Plasma concentration versus time plots compartment models

The first step in performing PK modeling is to graph the plasma concentration versus time profile to examine the shape of the curve and to get some preliminary ideas whether the data would fit a one-, two- or a three-compartment PK model. From the semi-logarithmic plot (Figure 1), it was obvious that the compound exhibited either two- or three-compartment kinetics. 

A one-compartment model (Figure 6.15) is based on a single compartment— here, the plasma—also referred to as the central compartment. A first-order rate constant kg determines how fast the drug is absorbed into the bloodstream, while the first-order elimination rate constant kei describes the speed at which the drug is removed. A logarithmic plot of plasma concentration versus time is linear with a slope of - kei/2.303. The plasma concentration as a function of time is described by the relationship ... 

Analysis of postinfusion data for a one-compartment IV infusion model is nearly identical to the analysis of plasma concentrations in the one-compartment bolus IV model. The first step is to calculate the natural logarithm of each of the measured postinfusion plasma concentration values. If the concentration (C7) is measured at < = T, then this value can be included in the postinfusion analysis as well. The values of In Cp) are plotted versus the time after infusion stopped t—T) for each sample. If the plot shows a series of points falling near a straight line, then the data can be represented by the one-compartment IV infusion model. Just as in the bolus IV case, early high points above the line formed by most of the data indicate the one-compartment model is not the best PK model for the data, and erratic late data points could mean the values are unreliable, as illustrated in Figure 10.32. 

Figure 4.6 Application of the trapezoidal rule to determine the area under the plasma concentration (Cp) versus time curve (AUC). (Rectilinear plot of plasma or serum concentration versus time following the administration of an intravenous bolus of a drug fitting a one-compartment model.)...

Figure 6.12 (a) Semilog plot of plasma concentration (Cp) versus time. Cp° is the intercept on the y-axis, and Kei is the elimination rate constant, (b) Single compartment model with rate constants for absorption, K, and for elimination, Kcl. 

Figure 6.13 (a) Semilog plot of plasma concentration for (Cp) versus time representative of a two-compartment model. The curve can be broken down into an a or X i distribution phase and ft or k2 elimination phase, (b) Two-compartment model with transfer rate constants, Kn and K2, and elimination rate constant, Ke. ... 

Estimation of multicompartment model parameters from measured plasma samples is very similar to the procedures described previously for the two-compartment first-order absorption model. The first step is to calculate bi(C ) for each of the measured plasma sample concentrations. The values of In(C ) are then plotted versus time (t), and the points on the terminal line are identified. Linear regression analysis of the terminal line provides values for B (B = c ) and In = —m). The first residual (/ i) values are then calculated as the difference between the measured plasma concentrations and the terminal line for points not used on the terminal line. A plot of ln(i i) versus t is then employed to identify points on the next terminal line, with linear regression analysis of this line used to determine and X -. Successive method of residuals analyses are then used to calculate the remaining B and A, values, with linear regression of the n-1 residual (Rn-i) values providing the values of Bi and Aj. If a first-order absorption model is being used, then one more set of residuals (R ) are calculated, and the linear regression analysis of these residuals then provides and kg. This type of analysis is typically performed by specialized PK software when the model contains more than two compartments. 

Figure 13.9 Atypical plasma concentration (Cp) versus time profile for a drug that obeys a two-compartment model following intravenous bolus administration (semilogarithmic plot).

Figure 13.10 A plasma concentration (Cp) versus time profile for a drug that obeys a two-compartment model following intravenous bolus administration plotted on semilogarithmic paper, p, slow disposition, or post-distribution, rate constant 6, empirical constant 4, apparent volume of distribution for the central compartment /C21, transfer rate constant Xq, administered dose a, distribution rate constant.

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