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

Abstract

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.