12:00:00">

Boomer Manual and Download
PharmPK Listserv and other PK Resources
Previous Page	Previous Chapter	Course Index	Next Chapter	Next Page

Method of Residuals

Starting with the equation for Cp versus time

Equation 18.2.1 Cp versus Time after Oral Administration

this can be written as

Equation 18.2.2 Simplified Equation for Cp versus Time

A =

Equation 18.2.3

Figure 18.2.1 Semi-log plot of Cp versus Time after Oral Administration

Click on the figure to view the Java Applet window
Java Applet as a Linear Plot

If one of the rate constants (ka or kel) is much larger than the other, the method works best if the difference is at least five times, then the faster differential will approach zero more quickly, and at later times can be ignored. If we plot Cp versus time on semi-log graph paper we will see that the slope will approach a straight line.

The equation for this straight line portion can be obtained from the equation for Cp by setting the faster term (usually e^-ka*t) to zero:

Figure 18.2.2 Semi-log Plot of Cp versus Time Showing Cp^late, Slope, and Intercept

then

Equation 18.2.4 Cp^late versus Time

and plotting Cp^late versus time gives a straight line on semi-log graph paper, with a slope (ln) = -kel and intercept = A.

Now looking at the equation for Cp versus time again.

Equation 18.2.5 Cp versus Time including Cp^late

therefore

Equation 18.2.6 Difference or Residual versus Time

Plotting the ln (Residual) versus time should give another straight line graph with a slope (ln) equal to - ka and the same intercept as before, i.e. A

Equation 18.2.7 ln(Residual) versus Time

Figure 18.2.3 Semi-log of Plot of Residual versus Time

This is the method of residual or "feathering".

It can give quite accurate values of kel, ka, and V/F if :-

i) One rate constant is at least five times larger than the other

and

ii) Both absorption and elimination are first order processes.

An Example Calculation Using the Method of Residuals

Table 18.2.1 Example Data for the Method of Residuals

Time
(hr) Plasma
Concentration
(mg/L) Cp(late)
(mg/L) Residual
[Col3 - Col2]
(mg/L)

0.25 1.91 5.23 3.32

0.5 2.98 4.98 2.00

0.75 3.54 4.73 1.19

1.0 3.80 4.50 0.70

1.5 3.84 4.07 0.23

2.0 3.62 3.69 0.07

3.0 3.04

4.0 2.49

5.0 2.04 Residual = 5.5 * e^{2.05 * t}

6.0 1.67 Cp^late = 5.5 * e^{0.2 * t}

7.0 1.37

Figure 18.2.4 Figure Illustrating the Method of Residuals

The objective of this panel is to illustrate the Method of Residuals for determining information about the drug absorption process.

First: Draw the Cp^late line by changing the intercept (A(k1)) and slope (k1) values. Press the Cp(late) button to plot the line and calculate the residual values.

Second: Draw the Residual line by changing the intercept (A(k2)) and slope (k2) values. Press the Plot Residual button to plot the residual line.

By trial and error best fit lines can be drawn and the parameters determined.

Up to eleven (11) different data points can be entered instead of the example data provided. Leave fields empty if there are fewer than 11 data points in your data set.

For practice try calculating the absorption rate constant, ka, using the method of residuals. Compare your answers with the computer! Note the value of the ration ka/kel.

This file was last modified:

Time (hr)	Plasma Concentration (mg/L)	Cp(late) (mg/L)	Residual [Col3 - Col2] (mg/L)
0.25	1.91	5.23	3.32
0.5	2.98	4.98	2.00
0.75	3.54	4.73	1.19
1.0	3.80	4.50	0.70
1.5	3.84	4.07	0.23
2.0	3.62	3.69	0.07
3.0	3.04
4.0	2.49
5.0	2.04		Residual = 5.5 * e^{2.05 * t}
6.0	1.67	Cp^late = 5.5 * e^{0.2 * t}
7.0	1.37