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

This repository contains the finite-element simulations used for validation in the paper "Mixture of Inverse Gaussians for Hemodynamic Transport (MIGHT) in Multiple-Input Multiple-Output Vascular Networks".

For the arXiv Version of the Paper: click here

Short Description of the Paper:

This work introduces MIGHT (Mixture of Inverse Gaussians for Hemodynamic Transport), the first closed-form analytical model for advection-diffusion-driven molecular communication (MC) in complex vessel networks (VNs), as prevalent, e.g., in the human cardiovascular system. The model represents spatiotemporal molecule transport in VNs via a weighted finite sum of inverse Gaussian distributions parameterized by physical network properties and supports both single-input, single-output (SISO)-VNs, i.e., networks with a single flow inlet and a single outlet and a single transmitter (Tx) and single receiver (Rx) and multiple-input, multiple-output (MIMO)-VNs, i.e., topologies with multiple flow inlets and outlets as well as multiple Txs and multiple Rxs. Model accuracy is validated through comparison with an existing convolution‑based VN model and three-dimensional (3-D) finite-element simulations performed in COMSOL Multiphysics®, which serve as a numerical "ground truth" for MC in complex large-scale VNs. The paper further illustrates exemplary applications of MIGHT, such as the structural reduction of VNs, vessel importance analysis, and VN topology estimation from observed molecular signals.

Simulation Description:

COMSOL simulations were carried out in 3-D space, using the Laminar Flow and Particle Tracing for Fluid Flow modules with Brownian motion and drag force. The inclusion of Brownian motion results in stochastic particle trajectories and, consequently, in noisy and fluctuating received signals. Fully Developed Flow, No Slip, and zero static pressure with suppressed backflow were assumed as the flow boundary conditions at the VN inlets, pipe walls, and outlets, respectively. Particles were initially randomly distributed according to a uniform distribution in the cross-section at the Tx(s) position(s). As particle boundary condition at the VN outlets, disappear was selected. A physics-controlled mesh at normal element size was used. Exact parameter values are given in Section III-E of the paper and can also be found in the simulation files provided below. All simulations were carried out using COMSOL 6.1 on a Windows desktop PC (Dell OptiPlex 7400 AIO) equipped with a 12th Gen Intel(R) Core(TM) i9-12900 processor (2.40 GHz), 32 GB RAM, and 1.86 TB SSD storage.

Data Description:

All finite-element simulations used for validation in the paper are provided in the file MIGHT_COMSOL_simulations.zip. The data includes simulations for six different VNs.

Top-Level Folders:
The dataset is divided into six main folders:

• VN_1: Contains files for SISO-VN 1 shown in Fig. 3a-1).
• VN_2: Contains files for SISO-VN 2 shown in Fig. 3a-2).
• VN_3: Contains files for SISO-VN 3 shown in Fig. 3a-3).
• VN_4: Contains files for MIMO-VN 4 shown in Fig. 3b-4).
• VN_5: Contains files for MIMO-VN 5 shown in Fig. 3b-5).
• VN_6: Contains files for MIMO-VN 6 shown in Fig. 3b-6).

Files in Top-Level Folders:
Each of the six top-level folders contains the following files:

• VN_X.mph: COMSOL simulation file containing model parameters, geometry, studies, and results. Here, "X" is a placeholder for the VN number.
• VN_X_COMSOL_received_signals.csv: Number of observed molecules over time for all Rxs in the simulation. Each .csv file is comma separated. The first column, named t, contains time in seconds. The subsequent columns contain the number of observed molecules (unitless) at the potentially multiple Rxs (one column per Rx, named N_Rx1(t), N_Rx2(t), ...).
• VN_X_particle_trajectories.gif: Gif showing the distribution of particles throughout the VN over time. Particles sizes are magnified for better visibility.

Contact:

If you have any questions or suggestions for improvements, feel free to contact us:

• Timo Jakumeit (timo.jakumeit@fau.de)
• Bastian Heinlein (bastian.heinlein@fau.de)
• Maximilian Schäfer (max.schaefer@fau.de)