Noncompartmental Pharmacokinetic Analysis

In pharmaceutical research and drug development, noncompartmental analysis is normally the first and standard approach used to analyze pharmacokinetic data. The aim is to characterize the disposition of the drug in each individual, based on available concentration-time data. The assessment of pharmacokinetic parameters relies on a minimum set of assumptions, namely that drug elimination occurs exclusively from the sampling compartment, and that the drug follows linear pharmacokinetics that is, drug disposition is characterized by first-order processes (see Chapter 7). Calculations of pharmacokinetic parameters with this approach are usually based on statistical moments, namely the area under the concentration-time profile (area under the zero moment curve, AUC) and the area under the first moment curve (AUMC), as well as the terminal elimination rate constant (Xz) for extrapolation of AUC and AUMC beyond the measured data. Other pharmacokinetic parameters such as half-life (t1/2), clearance (CL), and volume of distribution (V) can then be derived. 

An assumption concerning the number of compartments is, by nature, not required. For reliable results and precise parameter estimates, however, a relatively large number of data points per individual are required. Phase 1 studies of mAbs usually provide sufficient data for a noncompartmental analysis, but the assumption of linear pharmacokinetics is not valid for most mAbs. This prerequisite, however, was frequently neglected during the early years of therapeutic mAh development, and an overall estimate for CL, for example, was frequently reported in the literature. In dose-escalating studies, however, the concentration-time plots of the raw data clearly indicate that the slope of the terminal phase is not parallel for the different doses, but increases with increasing dose (Fig. 3.10). As a result, the listing of different clearance values for different doses can be found. For example, the clearance of trastuzumab was reported to be 88.3 mL/h for a 10-mg dose, 34.3 mL/h for a 50-mg dose, 25.0 mL/h for a 100-mg dose, 19.0 mL/h for a 250-mg dose, and 16.7 mL/h for a 300-mg dose. 

Despite these limitations, even today noncompartmental analysis approaches are sometimes the only way in which pharmacokinetic data of mAbs are analyzed. Especially for the mechanistic understanding of the behavior of mAbs in the body, a noncompartmental analysis cannot be recommended. 

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Limitations of Noncompartmental Pharmacokinetic Analysis of Biotech Drugs... 

A basic assumption related to both methods of analysis is that the elimination of drug from the body is exclusively from the sampling compartment (i. e., blood/ plasma), and that rate constants are first order. However, when some or all of the elimination occurs outside the sampling compartment - that is, in the peripheral or tissue compartment(s) - these types of analysis are prone to error in the estimation of Vss, but not CL. In compartmental modeling, the error is related to the fact that no longer do the exponents accurately reflect the inter-compartmental and elimination (micro) rate constants. This model mis specification will result in an error that is related to the relative magnitudes of the distribution rate constants and the peripheral elimination rate constant. However, less widely understood is the fact that this model mis specification will also result in errors in noncompartmental pharmacokinetic analysis. 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

Pharmacokinetics After Oral and Intravenous Administration. For proper characterization of an inhalation drug, information on the systemic pharmacokinetic properties needs to be provided. One of the major challenges for such studies is to provide a suitable formulation for injection, especially because new drug candidates are often very lipophilic. The resulting parameters of such studies (systemic clearance, volume of distribution, half-life, mean residence time) can then easily be extracted from concentration-time profiles after IV administration and subsequent standard pharmacokinetic analysis by noncompartmental approaches. In addition, a detailed compartmental analysis based on concentration-time profiles will be useful in evaluating the systemic distribution processes in sufficient detail. This will be especially important if deconvolution procedures (see later) are included for the assessment of the pulmonary absorption profiles. 

Foster D M (2001). Noncompartmental vs. compartmental approaches to pharmacokinetic analysis. In A J Atkinson, C E Daniels, R L Dedrick, et al. (eds.). Principles of Clinical Pharmacology Academic Press, New York, pp. 75-92. 

Pharmacokinetic Analysis. Standard noncompartmental analyses were conducted to assess ATI and ATF pharmacokinetics using WinNonlin software (v. 2.1) (Pharsight, Mountain View, CA). The areas under the plasma concentration versus time curve from time zero to inhnity (AUCint) were determined via the log-linear trapezoidal method. The terminal half-life was determined from the relationship of ti/2 = In 2/, where k is the negative slope of the terminal phase of the InC versus time plot. Systemic clearance (CL) was estimated by dividing the administered dose by AUCint. The volume of distribution at steady state (Vss) was determined by the product of clearance and the mean residence time. 

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Two classical methods used in the analysis of pharmacokinetic data are the fitting of sums of exponential functions (2- and 3-compartment mammillary models) to plasma and/or tissue data, and less frequently, the fitting of arbitrary polynomial functions to the data (noncompartmental analysis). 

