Extended mathematical model for “in vivo” quantification of the interaction betweeen atazanavir and bilirubin

Abstract

The objective of the present work was to conduct an "in vivo" analysis of the atazanavir-bilirubin interaction. We developed a new mathematical approach to PK/PDPK models for competitive interaction based on the Michaelis-Menten equation, which was applied to patients with polymorphisms in the gene for UDP-glucuronosyltransferase 1A1 (UGT1A1). Atazanavir is known to induce concentration-dependent increases in bilirubin plasma levels. Thus, we employed our mathematical model to analyse rises in steady state atazanavir and bilirubin concentrations, ultimately plotting a nomogram for detection of suboptimal atazanavir exposure. Application of our model revealed that an absolute value or a steady state increase in bilirubin falling below 3.8Φ µmol/L (where Φ is a correction factor, =1 for UGT1A1 wild type and ≠1 for UGT1A1 variants) could be used to predict suboptimal atazanavir exposure and treatment failure. Thus, we have successfully established a new mathematical approach for pharmacodynamic-pharmacokinetic modelling of the interaction between atazanavir and bilirubin, as it relates to genetic variants of UGT1A1. Taken together, our findings indicate that bilirubin plasma levels represent a valuable marker of atazanavir exposure.