The gamma and Erlang density functions describe a large class of lagged, 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 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 of 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 calculations from the data for all three indicators to estimate pulmonary capillary blood volume and mean transit time in the dog.

A thermally generated aerosol (TGA) system can effect reliable delivery of excipient-free drug to alveoli, resulting in rapid systemic drug absorption. We developed a pharmacokinetic model of prochlorperazine, administered by inhalation and as a rapid intravenous infusion, and we determined absolute TGA bioavailability in eight healthy volunteers in this institutional review board-approved, two-period crossover study. After the drug was administered as either a 5-s intravenous infusion or a TGA single-breath inhalation, blood was collected at various times for up to 24 h. Plasma prochlorperazine concentrations were measured using liquid chromatography-tandem mass spectrometry. Inhalation and rapid intravenous administration produced similar plasma prochlorperazine concentration profiles. Intravenous and inhalation pharmacokinetics were well characterized by a simultaneous two-compartment model with multiple absorption delays. Prochlorperazine pharmacokinetic parameters were similar to those reported for single intravenous doses. The geometric mean bioavailability after TGA delivery was 1.10. The administration of prochlorperazine by inhalation resulted in pharmacokinetics similar to that seen after intravenous administration, in terms of speed, extent, and consistency of absorption.

There is considerable variability in response to intravenously administered anesthetic drugs (e.g., hypnotics, benzodiazepines, and narcotics) that have a rapid onset of effect (such as hypnosis, anxiolysis, and analgesia) and a low margin of safety (because of cardiovascular or respiratory depression, etc.). Although the onset of effect for these drugs occurs seconds to minutes after injection, traditional pharmacokinetic models are based on blood samples that are first obtained after drug effects have peaked. As a result, many studies have failed to provide a pharmacokinetic rationale for dosage adjustments of these drugs.

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