Algorithm for application of fourier analysis for biorhythmic baselines ofpharmacodynamic indirect response models

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k(in)(t) and a first-order loss constant k(out). If k(in)(t) follows some biological rhythm (e.g., circadia n), then the response R(t) also displays a periodic behavior. A new approac h for describing the input function in indirect response models with biorhy thmic baselines of physiologic substances is introduced. The present approa ch uses the baseline (placebo) response Rb(t) to recover the equation for k (in)(t). Fourier analysis provides an approximate equation for R-b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k(in)(t), yielding the equation involving R-b(t) A com puter program was developed to perform the square L-2-norm approximation te chnique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was m odeled based on the inhibition of the secretion rate k(in)(t) using ADAPT I I. The pharmacodynamic parameters k(out) and IC50 were estimated from the,m odel equation with k(in)(t) derived by the new approach. The proposed metho d of describing the input function needs no assumption about the behavior o f k(in)(t), is as efficient as methods used previously, and is more flexibl e in describing the baseline data than the nonlinear regression method.