear particles to the synovium negatively impacts friction properties

Cartilage wear particles are released into the synovial fluid by mechanical and chemical degradation of the articular surfaces during osteoarthritis and attach to the synovial membrane. Accumulation of wear particles could alter key tissue-level mechanical properties of the synovium, hindering its characteristically low-friction interactions with underlying articular surfaces in the synovial joint. The present study employs a custom loading device to further the characterization of native synovium friction properties, while investigating the hypothesis that attachment of cartilage wear particles increases friction coefficient. Juvenile bovine synovium demonstrated characteristically low friction coefficients in sliding contact with glass, in agreement with historical measurements. Friction coefficient increased with higher normal load in saline, while lubrication with native synovial fluid maintained low friction coefficients at higher loads. Cartilage wear particles generated from juvenile bovine cartilage attached directly to synovium explants in static culture, with incorporation onto the tissue denoted by cell migration onto the particle surface. In dilute synovial fluid mimicking the decreased lubricating properties during osteoarthritis, wear particle attachment significantly increased friction coefficient against glass, and native cartilage and synovium. In addition to providing a novel characterization of synovial joint tribology this work highlights a potential mechanism for cartilage wear particles to perpetuate the degradative environment of osteoarthritis by modulating tissue-level properties of the synovium that could impact macroscopic wear as well as mechanical stimuli transmitted to resident cells.

Tissue engineered autologous cartilage-bone grafts for temporomandibular joint regeneration

Joint disorders can be detrimental to quality of life. There is an unmet need for precise functional reconstruction of native-like cartilage and bone tissues in the craniofacial space and particularly for the temporomandibular joint (TMJ). Current surgical methods suffer from lack of precision and comorbidities and frequently involve multiple operations. Studies have sought to improve craniofacial bone grafts without addressing the cartilage, which is essential to TMJ function. For the human-sized TMJ in the Yucatan minipig model, we engineered autologous, biologically, and anatomically matched cartilage-bone grafts for repairing the ramus-condyle unit (RCU), a geometrically intricate structure subjected to complex loading forces. Using image-guided micromilling, anatomically precise scaffolds were created from decellularized bone matrix and infused with autologous adipose-derived chondrogenic and osteogenic progenitor cells. The resulting constructs were cultured in a dual perfusion bioreactor for 5 weeks before implantation. Six months after implantation, the bioengineered RCUs maintained their predefined anatomical structure and regenerated full-thickness, stratified, and mechanically robust cartilage over the underlying bone, to a greater extent than either autologous bone-only engineered grafts or acellular scaffolds. Tracking of implanted cells and parallel bioreactor studies enabled additional insights into the progression of cartilage and bone regeneration. This study demonstrates the feasibility of TMJ regeneration using anatomically precise, autologous, living cartilage-bone grafts for functional, personalized total joint replacement. Inclusion of the adjacent tissues such as soft connective tissues and the TMJ disc could further extend the functional integration of engineered RCUs with the host.

Sustained Delivery of SB-431542, a Type I Transforming Growth Factor Beta-1 Receptor Inhibitor, to Prevent Arthrofibrosis

Fibrosis of the knee is a common disorder resulting from an aberrant wound healing response and is characterized by extracellular matrix deposition, joint contraction, and scar tissue formation. The principal regulator of the fibrotic cascade is transforming growth factor beta-1 (TGF-β1), a factor that induces rapid proliferation and differentiation of resident fibroblasts. In this study, we demonstrate successful inhibition of TGF-β1-driven myofibroblastic differentiation in human fibroblast-like synoviocytes using a small molecule TGF-β1 receptor inhibitor, SB-431542. We also demonstrate successful encapsulation of SB-431542 in poly(D,L-lactide-co-glycolide) (PLGA) as a potential prophylactic treatment for arthrofibrosis and characterize drug release and bioactivity in a three-dimensional collagen gel contraction assay. We assessed the effects of TGF-β1 and SB-431542 on cell proliferation and viability in monolayer cultures. Opposing dose-dependent trends were observed in cell proliferation, which increased in TGF-β1-treated cultures and decreased in SB-431542-treated cultures relative to control (p < 0.05). SB-431542 was not cytotoxic at the concentrations studied (0-50 μM) and inhibited TGF-β1-induced collagen gel contraction in a dose-dependent manner. Specifically, TGF-β1-treated gels contracted to 18% ± 1% of their initial surface area, while gels treated with TGF-β1 and ≥10 μM SB-431542 showed no evidence of contraction (p < 0.0001). Upon removal of the compound, all gels contracted to control levels after 44 h in culture, necessitating sustained delivery for prolonged inhibition. To this end, SB-431542 was encapsulated in PLGA microspheres (SBMS) that had an average diameter of 87.5 ± 24 μm and a loading capacity of 4.3 μg SB-431542 per milligram of SBMS. Functional assessment of SBMS revealed sustained inhibition of TGF-β1-induced gel contraction as well as hallmark features of myofibroblastic differentiation, including α-smooth muscle actin expression and connective tissue growth factor production. These results suggest that SB-431542 may be used to counter TGF-β1-driven events in the fibrotic cascade in the knee cartilage.

