To reach a predictive understanding of how particles travel through bifurcating vessels is of paramount importance in many biomedical settings, including embolization, thromboembolism, and drug delivery. Here we utilize an in vitro model in which solid particles are injected through a rigid vessel that symmetrically bifurcates in successive branching generations. The geometric proportion and fluid dynamics parameters are relevant to the liver embolization. The volumetric flow field is reconstructed via phase-contrast magnetic resonance imaging, from which the particle trajectories are calculated for a range of size and density using the particle equation of motion. The method is validated by directly tracking the injected particles via optical imaging. The results indicate that, opposite to the common assumption, the particles distribution is fundamentally different from the volumetric flow partition. In fact, the amount of delivered particles vary substantially between adjacent branches even when the flow is uniformly distributed. This is not due to the inertia of the particles, nor to gravity. The particle distribution is rather rooted in their different pathways, which in turn are linked to their release origin along the main vessel cross-section. Therefore, the tree geometry and the associated flow streamlines are the prime determinant of the particle fate, while local changes of volumetric flow rate to selected branches do not generally produce proportional changes of particle delivery.
Bibliographical noteFunding Information:
The authors would like to thank Sean Moen for his assistance in conducting MRI experiments and fruitful discussions on the matter. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing the computational resources required for this work. This work was partly supported by the University of Minnesota Department of Radiology.
© 2019, Biomedical Engineering Society.
Copyright 2019 Elsevier B.V., All rights reserved.
- Bifurcating vessels
- Lagrangian particle tracking
- Particle embolization