Dose-response-time modelling: Second-generation turnover model with integral feedback control

R. Andersson, M. Jirstrand, L. Peletier, M. J. Chappell, N. D. Evans, J. Gabrielsson. European Journal of Pharmaceutical Sciences, Vol 81, 1 January 2016, 189–200


This study presents a dose–response-time (DRT) analysis based on a large preclinical biomarker dataset on the interaction between nicotinic acid (NiAc) and free fatty acids (FFA). Data were collected from studies that examined different rates, routes, and modes of NiAc provocations on the FFA time course. All information regarding the exposure to NiAc was excluded in order to demonstrate the utility of a DRT model. Special emphasis was placed on the selection process of the biophase model. An inhibitory Imax-model, driven by the biophase amount, acted on the turnover rate of FFA. A second generation NiAc/FFA model, which encompasses integral (slow buildup of tolerance — an extension of the previously used NiAc/FFA turnover models) and moderator (rapid and oscillatory) feedback control, was simultaneously fitted to all time courses in normal rats. The integral feedback control managed to capture an observed 90% adaptation (i.e., almost a full return to baseline) when 10 days constant-rate infusion protocols of NiAc were used. The half-life of the adaptation process had a 90% prediction interval between 3.5–12 in the present population. The pharmacodynamic parameter estimates were highly consistent when compared to an exposure-driven analysis, partly validating the DRT modelling approach and suggesting the potential of DRT analysis in areas where exposure data are not attainable. Finally, new numerical algorithms, which rely on sensitivity equations to robustly and efficiently compute the gradients in the parameter optimization, were successfully used for the mixed-effects approach in the parameter estimation.

Authors and affiliations

  • Robert Andersson, School of Engineering, University of Warwick, Coventry, United Kingdom
  • Mats Jirstrand, Fraunhofer-Chalmers Centre, Chalmers Science Park, Göteborg, Sweden
  • Lambertus Peletier, Mathematical Institute, Leiden University, Leiden, The Netherlands
  • Michael J. Chappell, School of Engineering, University of Warwick, Coventry, United Kingdom
  • Neil D. Evans, School of Engineering, University of Warwick, Coventry, United Kingdom
  • Johan Gabrielsson, Division of Pharmacology and Toxicology, Department of Biomedical Sciences and Veterinary Public Health, Swedish University of Agriculture Sciences, Uppsala, Sweden

Photo credits: Nic McPhee