Use of gamma distributed residence times in pharmacokinetics.

Using a nonclassical statistically based pharmacokinetic concept, a theory is presented which can be applied to the analysis of concentration-time data fitted by power functions of time C = At-ae-bt, which is shown to be equivalent to the assumption of gamma distributed residence times of drugs. The shape and scale parameters a and b, respectively, are interpreted physiologically in terms of a recirculatory model. It is shown how the shape parameter a, which is only dependent on the coefficient of variation of residence times, is affected by the processes of drug distribution and elimination. The time course of the blood concentration following multiple doses and continuous infusion is predicted for gamma-like drug disposition curves. The assumption of gamma distributed disposition residence times is theoretically based on a random walk model of circulatory drug transport, and the conditions are investigated under which gamma curves can be empirically fitted to oral concentration-time data. The parameters of concentration-time profiles following solid dosage forms, for example, are explained by the means and coefficients of variation of the disposition residence time and dissolution time distribution, respectively. The advantages of this concept compared to the conventional method of fitting sums of exponentials to the data are described.