Axel C. Moore

An analytical model to predict interstitial lubrication of cartilage in migrating contact areas

For nearly a century, articular cartilage has been known for its exceptional tribological properties. For nearly as long, there have been research efforts to elucidate the responsible mechanisms for application toward biomimetic bearing applications. It is now widely accepted that interstitial fluid pressurization is the primary mechanism responsible for the unusual lubrication and load bearing properties of cartilage. Although the biomechanics community has developed elegant mathematical theories describing the coupling of solid and fluid (biphasic) mechanics and its role in interstitial lubrication, quantitative gaps in our understanding of cartilage tribology have inhibited our ability to predict how tribological conditions and material properties impact tissue function. This paper presents an analytical model of the interstitial lubrication of biphasic materials under migrating contact conditions. Although finite element and other numerical models of cartilage mechanics exist, they typically neglect the important role of the collagen network and are limited to a specific set of input conditions, which limits general applicability. The simplified approach taken in this work aims to capture the broader underlying physics as a starting point for further model development. In agreement with existing literature, the model indicates that a large Peclet number, Pe, is necessary for effective interstitial lubrication. It also predicts that the tensile modulus must be large relative to the compressive modulus. This explains why hydrogels and other biphasic materials do not provide significant interstitial pressure under high Pe conditions. The model quantitatively agrees with in-situ measurements of interstitial load support and the results have interesting implications for tissue engineering and osteoarthritis problems. This paper suggests that a low tensile modulus (from chondromalacia or local collagen rupture after impact, for example) may disrupt interstitial pressurization, increase shear stresses, and activate a condition of progressive surface damage as a potential precursor of osteoarthritis.

Tribological and material properties for cartilage of and throughout the bovine stifle: support for the altered joint kinematics hypothesis of osteoarthritis

OBJECTIVEnPrior studies suggest that ligament and meniscus tears cause osteoarthritis (OA) when changes in joint kinematics bring underused and underprepared regions of cartilage into contact. This study aims to test the hypothesis that material and tribological properties vary throughout the joint according to the local mechanical environment.nnnMETHODnThe local tribological and material properties of bovine stifle cartilage (Nxa0=xa010 joints with 20 samples per joint) were characterized under physiologically consistent contact stress and fluid pressure conditions.nnnRESULTSnOverall, cartilage from the bovine stifle had an equilibrium contact modulus of Ec0xa0=xa00.62xa0±xa00.10xa0MPa, a tensile modulus of Etxa0=xa04.3xa0±xa00.7xa0MPa, and a permeability of kxa0=xa02.8xa0±xa00.9xa0×xa010(-3)xa0mm(4)/Ns. During sliding, the cartilage had an effective friction coefficient of μeffxa0=xa00.024xa0±xa00.004, an effective contact modulus of Ecxa0=xa03.9xa0±xa00.7xa0MPa and a fluid load fraction of Fxa0=xa00.81xa0±xa00.03. Tibial cartilage exhibited significantly poorer material and tribological properties than femoral cartilage. Statistically significant differences were also detected across the femoral condyle and tibial plateau. The central femoral condyle exhibited the most favorable properties while the uncovered tibial plateau exhibited the least favorable properties.nnnCONCLUSIONSnOur findings support a previous hypothesis that altered loading patterns can cause OA by overloading underprepared regions. They also help explain why damage to the tibial plateau often precedes damage to the mating femoral condyle following joint injury in animal models. Because the variations are driven by fundamental biological processes, we anticipate similar variations in the human knee, which could explain the OA risk associated with ligament and meniscus tears.

Tribological rehydration of cartilage and its potential role in preserving joint health

OBJECTIVEnDuring exercise, cartilage recovers interstitial fluid lost during inactivity, which explains how tissue thickness and joint space are maintained over time. This recovery phenomenon is currently explained by a combination of osmotic swelling during intermittent bath exposure and sub-ambient pressurization during unloading. This paper tests an alternate hypothesis that cartilage can retain and recover interstitial fluid in the absence of bath exposure and unloading when physiological hydrodynamics are present.nnnMETHODnStationary cartilage-on-flat experiments were conducted to eliminate intermittent bath exposure as a potential contributor to fluid uptake. In situ compression measurements were used to monitor the loss, retention, and recovery of interstitial fluid during testing in saline. Samples were left larger than the contact area to preserve a convergence zone for hydrodynamic pressurization.nnnRESULTSnInterstitial fluid lost during static loading was recovered during sliding in the absence of unloading and contact migration; fluid recovery in a stationary contact cannot be explained by biphasic theory and suggests a fundamentally new contributor to the recovery process. We call the phenomenon tribological rehydration because recovery was induced by sliding rather than by unloading or migration. Sensitivities to sliding speed, surface permeability, and nature of the convergence wedge are consistent with the hypothesis that hydrodynamic effects underlie the tribological rehydration phenomenon.nnnCONCLUSIONSnThis study demonstrates that cartilage can retain and recover interstitial fluid without migration or unloading. The results suggest that hydrodynamic effects in the joint are not only important contributors to lubrication, they are likely equally important to the preservation of joint space.

