Corneal endothelial dysfunction of the human eye occurs when corneal endothelial cells are dramatically lost, and eventually results in vision loss. Corneal transplantation is presently the only viable solution. For patients with an endothelial disease such as Fuch’s endothelial dystrophy, endothelial keratoplasty (EK) is currently the mainstay of definitive treatment and path for restoration of vision (Stuart et al., 2018, Melles et al., 2006, Deng et al., 2018). The number of people estimated to have the Fuch’s subtype of endothelial dystrophy worldwide (>30 years) will increase from 300 million in 2020 to 415 million in 2050 (Aiello et al., 2022). In EK only a portion of the posterior cornea is removed and replaced by a ≈40μm thick and ≈ 8.5 mm diameter donor cornea (graft). In techniques such as Descemet’s membrane endothelial keratoplasty (DMEK) a gas, such as air or SF6, is injected into the anterior chamber (AC) to create a bubble that pushes onto the graft, ensuring sutureless adherence of the donor graft to the host cornea (Price et al., 2018) during healing. The maximal gas fill is patient dependent, however, up to approximately 80% is possible without an inferior iridotomy.

Studies (Tourtas et al., 2014), evaluated on 200 patients, have shown that gas left in the anterior chamber after surgery is completely absorbed within 48 to 72 h and that 90% of graft detachments are identified within this period.

Defining graft detachment as significant if the radial extent of the non adherent surface is at least 1 mm (on a 8 mm graft), a study (Tourtas et al., 2014) of 51 patients showed that the graft detachment rate 4 days after surgery was between 33.3% and 78.3% depending on the difference between the descemetorhexis and graft diameters. Note that in this study all patients were asked to stay 48 h in supine position after surgery.

Studies suggest that a larger bubble helps preventing graft detachment and the need for re-bubbling procedures (Ćirković et al., 2016, Leon et al., 2018), whereas gas overfill leads to complications such as pupillary block (Gonzalez et al., 2016) and raises concerns of possible endothelial toxicity (Kopsachilis et al., 2013, Landry et al., 2011). The optimal gas fill after DMEK is unknown, and a lack of knowledge of gas behavior in the anterior chamber hinders optimal surgical results.

Numerical analysis, as a support to investigate bio-mechanical problems, is nowadays common practice in a large number of applications. In the case of biofluid dynamics of the human eye, the methods ranges from semi analytical, to simulations of the fluid flow in one, two, and three dimensions: a few examples include (Isakova et al., 2017, Repetto et al., 2015, Isakova et al., 2014, Davvalo Khongar et al., 2019). Recent numerical experiments (Pralits et al., 2019) have indicated that gas fill is the most important variable for ensuring graft coverage in phakic eyes, i.e. eyes with a natural lens; both gas fill and patient positioning become important to ensure gas-graft coverage in pseudophakic eyes, i.e. eyes with artificial lens, especially as the anterior chamber depth (ACD) increases. However, these results do not account for the effect of changes in patient positioning during the postoperative period, and for the diminishing size of the gas bubble as time progresses.

In an effort to maximize graft coverage by intraocular gas, the aim of this paper is to provide a more complete understanding of gas coverage of the endothelial graft throughout the postoperative period. Moreover, the analysis also allows to examine relationships between one-dimensional bubble height (which is the surgeons’ common measure), two-dimensional gas-graft contact area, and three-dimensional gas volume. To this end, a numerical study of gas fill in model and patient-specific anterior chambers is carried out, including the DMEK graft. The true three-dimensional shape of the gas bubble is computed for both phakic and pseudophakic ACs, accounting for the properties of air and aqueous humor (AH). For each geometry the gas coverage on the graft is computed for different values of the gas fill and patient positioning. Moreover, a technique to evaluate the position is introduced which provides not only the gas coverage percentage, but also the spatial details of the coverage. This is particularly important when studying the causes of graft detachment (Price et al., 2018). Different cases of patient positioning over time are considered, and the difference between “best-case” and “worst-case” scenarios is quantified.