Determining ka using the WagnerNelson Method
Oral Dosing  Linear One Compartment
A 1000 mg oral dose of a drug was administered to a healthy volunteer. Eighteen 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. An earlier study with this same drug given by IV bolus indicated that the elimination rate constant, kel, was 0.2448 hr^{1}
Time (hr)

Cp (mg/L)






0

0.0






0.25 
8.759 





0.5 
14.533 





0.75 
19.793 





1 
17.453 





1.5 
18.837 





3 
14.094 





6 
7.196 





12 
1.618 





18 
0.348 





24 
0.082 





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). With these data
and the elimination rate constant from the IV bolus data we can estimate A/V versus time data using Equation 18.2.3
Estimate the maximum value of A/V and set this equal to A(max)/V. The next calculation is to calculate A(max)/V  A/V (or (A(max)  A)/v) at each times or at least up to the time of the peak Cp concentration. The plot of [A(max)/V  A/V] versus time on se
milog graph paper then provides an estimate of the absorption rate constant, ka if absorption is a first order process.
Estimate ka.
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The data above were calculated using the equations:
Equation 18.2.1 Drug Concentration, Cp, after Oral Administration (ka ≠ kel)
or
Equation 18.2.2 Drug Concentration, Cp, after Oral Administration (ka = kel)
Equation 18.2.3 Amount Remaining to be Absorbed/V (A/V) according the WagnerNelson method
In Equations 18.2.1 and 18.2.2 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.
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