Translational equation-based modeling

Abstract

Equation-based models have been the main mathematical framework used for the development of computational simulations in the physical sciences and more recently, in the biological sciences. Based on a solid mathematical foundation and mature methods, equation-based models represent biological mechanisms in terms of equations and are inherently causal in nature. Newer approaches offer methods to represent the inherent diversity of cells and organisms, the imperfect data gathered from bench and clinical experiments. These methods have created the opportunity for equation-based models to provide probabilistic assessment of system state in ways not accessible to alternative stochastic approaches, and therefore offer probabilistic forecasts of the evolution of complex systems, much like weather forecasting. Equation-based models are recently emerging as a useful translational tool, with application ranging from dosing of cancer chemotherapy to closed-loop control of blood sugar in diabetic patients, contributing to improving patient-centered outcomes. Future applications will expand to rational design of clinical trials including enhancing adapting design methodology, the development of mechanistically based goal-directed therapeutic interventions, and bedside clinical decision-support systems.