Visco-elastic behavior of articular cartilage under applied magnetic field and strain-dependent permeability

A computational study on dynamic behavior of articular cartilage under cyclic compressive loading and magnetic field

The dynamic behavior of articular cartilage (a soft porous biological tissue) with strain-dependent nonlinear permeability under cyclic compressive loading and magnetic field is investigated computationally. The compressive force is applied on top surface of the cylindrical plug of the tissue by means of a porous filter. The study of mechanical and deformational behavior of soft porous tissues such as articular cartilage under dynamic compressive loading and magnetic field is useful in understanding the underlying mechano-biological process that may lead to the development of a treatment and recovery protocol in a diseased state. In the present study, a linear biphasic mixture theory of porous media has been employed to derive the governing equations in terms of solid displacement and interstitial fluid pressure in the tissue. Exact solutions for the solid displacement, fluid pressure, and relative fluid velocity are provided for the constant permeability case which have also been used to validate the numerical method. On the other hand, the full nonlinear problem has been solved numerically using the method of lines and the outcomes are presented graphically to assess the effects of various emerging parameters. The results indicate that there is an increase in the solid dilatation due to application of magnetic field and this effect is more prominent at relatively high loading frequencies. In general, a repeated compressive force has generated an oscillating positive-negative hydrostatic pressure within the tissue, however, a strong magnetic field at comparatively high loading frequency enforces the tissue to have only the positive (supra-ambient) pressure. The outcomes have also revealed that the pattern of the dynamic behavior of the tissue is strongly dependent on the loading frequency. A considerable phase shift in the dilatation and fluid pressure has been noticed due to the loading frequency as well as magnetic effects. It has also been found that the permeability parameter has a minimal impact on the solid deformation and fluid pressure in all scenarios with a very small phase shift.

Low-Temperature Extrusion of Waterborne Polyurethane-Polycaprolactone Composites for Multi-Material Bioprinting of Engineered Elastic Cartilage

3D bioprinting of elastic cartilage tissues that are mechanically and structurally comparable to their native counterparts, while exhibiting favorable cellular behavior, is an unmet challenge. A practical solution for this problem is the multi-material bioprinting of thermoplastic polymers and cell-laden hydrogels using multiple nozzles. However, the processing of thermoplastic polymers requires high temperatures, which can damage hydrogel-encapsulated cells. In this study, the authors developed waterborne polyurethane (WPU)-polycaprolactone (PCL) composites to allow multi-material co-printing with cell-laden gelatin methacryloyl (GelMA) hydrogels. These composites can be extruded at low temperatures (50-60 °C) and high speeds, thereby reducing heat/shear damage to the printed hydrogel-capsulated cells. Furthermore, their hydrophilic nature improved the cell behavior in vitro. More importantly, the bioprinted structures exhibited good stiffness and viscoelasticity compared to native elastic cartilage. In summary, this study demonstrated low-temperature multi-material bioprinting of WPU-PCL-based constructs with good mechanical properties, degradation time-frames, and cell viability, showcasing their potential in elastic cartilage bio-fabrication and regeneration to serve broad biomedical applications in the future.

Ion-Induced Swelling Behavior of Articular Cartilage due to Non-Newtonian Flow and Its Effects on Fluid Pressure and Solid Displacement

In this study, we examine the behavior of articular cartilage equilibrated in a salt (NaCl) solution during non-Newtonian fluid flow that follows an Ostwald-de Waele model. A linearly elastic and isotropic rectangular strip of cartilage is considered for analysis. A continuum theory of mixtures has been employed to develop a coupled system of partial differential equations for the solid displacement and the fluid pressure by considering the important factor of the ion concentration by assuming the cartilage as a deformable porous media. The coupled system of partial differential equations is solved using the numerical method named method of lines. In most cases, shear-thinning fluid is compared to the shear-thickening fluid to magnify the difference. Graphical results show that shear-thickening fluids bring more solid deformation and shows less fluid pressure in comparison to the shear-thinning fluids.

Compressive stress relaxation behavior of articular cartilage and its effects on fluid pressure and solid displacement due to non-Newtonian flow

In this study, we investigate the effects of the power-law index and permeability parameter on the deformation of soft tissue (articular cartilage) which is bathed in the non-Newtonian fluid under stress-relaxation in compression. Ramp displacement is imposed on the surface of hydrated soft tissue. Deformation of the tissue and the fluid pressure is examined for the fast and slow rate of compression. We have employed a linear biphasic mixture theory to develop a mathematical model for compressive stress-relaxation behavior of articular cartilage for non-Newtonian flow. Numerical results indicate that shear-thinning fluids induce less solid deformation and exhibit more fluid pressure as compared to shear-thickening fluids for fast and slow rate of compression. The results also show that linear permeability induces more deformation as compared to strain-dependent nonlinear permeability due to viscoelastic nature of articular cartilage.