Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis.

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

Continuum Growth Mechanics: Reconciling Two Common Frameworks.

The objective of this study was to investigate whether the two most common growth mechanics modeling frameworks, the constrained-mixture growth model and the kinematic growth model, could be reconciled mathematically. The purpose of this effort was to provide practical guidelines for potential users of these modeling frameworks. Results showed that the kinematic growth model is mathematically consistent with a special form of the constrained-mixture growth model, where only one generation of a growing solid exists at any given time, overturning its entire solid mass at each instant of growth in order to adopt the reference configuration dictated by the growth deformation. The thermodynamics of the kinematic growth model, along with the specialized constrained-mixture growth model, requires a cellular supply of chemical energy to allow deposition of solid mass under a stressed state. A back-of-the-envelope calculation shows that the amount of chemical energy required to sustain biological growth under these models is negligibly small, when compared to the amount of energy normally consumed daily by the human body. In conclusion, this study successfully reconciled the two most popular growth theories for biological growth and explained the special circumstances under which the constrained-mixture growth model reduces to the kinematic growth model.

The Problem With National Institute of Standards and Technology Thermodynamics Tables in Continuum Mechanics.

Thermodynamics is a fundamental topic of continuum mechanics and biomechanics, with a wide range of applications to physiological and biological processes. This study addresses two fundamental limitations of current thermodynamic treatments. First, thermodynamics tables distributed online by the U.S. National Institute of Standards and Technology (NIST) report properties of fluids as a function of absolute temperature T and absolute pressure P. These properties include mass density ρ, specific internal energy u, enthalpy h=u+P/ρ, and entropy s. However, formulations of jump conditions across phase boundaries derived from Newton's second law of motion and the first law of thermodynamics employ the gauge pressure p=P-Pr, where Pr is an arbitrarily selected referential absolute pressure. Interchanging p with P is not innocuous as it alters tabulated NIST values for u while keeping h and s unchanged. Using p for functions of state and governing equations solves the problem with using NIST entries for the specific internal energy u in standard thermodynamics tables and analyses of phase transformation in continuum mechanics. Second, constitutive models for the free energy of fluids, such as water and air, are not typically provided in standard thermodynamics treatments. This study proposes a set of constitutive models and validates them against suitably modified NIST data.

Erratum: "A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity" [ASME J. Biomech Eng., 2023, 145(1), p. 011004; DOI: 10.1115/1.4054983].

In this erratum, we correct a mistake in a subcomponent of the numerical algorithm proposed in our recent study for modeling anisotropic reactive nonlinear viscoelasticity (doi:10.1115/1.4054983), for the special case where multiple weak bond families may be recruited with loading. This correction overcomes a nonphysical response noted under uni-axial cyclical loading.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Finite Element Implementation of Computational Fluid Dynamics With Reactive Neutral and Charged Solute Transport in FEBio.

The objective of this study was to implement a novel fluid-solutes solver into the open-source finite element software FEBio, that extended available modeling capabilities for biological fluids and fluid-solute mixtures. Using a reactive mixture framework, this solver accommodates diffusion, convection, chemical reactions, electrical charge effects, and external body forces, without requiring stabilization methods that were deemed necessary in previous computational implementations of the convection-diffusion-reaction equation at high Peclet numbers. Verification and validation problems demonstrated the ability of this solver to produce solutions for Peclet numbers as high as 1011, spanning the range of physiological conditions for convection-dominated solute transport. This outcome was facilitated by the use of a formulation that accommodates realistic values for solvent compressibility, and by expressing the solute mass balance such that it properly captured convective transport by the solvent and produced a natural boundary condition of zero diffusive solute flux at outflow boundaries. Since this numerical scheme was not necessarily foolproof, guidelines were included to achieve better outcomes that minimize or eliminate the potential occurrence of numerical artifacts. The fluid-solutes solver presented in this study represents an important and novel advancement in the modeling capabilities for biomechanics and biophysics as it allows modeling of mechanobiological processes via the incorporation of chemical reactions involving neutral or charged solutes within dynamic fluid flow. The incorporation of charged solutes in a reactive framework represents a significant novelty of this solver. This framework also applies to a broader range of nonbiological applications.

Damage Mechanics of Biological Tissues in Relation to Viscoelasticity.

This study examines the theoretical foundations for the damage mechanics of biological tissues in relation to viscoelasticity. Its primary goal is to provide a mechanistic understanding of well-known experimental observations in biomechanics, which show that the ultimate tensile strength of viscoelastic biological tissues typically increases with increasing strain rate. The basic premise of this framework is that tissue damage occurs when strong bonds, such as covalent bonds in the solid matrix of a biological tissue, break in response to loading. This type of failure is described as elastic damage, under the idealizing assumption that strong bonds behave elastically. Viscoelasticity arises from three types of dissipative mechanisms: (1) Friction between molecules of the same species, which is represented by the tissue viscosity. (2) Friction between fluid and solid constituents of a porous medium, which is represented by the tissue hydraulic permeability. (3) Dissipative reactions arising from weak bonds breaking in response to loading, and reforming in a stress-free state, such as hydrogen bonds and other weak electrostatic bonds. When a viscoelastic tissue is subjected to loading, some of that load may be temporarily supported by those frictional and weak bond forces, reducing the amount of load supported by elastic strong bonds and thus, the extent of elastic damage sustained by those bonds. This protective effect depends on the characteristic time response of viscoelastic mechanisms in relation to the loading history. This study formalizes these concepts by presenting general equations that can model the damage mechanics of viscoelastic tissues.

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.

Continuum Thermodynamics of Constrained Reactive Mixtures.

