Babbs, Charles F. and Lang, Mary V., "Rapid and efficient computation of cell trajectories during ultrasonic focusing" (2023). Weldon School of Biomedical Engineering Faculty Working Papers. Paper 28.
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acoustic cytometry, acoustic levitation, acoustic microstreaming, acoustophoresis, acoustic radiation pressure, antinode, beam, cytometry, hydrodynamic focus, CD4, leukocyte, microspheres, multi-node parallel flow cytometry, particle, particle separation, particle swarm, piezoelectric, pulse-echo, radiation pressure, ultrasound, scatterer, separation, viscosity, viscous fluid
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 antinodes 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--as opposed to air--and for small diameter microscopic spheroids such as living cells--as opposed to large diameter, macroscopic spheroids such as suspended polystyrene beads or levitated ping-pong balls. 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 very 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.