Pharmacokinetics parameters from compartmental

Recovering Pharmacokinetic Parameters from Compartmental Models... 

C. Dansirikul, M. Choi, and S. B. Duffnll, Estimation of pharmacokinetic parameters from non-compartmental variables using Microsoft Excel(R). Comp Biol Med 35 389-403 (2005). 

The primary analysis examined pharmacokinetic parameters calculated from plasma concentrations of CYS-conjugated XYZ1234 using non-compartmental techniques. The secondary analysis examined the pharmacokinetic parameters of unconjugated XYZ1234. 

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. 

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. 

The following discussion will describe how AUC and AUMC are estimated, how they are used to estimate specific pharmacokinetic parameters (including the assumptions), and what their relationship is to specific pharmacokinetic parameters estimated from compartmental models. Both moments, however, are used for other purposes. For example, AUC acts as a surrogate for exposure, and values of AUC from different dose levels of a drug have been used to justify assumptions of pharmacokinetic linearity. These uses will not be reviewed. 

Reaction rate parameters required for the distributed pharmacokinetic model generally come from independent experimental data. One source is the analysis of rates of metabolism of cells grown in culture. However, the parameters from this source are potentially subject to considerable artifact, since cofactors and cellular interactions may be absent in vitro that are present in vivo. Published enzyme activities are a second source, but these are even more subject to artifact. A third source is previous compartmental analysis of a tissue dosed uniformly by intravenous infusion. If a compartment in such a study can be closely identified with the organ or tissue later considered in distributed pharmacokinetic analysis, then its compartmental clearance constant can often be used to derive the required metabolic rate constant. 

The AUC can be determined from plasma concentration versus time data by employing the trapezoidal rule or an appropriate equation (depending on the route of dmg administration and the compartmental model chosen). In any case, the use of an equation requires the knowledge of pharmacokinetic parameters such as the... 

The two most commonly used methods for characterizing pharmacokinetic data are noncompartmental analysis and the fitting of compartmental models. The latter technique can range from simple one to three well-stirred compartments to physiologically-based pharmacokinetic (PBPK) models, which are covered in the next section. The choice of which method to utilize will be largely dictated by the goals and objectives of the analysis. For example, descriptions of major pharmacokinetic parameters for linear systems (i.e., net systemic exposure is dose-proportional) can be easily calculated from a noncompartmental... 

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. 

The principal parameter used to indicate the rate of drug absorption is Cmax, even though it is also influenced by the extent of absorption the observed fmaX is less reliable. Because of the uncertainty associated with Cmax, it has been suggested (Endrenyi Yan, 1993 Tozer, 1994) that Cmax/AUCo-loq/ where AUCo-loq is the area under the curve from time zero to the LOQ of the acceptable analytical method, may more reliably measure the rate of drug absorption, except when multiexponential decline is extensive. Estimation of the terms should be based on the observed (measured) plasma concentrationtime data and the use of non-compartmental methods rather than compart-mental pharmacokinetic models. MRTs, from time zero to the LOQ of the analytical method, for the test and reference products can be compared, assuming that first-order absorption and disposition of the drug apply (Jackson Chen, 1987). 

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. 

Often in pharmacokinetics the analyst has data on more than one individual. In a typical Phase 1 clinical trial, there might 12-18 subjects who have pharmacokinetic data collected. Applying a compartmental model to each individual s data generates a vector of parameter estimates, each row of which represents a realization from some probability distribution. For example,... 

From a pharmacokinetic point of view, the simplest ronte of administration is the intravenons (IV) bolns dose. Thns, the simplest compartmental model is the one-compartment model with IV bolns administration and first-order elimination of the drng (Fignre 12.1). This model inclndes an apparent volnme of distribution, V. This volume parameter is used to relate the amount of drug in the body with the concentration measured in plasma, serum, or blood (Equation... 

Compartmental modeling involves the specification of a structural mathematical model (commonly using either explicit or ordinary differential equations) and system parameters are estimated from fitting the model to pharmacokinetic data via non linear regression analysis or population mixed effects modeling. One popular structural model is the open two-compartment model shown in Figure 6.10. 

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