Simulating pharmacokinetic and pharmacodynamic fuzzy-parameterized models: a comparison of numerical methods

Statistical techniques have been traditionally used to deal with parametric variation in pharmacokinetic and pharmacodynamic models, but these require substantial data for estimates of probability distributions. In the presence of limited, inaccurate or imprecise information, simulation with fuzzy numbers represents an alternative tool to handle parametric uncertainty. Existing methods for implementing fuzzy arithmetic may, however, have significant shortcomings in overestimating (e.g., conventional fuzzy arithmetic) and underestimating (e.g., vertex method) the output uncertainty. The purpose of the present study is to apply and compare the applicability of conventional fuzzy arithmetic, vertex method and two recently proposed numerical schemes, namely transformation and optimization methods, for uncertainty modeling in pharmacokinetic and pharmacodynamic fuzzy-parameterized systems. A series of test problems were examined, including empirical pharmacokinetic and pharmacodynamic models, a function non-monotonic in its parameters, and a whole body physiologically based pharmacokinetic model. Our results verified that conventional fuzzy arithmetic can lead to overestimation of response uncertainty and should be avoided. For the monotonic pharmacokinetic and pharmacodynamic models, the vertex method accurately predicted fuzzy-valued output while incurring the least computational cost. It turned out that the choice of a suitable method for fuzzy simulation of the non-monotonic function depended on the required accuracy of the results: the vertex method was capable of eliciting an initial approximate solution with few function evaluations; for more accurate results, the transformation method was the most superior approach in terms of accuracy per unit CPU time.