An effective-diffusivity model of pulmonary capillary exchange: General theory, limiting cases, and sensitivity analysis

Abstract

A family of possible models of capillary-tissue exchange useful for interpreting multiple-tracer data from the pulmonary circulation was derived from the convective-diffusion equation. The models are simplifications of a uniform-transit-time model with two serial diffusion layers outside of the capillary. Modifications of this four-parameter model were derived, and the importance of simplifying assumptions were compared using moment analysis and transform-domain equivalence. A permeability-diffusion model was derived by assuming that the layer nearer the capillary contributed a constant resistance to tracer movement. Using sensitivity analysis, we found that the three parameters of this permeability-diffusion model could not be determined independently, and that further model simplification was highly desirable. Two distinct paths of further simplification were explored.The Sangren-Sheppard model was considered as one path. An alternative path of simplification led to a new model of tracer behavior which we have called an effective-diffusivity model. Moment matching was used to determine the relationships among these models. Sensitivity analysis of the Sangren-Sheppard and effective-diffusivity models showed that the parameters of both of these models were more easily identified. However, the sensitivity analysis also showed that these two models had quite different sensitivities to their respective volume parameters. The Sangren-Sheppard model prediction was affected at all times by a change in the extravascular volume parameter, while the effective-diffusivity model prediction was affected only at the longest times. We concluded that the effective-diffusivity model may be a better alternative to the Sangren-Sheppard model under some conditions. The parameters of the effective-diffusivity model provide a more reliable index of the physiology of capillary-tissue exchange as small molecules as measured by the multiple tracer method in the pulmonary circulation.