Multifield Modeling and Simulation of Nutrient Transport in Mechanically Stressed Meniscus Tissue.

Insights into the transport mechanisms of nutrients are essential for understanding the pathophysiology of menisci. In the present work, we focus on the modeling and numerical simulation of the transport of glucose molecules in mechanically stressed meniscus tissue. Therefore, a multifield model based on the theory of porous media is created. Due to a biphasic approach, the major phases of the solid and the fluid are represented. The description of the transport processes of the uncharged nutrient molecules, such as convection and diffusion, is given by three coupled partial differential equations valid for large deformations. Numerical simulations are performed for everyday types of stress such as (I) lying, (II) two-legged stance, (III) one-legged stance, (IV) level walking, and (V) stair descending using the finite element method. The results show that diffusion is the dominant process. However, in parts of the meniscus, the delivery of glucose can be improved by convection due to mechanical loading. Based on these basic insights, the model can now be adapted to individual patient's meniscus geometries. The model can thus give insights into the suitability of loading scenarios for rehabilitation after meniscus damage.

Modeling and simulation of diffusion and reaction processes during the staining of tissue sections on slides.

Histological slides are an important tool in the diagnosis of tumors as well as of other diseases that affect cell shapes and distributions. Until now, the research concerning an optimal staining time has been mainly done empirically. In experimental investigations, it is often not possible to stain an already-stained slide with another stain to receive further information. To overcome these challenges, in the present paper a continuum-based model was developed for conducting a virtual (re-)staining of a scanned histological slide. This model is capable of simulating the staining of cell nuclei with the dye hematoxylin (C.I. 75,290). The transport and binding of the dye are modeled (i) along with the resulting RGB intensities (ii). For (i), a coupled diffusion-reaction equation is used and for (ii) Beer-Lambert's law. For the spatial discretization an approach based on the finite element method (FEM) is used and for the time discretization a finite difference method (FDM). For the validation of the proposed model, frozen sections from human liver biopsies stained with hemalum were used. The staining times were varied so that the development of the staining intensity could be observed over time. The results show that the model is capable of predicting the staining process. The model can therefore be used to perform a virtual (re-)staining of a histological sample. This allows a change of the staining parameters without the need of acquiring an additional sample. The virtual standardization of the staining is the first step towards universal cross-site comparability of histological slides.

Shell-Forming Stimulus-Active Hydrogel Composite Membranes: Concept and Modeling.

The swelling of active hydrogels combined with passive layers allows the design of shell-forming structures. A shell-like structure offers different properties than a flat structure, e.g., variations in bending stiffness across different directions. A drastic increase of the bending stiffness is favorable e.g., in rollable/flexible displays: in their unrolled form, they have to be stiff enough to resist bending due to dead weight. At the same time, they have to be flexible enough to be rolled-up. This can be achieved by shell-forming. In the current modeling and simulation work, we present a basic concept of combined active-passive composites and demonstrate how they form shells. As the example material class, we use hydrogels with isotropic swelling capabilities. We demonstrate how to model the combined mechanical behavior with the Temperature-Expansion-Model. Afterwards, we show numerical results obtained by Finite Element simulations. We conclude that the envisioned structure has a great potential for obtaining soft rollable sheets that can be stiffened by intrinsic activation.

Swelling and shrinking in prestressed polymer gels: an incremental stress-diffusion analysis.

Polymer gels are porous fluid-saturated materials which can swell or shrink triggered by various stimuli. The swelling/shrinking-induced deformation can generate large stresses which may lead to the failure of the material. In the present research, a nonlinear stress-diffusion model is employed to investigate the stress and the deformation state arising in hydrated constrained polymer gels when subject to a varying chemical potential. Two different constraint configurations are taken into account: (i) elastic constraint along the thickness direction and (ii) plane elastic constraint. The first step entirely defines a compressed/tensed configuration. From there, an incremental chemo-mechanical analysis is presented. The derived model extends the classical linear poroelastic theory with respect to a prestressed configuration. Finally, the comparison between the analytical results obtained by the proposed model and a particular problem already discussed in literature for a stress-free gel membrane (one-dimensional test case) will highlight the relevance of the derived model.