Sliding enhances fluid and solute transport into buried articular cartilage contacts

OBJECTIVEnSolutes and interstitial water are naturally transported from cartilage by load-induced interstitial fluid pressures. Fluid and solute recovery during joint articulation have been primarily attributed to passive diffusion and mechanical pumping from dynamic loading. This paper tests if the sliding action of articulation is a significant and independent driver of fluid and solute transport in cartilage.nnnDESIGNnThe large osteochondral samples utilized in the present study preserve the convergent wedges necessary for physiological hydrodynamics. Following static load-induced fluid exudation and prior to sliding, a fluorescent solute (AlexaFluor 633) was added to the lubricant bath. In situ confocal microscopy was used to quantify the transport of solute from the bath into the buried stationary contact area (SCA) during sliding.nnnRESULTSnFollowing static exudation, significant reductions in friction and strain during sliding at 60xa0mm/s were accompanied by significant solute transport into the inaccessible center of the buried contact; no such transport was detected for the 0- or 1xa0mm/s sliding conditions. The results suggest that external hydrodynamic pressures from sliding induced advective flows that carried solutes from the bath toward the center of contact.nnnCONCLUSIONSnThese results provide the first direct evidence that the action of sliding is a significant contributor to fluid and solute recovery by cartilage. Furthermore, they indicate that the sliding-induced transport of solutes into the buried interface was orders of magnitude greater than that attributable to diffusion alone, a result with critical implications for disease prevention and tissue engineering.

Quantifying Cartilage Contact Modulus, Tension Modulus, and Permeability With Hertzian Biphasic Creep

This paper describes a new method, based on a recent analytical model (Hertzian biphasic theory (HBT)), to simultaneously quantify cartilage contact modulus, tension modulus, and permeability. Standard Hertzian creep measurements were performed on 13 osteochondral samples from three mature bovine stifles. Each creep dataset was fit for material properties using HBT. A subset of the dataset (Nu2009=u20094) was also fit using Oyens method and FEBio, an open-source finite element package designed for soft tissue mechanics. The HBT method demonstrated statistically significant sensitivity to differences between cartilage from the tibial plateau and cartilage from the femoral condyle. Based on the four samples used for comparison, no statistically significant differences were detected between properties from the HBT and FEBio methods. While the finite element method is considered the gold standard for analyzing this type of contact, the expertise and time required to setup and solve can be prohibitive, especially for large datasets. The HBT method agreed quantitatively with FEBio but also offers ease of use by nonexperts, rapid solutions, and exceptional fit quality (R2u2009=u20090.999u2009±u20090.001, Nu2009=u200913).

A review of methods to study hydration effects on cartilage friction

Abstract The mechanical and tribological responses of cartilage depend strongly on its hydration state, which is a function of the mechanical and tribological conditions of the contact. The interdependencies between stresses and water content make controlled studies of cartilage function difficult. This paper reviews some of the experimental challenges in cartilage tribology and the methods we have used to help address them. For example, we demonstrate a simple method to eliminate the frictional errors associated with sample curvature in the migrating contact area and show how in situ measurements can be used to assess hydration and its effect on friction. Finally, we demonstrate a new explant testing configuration, the convergent stationary contact area (cSCA), in which cartilage loses, maintains and recovers interstitial water in response to loading and sliding in a manner consistent with in vivo joint mechanics. We propose that the cSCA provides an ideal test bed for studying cartilage tribology, while maximising experimental control and physiological relevance.

Mapping the spatiotemporal evolution of solute transport in articular cartilage explants reveals how cartilage recovers fluid within the contact area during sliding

The interstitial fluid within articular cartilage shields the matrix from mechanical stresses, reduces friction and wear, enables biochemical processes, and transports solutes into and out of the avascular extracellular matrix. The balanced competition between fluid exudation and recovery under load is thus critical to the mechanical and biological functions of the tissue. We recently discovered that sliding alone can induce rapid solute transport into buried cartilage contact areas via a phenomenon termed tribological rehydration. In this study, we use in situ confocal microscopy measurements to track the spatiotemporal propagation of a small neutral solute into the buried contact area to clarify the fluid mechanics underlying the tribological rehydration phenomenon. Sliding experiments were interrupted by periodic static loading to enable scanning of the entire contact area. Spatiotemporal patterns of solute transport combined with tribological data suggested pressure driven flow through the extracellular matrix from the contact periphery rather than into the surface via a fluid film. Interestingly, these testing interruptions also revealed dynamic, repeatable and history-independent fluid loss and recovery processes consistent with those observed in vivo. Unlike the migrating contact area, which preserves hydration by moving faster than interstitial fluid can flow, our results demonstrate that the stationary contact area can maintain and actively recover hydration through a dynamic competition between load-induced exudation and sliding-induced recovery. The results demonstrate that sliding contributes to the recovery of fluid and solutes by cartilage within the contact area while clarifying the means by which it occurs.

