Plot Types
The plots presented before, for cumulative amount excreted into urine as unchanged drug versus time (U), rate of excretion versus time (R/E), and amount remaining to be excreted versus time (A.R.E.) versus time, have the same significance as earlier. Now that we don't have the restriction of only one elimination pathway these graphs provide more information about the routes of excretion.
Cumulative amount excreted versus time
The first of these plots is the linear plot of cumulative amount excreted into urine as unchanged drug versus time. Notice that the value of U∞ is no longer equal to the dose, it is somewhat less than dose. The remaining portion of the dose is found in the metabolites and other routes of excretion.
The equation for the cumulative amount excreted versus time is shown below in Equation 12.8.1.
Equation 12.8.1 Cumulative Amount excreted into Urine versus Time
This translates into the plot shown in Figure 12.8.1. Notice that the total amount excreted as unchanged drug, U∞, is less than the dose administered.
Figure 12.8.1 Linear Plot of U versus Time showing Approach to U∞ not equal to DOSE
Click on the figure to view the Java Applet window
Java Applet as a Semi-log Plot
Cumulative amount excreted plots are basically descriptive in nature. At most, you can get a general sense of how much drug is excreted, an estimate of U∞ and an appoximate estimate of t1/2.
Rate of excretion (R/E)
Equation 12.8.2. Natural log of Rate of Excretion versus Time
Note: The interecept (on semi-log graph paper) is ke • DOSE not kel • DOSE
Figure 12.8.2. Semi-log Plot of ΔU/Δt versus Timemidpoint Showing Slope = - kel
with fe = 0.75, kel = 0.2 hr-1; ke = 0.15 hr-1
Click on the figure to view the Java Applet window
Java Applet as a Linear Plot
Rate of excretion plots can be very useful in the determination of the parameters such as kel, ke and fe. Each data point tends to be independent, especially if the bladder is fully voided for each sample. This method can be used even if there is a missed sample. There can be a little more scatter that with the A.R.E. plot. For drugs that are excreted quickly collecting sufficient, early sample can be difficult. NOTE: This plot is rate of excretion versus midpoint of the collection interval, time.
Amount remaining to be excreted (A.R.E.)
Equation 12.8.3 Cumulative amount excreted versus time
rearranging gives
Equation 12.8.4 Amount Remaining to be Excreted as Unchanged Drug versus Time
and taking the log of both sides give the straight line equation:
Equation 12.8.5 Ln(ARE) versus time
where
Equation 12.8.6 U∞
Note ke and fe
Thus:
Equation 12.8.7 ARE versus time
Figure 12.8.3 Semi-log Plot of ARE versus time
Note ke
Click on the figure to view the Java Applet window
Java Applet as a Linear Plot
Amount remaining to be excreted (A.R.E.) plots use the U∞ value to estimate each data point. Error in any data is accumulated into U∞ and thus each A.R.E. value. This can lead to curved lines (instead of the expected straight lines) or an inability to use the method (with a missing sample). With good data these plots may be somewhat smoother.
For practice you can use these urine data collected after an IV bolus dose and estimate pharmacokinetic parameters.
Compare your answers with the computer!
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Copyright 2001-3 David W. A. Bourne (david@boomer.org)
This file was last modified:
Friday 23 Jan 2004 at 03:48 PM