Well-stirred model

In the second model (Fig. 2.16) the continuous well-stirred model, feed and product takeoff are continuous, and the reactor contents are assumed to he perfectly mixed. This leads to uniform composition and temperature throughout. Because of the perfect mixing, a fluid element can leave at the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

In fact, it is often possible with stirred-tank reactors to come close to the idealized well-stirred model in practice, providing the fluid phase is not too viscous. Such reactors should be avoided for some types of parallel reaction systems (see Fig. 2.2) and for all systems in which byproduct formation is via series reactions. 

KS Pang, M Rowland. Hepatic clearance of drugs. I. Theoretical considerations of a well-stirred model and a parallel tube model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance. J Pharmacokin Biopharm 5/6 625-653, 1977. 

This use of Equation 9.10 to relate AUCpo to kdeg is valid under the assumption that only hepatic elimination occurs, well-stirred model conditions and complete absorption occurs in the GI tract. 

Well-stirred model (i.e. mixing tank model)]... 

Hydrodynamics Well-stirred model, i.e. uniform concentration inside intestine Parallel tube model, i.e. concentration decrease exponentially down the length of the intestine... 

An alternative approach to relying simply upon allometric approaches for metaboli-cally-cleared compounds is to take into consideration their relative stability in vitro. Clearance by P450 enzymes observed in hepatic microsomes from different species provides a measure of the relative intrinsic clearance in different species. Using the equation for the well-stirred model ... 

Figure 6 Well-stirred model of hepatic clearance. The exchange of a drug between plasma and hepatocyte and its removal from this cell involves an unbound compound. Intrinsic clearance, CLint, relates the rate of the elimination (by formation of metabolites, CLint>f, and secretion of unchanged compound into bile, CLint5ex) to the unbound drug in the cell, CUr Cbout and CUout are the bound and unbound concentrations of the drug leaving the liver at total concentration Cout.

Figure 7 Influence of changes in (a) organ blood flow on clearance, (b) fraction of the drug unbound in plasma (/u) on extraction ratio, and (c) intrinsic clearance on extraction ratio as predicted by the well-stirred model of hepatic clearance.

Figure 3 Influence of clearance on systemic drug-drug interactions. For model compound A (

Figure 2 Comparison between the uptake clearance obtained in vivo and that extrapolated from the in vitro transport study of endothelin antagonists. In vivo uptake clearance of endothelin antagonists (BQ-123, BQ-518, BQ-485, compound A) was evaluated by integration plot analysis using the plasma concentration-time profile after intravenous administration (500 nmol/kg) and the amount of drug in the liver and that excreted in the bile. In vitro hepatic uptake clearance was measured using isolated rat hepatocytes and was extrapolated to the in vivo uptake clearance assuming the well-stirred model. Source From Ref. 5.

Flow-limited, well-stirred model for organ extraction... 

Mizuma T, Tsuji A, Hayashi M. Does the well-stirred model assess the intestinal first-pass effect well J Pharm Pharmacol 2004 56(12) 1597-1599. 

For a drug that is eliminated exclusively by the liver and that is completely absorbed following oral administration, the intrinsic clearance can be related to the area under the plasma concentration-time curve (AUCp0) if the well-stirred model of hepatic elimination is assumed (81,82) ... 

Due to its mathematical simplicity, most in vitro-in vivo correlations are based on a homogeneous, well-stirred model for the liver such that all metabolic enzymes in the liver are exposed to the same drug concentration [266]. Under steady-state conditions, the predicted hepatic clearance CLh for this model is... 

However, these two models assume either perfect mixing conditions (well-stirred model) or no mixing at all (parallel tube model) and cannot explain several experimental observations. Therefore, other approaches such as the distributed model [268], the dispersion model [269], and the interconnected tubes model [270,271] attempt to capture the heterogeneities in flow and an intermediate level of mixing or dispersion. Despite numerous comparisons [264,265,272-... 

Panel 5.2 Summary of the predictions of the well-stirred model of hepatic ... 

The well-stirred model, shown in Figure 7.1, is the model of hepatic clearance that is used most commonly in pharmacokinetics. If we apply the Pick equation (see Chapter 6) to this model, hepatic clearance can be defined as follows (2) ... 

In addition to the well-stirred model that is the basis for Equation 7.6, several other kinetic models of hepatic clearance have been developed (4). However, the following discussion will be based on the relationships defined by Equation 7.6, and the limiting cases represented by Equations 7.7 and 7.8. 

A reasonable assumption is that the active secretion mechanism in the kidney can also be described by the well-stirred model. However, the kidneys have several mechanisms that may determine renal clearance of a drug, including passive filtration and reabsorption. 

Thus far, for compound X, we have obtained good results in this context with the simplest of these, the well-stirred model (see Table 8.1 for the equations, with and without significant plasma... 

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