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.

中文翻译：

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具有扩散和层流的圆柱形 MC 通道的传递函数模型

圆柱环境中基于对流扩散的分子通信 (MC) 系统的分析和设计对于微流体和血管中的靶向药物递送等应用特别感兴趣。因此，相应的 MC 通道的准确建模非常重要。粒子在这些系统中的传播是由具有抛物线速度分布的扩散和流动的组合引起的，即层流。粒子的传播特性可以分为三种不同的状态：流动主导状态，其中扩散对粒子传输的影响可以忽略不计，扩散的影响比流动强得多的分散状态，以及两种影响的混合状态是重要的。对于限制制度，即 对于流动主导和分散状态，粒子传输有众所周知的解决方案和近似值。相比之下，混合状态没有通用的解析解，而是采用了近似、数值技术和基于粒子的模拟。在本文中，我们为圆​​柱形环境中的对流扩散问题开发了一个通用模型，该模型提供了适用于所有情况的解析解。建模程序基于传递函数方法，主要重点在于将层流合并到分析模型中。通过对不同场景（包括粒子的均匀释放和点释放）的数值评估来分析所提出模型的特性。