An extended soluble gas exchange model for estimating pulmonary perfusion. I. Derivation and implementation

A dynamic model for respiratory exchange of blood soluble gas is described. This model includes a general treatment of tidal breathing, an inhomogeneous lung comprising multiple distensible compartments, and nonlinearities due to multiple-gas effects. The motivation for this model is the continuing interest in estimating pulmonary perfusion from measurements of respiratory soluble gas exchange. Numerical simulation can be used to investigate the errors that result from simplifications made in the derivation of simpler models used for this purpose. Examples of such simplifications are the assumptions that ventilation is constant and unidirectional and that multiple soluble gases can be independently modeled. These results can delimit the boundaries within which perfusion estimates can be considered reliable. An example demonstrating the model and its numerical solution is presented.