Channel Modeling for Molecular Communication with Heterogeneous Circular/Spherical Boundary

Geometry is a key factor in channel modeling for molecular communication (MC), especially when considering its potential for enabling intrabody networks and healthcare applications. Driven by the complex geometries within biological entities, this paper proposes modeling the channel for an MC via diffusion (MCvD) system in bounded circular and spherical environments with a heterogeneous boundary. Specifically, the boundary comprises fully reflecting and absorbing portions, with properties that depend on the presence of absorbing receptors (APs). Moreover, the characteristics of the APs, such as their number, size, and spatial distribution, are variable to better align with realistic boundary conditions. To obtain an accurate channel impulse response (CIR), we employ the homogenization technique to convert the mixed Dirichlet-Neumann boundary into a Robin boundary. Accordingly, we derive a valid CIR expression for the bounded MCvD system, accommodating confined spaces with APs of arbitrary sizes, numbers, and locations. Numerical results based on particle-based simulations validate our analysis. Finally, we investigate the error performance of the MCvD system under various boundary conditions. Simulation results show that a heterogeneous boundary with appropriate parameters has the potential to achieve pulse shaping of the CIR and enhance the performance of point-to-point MCvD systems in both 2D and 3D environments.