Multiphasic modeling of charged solute transport across articular cartilage: Application of multi-zone finite-bath model

Contrast solution properties and scan parameters influence the apparent diffusivity of computed tomography contrast agents in articular cartilage

The inability to detect early degenerative changes to the articular cartilage surface that commonly precede bulk osteoarthritic degradation is an obstacle to early disease detection for research or clinical diagnosis. Leveraging a known artefact that blurs tissue boundaries in clinical arthrograms, contrast agent (CA) diffusivity can be derived from computed tomography arthrography (CTa) scans. We combined experimental and computational approaches to study protocol variations that may alter the CTa-derived apparent diffusivity. In experimental studies on bovine cartilage explants, we examined how CA dilution and transport direction (absorption versus desorption) influence the apparent diffusivity of untreated and enzymatically digested cartilage. Using multiphysics simulations, we examined mechanisms underlying experimental observations and the effects of image resolution, scan interval and early scan termination. The apparent diffusivity during absorption decreased with increasing CA concentration by an amount similar to the increase induced by tissue digestion. Models indicated that osmotically-induced fluid efflux strongly contributed to the concentration effect. Simulated changes to spatial resolution, scan spacing and total scan time all influenced the apparent diffusivity, indicating the importance of consistent protocols. With careful control of imaging protocols and interpretations guided by transport models, CTa-derived diffusivity offers promise as a biomarker for early degenerative changes.

Topographic features of nano-pores within the osteochondral interface and their effects on transport properties -a 3D imaging and modeling study

Recent insights suggest that the osteochondral interface plays a central role in maintaining healthy articulating joints. Uncovering the underlying transport mechanisms is key to the understanding of the cross-talk between articular cartilage and subchondral bone. Here, we describe the mechanisms that facilitate transport at the osteochondral interface. Using scanning electron microscopy (SEM), we found a continuous transition of mineralization architecture from the non-calcified cartilage towards the calcified cartilage. This refurbishes the classical picture of the so-called tidemark; a well-defined discontinuity at the osteochondral interface. Using focused-ion-beam SEM (FIB-SEM) on one osteochondral plug derived from a human cadaveric knee, we elucidated that the pore structure gradually varies from the calcified cartilage towards the subchondral bone plate. We identified nano-pores with radius of 10.71 ± 6.45 nm in calcified cartilage to 39.1 ± 26.17 nm in the subchondral bone plate. The extracted pore sizes were used to construct 3D pore-scale numerical models to explore the effect of pore sizes and connectivity among different pores. Results indicated that connectivity of nano-pores in calcified cartilage is highly compromised compared to the subchondral bone plate. Flow simulations showed a permeability decrease by about 2000-fold and solute transport simulations using a tracer (iodixanol, 1.5 kDa with a free diffusivity of 2.5 × 10^-10 m²/s) showed diffusivity decrease by a factor of 1.5. Taken together, architecture of the nano-pores and the complex mineralization pattern in the osteochondral interface considerably impacts the cross-talk between cartilage and bone.

Effects of human articular cartilage constituents on simultaneous diffusion of cationic and nonionic contrast agents

Contrast-enhanced computed tomography is an emerging diagnostic technique for osteoarthritis. However, the effects of increased water content, as well as decreased collagen and proteoglycan concentrations due to cartilage degeneration, on the diffusion of cationic and nonionic agents, are not fully understood. We hypothesize that for a cationic agent, these variations increase the diffusion rate while decreasing partition, whereas, for a nonionic agent, these changes increase both the rate of diffusion and partition. Thus, we examine the diffusion of cationic and nonionic contrast agents within degraded tissue in time- and depth-dependent manners. Osteochondral plugs (N = 15, d = 8 mm) were extracted from human cadaver knee joints, immersed in a mixture of cationic CA4+ and nonionic gadoteridol contrast agents, and imaged at multiple time-points, using the dual-contrast method. Water content, and collagen and proteoglycan concentrations were determined using lyophilization, infrared spectroscopy, and digital densitometry, respectively. Superficial to mid (0%-60% depth) cartilage CA4+ partitions correlated with water content (R < -0.521, P < .05), whereas in deeper (40%-100%) cartilage, CA4+ correlated only with proteoglycans (R > 0.671, P < .01). Gadoteridol partition correlated inversely with collagen concentration (0%-100%, R < -0.514, P < .05). Cartilage degeneration substantially increased the time for CA4+ compared with healthy tissue (248 ± 171 vs 175 ± 95 minute) to reach the bone-cartilage interface, whereas for gadoteridol the time (111 ± 63 vs 179 ± 163 minute) decreased. The work clarifies the diffusion mechanisms of two different contrast agents and presents depth and time-dependent effects resulting from articular cartilage constituents. The results will inform the development of new contrast agents and optimal timing between agent administration and joint imaging.

