An integer programming approach for optimal drug dose computation

Fractional calculus in pharmacokinetics

We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics". The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.

Identification and experimental validation of an HIV model for HAART treated patients

The objective of this paper is to identify the parameters of a human immunodeficiency virus (HIV) evolution model from a clinical data set of patients treated with two different highly active antiretroviral therapy (HAART) protocols. After introducing a model with six state variables, a preliminary step considers the reduction of the number of parameters to be identified by means of sensitivity analysis, and then identifiability items are discussed. A nonlinear optimization-based procedure for identification is developed, which divides the unknown parameters into two families: the group dependent and the patient dependent parameters. Numerical results show that the identified model can be individually adapted to each patient and this result is promising for predicting the effects (e.g., failures or successes) of therapeutic actions.