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. Proceedings of the 24th Annual meeting of the Population Approach Group in Europe, 2-5 June 2015, Crete, Greece.


Objectives: To demonstrate the utility of a dose-response-time (DRT) model using a large preclinical biomarker dataset of nicotinic acid (NiAc) induced changes on free fatty acids (FFA).

Methods: Data were collected from studies where different rates, routes, and modes of NiAc provocations on the FFA time course had been tested [1]. All information of the exposure were excluded in order to use a DRT approach. Different models structures, describing the biophase kinetics, were assessed and quantitatively and qualitatively compared. The modeled biophase drug amount was assumed to act as the `driving force`of an inhibitory Imax-model which acted on the turnover of FFA. An integral feedback controller was used to model the slow adaptation process that forces FFA levels back to baseline values under long-term NiAc provocations. Finally, new numerical algorithms were applied, which rely on sensitivity equations to robustly and efficiently compute the gradients of the approximate population likelihood function in mixed-effects modelling [2].

Results: The DRT model successfully captured the behaviour of all FFA time courses. The model predicted 90% adaptation within four days of constant-rate infusions of NiAc, using rates that lead to therapeutic concentrations. High consistency of the pharmacodynamic parameters was shown when compared to an exposure-driven study by Tapani et al. [3]. Conclusions: The versatility of the DRT approach was shown by successfully fitting a DRT model to all FFA time courses. Different feedback mechanisms were described, using moderator compartments and integral feedback control. The consistency in the pharmacodynamic parameters, when comparing to an exposure-driven approach, demonstrates the utility of DRT analysis in a wider context.


[1] Ahlström C. Modelling of tolerance and rebound in normal and diseased rats. Dissertation, University of Gothenburg. 2011.

[2] Almquist J, Leander J, Jirstrand M. Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood. J Pharmacokin Pharmacodyn. 2015.

[3] Tapani S, Almquist J, Leander J, Ahlström C, Peletier LA, Jirstrand M, Gabrielsson J. Joint feedback analysis modeling of nonesterified fatty acids in obese Zucker rats and normal Sprague-Dawley rats after different routes of administration of nicotinic acid. J Pharm Sci. 2014.

Photo credits: Nic McPhee