Pharmacokinetics descriptive parameters

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... 

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. 

Fig. 5.2 Descriptive pharmacokinetic parameters (a) plasma concentration-time plot and (b) semi-logarithmic plot.

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 ... 

Pharmacokinetics is defined as the study of the quantitative relationship between administered doses of a drug and the observed plasma/blood or tissue concentrations.1 The pharmacokinetic model is a mathematical description of this relationship. Models provide estimates of certain parameters, such as elimination half-life, which provide information about basic drug properties. The models may be used to predict concentration vs. time profiles for different dosing patterns. 

It is possible to predict what happens to Vd when fu or fur changes as a result of physiological or disease processes in the body that change plasma and/or tissue protein concentrations. For example, Vd can increase with increased unbound toxicant in plasma or with a decrease in unbound toxicant tissue concentrations. The preceding equation explains why because of both plasma and tissue binding, some Vd values rarely correspond to a real volume such as plasma volume, extracellular space, or total body water. Finally interspecies differences in Vd values can be due to differences in body composition of body fat and protein, organ size, and blood flow as alluded to earlier in this section. The reader should also be aware that in addition to Vd, there are volumes of distribution that can be obtained from pharmacokinetic analysis of a given data set. These include the volume of distribution at steady state (Vd]SS), volume of the central compartment (Vc), and the volume of distribution that is operative over the elimination phase (Vd ea). The reader is advised to consult other relevant texts for a more detailed description of these parameters and when it is appropriate to use these parameters. 

In conclusion, pharmacokinetics is a study of the time course of absorption, distribution, and elimination of a chemical. We use pharmacokinetics as a tool to analyze plasma concentration time profiles after chemical exposure, and it is the derived rates and other parameters that reflect the underlying physiological processes that determine the fate of the chemical. There are numerous software packages available today to accomplish these analyses. The user should, however, be aware of the experimental conditions, the time frame over which the data were collected, and many of the assumptions embedded in the analyses. For example, many of the transport processes described in this chapter may not obey first-order kinetics, and thus may be nonlinear especially at toxicological doses. The reader is advised to consult other texts for more detailed descriptions of these nonlinear interactions and data analyses. 

For the purposes of simplicity, the description of each study is limited to the collection, handling, and interpretation of pharmacokinetic data although clearly safety (and pharmacodynamic) parameters are also studied. 

Due to the small sample size, all variables were only presented descriptively for the different bioanalytical data and pharmacokinetic parameters calculated. 

Descriptive statistics for the primary pharmacokinetic parameters of XYZ1234 on days 1 and 7 are shown in Tables 1 1. 

If appropriate, pharmacokinetic parameters were compared descriptively between age groups (with/ without stratification), between genders (with/without stratification), and between fasted and fed subjects (with/without stratification and individually). Although not intending to show bioequivalence, the 90 % confidence intervals (Cl) for the differences in the log transformed exposure measurements were calculated. 

Due to the small sample size, all variables were only presented descriptively for the different bioanalytical data and pharmacokinetic parameters calculated number of relevant observations, geometric mean, geometric standard deviation, arithmetic mean, standard deviation, coefficient of variation, median, minimum and maximum. 

Plasma caffeine and paraxanthine Descriptive pharmacokinetic parameters (standard parameters including peak concentrations (Cmax), time of Cmax (Tmax), area-under-the-curve (AUC) between time 0 and time t where t = 24 h post dose (AUCo-t), AUC after extrapolation to infinity (AUCo-co), apparent terminal half-life total clearance (CL)) for... 

While formulation interactions often are subject to in vitro investigations, the section below presents a particular example of an in vivo formulation interaction study (CPMP/EWP/QWP/1401/98 2002) a potential interaction of a drug in medical practice frequently given concomitantly with another drug (i.e. both mixed in a syringe) was subject to a clinical study which is illustrated below. For the purposes of simplicity, the description is limited to the collection, handling, and interpretation of pharmacokinetic data although clearly safety and pharmacodynamic parameters were also studied. 

The data pertinent to the assessment of the impact of obesity on the disposition of the developmental drug from study described above, was evaluated as follows Descriptive pharmacokinetic parameters (total clearance (CL or CL/F), mean residence time (MRT),... 

For pharmacokinetics in plasma Individual concentrations of XYZ1234 will be tabulated together with descriptive statistics and plotted. Median profiles will be presented graphically by CYP 2C19 metabolizer status and gender. Pharmacokinetic parameters (at least Cmax, tmax, AUC(o-t) [t = 24 h and last > LOQ ], AUCinf, ti/2z, MT, as well as CL/f and Vz/f) will be determined based on plasma concentrations of X YZ1234 using non-compartmental procedures. 

It is important to emphasize that all pharmacokinetic, fixed effect and random parameters, i.e. 0, co2, and a2, are fitted in one step as mean values with standard error by NONMEM. A covariance matrix of the random effects can be calculated. For a detailed description of the procedure see Grasela and Sheiner (1991) and Sheiner and Grasela (1991). 

Description Of the Model. Travis et al. (1990) developed a model to describe the pharmacokinetics of benzene in mice, rats, and humans. The model contained five compartments, consisting of liver, fat, bone marrow, and muscle, and organs such as brain, heart, kidney, and viscera, connected by the arterial and venous blood pathways. Michaelis-Menten kinetics was assumed in all species, and occurred primarily in the liver, and to a lesser extent in the bone marrow. The species-specific physiological and chemical parameters were taken from the literature. The metabolic parameters were obtained by fitting the empirical data to the model. 

Description of the Model. Bois and Paxman (1992) produced a model that they used to explore the effect of exposure rate on the production of benzene metabolites. The model had three components, which described the pharmacokinetics of benzene and the formation of metabolites, using the rat as a model. Distribution and elimination of benzene from a five-compartment model, comprised of liver, bone marrow, fat, poorly perfused tissues, and well perfused tissues, made up the first component of the model. The five-compartment model included two sites for metabolism of benzene, liver and bone marrow. The bone marrow component was included for its relevance to human leukemia. Parameter values for this component were derived from the literature and from the previously published work of Rickert et al. 

Pharmacokinetic parameters fall basically into two categories. One category is qualitative or descriptive in that the parameters are observational, requiring no formula for calculation. Examples would include the maximal observed concentration of a drug or the amount of drug excreted in the urine during a given... 

Under what circumstances can the two methods be used to estimate the pharmacokinetic parameters of interest The answer to this question is the subject of this chapter. To begin, one must start with a definition of kinetics, since it is through this definition that one can introduce mathematical and statistical analyses to study the dynamic characteristics of a system. This can be used to define specific parameters of interest that can be estimated from data. From the definition of kinetics, the types of equations that can be used to provide a mathematical description of the system can be given. The assumptions underlying... 

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