Direct Osmotic Pressure Measurements in Articular Cartilage Demonstrate Nonideal and Concentration-Dependent Phenomena

The osmotic pressure in articular cartilage serves an important mechanical function in healthy tissue. Its magnitude is thought to play a role in advancing osteoarthritis. The aims of this study were to: (1) isolate and quantify the magnitude of cartilage swelling pressure in situ; and (2) identify the effect of salt concentration on material parameters. Confined compression stress-relaxation testing was performed on 18 immature bovine and six mature human cartilage samples in solutions of varying osmolarities. Direct measurements of osmotic pressure revealed nonideal and concentration-dependent osmotic behavior, with magnitudes approximately 1/3 those predicted by ideal Donnan law. A modified Donnan constitutive behavior was able to capture the aggregate behavior of all samples with a single adjustable parameter. Results of curve-fitting transient stress-relaxation data with triphasic theory in febio demonstrated concentration-dependent material properties. The aggregate modulus HA increased threefold as the external concentration decreased from hypertonic 2 M to hypotonic 0.001 M NaCl (bovine: HA=0.420±0.109 MPa to 1.266±0.438 MPa; human: HA=0.499±0.208 MPa to 1.597±0.455 MPa), within a triphasic theory inclusive of osmotic effects. This study provides a novel and simple analytical model for cartilage osmotic pressure which may be used in computational simulations, validated with direct in situ measurements. A key finding is the simultaneous existence of Donnan osmotic and Poisson-Boltzmann electrostatic interactions within cartilage.

Modeling Pulse Wave Propagation Through a Stenotic Artery With Fluid Structure Interaction: A Validation Study Using Ultrasound Pulse Wave Imaging

Pulse wave imaging (PWI) is an ultrasound-based method that allows spatiotemporal mapping of the arterial pulse wave propagation, from which the local pulse wave velocity (PWV) can be derived. Recent reports indicate that PWI can help the assessment of atherosclerotic plaque composition and mechanical properties. However, the effect of the atherosclerotic plaque's geometry and mechanics on the arterial wall distension and local PWV remains unclear. In this study, we investigated the accuracy of a finite element (FE) fluid-structure interaction (FSI) approach to predict the velocity of a pulse wave propagating through a stenotic artery with an asymmetrical plaque, as quantified with PWI method. Experiments were designed to compare FE-FSI modeling of the pulse wave propagation through a stenotic artery against PWI obtained with manufactured phantom arteries made of polyvinyl alcohol (PVA) material. FSI-generated spatiotemporal maps were used to estimate PWV at the plaque region and compared it to the experimental results. Velocity of the pulse wave propagation and magnitude of the wall distension were correctly predicted with the FE analysis. In addition, findings indicate that a plaque with a high degree of stenosis (>70%) attenuates the propagation of the pulse pressure wave. Results of this study support the validity of the FE-FSI methods to investigate the effect of arterial wall structural and mechanical properties on the pulse wave propagation. This modeling method can help to guide the optimization of PWI to characterize plaque properties and substantiate clinical findings.

Immature bovine cartilage wear by fatigue failure and delamination

This study investigated wear damage of immature bovine articular cartilage using reciprocal sliding of tibial cartilage strips against glass or cartilage. Experiments were conducted in physiological buffered saline (PBS) or mature bovine synovial fluid (SF). A total of 63 samples were tested, of which 47 exhibited wear damage due to delamination of the cartilage surface initiated in the middle zone, with no evidence of abrasive wear. There was no difference between the friction coefficient of damaged and undamaged samples, showing that delamination wear occurs even when friction remains low under a migrating contact area configuration. No difference was observed in the onset of damage or in the friction coefficient between samples tested in PBS or SF. The onset of damage occurred earlier when testing cartilage against glass versus cartilage against cartilage, supporting the hypothesis that delamination occurs due to fatigue failure of the collagen in the middle zone, since stiffer glass produces higher strains and tensile stresses under comparable loads. The findings of this study are novel because they establish that delamination of the articular surface, starting in the middle zone, may represent a primary mechanism of failure. Based on preliminary data, it is reasonable to hypothesize that delamination wear via subsurface fatigue failure is similarly the primary mechanism of human cartilage wear under normal loading conditions, albeit requiring far more cycles of loading than in immature bovine cartilage.

