Modeling/simulation compartmental models

Other than the different approaches mentioned above, commercial packages such as GastroPlus (Simulations Plus, Lancaster, CA) [19] and IDEA (LionBioscience, Inc. Cambridge, MA) [19] are available to predict oral absorption and other pharmacokinetic properties. They are both based on the advanced compartmental absorption and transit (CAT) model [20], which incorporates the effects of drug moving through the gastrointestinal tract and its absorption into each compartment at the same time (see also Chapter 22). 

PBPK and classical pharmacokinetic models both have valid applications in lead risk assessment. Both approaches can incorporate capacity-limited or nonlinear kinetic behavior in parameter estimates. An advantage of classical pharmacokinetic models is that, because the kinetic characteristics of the compartments of which they are composed are not constrained, a best possible fit to empirical data can be arrived at by varying the values of the parameters (O Flaherty 1987). However, such models are not readily extrapolated to other species because the parameters do not have precise physiological correlates. Compartmental models developed to date also do not simulate changes in bone metabolism, tissue volumes, blood flow rates, and enzyme activities associated with pregnancy, adverse nutritional states, aging, or osteoporotic diseases. Therefore, extrapolation of classical compartmental model simulations... 

A special case in dissolution-limited bioavailability occurs when the assumption of sink condition in vivo fails that is, the drug concentration in the intestine is dose to the saturation solubility. Class IV compounds, according to BCS, are most prone to this situation due to the combination of low solubility and low permeability, although the same could also happen for class II compounds, depending primarily on the ratio between dose and solubility. Non-sink conditions in vivo lead to less than proportional increases of bioavailability for increased doses. This is illustrated in Fig. 21.8, where the fraction of drug absorbed has been simulated by use of an compartmental absorption and intestinal transit model [35] for different doses and for different permeabilities of a low-solubility, aprotic compound. 

To understand the impact of individual processes on the compartmental distribution of DDT, model runs with a non-steady-state, zero-dimensional, multimedia mass balance box model (MPI-MBM) [Lammel (2004)] were conducted in addition to MPI-MCTM experiments. Parameterisations of intra- and intercompartmental mass exchange and conversion process in MPI-MBM are similar to those in MPI-MCTM. A detailed description of differences and a comparison of both models can be found in Lammel et al (2007). The DDT emissions were the global mean temporally varying DDT applications for the years 1950 to 1990. A repeating annual cycle around constant mean temperatures was simulated. Surface and air temperatures differ by 14 K constantly. 

Fig. 2.21 Compartmental burden [t] (left panel), solid lines model experiment with aggregation of marine snow (AGG), dashed lines experiment with satellite assimilation (SAT). Migration of the centre of gravity of the total environmental burden (right panel). Dashed lines show the location of the COG at the end of the simulation. The COG of the SAT experiment is shown in blue, the COG of the AGG experiment in red. Circles represent monthly mean COGs.

Ten Cate, A., Bermingham, S. K., Derksen, J. J., and Kramer, H. M. J., Compartmental Modeling of a 1,100 L Crystallizer Based on Large Eddy Flow Simulation . Proceedings of the 10th European Conference on Mixing, Delft, Netherlands, 255-264 (2000). 

The environmental impact of a new product needs to be assessed before it can be released for general use. Chemicals released into the environment can enter the food chain and be concentrated in plants and animals. Aquatic ecosystems are particularly sensitive, in this respect, since chemicals, when applied to agricultural land, can be transported in the ground water to rivers and then to the lakes, where they can accumulate in fish and plant life. The ecokinetic model presented here is based on a simple compartmental analysis and is based on laboratory ecosystem studies (Blau et ah, 1975). The model is useful in simulating the results of events, such as the accidental spillage of an agrochemical into a pond, where it is not ethical to perform actual experimental studies. 

