# Determining ka using the Wagner-Nelson Method

## Oral Dosing - Linear One Compartment

A 750 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 0.1139 hr-1

 Time (hr) Cp (mg/L) 0 0.0 0.25 26.281 0.5 37.484 0.75 41.241 1 41.819 1.5 42.062 3 36.276 6 27.125 12 13.647 18 7.21 24 3.155

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 mi-log 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 Wagner-Nelson 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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