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.