A quantitative model for lateral flow assays

A simple mathematical model that quantitatively describes the dynamics of analyte capture in lateral flow assays is presented. The formulation accounts for the capillary-driven flow through the porous membrane, the advective transport of analyte, and the immunoreactions that take place in the detection line. Model predictions match the numerical results obtained by computer simulations of the full advection-diffusion-reaction problem in the operating regime of lateral flow assays. The main system parameters were condensed into two dimensionless numbers, namely the relative fluid velocity and the relative analyte concentration. The system is then completely characterized in the space of these critical numbers. The model is also able to describe the time evolution of analyte binding by using alternative timescalings, which discriminate different experimental conditions. The equations reported are practical tools for the design and optimization lateral flow tests, enabling informed decisions on basic questions such as the appropriate flow rate, sample volume, or assay time. Beyond lateral flow assays, the work offers an improved understanding of the underlying physicochemical processes involved in paper-based microfluidics.