Pulsed electromagnetic fields promote repair of focal articular cartilage defects with engineered osteochondral constructs

Articular cartilage injuries are a common source of joint pain and dysfunction. We hypothesized that pulsed electromagnetic fields (PEMFs) would improve growth and healing of tissue-engineered cartilage grafts in a direction-dependent manner. PEMF stimulation of engineered cartilage constructs was first evaluated in vitro using passaged adult canine chondrocytes embedded in an agarose hydrogel scaffold. PEMF coils oriented parallel to the articular surface induced superior repair stiffness compared to both perpendicular PEMF (p = .026) and control (p = .012). This was correlated with increased glycosaminoglycan deposition in both parallel and perpendicular PEMF orientations compared to control (p = .010 and .028, respectively). Following in vitro optimization, the potential clinical translation of PEMF was evaluated in a preliminary in vivo preclinical adult canine model. Engineered osteochondral constructs (∅ 6 mm × 6 mm thick, devitalized bone base) were cultured to maturity and implanted into focal defects created in the stifle (knee) joint. To assess expedited early repair, animals were assessed after a 3-month recovery period, with microfracture repairs serving as an additional clinical control. In vivo, PEMF led to a greater likelihood of normal chondrocyte (odds ratio [OR]: 2.5, p = .051) and proteoglycan (OR: 5.0, p = .013) histological scores in engineered constructs. Interestingly, engineered constructs outperformed microfracture in clinical scoring, regardless of PEMF treatment (p < .05). Overall, the studies provided evidence that PEMF stimulation enhanced engineered cartilage growth and repair, demonstrating a potential low-cost, low-risk, noninvasive treatment modality for expediting early cartilage repair.

Sustained low-dose dexamethasone delivery via a PLGA microsphere-embedded agarose implant for enhanced osteochondral repair

Articular cartilage defects are a common source of joint pain and dysfunction. We hypothesized that sustained low-dose dexamethasone (DEX) delivery via an acellular osteochondral implant would have a dual pro-anabolic and anti-catabolic effect, both supporting the functional integrity of adjacent graft and host tissue while also attenuating inflammation caused by iatrogenic injury. An acellular agarose hydrogel carrier with embedded DEX-loaded poly(lactic-co-glycolic) acid (PLGA) microspheres (DLMS) was developed to provide sustained release for at least 99 days. The DLMS implant was first evaluated in an in vitro pro-inflammatory model of cartilage degradation. The implant was chondroprotective, as indicated by maintenance of Young's modulus (EY) (p = 0.92) and GAG content (p = 1.0) in the presence of interleukin-1β insult. In a subsequent preliminary in vivo experiment, an osteochondral autograft transfer was performed using a pre-clinical canine model. DLMS implants were press-fit into the autograft donor site and compared to intra-articular DEX injection (INJ) or no DEX (CTL). Functional scores for DLMS animals returned to baseline (p = 0.39), whereas CTL and INJ remained significantly worse at 6 months (p < 0.05). DLMS knees were significantly more likely to have improved OARSI scores for proteoglycan, chondrocyte, and collagen pathology (p < 0.05). However, no significant improvements in synovial fluid cytokine content were observed. In conclusion, utilizing a targeted DLMS implant, we observed in vitro chondroprotection in the presence of IL-1-induced degradation and improved in vivo functional outcomes. These improved outcomes were correlated with superior histological scores but not necessarily a dampened inflammatory response, suggesting a primarily pro-anabolic effect. STATEMENT OF SIGNIFICANCE: Articular cartilage defects are a common source of joint pain and dysfunction. Effective treatment of these injuries may prevent the progression of osteoarthritis and reduce the need for total joint replacement. Dexamethasone, a potent glucocorticoid with concomitant anti-catabolic and pro-anabolic effects on cartilage, may serve as an adjuvant for a variety of repair strategies. Utilizing a dexamethasone-loaded osteochondral implant with controlled release characteristics, we demonstrated in vitro chondroprotection in the presence of IL-1-induced degradation and improved in vivo functional outcomes following osteochondral repair. These improved outcomes were correlated with superior histological cartilage scores and minimal-to-no comorbidity, which is a risk with high dose dexamethasone injections. Using this model of cartilage restoration, we have for the first time shown the application of targeted, low-dose dexamethasone for improved healing in a preclinical model of focal defect repair.

