Pharmacokinetics clearance equations

Clearance (Cl) and volumes of distribution (VD) are fundamental concepts in pharmacokinetics. Clearance is defined as the volume of plasma or blood cleared of the drug per unit time, and has the dimensions of volume per unit time (e.g. mL-min-1 or L-h-1). An alternative, and theoretically more useful, definition is the rate of drug elimination per unit drug concentration, and equals the product of the elimination constant and the volume of the compartment. The clearance from the central compartment is thus VVklO. Since e0=l, at t=0 equation 1 reduces to C(0)=A+B+C, which is the initial concentration in VI. Hence, Vl=Dose/(A+B-i-C). The clearance between compartments in one direction must equal the clearance in the reverse direction, i.e. Vl.K12=V2-k21 and VVkl3=V3-k31. This enables us to calculate V2 and V3. 

Cheng-Prasoff relationship, 65-66, 214 Cholecystokinin receptor antagonists, 80 Cimetidine, 9-10 Clark, Alfred J., 3, 3f, 12, 41 Clark plot, 114 Clearance, 165—166 Clinical pharmacokinetics, 165 Cocaine, 149, 150f Competitive antagonism description of, 114 Gaddum equation for, 101-102, 113,... 

Drugs can be cleared from the body by metabolism as well as renal excretion, and when this occurs it is not possible to measure directly the amount cleared by metabolism. However, the total clearance rate (TCR), or total body clearance, of the drug can be calculated from its pharmacokinetic parameters using the following equation ... 

Studies interested in the determination of macro pharmacokinetic parameters, such as total body clearance or the apparent volume of distribution, can be readily calculated from polyexponential equations such as Eq. (9) without assignment of a specific model structure. Parameters (i.e., Ah Xt) associated with such an equation are initially estimated by the method of residuals followed by nonlinear least squares regression analyses [30],... 

Another term which is important in pharmacokinetics is the half-life (fi/2) of a drug. This value is related to the Vd and the total clearance. If it is assumed that the body is a single compartment in which the size of the compartment equals the Vd, the fi/2 may be calculated from the equation ... 

The importance of these equations is that drugs can have different half-lives due either to changes in clearance or changes in volume (see Section 2.7). This is illustrated in Figure 2.3 for a simple single compartment pharmacokinetic model where the half-life is doubled either by reducing clearance to 50 % or by doubling the volume of distribution. 

Physicians may be surprised to see that mention of half-life has been dealt with so late in this chapter, as it is likely to be the pharmacokinetic term most familiar to them. The key concepts are summarised in Box 5.5. As mentioned earlier, half-life is not only a primary pharmacokinetic parameter but is also one of the descriptive terms. Although many physicians will readily accept that changes in clearance wiU alter half-life, what is not quite so obvious is that half-life is equally determined by volume of distribution and in fact there is an equation relating these three terms ... 

Estimates of dosing rate and average steady-state concentrations, which may be calculated using clearance, are independent of any specific pharmacokinetic model. In contrast, the determination of maximum and minimum steady-state concentrations requires further assumptions about the pharmacokinetic model. The accumulation factor (equation... 

Estimates of dosing rate and average steady-state concentrations, which may be calculated using clearance, are independent of any specific pharmacokinetic model. In contrast, the determination of maximum and minimum steady-state concentrations requires further assumptions about the pharmacokinetic model. The accumulation factor (equation [7]) assumes that the drug follows a one-compartment body model (Figure 3-2 B), and the peak concentration prediction assumes that the absorption rate is much faster than the elimination rate. For the calculation of estimated maximum and minimum concentrations in a clinical situation, these assumptions are usually reasonable. 

The preceding discussion has been intent upon breaking down equations and making sense of different variables and how each may be calculated from experimental Cp-time data. At the outset of this chapter, two parameters—clearance and volume of distribution—were set apart as the key pharmacokinetic variables for a drug. This brief section tries to establish the importance and utility of these two variables. The highlight of this subsection is Equation 7.12, which is shown again here. A rearranged form of Equation 7.12 is Equation 7.33. 

