Intramembrane cavitation as a unifying mechanism for ultrasound-induced bioeffects.

The purpose of this study was to develop a unified model capable of explaining the mechanisms of interaction of ultrasound and biological tissue at both the diagnostic nonthermal, noncavitational (<100 mW · cm(-2)) and therapeutic, potentially cavitational (>100 mW · cm(-2)) spatial peak temporal average intensity levels. The cellular-level model (termed "bilayer sonophore") combines the physics of bubble dynamics with cell biomechanics to determine the dynamic behavior of the two lipid bilayer membrane leaflets. The existence of such a unified model could potentially pave the way to a number of controlled ultrasound-assisted applications, including CNS modulation and blood-brain barrier permeabilization. The model predicts that the cellular membrane is intrinsically capable of absorbing mechanical energy from the ultrasound field and transforming it into expansions and contractions of the intramembrane space. It further predicts that the maximum area strain is proportional to the acoustic pressure amplitude and inversely proportional to the square root of the frequency (ε A,max ∝ P(A)(0.8f - 0.5) and is intensified by proximity to free surfaces, the presence of nearby microbubbles in free medium, and the flexibility of the surrounding tissue. Model predictions were experimentally supported using transmission electron microscopy (TEM) of multilayered live-cell goldfish epidermis exposed in vivo to continuous wave (CW) ultrasound at cavitational (1 MHz) and noncavitational (3 MHz) conditions. Our results support the hypothesis that ultrasonically induced bilayer membrane motion, which does not require preexistence of air voids in the tissue, may account for a variety of bioeffects and could elucidate mechanisms of ultrasound interaction with biological tissue that are currently not fully understood.

Modeling photothermal and acoustical induced microbubble generation and growth.

Previous experimental studies showed that powerful heating of nanoparticles by a laser pulse using energy density greater than 100 mJ/cm(2), could induce vaporization and generate microbubbles. When ultrasound is introduced at the same time as the laser pulse, much less laser power is required. For therapeutic applications, generation of microbubbles on demand at target locations, e.g. cells or bacteria can be used to induce hyperthermia or to facilitate drug delivery. The objective of this work is to develop a method capable of predicting photothermal and acoustic parameters in terms of laser power and acoustic pressure amplitude that are needed to produce stable microbubbles; and investigate the influence of bubble coalescence on the thresholds when the microbubbles are generated around nanoparticles that appear in clusters. We develop and solve here a combined problem of momentum, heat and mass transfer which is associated with generation and growth of a microbubble, filled with a mixture of non-vaporized gas (air) and water vapor. The microbubble's size and gas content vary as a result of three mechanisms: gas expansion or compression, evaporation or condensation on the bubble boundary, and diffusion of dissolved air in the surrounding water. The simulations predict that when ultrasound is applied relatively low threshold values of laser and ultrasound power are required to obtain a stable microbubble from a single nanoparticle. Even lower power is required when microbubbles are formed by coalescence around a cluster of 10 nanoparticles. Laser pulse energy density of 21 mJ/cm(2) is predicted for instance together with acoustic pressure of 0.1 MPa for a cluster of 10 or 62 mJ/cm(2) for a single nanoparticle. Those values are well within the safety limits, and as such are most appealing for targeted therapeutic purposes.

Subharmonic response of encapsulated microbubbles: conditions for existence and amplification.

The response of encapsulated microbubbles at half the ultrasound insonation frequency, termed subharmonic response, may have potential applications in diagnosis and therapy. The subharmonic signal, emitted by Definity microbubble cloud sonicated by ultrasound was studied theoretically and experimentally. The size distribution of the microbubbles was optically analyzed and resonance frequency of 2.7 MHz was determined. An asymptotic model has been developed that generates subharmonic response of a single and of a cloud of bubbles of various sizes. Threshold conditions for existence and the intensity of the subharmonic signal are predicted to depend on microbubbles size distribution and shell properties, as well as on the driving field frequency and pressure. Thin tubes filled with Definity solution were insonated at acoustic pressures from 100 to 630 kPa. The intensities of the emitted fundamental harmonics and subharmonics were measured. At frequency 5.5MHz, twice the resonance frequency, the subharmonic signals were observed only at pressures greater than 190 kPa. The subharmonic to fundamental harmonics intensity ratio was within -12 to -1 dB. The experimental results showed good correlation with the theoretical results in the range of validity of the asymptotic solution, thus supporting the model assumptions.

