A preliminary evaluation of the effects of primary and secondary radiation forces on acoustic contrast agents

Primary and secondary radiation forces result from pressure gradients in the incident and scattered ultrasonic fields. These forces and their dependence on experimental parameters are described, and the theory for primary radiation force is extended to consider a pulsed traveling wave. Both primary and secondary radiation forces are shown to have a significant effect on the flow of microbubbles through a small vessel during insonation. The primary radiation force produces displacement of microspheres across a 100 micron vessel radius for a small transmitted acoustic pressure. The displacement produced by primary radiation force is shown to display the expected linear dependence on the pulse repetition frequency and a nonlinear dependence on transmitted pressure. The secondary radiation force produces a reversible attraction and aggregation of microspheres with a significant attraction over a distance of approximately 100 microns. The magnitude of the secondary radiation force is proportional to the inverse of the squared separation distance, and thus two aggregates accelerate as they approach one another. We show that this force is sufficient to produce aggregates that remain intact for a physiologically appropriate shear rate. Brief interruption of acoustic transmission allows an immediate disruption of the aggregate.