Excretion-retention diagram to evaluate gas exchange properties of vertebrate respiratory systems

Excretion [E = (PE - PI)/(PV - PI)] and retention [R = (Pa - PI)/(PV -PI)]are completely model-free defined variables which describe the dual input-output black-box representation of vertebrate respiratory systems under steady-state conditions. In the excretion-retention diagram (E-R diagram), E is plotted as a function of R. The application of the principle of mass conservation confines the possible combinations of E and R for a gas with a blood-gas partition coefficient, lambda, in a respiratory system with an overall ventilation, VT, and an overall perfusion, QT, to E = (lambda QT/VT) (1 - R). In general, E can be described as a continuous function of R. The mathematical formulation of this function depends on the configuration of the respiratory system. Easily recognizable curvatures are obtained for counter-cross, and cocurrent systems with and without parallel inhomogeneities. Visual inspection of actual E and R data displayed in an E-R diagram therefore allows the correct choice of the configuration of the respiratory system to be eventually used for further parameter estimation schemes. The E-R diagram is also a powerful tutorial tool for visualizing the complex relationships between the gas exchange of agents with different physical properties and the consequences of changes in ventilation and perfusion distribution within the respiratory system on gas transport.