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

A theoretical model is developed to study the deformation dynamics of a biconcave red blood cell (RBC) in a viscous fluid driven by an ultrasonic standing wave. The model considers the true physiological shape of RBCs with biconcave geometry, overcoming the challenges of modelling the nonlinear acoustomechanical coupling of complex biconcave curved shells. The hyperelastic shell theory is used to describe the cell membrane deformation. The acoustic perturbation method is employed to divide the Navier–Stokes equations for viscous flows into the acoustic wave propagation equation and the mean time-averaged dynamic equation. The time-average flow–membrane interaction is considered to capture the cell deformation in acoustic waves. Numerical simulations are performed using the finite element method by formulating the final governing equation in weak form. And a curvature-adaptive mesh refinement algorithm is specifically developed to solve the error problem caused by the nonlinear response of biconcave boundaries (such as curvature transitions) in fluid–structure coupling calculations. The results show that when the acoustic input is large enough, the shape of the cell at the acoustic pressure node changes from a biconcave shape to an oblate disk shape, thereby predicting and discovering for the first time the snap-through instability phenomenon in bioncave RBCs driven by ultrasound. The effects of fluid viscosity, surface shear modulus and membrane bending stiffness on the deformation of the cell are analysed. This numerical model has the ability to accurately predict the acoustic streaming fields and associated time-averaged fluid stress, thus providing insights into the acoustic deformation of complex-shaped particles. Given the important role of the mechanical properties of RBCs in disease diagnosis and biological research, this work will contribute to the development of acoustofluidic technology for the detection of RBC-related diseases.