title: Pharmacokinetic model identification and parameter estimation as an ill-posed problem.
abstract: For model identification and parameter estimation in the framework of linear pharmacokinetics it is most often assumed that the disposition function is a finite sum of exponential functions with time constants lambda i and associated coefficients Ci. Least-square fitting procedures are used to estimate the coefficients Ci and the corresponding discrete locations lambda i on the lambda-axes. This work presents an alternative approach. It does not assume that the non-zero coefficients are located at sharply defined values of lambda, but that they are represented by a continuous function h(lambda), the spectrum of the disposition function. This turns the non-linear least-square problem into a linear problem, which is known to be as so-called "ill-posed". Regularization methods have been developed in recent years as suitable tools for the treatment of such ill-posed problems. Application of Tikhonov regularization to the case of the bolus kinetics of propofol in 8 volunteers is demonstrated. In 7 of the 8 cases a spectrum with 4 to 5 peaks was found, and in one volunteer there were only 2 peaks. All spectra with more than 2 peaks showed negative values of h(lambda). The method used is described and the results are compared with those of conventional compartment analysis.
authors.affiliation: Klinik für Anästhesiologie und spezielle Intensivmedizin der Universität Bonn, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Schwilden
authors.forename: J
authors.initials: J
authors.lastname: Honerkamp
authors.forename: C
authors.initials: C
authors.lastname: Elster
mesh_terms: D006801:Humans; D008954:Models, Biological; D010599:Pharmacokinetics; D015742:Propofol / Q000008:administration & dosage / Q000097:blood / Q000493:pharmacokinetics
chemical_list: D015742:Propofol