  The analysis and design of advection-diffusion based molecular communication
(MC) systems in cylindrical environments is of particular interest for
applications such as micro-fluidics and targeted drug delivery in blood
vessels. Therefore, the accurate modeling of the corresponding MC channel is of
high importance. The propagation of particles in these systems is caused by a
combination of diffusion and flow with a parabolic velocity profile, i.e.,
laminar flow. The propagation characteristics of the particles can be
categorized into three different regimes: The flow dominant regime where the
influence of diffusion on the particle transport is negligible, the dispersive
regime where diffusion has a much stronger impact than flow, and the mixed
regime where both effects are important. For the limiting regimes, i.e., the
flow dominant and dispersive regimes, there are well-known solutions and
approximations for particle transport. In contrast, there is no general
analytical solution for the mixed regime, and instead, approximations,
numerical techniques, and particle based simulations have been employed. In
this paper, we develop a general model for the advection-diffusion problem in
cylindrical environments which provides an analytical solution applicable in
all regimes. The modeling procedure is based on a transfer function approach
and the main focus lies on the incorporation of laminar flow into the
analytical model. The properties of the proposed model are analyzed by
numerical evaluation for different scenarios including the uniform and point
release of particles. We provide a comparison with particle based simulations
and the well-known solutions for the limiting regimes to demonstrate the
validity of the proposed analytical model.