Unexpected Tribological Synergy in Polymer Blend Coatings: Leveraging Phase Separation to Isolate Domain Size Effects and Reduce Friction

We employed a systematic processing approach to control phase separation in polymer blend thin films and significantly reduce dynamic friction coefficients (μ)s. We leveraged this modulation of phase separation to generate composite surfaces with dynamic friction coefficients that were substantially lower than expected on the basis of simple mixing rules, and in several cases, these friction coefficients were lower than those of both pure components. Using a model polyisoprene [PI]/polystyrene [PS] composite system, a minimum μ was found in films with PS mass fractions between 0.60 and 0.80 (μblend = 0.11 ± 0.03); that value was significantly lower than the friction coefficient of PS (μPS = 0.52 ± 0.01) or PI (μPI = 1.3 ± 0.09) homopolymers and was comparable to the friction coefficient of poly(tetrafluoroethylene) [PTFE] (μPTFE = 0.09 ± 0.01) measured under similar conditions. Additionally, through experiments in which the domain size was systematically varied at constant composition (through an annealing process), we demonstrated that μ decreased with decreasing characteristic domain size. Thus, the tribological synergy between PS and PI domains (discrete size, physical domain isolation, and overall film composition) was shown to play an integral role in the friction and wear of these PS/PI composites. Overall, our results suggest that even high friction polymers can be used to create low friction polymer blends by following appropriate design rules and demonstrate that engineering microstructure is critical for controlling the friction and adhesion properties of composite films for tribologically relevant coatings.

Glycosylated superparamagnetic nanoparticle gradients for osteochondral tissue engineering

In developmental biology, gradients of bioactive signals direct the formation of structural transitions in tissue that are key to physiological function. Failure to reproduce these native features in an in vitro setting can severely limit the success of bioengineered tissue constructs. In this report, we introduce a facile and rapid platform that uses magnetic field alignment of glycosylated superparamagnetic iron oxide nanoparticles, pre-loaded with growth factors, to pattern biochemical gradients into a range of biomaterial systems. Gradients of bone morphogenetic protein 2 in agarose hydrogels were used to spatially direct the osteogenesis of human mesenchymal stem cells and generate robust osteochondral tissue constructs exhibiting a clear mineral transition from bone to cartilage. Interestingly, the smooth gradients in growth factor concentration gave rise to biologically-relevant, emergent structural features, including a tidemark transition demarcating mineralized and non-mineralized tissue and an osteochondral interface rich in hypertrophic chondrocytes. This platform technology offers great versatility and provides an exciting new opportunity for overcoming a range of interfacial tissue engineering challenges.

Cellular interactions with hydrogel microfibers synthesized via interfacial tetrazine ligation.

Fibrous proteins found in the natural extracellular matrix (ECM) function as host substrates for migration and growth of endogenous cells during wound healing and tissue repair processes. Although various fibrous scaffolds have been developed to recapitulate the microstructures of the native ECM, facile synthesis of hydrogel microfibers that are mechanically robust and biologically active have been elusive. Described herein is the use of interfacial bioorthogonal polymerization to create hydrogel-based microfibrous scaffolds via tetrazine ligation. Combination of a trifunctional strained trans-cyclooctene monomer and a difunctional s-tetrazine monomer at the oil-water interface led to the formation of microfibers that were stable under cell culture conditions. The bioorthogonal nature of the synthesis allows for direct incorporation of tetrazine-conjugated peptides or proteins with site-selectively, genetically encoded tetrazines. The microfibers provide physical guidance and biochemical signals to promote the attachment, division and migration of fibroblasts. Mechanistic investigations revealed that fiber-guided cell migration was both F-actin and microtubule-dependent, confirming contact guidance by the microfibers. Prolonged culture of fibroblasts in the presence of an isolated microfiber resulted in the formation of a multilayered cell sheet wrapping around the fiber core. A fibrous mesh provided a 3D template to promote cell infiltration and tissue-like growth. Overall, the bioorthogonal approach led to the straightforward synthesis of crosslinked hydrogel microfibers that can potentially be used as instructive materials for tissue repair and regeneration.