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Microbubbles are widely used in biomedicine for ultrasound contrast imaging and are a promising vehicle for targeted drug and gene delivery. The ability to control the oscillations of bubbles through the applied ultrasound can improve the effectiveness of these treatments, for example, by enhancing the acoustic echo or inciting bubble rupture at precise locations. Koopman operator theory has gained interest in the past decade as a framework for rigorously 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 purely through machine learning and data-driven methodologies, which then enables the application of classical linear control strategies to strongly nonlinear systems. Here, we use a Koopman linear quadratic regulator (LQR) to control the nonlinear dynamics of spherical bubbles, as described by the well-known Rayleigh-Plesset equation, with two novel objectives: (1) stabilization of the bubble at a nonequilibrium radius and (2) simple harmonic oscillation at amplitudes large enough to incite nonlinearities. Control is implemented through both broadband and single-frequency transducers that are modulated by the Koopman LQR controller. We repeat these results using Koopman model predictive control (MPC), which allows for the implementation of constraints. This work is a step towards controlling nonspherical shape modes of encapsulated microbubbles.

Encapsulated microbubbles (EMBs) were originally developed as contrast agents for ultrasound imaging but are more recently emerging as vehicles for intravenous drug and gene delivery. Ultrasound can excite nonspherical oscillations, or shape modes, that can enhance the acoustic signature of an EMB and also incite rupture, which promotes drug and gene delivery at targeted sites. Therefore, the ability to control shape modes can improve the efficacy of both the diagnosis and treatment mediated by EMBs. This work uses optimal control theory to determine the ultrasound input that maximizes a desired nonspherical EMB response (e.g., to enhance scattering or rupture), while minimizing the total acoustic input in order to enhance patient safety and reduce unwanted side effects. The optimal control problem is applied to a model of an EMB that accounts for small amplitude shape deformations. This model is solved subject to a cost function that maximizes the incidence of rupture or acoustic echo while minimizing the acoustic energy input. The optimal control problem is solved numerically through pseudospectral collocation methods using commercial optimization software. Single frequency and broadband acoustic forcing schemes are explored and compared. The results show that broadband forcing significantly reduces the acoustic effort required to incite EMB rupture relative to single frequency schemes. Furthermore, the acoustic effort required depends strongly on the shape mode that is forced to become unstable.

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. In this work, the shape stability of an EMB subject to translation is investigated through development of an axisymmetric model for the case of small deformations. The potential flow in the bulk volume of the external flow is modeled using an asymptotic analysis. Viscous effects within the thin boundary layer at the interface are included, owing to the no-slip boundary condition, using Prosperetti's theory [Q. Appl. Math. 34, 339 (1977)]. In-plane stress and bending moment due to the encapsulation are incorporated into the model through the dynamic boundary condition at the interface. The evolution equations for radial oscillation, translation, and shape oscillation of an EMB are derived, which can be reduced to model an uncoated gas bubble by neglecting the encapsulation properties. These equations are solved numerically to analyze the shape mode stability of an EMB and a gas bubble subject to an acoustic, traveling plane wave. The findings demonstrate the counterintuitive result that translation has a more destabilizing effect on an EMB than on a gas bubble. The no-slip condition at the encapsulating membrane is the main factor responsible for mediating this interfacial instability due to translation.

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., transfection, drug loading and cell labeling), as well as molecular extraction for measuring intracellular biomarkers, such as proteins and mRNA. Prior research focusing mainly on the effects of acoustic forcing with polydisperse microbubbles has identified a "soft limit" of sonoporation efficiency at 50% when including dead and lysed cells. We show here that this limit can be exceeded with the judicious use of monodisperse microbubbles driven by a physiotherapy device (1.0 MHz, 2.0 W/cm(2), 10% duty cycle). We first examined the effects of microbubble size and found that small-diameter microbubbles (2 µm) deliver more instantaneous power than larger microbubbles (4 & 6 µm). However, owing to rapid fragmentation and a short half-life (0.7 s for 2 µm; 13.3 s for 6 µm), they also deliver less energy over the sonoporation time. This translates to a higher ratio of FITC-dextran (70 kDa) uptake to cell death/lysis (4:1 for 2 µm; 1:2 for 6 µm) in suspended HeLa cells after a single sonoporation. Sequential sonoporations (up to four) were consequently employed to increase molecular delivery. Peak uptake was found to be 66.1 ± 1.2% (n=3) after two sonoporations when properly accounting for cell lysis (7.0 ± 5.6%) and death (17.9 ± 2.0%), thus overcoming the previously reported soft limit. Substitution of TRITC-dextran (70 kDa) on the second sonoporation confirmed the effects were multiplicative. Overall, this study demonstrates the possibility of utilizing monodisperse small-diameter microbubbles as a means to achieve multiple low-energy sonoporation bursts for efficient in vitro cellular uptake and sequential molecular delivery.

