A mathematical model of diffusion-limited gas bubble dynamics in tissue with varying diffusion region thickness

The three-region model of gas bubble dynamics consists of a bubble and a well-stirred tissue region with an intervening unperfused diffusion region previously assumed to have constant thickness and uniform gas diffusivity. As a result, the diffusion region gas content remains unchanged as its volume increases with bubble growth, causing dissolved gas in the region to violate Henry's law. Earlier work also neglected the relationship between the varying diffusion region volume and the fixed total tissue volume. The present work corrects these theoretical inconsistencies by postulating a difference in gas diffusivity between an infinitesimally thin layer at the bubble surface and the remainder of the diffusion region, thus allowing both thickness and gas content of the diffusion region to vary during bubble evolution. The corrected model can yield bubble lifetimes considerably longer than those yielded by earlier three-region models, and meets a need for theoretically consistent but relatively simple bubble dynamics models for use in studies of decompression sickness (DCS) in human subjects.