Mathematical Models of Diffusion-Limited Gas Bubble Evolution in Perfused Tissue

Mathematical models of gas and bubble dynamics in tissue are used in various algorithms to mitigate the incidence and severity of decompression sickness (DCS) in man. These are simple models that describe the diffusion and perfusion processes that underlie gas bubble growth and resolution in terms of ordinary differential equations with relatively small numbers of parameters. The models fall into two distinct classes well-stirred tissue and unstirred tissue based on different representations of gas exchange between bubble and tissue. A series of models of gas and bubble dynamics developed to illuminate the strengths and limitations of models in these classes are reviewed here in the logical order in which they evolved. The final model in the series addresses the growth of multiple bubbles in a finite-sized tissue and accounts for the effects of spherically asymmetric diffusion and non-uniform blood flow. It is a comprehensive model with only a few underlying assumptions, valid for assessing bubble evolution in extravascular tissue. Yet it is computationally simple and readily applied in practical algorithms for limiting the incidence and severity of DCS in man during diving, altitude, and flying-after-diving profiles of arbitrary complexity.