Secondary Bjerknes Forces Deform Targeted Microbubbles

Tom J.A. Kokhuis, Valeria Garbin, Klazina Kooiman, Benno A. Naaijkens, Lynda J.M. Juffermans, Otto Kamp, Antonius F.W. van der Steen, Michel Versluis, Nico de Jong

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In this study, we investigated the effect of secondary Bjerknes forces on targeted microbubbles using high-speed optical imaging. We observed that targeted microbubbles attached to an underlying surface and subject to secondary Bjerknes forces deform in the direction of their neighboring bubble, thereby tending toward a prolate shape. The deformation induces an elastic restoring force, causing the bubbles to recoil back to their equilibrium position; typically within 100 μs after low-intensity ultrasound application. The temporal dynamics of the recoil was modeled as a simple mass-spring system, from which a value for the effective spring constant k of the order 10−3 Nm−1 was obtained. Moreover, the translational dynamics of interacting targeted microbubbles was predicted by a hydrodynamic point particle model, including a value of the spring stiffness k of the very same order as derived experimentally from the recoiling curves. For higher acoustic pressures, secondary Bjerknes forces rupture the molecular adhesion of the bubbles to the surface. We used this mutual attraction to quantify the binding force between a single biotinylated microbubble and an avidin-coated surface, which was found to be between 0.9 and 2 nanonewtons (nN). The observation of patches of lipids left at the initial binding site suggests that lipid anchors are pulled out of the microbubble shell, rather than biotin molecules unbinding from avidin. Understanding the effect of ultrasound application on targeted microbubbles is crucial for further advances in the realm of molecular imaging.
Original languageEnglish
Pages (from-to)490-506
Number of pages17
JournalUltrasound in medicine and biology
Issue number3
Publication statusPublished - 2013


  • Targeted microbubbles
  • Binding force
  • Acoustic radiation force
  • Secondary Bjerknes force
  • Translational dynamics
  • Microbubble detachment
  • Ultrasound contrast agents
  • Lipid pullout
  • Bubble deformation
  • Molecular imaging


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