C (max) and t (max) verification using Fibonacci sequence and absorption rate

Abstract

The aim of this study was to verify the values of maximal observed concentration (C max,obs) and the time, at which maximum concentration is observed (t max,obs) using the analysis of the absorption rate constant (k ab). It focused on the changes in concentration over time (C-T) for drugs, for which several peaks of concentration occur. In addition, the attempt was made to use Fibonacci sequence to facilitate the visual analysis of the dynamics in changes of concentration on C-T graphs. The analyses were conducted with the use of three hypothetical data groups (groups I, II and III), which had distinct C-T profiles, and with the in vivo data form healthy subjects (n = 10) taking part in a bioequivalence study, who was given a single oral dose of topiramate (100 mg). The comparison of hypothetical and real in vivo data demonstrated that for the C-T curves, in which there are several peaks of concentration C max,obs and t max,obs values can easily be miscalculated when the increase in concentration is not properly related to the appropriate absorption phase (63.2, 87.50, 96.88 %). It was also demonstrated that the data transformation with the use of Fibonacci sequence exposes slight differences in the observed concentration values in a semi-logarithmic scale. The results of this study show that in case of C-T curves with several peaks of concentration, the verification of C max and t max data obtained taking into account different absorption phases enables more precise evaluation of these parameters.