Encapsulated microbubbles (EMBs) are widely used to enhance contrast in ultrasound sonography and are finding increasing use in biomedical therapies such as drug/gene delivery and tissue ablation. EMBs consist of a gas core surrounded by a stabilizing shell made of various materials, including polymers, lipids, and proteins. Lipid-coated EMBs present a unique challenge for modeling due to their relatively large oscillations and nonlinear, viscoelastic properties. We propose a novel model for a lipid-coated, spherical EMB that utilizes a statistically based continuum theory based on transient networks to simulate the encapsulating material. The use of transient network theory permits the viscoelastic properties of the encapsulation—such as stress, elastic energy and entropy—to be calculated locally based on the configuration of lipid molecules. The model requires a minimum number of parameters that include the lipid concentration, and the rates of attachment and detachment of lipids to and from the network. The model closely reproduces the experimentally measured radial response of an ultrasonically driven, lipid-coated microbubble. The model also reproduces experimentally observed nonlinear behavior, such as compression and expansion-dominated oscillations. Furthermore, the model can be readily extended to large nonspherical EMB deformations, which are important in many biomedical applications.

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.

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. Corresponding calculations of Lyapunov exponents provide quantitative data on the system dynamics. The results indicate that Albunex and polymer shells sufficiently stabilize the response to prevent transition to the chaotic regime throughout typical clinical ranges of ultrasound pressure and frequency. By contrast, Sonazoid shells delay the onset of chaos relative to an unshelled bubble but do not prevent it. A contour plot identifying regions of periodic and chaotic behavior over clinical ranges of ultrasound pressure and frequency is provided for Sonazoid. This work characterizes the nonlinear response of various ultrasound contrast agents, and shows that shell properties have a profound influence on the dynamics.

Ultrasound contrast agents (UCAs) are shell encapsulated, gas-filled microbubbles developed originally for ultrasound imaging enhancement. UCAs are approximately 1–10 micrometers in diameter with a shell typically comprised of lipid, protein, or polymer. When injected into the bloodstream, the high compressibility of these microbubbles, relative to the surrounding blood and tissue, and their highly nonlinear response to ultrasound, leads to strong enhancement of the blood-tissue contrast in the resulting ultrasound image. While UCAs have been commercially available since the early 1990’s [1] for ultrasound imaging, they are more recently being exploited for therapeutic applications, for example, as vehicles for drug delivery and gene therapy, and thermal and mechanical tissue ablation. The effectiveness of UCAs in therapeutic applications depends strongly on the nonspherical character of the bubble oscillation, which can effect the breakup and release of therapeutic agents from the UCA, as well as the formation of high-speed jets near the tissue interface. In this work, two different models for nonspherical oscillation of UCAs are presented: one for small shape oscillations of a lipid-coated bubble, and one for large nonspherical oscillations of a polymer-coated bubble. Nonspherical shape mode stability and dynamics are investigated with each model for ranges of ultrasonic frequency and amplitude relevant to medical applications.

In this paper we use the boundary integral method to model the non-spherical collapse of bubbles excited by lithotripter shock waves near a rigid boundary. The waves we consider are representative of those developed by shock wave lithotripsy or shock wave therapy devices, and the rigid boundaries we consider are representative of kidney stones and reflective bony tissue. This study differs from previous studies in that we account for the reflection of the incident wave and also the asymmetry of the collapse caused by the presence of the rigid surface. The presence of the boundary causes interference between reflected and incident waves. Quantities such as kinetic energy, Kelvin impulse and centroid translation are calculated in order to illuminate the physics of the collapse process. The main finding is that the dynamics of the bubble collapse depend strongly on the distance of the bubble relative to the wall when reflection is taken into account, but much less so when reflection is omitted from the model. The reflection enhances the expansion and subsequent collapse of bubbles located near the boundary owing to constructive interference between incident and reflected waves; however, further from the boundary, the dynamics of collapse are suppressed owing to destructive interference of these two waves. This result holds regardless of the initial radius of the bubble or its initial state at the time of impact with the lithotripter shock wave. Also, the work done by the lithotripter shock wave on the bubble is shown to predict strongly the maximum bubble volume regardless of the standoff distance and the presence or absence of reflection; furthermore, allowing for non-sphericity, these predictions match almost exactly those of a previously developed spherical model.

Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents.

Linear PID and nonlinear sliding mode controllers are developed and applied to a spherical model of a contrast agent microbubble that describes its radial response to ultrasound input. The plant model is a compressible form of the Rayleigh-Plesset equation combined with a thin-shell model. A nonlinear control law for the second-order plant model is developed and used to design and simulate the sliding mode controller and is compared to the performance of a fixed-gain PID controller. The performance of the nonlinear controller on the contrast agent response is evaluated for various control scenarios. This work shows the feasibility of using a nonlinear control system to modulate the dynamic response of ultrasound contrast agents, and highlights the need for improved feedback mechanisms and control input methods. Applications of the nonlinear control system in this work include bubble radius stabilization in the presence of an acoustic wave, radial bubble growth and subsequent collapse, and periodic radial oscillation response while a bubble is within an acoustic forcing regime known to cause a chaotic response.Copyright © 2013 by ASME

An axisymmetric model of an intracranial saccular aneurysm is presented and analyzed. The model assumes a simplified spherical geometry for the aneurysm in order to develop insight into the mechanisms that effect wall shear stress and deformation of the membrane. A theoretical model is first developed based on Stokes’ equations for viscous flow in order to derive a stream function that describes vortical flow inside a sphere representative of flow inside a real aneurysm. This flow pattern is implemented in a finite element model of a spherical aneurysm using the software COMSOL Multiphysics. The results indicate close agreement between the theoretical and computational models in terms of the flow streamlines and location of the maximum wall shear stress. Furthermore, the computational model accounts for the deformation and stress of the membrane, showing regions of maximum tension and compression at opposite poles of the saccular membrane. This work elucidates many important results regarding the mechanics of saccular aneurysms and provides a basis for developing more physiologically realistic analyses.Copyright © 2013 by ASME

The nonlinear response of ultrasound contrast agent microbubbles is investigated through various simulations in regimes of clinical relevance. A spherical model is used based on a compressible form of the Rayleigh-Plesset equation that is combined with a thin-shell model developed by Lars Hoff to simulate the radial response of contrast agents subject to ultrasound. The response of a Sonazoid contrast agent is analyzed through the application of techniques from dynamical systems theory such as phase portraits, Poincare sections, bifurcation diagrams, and Lyapunov exponents to illustrate the qualitative dynamics and transition to chaos that occurs under certain changes in system parameters. The dynamic response of the contrast agent is shown to be similar regardless of the filling gas assumed or the presence of blood or water as the external medium. The effect of continuous and pulsed acoustic forcing is also compared. Furthermore, an experimental setup for investigating the dynamic response of contrast agents subject to ultrasound is presented that uses a standing acoustic wave to trap and drive bubbles at a prescribed frequency. The feasibility of the apparatus is demonstrated through high-speed images of an air bubble trapped at the antinode of the acoustic chamber.Copyright © 2013 by ASME

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. The simulation process is repeated until the two opposite sides of the bubble surface collide with each other (i.e. the formation of a jet along the shockwave propagation direction). The collapse time of the bubble, its shape and the velocity of the jet are calculated. Moreover, the impact pressure is estimated based on water-hammer pressure theory. The Kelvin impulse, kinetic energy and bubble displacement (all at the moment of jet impact) are also determined. Overall, the simulated results compare favourably with experimental observations of lithotripter shockwave interaction with single bubbles (using laser-induced bubbles at various oscillation stages). The simulations confirm the experimental observation that the most intense collapse, with the highest jet velocity and impact pressure, occurs for bubbles with intermediate size during the contraction phase when the collapse time of the bubble is approximately equal to the compressive pulse duration of the shock wave. Under this condition, the maximum amount of energy of the incident shockwave is transferred to the collapsing bubble. Further, the effect of the bubble contents (ideal gas with different initial pressures) and the initial conditions of the bubble (initially oscillating vs. non-oscillating) on the dynamics of the shockwave-bubble interaction are discussed.

