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.

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 NIST 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 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.

Simulating Cerebral Edema and Ischemia After Traumatic Acute Subdural Hematoma Using Triphasic Swelling Biomechanics

Poor outcome following traumatic acute subdural hematoma (ASDH) is associated with the severity of the primary injury and secondary injury including cerebral edema and ischemia. However, the underlying secondary injury mechanism contributing to elevated intracranial pressure (ICP) and high mortality rate remains unclear. Cerebral edema occurs in response to the exposure of the intracellular fixed charge density (FCD) after cell death, causing ICP to increase. The increased ICP from swollen tissue compresses blood vessels in adjacent tissue, restricting blood flow and leading to ischemic damage. We hypothesize that the mass occupying effect of ASDH exacerbates the ischemic injury, leading to ICP elevation, which is an indicator of high mortality rate in the clinic. Using FEBio (febio.org) and triphasic swelling biomechanics, this study modeled clinically relevant ASDHs and simulated post-traumatic brain swelling and ischemia to predict ICP. Results showed that common convexity ASDH significantly increased ICP by exacerbating ischemic injury, and surgical removal of the convexity ASDH may control ICP by preventing ischemia progression. However, in cases where the primary injury is very severe, surgical intervention alone may not effectively decrease ICP, as the contribution of the hematoma to the elevated ICP is insignificant. In addition, interhemispheric ASDH, located between the cerebral hemispheres, does not significantly exacerbate ischemia, supporting the conservative surgical management generally recommended for interhemispheric ASDH. The joint effect of the mass occupying effect of the blood clot and resulting ischemia contributes to elevated ICP which may increase mortality. Our novel approach may improve the fidelity of predicting patient outcome after motor vehicle crashes and traumatic brain injuries due to other causes.

Region-Dependent Mechanical Properties of Human Brain Tissue Under Large Deformations Using Inverse Finite Element Modeling

This study aims to facilitate intracranial simulation of traumatic events by determining the mechanical properties of different anatomical structures of the brain. Our experimental indentation paradigm used fresh, post-operative human tissue, which is highly advantageous in determining mechanical properties without being affected by postmortem time. This study employed an inverse finite element approach coupled with experimental indentation data to characterize mechanical properties of the human hippocampus (CA1, CA3, dentate gyrus), cortex white matter, and cortex grey matter. We determined that an uncoupled viscoelastic Ogden constitutive formulation was most appropriate to represent the mechanical behavior of these different regions of brain. Anatomical regions were significantly different in their mechanical properties. The cortex white matter was stiffer than cortex grey matter, and the CA1 and dentate gyrus were both stiffer than cortex grey matter. Although no sex dependency was observed, there were trends indicating that male brain regions were generally stiffer than corresponding female regions. In addition, there were no statistically significant age dependent differences. This study provides a structure-specific description of fresh human brain tissue mechanical properties, which will be an important step toward explicitly modeling the heterogeneity of brain tissue deformation during TBI through finite element modeling.

Immature bovine cartilage wear is due to fatigue failure from repetitive compressive forces and not reciprocating frictional forces

OBJECTIVE

Wear of articular cartilage is not well understood. We hypothesize that cartilage wears due to fatigue failure in repetitive compression instead of reciprocating friction.

DESIGN

This study compares reciprocating sliding of immature bovine articular cartilage against glass in two testing configurations: (1) a stationary contact area configuration (SCA), which results in static compression, interstitial fluid depressurization, and increasing friction coefficient during reciprocating sliding, and (2) a migrating contact area configuration (MCA), which maintains pressurization and low friction while producing repetitive compressive loading in addition to reciprocating sliding. Contact pressure, sliding duration, and sliding distance were controlled to be similar between test groups.

RESULTS

SCA tests exhibited an average friction coefficient of μ=0.084±0.032, while MCA tests exhibited a lower average friction coefficient of μ=0.020±0.008 (p<10-4). Despite the lower friction, MCA cartilage samples exhibited clear surface damage with a significantly greater average surface deviation from a fitted plane after wear testing (Rq=0.125±0.095 mm) than cartilage samples slid in a SCA configuration (Rq=0.044±0.017 mm, p=0.002), which showed minimal signs of wear. Polarized light microscopy confirmed that delamination damage occurred between the superficial and middle zones of the articular cartilage in MCA samples.

CONCLUSIONS

The greatest wear was observed in the group with lowest friction coefficient, subjected to cyclical instead of static compression, implying that friction is not the primary driver of cartilage wear. Delamination between superficial and middle zones implies the main mode of wear is fatigue failure under cyclical compression, not fatigue or abrasion due to reciprocating frictional sliding.

