The systems pharmacology model was built in two consecutive phases. First, a largely empirical PKPD model with minimum parameterization was built to capture basic biological variations in the data. In practice, this entailed fitting a basic 1-, 2-, or 3-compartment model to the pharmacokinetics of benazeprilat, and then linking the PK to the RAAS biomarkers concentrations via various indirect and direct response models. Whenever possible we opted for direct over indirect effects models, and fewer compartments, to reduce the number of total estimated parameters during model fit.
Then, in an iterative fashion, model components were replaced with more mechanistic structures. To do this, we modeled the cascade of peptides which define the alternative and classical RAAS pathways. We also tested whether we could expand the mathematical model to include important biological systems such as the clearance of angiotensins via the liver vs. kidneys, non-specific plasma binding, first-pass metabolism, and site-specific metabolism. Some components and parameters of the model structure were arbitrarily fixed to literature or exploratory values to preserve fidelity to relevant biological systems. For example, our model equations were rewritten so that the production of AngII was always one-to-one proportional with catalysis of AngI via the angiotensin converting enzyme. The final model was refined through various arithmetic simplifications and parameter search optimizations to improve precision of parameter estimates as much as possible without comprising fit to experimental data. The significance of bodyweight, sex, sodium intake, and benazepril dose on parameters estimates was further evaluated using the automated Pearson’s correlation test and ANOVA method as implemented in Monolix 2020 R1.
Then, in an iterative fashion, model components were replaced with more mechanistic structures. To do this, we modeled the cascade of peptides which define the alternative and classical RAAS pathways. We also tested whether we could expand the mathematical model to include important biological systems such as the clearance of angiotensins via the liver vs. kidneys, non-specific plasma binding, first-pass metabolism, and site-specific metabolism. Some components and parameters of the model structure were arbitrarily fixed to literature or exploratory values to preserve fidelity to relevant biological systems. For example, our model equations were rewritten so that the production of AngII was always one-to-one proportional with catalysis of AngI via the angiotensin converting enzyme. The final model was refined through various arithmetic simplifications and parameter search optimizations to improve precision of parameter estimates as much as possible without comprising fit to experimental data. The significance of bodyweight, sex, sodium intake, and benazepril dose on parameters estimates was further evaluated using the automated Pearson’s correlation test and ANOVA method as implemented in Monolix 2020 R1.
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