Spheroidal Molecular Communication via Diffusion: Signaling Between Homogeneous Cell Aggregates

TL;DR

This work addresses realistic molecular communication (MC) by modeling spheroidal cell aggregates as transceivers in diffusive environments. It derives Green's functions for concentration inside and outside spheroids using a porous-medium diffusion framework with $D_{ m eff} = \frac{\varepsilon}{\tau} D$, $\tau = \varepsilon^{-1/2}$, and a boundary jump factor $\kappa = \sqrt{D/D_{ m eff}}$, and validates these results against particle-based simulations. The study demonstrates that receiver porosity amplifies the diffusive signal but introduces dispersion (delayed and broadened peaks), while transmitter porosity disperses and attenuates the signal; system performance is quantified via BER under inter-symbol interference for on-off keying. Overall, the paper establishes a foundational end-to-end spheroidal MC model that can be extended to more complex organ-on-chip contexts and multi-spheroid networks, enabling more realistic signaling dynamics in biomedical microenvironments.

Abstract

Recent molecular communication (MC) research has integrated more detailed computational models to capture the dynamics of practical biophysical systems. This research focuses on developing realistic models for MC transceivers inspired by spheroids - three-dimensional cell aggregates commonly used in organ-on-chip experimental systems. Potential applications that can be used or modeled with spheroids include nutrient transport in an organ-on-chip system, the release of biomarkers or reception of drug molecules by a cancerous tumor site, or transceiver nanomachines participating in information exchange. In this paper, a simple diffusive MC system is considered where a spheroidal transmitter and receiver are in an unbounded fluid environment. These spheroidal antennas are modeled as porous media for diffusive signaling molecules, then their boundary conditions and effective diffusion coefficients are characterized. Further, for either a point source or spheroidal transmitter, Green's function for concentration (GFC) outside and inside the receiving spheroid is analytically derived and formulated in terms of an infinite series and confirmed by a particle-based simulator (PBS). The provided GFCs enable computation of the transmitted and received signals in the spheroidal communication system. This study shows that the porous structure of the receiving spheroid amplifies diffusion signals but also disperses them, thus there is a trade-off between porosity and information transmission rate. Also, the results reveal that the porous arrangement of the transmitting spheroid not only disperses the received signal but also attenuates it. System performance is also evaluated in terms of bit error rate (BER). Decreasing the porosity of the receiving spheroid is shown to enhance system performance. Conversely, reducing the porosity of the transmitting spheroid can adversely affect system performance.

Figures (10)

• Figure 1: System model schematic where the red and greenish-black spheres represent the signaling molecules and cells, respectively. The receiving spheroid is centrally positioned at the coordinate system's origin, and the transmitting spheroid is centered at a distance of $r_{\rm tx}$ along the coordinate system.
• Figure 2: Porosity ($\varepsilon$) and concentration ratio at the boundary ($\kappa$) versus the number of cells $N_\mathrm{c}$ of fixed volume $V_\mathrm{c}=3.14\times 10^{-15}$ m^3 inside a spheroid of fixed radius $\gamma_\mathrm{s}=275$ μ m.
• Figure 3: Molecule concentration obtained by PBS at the inside ($c_{\rm rx}$) and outside ($c_{\rm orx}$) of the receiving spheroid boundary ($\bar{r}=(275\,\mu m,\pi/2,0)$) versus time for $N_\mathrm{c}^{\rm rx}=24000$ and $\bar{r}_{\rm tx}=(500\,\mu m,\pi/2,0)$, where $\kappa=\sqrt{\frac{D}{D_{\rm eff}}}$.
• Figure 4: Molecule concentration obtained by analysis and PBS within the spheroidal receiver at different points versus time obtained from analysis and PBS, where $N_\mathrm{c}^{\rm rx}=24000$, $\bar{r}_{0}=(500\,\mu m,\pi/2,0)$, and $\bar{r}= (r,\pi/2,0)$.
• Figure 5: Molecule release rate from the transmitting spheroid for $N_\mathrm{c}^{\rm tx}=24000$.