An explicitly multi-component arterial gas embolus dissolves much more slowly than its one-component approximation

We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a maximum of five components (water, carbon dioxide, oxygen, nitrogen and helium). The rate equations were straight-forward extensions of those for a one-component gas bubble. They were derived by using the Young-Laplace equation and Dalton's law for the pressure in the AGE, the Laplace equation for the dissolved solute concentration gradients in solution, Henry's law for gas solubilities, and Fick's law for diffusion rates across the AGE/arterial blood interface. We found that the 1-component approximation, under which the contents of the AGE are approximated by its dominant component, greatly overestimates the dissolution rate and underestimates the total dissolution time of an AGE. This is because the 1-component approximation manifestly precludes equilibration between the AGE and arterial blood of the inspired volatile solutes (O₂, N₂, He) in arterial blood. Our calculations uncovered an important practical result, namely that the administration of Heliox, as an adjunct to recompression therapy for treating a suspected N₂-rich AGE must be done with care. While Helium is useful for preventing nitrogen narcosis which can arise in aggressive recompression therapy wherein the N₂ partial pressure can be quite high (e.g.∼5 atm), it also temporarily expands the AGE, beyond the expansion arising from the use of Oxygen-rich Nitrox. For less aggressive recompression therapy wherein nitrogen narcosis is not a significant concern, Oxygen-rich Nitrox is to be preferred, both because it does not temporarily expand the AGE as much as Heliox, and because it is much cheaper and more conservation-minded.