Kausik Sarkar

Characterization of ultrasound contrast microbubbles using in vitro experiments and viscous and viscoelastic interface models for encapsulation

Zero-thickness interface models are developed to describe the encapsulation of microbubble contrast agents. Two different rheological models of the interface, Newtonian (viscous) and viscoelastic, with rheological parameters such as surface tension, surface dilatational viscosity, and surface dilatational elasticity are presented to characterize the encapsulation. The models are applied to characterize a widely used microbubble based ultrasound contrast agent. Attenuation of ultrasound passing through a solution of contrast agent is measured. The model parameters for the contrast agent are determined by matching the linearized model dynamics with measured attenuation data. The models are investigated for its ability to match with other experiments. Specifically, model predictions are compared with scattered fundamental and subharmonic responses. Experiments and model prediction results are discussed along with those obtained using an existing model [Church, J. Acoust. Soc. Am. 97, 1510 (1995) and Hoff et al., J. Acoust. Soc. Am. 107, 2272 (2000)] of contrast agents.

A Newtonian rheological model for the interface of microbubble contrast agents

A quantitative model of the dynamics of an encapsulated microbubble contrast agent will be a valuable tool in contrast ultrasound (US). Such a model must have predictive ability for widely varying frequencies and pressure amplitudes. We have developed a new model for contrast agents, and successfully investigated its applicability for a wide range of operating parameters. The encapsulation is modeled as a complex interface of an infinitesimal thickness. A Newtonian rheology with surface viscosities and interfacial tension is assumed for the interface, and a modified Rayleigh-Plesset equation is derived. The rheological parameters (surface tension and surface dilatational viscosity) for a number of contrast agents (Albunex, Optison and Quantison) are determined by matching the linearized model dynamics with experimentally obtained attenuation data. The model behavior for Optison (surface tension 0.9 N/m and surface dilatational viscosity 0.08 msP) was investigated in detail. Specifically, we have carried out a detailed interrogation of the model, fitted in the linear regime, for its nonlinear prediction. In contrast to existing models, the new model is found to capture the characteristic subharmonic emission of Optison observed by. A detailed parametric study of the bubble behavior was executed using the ratio of scattering to attenuation (STAR). It shows that the encapsulation drastically reduces the influence of resonance frequency on scattering cross-section, suggesting possible means of improvement in imaging at off-resonant frequencies. The predictive capability of the present model indicates that it can be used for characterizing different agents and designing new ones.

Growth and dissolution of an encapsulated contrast microbubble: effects of encapsulation permeability

Gas diffusion from an encapsulated microbubble is modeled using an explicit linear relation for gas permeation through the encapsulation. Both the cases of single gas (air) and multiple gases (perfluorocarbon inside the bubble and air dissolved in surrounding liquid) are considered. An analytical expression for the dissolution time for an encapsulated air bubble is obtained; it showed that for small permeability the dissolution time increases linearly with decreasing permeability. A perfluorocarbon-filled contrast microbubble such as Definity was predicted to experience a transient growth because of air infusion before it dissolves in conformity with previous experimental findings. The growth phase occurs only for bubbles with a critical value of initial mole fraction of perfluorocarbon relative to air. With empirically obtained property values, the dissolution time of a 2.5-micron diameter (same as that of Definity), lipid-coated octafluoropropane bubble, with surface tension 25 mN/m, is predicted to be 42 min in an air-saturated medium. The properties such as shell permeability, surface tension and relative mole fraction of octafluoropropane are varied to investigate their effects on the time scales of bubble growth and dissolution, including their asymptotic scalings where appropriate. The dissolution dynamics scales with permeability, in that when the time is nondimensioanlized with permeability, curves for different permeabilities collapse on a single curve. Investigation of bubbles filled with other gases (nonoctafluoropropane perfluorocarbon and sulfur hexafluoride) indicates longer dissolution time because of lower solubility and lower diffusivity for larger gas molecules. For such micron-size encapsulated bubbles, lifetime of hours is possible only at extremely low surface tension (<1 mN/m) or at extreme oversaturation.

Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane

The dynamics of a liquid capsule enclosed by an elastic membrane in a shear flow is investigated using a front tracking finite difference method. We compute deformation, orientation and tank-treading of the capsule, as functions of the forcing (capillary number) and the viscosity ratio for two different membrane constitutive equations - Neo-Hookean and Skalak. The computed results compare very well with those obtained by high-order boundary element methods as well as the small deformation perturbation analysis. The simulation shows that a drop and a capsule, even under those circumstances that result in the same Taylor deformation criterion for both, attain very different shapes. The tank-treading period even for different capillary numbers as well as capsules with different constitutive laws, is primarily determined by the deformation and the viscosity ratio. At low capillary numbers the simulation predicts buckling due to large compressive stresses on the membrane. However, we show that in shear, unlike in extension, the tank-treading motion can inhibit the buckling instability and gives rise to a stable evolution even in presence of membrane compressive stresses. At large capillary numbers the capsule experiences large bounded shape followed by tip buckling indicating possible membrane breakup.

Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear

The deformation of a viscoelastic drop suspended in a Newtonian fluid subjected to a steady shear is investigated using a front-tracking finite-difference method. The viscoelasticity is modelled using the Oldroyd-B constitutive equation. The drop response with increasing relaxation time λ and varying polymeric to the total drop viscosity ratio β is studied and explained by examining the elastic and viscous stresses at the interface. Steady-state drop deformation was seen to decrease from its Newtonian value with increasing viscoelasticity. A slight non-monotonicity in steady-state deformation with increasing Deborah number is observed at high Capillary numbers. Transient drop deformation displays an overshoot before settling down to a lower value of deformation. The overshoot increases with increasing β. The drop shows slightly decreased alignment with the flow with increasing viscoelasticity. A simple ordinary differential equation model is developed to explain the various behaviours and the scalings observed numerically. The critical Capillary number for drop breakup is observed to increase with Deborah number owing to the inhibitive effects of viscoelasticity, the increase being linear for small Deborah number.

Multifunctional polymersomes for cytosolic delivery of gemcitabine and doxorubicin to cancer cells

Although liposomes are widely used as carriers of drugs and imaging agents, they suffer from a lack of stability and the slow release of the encapsulated contents at the targeted site. Polymersomes (vesicles of amphiphilic polymers) are considerably more stable compared to liposomes; however, they also demonstrate a slow release for the encapsulated contents, limiting their efficacy as a drug-delivery tool. As a solution, we prepared and characterized echogenic polymersomes, which are programmed to release the encapsulated drugs rapidly when incubated with cytosolic concentrations of glutathione. These vesicles encapsulated air bubbles inside and efficiently reflected diagnostic-frequency ultrasound. Folate-targeted polymersomes showed an enhanced uptake by breast and pancreatic-cancer cells in a monolayer as well as in three-dimensional spheroid cultures. Polymersomes encapsulated with the anticancer drugs gemcitabine and doxorubicin showed significant cytotoxicity to these cells. With further improvements, these vesicles hold the promise to serve as multifunctional nanocarriers, offering a triggered release as well as diagnostic ultrasound imaging.

Effects of encapsulation elasticity on the stability of an encapsulated microbubble.

