Dexter M Easton1. 1. Department of Biological Sciences, Florida State University, Tallahassee 32306-4370, USA. easton@bio.fsu.edu
Abstract
PURPOSE: Disposition of drugs among compartments of the body usually occurs at changing rates that are commonly modeled as sums of exponential terms with different rate constants. This paper describes an alternative. Gompertz kinetics, in which the rates can change systematically. METHODS: Differential equations were developed and solved that fit typical examples taken from the literature. The three or four constants required for a visually satisfactory fit to data could readily be found by successive adjustment "by hand," but strategies and results are presented for computer fitting of the data. RESULTS: In four examples, the amount remaining in the blood decreases as an exponentially declining fraction of the amount present at any moment, but the antecedent processes responsible for that amount differ as follows: (a) In simple i.v. disposition (e.g., lidocaine) concentration falls as a decelerated exponential decay. (b) Delayed i.v. disposition (e.g., hexobarbital) requires, as well, a decelerated exponential growth function. (c) In simple disposition after oral administration, the concentration in the blood initially increases at a decelerating rate. (d) In biphasic oral disposition (e.g., Li+ carbonate), the initial Gompertz growth is followed by decelerated exponential decay. CONCLUSIONS: Gompertz kinetics provides an accurate and parsimonious mathematical model describing drug disposition.
PURPOSE: Disposition of drugs among compartments of the body usually occurs at changing rates that are commonly modeled as sums of exponential terms with different rate constants. This paper describes an alternative. Gompertz kinetics, in which the rates can change systematically. METHODS: Differential equations were developed and solved that fit typical examples taken from the literature. The three or four constants required for a visually satisfactory fit to data could readily be found by successive adjustment "by hand," but strategies and results are presented for computer fitting of the data. RESULTS: In four examples, the amount remaining in the blood decreases as an exponentially declining fraction of the amount present at any moment, but the antecedent processes responsible for that amount differ as follows: (a) In simple i.v. disposition (e.g., lidocaine) concentration falls as a decelerated exponential decay. (b) Delayed i.v. disposition (e.g., hexobarbital) requires, as well, a decelerated exponential growth function. (c) In simple disposition after oral administration, the concentration in the blood initially increases at a decelerating rate. (d) In biphasic oral disposition (e.g., Li+ carbonate), the initial Gompertz growth is followed by decelerated exponential decay. CONCLUSIONS: Gompertz kinetics provides an accurate and parsimonious mathematical model describing drug disposition.