Mixture of Inverse Gaussians for Hemodynamic Transport (MIGHT) in Multiple-Input Multiple-Output Vascular Networks

Synthetic molecular communication (MC) in the cardiovascular system is a key enabler for many envisioned medical applications inside the human body, such as targeted drug delivery, early disease detection, and continuous health monitoring. The design of synthetic MC systems for such applications requires suitable models for the signaling molecule propagation through complex vessel networks (VNs). Existing theoretical models offer limited analytical tractability and lack closed-form solutions, making the analysis of realistic large-scale VNs either infeasible or not insightful. To overcome these limitations, in this paper, we propose a novel closed-form physical model, termed mixture of inverse Gaussians for hemodynamic transport (MIGHT), for the advection-diffusion-driven transport of signaling molecules through complex VNs. The model represents the received molecule flux as a weighted sum of inverse Gaussian distributions, parameterized by the physical properties of the underlying VN. We show that MIGHT is capable of accurately representing the transport dynamics of signaling molecules in large-scale VNs ranging from simple single-input single-output (SISO) to complex multiple-input multiple-output (MIMO) network topologies. The accuracy of the proposed model is validated by comparison to the results from an existing convolution-based model and numerical finite-element simulations, with all finite-element simulation data available on Zenodo. Furthermore, we investigate three applications of the model, namely the reduction of SISO-VNs to obtain simplified representations preserving the essential transport dynamics, the identification and analysis of network regions that are most important for molecule transport in MIMO-VNs comprising multiple transmitters and multiple receivers, and the estimation of representative SISO-VNs that can reproduce the received signal of an unknown SISO-VN.

💡 Research Summary

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The paper addresses a fundamental challenge for synthetic molecular communication (MC) in the human cardiovascular system: how to accurately and analytically model the propagation of signaling molecules through large, topologically complex vascular networks (VNs). Existing channel models either focus on isolated vessels or rely on convolution‑based formulations that quickly become intractable when many branches, bifurcations, and multiple transmitters/receivers (MIMO) are present. To overcome these limitations, the authors introduce a novel closed‑form model called MIGHT (Mixture of Inverse Gaussians for Hemodynamic Transport).

The key physical insight behind MIGHT is that the first‑passage time (FPT) of a molecule traveling in an advective‑diffusive pipe follows an inverse Gaussian (IG) distribution, with its mean and variance determined by pipe length, radius, flow velocity, and molecular diffusion coefficient. By representing a VN as a directed multigraph composed of 1‑D pipe edges and 0‑D nodes (inlets, outlets, bifurcations, junctions), the authors extend the IG‑based description from a single pipe to an arbitrary network. Each distinct source‑to‑destination path is associated with an IG distribution; the overall received molecule flux at any receiver is expressed as a finite weighted sum (mixture) of these IG components. The weights capture flow splitting ratios at bifurcations, possible losses (e.g., sorption or degradation), and the number of parallel paths.

MIGHT is derived for both single‑input single‑output (SISO) and multiple‑input multiple‑output (MIMO) configurations. In the MIMO case, every transmitter–receiver pair has its own set of paths, and the total signal is simply the superposition of the corresponding mixtures, preserving analytical tractability regardless of network size.

Validation is performed on three fronts: (1) comparison with the authors’ earlier convolution‑based model