Deriving mechanism-based pharmacodynamic models by reducing quantitative systems pharmacology models: An application to warfarin

Quantitative systems pharmacology (QSP) models integrate comprehensive qualitative and quantitative knowledge about pharmacologically relevant processes. We previously proposed a first approach to leverage the knowledge in QSP models to derive simpler, mechanism-based pharmacodynamic (PD) models. Their complexity, however, is typically still too large to be used in the population analysis of clinical data. Here, we extend the approach beyond state reduction to also include the simplification of reaction rates, elimination of reactions, and analytic solutions. We additionally ensure that the reduced model maintains a prespecified approximation quality not only for a reference individual but also for a diverse virtual population. We illustrate the extended approach for the warfarin effect on blood coagulation. Using the model-reduction approach, we derive a novel small-scale warfarin/international normalized ratio model and demonstrate its suitability for biomarker identification. Due to the systematic nature of the approach in comparison with empirical model building, the proposed model-reduction algorithm provides an improved rationale to build PD models also from QSP models in other applications

Sample‐based robust model reduction for non‐linear systems biology models

Complex non-linear systems biology models comprise relevant knowledge on processes of pharmacological interest. They are, however, too complex to be used in inferential settings, for example, to allow for the estimation of patient-specific parameters for individual dose optimisation. Thus, there is a need for simple models with interpretable components to infer the drug effect in a clinical setting. In particular, it is essential to accurately quantify and simulate the interindividual variability in the drug response in order to account for covariates like body weight, age and genetic disposition. To this end, non-linear model order reduction and simplification methods can be used if they maintain model interpretability during reduction and consider an entire population rather than just a single reference individual. We present a sample-based approach for robust model order reduction and propose two improvements for efficiency. In particular, we introduce a new sampling method to generate the virtual population based on transformed latin hypercube sampling. Thereby, the sample is stratified in the relevant parameter-space directions, which are identified using empirical observability Gramians. We illustrate our approach in application to a blood coagulation pathway model, where we reduce the complexity from a 62-dimensional highly non-linear to a six-dimensional and a nine-dimensional system of ordinary differential equations for two scenarios, respectively

Leveraging QSP Models for MIPD: A Case Study for Warfarin/INR

Warfarin dosing remains challenging due to substantial inter-individual variability, which can lead to unsafe or ineffective therapy with standard dosing. Model-informed precision dosing (MIPD) can help individualize warfarin dosing, requiring the selection of a suitable model. For models developed from clinical data, the dependence on the study design and population raises questions about generalizability. Quantitative system pharmacology (QSP) models promise better extrapolation abilities; however, their complexity and lack of validation on clinical data raise questions about applicability in MIPD. We have previously derived a mechanistic warfarin/international normalized ratio (INR) model from a blood coagulation QSP model. In this article, we evaluated the predictive performance of the warfarin/INR model in the context of MIPD using an external dataset with INR data from patients starting warfarin treatment. We assessed the accuracy and precision of model predictions, benchmarked against an empirically based reference model. Additionally, we evaluated covariate contributions and assessed the predictive performance separately in the more challenging outpatient data. The warfarin/INR model performed comparably to the reference model across various measures despite not being calibrated with warfarin initiation data. Including CYP2C9 and/or VKORC1 genotypes as covariates improved the prediction quality of the warfarin/INR model, even after assimilating 4 days of INR data. The outpatient INR exhibited higher unexplained variability, and predictions slightly exceeded observed values, suggesting that model adjustments might be necessary when transitioning from an inpatient to an outpatient setting. Overall, this research underscores the potential of QSP-derived models for MIPD, offering a complementary approach to empirical model development

Model reduction for Ca²+ -induced vesicle fusion dynamics

In this work, we adapt an established model for the Ca²+ -induced fusion dynamics of synaptic vesicles and employ a lumping method to reduce its complexity. In the reduced system, sequential Ca²+ -binding steps are merged to a single releasable state, while keeping the important dependence of the reaction rates on the local Ca²+ concentration. We examine the feasibility of this model reduction for a representative stimulus train over the physiologically relevant site-channel distances. Our findings show that the approximation error is generally small and exhibits an interesting nonlinear and non-monotonic behavior where it vanishes for very low distances and is insignificant at intermediary distances. Furthermore, we give expressions for the reduced model's reaction rates and suggest that our approach may be used to directly compute effective fusion rates for assessing the validity of a fusion model, thereby circumventing expensive simulations