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A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

Published online by Cambridge University Press:  19 December 2017

Achim Guckenberger Open the ORCID record for Achim Guckenberger [Opens in a new window]  and
Stephan Gekle Open the ORCID record for Stephan Gekle [Opens in a new window]
Achim Guckenberger*
Affiliation:
Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, 95440 Bayreuth, Germany
Stephan Gekle
Affiliation:
Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, 95440 Bayreuth, Germany
*
†Email address for correspondence: [email protected]
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Abstract

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

JFM classification

Biological Fluid Dynamics: Blood flow Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 952 - 997
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Copyright
© 2017 Cambridge University Press 

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Guckenberger and Gekle supplementary movie

Video showing an excerpt from the simulation depicted in fig. 4 (a) in the main text. The ultrasound is switched on at around 4s.

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Supplementary material: PDF

Guckenberger and Gekle supplementary material

Supplementary Information

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