USE OF PARALLEL ERLANG DENSITY-FUNCTIONS TO ANALYZE FIRST-PASS PULMONARY UPTAKE OF MULTIPLE INDICATORS IN DOGS

The gamma and Erlang density functions describe a large class of lagge d, right-skewed distributions. The Erlang distribution has been shown to be the analytic solution for a chain of compartments with identical rate constants. This relationship makes it useful for the analysis of first-pass pulmonary drug uptake data following intravenous bolus adm inistration and the incorporation of this analysis into an overall sys temic drug disposition model. However; others have shown that one Erla ng density function characterizes the residence time distribution of s olutes in single tissues with significant systematic error. We propose a model of two Erlang density functions in parallel that does charact erize well the arterial appearance of indocyanine green, antipyrine, a nd alfentanil administered simultaneously by right atrial bolus inject ion. We derive the equations that permit calculation of the higher ord er moments of a system consisting of two parallel Erlang density funct ions and use the results of these calculations from the data for all t hree indicators to estimate pulmonary capillary blood volume and mean transit time in the dog.