Molecular Communication Model for Drug Delivery in Multi-Layered Spherical Channels

Spherical multi-layered structures are prevalent in numerous biological systems and engineered applications, including tumor spheroids, layered tissues, and multi-shell nanoparticles for targeted drug delivery. Despite their widespread occurrence, there remains a gap in modeling particle propagation through these complex structures from a molecular communication (MC) perspective. This paper introduces a generalized analytical framework for modeling diffusion-based MC in multilayered spherical environments. The framework is capable of supporting an arbitrary number of layers and flexible transmitter-receiver positioning. As an example, the detailed formulation is presented for the three-layer sphere, which is particularly relevant for different biological models such as tumor spheroids. Through this analytical model, two drug delivery scenarios for a three-layered tumor spheroid are investigated: (1) conventional drug delivery from a point source transmitter, and (2) targeted delivery utilizing pH-sensitive carriers that release their payload within the spheroid's acidic necrotic core (i.e., innermost layer). The analytical results are validated using particle-based simulation (PBS) for configurations with short inter-layer distances. These findings advance the understanding of molecular transport mechanisms in multi-layered spheroids and provide a theoretical foundation for designing more efficient targeted drug delivery strategies.