Numerical model to predict and compare the hypotensive efficacy and safety of minimally invasive glaucoma surgery devices.

PURPOSE: To predict and compare the hypotensive efficacy of three minimally-invasive glaucoma surgery (MIGS) implants through a numerical model. METHODS: Post-implant hypotensive efficacy was evaluated by using a numerical model and a computational fluid dynamics simulation. Three different devices were compared: the XEN 45 stent (tube diameter, 45 µm), the XEN 63 stent (63 µm) and the PreserFlo microshunt (70 µm). The influence of the filtration bleb pressure (Bp) and tube diameter, length, and position within the anterior chamber (AC) on intraocular pressure (IOP) were evaluated. RESULTS: Using baseline IOPs of 25, 30 and 50 mmHg, respectively, the corresponding computed post-implant IOPs for each device were as follows: XEN 45: 17 mmHg (29% decrease), 19 mmHg (45%) and 20 mmHg (59%) respectively; XEN 63: 13 mmHg (48%), 13 mmHg (62%), and 13 mmHg (73%); PreserFlo: 12 mmHg (59%), 13 mmHg (73%) and 13 mmHg (73%). At a baseline IOP of 35 mmHg with an increase in the outflow resistance within the Bp from 5 to 17 mmHg, the hypotensive efficacy for each device was reduced as follows: XEN45: 54% to 37%; XEN 63: 74% to 46%; and PreserFlo: 75% to 47%. The length and the position of the tube in the AC had only a minimal (non-significant) effect on IOP (<0.1 mmHg). CONCLUSIONS: This hydrodynamic/numerical model showed that implant diameter and bleb pressure are the two most pertinent determinants of hypotensive efficacy. In distinction, tube length and position in the AC do not significantly influence IOP.

Diffusion of impurities in a granular gas.

Diffusion of impurities in a granular gas undergoing homogeneous cooling state is studied. The results are obtained by solving the Boltzmann-Lorentz equation by means of the Chapman-Enskog method. In the first order in the density gradient of impurities, the diffusion coefficient D is determined as the solution of a linear integral equation which is approximately solved by making an expansion in Sonine polynomials. In this paper, we evaluate D up to the second order in the Sonine expansion and get explicit expressions for D in terms of the coefficients of restitution for the impurity-gas and gas-gas collisions as well as the ratios of mass and particle sizes. To check the reliability of the Sonine polynomial solution, analytical results are compared with those obtained from numerical solutions of the Boltzmann equation by means of the direct simulation Monte Carlo method. In the simulations, the diffusion coefficient is measured via the mean-square displacement of impurities. The comparison between theory and simulation shows in general an excellent agreement, except for the cases in which the gas particles are much heavier and/or much larger than impurities. In these cases, the second Sonine approximation to D improves significantly the qualitative predictions made from the first Sonine approximation. A discussion on the convergence of the Sonine polynomial expansion is also carried out.