Pharmacokinetic model identification and parameter estimation as an ill-posed problem

• Published in: European journal of clinical pharmacology 1993-12, Vol.45 (6), p.545-550
• Main Authors: SCHWILDEN, H, HONERKAMP, J, ELSTER, C
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; General pharmacology; Humans; Medical sciences; Models, Biological; Pharmacokinetics; Pharmacokinetics. Pharmacogenetics. Drug-receptor interactions; Pharmacology. Drug treatments; Propofol - administration & dosage; Propofol - blood; Propofol - pharmacokinetics
• ISSN: 0031-6970; 1432-1041
• DOI: 10.1007/BF00315312

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.