On the computation of output bounds on parallel inputs pharmacokinetic models with parametric uncertainty

Pharmacokinetic models are of utmost importance in drug and medical research. The class of parallel inputs models consists of two or more linear chains connected together in parallel. It has been used to represent pharmacokinetic processes in which the input shows effects on the output with different delays in time.Due to physiological variability, the exact values of the model parameters are uncertain, but they can be bounded by intervals. In this case, the computation of output bounds can be posed as the solution of an initial value problem (IVP) for ordinary differential equations (ODEs) with uncertain initial conditions. However, current methods may produce a significant overestimation.In this paper, a new method to minimise overestimation when using the parallel inputs model is proposed and applied to two cases: subcutaneous insulin absorption for artificial pancreas research, and the study of the double-peak phenomenon observed for certain drugs. Our proposal consists in performing a model reduction in conjunction with analytical solutions of the input chains and a monotonicity analysis of model states and parameters. This method allows obtaining tighter output bounds with low computational cost compared to the latest techniques.