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.

Computational study of biomechanical drivers of renal cystogenesis

Renal cystogenesis is the pathological hallmark of autosomal dominant polycystic kidney disease, caused by PKD1 and PKD2 mutations. The formation of renal cysts is a common manifestation in ciliopathies, a group of syndromic disorders caused by mutation of proteins involved in the assembly and function of the primary cilium. Cystogenesis is caused by the derailment of the renal tubular architecture and tissue deformation that eventually leads to the impairment of kidney function. However, the biomechanical imbalance of cytoskeletal forces that are altered in cells with Pkd1 mutations has never been investigated, and its nature and extent remain unknown. In this computational study, we explored the feasibility of various biomechanical drivers of renal cystogenesis by examining several hypothetical mechanisms that may promote morphogenetic markers of cystogenesis. Our objective was to provide physics-based guidance for our formulation of hypotheses and our design of experimental studies investigating the role of biomechanical disequilibrium in cystogenesis. We employed the finite element method to explore the role of (1) wild-type versus mutant cell elastic modulus; (2) contractile stress magnitude in mutant cells; (3) localization and orientation of contractile stress in mutant cells; and (4) sequence of cell contraction and cell proliferation. Our objective was to identify the factors that produce the characteristic tubular cystic growth. Results showed that cystogenesis occurred only when mutant cells contracted along the apical-basal axis, followed or accompanied by cell proliferation, as long as mutant cells had comparable or lower elastic modulus than wild-type cells, with their contractile stresses being significantly greater than their modulus. Results of these simulations allow us to focus future in vitro and in vivo experimental studies on these factors, helping us formulate physics-based hypotheses for renal tubule cystogenesis.

Modeling Inelastic Responses Using Constrained Reactive Mixtures

This study reviews the progression of our research, from modeling growth theories for cartilage tissue engineering, to the formulation of constrained reactive mixture theories to model inelastic responses in any solid material, such as theories for damage mechanics, viscoelasticity, plasticity, and elasto-plastic damage. In this framework, multiple solid generations α can co-exist at any given time in the mixture. The oldest generation is denoted by α = s and is called the master generation, whose reference configuration X s is observable. The solid generations α are all constrained to share the same velocity v s , but may have distinct reference configurations X α . An important element of this formulation is that the time-invariant mapping F α s = ∂ X α / ∂ X s between these reference configurations is a function of state, whose mathematical formulation is postulated by constitutive assumption. Thus, reference configurations X α are not observable ( α ≠ s ) . This formulation employs only observable state variables, such as the deformation gradient F s of the master generation and the referential mass concentrations ρ r α of each generation, in contrast to classical formulations of inelastic responses which rely on internal state variable theory, requiring evolution equations for those hidden variables. In constrained reactive mixtures, the evolution of the mass concentrations is governed by the axiom of mass balance, using constitutive models for the mass supply densities ρ ˆ r α . Classical and constrained reactive mixture approaches share considerable mathematical analogies, as they both introduce a multiplicative decomposition of the deformation gradient, also requiring evolution equations to track some of the state variables. However, they also differ at a fundamental level, since one adopts only observable state variables while the other introduces hidden state variables. In summary, this review presents an alternative foundational approach to the modeling of inelastic responses in solids, grounded in the classical framework of mixture theory.

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 1e11, 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 non-biological 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.

Pulse wave imaging of a stenotic artery model with plaque constituents of different stiffnesses: Experimental demonstration in phantoms and fluid-structure interaction simulation

Vulnerable plaques associated with softer components may rupture, releasing thrombotic emboli to smaller vessels in the brain, thus causing an ischemic stroke. Pulse Wave Imaging (PWI) is an ultrasound-based method that allows for pulse wave visualization while the regional pulse wave velocity (PWV) is mapped along the arterial wall to infer the underlying wall compliance. One potential application of PWI is the non-invasive estimation of plaque's mechanical properties for investigating its vulnerability. In this study, the accuracy of PWV estimation in stenotic vessels was investigated by computational simulation and PWI in validation phantoms to evaluate this modality for assessing future stroke risk. Polyvinyl alcohol (PVA) phantoms with plaque constituents of different stiffnesses were designed and constructed to emulate stenotic arteries in the experiment, and the novel fabrication process was described. Finite-element fluid-structure interaction simulations were performed in a stenotic phantom model that matched the geometry and parameters of the experiment in phantoms. The peak distension acceleration of the phantom wall was tracked to estimate PWV. PWVs of 2.57 ms-1, 3.41 ms-1, and 4.48 ms-1 were respectively obtained in the soft, intermediate, and stiff plaque material in phantoms during the experiment using PWI. PWVs of 2.10 ms-1, 3.33 ms-1, and 4.02 ms-1 were respectively found in the soft, intermediate, and stiff plaque material in the computational simulation. These results demonstrate that PWI can effectively distinguish the mechanical properties of plaque in phantoms as compared to computational simulation.

