Application of nonlinear sliding mode control to ultrasound contrast agent microbubbles

A sliding mode control system is developed and applied to a spherical model of a contrast agent microbubble that simulates its radial response to ultrasound. The model uses a compressible form of the Rayleigh-Plesset equation combined with a thin-shell model. A nonlinear control law for the second-order model is derived and used to design and simulate the controller. The effect of the controller on the contrast agent response is investigated for various control scenarios. This work demonstrates the feasibility of using a nonlinear control system to modulate the dynamic response of ultrasound contrast agents, but highlights the need for improved feedback mechanisms and control input methods. Possible applications of the nonlinear control system to contrast agents illustrated in this work include radius stabilization in the presence of an acoustic wave, radial growth and subsequent collapse, and generation of periodic radial oscillations while a contrast agent is within an acoustic forcing regime known to cause a chaotic response.