Simulating cerebral edema and delayed fatality after traumatic brain injury using triphasic swelling biomechanics

Objectives: Contemporary finite element (FE) models, like that from the Global Human Body Models Consortium (GHBMC), have been useful for developing safety systems to reduce the severity of injuries in motor vehicle crashes (MVCs), including traumatic brain injury (TBI). However, not all injury occurs during the MVC. Cerebral edema after TBI contributes to mortality by increasing intracranial pressure (ICP) and preventing adequate cerebral blood supply. The focus of this study was to model post-traumatic cerebral edema and subsequent mortality due to increased ICP.Methods: Brain tissue swells in a manner consistent with triphasic biomechanics, which models biological tissues as a charged deformable porous solid matrix (fixed charge density [FCD]), a solvent, and monovalent counter-ions (cerebrospinal fluid). Fluid uptake into the brain is driven by the Gibbs-Donnan osmotic pressure as the FCD is exposed when cells die. Post-TBI edema was simulated in FEBio (febio.org), which includes triphasic material formulations.The GHBMC mesh was imported into FEBio, and each element was assigned a FCD to represent impact-related cell death based on its maximum principal strain (MPS) experienced during the crash-simulation using the stock GHBMC model and LS-DYNA. The ensuing pathophysiology was simulated in FEBio in two steps. First, the brain swelled in response to exposure of FCD, causing some adjacent elements to compress as fluid was redistributed. Biologically, the compression was assumed to reduce blood flow and cause ischemic cell death, represented by additional exposure of FCD, swelling, and increased ICP. Using published prognostic models of clinical outcome, mortality was predicted based on ICP.Results: Post-traumatic volume ratio of elements ranged from less than 30% (compaction) to greater than 200% (swelling). Predicted ICP values for a fatal impact were as high as 8.55 kPa (64.1 mmHg), which is associated with a 99% probability of death.Conclusion: To the best of our knowledge, this is the first study to simulate post-traumatic brain swelling to predict outcome. By incorporating swelling, ischemia, and cell death, our novel approach may improve fidelity of predicting outcome after MVCs. A strength of our approach is relying on the validated GHBMC model to predict brain deformation in the crash-scenario. The main goal of the current study was to demonstrate feasibility of simulating post-injury swelling using triphasic biomechanics. We successfully predicted clinically relevant increases in ICP that suggest a high likelihood of death when simulating a fatal impact scenario, however, more validation of our methodology is needed.

A Surface-to-Surface Finite Element Algorithm for Large Deformation Frictional Contact in febio

This study formulates a finite element algorithm for frictional contact of solid materials, accommodating finite deformation and sliding. The algorithm uses a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints in a nonmortar surface-to-surface approach. Use of a novel kinematical approach to contact detection and enforcement of frictional constraints allows solution of complex problems previously requiring mortar methods or contact smoothing algorithms. Patch tests are satisfied to a high degree of accuracy with a single-pass penalty method, ensuring formulation errors do not affect the solution. The accuracy of the implementation is verified with Hertzian contact, and illustrations demonstrating the ability to handle large deformations and sliding are presented and validated against prior literature. A biomechanically relevant example addressing finger friction during grasping demonstrates the utility of the proposed algorithm. The algorithm is implemented in the open source software febio, and the source code is made available to the general public.

Cartilage Wear Particles Induce an Inflammatory Response Similar to Cytokines in Human Fibroblast-Like Synoviocytes