Toward defining the role of the synovium in mitigating normal articular cartilage wear and tear

Cartilage repair has been studied extensively in the context of injury and disease, but the joint's management of regular sub-injurious damage to cartilage, or 'wear and tear,' which occurs due to normal activity, is poorly understood. We hypothesize that this cartilage maintenance is mediated in part by cells derived from the synovium that migrate to the worn articular surface. Here, we demonstrate in vitro that the early steps required for such a process can occur. First, we show that under physiologic mechanical loads, chondrocyte death occurs in the cartilage superficial zone along with changes to the cartilage surface topography. Second, we show that synoviocytes are released from the synovial lining under physiologic loads and attach to worn cartilage. Third, we show that synoviocytes parachuted onto a simulated or native cartilage surface will modify their behavior. Specifically, we show that synoviocyte interactions with chondrocytes lead to changes in synoviocyte mechanosensitivity, and we demonstrate that cartilage-attached synoviocytes can express COL2A1, a hallmark of the chondrogenic phenotype. Our findings suggest that synoviocyte-mediated repair of cartilage 'wear and tear' as a component of joint homeostasis is feasible and is deserving of future study.

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.

Pulsed Electromagnetic Field Therapy and Direct Current Electric Field Modulation Promote the Migration of Fibroblast-like Synoviocytes to Accelerate Cartilage Repair In Vitro

Articular cartilage injuries are a common source of joint pain and dysfunction. As articular cartilage is avascular, it exhibits a poor intrinsic healing capacity for self-repair. Clinically, osteochondral grafts are used to surgically restore the articular surface following injury. A significant challenge remains with the repair properties at the graft-host tissue interface as proper integration is critical toward restoring normal load distribution across the joint. A key to addressing poor tissue integration may involve optimizing mobilization of fibroblast-like synoviocytes (FLS) that exhibit chondrogenic potential and are derived from the adjacent synovium, the specialized connective tissue membrane that envelops the diarthrodial joint. Synovium-derived cells have been directly implicated in the native repair response of articular cartilage. Electrotherapeutics hold potential as low-cost, low-risk, non-invasive adjunctive therapies for promoting cartilage healing via cell-mediated repair. Pulsed electromagnetic fields (PEMFs) and applied direct current (DC) electric fields (EFs) via galvanotaxis are two potential therapeutic strategies to promote cartilage repair by stimulating the migration of FLS within a wound or defect site. PEMF chambers were calibrated to recapitulate clinical standards (1.5 ± 0.2 mT, 75 Hz, 1.3 ms duration). PEMF stimulation promoted bovine FLS migration using a 2D in vitro scratch assay to assess the rate of wound closure following cruciform injury. Galvanotaxis DC EF stimulation assisted FLS migration within a collagen hydrogel matrix in order to promote cartilage repair. A novel tissue-scale bioreactor capable of applying DC EFs in sterile culture conditions to 3D constructs was designed in order to track the increased recruitment of synovial repair cells via galvanotaxis from intact bovine synovium explants to the site of a cartilage wound injury. PEMF stimulation further modulated FLS migration into the bovine cartilage defect region. Biochemical composition, histological analysis, and gene expression revealed elevated GAG and collagen levels following PEMF treatment, indicative of its pro-anabolic effect. Together, PEMF and galvanotaxis DC EF modulation are electrotherapeutic strategies with complementary repair properties. Both procedures may enable direct migration or selective homing of target cells to defect sites, thus augmenting natural repair processes for improving cartilage repair and healing.

Superficial zone chondrocytes can get compacted under physiological loading: A multiscale finite element analysis

