A Petri Net Approach to Physiologically Based Toxicokinetic Modeling

Abstract

Physiologically based toxicokinetic (PBTK) modeling enables researchers to predict internal tissue concentrations for various species exposed to exogenous compounds through different routes at varying concentrations without having to run in vivo experiments for each scenario. Parameters for the models may be gathered from in vivo or in vitro measurements, cross‐species or cross‐chemical extrapolations, literature reviews, or other models. The PBTK models, described using ordinary differential equations (ODEs), are then simulated using these parameters for a given compound/exposure/species scenario. Although they are potentially useful for regulatory toxicology, the complexity of ODE programming and simulation remains a barrier for many would‐be researchers. Petri nets, a graphical modeling framework, offers a more intuitive approach to PBTK modeling. To demonstrate their utility and ease of use, we present a model of waterborne fluoranthene exposure to rainbow trout (Oncorhynchus mykiss) written and simulated in Snoopy, a graphical Petri net development and simulation software package. We converted an existing ODE PBTK model and evaluated the Petri net model against the ODE model results. The simulated tissue concentrations of the Petri net model closely mirrored the simulated concentrations of the ODE model. To convert the ODE model to a Petri net model, we introduced a new parameter, blood volume (V BLOOD). Sensitivity analysis found V BLOOD to be very robust when varied over an order of magnitude. The resulting Petri net PBTK model has a number of advantages over ODE models, while maintaining equivalent predictive functionality. Environ Toxicol Chem 2019;00:1–10. © 2019 SETAC

Patients’ Perceptions at Diagnosis: Lung Cancer Discovery and Provider Relationships

“…The size reflects the number of coded items within a theme. More codes within a theme produce a larger rectangle (see Figure 1 for conceptual hierarchy) 21 . Another visualization technique, Explore Diagrams, was used to represent the connection of predominant themes to study participants (Figures 2 and 3).…”

“…Another visualization technique, Explore Diagrams, was used to represent the connection of predominant themes to study participants (Figures 2 and 3). 21 …”

PBTK Optimizer: An Open Source Application for PBTK Model Parameter Optimization in Python

“…Equation 1 is an example equation from the system of ODEs (which is attached in the supplementary materials). dc_F_/dt = (c_A_/p_Vblood_*p_Qf_)-((c_F_*p_Qf_)/(p_Vf_*p_Pf_)) (1) The PBTK model used as a case study was written as a Petri net in the software "Snoopy" [6], which can export a Petri net as an ODE. When parameters are named with 'p_' and '_' and compartments are named with 'c_' and '_', then the exported ODE text file will be properly formatted for use in PBTK Optimizer.…”

“…In the Smith (2003) PBTK model, from which the Edhlund and Lee (2019) model was based, the parameters which account for biotransformation of fluoranthene in the liver, kidneys, and rapidly perfused tissues (RPT) were not measured experimentally [6,15]. Instead, they were inferred from literature reviews of other PAHs.…”

“…In contrast, a Petri net (PN) is a discrete event dynamical system. A continuous PN, which incorporates vectors into the PN system, has been proposed as a method for PBTK modeling and distribution [6]. The PN PBTK models rely on open source software, such as Snoopy [7], for development, simulation, and distribution.…”