Digital Twins for Tissue Culture Techniques—Concepts, Expectations, and State of the Art

Techniques to provide in vitro tissue culture have undergone significant changes during the last decades, and current applications involve interactions of cells and organoids, three-dimensional cell co-cultures, and organ/body-on-chip tools. Efficient computer-aided and mathematical model-based methods are required for efficient and knowledge-driven characterization, optimization, and routine manufacturing of tissue culture systems. As an alternative to purely experimental-driven research, the usage of comprehensive mathematical models as a virtual in silico representation of the tissue culture, namely a digital twin, can be advantageous. Digital twins include the mechanistic of the biological system in the form of diverse mathematical models, which describe the interaction between tissue culture techniques and cell growth, metabolism, and the quality of the tissue. In this review, current concepts, expectations, and the state of the art of digital twins for tissue culture concepts will be highlighted. In general, DT’s can be applied along the full process chain and along the product life cycle. Due to the complexity, the focus of this review will be especially on the design, characterization, and operation of the tissue culture techniques.

Combined Experimental Approach and Finite Element Modeling of Small Molecule Transport Through Joint Synovium to Measure Effective Diffusivity

Trans-synovial solute transport plays a critical role in the clearance of intra-articularly (IA) delivered drugs. In this study, we present a computational finite element model (FEM) of solute transport through the synovium validated by experiments on synovial explants. Unsteady diffusion of urea, a small uncharged molecule, was measured through devitalized porcine and human synovium using custom-built diffusion chambers. A multiphasic computational model was constructed and optimized with the experimental data to extract effective diffusivity for urea within the synovium. A monotonic decrease in urea concentration was observed in the donor bath over time, with an effective diffusivity found to be an order of magnitude lower in synovium versus that measured in free solution. Parametric studies incorporating an intimal cell layer with varying thickness and varying effective diffusivities were performed, revealing a dependence of drug clearance kinetics on both parameters. The findings of this study indicate that the synovial matrix impedes urea solute transport out of the joint with little retention of the solute in the matrix.

MODELING AND INJURY REPAIR ANALYSIS OF ARTICULAR CARTILAGE BASED ON FIBER CONTENT

It has great guiding significance for the prevention of osteoarthritis and the mechanical state of cartilage after tissue engineering repair to study the relationship between the mechanical properties of cartilage and its structure. This paper considered both the consideration of the solid phase, liquid phase, fiber-reinforced phase in the cartilage and the influence of the contents of major fibers and minor fibers near the cartilage surface. Based on these, a tangential zone of cartilage was established, and a certain improvement and optimization of the fiber-reinforced porous elastic model was performed. The Abaqus software and the Fortran language were used to complete simulation. Simulation results were compared with experiment’s results to verify the validity of the model. Finally, the model was used to perform finite element analysis of different degrees of repairable depth under sliding conditions. Several results were obtained. When the indenter is farther from the interface at the repair site, the mechanical changes in the cartilage are relatively stable. The contact stress of the tangential layer repair and the full-layer repair is small. The volume fraction of the liquid phase in the tangential layer and the full layer repair is lower than that in the other layer regions. The liquid flow rate and the Von Mises stress at the junction of the tangential layer repair are very high. Simulation results were used to explore differences in cartilage mechanical properties of different repairable depths, so as to select the best repairable depth for cartilage.

Contrast enhanced computed tomography for real-time quantification of glycosaminoglycans in cartilage tissue engineered constructs

Tissue engineering and regenerative medicine are two therapeutic strategies to treat, and to potentially cure, diseases affecting cartilaginous tissues, such as osteoarthritis and cartilage defects. Insights into the processes occurring during regeneration are essential to steer and inform development of the envisaged regenerative strategy, however tools are needed for longitudinal and quantitative monitoring of cartilage matrix components. In this study, we introduce a contrast-enhanced computed tomography (CECT)-based method using a cationic iodinated contrast agent (CA4+) for longitudinal quantification of glycosaminoglycans (GAG) in cartilage-engineered constructs. CA4+ concentration and scanning protocols were first optimized to ensure no cytotoxicity and a facile procedure with minimal radiation dose. Chondrocyte and mesenchymal stem cell pellets, containing different GAG content were generated and exposed to CA4+. The CA4+ content in the pellets, as determined by micro computed tomography, was plotted against GAG content, as measured by 1,9-dimethylmethylene blue analysis, and showed a high linear correlation. The established equation was used for longitudinal measurements of GAG content over 28 days of pellet culture. Importantly, this method did not adversely affect cell viability or chondrogenesis. Additionally, the CA4+ distribution accurately matched safranin-O staining on histological sections. Hence, we show proof-of-concept for the application of CECT, utilizing a positively charged contrast agent, for longitudinal and quantitative imaging of GAG distribution in cartilage tissue-engineered constructs. STATEMENT OF SIGNIFICANCE: Tissue engineering and regenerative medicine are promising therapeutic strategies for different joint pathologies such as cartilage defects or osteoarthritis. Currently, in vitro assessment on the quality and composition of the engineered cartilage mainly relies on destructive methods. Therefore, there is a need for the development of techniques that allow for longitudinal and quantitative imaging and monitoring of cartilage-engineered constructs. This work harnesses the electrostatic interactions between the negatively-charged glycosaminoglycans (GAGs) and a positively-charged contrast agent for longitudinal and non-destructive quantification of GAGs, providing valuable insight on GAG development and distribution in cartilage engineered constructs. Such technique can advance the development of regenerative strategies, not only by allowing continuous monitoring but also by serving as a pre-implantation screening tool.

