Isabelle Kuan (1), Daniel Wright (1), Stephen Duffull (1)
(1) School of Pharmacy, University of Otago, New Zealand
Objectives: The term ‘flip-flop’ is used to describe the scenario where the rate constant of absorption and rate constant of elimination for extravascularly administered drugs can swap over. Drugs that undergo absorption limited elimination (where k > ka) are often said to be ‘flip-flop’ but in reality they are usually just ‘flip’ or ‘flop’ although during estimation a local search algorithm may swap them several times during the search. Of note, flip-flop can occur (between patients) for a drug with slow absorption from the gastrointestinal tract and with rapid and extensive renal clearance. In this setting, for patients with normal renal function the usual finding will be that k > ka, however in patients with impaired renal function we may find k < ka.
Flip-flop pharmacokinetics is in reality a permutation of the rank order of the parameter values and is therefore an issue of local identifiability in that there exists a finite set of parameters values (rather than a single set) that solves for the problem. The simplest example is a one compartment model with first-order input and output which has two sets of permutations of parameter values that provide the same input-output relationship. The possible permutations (using CL, V, ka parameterisation) are: (i) ka’=ka, CL’=CL, V’=V and (ii) ka’=CL/V, CL’=CL, V’=CL/ka. Here, it can be seen that volume of distribution (V) becomes a function of clearance (CL) and ka, and, that CL is invariant to flip-flop where AUC=Dose/CL irrespective of whether the system is in a state of ‘flip’ or ‘flop’. Note here that non-compartmental analyses are unaffected by a model being in either a ‘flip’ or a ‘flop’ state.
In theory, the issue of local identifiability (flip-flop behaviour) can be addressed by incorporating a mechanistic model of the absorption and elimination that accounts for the underlying processes. This is, however, generally not possible in a standard top-down estimation setting. A simpler alternative is to consider that there is a value of the function of the elimination organ at which the absorption and elimination rate constants flip around and that this transition cut-off value could be estimated. The model could then be stabilised into either its flip or flop state for any given individual and hence avoid flip-flop to yield a globally identifiable model.
We apply the concept of a transition cut-off to pharmacokinetic data arising from metformin. Metformin is an antihyperglycaemic agent that is reported to exhibit absorption mediated elimination [1, 2]. It is predominantly renally eliminated as unchanged drug via tubular secretion [1, 3]. However, it is not known if and at what level of renal impairment does the terminal slope of metformin’s concentration profile change from being absorption rate limited to elimination rate limited.
The aim of this research was to explore the influence of flip-flop in population PK models using metformin as a motivating example. The specific objectives were to:
- Determine whether it is possible to estimate the flip-flop change point in order to parameterise a model that disallows flip-flop
- Investigate the application of constraining parameters to address flip-flop
- Investigate whether the inclusion of IV data addresses issues associated with flip-flop
- Investigate the influence of flip-flop kinetics using covariate modelling
Methods: A one compartment PK model with first-order absorption and elimination were implemented with parameter constraints using an estimated flip-flop transition point (believed to be when CL/V=ka) to force the relative relationship between calculated k and ka to be: (i) k>ka in subjects with a CL greater than the flip-flop transition point, and, (ii) k
The PK models were run with PO concentration data only, and, PO and IV concentration data. The models were parameterised using: (i) CL, V, ka and (ii) k, V, ka.
The application of parameter constraints was assessed by calculating the percentage of cases whose empirical Bayesian estimates (EBEs) were as theoretically anticipated (i.e. k>ka in subjects with a CL > flip-flop transition point and k
The models were implemented using NONMEM (version 7.3) using the first-order conditional estimation method with interaction for parameter estimation. Pre- and post- processing was conducted using Perl-speaks-NONMEM (version 4.9.0) and R (version 3.5.3).
Data. A total of 426 plasma metformin concentrations were available from 55 subjects with varying levels of renal function (CLcr ranging from 14.8 to 165.3 mL/min). All subjects received metformin PO, with three subjects receiving metformin both PO and IV.
Results: A flip-flop change point could not be estimated from the data available for analysis and was therefore chosen based on theoretical considerations. The fully constrained model performed the best at constraining the rank order of model parameters. This was demonstrated by the rank order of EBEs always being as theoretically anticipated when using the fully constrained model. The rank order of output EBEs for subjects with PO and IV data were always as theoretically anticipated regardless of whether the model was constrained. This indicates the presence IV data for some subjects can address issues of local identifiability across all. A relationship was identified between CLcr and ka for the unconstrained model in circumstances when the relationship between CLcr and CL (or k) had not been accounted for. This finding aligns with other reports in the literature [4]. We believe this is spurious.
Conclusions: In this study, we explore the influence of the ‘flip-flop’ problem in modelling and propose an approach to solve the ‘flip-flop’ problem in population PK modelling. In the absence of IV data a fully constrained design is needed. Unattended flip-flop may result in spurious relationships being found. Denser data may allow for the flip-flop transition point to be found.
References:
[1] Pentikainen PJ, Neuvonen PJ, Penttila A. Pharmacokinetics of metformin after intravenous and oral administration to man. Eur J Clin Pharmacol. 1979;16(3):195-202.
[2] Tucker GT, Casey C, Phillips PJ, Connor H, Ward JD, Woods HF. Metformin kinetics in healthy subjects and in patients with diabetes mellitus. British journal of clinical pharmacology. 1981;12(2):235-46.
[3] Sirtori CR, Franceschini G, Galli-Kienle M, Cighetti G, Galli G, Bondioli A et al. Disposition of metformin (N,N-dimethylbiguanide) in man. Clinical pharmacology and therapeutics. 1978;24(6):683-93.
[4] Hutmacher MM, Kowalski KG. Covariate selection in pharmacometric analyses: a review of methods. British journal of clinical pharmacology. 2015;79(1):132-47. doi:10.1111/bcp.12451.
Reference: PAGE () Abstr 9312 [www.page-meeting.org/?abstract=9312]
Poster: Oral: Methodology - New Modelling Approaches