Noncompartmental analysis is limited in that it is not descriptive or predictive concentrations must be interpolated from data. The appeal of noncompartmental analysis is that the shape of the blood concentration-versus-time curve is not assumed to be represented by an exponential function and, therefore, estimates of metabolic and pharmacokinetic parameters are not biased by this assumption. In order to minimize errors in parameter estimates that are introduced by interpolation, a large number of data points that adequately define the concentration-versus-tie curve are needed. 

In contrast to noncompartmental analysis, in compartmental analysis a decision on the number of compartments must be made. For mAbs, the standard compartment model is illustrated in Fig. 3.11. It comprises two compartments, the central and peripheral compartment, with volumes VI and V2, respectively. Both compartments exchange antibody molecules with specific first-order rate constants. The input into (if IV infusion) and elimination from the central compartment are zero-order and first-order processes, respectively. Hence, this disposition model characterizes linear pharmacokinetics. For each compartment a differential equation describing the change in antibody amount per time can be established. For... 

From previous chapters it is clear that the evaluation. of pharmacokinetic parameters is an essential part of understanding how drugs function in the body. To estimate these parameters studies are undertaken in which transient data are collected. These studies can be conducted in animals at the preclinical level, through all stages of clinical trials, and can be data rich or sparse. No matter what the situation, there must be some common means by which to communicate the results of the experiments. Pharmacokinetic parameters serve this purpose. Thus, in the field of pharmacokinetics, the definitions and formulas for the parameters must be agreed upon, and the methods used to calculate them understood. This understanding includes assumptions and domains of validity, for the utility of the parameter values depends upon them. This chapter focuses on the assumptions and domains of validity for the two commonly used methods — noncompartmental and compartmental analysis. Compartmental models have been presented in earlier chapters. This chapter expands upon this, and presents a comparison of the two methods. 

The quantitative parameters require not only a mathematical formalism but also data from which to estimate them. As noted, the two most common methods used for pharmacokinetic estimation are noncompartmental and compartmental analysis. A comparison of the two methods has been given by Gillespie (1). Comparisons regarding the two methodologies as applied to metabolic studies have been provided by DiStefano III (2) and Cobelli and Toffolo (3). Coveil et al. (4) have made an extensive theoretical comparison of the two methods. 

Using the definition of pharmacokinetics given in terms of spatial and temporal distributions, one can easily progress to a description of the underlying assumptions and mathematics of noncompartmental and compartmental analysis, and, from there, proceed to the processes involved in estimating the pharmacokinetic parameters. This will permit a better understanding of the domain of validity of noncompartmental vs compartmental parameter estimation. 

Moments of a function will play an essential role in estimating specific pharmacokinetic parameters. The modern use of moments in the analysis of pharmacokinetic data and the notions of noncompartmental or integral equation analysis can be traced to Yamaoka et al. (10), although these authors correctly point out that the formulas were known since the late 1930s. 

One of the most common transformations is the natural logarithmic transformation of multiplicative models. Many pharmacokinetic parameters, such as area under the curve (AUC) and maximal concentration, are log-normal in distribution (Lacey et al., 1997), and hence, using the Ln-transformation results in approximate normality. The rationale is as follows (Westlake, 1988). For a drug that has linear kinetics and elimination occurs from the central compartment (the usual assumptions for a noncompartmental analysis) then... 

One must carefully interpret the volumes of distribution of peptides and proteins reported in the literature. Most studies rely on a so-called noncompartmental analysis to estimate primary pharmacokinetic parameters (see Section 3.2.3.1). However, this method is only valid for linear systems, assuming that the site of drug elimination is in rapid equilibrium with the sampling site (plasma). The former... 

Intravenous Drug Disposition. The estimation of primary pharmacokinetic parameters using noncompartmental analysis is based on statistical moment theory [45, 46]. The relationships dehned by this theory are valid under the assumption that the system is linear and time-invariant. For simplicity, we further assume that drug is irreversibly removed only from a single accessible pool (e.g., plasma space). Regardless of the route of administration, the temporal profile of plasma drug concentrations, Cp(t), can represent a statistical distribution curve. As such, the zeroth and first statistical moments (Mo and Mi) are defined as ... 

The noncompartmental analysis of pharmacokinetic data after extravascular drug administration, when coupled with that of IV dosing, can yield additional relevant pharmacokinetic parameters, particularly regarding absorption processes. For example, the systemic availability F), which represents the net fraction of the drug dose reaching the systemic circulation after extravascular administration, is defined as ... 

TABLE 6.5-2. Pharmacokinetic Parameters Estimated by Noncompartmental Analysis for (A) ATI and (B) ATF... 

Statistical moment analysis is a noncompartmental method, based on statistical moment theory, for calculation of the absorption, distribution, and elimination parameters of a drug. This approach to estimating pharmacokinetic parameters has gained considerable attention in recent years. 

Pharmacokinetic evaluation typically includes noncompartmental analysis to characterize pharmacokinetics in terms of AUC or clearance, V, and... 

The pre-exponential terms, Q, and the exponential terms, are used in the noncompartmental analysis to calculate a number of descriptive pharmacokinetic terms that describe the disposition of the drug. Each exponential term has a half-life associated with it. 

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