Recent in vivo and in vitro studies have demonstrated that superficial zone (SZ) chondrocytes within articular layers of diarthrodial joints die under normal physiologic loading conditions. In order to further explore the implications of this observation in future investigations, we first needed to understand the mechanical environment of SZ chondrocytes that might cause them to die under physiological sliding contact conditions. In this study we performed a multiscale finite element analysis of articular contact to track the temporal evolution of a SZ chondrocyte's interstitial fluid pressure, hydraulic permeability, and volume under physiologic loading conditions. The effect of the pericellular matrix modulus and permeability was parametrically investigated. Results showed that SZ chondrocytes can lose ninety percent of their intracellular fluid after several hours of intermittent or continuous contact loading, resulting in a reduction of intracellular hydraulic permeability by more than three orders of magnitude. These findings are consistent with loss of cell viability due to the impediment of cellular metabolic pathways induced by the loss of fluid. They suggest that there is a simple mechanical explanation for the vulnerability of SZ chondrocytes to sustained physiological loading conditions. Future studies will focus on validating these specific findings experimentally. STATEMENT OF SIGNIFICANCE: As with any mechanical system, normal 'wear and tear' of cartilage tissue lining joints is expected. Yet incidences of osteoarthritis are uncommon in individuals younger than 45. This counter-intuitive observation suggests there must be an intrinsic repair mechanism compensating for this wear and tear over many decades of life. Recent experimental studies have shown superficial zone chondrocytes die under physiologic loading conditions, suggesting that this repair mechanism may involve cell replenishment. To better understand the mechanical environment of these cells, we performed a multiscale computational analysis of articular contact under loading. Results indicated that normal activities like walking or standing can induce significant loss of intracellular fluid volume, potentially hindering metabolic activity and fluid transport properties, and causing cell death.

A Friction Testing-Bioreactor Device for Study of Synovial Joint Biomechanics, Mechanobiology, and Physical Regulation

In primary osteoarthritis (OA), normal 'wear and tear' associated with aging inhibits the ability of cartilage to sustain its load-bearing and lubrication functions, fostering a deleterious physical environment. The frictional interactions of articular cartilage and synovium may influence joint homeostasis through tissue level wear and cellular mechanotransduction. To study these mechanical and mechanobiological processes, a device capable of replicating the motion of the joint is described. The friction testing device controls the delivery of reciprocal translating motion and normal load to two contacting biological counterfaces. This study adopts a synovium-on-cartilage configuration, and friction coefficient measurements are presented for tests performed in a phosphate-buffered saline (PBS) or synovial fluid (SF) bath. The testing was performed for a range of contact stresses, highlighting the lubricating properties of SF under high loads. This friction testing device can be used as a biomimetic bioreactor for studying the physical regulation of living joint tissues in response to applied physiologic loading associated with diarthrodial joint articulation.

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.

Toward Development of a Diabetic Synovium Culture Model

Osteoarthritis (OA) is a degenerative joint disease characterized by articular cartilage degradation and inflammation of synovium, the specialized connective tissue that envelops the diarthrodial joint. Type 2 diabetes mellitus (DM) is often found in OA patients, with nearly double the incidence of arthritis reported in patients with diabetes (52%) than those without it (27%). The correlation between OA and DM has been attributed to similar risk factors, namely increasing age and joint loading due to obesity. However, a potential causative link is not well understood due to comorbidities involved with treating diabetic patients, such as high infection rates and poor healing response caused by hyperglycemia and insulin resistance. The purpose of this study was to investigate the effect of hyperglycemic and insulin culture conditions on synovium properties. It was hypothesized that modeling hyperglycemia-induced insulin resistance in synovium would provide novel insights of OA pathogenesis in DM patients. To simulate DM in the synovial joint, healthy synovium was preconditioned in either euglycemic (EG) or hyperglycemic (HG) glucose concentrations with insulin in order to induce the biological response of the diseased phenotype. Synovium biochemical composition was evaluated to determine ECM remodeling under hyperglycemic culture conditions. Concurrent changes in AKT phosphorylation, a signaling pathway implicated in insulin resistance, were measured along with gene expression data for insulin receptors, glucose transporters, and specific glycolysis markers involved in glucose regulation. Since fluid shear stress arising during joint articulation is a relevant upstream stimulus for fibroblast-like synoviocytes (FLS), the predominant cell type in synovium, FLS mechanotransduction was evaluated via intracellular calcium ([Ca²⁺]_i). Incidence and length of primary cilia, a critical effector of cell mechanosensing, were measured as potential mechanisms to support differences in [Ca²⁺]_i responses. Hyperglycemic culture conditions decreased collagen and GAG content compared to EG groups, while insulin recovered ECM constituents. FLS mechanosensitivity was significantly greater in EG and insulin conditions compared to HG and non-insulin treated groups. Hyperglycemic treatment led to decreased incidence and length of primary cilia and decreased AKT phosphorylation, providing possible links to the mechanosensing response and suggesting a potential correlation between glycemic culture conditions, diabetic insulin resistance, and OA development.

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.

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.

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.

