PHARMACOKINETIC MODEL IDENTIFICATION AND PARAMETER-ESTIMATION AS AN ILL-POSED PROBLEM

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 C(i). Least-square fitting procedures are used to estimate the coefficients C(i) 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''. Regularisation methods have been developed in recent years as suitable tools for the treatment of such ill-posed problems. Application of Tikhonov regularisation 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.