Hydraulic analog for simultaneous representation of pharmacokinetics and pharmacodynamics: application to vecuronium

To facilitate teaching the pharmacologic determinants of clinically observed drug effect, we expand on the hydraulic representation of the pharmacokinetics and pharmacodynamics of intravenous drugs.

There are two significant barriers to understanding the pharmacological determinants underlying clinically observed drug responses. The first obstacle is the mathematical nature of traditional descriptions of these phenomena; the second barrier to understanding is that most educational texts focus solely on pharmacokinetics. However, pharmacokinetics alone do not explain the action at the effect site. The scientific and educational literature has used analogs of pharmacokinetic phenomena to make the concepts more intuitive. This manuscript extends the use of a hydraulic analog to include the effect site, allowing a simultaneous representation of pharmacokinetics and pharmacodynamics.

In the described hydraulic analog, fluid delivered into a central reservoir is representative of drug infusion, and the heights of the fluid columns in the central and peripheral reservoirs are representative of the drug concentrations in the corresponding pharmacologic compartments. The height of the fluid column in an 'effect reservoir' is representative of the apparent effect site concentration in a simultaneous pharmacokinetic-pharmacodynamic model. A non-linear scale on the effect reservoir represents the relationship between the effect site concentration and the clinical effect. Reservoir surface areas are equivalent to volumes of distribution and hydraulic resistances are inversely proportional to drug clearances. The proof of mathematical equivalency of the presented analog to simultaneous pharmacokinetic-pharmacodynamic models is given in an appendix. ILLUSTRATION OF THE EDUCATIONAL APPLICATION: The effect window can represent monitored twitch response following the administration of a neuromuscular blocking agent. Using pharmacokinetic-pharmacodynamic parameter values for vecuronium, we demonstrate how the hydraulic analog can be used to explain the priming principle and the clinically observed time-course disparity of two effect sites: the larynx and the adductor pollicis. (A companion web site: http://www.anest.ufl.edu/ha.html presents an interactive animation of the described analog.)