Well-stirred model, clearance

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. 

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.

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... 

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. 

Table 8.1 Equations for predicting hepatic clearance using the well-stirred model...

The blood clearance can then be obtained through one of the several approaches, for example, the well-stirred model and fraction unbound (/[, obtained from plasma... 

Oxidative Biotransformation in Microsomes The rapid determination of pharmacokinetic parameters, solubility, permeability, and in vitro stability in plasma or liver tissue can often provide a reasonable explanation of the mechanisms limiting oral bioavailability. An approach that is often used is to extrapolate the in vitro rate of metabolism to estimate the hepatic clearance using in vitro-in vivo correlation methods.82-86 These methods use in vitro kinetic parameters, usually Vmllx/Km or in vitro t ji, to determine the intrinsic clearance, which is then scaled to hepatic clearance using the amount of tissue in the in vitro incubation, the weight of the liver, and the well-stirred model for hepatic clearance. 

From the material presented so far, one may intuitively imagine that hepatic drug clearance will be influenced by hepatic blood flow, fraction unbound, and intrinsic clearance that is, the intrinsic ability of the organ to clear unbound drug. The simplest model that describes hepatic clearance in terms of these physiological parameters is the well-stirred model (6). Assuming instantaneous and complete mixing, the well-stirred model states that hepatic clearance (with respect to blood concentration) is... 

The well-stirred model [eqn (13.5)] is a simplified model of hepatic drug clearance and relates in vivo intrinsic clearance, which is the clearance of the drug experiences at the enzyme level, to blood flow and liver distribution. The in vivo C/int can be estimated from an in vitro C/ nt measurement by scaling the in vitro measurement to the in vivo situation, using estimates of microsomal protein yield per gram of liver and liver weights (for microsomal estimates of C/int) or hepatocyte numbers per gram of liver for in vitro C/int values derived from hepatocytes. See eqn (13.5). 

The well-stirred model therefore allows prediction of in vivo clearance from intrinsic clearance estimates, generated from simple enzyme, sub-cellular or cellular assays. 

Transporters are involved in biliary and renal excretions that are the two common routes of drug elimination. In the liver, a drug is first taken up into hepatocytes, then either secreted back to the systemic circulation or excreted to the bile in an intact form or as metabolites via Phase I and/or Phase II enzymes. Given the involvement of transporters in both uptake at the sinusoidal membrane and efflux at the sinusoidal and canulicular membranes (Fig. 6.1c), the hepatic clearance can be expressed based on well-stirred model as the following equation (Shitara et al., 2005 Yamazaki et al., 1996) ... 

In vivo Prediction Hepatic clearance (CLh) in the well-stirred model can be expressed as... 

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