Deformation of biological cells in the acoustic field of an oscillating bubble

In this work we develop a theoretical framework of the interaction of microbubbles with bacteria in the ultrasound field using a shell model of the bacteria, following an approach developed previously [P. V. Zinin , Phys. Rev. E 72, 61907 (2005)]. Within the shell model, the motion of the cell in an ultrasonic field is determined by the motion of three components: the internal viscous fluid, a thin elastic shell, and the surrounding viscous fluid. Several conclusions can be drawn from the modeling of sound interaction with a biological cell: (a) the characteristics of a cell’s oscillations in an ultrasonic field are determined both by the elastic properties of the shell the viscosities of all components of the system, (b) for dipole quadrupole oscillations the cell’s shell deforms due to a change in the shell area this oscillation depends on the surface area modulus K_A , (c) the relative change in the area has a maximum at frequency f_K∼(1)/(2π)K_A/(ρa³) , where a is the cell’s radius and ρ is its density. It was predicted that deformation of the cell wall at the frequency f_K is high enough to rupture small bacteria such as E . coli in which the quality factor of natural vibrations is less than 1 (Q<1) . For bacteria with high value quality factors (Q>1) , the area deformation has a strong peak near a resonance frequency f_K ; however, the value of the deformation near the resonance frequency is not high enough to produce sufficient mechanical effect. The theoretical framework developed in this work can be extended for describing the deformation of a biological cell under any arbitrary, external periodic force including radiation forces unduced by acoustical (acoustical levitation) or optical waves (optical tweezers).