How do we develop a ‘standard’ population PK model? We obtain blood/plasma concentrations over time of the drug of interest, in multiple individuals, and we apply our population NLME modelling techniques to quantify the parameters. This data is sufficient to provide us with information on the absorption rate constant, the volume of distribution, the clearance, and the inter-individual variability in the population.
Now, lets say that the parent compound is partially converted to a metabolite by a CYP enzyme in the liver. We already have the blood samples collected which we can analyse for the metabolite concentrations with our assay. Can we extract the same amount of information on the metabolite pharmacokinetics as we did for the parent compound based on this information? Unfortunately, the answer is no. Have a look at the following research questions that we cannot answer using this data without making some serious assumptions:
Research questions in parent-metabolite studies:
- What is the volume of distribution of the metabolite?
- What is the fraction of the parent that is metabolized?
- Did the fraction metabolized change in this new population that we have studied?
Parameter identifiability
The first item that we need to clarify is that when we add the metabolite data to the model, we need to add some new parameters to our PK model.
Once we have the structural model of the parent, we have identified a total clearance of the parent compound. This clearance is actually divided in 2 parts, the unchanged elimination of the parent and the part that is metabolized to the metabolite. This fraction then goes to the central compartment of the metabolite, from which the metabolite is eliminated. See the structural outline of this model below:
The problem that arises is the following: what fraction of the total amount of the parent that is eliminated gets metabolized to the metabolite?
Since we only measure the parent and metabolite observations, we are unable to quantify if a large fraction is metabolized which gets diluted in a large metabolite volume or if only a small fraction is metabolized which moves to a small distribution volume. Both scenario’s would result in exactly the same metabolite concentrations, highlighting the point of parameter (un)identifiability. Multiple combinations of parameters exist that result in exactly the same predictions.
Assumptions
In order to solve the parameter identifiability issues we encounter in the modelling of metabolite data, we need to make assumptions in the model:
- The parent is fully converted to the metabolite.
- The volume of distribution of the metabolite is equal to the volume of the parent
- Fix model parameters to literature values
Assumption 1: The parent is fully converted to the metabolite.
This assumption is similar to the modelling of an oral drug, from which we can’t quantify the bioavailability parameter. This results in the parameters being defined as V/F, in which for example the volume of distribution is scaled by the F.
In this case, the metabolite parameters would be scaled by the fraction that is metabolized and we can estimate the metabolite parameters. With this assumption, it is important to note that when we identify a covariate relationship on the volume of the metabolite, this may actually originate from differences in the formation rate. The volume of distribution for the metabolite should thus be reported as V/(fraction metabolized) and the limitations of this assumption should be discussed.
Assumption 2 + 3
If there is sufficient literature information and/or biochemical information present on the parent and the metabolite, you can identify whether it is expected that there would be significant differences in the distribution volume between the parent and metabolite. Fixing the volume enables us to once again estimate both clearances routes of the parent compound and quantify the fraction metabolized.
However, fixing a parameter to literature values always has the intrinsic challenge that the study design, population, age/weight range, etc. should be as similar as possible to the literature study. Differences between studies may introduce a bias in the results and therefore in the interpretation of the results of such a model.
The solution
The solution to all these problems in is in the pee. Once we have information on the total amount excreted in a certain time period (e.g. 24h), or preferably in different time intervals (0-6h, 6-12h, 12-4h) we can calculate the total amount of mass transfer via each route. This enables the estimation of all parameters in our model and enables us to answer all of the research questions defined above!
So what if this is not possible? There are many scenario’s that we can imagine in which the collection of urine is not feasible or if it is a retrospective study, in which no changes to the study design can be made and the pharmacometrician is contacted afterwards. If this is the case, take note of all the assumptions that need to be made in the metabolite model and the resulting effect that these assumptions have on the estimated parameters. Providing information on the PK of a metabolite without urine data is still highly valuable, the modelling process and the assumptions made should therefore be correctly documented to be adapted and implemented in new models once urine data becomes available.
General note
More information? The authors Ahlers and Välitalo et al. have written a very nice piece on this topic in the appendix of their manuscript:
https://insights.ovid.com/pubmed?pmid=26332855
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