Pharmaceutical Research

, Volume 22, Issue 8, pp 1227–1235 | Cite as

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

  • Chantal Csajka
  • David Drover
  • Davide VerottaEmail author
Research Paper


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.


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®.


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.


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®).

Key Words

complex absorption input model inverse Gaussian functions pharmacokinetics splines 



This study was supported by NIH Grant A150587.


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Biopharmaceutical SciencesUniversity of CaliforniaSan FranciscoUSA
  2. 2.Department of AnesthesiaStanford University School of MedicineStanfordUSA
  3. 3.Department of BiostatisticsUniversity of CaliforniaSan FranciscoUSA

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