The synovium plays a key role in the development of osteoarthritis, as evidenced by pathological changes to the tissue observed in both early and late stages of the disease. One such change is the attachment of cartilage wear particles to the synovial intima. While this phenomenon has been well observed clinically, little is known of the biological effects that such particles have on resident cells in the synovium. The present work investigates the hypothesis that cartilage wear particles elicit a pro-inflammatory response in diseased and healthy human fibroblast-like synoviocytes, like that induced by key cytokines in osteoarthritis. Fibroblast-like synoviocytes from 15 osteoarthritic human donors and a subset of three non-osteoarthritic donors were exposed to cartilage wear particles, interleukin-1α or tumor necrosis factor-α for 6 days and analyzed for proliferation, matrix production, and release of pro-inflammatory mediators and degradative enzymes. Wear particles significantly increased proliferation and release of nitric oxide, interleukin-6 and -8, and matrix metalloproteinase-9, -10, and -13 in osteoarthritic synoviocytes, mirroring the effects of both cytokines, with similar trends in non-osteoarthritic cells. These results suggest that cartilage wear particles are a relevant physical factor in the osteoarthritic environment, perpetuating the pro-inflammatory and pro-degradative cascade by modulating synoviocyte behavior at early and late stages of the disease. Future work points to therapeutic strategies for slowing disease progression that target cell-particle interactions. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:1979-1987, 2019.

Finite Element Framework for Computational Fluid Dynamics in FEBio

The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid-structure interactions (FSIs).

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.

A Functional Tissue-Engineered Synovium Model to Study Osteoarthritis Progression and Treatment

IMPACT STATEMENT

The synovium envelops the diarthrodial joint and plays a key regulatory role in defining the composition of the synovial fluid through filtration and biosynthesis of critical boundary lubricants. Synovium changes often precede cartilage damage in osteoarthritis. We describe a novel in vitro tissue engineered model, validated against native synovium explants, to investigate the structure-function of synovium through quantitative solute transport measures. Synovium was evaluated in the presence of a proinflammatory cytokine, interleukin-1, or the clinically relevant corticosteroid, dexamethasone. We anticipate that a better understanding of synovium transport would support efforts to develop more effective strategies aimed at restoring joint health.

A Formulation for Fluid Structure-Interactions in FEBio Using Mixture Theory

Many physiological systems involve strong interactions between fluids and solids, posing a signicant challenge when modeling biomechanics. The objective of this study was to implement a fluid-structure interaction (FSI) solver in the free, open-source finite element code FEBio (febio.org), that combined the existing solid mechanics and rigid body dynamics solver with a recently-developed computational fluid dynamics (CFD) solver. A novel Galerkin-based finite element FSI formulation was introduced based on mixture theory, where the FSI domain was described as a mixture of fluid and solid constituents that have distinct motions. The mesh was defined on the solid domain, specialized to have zero mass, negligible stiffness and zero frictional interactions with the fluid, whereas the fluid was modeled as isothermal and compressible. The mixture framework provided the foundation for evaluating material time derivatives in a material frame for the solid and in a spatial frame for the fluid. Similar to our recently reported CFD solver, our FSI formulation did not require stabilization methods to achieve good convergence, producing a compact set of equations and code implementation. The code was successfully verified against benchmark problems and an analytical solution for squeeze-film lubrication. It was validated against experimental measurements of the flow rate in a peristaltic pump, and illustrated using non-Newtonian blood flow through a bifurcated carotid artery with a thick arterial wall. The successful formulation and implementation of this FSI solver enhances the multiphysics modeling capabilities in FEBio relevant to the biomechanics and biophysics communities.

Physiologic Medium Maintains the Homeostasis of Immature Bovine Articular Cartilage Explants in Long-Term Culture

The ability to maintain living articular cartilage tissue in long-term culture can serve as a valuable analytical research tool, allowing for direct examination of mechanical or chemical perturbations on tissue behavior. A fundamental challenge for this technique is the recreation of the salient environmental conditions of the synovial joint in culture that are required to maintain native cartilage homeostasis. Interestingly, conventional media formulations used in explanted cartilage tissue culture investigations often consist of levels of metabolic mediators that deviate greatly from their concentrations in synovial fluid. Here, we hypothesize that the utilization of a culture medium consisting of near-physiologic levels of several highly influential metabolic mediators (glucose, amino acids, cortisol, insulin, and ascorbic acid) will maintain the homeostasis of cartilage explants as assessed by their mechanical properties and extracellular matrix contents. Results demonstrate that the aforementioned mediators have a strong effect on the mechanical and biochemical stability of skeletally immature bovine cartilage explants. Most notably, 1) in the absence of cortisol, explants exhibit extensive swelling and tissue softening and 2) in the presence of supraphysiologic levels of anabolic mediators (glucose, amino acids, insulin), explants exhibit increased matrix accumulation and tissue stiffening. In contrast, the administration of physiologic levels of these mediators (as present in native synovial fluid) greatly improves the stability of live cartilage explants over one month of culture. These results may have broad applicability for articular cartilage and other musculoskeletal tissue research, setting the foundation for important culture formulations required for examinations into tissue behavior.

