Transfer Function Models for Cylindrical MC Channels With Diffusion and Laminar Flow

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, well-known solutions and approximations for particle transport exist. For the mixed regime, approximations, numerical techniques, and particle based simulations are employed. However, the few analytical models that are applicable in all three regimes impose significant constraints on the possible transmitter locations and particle release profiles. In this paper, we develop a more general analytical model for the advection-diffusion problem in cylindrical environments, which is applicable in all three regimes and accounts for general particle release models. The proposed model exhibits a higher accuracy than existing models and is based on a transfer function approach, where the main challenge is the incorporation of laminar flow. 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 existing analytical models from the literature to demonstrate the validity of the proposed analytical model.