Katiyar A, Sarkar K 2012 “Effects of encapsulation damping on excitation threshold for subharmonic generation from contrast microbubbles,” Journal of the Acoustical Society of America, 132, 3576-3585.
A recent study [Katiyar and Sarkar (2011). J. Acoust. Soc. Am.130, 3137–3147] showed that incontrast to the analytical result for free bubbles, the minimum threshold for subharmonic generationfor contrast microbubbles does not necessarily occur at twice the resonance frequency. Hereincreased damping—either due to the small radius or the encapsulation—is shown to shift the mini-mum threshold away from twice the resonance frequency. Free bubbles as well as four modelsof the contrast agent encapsulation are investigated varying the surface dilatational viscosity.Encapsulation properties are determined using measured attenuation data for a commercial contrastagent. For sufficiently small damping, models predict two minima for the threshold curve—one attwice the resonance frequency being lower than the other at resonance frequency—in accord withthe classical analytical result. However, increased damping damps the bubble response more attwice the resonance than at resonance, leading to a flattening of the threshold curve and a gradualshift of the absolute minimum from twice the resonance frequency toward the resonance frequency.The deviation from the classical result stems from the fact that the perturbation analysis employedto obtain it assumes small damping, not always applicable for contrast microbubbles.
Echogenic liposomes (ELIP) are an excellent candidate for concurrent imaging and drug delivery applica-tions. They combine the advantages of liposomes-biocompatibility and ability to encapsulate both hydro-phobic and hydrophilic drugs-with strong reflections of ultrasound. The objective of this study is toperform a detailedin vitroacoustic characterization – including nonlinear scattering that has not beenstudied before – along with an investigation of the primary mechanism of echogenicity. Both componentsare critical for developing viable clinical applications of ELIP. Mannitol, a cryoprotectant, added duringthe preparation of ELIP is commonly believed to be critical in making them echogenic. Accordingly, hereELIP prepared with varying amount of mannitol concentration are investigated for their pressure depen-dent linear and non-linear scattered responses. The average diameter of these liposomes is measured tobe 125–185 nm. But they have a broad size distribution including liposomes with diameters over a micro-meter as observed by TEM and AFM. These larger liposomes are critical for the overall echogenicity.Attenuation through liposomal solution is measured with four different transducers (central frequencies2.25, 3.5, 5, 10 MHz). Measured attenuation increases linearly with liposome concentration indicatingabsence of acoustic interactions between liposomes. Due to the broad size distribution, the attenuationshows a flat response without a distinct peak in the range of frequencies (1–12 MHz) investigated. A15–20 dB enhancement with 1.67lg/ml of lipids is observed both for the scattered fundamental andthe second harmonic responses at 3.5 MHz excitation frequency and 50–800 kPa amplitude. It demon-strates the efficacy of ELIP for fundamental as well as harmonic ultrasound imaging. The scatteredresponse however does not show any distinct subharmonic peak for the acoustic excitation parametersstudied. Small amount of mannitol proves critical for echogenicity. However, mannitol concentrationabove 100 mM shows no effect.
The extracellular enzyme matrix metalloproteinase-9(MMP-9) is overexpressed in atherosclerotic plaques and in metastaticcancers. The enzyme is responsible for rupture of the plaques and forthe invasion and metastasis of a large number of cancers. The ability ofultrasonic excitation to induce thermal and mechanical effects has beenused to release drugs from different carriers. However, the majority ofthese studies were performed with low frequency ultrasound (LFUS) atkilohertz frequencies. Clinical usage of LFUS excitations will be limiteddue to harmful biological effects. Herein, we report our results on therelease of encapsulated contents from substrate lipopeptide incorpo-rated echogenic liposomes triggered by recombinant human MMP-9.The contents release was further enhanced by the application ofdiagnostic frequency (3 MHz) ultrasound. The echogenic liposomeswere successfully imaged employing a medical ultrasound transducer(4−15 MHz). The conditioned cell culture media from cancer cells (secreting MMP-9) released the encapsulated dye from theliposomes (30−50%), and this release is also increased (50−80%) by applying diagnostic frequency ultrasound (3 MHz) for 3min. With further developments, these liposomes have the potential to serve as multimodal carriers for triggered release andsimultaneous ultrasound imaging.
