# Physiologic model of the cerebrovascular system using supply and demand between arteries and tissues

## TL;DR

This paper introduces a new model for simulating blood flow in the brain by linking arteries and tissues through supply and demand, validated with medical images.

## Contribution

A novel physiologic model for cerebrovascular blood flow based on supply-demand relationships and Voronoi tessellation.

## Key findings

- Estimated blood flows align with known physiological values for major cerebral arteries.
- Perfusion territories match literature and perfusion imaging results.
- The model is more robust to segmentation errors than Murray’s law.

## Abstract

Image-based modeling heavily relies on boundary conditions to obtain realistic blood flow and pressure. For the cerebrovascular system, boundary conditions are derived using in-vivo measurements or geometry-based models such as Murray’s law, but these are constrained by the image resolution or high sensitivity to the segmented geometry. We propose a physiologic model of the cerebrovascular system based on a supply and demand relationship between arteries and tissues. Blood flow and perfusion territory are determined by associating brain tissues with nearby vessels using Voronoi tessellation. The model was evaluated for 40 healthy young individuals and two diseased patients, and was validated by comparing the estimated blood flows and perfusion territories against literature data and perfusion imaging. The estimated blood flows are within the physiologically reported values for major cerebral arteries and the predicted perfusion territories are similar to the literature and perfusion imaging. Further, the model demonstrates more robustness to segmentation uncertainties compared to Murray’s law. The proposed model is shown to estimate physiologically plausible cerebrovascular blood flow and perfusion territory in a subject-specific manner using medical image data only. It may be used to simulate blood flow more realistically by developing boundary conditions based on this model in the cerebrovascular system.

The online version contains supplementary material available at 10.1038/s41598-025-10223-7.