Fibroblast-like synoviocyte mechanosensitivity to fluid shear is modulated by interleukin-1α

Fibroblast-like synoviocytes (FLS) reside in the synovial membrane of diarthrodial joints and are exposed to a dynamic fluid environment that presents both physical and chemical stimuli. The ability of FLS to sense and respond to these stimuli plays a key role in their normal function, and is implicated in the alterations to function that occur in osteoarthritis (OA). The present work characterizes the response of FLS to fluid flow-induced shear stress via real-time calcium imaging, and tests the hypothesis that this response is modulated by interleukin-1α (IL-1α), a cytokine elevated in OA. FLS demonstrated a robust calcium signaling response to fluid shear that was dose dependent upon stress level and required both external and internal calcium sources. Preconditioning with 10ng/mL IL-1α for 24h heightened this shear stress response by significantly increasing the percent of responding cells and peak magnitude, while significantly decreasing the time for a peak to occur. Intercellular communication via gap junctions was found to account for a portion of the FLS population response in normal conditions, and was significantly increased by IL-1α preconditioning. IL-1α was also found to significantly increase average length and incidence of the primary cilium, an organelle commonly implicated in shear mechanosensing. These findings suggest that the elevated levels of IL-1α found in the OA environment heighten FLS sensitivity to fluid shear by altering both intercellular communication and individual cell sensitivity, which could affect downstream functions and contribute to progression of the disease state.

Transient expression of the diseased phenotype of osteoarthritic chondrocytes in engineered cartilage

Due to the degradation of osteoarthritic (OA) cartilage in post-traumatic OA (PTOA), these tissues are challenging to study and manipulate in vitro. In this study, chondrocytes isolated from either PTOA (meniscal-release (MR) model) or normal (contralateral limb) cartilage of canine knee joints were used to form micropellets to assess the maintenance of the OA chondrocyte phenotype in vitro. Media samples from the micropellet cultures were used to measure matrix metalloproteinase (MMP), chemokine, and cytokine concentrations. Significant differences in matrix synthesis were observed as a function of disease with OA chondrocytes generally synthesizing more extracellular matrix with increasing time in culture. No donor dependent differences were detected. Luminex multiplex analysis of pellet culture media showed disease and time-dependent differences in interleukin (IL)-8, keratinocyte chemoattractant (KC)-like protein, MMP-1, MMP-2, and MMP-3, which are differentially expressed in OA. This memory of their diseased phenotype persists for the first 2 weeks of culture. These results demonstrate the potential to use chondrocytes from an animal model of OA to study phenotype alterations during the progression and treatment of OA. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:829-836, 2017.

* Constrained Cage Culture Improves Engineered Cartilage Functional Properties by Enhancing Collagen Network Stability

When cultured with sufficient nutrient supply, engineered cartilage synthesizes proteoglycans rapidly, producing an osmotic swelling pressure that destabilizes immature collagen and prevents the development of a robust collagen framework, a hallmark of native cartilage. We hypothesized that mechanically constraining the proteoglycan-induced tissue swelling would enhance construct functional properties through the development of a more stable collagen framework. To test this hypothesis, we developed a novel "cage" growth system to mechanically prevent tissue constructs from swelling while ensuring adequate nutrient supply to the growing construct. The effectiveness of constrained culture was examined by testing constructs embedded within two different scaffolds: agarose and cartilage-derived matrix hydrogel (CDMH). Constructs were seeded with immature bovine chondrocytes and cultured under free swelling (FS) conditions for 14 days with transforming growth factor-β before being placed into a constraining cage for the remainder of culture. Controls were cultured under FS conditions throughout. Agarose constructs cultured in cages did not expand after the day 14 caging while FS constructs expanded to 8 × their day 0 weight after 112 days of culture. In addition to the physical differences in growth, by day 56, caged constructs had higher equilibrium (agarose: 639 ± 179 kPa and CDMH: 608 ± 257 kPa) and dynamic compressive moduli (agarose: 3.4 ± 1.0 MPa and CDMH 2.8 ± 1.0 MPa) than FS constructs (agarose: 193 ± 74 kPa and 1.1 ± 0.5 MPa and CDMH: 317 ± 93 kPa and 1.8 ± 1.0 MPa for equilibrium and dynamic properties, respectively). Interestingly, when normalized to final day wet weight, cage and FS constructs did not exhibit differences in proteoglycan or collagen content. However, caged culture enhanced collagen maturation through the increased formation of pyridinoline crosslinks and improved collagen matrix stability as measured by α-chymotrypsin solubility. These findings demonstrate that physically constrained culture of engineered cartilage constructs improves functional properties through improved collagen network maturity and stability. We anticipate that constrained culture may benefit other reported engineered cartilage systems that exhibit a mismatch in proteoglycan and collagen synthesis.