Time-dependent deformation of biological tissue under ultrasonic irradiation

This work proposes a theoretical model for analyzing the time-dependent deformation of poroelastic materials, as a tissue model, under the action of an ultrasonic field, which considers the diffusion fluid transport that obeys Darcy's law. An acoustomechanical constitutive law is developed, which takes into account the mechanical stress generated by poroelastic deformation based on the classical poroelastic theory and the acoustic radiation stress generated by propagating ultrasonic waves. As an example, the time-dependent deformation of a poroelastic sheet subjected to two counter-propagating waves is calculated using the theoretical model, which is also verified by our finite element model. The results show that the sheet can be stretched or compressed, which depends on the ratio of the sheet thickness to the acoustic wavelength. Additionally, by exploring the relaxation process of the acoustic deformation, the role of the sheet thickness and porosity in determining the time of poroelastic relaxation is examined. This work is very helpful for understanding the deformation of tissues under ultrasonic fields, and also provides a method to extract the mechanical properties of tissues.