Diffusive Molecular Communication in a Biological Spherical Environment with Partially Absorbing Boundary

TL;DR

This paper analytically models diffusive molecular communication within a bounded spherical biological environment with partially absorbing boundaries, revealing the channel reciprocity and highlighting inaccuracies of unbounded assumptions.

Contribution

It derives the concentration Green's function for a bounded sphere with reactive boundaries, providing a new analytical framework for molecular communication in biological environments.

Findings

The channel is reciprocal, unaffected by transmitter-receiver swapping.

Analytical CGF accounts for boundary reactions and degradation.

Unbounded models may misrepresent real biological environments.

Abstract

Diffusive molecular communication (DMC) is envisioned as a promising approach to help realize healthcare applications within bounded biological environments. In this paper, a DMC system within a biological spherical environment is considered, inspired by bounded biological sphere-like structures throughout the body. As a biological environment, it is assumed that the inner surface of the sphere's boundary is fully covered by biological receptors that may irreversibly react with hitting molecules. Moreover, information molecules diffusing in the sphere may undergo a degradation reaction and be transformed to another molecule type. Concentration Green's function (CGF) of diffusion inside this environment is analytically obtained in terms of a convergent infinite series. By employing the obtained CGF, the information channel between transmitter and transparent receiver of DMC in this environment is characterized. Interestingly, it is revealed that the information channel is reciprocal, i.e., interchanging the position of receiver and transmitter does not change the information channel. Our results indicate that the conventional simplifying assumption that the environment is unbounded may lead to an inaccurate characterization in such biological environments.