The lifetimes of small arterial gas emboli, and their possible connection to Inner Ear Decompression Sickness

• The dynamics of dissolution of small arterial gas emboli (AGE) is predicted.
• The Diffusion and Laplace equations are solved.
• Dirichlet and Neumann boundary conditions are each applied, and compared.
• AGE exposure times in a simplified model of arterial blood flow are estimated.
• AGE lifetimes, their sizes, and Inner Ear Decompression Sickness are connected.

We solved both the Diffusion and Laplace equations which predicted very similar results for the problem of a dissolving small gas bubble suspended in a liquid medium. These bubbles dissolved both because of surface tension and solute concentration effects. We focused on predicting bubble lifetimes (“tdtd”), and dissolution dynamics — radius vs time (R vs t  ) for these contracting bubbles. We also presented a direct comparison of the predicted results, obtained by applying either Dirichlet or Neumann boundary conditions, to the bubble/medium interface. To the best of our knowledge, this is the first direct comparison that has ever been published on the application of these different boundary conditions to a moving gas/liquid boundary. We found that the results obtained by applying either Dirichlet or Neumann boundary conditions were very similar for small, short-lived bubbles (R0<25μ,td<40 s), but diverged considerably for larger, longer-lived bubbles. We applied our expressions to the timely problem of Inner Ear Decompression Sickness, where we found that our predictions were consistent with much of what is known about this condition.