General Molecular Communication Model in Multi-Layered Spherical Channels

TL;DR

The paper tackles diffusion-based molecular communication in multi-layered spherical channels, such as tumor spheroids and layered drug carriers. It develops a generalized analytical framework using Green's functions $G^i$, channel responses $U^j$, and spherical-harmonic expansions to handle any number of layers and arbitrary source/receiver placements, including a detailed three-layer special case. The authors provide closed-form expressions for the Green's function in the layer containing the source and the impulse response in other layers, along with a boundary-matching procedure for interfaces, and validate the results with particle-based simulations, confirming accuracy for short inter-layer distances. A key finding is that layer properties, especially outer-layer porosity, profoundly shape diffusion both inside the spheroid and in the surrounding medium, with direct implications for drug release optimization and toxicity minimization. The framework offers a versatile tool for predicting diffusion dynamics in complex spherical geometries and can be extended to other geometries and physiology-driven parameters.

Abstract

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.

Figures (6)

• Figure 1: Cross-section of a multi-layer spherical structure with $N_{\mathrm{L}}$ layers. Each layer $i$ is characterized by a diffusion coefficient $D_i$ and width $L_i$.
• Figure 2: Concentration profiles at points $\bar{r}=(r\, \mathrm{\mu m}, \pi/2, 0)$ across two distinct spheroid layers and the external medium, where $r$ values are specified in the figure. A point transmitter is located at $\bar{r}_0 = (45.83\, \mathrm{\mu m}, \pi/2, \pi/2)$.
• Figure 3: Impact of the outer layer (layer 3) porosity on molecular diffusion outside a three-layer spheroid, with the transmitter positioned at $\bar{r}_0 = (45.83\, \mathrm{\mu m}, \pi/2, \pi/2)$.
• Figure 4: Temporal evolution of total molecule count outside the spheroid for three different layer 3 porosity values, simulated using PBS, with the transmitter located at $\bar{r}_0 = (45.83\, \mathrm{\mu m}, \pi/2, \pi/2)$.
• Figure 5: Impact of the outer layer (layer 3) porosity on molecular diffusion within the inner layer (layer 1) of a three-layer spheroid, with the transmitter positioned at $\bar{r}_0 = (600\, \mathrm{\mu m}, \pi/2, \pi/2)$.