Alexey Kabalnov

Dissolution of multicomponent microbubbles in the bloodstream: 1. theory

The problem of dissolution of a bubble in the bloodstream is examined. The bubble is assumed to be filled with a mixture of a sparingly water-soluble gas (osmotic agent) and air. The dissolution of the bubble has three definite stages. In Stage 1, the bubble quickly swells in air. The swelling ratio depends on the surface tension, blood pressure, level of oxygen metabolism and initial mole fraction of osmotic agent in the bubble. In Stage 2, the osmotic agent slowly diffuses out of the bubble. The squared radius decreases nearly linearly with time, at a rate proportional to the Ostwald coefficient and diffusivity of the osmotic agent. In Stage 3, the partial pressure of the osmotic agent becomes so high that it condenses into a liquid. In order to prolong the lifetime of 5-micron bubbles in the bloodstream from < 1 s (as found with pure air), the osmotic agent must have a low Ostwald coefficient (< or = 10(-4)) and a relatively high saturated vapor pressure at body temperature (> or = 0.3 atm = 3 x 10(4) Pa).

Ostwald Ripening and Related Phenomena

Ostwald ripening in multicomponent systems is discussed in terms of thermodynamic stability and metastability. While the insoluble species trapped in the bulk of the drops can provide thermodynamic stability, only metastability is possible when the species is trapped at the interface between the phases. Similarly, a Helfrich-type dependence of the surface tension on curvature can produce metastability, but not thermodynamic stability. When the drops are encapsulated with a cross-linked permeable membrane, or with an insoluble surfactant monolayer, the membrane must be able to withstand the stress of the Laplace pressure and not collapse; this condition is in general hard to implement unless the emulsion drops are small, ∼10–100 nm. The effect of micelles on various mass transfer processes in surfactant systems, such as Ostwald ripening, composition ripening, adsorption from micellar solutions, and solubilization kinetics are discussed. Two mechanisms are possible: In the first, micelles fuse directly with the macroscopic interfaces; in the second, the fusion-fission is prohibited and micelles affect the mass transfer only by participating in the dynamic equilibrium between the micelles and monomers. It is argued that whether or not the direct fusion of the micelles with the interface is allowed, is controlled by the free energy of the transition state (e.g., for ripening, the energy of the neck joining a micelle and a drop). Because of this, direct adsorption of micelles at the air-water interface is strongly unfavorable. However, it is possible at the oil-water interface, if the system is close enough to the balanced point. This means that Ostwald ripening and composition ripening can be strongly affected by micelles only if the system is in the narrow range of spontaneous curvatures in the vicinity of the balanced point, where the fusion of micelles with the interface is significant, but the rate of coalescence remains small. The experimental data supporting and contradicting this point of view are discussed.

Dissolution of multicomponent microbubbles in the bloodstream: 2. experiment

The effect of the nature of the filling gas on the persistence of microbubbles in the bloodstream was studied. All the microbubbles were covered with the same shells. Various perfluorocarbons and perfluoropolyethers alone and as mixtures with nitrogen were used as the filling gases. The persistence time of microbubbles in the bloodstream tau increased with the molecular weight of the filling gas, from approximately 2 min for perfluorethane, to > 40 min for perfluorodiglyme, C6F14O3, and then decreased again to 8 min for C6F14O5. An acceptable ultrasound scattering efficacy was exhibited by the filling gases with intermediate molecular weights that possessed both a high saturated vapor pressure and a comparatively low water solubility (Ostwald coefficient). On the basis of the experimental data, it is concluded that the microbubble persistence tau is controlled primarily by the dissolution of microbubbles and not by the removal of the microbubbles by the reticular endothelial system. Although the qualitative experimental trends are in good agreement with the theoretical model developed previously, there are some quantitative differences. Possible reasons for these differences are discussed.