A Plugin Framework for Extending the Simulation Capabilities of FEBio

The FEBio software suite is a set of software tools for nonlinear finite element analysis in biomechanics and biophysics. FEBio employs mixture theory to account for the multiconstituent nature of biological materials, integrating the field equations for irreversible thermodynamics, solid mechanics, fluid mechanics, mass transport with reactive species, and electrokinetics. This communication describes the development and application of a new "plugin" framework for FEBio. Plugins are dynamically linked libraries that allow users to add new features and to couple FEBio with other domain-specific software applications without modifying the source code directly. The governing equations and simulation capabilities of FEBio are reviewed. The implementation, structure, use, and application of the plugin framework are detailed. Several example plugins are described in detail to illustrate how plugins enrich, extend, and leverage existing capabilities in FEBio, including applications to deformable image registration, constitutive modeling of biological tissues, coupling to an external software package that simulates angiogenesis using a discrete computational model, and a nonlinear reaction-diffusion solver. The plugin feature facilitates dissemination of new simulation methods, reproduction of published results, and coupling of FEBio with other domain-specific simulation approaches such as compartmental modeling, agent-based modeling, and rigid-body dynamics. We anticipate that the new plugin framework will greatly expand the range of applications for the FEBio software suite and thus its impact.

Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio (febio.org), 3D models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as 2D surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees of freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix, accounting for solvent and solute transport.

FEBio: History and Advances

The principal goal of the FEBio project is to provide an advanced finite element tool for the biomechanics and biophysics communities that allows researchers to model mechanics, transport, and electrokinetic phenomena for biological systems accurately and efficiently. In addition, because FEBio is geared toward the research community, the code is designed such that new features can be added easily, thus making it an ideal tool for testing novel computational methods. Finally, because the success of a code is determined by its user base, integral goals of the FEBio project have been to offer support and outreach to our community; to provide mechanisms for dissemination of results, models, and data; and to encourage interaction between users. This review presents the history of the FEBio project, from its initial developments through its current funding period. We also present a glimpse into the future of FEBio.

Reactive Constrained Mixtures for Modeling the Solid Matrix of Biological Tissues

This article illustrates our approach for modeling the solid matrix of biological tissues using reactive constrained mixtures. Several examples are presented to highlight the potential benefits of this approach, showing that seemingly disparate fields of mechanics and chemical kinetics are actually closely interrelated and may be elegantly expressed in a unified framework. Thus, constrained mixture models recover classical theories for fibrous materials with bundles oriented in different directions or having different reference configurations, that produce characteristic fiber recruitment patterns under loading. Reactions that exchange mass among various constituents of a mixture may be used to describe tissue growth and remodeling, which may also alter the material's anisotropy. Similarly, reactions that describe the breaking and reforming of bonds may be used to model free energy dissipation in a viscoelastic material. Therefore, this framework is particularly well suited for modeling biological tissues.

Toward understanding the role of cartilage particulates in synovial inflammation

OBJECTIVE

Arthroscopy with lavage and synovectomy can remove tissue debris from the joint space and the synovial lining to provide pain relief to patients with osteoarthritis (OA). Here, we developed an in vitro model to study the interaction of cartilage wear particles with fibroblast-like synoviocytes (FLS) to better understand the interplay of cartilage particulates with cytokines on cells of the synovium.

METHOD

In this study sub-10 μm cartilage particles or 1 μm latex particles were co-cultured with FLS ±10 ng/mL interleukin-1α (IL-1α) or tumor necrosis factor-α (TNF-α). Samples were analyzed for DNA, glycosaminoglycan (GAG), and collagen, and media samples were analyzed for media GAG, nitric oxide (NO) and prostaglandin-E2 (PGE2). The nature of the physical interaction between the particles and FLS was determined by microscopy.

RESULTS

Both latex and cartilage particles could be phagocytosed by FLS. Cartilage particles were internalized and attached to the surface of both dense monolayers and individual cells. Co-culture of FLS with cartilage particulates resulted in a significant increase in cell sheet DNA and collagen content as well as NO and PGE2 synthesis compared to control and latex treated groups.

CONCLUSION

The proliferative response of FLS to cartilage wear particles resulted in an overall increase in extracellular matrix (ECM) content, analogous to the thickening of the synovial lining observed in OA patients. Understanding how cartilage particles interface with the synovium may provide insight into how this interaction contributes to OA progression and may guide the role of lavage and synovectomy for degenerative disease.