Deformation dynamics of spherical red blood cells in viscous fluid driven by ultrasound

In this paper, the deformation dynamics of spherical red blood cells in viscous fluid driven by ultrasound are theoretically and numerically studied. Red blood cells are considered to be composed of a homogenous cytoplasm enclosed by a biological membrane. The developed theoretical framework consists of two sets of equations, which describe the acoustic wave propagation and the time-averaged mean dynamics of the fluid-cell system, respectively. Specifically, the separated acoustics and mean responses of viscous fluid are formulated based on the acoustic perturbation method in a generalized Lagrangian framework. Considering the viscoelasticity of the membrane, the cell deformation is coupled to the fluid mean motion through the time-averaged fluid-membrane coupling boundary conditions. A computational model is established by deriving weak form formulations of the final governing equations and implementing them by the finite element method. The computational model is verified by comparing the steady-state deformation of the numerical results with previous experimental results. This model can accurately characterize the deformation of cells over time, which helps to extract the viscoelastic properties of cells.