Rapid and Efficient Computation of Cell Paths During Ultrasonic Focusing

This biophysical analysis explores the first-principles physics of movement of white blood cell sized particles, suspended in an aqueous fluid and experiencing progressive or standing waves of acoustic pressure. In many current applications the cells are gradually nudged or herded toward the nodes of the standing wave, providing a degree of acoustic focusing and concentration of the cells in layers perpendicular to the direction of sound propagation. Here the underlying biomechanics of this phenomenon are analyzed specifically for the viscous regime of water and for small diameter microscopic spheroids such as living cells. The resulting mathematical model leads to a single algebraic expression for the creep or drift velocity as a function of sound frequency, amplitude, wavelength, fluid viscosity, boundary dimensions, and boundary reflectivity. This expression can be integrated numerically by a simple and fast computer algorithm to demonstrate net movement of particles as a function of time, providing a guide to optimization in a variety of emerging applications of ultrasonic cell focusing.