Determining ka using the Method of Residuals

Oral Dosing - Linear One Compartment

A 250 mg oral dose of a drug was administered to a healthy volunteer. Blood samples were collected and plasma was separated from each blood sample and analyzed for drug concentration. The collected data are shown in the table below.

Estimate kel, ka and V/F. Does the ratio of ka to kel satisfy the requirement of the method of residuals?

Time (hr) Cp (mg/L)    
0.2 4.534    
0.3 6.031    
0.5 7.833    
0.6 8.258    
0.8 8.645    
0.9 8.911    
1.75 7.604    
3.5 4.327    
5.5 2.094    
7 1.258    

The table above provides a set of data for you to analyze. With just data collected after oral administration the F/V term is combined into a single parameter, typically the reciprocal V/F (and S is known and combined with the dose value). Using these data you should be able to estimate the slow rate constant, usually the elimination rate constant (kel) (unless there is a flip-flop) from the plot of Cplate versus time on semi-log graph paper. You can then calculate the residual as the difference between early observed drug concentration values and the extrapolated Cplate values. The plot of this residual on semi-log graph paper then provides an estimate of the faster rate constant, usually the absorption rate constant, ka.


If you want to see how the program graphs the data and performs the first step click the button below. The program will calculate the kel and intercept.

NOTE: Clicking the button above
will prevent you getting credit for this problem

Print this page if you want, work the problems and

You will have one chance to submit your answers for this problem [# 1970016514]. You can try the homework problem more than once with different data to improve your grade. Your highest score is recorded. After submitting your answers you can use the browser back arrow to get back here and see how the compuer worked the problem.


The data above were calculated using the equations:

Cp after oral adminstration (ka not equal to kel)

Equation 17.4.1 Drug Concentration, Cp, after Oral Administration (ka ≠ kel)

Cp after oral administration (ka = kel)

Equation 17.4.2 Drug Concentration, Cp, after Oral Administration (ka = kel)

In Equations 17.4.1 and 17.4.2 the S term takes into account the different molecular weight of the measured drug and the salt or other form of the drug that may be administered. A value of S equal to one can often be used especially if the labled dose is expressed in drug weight equivalents. For some drugs this might be considerably lower. For example, aminophylline (M.Wt. 420.44 with two parts theophylline) could be administered to deliver theophylline (M.Wt. 180.17) which gives a ratio of 2 x 180.17/420.44 = 0.86 = S.


Last update: Sat 20 Apr 2019 07:15:57 pm
Privacy Statement - 25 May 2018

Material on this website should be used for Educational or Self-Study Purposes Only

iBook and pdf versions of this material and other PK material is available

Copyright © 2002-19 David Bourne (david@boomer.org)