Data-driven acoustic control of a spherical bubble using a Koopman linear quadratic regulator.

Koopman operator theory has gained interest as a framework for transforming nonlinear dynamics on the state space into linear dynamics on abstract function spaces, which preserves the underlying nonlinear dynamics of the system. These spaces can be approximated through data-driven methodologies, which enables the application of classical linear control strategies to nonlinear systems. Here, a Koopman linear quadratic regulator (KLQR) was used to acoustically control the nonlinear dynamics of a single spherical bubble, as described by the well-known Rayleigh-Plesset equation, with several objectives: (1) simple harmonic oscillation at amplitudes large enough to incite nonlinearities, (2) stabilization of the bubble at a nonequilibrium radius, and (3) periodic and quasiperiodic oscillation with multiple frequency components of arbitrary amplitude.

Shape oscillation and stability of an encapsulated microbubble translating in an acoustic wave.

Encapsulated microbubbles (EMBs) are associated with a wide variety of important medical applications, including sonography, drug delivery, and sonoporation. The nonspherical oscillations, or shape modes, of EMBs strongly affect their stability and acoustic signature, and thus are an important factor to consider in the design and utilization of EMBs. Under acoustic forcing, EMBs often translate with significant velocity, which can excite shape modes, yet few studies have addressed the effect of translation on the shape stability of EMBs.

High Efficiency Molecular Delivery with Sequential Low-Energy Sonoporation Bursts.

Microbubbles interact with ultrasound to induce transient microscopic pores in the cellular plasma membrane in a highly localized thermo-mechanical process called sonoporation. Theranostic applications of in vitro sonoporation include molecular delivery (e.g.

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.

Dynamical analysis of the nonlinear response of ultrasound contrast agent microbubbles.

The nonlinear response of spherical ultrasound contrast agent microbubbles is investigated to understand the effects of common shells on the dynamics. A compressible form of the Rayleigh-Plesset equation is combined with a thin-shell model developed by Lars Hoff to simulate the radial response of contrast agents subject to ultrasound. The responses of Albunex, Sonazoid, and polymer shells are analyzed through the application of techniques from dynamical systems theory such as Poincaré sections, phase portraits, and bifurcation diagrams to illustrate the qualitative dynamics and transition to chaos that occurs under certain changes in system parameters.

Interaction of lithotripter shockwaves with single inertial cavitation bubbles.

The dynamic interaction of a shockwave (modelled as a pressure pulse) with an initially spherically oscillating bubble is investigated. Upon the shockwave impact, the bubble deforms non-spherically and the flow field surrounding the bubble is determined with potential flow theory using the boundary-element method (BEM). The primary advantage of this method is its computational efficiency.

Theoretical study of BOLD response to sinusoidal input.

This is a theoretical study of a compelling model of blood oxygen level-dependent (BOLD) response dynamics, measured in functional magnetic resonance imaging (fMRI). The novelty of this study involves the way the model is driven sinusoidally, in order to avoid onset and offset transients that pose difficulties in data analysis and interpretation. The driving frequency ranges over the natural time scales of the hemodynamic response (0.