Channel characteristics for diffusive molecular communications in a spherical shell

Diffusive molecular communication (DMC) is a bio-mimicking communications paradigm that exploits the Brownian motion of dedicated information carrying molecules for signal transmission. The characteristics of the communication channel in a DMC system heavily depends on the transmitter and receiver mechanisms, on the medium of propagation and its boundaries, and on the way they interact with the molecules. In this work, we investigate the DMC channel in a spherical shell, with inner and outer surfaces which may be partially or perfectly absorptive, or reflective, where either of the boundary surfaces can be considered as the DMC receiver. These geometry and boundary conditions can be used to model a variety of practically relevant scenarios, which are investigated in detail. We derive the general parametric solution of the partial differential equation for this case and provide, for the first time in the literature, expressions for the resulting channel response. We verify the results of our analysis numerically via particle based simulations.