# Three‐dimensional modeling of flow through microvascular beds and surrounding interstitial spaces

## TL;DR

This paper introduces a 3D modeling framework to study fluid flow and forces in microvascular networks and surrounding spaces, improving understanding of vascular function.

## Contribution

A novel bottom-up 3D computational model incorporating endothelial lining and interstitial flow dynamics in engineered vessel networks.

## Key findings

- Including endothelial lining and interstitium significantly affects predicted flow magnitude and profiles.
- Cytokine treatment increased vessel permeability, reducing wall shear stresses and intraluminal flow velocities.
- The framework enables robust study of flow dynamics in 3D in vitro vessel networks.

## Abstract

The health and function of microvascular beds are dramatically impacted by the mechanical forces that they experience due to fluid flow. These fluid flow‐generated forces are challenging to measure directly and are typically calculated from experimental flow data. However, current computational fluid dynamics (CFD) models either employ truncated 2D models or overlook the presence of extraluminal flows within the interstitial space between vessels that result from the permeability of the endothelium lining the vessels, which are crucial components affecting flow dynamics. To address this, we present a bottom‐up modeling approach that assesses fluid flow in 3D‐engineered vessel networks featuring an endothelial lining and interstitial space. Using image processing algorithms to segment 3D confocal image stacks from engineered capillary networks, we reconstructed a 3D computational model of the networks. We incorporated vascular permeability and matrix porosity values to model the contributions of the endothelial lining and interstitial spaces to the flow dynamics in the networks. Simulations suggest that including the endothelial monolayer and the interstitium significantly affects the predicted flow magnitude in the vessels and flow profiles in the interstitium. To demonstrate the importance of these factors, we showed experimentally and computationally that while cytokine (IL‐1β) treatment did not affect the network architecture, it significantly increased vessel permeability and resulted in a dramatic decrease in wall shear stresses and flow velocities intraluminally within the networks. In conclusion, this framework offers a robust methodology for studying flow dynamics in 3D in vitro vessel networks, enhancing our understanding of vascular physiology and pathology.

A pipeline to model and solve fluid flow and resulting forces in 3D microvascular networks and surrounding interstitial spaces within microfluidic chips, starting from confocal image stacks of the vascularized tissue.