Hepatic clearance equations

The calculation of clearance using this equation is illustrated by the following example. Aspirin is metabolized primarily in the liver. Normal hepatic blood flow (Q) equals 1500 mL/min. If the blood entering the liver contains 200 fxg/mL of aspirin (Ci) and the blood leaving the liver contains 134 fxg/mL (Co), hepatic clearance of aspirin is calculated as follows ... 

From either a Cp or In Cp versus time plot, one feature is immediately clear the drug concentration drops over time. This process is called elimination and is determined by clearance (CL). Clearance is the process of removal of drug from the bloodstream. As was discussed in Chapter 3, clearance occurs primarily either through filtration of a drug by the kidneys (renal clearance, CLR) or metabolism of a drug in the liver by the action of enzymes (hepatic clearance, CLH). Other clearance processes are possible, but CLR and CLh normally comprise the large majority of total clearance (CLy or simply CL) (Equation 7.6). 

Hepatic clearance (CLH) can be crudely approximated from bioavailability (F) according to Equation 7.34. 

A high CLR indicates the liver efficiently removes a drug from incoming blood, so F is low. A low f/. [ indicates high F. Hepatic clearance can range in value from 0 to 25 mL/min/kg. With this information, we can begin to put Equation 7.33 to its full use. 

It has been demonstrated that hepatic extraction ratio (ER) is also influenced by blood flow. A number of mathematical models have been proposed to explain this observation, but the simplest model, and the one that is easiest to apply to clinical practice, is the well stirred or venous equilibrium model (Equation 5.3). This model relates hepatic clearance to hepatic blood flow (Q), the fraction of drug concentration that is unbound in plasma (fu) and the intrinsic clearance of the unbound drug (Clyint) [1]. Intrinsic clearance represents the maximum clearance of drug in the absence of any restrictions caused by blood flow, binding or access to the metabolising enzymes. The model states that ... 

Hepatic clearance (CLh) may be defined as the volume of blood perfusing the liver that is cleared of drug per unit time. Usually, hepatic clearance is equated with nonrenal clearance and is calculated as total body clearance (CLe) minus renal clearance (CLr) ... 

The factors that affect hepatic clearance include blood flow to the liver (Q), the fraction of drug not bound to plasma proteins (fu), and intrinsic clearance (CGjjf) (1, 2). Intrinsic clearance is simply the hepatic clearance that would be observed in the absence of blood flow and protein binding restrictions. As discussed in Chapter 2, hepatic clearance usually can be considered to be a first-order process. In those cases, intrinsic clearance represents the ratio of Vmax l m, and this relationship has been used as the basis for correlating in vitro studies of drug metabolism with in vivo results (3). However, for phenytoin and several other drugs, the Michaelis-Menten equation is needed to characterize intrinsic clearance. 

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) ... 

By substituting this expression for extraction ratio into Equation 7.2, hepatic clearance can be expressed as... 

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. 

Few drugs exhibit an intermediate extraction ratio. Evaluation of the hepatic clearance of these drugs requires consideration of all of the parameters included in Equation 7.6. Disease-associated or drug-induced alterations in protein binding, hepatic blood flow, or intrinsic clearance may alter hepatic clearance significantly. 

The corresponding impact on hepatic clearance is given by the following equation ... 

Equation 7.13 emphasizes the central point that changes in perfusion and protein binding, as well as intrinsic clearance, will affect the hepatic clearance of a number of drugs. The intact hepatocyte theory has been proposed as a means of simplifying this complexity (33). This theory is analogous to the intact nephron theory (see Chapter 5) in that it assumes that the increase in portocaval shunting parallels the loss of functional cell mass, and that the reduced mass... 

Vmax and Km for MDZ 1 -liydroxylation. V,nax determined for each biopsy sample was then scaled to the estimated total liver mass and intrinsic clearance estimated as total liver Vmax/Kn- Hepatic clearance then was predicted from Equation 7.6 in Chapter 7. Figure 30.13 compares the observed total elimination clearance with predicted hepatic clearance based on the assumption that the E-hydroxylation pathway accounts for 70% of the substrate loss. The prediction is quite good. The average absolute deviation between the five observed data points and their predicted values is only 28% and the differences are uniformly distributed. 

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

They showed that the degree of the reduction in the hepatic clearance was overestimated by a simple calculation of the product of the reduction in the hepatic uptake and biliary excretion (Equation 11.6) and this method is useful to avoid the falsenegative predictions [246]. 

At this point, the standard equation for hepatic clearance (see Equations 9.9 and 9.12) is used to convert CLillt to in vivo human clearance (CLH(Caic)) ... 

Equation 17.5 advises that hepatic clearance is the product of hepatic blood flow and hepatic extraction ratio. Therefore, as shown in Equation 17.13, the hepatic extraction ratio is... 

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) ... 

This equation shows the independent parameters responsible for the magnitude of hepatic clearance for a given patient receiving a given drug. 

The general equation expressing hepatic clearance as a function of its contributing parameters is Eq. 16.5 ... 

This equation does not contain the expression /ut and, therefore, hepatic clearance is independent of changes in tissue binding of drug. 

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 ... 

The equation can be solved for intrinsic clearance (Clj) based upon systemic clearance (Clj) obtained after i.v. administration and hepatic blood flow (Q) in the test species. Intrinsic clearance in man can then be estimated based upon relative in vitro microsomal stabibty and the equation solved to provide an estimate for human systemic clearance. Hence this approach combines aUometry (by considering differences in organ blood flow) and species-specific differences in metabolic clearance. 

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