Plasma concentration model parameter estimation

PK models can be employed in two distinct modes. The previous section described using known PK parameters from the literature to estimate plasma concentrations. This section explains how to use measured plasma concentration data to estimate the model parameters for the one-compartment bolus IV model. 

The quantities AUMC and AUSC can be regarded as the first and second statistical moments of the plasma concentration curve. These two moments have an equivalent in descriptive statistics, where they define the mean and variance, respectively, in the case of a stochastic distribution of frequencies (Section 3.2). From the above considerations it appears that the statistical moment method strongly depends on numerical integration of the plasma concentration curve Cp(r) and its product with t and (r-MRT). Multiplication by t and (r-MRT) tends to amplify the errors in the plasma concentration Cp(r) at larger values of t. As a consequence, the estimation of the statistical moments critically depends on the precision of the measurement process that is used in the determination of the plasma concentration values. This contrasts with compartmental analysis, where the parameters of the model are estimated by means of least squares regression. 

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. 

Figure 30.6 shows a prediction of the plasma concentration of ARA-C and total radioactivity (ARA-C plus ARA-U) following administration of two separate bolus intravenous injections of 1.2 mg/kg to a 70-kg woman. All compartment sizes and blood flow rates were estimated a -priori, and all enzyme kinetic parameters were determined from published in vitro studies. None of the parameters was selected specifically for this patient only the dose per body weight was used in the simulation. The prediction has the correct general shape and magnitude. It can be made quantitative by relatively minor changes in model parameters with no requirement to adjust the parameters describing metabolism. 

Conceptual models of percutaneous absorption which are rigidly adherent to general solutions of Pick s equation are not always applicable to in vivo conditions, primarily because such models may not always be physiologically relevant. Linear kinetic models describing percutaneous absorption in terms of mathematical compartments that have approximate physical or anatomical correlates have been proposed. In these models, the various relevant events, including cutaneous metabolism, considered to be important in the overall process of skin absorption are characterized by first-order rate constants. The rate constants associated with diffusional events in the skin are assumed to be proportional to mass transfer parameters. Constants associated with the systemic distribution and elimination processes are estimated from pharmacokinetic parameters derived from plasma concentration-time profiles obtained following intravenous administration of the penetrant. 

Unlike the estimates of dosage rates and average steady-state plasma concentrations, which may be determined independently of any pharmacokinetic model in that systemic clearance is the only pharmacokinetic parameter used, the prediction of peak and trough steady-state concentrations requires pharmacokinetic compartmental model assumptions. It is assumed that, (i) drug disposition can be adequately described by a one-compartment pharmacokinetic model, (ii) disposition is independent of dose (i.e. linear pharmacokinetics apply), and (iii) the absorption rate is much faster than the rate of elimination of the drug, which is always valid when the drug is administered intravenously. For clinical applications, these assumptions are reasonable. 

Gibaldi M. Estimation of the pharmacokinetic parameters of the two-compartment open model from post-infusion plasma concentration data. J Pharm Sci 1969 58 1133-1135. 

Hence, intravenous data were modeled first, followed by inhalational, then intranasal. Once the pharmacokinetics of each individual route of administration was established, all model parameters were then estimated simultaneously. Initial values for cocaine pharmacokinetics after intravenous administration were estimated using noncompartmental methods. Total systemic clearance was estimated at 100 L/h and volume of distribution at steady-state was estimated at 232 L. Central compartment clearance and intercompartmental clearance were set equal to one-half total systemic clearance (50 L/h), whereas central and peripheral compartment volumes were set equal to one-half volume of distribution (116 L). Data were weighed using a constant coefficient of variation error model based on model-predicted plasma concentrations. All models were fit using SAAM II (SAAM Institute, Seattle, WA). An Information-Theoretic approach was used for model selection, i.e., model selection was based on the AIC. 

Figure 5.9 Scatter plot and model predicted overlay of cocaine plasma concentrations after intranasal administration. The final model was Model 6 in Fig. 5.5 with only the absorption parameters related to intranasal administration treated as estimable all other model parameters were fixed.

The second way that an independent data set is used in validation is to fix the parameter estimates under the final model and then obtain summary measures of the goodness of fit under the independent data set (Kimko, 2001). For example, Mandema et al. (1996) generated a PopPK model for immediate release (IR) and con-trolled-release (CR) oxycodone after single dose administration. The plasma concentrations after four days administration were then compared to model predictions. The log-prediction error (LPE) between observed concentrations (Cp) and model predicted concentrations (Cp j was calculated as... 

Measured Plasma Concentration Data 221 10.10.4 Estimating Model Parameters from... 

The previous section explained how to estimate plasma concentrations based on known PK parameters for a drug this section provides the methods for estimating the PK parameters of a drug based on experimental plasma measurements. The data analysis methods for each model have some steps in common, but each also contains calculations specific to the given model. 

The one-compartment bolus IV injection model is mathematically the simplest of aU PK models. Drug is delivered directly into the systemic circulation by a rapid injection over a very short period of time. Thus the bolus rV injection offers a near perfect example of an instantaneous absorption process. Representation of the body as a single compartment implies that the distribution process is essentially instantaneous as well. The exact meaning of the assumptions inherent in this model are described in the next section. Model equations are then introduced that allow the prediction of plasma concentrations for drugs with known PK parameters, or the estimation of PK parameters from measured plasma concentrations. Situations in which the one-compartment instantaneous absorption model can be used to reasonably approximate other types of drug delivery are described later in Section 10.7.5. 

Plasma samples for PK analysis by a one-compartment IV infusion model can be collected either during the infusion period and/or during the postinfusion period. However, plasma samples from the postexposure period are easier to analyze by standard PK methods. PK parameters can be estimated from plasma concentration data collected during the infusion period only if the infusion is continued long enough (T > 7 ty eiim) to provide a reasonable estimate for the steady-state plasma concentration (Q ). 

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