Influence of bubble size and blood perfusion on absorption of gas bubbles in tissues

We have developed a mathematical theory to predict behavior of tissue gas bubbles such as those occurring in decompression sickness. According to the theory, rate of change of diameter of a spherical bubble is proportional to the sum of a) a factor that accounts for the divergence of the paths of molecules as they diffuse outward from the bubble, and b) a factor that accounts for blood perfusion of the tissues around the bubble. For bubbles of radius below 10 microns, the perfusion factor is negligible in comparison to the divergence factor. This finding and assumptions that unsteady-state effects and surface tension are negligible allow the rate of growth or decay of small bubbles to be approximated by a relatively simple differential equation. According to the epuation, rate of radius change is directly proportional to the inert gas partial pressure difference between the inside and outside of the bubble, inversely proportional to the pressure of the gas inside the bubble, and inversely proportional to the bubble radius.