First-order absorption models plasma concentration versus time

Elimination parameters are determined by linear regression analysis of the measured plasma concentration data falling on the terminal line. As always, the first step is to calculate the natural logarithm of each of the measured plasma concentration values. The values of In(C ) are then plotted versus time (t). If the plot shows later points falling near a straight terminal line with no early points above the terminal line, then the data can be well represented by the one-compartment first-order absorption model. As with previous one-compartment models, early high points above the terminal line indicate that 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 10.47. 

Figure 10.79 Graphical representation of the plasma concentration (Cp) versus time (f) and In(Cp) versus f for a two-compartment first-order absorption model.

The plasma concentration versus time equation for the two-compartment first-order absorption model contains three exponential decay terms, and three corresponding phases in Figure 10.80. The first exponential decay term contains the larger hybrid rate constant (/li), which dominates just after t ax during the distribution phase. Hence li is called the hybrid distribution rate constant. The second exponential decay term contains the smaller hybrid rate constant I2), which dominates at later times during the elimination phase. The third exponential decay curve contains and dominates the early rising absorption phase. The two-compartment elimination half-lrfe is then written in terms of as... 

Each of the exponential decay terms in the generalized multicompartment models represent a distinct phase or change in shape of the plasma concentration versus time curve. The extra (n+l) exponential term for first-order absorption always has the absorption rate constant (ka) in the exponent, and always represents an absorption phase. The exponential term with the smallest rate constant (A ) always represents the elimination phase, and this rate constant always represents the elimination rate constant and always equals the terminal line slope m= — A J. All other exponential terms represent distinct distribution phases caused by the different rates of distribution to different tissue compartments. 

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. 

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