# Embolus Transport Simulations with Fully Resolved Particle Surfaces

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## Abstract

### Purpose

There has been interest in recent work in using computational fluid dynamics with Lagrangian analysis to calculate the trajectory of emboli-like particles in the vasculature. While previous studies have provided an understanding of the hemodynamic factors determining the fates of such particles and their relationship to risk of stroke, most analyses have relied on a particle equation of motion that assumes the particle is “small” e.g., much less than the diameter of the vessel. This work quantifies the limit when a particle can no longer be considered “small”.

### Methods

The motion of embolus-like particles are simulated using an overset mesh technique. This allows the fluid stresses on the particle surface to be fully resolved. Consequently, the particles can be of arbitrary size or shape. The trajectory of resolved particles and “small” particles are simulated through a patient-specific carotid artery bifurcation model with particles 500, 1000, and 2000 *μ*m in diameter. The proportions of particles entering the internal carotid artery are treated as the outcome of the particle fate, and statistical comparisons are made to ascertain the importance of non-small particle effects.

### Results

For the 2000 *μ*m embolus, the proportion of particles traveling to the internal carotid artery is 74.7 ± 1.3% (mean ± 95% confidence margin) for the “small” particle model and is 85.7 ± 5.4% for a resolved particle model. The difference is statistically significant, \(p< 0.05\), based on the binomial test for the particle outcomes. No statistically discernible differences are found for the smaller diameter particles.

### Conclusions

Quantitative differences are observable for the 2000 *μ*m trajectories between the “small” and resolved particle models which is a particle diameter 27% relative to the common carotid artery diameter. A fully resolved particle model ought to be considered for emboli trajectory simulations when the particle size ratio is ≳ 20%.

## Notes

### Acknowledgments

Thanks to Bradley Davidson, Kristian Debus, and Ehsan Rajabi for helpful comments during the preparation of the manuscript.

### Conflict of interest

P. M. McGah is an employee of Siemens PLM Software Inc., the company that produces and sells Simcenter STAR-CCM+.

### Human Subjects and Animal Subjects Ethical Statement

No animal studies were conducted by the author for this article. No human studies were conducted by the author for this article.

## Supplementary material

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