Modelling Red Blood Cell Data

The overarching aim of this work was to utilise modelling and simulation methodology to obtain a better understanding of clinical data generated from or in red blood cells (RBCs). It focussed on RBC survival and the use of RBCs as a matrix for pharmacokinetic (PK) data. Firstly, a novel statistical model for RBC survival was developed based on prior knowledge of the underlying physiological mechanisms using a bottom-up model building approach. The model was developed within the statistical framework of survival analysis and uses a highly flexible probability density function to describe a hypothetical RBC lifespan distribution that is able to account for plausible physiological processes of RBC destruction. These mechanisms include death due to old age (senescence), random destruction, and early or delayed failure. The model was extended to describe in vivo RBC survival studies using different RBC labelling techniques and flaws inherent in the most commonly used labelling methods. Using an information theoretical approach, it was determined that full parameter estimation would be possible based on ideal labelling methods, but also based on the currently available, flawed labelling methods under an optimised study design with an intensive sampling strategy. The model was applied to in vivo RBC survival data obtained in patients with chronic kidney disease (CKD) as well as healthy controls (using data obtained from the work of other investigators). RBC survival was found to be significantly reduced in CKD patients compared to controls, and the results suggest that increased random destruction is the likely cause of this reduction rather than accelerated senescence. Secondly, a catenary compartment model describing the intracellular population PK of methotrexate (MTX) and its polyglutamated metabolites (MTXPGs) in RBCs was developed using a data driven, top-down modelling approach. Model development was based on data obtained from 48 patients with rheumatoid arthritis (RA) receiving once weekly low-dose MTX. The developed model was used to test different hypotheses related to the mechanism of enzymatic deglutamation of MTXPGs, the loss of MTXPGs from RBCs, and the significance of genotypic and phenotypic covariates. The final model was able to describe the time profiles of MTX and MTXPGs inside RBCs in all 48 patients, and thus can form the basis of a full pharmacokinetic-pharmacodynamic (PKPD) model for low-dose MTX treatment in RA in future work. Such a PKPD model could be used to assess whether RBC MTX or MTXPG concentrations are suitable biomarkers to monitor low-dose MTX treatment, which is currently debated in literature. In conclusion, two different approaches were successfully applied in this thesis to develop mathematical models that are able to describe different types of RBC derived clinical data: a novel statistical RBC survival model that is able to provide a deeper insight into physiological processes of RBC destruction in the future, and a compartmental PK model describing the intracellular accumulation of MTX and MTXPGs in RBCs that can form the basis of a full PKPD model in further work