Journal of Pharmacokinetics and Biopharmaceutics, Vol. 24, No. 6, 1996 Use of Parallel Erlang Density Functionsto Analyze First-Pass Pulmonary Uptake of Multiple Indicators in Dogs T. C. Krejeie, z'4 J. A. Jaequez, 3 M. J. Avram, 2 C. U. Niemann, 2 C. A. Shanks, 2 and T. K. Henthorn 2 Received October 24, 1995--Final January 8, 1997 The gamma and Erlang density functions describe a large class of lagged, right-skewed distribu- tions. The Erlang distribution has been shown to be the analytic solution for a chain of compart- ments with identical rate constants. This relationship makes it useful for the analysis offirst-pass pulmonary drug uptake data following intravenous bolus administration and the incorporation of this analysis into an overall systemic drug disposition model. However, others have shown that one Erlang density function characterizes the residence time distribution of solutes in single tissues with significant systematic error, We propose a model of two Erlang density functions in parallel that does characterize well the arterial appearance o f indocyanine green, antipyrine, and alfentanil administered simultaneously by right atrial bolus injection. We derive the equations that permit calculation of the higher order moments of a system consisting of two parallel Erlang density functions and use the results of these calculationsfrom the data for all three indicators to estimate pulmonary capillary blood volume and mean transit time in the dog. KEY WORDS: indocyanine green; antipyrine; alfentanil; tissue distribution; physiologic models; dogs; pulmonary uptake; pulmonary capillary blood volume; pulmonary capillary transit time. INTRODUCTION The drug concentration vs. time profile of the initial arterial appearance, after rapid intravenous (bolus) administration, of drugs that interact strongly with pulmonary tissue (e.g., basic amines) is significantly different JSupported in part by the National Institute of General Medical Sciences, RO1-GM-43776, ROI-GM-47502, and PO1-GM-47819. 2Department of Anesthesiology, Northwestern UniversityMedical School, CH-WI39, 303 E. Chicago Avenue, Chicago, Illinois 60611-3008. 3Department of Physiology,Universityof Michigan, 7808 Medical Sciences II, Ann Arbor, Michigan 48109-0622. 4To whom correspondenceshould be addressed. 569 0090-466X/96/1200-0569509.50/0 9 1996 Plenum Publishin~ Comoration