Mathematics of Pharmacokinetics and Pharmacodynamics: Diversity of Topics, Models and Methods

Abstract

A short review on pharmacokinetics-pharmacodynamics (PK-PD) presented below aims to show the evolution of some concepts and ideas in this field. Some of them are developed in more detail in the papers of this issue. The key question for a practical application of PK-PD models is the ability to estimate the model parameters using patients data. In [1] a novel approach to an accurate quantification of the uncertainty in parameter estimates attributed to inter-individual variability is proposed. The analyzed PK-PD model is formulated as a compartmental ODE system. The methodology of recognizing and capturing the uncertainty in predicted quantities of interest due to inter-individual variability when the individual is not available for repeated measurements may prove to be invaluable in the risk assessment of future experiments and drug applications. Anticancer molecular PK-PD in a cell population dynamics model with drug delivery optimisation is discussed in [2]. The works [3] and [4] deal with various aspects of hemostasis modelling, and [5] with metabolic aspects in a whole-body setting. These studies represent the diversity of aspects of PK-PD modelling nowadays: theoretical about parameter estimation in general versus applied to medical questions in particular, localised cell population versus whole-body settings, cell population and whole-body versus patient population settings.

Improving cancer treatments via dynamical biophysical models

“…It also includes what the body does to the drug, namely its pharmacokinetics (PK), resulting in so-called PK-PD models [95].…”

“…Anticancer drugs are most of the time delivered to the whole organism, so that constraints on their toxicity to healthy cells, and acquired resistance, by adaptation, of cancer cell populations to their use should as much as possible be considered. These are the elements of any optimization scenario in oncology: given targets to be hit and For such drugs, some must be known of their mechanisms of action and, in as much as their use should go to clinical oncology, of their fate in the organism before they reach their targets, i.e., as detailed in Section 2.2, the object of PK-PD [95]. Optimization of pharmacotherapy concerns mainly pharmacodynamics, as pharmacokinetics have only to be known, not modified, to represent the journey from actual delivery to the patient by infusion or ingestion to the wanted as well as unwanted drug targets.…”