A model for gas transport from an encapsulated microbubble into the surrounding medium is developed and investigated incorporating the effects of encapsulation elasticity. Encapsulation elasticity stabilizes microbubbles against dissolution and explains the long shelf life of microbubble contrast agent. We consider air bubbles as well as bubbles containing perfluorocarbon gas. Analytical conditions between saturation level, surface tension and interfacial dilatational elasticity are determined for attaining non-zero equilibrium radius for these microbubbles. Numerical solution of the equation verifies the stability of the equilibrium radii. In an undersaturated medium all encapsulated bubbles dissolve. In a saturated medium, an encapsulated bubble is found to achieve a long-time stable radius when interfacial dilatational elasticity is larger than equilibrium surface tension. For bubbles with interfacial dilatational elasticity smaller than the equilibrium surface tension, stable bubble of non-zero radius can be achieved only when the saturation level is greater than a critical value. Even if they initially contain a gas other than air, bubbles that reach a stable radius finally become air bubbles. The model is applied to an octafluoropropane filled lipid-coated 2.5 microm bubble, which displayed a transient swelling due to air intake before reaching an equilibrium size. Effects of elasticity, shell permeability, initial mole fraction, initial radius and saturation level are investigated and discussed. Shell permeability and mole fraction do not affect the final equilibrium radius of the microbubble but affect the time scale and the transient dynamics. Similarly, the ratio of equilibrium radius to initial radius remains unaffected by the variation in initial radius.

Excitation threshold for subharmonic generation from contrast microbubbles

Six models of contrast microbubbles are investigated to determine the excitation threshold for subharmonic generation. The models are applied to a commercial contrast agent; its characteristic parameters according to each model are determined using experimentally measured ultrasound attenuation. In contrast to the classical perturbative result, the minimum threshold for subharmonic generation is not always predicted at excitation with twice the resonance frequency; instead it occurs over a range of frequencies from resonance to twice the resonance frequency. The quantitative variation of the threshold with frequency depends on the model and the bubble radius. All models are transformed into a common interfacial rheological form, where the encapsulation is represented by two radius dependent surface properties-effective surface tension and surface dilatational viscosity. Variation of the effective surface tension with radius, specifically having an upper limit (resulting from strain softening or rupture of the encapsulation during expansion), plays a critical role. Without the upper limit, the predicted threshold is extremely large, especially near the resonance frequency. Having a lower limit on surface tension (e.g., zero surface tension in the buckled state) increases the threshold value at twice the resonance frequency, in some cases shifting the minimum threshold toward resonance.

Ultrasound-mediated destruction of contrast microbubbles used for medical imaging and drug delivery

Micron-size bubbles encapsulated by a stabilizing layer of surface-active materials are used in medical ultrasound imaging and drug delivery. Their destruction stimulated by ultrasound in vivo plays a critical role in both applications. We investigate the destruction process of microbubbles in a commercially available contrast agent by measuring the attenuation of ultrasound through it. The measurement is performed with single-cycle bursts from an unfocused transducer (with a center frequency of 5MHz) for varying pressure amplitudes at 50-, 100-, and 200-Hz pulse repetition frequencies (PRF) with duty cycles 0.001%, 0.002%, and 0.004%, respectively. At low excitation, the attenuation is found to increase with time. With increased excitation level, the attenuation level decreases with time, indicating destruction of microbubbles. There is a critical pressure amplitude (∼1.2MPa) for all three PRFs, below which there is no significant bubble destruction. Above the critical pressure amplitudes the rate of des...

Effects of inertia on the rheology of a dilute emulsion of drops in shear

Effects of inertia on the rheology of dilute Newtonian emulsion of drops in shear flow are investigated using direct numerical simulation. The drop shape and flow are computed by solving the Navier-Stokes equation in two phases using Front-tracking method. Effective stress is computed using Batchelor’s formulation, where the interfacial stress is obtained from the simulated drop shape and the perturbation stress from the velocity field. At low Reynolds number, the simulation shows good agreement with various analytical results and experimental measurements. At higher inertia deformation is enhanced and the tilt angle of the drop becomes larger than forty-five degree. The inertial morphology directly affects interfacial stresses. The first and the second interfacial normal stress differences are found to change sign due to the change in drop orientation. The interfacial shear stress is enhanced by inertia and decreases with capillary number at lower inertia but increases at higher inertia. The total excess...