Vessel Network Topology in Molecular Communication: Insights from Experiments and Theory

TL;DR

The paper tackles the lack of experimentally validated MC models for complex vessel networks by introducing an end-to-end VN channel model that integrates advection, diffusion (including turbulence), and wall sorption, specialized to SPION signaling with a planar inductive RX. It defines two topology-dispersion metrics—molecule delay and multi-path spread—forming a dispersion space that maps VN structure to signal quality, validated through branched SPION testbeds. Experimental results show sorption is essential for accurate transport modeling and demonstrate good agreement between theory and measurements across multiple VN topologies, while dispersion space effectively predicting SNR from topology. The framework enables optimized sensor placement and testbed design and provides a foundation for abstract MC models of CVS-scale networks in the future.

Abstract

The notion of synthetic molecular communication (MC) refers to the transmission of information via signaling molecules and is foreseen to enable innovative medical applications in the human cardiovascular system (CVS). Crucially, the design of such applications requires accurate and experimentally validated channel models that characterize the propagation of signaling molecules, not just in individual blood vessels, but in complex vessel networks (VNs), as prevalent in the CVS. However, experimentally validated models for MC in VNs remain scarce. To address this gap, we propose a novel channel model for MC in complex VN topologies, which captures molecular transport via advection, molecular and turbulent diffusion, as well as adsorption and desorption at the vessel walls. We specialize this model for superparamagnetic iron-oxide nanoparticles (SPIONs) as signaling molecules by introducing a new receiver (RX) model for planar coil inductive sensors, enabling end-to-end experimental validation with a dedicated SPION testbed. Validation covers a range of channel topologies, from single-vessel topologies to branched VNs with multiple paths between transmitter (TX) and RX. Additionally, to quantify how the VN topology impacts signal quality, and inspired by multi-path propagation models in conventional wireless communications, we introduce two metrics, namely molecule delay and multi-path spread. We show that these metrics link the VN structure to molecule dispersion induced by the VN and mediately to the resulting signal-to-noise ratio (SNR) at the RX. The proposed VN structure-SNR link is validated experimentally, demonstrating that the proposed framework can support tasks such as optimal sensor placement in the CVS or the identification of suitable testbed topologies for specific SNR requirements. All experimental data are openly available on Zenodo.

Figures (10)

• Figure 1: System model.a)$N$ signaling molecules are uniformly released in the cross-section of the network inlet (TX) according to injection function $\lambda (t)$, propagate through an exemplary VN comprised of pipes, bifurcations, and junctions, and are received by a transparent RX. b) The flow rate $Q_i$ in pipe $p_i$ and the cross-sectional average flow velocity $\overline{u}_i=Q_i/(\pi r_i^2)$ are determined using an equivalent electrical circuit that models hydraulic resistance. c) Molecule transport is governed by molecular and turbulent diffusion, advection, and reversible sorption at the channel walls. d) Through the specialization of the generic RX model, any transparent real-world sensor can be modeled. In any received signal, there is a contribution from molecules in fluid- and solid-phase (i.e., wall-bound).
• Figure 2: Channel model behavior.a) Sorption kernels and b) resulting concentrations for various sorption rate constants in a single pipe $p_1$. The advection-diffusion-driven concentration $\tilde{c}_1(z,t)$ is compared to the advection-diffusion-sorption-driven fluid-phase concentration $c_1(z,t)$, the solid-phase concentration $s_1(z,t)$, and the total concentration in fluid- and solid-phase $c_1(z,t)+s_1(z,t)$. Here, $z=0.2m$, $r_1=7.95e-4m$, $\overline{u}_1=0.02m\per s$, $N=1e4$, $\alpha =1$, and $D=1.12e-11m\squared\per s$ are used.
• Figure 3: Dispersion space. The position of any VN in the 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. The colors of the space are indicative of the hypothesized received SNR. Two exemplary VN 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 pink curve shows the total signal resulting from the superposition of the path contributions.
• Figure 4: Branched SPION-testbed.a) Testbed components. b)--e) Branched channel topologies. f) Tubing material before use and after days of use, showing indications for SPION adsorption to the tube walls.
• Figure 5: Measurement procedure.a) Repeated CIR measurements. Repetitions are of $40s$ duration to avoid ISI. Initial transient effects in the testbed are omitted through an initial buffer interval (yellow) and the discarding of the first measured CIR (red). b) Micropump injections occur over a $360ms$ period. c) The resulting ensemble-average CIR for a single pipe channel.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4