The Use of a Sum of Inverse Gaussian Functions to Describe the Absorption Profile of Drugs Exhibiting Complex Absorption

Purpose

The aim of this study was to evaluate the utility of a parametric deconvolution method using a sum of inverse Gaussian functions (IG) to characterize the absorption and concentrations vs. time profile of drugs exhibiting complex absorption.

Methods

For a linear time-invariant system the response, Y(t), following an arbitrary input function I(t), is the convolution of I(t) with the disposition function, H(t), of the system: $Y{\left( t \right)} = {\int\limits_0^t {I{\left( \tau \right)}H{\left( {t - \tau } \right)}d\tau } }$. The method proposed uses a sum of n inverse Gaussian functions to characterize I(t). The approach was compared with a standard nonparametric method using linear splines. Data were provided from previously published studies on two drugs (hydromorphone and veralipride) showing complex absorption and analyzed with NONMEM®.

Results

A satisfactory fit for hydromorphone and veralipride data following oral administration was achieved by fitting a sum of two or three IG functions. The predictions of the input functions were very similar to those using linear splines.

Conclusions

The use of a sum of IG as opposed to nonparametric functions, such as splines, offers a simpler implementation, a more intuitive interpretation of the results, a built-in extrapolation, and an easier implementation in a population context. Disadvantages are an apparent greater sensitivity to initial value estimates (when used with NONMEM®).