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

In the present article, we investigate the biomechanical response of a fiber reinforced solid matrix (soft tissue) saturated with an electrically conducting fluid. A constant magnetic field was exposed to the binary mixture of fluid and deformable porous solid. The governing mechanism of multiphasic deformation was based on the loading imposed at the rigid bony interface. The fluid flow through the cartilage network depends upon the rate of applied compression and strain-dependent permeability of the solid matrix. The components of the mixture were intrinsically incompressible; however, in the derivation of governing dynamics, the visco-elastic behavior of the solid and an interstitial fluid was developed. The continuum mixture theory was employed in modeling solid deformation and local fluid pressure. We incorporated strain-dependent permeability in the governing equations of binary mixture that was found in an early experimental study. The governing non-linear coupled system of partial differential equations was developed for the solid deformation and fluid pressure in the presence of Lorentz forces. In the case of strain-dependent permeability, a numerical solution is computed using the method of lines (MOL), whereas, the exact solution is provided when permeability is kept constant. Graphical results highlight the influence of various physical parameters on both solid displacement and fluid pressure.

The effect of magnetic field on flow induced-deformation in absorbing porous tissues.

In order to understand the interaction between magnetic field and biological tissues in a physiological system, we present a mathematical model of flow-induced deformation in absorbing porous tissues in the presence of a uniform magnetic field. The tissue is modeled as a deformable porous material in which high cavity pressure drives fluid through the tissue where it is absorbed by capillaries and lymphatics. A biphasic mixture theory is used to develop the model under the assumptions of small solid deformation and strain-dependent linear permeability. A spherical cavity formed during injection of fluid in the tissue is used to find fluid pressure and solid displacement as a function of radial distance and time. The governing nonlinear PDE for fluid pressure is solved numerically using method of lines whereas tissue solid displacement is computed by employing trapezoidal rule. The effect of magnetic parameter on fluid pressure, solid displacement and tissue permeability is illustrated graphically.

On tear film breakup (TBU): dynamics and imaging.

We report the results of some recent experiments to visualize tear film dynamics. We then study a mathematical model for tear film thinning and tear film breakup (TBU), a term from the ocular surface literature. The thinning is driven by an imposed tear film thinning rate which is input from in vivo measurements. Solutes representing osmolarity and fluorescein are included in the model. Osmolarity causes osmosis from the model ocular surface, and the fluorescein is used to compute the intensity corresponding closely to in vivo observations. The imposed thinning can be either one-dimensional or axisymmetric, leading to streaks or spots of TBU, respectively. For a spatially-uniform (flat) film, osmosis would cease thinning and balance mass lost due to evaporation; for these space-dependent evaporation profiles TBU does occur because osmolarity diffuses out of the TBU into the surrounding tear film, in agreement with previous results. The intensity pattern predicted based on the fluorescein concentration is compared with the computed thickness profiles; this comparison is important for interpreting in vivo observations. The non-dimensionalization introduced leads to insight about the relative importance of the competing processes; it leads to a classification of large vs small TBU regions in which different physical effects are dominant. Many regions of TBU may be considered small, revealing that the flow inside the film has an appreciable influence on fluorescence imaging of the tear film.

A model for tear film thinning with osmolarity and fluorescein.

PURPOSE: We developed a mathematical model predicting dynamic changes in fluorescent intensity during tear film thinning in either dilute or quenching regimes and we model concomitant changes in tear film osmolarity. METHODS: We solved a mathematical model for the thickness, osmolarity, fluorescein concentration, and fluorescent intensity as a function of time, assuming a flat and spatially uniform tear film. RESULTS: The tear film thins to a steady-state value that depends on the relative importance of the rates of evaporation and osmotic supply, and the resulting increase of osmolarity and fluorescein concentrations are calculated. Depending on the initial thickness, the rate of osmotic supply and the tear film thinning rate, the osmolarity increase may be modest or it may increase by as much as a factor of eight or more from isosmotic levels. Regarding fluorescent intensity, the quenching regime occurs for initial concentrations at or above the critical fluorescein concentration where efficiency dominates, while lower concentrations show little change in fluorescence with tear film thinning. CONCLUSIONS: Our model underscores the importance of using fluorescein concentrations at or near the critical concentration clinically so that quenching reflects tear film thinning and breakup. In addition, the model predicts that, depending on tear film and osmotic factors, the osmolarity within the corneal compartment of the tear film may increase markedly during tear film thinning, well above levels that cause marked discomfort.