  In this paper, we use Time Scale Calculus (TSC) to formulate and solve
pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical
framework that allows the modeling of dynamical systems comprising continuous
and discrete processes. This characteristic makes TSC particularly suited for
multi-dose pharmacokinetic problems, which inherently feature a blend of
continuous processes (such as absorption, metabolization, and elimination) and
discrete events (drug intake). We use this toolkit to derive analytical
expressions for blood concentration trajectories under various multi-dose
regimens across several flagship pharmacokinetic models. We demonstrate that
this mathematical framework furnishes an alternative and simplified way to
model and retrieve analytical solutions for multi-dose dynamics. For instance,
it enables the study of blood concentration responses to arbitrary dose
regimens and facilitates the characterization of the long-term behavior of the
solutions, such as their steady state.
