Seminars

Encapsulated microbubbles (EMBs) are used in biomedicine for both diagnostic and therapeutic purposes that include ultrasound imaging and targeted drug delivery. A data-driven method to control the oscillations of EMBs using the applied acoustic field is presented based on Koopman operator theory, which is a method for transforming a nonlinear dynamical system on a state space into a linear system on an infinite-dimensional function space. This method preserves the underlying nonlinear dynamics of the system, and the function spaces can be approximated through data-driven methodologies, which enables the application of classical linear control strategies to the nonlinear system. Here, we apply a Koopman linear quadratic regulator (KLQR) to control the nonlinear oscillations of a EMB through the applied acoustic field.  Results are presented that demonstrate the effectiveness of the modified KLQR controller in driving the EMB to follow arbitrarily-prescribed radial oscillations and stabilize at nonequilibrium radii.