OpenCFD Ltd has been managing and developing OpenFOAM since its debut in 2004, releasing all versions prior to 8th August 2011, when OpenCFD transferred the IP rights to the US foundation \"OpenFOAM Foundation, inc.\". After that date OpenCFD Ltd. continued to manage and develop OpenFOAM, preparing all releases whose IP was later transferred to and released by OpenFOAM Foundation Inc. until 2014. Thereafter OpenCFD Ltd. the owner of the OpenFOAM Trademark directly released its version of OpenFOAM from January 2016 to the present day.
Quantitative methods to predict pharmacokinetics range in complexity from static mechanistic predictions of specific PK parameters to dynamic physiologically based PK (PBPK) models used to predict plasma concentration-time curves. Static mechanistic methods typically use one or two in vitro parameters to predict specific human PK parameters, and can therefore be easily adopted in screening programs to prioritize and triage compounds based on undesirable pharmacokinetics. Static prediction methods have been used extensively to predict human metabolic (Gillette, 1971; Rowland et al., 1973; Iwatsubo et al., 1997; Obach et al., 1997) and transporter-mediated clearance (Liu and Pang, 2005; Barton et al., 2013; Varma et al., 2013) and drug-drug interactions (Mayhew et al., 2000; Wang et al., 2004; Obach et al., 2007; Fahmi et al., 2008). However, while static models are very useful for predictions of overall drug exposures in humans or the overall magnitude of DDIs, they rely on steady-state assumptions and hence cannot predict the overall shape of the plasma concentration-time curve, time-varying changes in enzyme or transporter inhibition, or the distribution kinetics of new drugs. In contrast, PBPK models provide simulated concentration versus time profiles of a drug and its metabolite(s) in plasma or an organ of interest and simultaneously allow for estimation of maximum plasma concentrations, absorption kinetics, distribution kinetics, and drug elimination. While the simultaneous modeling of drug disposition processes provides multiple advantages (Rostami-Hodjegan and Tucker, 2007; Almond et al., 2009; Fahmi et al., 2009; Jamei et al., 2009a; Rowland et al., 2011; Huang and Rowland, 2012; Di et al., 2013; Shardlow et al., 2013; Galetin, 2014; Tsamandouras et al., 2015; Varma et al., 2015b), it also makes PBPK modeling labor intensive and requires considerably more parameter estimates and more detailed physiologic and drug-specific data than static predictions. The simulated concentration-time profiles can aid in selection of optimal sampling times or dosing strategies in different study populations, including vulnerable subjects (Rowland et al., 2011). They can also aid in design of DDI studies in which the timing of the dosing of the perpetrator drug and the victim drug is critical (Zhao et al., 2009; Shardlow et al., 2013), or in situations where perpetrator concentrations fluctuate over the sampling and dosing interval (Almond et al., 2009; Fahmi et al., 2009; Pang and Durk, 2010; Di et al., 2013). Additionally, the simulated concentrations can be linked to pharmacodynamic endpoints to allow for PK/PD (pharmacokinetic-pharmacodynamic) simulations. Furthermore, because PBPK models account for sequential metabolism and permeability limited processes, they may provide advantages for predicting bioavailability when compared with static models (Fan et al., 2010; Chow and Pang, 2013). This can have important implications for first in human dose selection, particularly for drugs with active or toxic metabolites. In some cases, PBPK models incorporate interindividual variability, thus allowing for the prospective simulation of the population variability in the pharmacokinetics of a given drug. Population variability is not typically accounted for in static models but can provide insight into variability in exposure and drug response in a given population (Rostami-Hodjegan and Tucker, 2007; Jamei et al., 2009a; Cubitt et al., 2011; Brown et al., 2012). Finally, the separation of drug-specific and physiologic parameters within the model can allow a more mechanistic understanding of the sources of interindividual variability than can be provided by population and compartmental modeling techniques (Rostami-Hodjegan and Tucker, 2007; Vinks, 2013; Tsamandouras et al., 2015). However, detailed understanding of physiologic variables in the population of interest is required but not always available, which can hinder the use of PBPK modeling in special populations.