Intermolecular interactions play a role in the distribution and transport of charged contrast agents in a cartilage model

The transport and distribution of charged molecules in polyelectrolyte solutions are of both fundamental and practical importance. A practical example, which is the specific subject addressed in the present paper, is the transport and distribution of charged species into cartilage. The charged species could be a contrast agent or a drug molecule involved in diagnosis or treatment of the widespread degenerative disease osteoarthritis, which leads to degradation of articular cartilage. Associated scientific issues include the rate of transport and the equilibrium concentrations of the charged species in the cartilage and the synovial fluid. To address these questions, we present results from magnetic resonance micro-imaging experiments on a model system of articular cartilage. The experiments yield temporally and spatially resolved data on the transport of a negatively charged contrast agent (charge = -2), used in medical examinations of cartilage, into a polyelectrolyte solution, which is designed to capture the electrostatic interactions in cartilage. Also presented is a theoretical analysis of the transport where the relevant differential equations are solved using finite element techniques as well as treated with approximate analytical expressions. In the analysis, non-ideal effects are included in the treatment of the mobile species in the system. This is made possible by using results from previous Monte Carlo simulations. The results demonstrate the importance of taking non-idealities into account when data from measurements of transport of charged solutes in a system with fixed charges from biological polyelectrolytes are analyzed.

The Effect of Charge and Mechanical Loading on Antibody Diffusion Through the Articular Surface of Cartilage

Molecular transport of osteoarthritis (OA) therapeutics within articular cartilage is influenced by many factors, such as solute charge, that have yet to be fully understood. This study characterizes how solute charge influences local diffusion and convective transport of antibodies within the heterogeneous cartilage matrix. Three fluorescently tagged solutes of varying isoelectric point (pI) (4.7–5.9) were tested in either cyclic or passive cartilage loading conditions. In each case, local diffusivities were calculated based on local fluorescence in the cartilage sample, as observed by confocal microscopy. In agreement with past research, local solute diffusivities within the heterogeneous cartilage matrix were highest around 200–275 μm from the articular surface, but 3–4 times lower at the articular surface and in the deeper zones of the tissue. Transport of all 150 kDa solutes was significantly increased by the application of mechanical loading at 1 Hz, but local transport enhancement was not significantly affected by changes in solute isoelectric point. More positively charged solutes (higher pI) had significantly higher local diffusivities 200–275 μm from the tissue surface, but no other differences were observed. This implies that there are certain regions of cartilage that are more sensitive to changes in solute charge than others, which could be useful for future development of OA therapeutics.

An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage

Osteoarthritis (OA) is a debilitating disease that is associated with degeneration of articular cartilage and subchondral bone. Degeneration of articular cartilage impairs its load-bearing function substantially as it experiences tremendous chemical degradation, i.e. proteoglycan loss and collagen fibril disruption. One promising way to investigate chemical damage mechanisms during OA is to expose the cartilage specimens to an external solute and monitor the diffusion of the molecules. The degree of cartilage damage (i.e. concentration and configuration of essential macromolecules) is associated with collisional energy loss of external solutes while moving across articular cartilage creates different diffusion characteristics compared to healthy cartilage. In this study, we introduce a protocol, which consists of several steps and is based on previously developed experimental micro-Computed Tomography (micro-CT) and finite element modeling. The transport of charged and uncharged iodinated molecules is first recorded using micro-CT, which is followed by applying biphasic-solute and multiphasic finite element models to obtain diffusion coefficients and fixed charge densities across cartilage zones.

Application of multiphysics models to efficient design of experiments of solute transport across articular cartilage

Transport of solutes helps to regulate normal physiology and proper function of cartilage in diarthrodial joints. Multiple studies have shown the effects of characteristic parameters such as concentration of proteoglycans and collagens and the orientation of collagen fibrils on the diffusion process. However, not much quantitative information and accurate models are available to help understand how the characteristics of the fluid surrounding articular cartilage influence the diffusion process. In this study, we used a combination of micro-computed tomography experiments and biphasic-solute finite element models to study the effects of three parameters of the overlying bath on the diffusion of neutral solutes across cartilage zones. Those parameters include bath size, degree of stirring of the bath, and the size and concentration of the stagnant layer that forms at the interface of cartilage and bath. Parametric studies determined the minimum of the finite bath size for which the diffusion behavior reduces to that of an infinite bath. Stirring of the bath proved to remarkably influence neutral solute transport across cartilage zones. The well-stirred condition was achieved only when the ratio of the diffusivity of bath to that of cartilage was greater than ≈1000. While the thickness of the stagnant layer at the cartilage-bath interface did not significantly influence the diffusion behavior, increase in its concentration substantially elevated solute concentration in cartilage. Sufficient stirring attenuated the effects of the stagnant layer. Our findings could be used for efficient design of experimental protocols aimed at understanding the transport of molecules across articular cartilage.