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 molecular communication in multi-layered 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. The analytical results are validated using particle-based simulation (PBS) in scenarios that have short inter-layer distances. The findings reveal that the characteristics of each layer significantly impact molecule propagation throughout the entire structure, making their consideration crucial for designing targeted therapies and optimizing drug delivery systems.

翻译：球形多层结构广泛存在于众多生物系统和工程应用中，包括肿瘤球体、分层组织以及用于靶向药物递送的多壳层纳米颗粒。尽管这类结构普遍存在，但从分子通信（MC）的角度对粒子在这些复杂结构中传播进行建模的研究仍存在空白。本文提出了一个通用的分析框架，用于建模多层球形环境中基于扩散的分子通信。该框架能够支持任意数量的层以及灵活的发射器-接收器定位。作为一个示例，本文详细推导了三层球体的具体公式，该模型尤其适用于肿瘤球体等不同生物模型。在层间距离较短的场景下，通过基于粒子的模拟（PBS）验证了分析结果。研究结果表明，每一层的特性对整个结构中的分子传播具有显著影响，因此在设计靶向疗法和优化药物递送系统时，必须充分考虑这些特性。