In recent years, the number of publications (Rowland et al., 2011; Rostami-Hodjegan et al., 2012) and regulatory submissions (Zhao et al., 2011; Huang et al., 2013; Sinha et al., 2014) referencing or including PBPK modeling has increased substantially. The development of user-friendly software tools such as Simcyp, GastroPlus, and PK-Sim have made modeling more accessible to those without extensive modeling and/or programming experience (Zhao et al., 2011; Chen et al., 2012; Huang et al., 2013). However, it is possible that many users are not completely familiar with, or aware of, the assumptions made and equations used during model building and implementation. As such, the increased implementation of PBPK modeling has led to a need for comprehensive software and modeling-focused education as well as the need to confirm the sound knowledge of users in ADME principles and fundamental physiology (Jones et al., 2015). A recommendation for the presence of a modeling expert for advice and to review models has also been made to ensure appropriate decision making and interpretation of the modeling (Jones et al., 2015). Advancements in computer science and physiologically based mathematical models have led to the expansion of the potential applications of PBPK modeling. For example, more complex absorption models such as advanced dissolution, absorption, and metabolism (ADAM) models (Jamei et al., 2009b) and advanced compartmental absorption and transit (ACAT) models (Agoram et al., 2001) have been developed that enable the use of PBPK modeling for the simulation of food effects (Shono et al., 2009; Turner et al., 2012; Heimbach et al., 2013; Xia et al., 2013b; Patel et al., 2014; Zhang et al., 2014), the impact of drug properties on absorption kinetics (Kambayashi et al., 2013; Parrott et al., 2014), and intestinal interactions (Fenneteau et al., 2010). The development of sophisticated models that allow for the simulation of multiple inhibitors or inducers, relevant metabolites, and multiple mechanisms of interaction have permitted the prediction of complex DDIs involving enzymes, transporters, and multiple interaction mechanisms (Zhang et al., 2009; Rekić et al., 2011; Varma et al., 2012, 2013; Dhuria et al., 2013; Gertz et al., 2013, 2014; Guo et al., 2013; Kudo et al., 2013; Siccardi et al., 2013; Wang et al., 2013a; Sager et al., 2014; Chen et al., 2015; Shi et al., 2015). Furthermore, the mechanistic understanding of ADME changes that occur in different age groups or disease states has improved, and consequently PBPK modeling has been used to simulate drug disposition in special populations including hepatic (Johnson et al., 2014) and renal impairment populations (Li et al., 2012; Zhao et al., 2012a; Lu et al., 2014; Sayama et al., 2014), children (Leong et al., 2012), and pregnant women (Andrew et al., 2008; Gaohua et al., 2012; Horton et al., 2012; Ke et al., 2012, 2013, 2014; Lu et al., 2012).
Despite the increasing use of PBPK modeling, there are many challenges that limit the utility of PBPK modeling and simulation. In general, IVIVE using PBPK models requires considerably more experimental and in silico data than static models. Due to the large number of parameters required for PBPK modeling and the limited availability of in vivo data to verify individual parameters, model predictions can be confounded by lack of confidence in individual parameters. For example, for drugs that have not been administered intravenously to humans, distribution and absorption parameters cannot be validated or verified experimentally, which introduces uncertainty into model parameters and output. The application of PBPK modeling to predict the pharmacokinetics in disease populations is hindered by lack of in vivo data in patient populations, poor understanding of the physiologic changes that occur in certain populations, and limited knowledge of tissue-specific changes in enzyme and transporter expression (Edginton and Joshi, 2011; Sjöstedt et al., 2014; Jones et al., 2015). Furthermore, absolute abundances of transporters and non-P450 enzymes in the liver and other tissues are not well established, resulting in poor IVIVE of the kinetics of non-P450 substrates and permeability limited drugs (Edginton and Joshi, 2011; Jones et al., 2012, 2015; Varma et al., 2012; Harwood et al., 2013). Additionally, a lack of selective substrates and inhibitors for some non-P450 enzymes and transporters has prevented model validation against in vivo data (Jones et al., 2015). While efforts are being made to characterize tissue-specific transporter expression, current models of the disposition of transporter substrates rely on the incorporation of empirical scaling factors (Varma et al., 2015b). Although scaling factors have allowed for predictions of the kinetics of a number of uptake transporter substrates (Varma et al., 2012, 2014, 2015a; Kudo et al., 2013; Gertz et al., 2014; Jamei et al., 2014), it is not possible to experimentally verify whether unbound tissue exposures are adequately predicted (Chu et al., 2013; Jones et al., 2015; Varma et al., 2015b). This could have important implications for IVIVE of efflux clearance, metabolism-transporter interplay, and predictions of pharmacological effects. The utility of PBPK modeling in the prediction of therapeutic protein disposition is still relatively limited, as was recently discussed (Jones et al., 2015). Whi