Optimization of patient positioning for improved healing after corneal transplantation.

Corneal transplantation is the only solution which avoids loss of vision, when endothelial cells are dramatically lost. The surgery involves injecting gas into the anterior chamber of the eye, to create a bubble that pushes onto the donor cornea (graft), achieving sutureless adherence to the host cornea. During the postoperative period, patient positioning affects the bubble. To improve healing, we study the shape of the gas-bubble interface throughout the postoperative period, by numerically solving the equations of fluid motion. Patient-specific anterior chambers (ACs) of variable anterior chamber depths (ACD) are considered, for either phakic (with natural lens) and pseudophakic (with artificial lens) eyes. For each AC, gas-graft coverage is computed for different gas fill and patient positioning. The results show that the influence of positioning is negligible, regardless of gas filling, as long as the ACD is small. However, when the ACD value increases, patient positioning becomes important, especially for pseudophakic ACs. The difference between best and worst patient positioning over time, for each AC, is negligible for small ACD but significant for larger ACD, especially for pseudophakic eyes, where guidelines for optimal positioning become essential. Finally, mapping of the bubble position highlights the importance of patient positioning for an even gas-graft coverage.

Minimal model for zero-inertia instabilities in shear-dominated non-Newtonian flows.

The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The finite-time shear-induced order-disorder transition of the non-Newtonian microstructure and the corresponding viscosity change from lower to higher values are the crucial ingredients for the instabilities to emerge. The finite-time low-to-high viscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. The lack of instabilities arbitrarily close to zero Reynolds number is also observed for thixotropic fluids, in spite of the fact that the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansions (multiple-scale expansions), energy-based arguments (on the linearized equations of motion), and numerical results (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, as in microfluidic applications. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.