Quantitative systems pharmacology (QSP) modeling has become increasingly important in pharmaceutical research and development, and is a powerful tool to gain mechanistic insights into the complex dynamics of biological systems in response to drug treatment. However, even once a suitable mathematical framework to describe the pathophysiology and mechanisms of interest is established, final model calibration and the exploration of variability can be challenging and time consuming. QSP models are often formulated as multi-scale, multi-compartment nonlinear systems of ordinary differential equations. Commonly accepted modeling strategies, workflows, and tools have promise to greatly improve the efficiency of QSP methods and improve productivity. In this paper, we present the QSP Toolbox, a set of functions, structure array conventions, and class definitions that computationally implement critical elements of QSP workflows including data integration, model calibration, and variability exploration. We present the application of the toolbox to an ordinary differential equations-based model for antibody drug conjugates. As opposed to a single stepwise reference model calibration, the toolbox also facilitates simultaneous parameter optimization and variation across multiple in vitro, in vivo, and clinical assays to more comprehensively generate alternate mechanistic hypotheses that are in quantitative agreement with available data. The toolbox also includes scripts for developing and applying virtual populations to mechanistic exploration of biomarkers and efficacy. We anticipate that the QSP Toolbox will be a useful resource that will facilitate implementation, evaluation, and sharing of new methodologies in a common framework that will greatly benefit the community.
Keywords: optimization; ordinary differential equations; quantitative systems pharmacology; virtual patient; virtual population.