Mathematical models of diffusion-limited gas bubble dynamics in tissue

Mathematical models of bubble evolution in tissue have recently been incorp orated into risk functions for predicting the incidence of decompression si ckness (DCS) in human subjects after diving and/or flying exposures. Bubble dynamics models suitable for these applications assume the bubble to be ei ther contained in an unstirred tissue (two-region model) or surrounded by a boundary layer within a well-stirred tissue (three-region model). The cont rasting premises regarding the bubble-tissue system lead to different expre ssions for bubble dynamics described in terms of ordinary differential equa tions. However, the expressions are shown to be structurally similar with d ifferences only in the definitions of certain parameters that can be transf ormed to make the models equivalent at large tissue volumes. It is also sho wn that the tao-region model is applicable only to bubble evolution in tiss ues of infinite extent and cannot be readily applied to bubble evolution in finite tissue volumes to simulate how such evolution is influenced by inte ractions among multiple bubbles in a given tissue. Tao-region models that a re incorrectly applied in such cases yield results that may be reinterprete d in terms of their three-region model equivalents but only if the paramete rs in the two-region model transform into consistent values in the three-re gion model. Then such transforms field inconsistent parameter values for th e three-region model, results may be qualitatively correct but are in subst antial quantitative error. Obviation of these errors through appropriate us e of the different models may improve performance of probabilistic models o f DCS occurrence that express DCS risk in tel ms of simulated in vivo gas a nd bubble dynamics.