Abstract
Quantitative systems pharmacology (QSP) modelling, being an integral part of pharmacometrics, is attracting a great amount of attention in drug development and clinical therapy as QSP models are used to identify drug targets and biomarkers of response. The QSP model based approach was used to address the clinical challenges with azathioprine dosing in inflammatory bowel disease. The Overarching aim of the thesis was to understand unknown mechanism to toxicities associated with azathioprine metabolism using a QSP approach. However some unanticipated challenges resulted during development of the azathioprine QSP model which, ultimately, was found to not be able to describe the various clinical scenarios. These challenges did, however, provide an opportunity to understand some issues that might arise during QSP model development and develop methods to solve them.
A 30 state QSP model was developed for azathioprine metabolism based on known purine metabolic pathways supported by literature and expert opinion (Chapter 2). The model provided a good prediction of both extraceullar and intracellular metabolite formation after azathioprine dosing for the typical clinical scenario. The model was then used to test the existing hypotheses for abnormal enzyme activities for two atypical clinical scenarios. The results indicated that the model could not reflect the reference concentrations for either atypical scenario. This raised the following questions: whether the hypothesised enzymes that were considered to be responsible for the atypical clinical scenarios were not responsible, whether the model was correct but the set of parameters for the whole system were incorrect or whether the structure was incorrect.
The first two questions were addressed simultaneously by proposing a combined question, does a set of parameter values exist that could describe the typical and both atypical scenarios. If a set existed then the model was described as being complete. To address the model completeness issue in a QSP framework a global search algorithm was developed to optimise the model parameter values across all pathways and altered enzyme activity for the atypical scenarios (Chapter 3). No sets of parameter values were found that adequately described the reference data from both the typical and both atypical scenarios. The model was therefore deemed to be incomplete. The conclusion from this evaluation was that the model structure was incorrect.
Given the outcome from the search for model completeness, it was necessary to determine alternative structures that could solve for the reference data. In the next work (Chapter 4) a search across potential model structures was implemented using simulated annealing. A method was developed that used a combination of binary logic and continuous flux to search across model structures and parameter values, respectively. The search was found to be stable and was unaffected by dimensionality and identifiability issues (within the confines of the models evaluated). Four alternative model structures were identified by the search that when implemented in the azathioprine model yielded appropriate predictions of the reference data for all clinical scenarios. These structures suggested missing mechanisms in the pathway. Overall this work offered a method to provide alternative hypotheses where the underpinning knowledge for a developed model was incomplete.
Lastly, a methodological concept called internal deterministic identifiability was introduced (Chapter 5) to address the precision of the parameter estimates under the optimal design setting. Internal deterministic identifiability was defined as a setting whether the parameter values were imprecisely estimated despite the model being structurally identifiable and the design being optimal. The theory was explored using three commonly used PK and PKPD models. This methodology might be helpful to provide awareness about the situations where modelling results in poor precision of parameter estimates.
In this work a systematic approach is used to explore weaknesses of QSP models using azathioprine model as a case example. Two mathematical approaches were proposed and explored to understand the nature of the issues. These approaches can be extendable to any complex models with simple adjustments. Ultimately, however, azathioprine dosing was not able to be optimised at this stage. This remains an ongoing goal.