Molecular Signal Reception in Complex Vessel Networks: The Role of the Network Topology

TL;DR

This work tackles how the topology of linear branched vessel networks (LBVNs) shapes molecular signal reception by developing an end-to-end diffusion-advection model that extends CIR-based channel modeling to include injection-site turbulence and branching points. It specializes the framework to SPION signaling with a planar coil RX, deriving an inductive sensing mechanism and a planar electromagnetics-based reception model, and introduces topology-derived metrics—molecule delay $t_{n_1}^{n_V}$ and multi-path spread $\sigma_{n_1}^{n_V}$—to quantify dispersion and relate it to the SNR at the network outlet. The authors validate the model against testbed data, estimate diffusion-related parameters, and demonstrate that dispersion space effectively captures the topology-SNR relationship, enabling topology-aware sensor placement and testbed design in CVS-like networks. Collectively, the findings provide a topology-centric methodology to predict and optimize molecular communication performance in complex vascular networks, with practical implications for IoBNT and CVS sensing applications.

Abstract

The notion of synthetic molecular communication (MC) refers to the transmission of information via molecules and is largely foreseen for use within the human body, where traditional electromagnetic wave (EM)-based communication is impractical. MC is anticipated to enable innovative medical applications, such as early-stage tumor detection, targeted drug delivery, and holistic approaches like the Internet of Bio-Nano Things (IoBNT). Many of these applications involve parts of the human cardiovascular system (CVS), here referred to as networks, posing challenges for MC due to their complex, highly branched vessel structures. To gain a better understanding of how the topology of such branched vessel networks affects the reception of a molecular signal at a target location, e.g., the network outlet, we present a generic analytical end-to-end model that characterizes molecule propagation and reception in linear branched vessel networks (LBVNs). We specialize this generic model to any MC system employing superparamagnetic iron-oxide nanoparticles (SPIONs) as signaling molecules and a planar coil as receiver (RX). By considering components that have been previously established in testbeds, we effectively isolate the impact of the network topology and validate our theoretical model with testbed data. Additionally, we propose two metrics, namely the molecule delay and the multi-path spread, that relate the LBVN topology to the molecule dispersion induced by the network, thereby linking the network structure to the signal-to-noise ratio (SNR) at the target location. This allows the characterization of the SNR at any point in the network solely based on the network topology. Consequently, our framework can, e.g., be exploited for optimal sensor placement in the CVS or identification of suitable testbed topologies for given SNR requirements.

Figures (4)

• Figure 1: System model: a) $N$ signaling molecules are uniformly released in the cross-section of the network inlet (TX), propagate through an LBVN comprised of pipes, bifurcations, and junctions, influenced by advection as well as molecular and turbulent diffusion, and are received by a transparent RX. b) The cross-sectional average flow velocity $\overline{u}_i$ in pipe $p_i$ is determined using an equivalent electrical circuit that models hydraulic resistance. c) SPION as signaling molecules are received by a planar coil connected to an LC oscillator, yielding resonance frequency shift $\Delta f_\mathrm{res}(t)$ as received signal. The magnetic field around the coil is nonuniform and captured by the weighting function $w(z)$. Detailed explanations of the system components and notation are provided in the text, relevant equations are marked in yellow in the figure.
• Figure 2: The position of any LBVN in the dispersion space is solely based on its topology, as $t_{n_1}^{n_V}$ and $\sigma_{n_1}^{n_V}$ characterize the dispersion of the molecules propagating from TX to RX. Two exemplary LBVN with identical pipe radii and pipe lengths of either $l$ or $2l$, along with their received signals $N^\mathrm{obs}(t)$, are shown. Thin colored curves show individual path contributions; the green curve shows the total signal.
• Figure 3: Comparison of testbed CIR in Bartunik2023 and model CIR at varying flow rates $Q$ in terms of peak height and FWHM.
• Figure 4: Dispersion space filled with LBVN. a) 28 networks are generated from four template LBVN by removing one pipe per iteration in the indicated removal order. Pipe lengths in $cm$ are given as edge weights, with $r=1mm$. b) Markers correspond to different LBVN and color-code the SNR at the network outlets. The clear pattern between location in the space and SNR enables the characterization of the SNR based on the topology alone.