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 (0.01-1 Hz), which also corresponds to the period in typical boxcar stimulus designs. At low stimulus amplitude, the predicted BOLD response is quasi-linear. The amplitude exhibits a mild peak near the modulation frequency 0.1 Hz, and falls rapidly for higher frequencies. The phase lag relative to the stimulus is a monotonically increasing function of the modulation frequency. These findings illustrate the dynamical nature of the BOLD response, and could be used to optimize experimental designs that admit sinusoidal modulation. Higher stimulus amplitude elicits nonlinear behavior characterized by a double peak during the positive deflection of the BOLD response. This finding is particularly interesting, because similar double peaks are seen frequently in BOLD data.

Ultrasound contrast agents (UCAs) are microbubbles stabilized with a shell typically of lipid, polymer, or protein and are emerging as a unique tool for noninvasive therapies ranging from gene delivery to tumor ablation. While various models have been developed to describe the spherical oscillations of contrast agents, the treatment of nonspherical behavior has received less attention. However, the nonspherical dynamics of contrast agents are thought to play an important role in therapeutic applications, for example, enhancing the uptake of therapeutic agents across cell membranes and tissue interfaces, and causing tissue ablation. In this paper, a model for nonspherical contrast agent dynamics based on the boundary integral method is described. The effects of the encapsulating shell are approximated by adapting Hoff’s model for thin-shell, spherical contrast agents. A high-quality mesh of the bubble surface is maintained by implementing a hybrid approach of the Lagrangian method and elastic mesh technique. The numerical model agrees well with a modified Rayleigh-Plesset equation for encapsulated spherical bubbles. Numerical analyses of the dynamics of UCAs in an infinite liquid and near a rigid wall are performed in parameter regimes of clinical relevance. The oscillation amplitude and period decrease significantly due to the coating. A bubble jet forms when the amplitude of ultrasound is sufficiently large, as occurs for bubbles without a coating; however, the threshold amplitude required to incite jetting increases due to the coating. When a UCA is near a rigid boundary subject to acoustic forcing, the jet is directed towards the wall if the acoustic wave propagates perpendicular to the boundary. When the acoustic wave propagates parallel to the rigid boundary, the jet direction has components both along the wave direction and towards the boundary that depend mainly on the dimensionless standoff distance of the bubble from the boundary. In all cases, the jet directions for the coated and uncoated bubble are similar but the jet width and jet velocity are smaller for a coated bubble. The effects of shell thickness and shell viscosity are analyzed and determined to affect the bubble dynamics, including jet development.

The Specimen Chamber Service Unit, a component of the Space Station Centrifuge Facility, must provide a clean enclosure on a continuing basis for the facility's plant, rodent and primate specimens. The specimen chambers can become soiled and can require periodic servicing to maintain a clean environment for the specimens. Two methods of servicing the specimen chambers are discussed: washing the chambers with an on-board washer, or disposing of the soiled chambers and replacing them with clean ones. Many of these issues are addressed by developing several servicing options, using either cleaning or replacement as the method of providing clean specimen chambers, and then evaluating each option according to a set of established quantitative and qualitative criteria. Disposing and replacing the Specimen Chambers is preferable to washing them.

Acoustically driven bubbles can develop shape instabilities and, if forced sufficiently strongly, distort greatly and break up. Perturbation theory provides some insight as to how these nonspherical shape modes grow initially but loses validity for large deformations. To validate the perturbation theory, we use a numerical model based on the boundary integral method capable of simulating nonspherical, axisymmetric bubbles subject to acoustic driving. The results show that the perturbation theory compares well with numerical simulations in predicting bubble breakup and stability. Thereafter, we compare the peak temperatures and pressures of spherical to nonspherical bubble collapses by forcing them with standing waves and traveling waves, respectively. This comparison is made in parameter ranges of relevance to both single bubble sonoluminescence and multibubble sonoluminescence and sonochemistry. At moderate forcing, spherical and nonspherical collapses achieve similar peak temperatures and pressures but, as the forcing is increased, spherical collapses become much more intense. The reduced temperature of nonspherical collapses at high forcing is due to residual kinetic energy of a liquid jet that pierces the bubble near the time of minimum volume. This is clarified by a calculation of the (gas) thermal equivalent of this liquid kinetic energy.