Deformation and sedimentation velocities of a viscoelastic drop falling through a Newtonianmedium are numerically investigated using a front-tracking finite difference method. In contrast toa viscous drop, viscoelasticity deforms an initially spherical drop into an oblate shape and decreasesits sedimentation velocity. Further increase of elasticity results in a dimple at the rear end, as theviscoelastic stress at the trailing end of the drop pulls the drop interface inward. The dimplebecomes more prominent with increasing Deborah number, amount of polymeric viscosity, andcapillary number. An approximate analysis is performed to model the stress development along theaxis of symmetry, specifically its increase at the rear end that governs the dimple formation. Foreven higher values of Deborah number, the interfacial tension cannot balance the viscoelasticstresses leading to an unstable situation toward a toroidal shape. We numerically find the criticalDeborah number for the transition. It shows an approximate inverse scaling with capillary number.For unstable cases, downward progressing dimple develops a globular end. Development of theglobular end results in a sudden increase in the cross-sectional area of the drop and a sharp decreaseof the settling velocity.
Variation of subharmonic response from contrast microbubbles with ambient pressure is numericallyinvestigated for non-invasive monitoring of organ-level blood pressure. Previously, several contrastmicrobubbles bothin vitroandin vivoregistered approximately linear (5–15 dB) subharmonicresponse reduction with 188 mm Hg change in ambient pressure. In contrast, simulated subharmonicresponse from a single microbubble is seen here to either increase or decrease with ambient pressure.This is shown using the code BUBBLESIM for encapsulated microbubbles, and then the underlyingdynamics is investigated using a free bubble model. The ratio of the excitation frequency to the natu-ral frequency of the bubble is the determining parameter—increasing ambient pressure increases nat-ural frequency thereby changing this ratio. For frequency ratio below a lower critical value,increasing ambient pressure monotonically decreases subharmonic response. Above an upper criticalvalue of the same ratio, increasing ambient pressure increases subharmonic response; in between, thesubharmonic variation is non-monotonic. The precise values of frequency ratio for these three differ-ent trends depend on bubble radius and excitation amplitude. The modeled increase or decrease ofsubharmonic with ambient pressure, when one happens, is approximately linear only for certain rangeof excitation levels. Possible reasons for discrepancies between model and previous experiments arediscussed.
Deformation of a viscous drop in shear at finite inertia and the streamlines around itare numerically investigated. Inertia destroys the closed streamlines found in Stokesflow. It creates reversed streamlines and streamlines spiralling around the vorticityaxis. Spiralling streamlines spiral either towards the central shear plane or away fromit depending on the viscosity ratio and the inertia. The zones of open or reversedstreamlines as well as streamlines spiralling towards or away from the central shearplane are delineated for varying viscosity ratio and Reynolds number. In contrast tothe infinite extent of the closed Stokes streamlines around a rigid sphere in shear, theregion of the spiralling streamlines in the vorticity direction both for a rigid sphere anda drop shrinks with inertia. Inertia increases deformation, and introduces oscillations indrop shape. An approximate analysis explains the scaling of oscillation frequency anddamping with Reynolds and capillary numbers. The steady-state drop inclination anglewith the flow axis increases with increasing Reynolds number for small Reynoldsnumber. But it decreases at higher Reynolds number, especially for larger capillarynumbers. For smaller capillary numbers, drop inclination reaches higher than 45?(thedirection of maximum extension), critically affecting the interfacial stresses due tothe drop. It changes the sign of first and second normal interfacial stress differences(and thereby these components of the effective stresses of an emulsion of such drops).Increasing viscosity ratio orients the drop towards the flow axis, which increases thecritical Reynolds number above which the drop inclination reaches more than 45?.
Six models of contrast microbubbles are investigated to determine the excitation threshold for sub-harmonic generation. The models are applied to a commercial contrast agent; its characteristic pa-rameters according to each model are determined using experimentally measured ultrasoundattenuation. In contrast to the classical perturbative result, the minimum threshold for subharmonicgeneration is not always predicted at excitation with twice the resonance frequency; instead itoccurs over a range of frequencies from resonance to twice the resonance frequency. The quantita-tive variation of the threshold with frequency depends on the model and the bubble radius. All mod-els are transformed into a common interfacial rheological form, where the encapsulation isrepresented by two radius dependent surface properties—effective surface tension and surface dila-tational viscosity. Variation of the effective surface tension with radius, specifically having anupper limit (resulting from strain softening or rupture of the encapsulation during expansion), playsa critical role. Without the upper limit, the predicted threshold is extremely large, especially nearthe resonance frequency. Having a lower limit on surface tension (e.g., zero surface tension in thebuckled state) increases the threshold value at twice the resonance frequency, in some cases shiftingthe minimum threshold toward resonance.