Mixture theory models continua consisting of multiple constituents with independent motions. In constrained mixtures, all constituents share the same velocity but they may have different reference configurations. The theory of constrained reactive mixtures was formulated to analyze growth and remodeling in living biological tissues. It can also reproduce and extend classical frameworks of damage mechanics and viscoelasticity under isothermal conditions, when modeling bonds that can break and reform. This study focuses on establishing the thermodynamic foundations of constrained reactive mixtures under more general conditions, for arbitrary reactive processes where temperature varies in time and space. By incorporating general expressions for reaction kinetics, it is shown that the residual dissipation statement of the Clausius-Duhem inequality must include a reactive power density, while the axiom of energy balance must include a reactive heat supply density. Both of these functions are proportional to the molar production rate of a reaction, and they depend on the chemical potentials of the mixture constituents. We present novel formulas for the classical thermodynamic concepts of energy of formation and heat of reaction, making it possible to evaluate the heat supply generated by reactive processes from the knowledge of the specific free energy of mixture constituents as well as the reaction rate. We illustrate these novel concepts with mixtures of ideal gases, and isothermal reactive damage mechanics and viscoelasticity, as well as reactive thermoelasticity. This framework facilitates the analysis of reactive tissue biomechanics and physiological and biomedical engineering processes where temperature variations cannot be neglected.

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

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

How Does Chondrolabral Damage and Labral Repair Influence the Mechanics of the Hip in the Setting of Cam Morphology? A Finite-Element Modeling Study.

BACKGROUND: Individuals with cam morphology are prone to chondrolabral injuries that may progress to osteoarthritis. The mechanical factors responsible for the initiation and progression of chondrolabral injuries in these individuals are not well understood. Additionally, although labral repair is commonly performed during surgical correction of cam morphology, the isolated mechanical effect of labral repair on the labrum and surrounding cartilage is unknown. QUESTION/PURPOSES: Using a volunteer-specific finite-element analysis, we asked: (1) How does cam morphology create a deleterious mechanical environment for articular cartilage (as evaluated by shear stress, tensile strain, contact pressure, and fluid pressure) that could increase the risk of cartilage damage compared with a radiographically normal hip? (2) How does chondrolabral damage, specifically delamination, delamination with rupture of the chondrolabral junction, and the presence of a chondral defect, alter the mechanical environment around the damage? (3) How does labral repair affect the mechanical environment in the context of the aforementioned chondrolabral damage scenarios? METHODS: The mechanical conditions of a representative hip with normal bony morphology (characterized by an alpha angle of 37°) and one with cam morphology (characterized by an alpha angle of 78°) were evaluated using finite-element models that included volunteer-specific anatomy and kinematics. The bone, cartilage, and labrum geometry for the hip models were collected from two volunteers matched by age (25 years with cam morphology and 23 years with normal morphology), BMI (both 24 kg/m2), and sex (both male). Volunteer-specific kinematics for gait were used to drive the finite-element models in combination with joint reaction forces. Constitutive material models were assigned to the cartilage and labrum, which simulate a physiologically realistic material response, including the time-dependent response from fluid flow through the cartilage, and spatially varied response from collagen fibril reinforcement. For the cam hip, three models were created to represent chondrolabral damage conditions: (1) "delamination," with the acetabular cartilage separated from the bone in one region; (2) "delamination with chondrolabral junction (CLJ) rupture," which includes separation of the cartilage from the labrum tissue; and (3) a full-thickness chondral defect, referred to throughout as "defect," where the acetabular cartilage has degraded so there is a void. Each of the three conditions was modeled with a labral tear and with the labrum repaired. The size and location of the damage conditions simulated in the cartilage and labrum were attained from reported clinical prevalence of the location of these injuries. For each damage condition, the contact area, contact pressure, tensile strain, shear stress, and fluid pressure were predicted during gait and compared. RESULTS: The cartilage in the hip with cam morphology experienced higher stresses and strains than the normal hip. The peak level of tensile strain (25%) and shear stress (11 MPa) experienced by the cam hip may exceed stable conditions and initiate damage or degradation. The cam hip with simulated damage experienced more evenly distributed contact pressure than the intact cam hip, as well as decreased tensile strain, shear stress, and fluid pressure. The peak levels of tensile strain (15% to 16%) and shear stress (2.5 to 2.7 MPa) for cam hips with simulated damage may be at stable magnitudes. Labral repair only marginally affected the overall stress and strain within the cartilage, but it increased local tensile strain in the cartilage near the chondrolabral junction in the hip with delamination and increased the peak tensile strain and shear stress on the labrum. CONCLUSION: This finite-element modeling pilot study suggests that cam morphology may predispose hip articular cartilage to injury because of high shear stress; however, the presence of simulated damage distributed the loading more evenly and the magnitude of stress and strain decreased throughout the cartilage. The locations of the peak values also shifted posteriorly. Additionally, in hips with cam morphology, isolated labral repair in the hip with a delamination injury increased localized strain in the cartilage near the chondrolabral junction. CLINICAL RELEVANCE: In a hip with cam morphology, labral repair alone may not protect the cartilage from damage because of mechanical overload during the low-flexion, weightbearing positions experienced during gait. The predicted findings of redistribution of stress and strain from damage in the cam hip may, in some cases, relieve disposition to damage progression. Additional studies should include volunteers with varied acetabular morphology, such as borderline dysplasia with cam morphology or pincer deformity, to analyze the effect on the conclusions presented in the current study. Further, future studies should evaluate the combined effects of osteochondroplasty and chondrolabral treatment.

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.

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.

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.

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.

A Formulation for Fluid-Structure Interactions in febio Using Mixture Theory.

Many physiological systems involve strong interactions between fluids and solids, posing a significant 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, 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 from the FSI literature 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 enhance 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 (SF). 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 (ECM) 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 SF) 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.

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.