Hydrostatic Pressurization of Lung Surfactant Microbubbles: Observation of a Strain-Rate Dependent Elasticity

Curvature and shape relaxation in surface-viscous domains

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Buckling of lipidic ultrasound contrast agents under quasi-static load

Collapse of lipidic ultrasound contrast agents under high-frequency compressive load has been historically interpreted by the vanishing of surface tension. By contrast, buckling of elastic shells is known to occur when costly compressible stress is released through bending. Through quasi-static compression experiments on lipidic shells, we analyse the buckling events in the framework of classical elastic buckling theory and deduce the mechanical characteristics of these shells. They are then compared with that obtained through acoustic characterization. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Multiscale geometry and mechanics of lipid monolayer collapse

Langmuir monolayers at gas/liquid interfaces provide a rich framework to investigate the interplay between multiscale geometry and mechanics. Monolayer collapse is investigated at a topological and geometric level by building a scale space M from experimental imaging data. We present a general lipid monolayer collapse phase diagram, which shows that wrinkling, folding, crumpling, shear banding, and vesiculation are a continuous set of mechanical states that can be approached by either tuning monolayer composition or temperature. The origin of the different mechanical states can be understood by investigating the monolayer geometry at two scales: fluorescent vs atomic force microscopy imaging. We show that an interesting switch in continuity occurs in passing between the two scales, C_AFM∈M_AFM≠C_FM∈M. Studying the difference between monolayers that fold vs shear band, we show that shear banding is correlated to the persistence of a multi-length scale microstructure within the monolayer at all surface pressures. A detailed analytical geometric formalism to describe this microstructure is developed using the theory of structured deformations. Lastly, we provide the first ever finite element simulation of lipid monolayer collapse utilizing a direct mapping from the experimental image space M into a simulation domain P. We show that elastic dissipation in the form of bielasticity is a necessary and sufficient condition to capture loss of in-plane stability and shear banding.

Contrast-Enhanced Sonography with Biomimetic Lung Surfactant Nanodrops

Nanodrops comprising a perfluorocarbon liquid core can be acoustically vaporized into echogenic microbubbles for ultrasound imaging. Packaging the microbubble in its condensed liquid state provides some advantages, including in situ activation of the acoustic signal, longer circulation persistence, and the advent of expanded diagnostic and therapeutic applications in pathologies which exhibit compromised vasculature. One obstacle to clinical translation is the inability of the limited surfactant present on the nanodrop to encapsulate the greatly expanded microbubble interface, resulting in ephemeral microbubbles with limited utility. In this study, we examine a biomimetic approach to stabilize an expanding gas surface by employing the lung surfactant replacement, beractant. Lung surfactant contains a suite of lipids and proteins that provide efficient shuttling of material from bilayer folds to the monolayer surface. We hypothesized that beractant would improve stability of acoustically vaporized microbubbles. To test this hypothesis, we characterized beractant surface dilation mechanics and revealed a novel biophysical phenomenon of rapid interfacial melting, spreading, and resolidification. We then harnessed this unique functionality to increase the stability and echogenicity of microbubbles produced after acoustic droplet vaporization for in vivo ultrasound imaging. Such biomimetic lung surfactant-stabilized nanodrops may be useful for applications in ultrasound imaging and therapy.

Ultrasound Contrast Agent Modeling: A Review

Ultrasound is extensively used in medical imaging, being safe and inexpensive and operating in real time. Its scope of applications has been widely broadened by the use of ultrasound contrast agents (UCAs) in the form of microscopic bubbles coated by a biocompatible shell. Their increased use has motivated a large amount of research to understand and characterize their physical properties as well as their interaction with the ultrasound field and their surrounding environment. Here we review the theoretical models that have been proposed to study and predict the behavior of UCAs. We begin with a brief introduction on the development of UCAs. We then present the basics of free-gas-bubble dynamics upon which UCA modeling is based. We review extensively the linear and non-linear models for shell elasticity and viscosity and present models for non-spherical and asymmetric bubble oscillations, especially in the presence of surrounding walls or tissue. Then, higher-order effects such as microstreaming, shedding and acoustic radiation forces are considered. We conclude this review with promising directions for the modeling and development of novel agents.

