Preliminary Flow Modeling by Hybrid Automata Alternating Continuous Reaction and Discrete Transit for Pharmacokinetics

Abstract

In traditional pharmacokinetic models, blood flow or liquid transit is often expressed as first-order kinetics. When the flow expression by first-order kinetics is used for dynamic simulation, the flow velocity illogically depends on the step size of a solver of ordinary differential equations. In this study, we propose flow modeling using hybrid automata that combine ordinary differential equations and recursive equations, and we have preliminarily applied the constructed models to several examples. The blood concentration–time profiles of p-aminohippurate and propranolol after intravenous administration were successfully reproduced by simple hybrid automata. The simulation results of one-dimensional tube flow have demonstrated that the fluid velocity in the hybrid automata was independent of the step size of the ordinary differential equation solver. A body fluid model coordinated various flows in a human body with scheduled daily activities and could be used as a drug container to describe formulation-dependent disposition of 5-aminosalicylic acid and enterohepatic circulation of a virtual drug. These findings suggested that flow modeling using hybrid automata could avoid the logical inconsistency in the traditional pharmacokinetic modeling and that the hybrid automata have high versatility and a wide range of applicability to pharmacokinetic analysis. Because our method can define various intervals for multiple recursive equations, the resolution of a specific part of a model can be adjusted relatively freely while the whole body is being roughly modeled, which would be beneficial to refine a coarse model into a fine model in future. SIGNIFICANCE STATEMENT There is a logical inconsistency in flow expression by first-order kinetics in ordinary differential equations used in traditional pharmacokinetic modeling. It is difficult to model a whole human body using flow models in partial differential equations because of the excessive calculation costs. Our simulations on tube flow and body fluids have demonstrated that the flow modeling using hybrid automata could avoid the problems. The preliminary applications of hybrid automata to several examples highlighted its high versatility in pharmacokinetic analysis.