A HIERARCHICAL FUNCTIONAL DATA ANALYTIC APPROACH FOR ANALYZING PHYSIOLOGICALLY BASED PHARMACOKINETIC MODELS.

Ordinary differential equation (ODE) based models find application in a wide variety of biological and physiological phenomena. For instance, they arise in the description of gene regulatory networks, study of viral dynamics and other infectious diseases, etc. In the field of toxicology, they are used in physiologically based pharmacokinetic (PBPK) models for describing absorption, distribution, metabolism and excretion (ADME) of a chemical in-vivo. Knowledge about the model parameters is important for understanding the mechanism of action of a chemical and are often estimated using non-linear least squares methodology. However, there are several challenges associated with the usual methodology. Using functional data analytic methodology, in this article we develop a general framework for drawing inferences on parameters in models described by a system of differential equations. The proposed methodology takes into account variability between and within experimental units. The performance of the proposed methodology is evaluated using a simulation study and data obtained from a benzene inhalation study. We also describe a R-based software developed towards this purpose.