Shape morphology of dipolar domains in planar and spherical monolayers

We present a continuum theory for predicting the equilibrium shape and size of dipolar domains formed during liquid-liquid phase coexistence in planar and spherical monolayers. Our main objective is to assess the impact of the monolayer surface curvature on domain morphology. Following previous investigators, we base our analysis around minimizing the free energy, with contributions from line tension and electrostatic dipolar repulsions. Assuming a monodisperse system of circularly symmetric domains, we calculate self-energies and interaction energies for planar and spherical monolayers and determine the equilibrium domain size from the energy minima. We subsequently evaluate the stability of the circularly symmetric domain shapes to an arbitrary, circumferential distortion of the perimeter via a linear stability analysis. We find that the surface curvature generally promotes the formation of smaller, circularly symmetric domains instead of larger, elongated domains. We rationalize these results by examining the effect of the curvature on the intra- and inter-domain dipolar repulsions. We then present a phase diagram of domain shape morphologies, parameterized in terms of the domain area fraction and the monolayer curvature. For typical domain dimensions of 1-30 µm, our theoretical results are relevant to monolayers (and possibly also bilayers) in liquid-liquid phase coexistence with radii of curvature of 1-100 µm.

Intermolecular Forces Model for Lipid Microbubble Shells

Lipid-coated microbubbles are currently used clinically as ultrasound contrast agents for echocardiography and radiology and are being developed for many new diagnostic and therapeutic applications. Accordingly, there is a growing need to engineer specific formulations by employing rational design to guide lipid selection and processing. This approach requires a quantitative relationship between lipid chemistry and interfacial properties of the microbubble shell. Just such a model is proposed here on the basis of lateral Coulomb and van der Waals interactions between lipid head- and tailgroups, using previous coarse graining and force fields developed for molecular dynamics simulations. The model predicts with sufficient accuracy the monolayer permeability, the elasticity as a function of either lipid composition or temperature, and the equilibrium spreading surface tension of the lipid onto an air/water interface. In the future, the intermolecular forces model could be employed to elucidate more complex phenomena and to engineer novel microbubble formulations.

High-precision acoustic measurements of the nonlinear dilatational elasticity of phospholipid coated monodisperse microbubbles

The acoustic response of phospholipid-coated microbubble ultrasound contrast agents (UCA) is dramatically affected by their stabilizing shell. The interfacial shell elasticity increases the resonance frequency, the shell viscosity increases damping, and the nonlinear shell viscoelasticity increases the generation of harmonic echoes that are routinely used in contrast-enhanced ultrasound imaging. To date, the surface area-dependent interfacial properties of the phospholipid coating have never been measured due to the extremely short time scales of the MHz frequencies at which the microscopic bubbles are driven. Here, we present high-precision acoustic measurements of the dilatational nonlinear viscoelastic shell properties of phospholipid-coated microbubbles. These highly accurate measurements are now accessible for the first time by tuning the surface dilatation, that is, the lipid packing density, of well-controlled monodisperse bubble suspensions through the ambient pressure. Upon compression, the shell elasticity of bubbles coated with DPPC and DPPE-PEG5000 was found to increase up to an elasticity of 0.6 N m-1 after which the monolayer collapses and the elasticity vanishes. During bubble expansion, the elasticity drops monotonically in two stages, first to an elasticity of 0.35 N m-1, and then more rapidly to zero. Integration of the elasticity vs. surface area curves showed that, indeed, a phospholipid-coated microbubble is in a tensionless state upon compression, and that it reaches the interfacial tension of the surrounding medium upon expansion. The measurements presented in this work reveal the detailed features of the nonlinear dilatational shell behavior of micron-sized lipid-coated bubbles.

Reverse engineering the ultrasound contrast agent

In this review, a brief history and current state-of-the-art is given to stimulate the rational design of new microbubbles through the reverse engineering of current ultrasound contrast agents (UCAs). It is shown that an effective microbubble should be biocompatible, echogenic and stable. Physical mechanisms and engineering calculations have been provided to illustrate these properties and how they can be achieved. The reverse-engineering design paradigm is applied to study current FDA-approved and commercially available UCAs. Given the sophistication of microbubble designs reported in the literature, rapid development and adoption of ultrasound device hardware and techniques, and the growing number of revolutionary biomedical applications moving toward the clinic, the field of Microbubble Engineering is fertile for breakthroughs in next-generation UCA technology. It is up to current and future microbubble engineers and clinicians to push forward with regulatory approval and clinical adoption of advanced UCA technologies in the years to come.