GastroPlus [137] and IDEA [138] are absorption-simulation models based on in vitro input data like solubility, Caco-2 permeability and others. They are based on advanced compartmental absorption and transit (ACAT) models in which physicochemical concepts are incorporated. Both approaches were recently compared and are shown to be suitable to predict the rate and extent of human absorption [139]. 

In a second stage GastroPlus was used to simulate oral absorption, and oral profiles were produced by feeding this predicted input into a compartmental disposition model fitted to the mean observed intravenous data. 

Various PK parameters such as CL, Vd, F%, MRT, and T /2 can be determined using noncompartmental methods. These methods are based on the empirical determination of AUC and AUMC described above. Unlike compartmental models (see below), these calculation methods can be applied to any other models provided that the drug follows linear PK. However, a limitation of the noncompartmental method is that it cannot be used for the simulation of different plasma concentration-time profiles when there are alterations in dosing regimen or multiple dosing regimens are used. 

PB-PK models, sometimes referred to as biologically-based disposition models, allow for accurate extrapolation of rodent data to estimate human dose-response relationships (Paustenbach, 1995). PB-PK models, unlike compartmental models, have the capability of simulating a chemical s behavior in biological systems. The purpose of a PB-PK model is to predict the human dose-response relationship based on animal data by quantitatively estimating the delivered dose of the biologically relevant chemical species in a target tissue (Andersen etal., 1987 Clewell etal., 1994 Leung and Paustenbach, 1995 Ramsey and Andersen, 1984). 

As previously, initial conditions for the compartmental model and the enzymatic reaction were set to tiq = [100 50], and so = 100, eo = 50, and cq = 0, respectively. Figures 9.31 and 9.32 show the deterministic prediction, a typical run, and the average and confidence corridor for 100 runs from the stochastic simulation algorithm for the compartmental system and the enzyme reaction, respectively. Figures 9.33 and 9.34 show the coefficient of variation for the number of particles in compartment 1 and for the substrate particles, respectively. 

A step-by-step simulation of the system can be carried out by numerical calculations when the initial values of capacitances and the values of parameters (constants) are assigned. The calculations have been performed using the model from Table 13.1 after assuming n = A. This value is sufficient [86] to achieve reliable simulation data of typical liquid transport processes under study. However, it should be noted that the increase in the number of layers, i.e., increasing in n will always result in more precise calculations and predictions comparable to those achieved by analytic calculation methods. The n-value equal to 4 should be treated as the lowest limit required for obtaining quantitative data sufficient for the interpretation of the separation effects. The problem of proper compartmentalization can be especially significant when reactions locally attain quasi-equUibrium conditions. 

Minekus, M. Marteau, P. Havenaar, R. Huiin t Veld, J.H. A multi compartmental dynamic computer-controlled model simulating the stomach and small intestine. Alta 1995, 23, 197-209. 

We have developed a two-step procedure for the in silico screening of compound libraries based on biopharmaceutical property estimation linked to a mechanistic simulation of GI absorption. The first step involves biopharmaceutical property estimation by application of machine learning procedures to empirical data modeled with a set of molecular descriptors derived from 2D and 3D molecular structures. In silico methods were used to estimate such biopharmaceutical properties as effective human jejunal permeability, cell culture permeability, aqueous solubility, and molecular diffusivity. In the second step, differential equations for the advanced compartmental absorption and transit model were numerically integrated to determine the rate, extent, and approximate GI location of drug liberation (for controlled release), dissolution, and absorption. Figure 17.3 shows the schematic diagram of the ACAT model in which each one of the arrows represents an ordinary differential equation (ODE). 

Several models have been suggested to simulate the behavior inside a reactor [53, 71, 72]. Accordingly, homogeneous flow models, which are the subject of this chapter, may be classified into (1) velocity profile model, for a reactor whose velocity profile is rather simple and describable by some mathematical expression, (2) dispersion model, which draws analogy between mixing and diffusion processes, and (3) compartmental model, which consists of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., in order to describe a non-ideal flow reactor. 

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