Mathematical models of diffusion-limited gas bubble dynamics in
tissue.
Gerth, R. Srini Srinivasan Wayne A., and Michael R. Powell.
1Wyle Laboratories, Houston, Texas 77058, 2Department of
Anesthesiology, Duke University Medical Center, Durham, North
Carolina 27710, 3Environmental Physiology Laboratory, NASA Johnson
Space Center, Houston, Texas 77058
APStracts 5:0414A, 1998.
Mathematical models of bubble evolution in tissue have recently been
incorporated into risk functions for predicting the incidence of
decompression sickness in human subjects following diving and/or
flying exposures. Bubble dynamics models suitable for these
applications assume the bubble to be either contained in an unstirred
tissue (Two-Region model) or surrounded by a boundary layer within a
well-stirred tissue (Three-Region model). The contrasting premises
regarding the bubble-tissue system lead to different expressions for
bubble dynamics described in terms of ordinary differential
equations. However, the expressions are shown to be structurally
similar with differences only in the definitions of certain
parameters that can be transformed to make the models equivalent at
large tissue volumes. It is also shown that the Two-Region model is
applicable only to bubble evolution in tissues of infinite extent,
and cannot be readily applied to bubble evolution in finite tissue
volumes to simulate how such evolution is influenced by interactions
between multiple bubbles in a given tissue. Two-Region models that
are incorrectly applied in such cases yield results that may be
reinterpreted in terms of their Three-Region model equivalents, but
only if the parameters in the Two-Region model transform into
consistent values in the Three-Region model. When such transforms
yield inconsistent parameter values for the Three-Region model,
results may be qualitatively correct, but are in substantial
quantitative error. Obviation of these errors through appropriate use
of the different models may improve performance of probabilistic
models of DCS occurrence that express DCS risk in terms of simulated
in vivo gas and bubble dynamics.
Received 22 January 1998; accepted in final form 23 September
1998.
APS Manuscript Number A66-8.
Article publication pending Journal of Applied Physiology.
ISSN 1080-4757 Copyright 1998 The American Physiological Society.
Published in APStracts on 12 November 1998