# An *In*-*Vitro* Flow Study Using an Artificial Circle of Willis Model for Validation of an Existing One-Dimensional Numerical Model

## Abstract

A one-dimensional (1D) numerical model has been previously developed to investigate the hemodynamics of blood flow in the entire human vascular network. In the current work, an experimental study of water–glycerin mixture flow in a 3D-printed silicone model of an anatomically accurate, complete circle of Willis (CoW) was conducted to investigate the flow characteristics in comparison with the simulated results by the 1D numerical model. In the experiment, the transient flow and pressure waveforms were measured at 13 selected segments within the flow network for comparisons. In the 1D simulation, the initial parameters of the vessel network were obtained by a direct measurement of the tubes in the experimental setup. The results verified that the 1D numerical model is able to capture the main features of the experimental pressure and flow waveforms with good reliability. The mean flow rates measurement results agree with the predictions of the 1D model with an overall difference of less than 1%. Further experiment might be needed to validate the 1D model in capturing pressure waveforms.

## Keywords

*In*-

*vitro*experiment Hemodynamics 1D modeling Circle of Willis Blood flow

## Notes

### Acknowledgments

The authors would like to acknowledge the Translational Research Development Grants from the Office of Research Affairs at Wright State University.

### Conflict of interest

There are no conflicts of interest that could inappropriately influence this research work.

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