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.

Importance of the numerical schemes in the CFD of the human nose.

Computational fluid dynamics of the air flow in the human nasal cavities, starting from patient-specific Computer Tomography (CT) scans, is an important tool for diagnostics and surgery planning. However, a complete and systematic assessment of the influence of the main modelling assumptions is still lacking. In designing such simulations, choosing the discretization scheme, which is the main subject of the present work, is an often overlooked decision of primary importance. We use a comparison framework to quantify the effects of the major design choices. The reconstructed airways of a healthy, representative adult patient are used to set up a computational study where such effects are systematically measured. It is found that the choice of the numerical scheme is the most important aspect, although all varied parameters impact the solution noticeably. For a physiologically meaningful flow rate, changes of the global pressure drop up to more than 50% are observed; locally, velocity differences can become extremely significant. Our results call for an improved standard in the description of this type of numerical studies, where way too often the order of accuracy of the numerical scheme is not mentioned.

Numerical simulation of thermal water delivery in the human nasal cavity.

This work describes an extensive numerical investigation of thermal water delivery for the treatment of inflammatory disorders in the human nasal cavity. The numerical simulation of the multiphase air-droplets flow is based upon the Large Eddy Simulation (LES) technique, with droplets of thermal water described via a Lagrangian approach. Droplet deposition is studied for different sizes of water droplets, corresponding to two different thermal treatments, i.e. aerosol and inhalation. Numerical simulations are conducted on a patient-specific anatomy, employing two different grid sizes, under steady inspiration at two breathing intensities. The results are compared with published in vivo and in vitro data. The effectiveness of the various thermal treatments is then assessed qualitatively and quantitatively, by a detailed analysis of the deposition patterns of the droplets. Discretization effects on the deposition dynamics are addressed. The level of detail of the present work, together with the accuracy afforded by the LES approach, leads to an improved understanding of how the mixture of air-water droplets is distributed within the nose and the paranasal sinuses.

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction.

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU w ≡ 2U w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity uτ , and h is the half-height of the channel. This leads to a one-dimensional family of flows of varying Reynolds number Re ≡ U w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of 2 each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend's hypothesis of universal behavior for the velocity and shear stress, when they are normalized with uτ and h; universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The behavior at very high Re is unknown. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress, but could suggest a low value for the Karman constant κ, possibly near 0.37. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford's conjectures, suggesting that at least in this idealized flow geometry the theory is successful like it was for the classical law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, again that does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.