Modelling 1D Partially Absorbing Boundaries for Brownian Molecular Communication Channels

Molecular Communication (MC) architectures suffer from molecular build-up in the channel if they do not have appropriate reuptake mechanisms. The molecular build-up either leads to intersymbol interference (ISI) or reduces the transmission rate. To measure the molecular build-up, we derive analytic expressions for the incidence rate and absorption rate for one-dimensional MC channels where molecular dispersion obeys the Brownian Motion. We verify each of our key results with Monte Carlo simulations. Our results contribute to the development of more complicated models and analytic expressions to measure the molecular build-up and the impact of ISI in MC.