Roberto Bizzotto (1), Bo Ahrén (2), Andrea Mari (1)
(1) Neuroscience Institute, National Research Council, Padova, Italy; (2) Department of Clinical Sciences, Lund University, Lund, Sweden
Objectives: The estimation of a model input by deconvolution is a complex problem which has been addressed in multiple ways [1]. Restrictive assumptions were made when employing mixed-effect methods [2]. Using data of paracetamol kinetics, we developed a new mixed-effect approach estimating the autocorrelation of non-parametric input functions and we compared its performance with a previously developed single subject deconvolution method based on regularized least square estimation.
Methods: Paracetamol plasma concentration was measured after ingestion of a tablet (1.5 g) dissolved in a liquid meal with variable composition [3]. The kinetics profiles (N=52) from 38 subjects were analysed with a two-compartmental distribution model (with typical parameter values as from the literature [4]) and a non-parametric representation of the rate of appearance of oral paracetamol (RaO). A mixed-effect implementation was developed with Monolix, in which inter-individual variability (IIV) is assumed on all parameters and RaO is the piecewise linear interpolation of log-normal parameters estimated at 10-min intervals and correlated between each other. This method (A) was compared with a single-subject implementation (B) assuming no IIV on kinetic parameters and a piecewise constant RaO with 2-min steps, determined with Matlab through regularized least square estimation with minimization of the second derivatives [5], [6].
Results: The correlation between the estimated RaO integrals was 89%. Method A produced a worse fit of the data: the coefficient of variation for the residual error was 20.6% vs 10.3%. However, the derived median bioavailability was more in line with literature values (60% to 90% [4]): 66% vs 47%. Moreover, A ensures RaO is always positive, whilst B produced negative values whose integral was 31% (median) of the positive values integral. Method A produced sharper Rao profiles: the mean number of peaks above 50 μmol/min was 2.1 vs 1.6, and the median standard deviation of the differences in RaO over 2-min intervals was 13.6 μmol/min vs 9.0 μmol/min.
Conclusions: Compared to a traditional single-subject deconvolution method, a new mixed-effect approach applied on paracetamol data revealed to be more reliable in terms of bioavailability estimation and could fit the data with always positive, although highly variable, rates of appearance. This method may prove useful in many scenarios, e.g. for the assessment of gastric emptying.
References:
[1] D. Commenges, “The deconvolution problem: Fast algorithms including the preconditioned conjugate-gradient to compute a MAP estimator,” IEEE Trans. Autom. Control, vol. 29, no. 3, pp. 229–243, Mar. 1984.
[2] K. E. Fattinger and D. Verotta, “A nonparametric subject-specific population method for deconvolution: I. Description, internal validation, and real data examples,” J. Pharmacokinet. Biopharm., vol. 23, no. 6, pp. 581–610, Dec. 1995.
[3] W. Alsalim, A. Tura, G. Pacini, B. Omar, R. Bizzotto, A. Mari, and B. Ahrén, “Mixed meal ingestion diminishes glucose excursion in comparison with glucose ingestion via several adaptive mechanisms in people with and without type 2 diabetes,” Diabetes Obes. Metab., vol. 18, no. 1, pp. 24–33, Jan. 2016.
[4] M. D. Rawlins, D. B. Henderson, and A. R. Hijab, “Pharmacokinetics of paracetamol (acetaminophen) after intravenous and oral administration,” Eur. J. Clin. Pharmacol., vol. 11, no. 4, pp. 283–286, Apr. 1977.
[5] D. L. Phillips, “A Technique for the Numerical Solution of Certain Integral Equations of the First Kind,” J ACM, vol. 9, no. 1, pp. 84–97, Jan. 1962.
[6] S. Twomey, “The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements,” J. Frankl. Inst., 1965.
Reference: PAGE 25 (2016) Abstr 5985 [www.page-meeting.org/?abstract=5985]
Poster: Methodology - New Modelling Approaches