Stability of an encapsulated bubble shell.

The stability of an encapsulated bubble filled with gas is studied where gas is allowed to diffuse out of the bubble. A mechanistic model that takes into account shell stiffness and surface tension is considered. A critical shell radius for loss of mechanical stability is derived based on a technique adapted for small radius, where surface tension effects become substantial. A new parameter is defined that determines the relative importance of surface tension forces and shell stiffness for shell stability. The developed technique allows to predict, for a given bubble population and gas saturation level of the surrounding liquid, a range of bubble sizes which may collapse in time. Surface tension effects are dominant in determining the critical radius but have a negligible effect on the minimal radius for collapse. The influence of the surface tension on the stability of the shell is illustrated for Optison, a typical ultrasound contrast agent.

Drops down the hill: theoretical study of limiting contact angles and the hysteresis range on a tilted plate.

The limiting inclination angle (slip angle), for which a two-dimensional water drop may be at equilibrium on a chemically heterogeneous surface, is exactly calculated for a variety of cases. The main conclusion is that, in the cases studied, the contact angles at the upper and lower contact line do not always simultaneously equal the receding and advancing contact angles, respectively. On a hydrophobic surface, the lowest contact angle (at the upper contact line) tends to be approximately equal to the receding contact angle, while the highest contact angle (at the lower contact line) may be much lower than the advancing contact angle. For hydrophilic surfaces, the opposite is true. These conclusions imply that the hysteresis range cannot in general be measured by analyzing the shape of a drop on an inclined plane. Also, the limiting inclination angle cannot in general be calculated from the classical equation based only on the advancing and receding contact angles.

Shear stress induced by a gas bubble pulsating in an ultrasonic field near a wall.

Some of the effects that therapeutic ultrasound has in medicine and biology may be associated with steady oscillations of gas bubbles in liquid, very close to tissue surface. The bubble oscillations induce on the surface steady shear stress attributed to microstreaming. A mathematical simulation of the problem for both free and capsulated bubbles, known as contrast agents, is presented here. The simulation is based on a solution of Laplace's equation for potential flow and existing models for microstreaming. The solution for potential flow was obtained numerically using a boundary integral method. The solution provides the evolution of the bubble shape, the distribution of the velocity potential on the surface, and the shear stress along the surface. The simulation shows that significant shear stresses develop on the surface when the bubble bounces near the tissue surface. In this case, pressure amplitude of 20 kPa generates maximal steady shear stress of several kilo Pascal. Substantial shear stress on the tissue surface takes place inside a circular zone with a radius about half of the bubble radius. The predicted shear stress is greater than stress that causes hemolysis in blood and several orders of magnitude greater than the physiological stress induced on the vessel wall by the flowing blood.

Ultrasound attenuation by encapsulated microbubbles: time and pressure effects.

Ultrasound (US) contrast agents (UCA) consist of artificial encapsulated microbubbles filled with low-diffusivity gas. This study evaluated, both experimentally and theoretically, the behavior of a cloud of encapsulated microbubbles while the surrounding pressure was modified within the physiological range. The theoretical analysis included calculation of US attenuation caused by a bubble cloud. The radius and gas content of each bubble were determined from a solution of a diffusion problem. Shell permeability and rigidity were taken into account. Both experiments and theory demonstrated that, for fixed ambient pressures, higher pressures result in increased rate of attenuation decay. Pulsatile ambient pressure induces pulsations of attenuation of the same frequency. In general, theoretical predictions are in good agreement with experimental data.

A blood vessel exposed to ultrasound: a mathematical simulation of the temperature field.

In this article we present a mathematical simulation of the temperature field in and around a blood vessel when it is sonicated by a focused ultrasound beam. A simplified geometry is considered: a cylindrical blood vessel is embedded in tissue parallel to a flat skin surface. The ultrasound transducer is placed on the skin above the blood vessel, perpendicular to the skin surface. The 3D geometry of the problem is simplified by transformation, which maps the domain into a parallelepiped. A computational algorithm and computer program were developed. The simulation provides the conditions for successful occlusion of a blood vessel and demonstrates the significant role of the blood flow rate on the temperature difference between the vessel wall and the surrounding tissue. Comparing the predictions with published experimental data tested the validity of the method.