In a study investigating the allometric relationships of pharmacokinetic parameters for five therapeutic proteins, the allometric equations for clearance and volumes of distribution, however, were found to be different for each protein [102]. This variability was attributed to possible species specificity and immune-mediated clearance mechanisms. Species specificity refers to the inherent differences in structure and activity across species. Minute differences in the amino acid sequence may render an agent inactive when administered to foreign species, and may even generate an immunogenic response. Immunogenicity has been clearly demonstrated in a study with the tumor necrosis factor receptor-immunoglobulin fusion protein lenercept. This all-human sequence protein elicits an immune response in laboratory animals which ultimately results in the rapid clearance of the protein [103]. 

Since there is a directly proportionate relationship between administered drug dose and steady-state plasma levels Equations 2.2 and 2.3 provide a straightforward guide to dose adjustment for drugs that are eliminated by first-order kinetics. Thus, to double the plasma levels the dose simply should be doubled. Con-versely to halve the plasma level, the dose should be halved. It is for this reason that Equations 2.2 and 2.3 are the most clinically important pharmacokinetic equations. Note that, as is apparent from Eigure 2.6, these equations also stipulate that the steady-state level is determined only by the maintenance dose and elimination clearance. The loading dose does not appear in the equations and does not influence the eventual steady-state level. 

The three estimates of distribution volume that we have encountered have slightly different properties (24). Of the three, Vd(ss) has the strongest physiologic rationale for multicompartment systems of drug distribution. It is independent of the rate of both drug distribution and elimination, and is the volume that is referred to in Equations 3.1 and 3.2. On the other hand, estimates of V ( area) most useful in clinical pharmacokinetics, since it is this volume that links elimination clearance to elimination half-life in the equation... 

Considerable confusion surrounds the proper use of Equation 6.2 to calculate dialysis clearance. There is general agreement that blood clearance is calculated when Q is set equal to blood flow and A and V are expressed as blood concentrations. In conventional practice -plasma clearance is obtained by setting Q equal to plasma flow and expressing A and V as plasma concentrations. In facb this estimate of plasma clearance is only the same as plasma clearance calculated by standard pharmacokinetic techniques when the solute is totally excluded from red blood cells. 

Equation 6.3 provides an estimate of dialysis plasma clearance (CLp) that is pharmacokinetically consistent with estimates of elimination and intercompartmen-tal clearance that are based on plasma concentration measurements. On the other hand, if the average drug concentration in blood entering the dialyzer (B) is substituted for P, a valid estimate of blood clearance (CLg) is obtained ... 

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) ... 

As discussed in Chapter 30 and elsewhere (13), interspecies scaling is based upon allometry (an empirical approach) or physiology. Protein pharmacokinetic parameters such as volume of distribution (Pd), elimination half-life (b/2)/ and elimination clearance (CL) have been scaled across species using the standard allometric equation (14) ... 

It can be seen from Equation 9.25 that there is a linear relationship between the plasma concentration and dosage of drug required to maintain it (linear pharmacokinetics). For example, for a drug with a clearance of 10 L h, a dosage rate of 30 pg h 1 is required for a Css of 3 pg L If an increase in the steady-state concentration to 6 pg L 1 is required, a concentration of 60 pg h 1 would have to be administered. In the case of nonlinear pharmacokinetics, [S] is not << Km and the relationship between DR and Css is given by... 

Attempts were made to fit the in vivo serum concentration results to pharmacokinetic models based on revised diffusion-model equations for the uncoated and coated valve-rim Inserts. To couple the in vitro diffusion equations to an in vivo simulation, a classical one-compartment model of drug distribution was employed. The mean apparent volume of distribution, = 5.63 liters, and the first order eliminating constant, K = 0.695/hr, for gentamicin were determined in the intravenous fnjection-clearance studies. 

The elimination half-life (T1/2) is the time it takes for the elimination processes to reduce the plasma concentration or the amount of drug in the body by 50%. Elimination half-Ufe is a composite pharmacokinetic parameter determined by both clearance and volume of distribution (Vj), as described by the following equation ... 

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