Dissolution of multicomponent microbubbles in the bloodstream: 1. theory

Abstract

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-μm bubbles in the bloodstream from < 1 s (as found with pure air), the osmotic agent must have a low Ostwald coefficient (≤ 10 −4) and a relatively high saturated vapor pressure at body temperature (≥ 0.3 atm = 3 × 10 4 Pa).