Variance based Global Sensitivity Analysis of a Physiological Absorption model for compounds in different BCS classes
Nicola Melillo (1,2), Leon Aarons (2), Paolo Magni (1) and Adam S. Darwich (2).
(1) Laboratory of Bioinformatics, Mathematical Modelling and Synthetic Biology, Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy. (2) Centre for Applied Pharmacokinetic Research, Division of Pharmacy & Optometry, The University of Manchester, Manchester, UK.
Objectives:
There is a strong regulatory interest in the use of sensitivity analysis to evaluate physiologically-based pharmacokinetic models for use in pharmaceutical research & development [1]. One possible application is the prediction of fraction absorbed and bioavailability for drugs following oral administration. The OrBiTo project (Innovative Medicines Initiative) executed a large scale evaluation of various physiological models for drug absorption, where the results showed high variability in the performance [2]. In this context, we performed a variance based global sensitivity analysis (GSA) on an in-house compartmental physiological model for drug absorption, with the aim of identifying key parameters that influence the fraction absorbed. This analysis was done for four different classes of drugs according to the Biopharmaceutics Classification System, differentiating compounds by permeability and solubility.
Methods:
Variance based GSA aims to quantify the importance of each model parameter with respect to a model output Y, considering all the parameters in their whole range of variation. Two sensitivity indices are derived by the decomposition of the variance (V) of Y [3, 4]. These indices are known as the main effect Si and total effect STi. They are always between 0 and 1. The higher Si and STi are, the more the i-th parameter explains V(y) and so the more important it is. Conversely, a parameter is considered less important if has low STi.
A variance based GSA was performed on an in-house compartmental absorption model, based on the CAT model [5], for neutral, acidic and basic compounds for each of the four BCS classes: class I (highly permeable, highly soluble); class II (highly permeable, lowly soluble); class III (lowly permeable, highly soluble); and class IV (lowly permeable, lowly soluble).
The input parameter that controlled the absorption was the absorption rate constant ka, that was derived from human effective jejunal permeability, Peff. The cut-off value for Peff that distinguish between high and low permeability was set to 1.5x10-4 cm/s, according to [6]. One parameter that could distinguish between high and low solubility is the dose number D0 [7, 8]. If D0<1 a compound is highly soluble, while if the D0>1 it has low solubility [8].
Results:
Considering the neutral case, for class I drugs given at doses up to 100 mg, the most important parameters for the fraction absorbed were related to the dissolution, whereas for a dose of 1000 mg the key parameters were related to absorption. This could be explained given the fact that within a certain class, drugs administered with higher doses have typically higher solubility, so, for these drugs the rate limiting step is no longer the dissolution, but the absorption.
For class II neutral drugs the most important parameters were always related to the dissolution process. For class III compounds administered at low doses (0.1, 1, 10 mg) a similar situation was observed as for class I drugs, most likely because the dissolution process was not fast enough and became the rate limiting step. At higher doses, an increased importance of absorption processes was observed. This happens because there is an increase in the dissolution and so the rate limiting step becomes the absorption. A more complicated situation was seen for class IV compounds, where parameters related to both dissolution and absorption were always important.
For an acidic drug, the results were similar to the case of a neutral one. For basic compounds the results started to deviate compared to the previous cases. One difference was that the drug’s pKa became the most important parameter up to doses of 10 mg in class I and for all the doses in classes II and IV. This could happen because, dependent on the value of pKa, the solubility in the stomach may be enhanced, compared to the small intestine.
Conclusions:
In mechanistic physiological models we often encounter uncertainty in the parameters values. Typically, when these models are used, there is a tendency to fix some uncertain parameters to their mean value or to use in silico methods, such as QSAR models, to predict parameter values, without sufficiently exploring the impact on model development and on predictions.
This work aimed to identify the importance of different parameters for varied types of drugs, to improve the knowledge of the model and inform the choice of what parameters that need to be more carefully considered.
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