Mean first passage time and its application in ocular drug development

PatriciaLamirande

University of Oxford

"Mean first passage time and its application in ocular drug development"

Standard of care for various retinal diseases involves recurrent intravitreal injections. This motivates math- ematical modelling efforts to identify influential factors for drug residence time, aiming to minimise the administration frequency. To this end, we developed a mean first passage time (MFPT) modelling frame- work, to investigate the scaling relationships of ocular pharmacokinetics in humans and animal species and to inform drug development. The MFPT describes how long it takes, on average, for a random walker to reach a given target, and is a valuable method to quantify the efficacy of diffusion transport. In this work, we derived a partial differen- tial equation system for the MFPT to quantify drug residence time, and solved it in detailed anatomical 3D geometries of eyes of animal species used in drug development assessments. For human eyes, we investigated the impact of variability in vitreous cavity size and eccentricity, and in injection location, on drug elimination. Model simulations revealed a dependence of residence time on ocular size and injection location. Inter- individual variability in human eyes had a significant influence on residence time (half-life range of 5-7 days), showing a strong correlation to axial length and vitreal volume. The modelling results suggest that experimental variability in ocular half-life is partially attributed to anatomical differences and injection site location.
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