This study presents an extensive dose-response-time (DRT) meta-analysis of the nicotinic acid-induced inhibition of free fatty acids and insulin release. The purpose was to quantify the implications of lacking exposure data when analysing complex pharmacodynamic systems. The DRT model successfully characterised various response behaviours-including time-delays, rebound, feedback mechanisms, and adaptation-on both the individual and the population level. Comparing the fitted DRT model to an exposure-driven reference analysis showed that bias and uncertainty were introduced in the parameter estimates. However, most estimates were within one standard error from the reference. In both approaches, a few parameters suffered from practical identifiability issues, likely due to large differences in half-lives of the different rate processes. Moreover, the optimal dosing strategies predicted by the DRT model differed slightly from those of the exposure-driven analysis, having a lower optimal steady-state reduction of free fatty acids exposure.

The most common approach to in vivo pharmacokinetic and pharmacodynamic analyses involves sequential analysis of the plasma concentration- and response-time data, such that the plasma kinetic model provides an independent function, driving the dynamics. However, in situations when plasma sampling may jeopardize the effect measurements or is scarce, nonexistent, or unlinked to the effect (e.g., in intensive care units, pediatric or frail elderly populations, or drug discovery), focusing on the response-time course alone may be an adequate alternative for pharmacodynamic analyses. Response-time data inherently contain useful information about the turnover characteristics of response (target turnover rate, half-life of response), as well as the drug's biophase kinetics (biophase availability, absorption half-life, and disposition half-life) pharmacodynamic properties (potency, efficacy). The use of pharmacodynamic time-response data circumvents the need for a direct assay method for the drug and has the additional advantage of being applicable to cases of local drug administration close to its intended targets in the immediate vicinity of target, or when target precedes systemic plasma concentrations. This review exemplifies the potential of biophase functions in pharmacodynamic analyses in both preclinical and clinical studies, with the purpose of characterizing response data and optimizing subsequent study protocols. This article illustrates crucial determinants to the success of modeling dose-response-time (DRT) data, such as the dose selection, repeated dosing, and different input rates and routes. Finally, a literature search was also performed to gauge how frequently this technique has been applied in preclinical and clinical studies. This review highlights situations in which DRT should be carefully scrutinized and discusses future perspectives of the field.

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc–FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague–Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional \(I_{\text{max}}\) model. Insulin was incorporated in parallel with NiAc as the main endogenous co-variate of FFA dynamics. The model captured profound insulin resistance and complete drug resistance in obese rats. The efficacy of NiAc as an inhibitor of FFA release went from 1 to approximately 0 during sustained exposure in obese rats. The potency of NiAc as an inhibitor of insulin and of FFA release was estimated to be 0.338 and 0.436 \({\upmu {\text{M}}}\), respectively, in obese rats. A range of dosing regimens was analyzed and predictions made for optimizing NiAc delivery to minimize FFA exposure. Given the exposure levels of the experiments, the importance of washout periods in-between NiAc infusions was illustrated. The washout periods should be \(\sim\)2 h longer than the infusions in order to optimize 24 h lowering of FFA in rats. However, the predicted concentration-response relationships suggests that higher AUC reductions might be attained at lower NiAc exposures.

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. References: [1] Ahlstrom 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, Ahlstrom 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.

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.

Background: Structural identifiability concerns whether the parameters in a postulated model structure can be uniquely determined given the input and output functions to and from that model. What this means in practice is that if a model is structurally unidentifiable, the model structure itself allows a subset (or all) of the model parameters to vary while the model output remains unchanged. Conclusions drawn from such a model are potentially unreliable. For instance, if the estimated value of Emax is of interest, but if Emax is a member of the subset of unidentifiable parameters as a result of the model structure, the estimated value of Emax is effectively meaningless. For deterministic models, there exist several different structural identifiability analysis techniques for both linear and nonlinear systems. However, little has been done on the identifiability analysis of models having a mixed-effects framework. Here the main challenge comes from the fact that, apart from having a deterministic part describing the typical individual, there is also an additional statistical sub-model describing the random effects for the parameters and the covariance between them. In population modelling, these parameters represent the variability in the population. Since estimation of the variability is often one of the main goals in population modelling, it is important to determine whether these parameters can be uniquely determined or otherwise. This motivates the need to extend the concept of structural identifiability for deterministic models to non-deterministic models such as mixed-effects models. Aim: To develop ways of analysing structural identifiability in mixed-effects models. Methods: In statistics, and in particular statistical inference, there exist problems which are similar to those encountered in parameter estimation for mixed-effect models. In this work, we make use of these similarities and use these relevant relations to study structural identifiability in mixed-effects models. Results: Some initial results from a structural identifiability analysis on a particular mixed-effects model structure are presented.