Calculation of F

Returning to the equation for Cp as a function of time

Equation 18.5.1 Drug Concentration versus Time after Oral Administration

We can calculate ka and kel given Cp versus time data. From the method of residuals, the intercept can be determined as

Since we know the DOSE and have calculated ka and kel, it is possible to calculate F/V. However, with only data from a single administration available that's all we can determine, we cannot separate V and F. Of course if we have IV data for kel and V, we could use this to determine F.

Thus F must be determined by comparison with another dose administration. If the other dosage form is an intravenous form then the F value is termed the absolute bioavailability. In the case where the reference dosage form is another oral product, the value for F is termed the relative bioavailability.

Using plasma data

When a bioavailability study is conducted at least two dosage forms are administered to each subject. One dosage form is the product to be tested, while the other dosage form is a standard or reference dosage form. This may be an IV dose, oral solution or most commonly the original manufacturer's product. The doses are given with sufficient time between administrations for the drug to "washout" or be completely eliminated. We usually assume that each subject eliminates each dosage form at the same rate.

During the derivation of the Wagner-Nelson equations we calculated Amax, the maximum amount absorbed as:-

Equation 18.5.2 A_max, Total Amount Absorbed

or

and since

therefore

Equation 18.5.3 Bioavailability or Fraction Absorbed

Now by giving two dosage forms A and B, and calculating AUC values for each.

Equation 18.5.4 Bioavailability of Product A Relative to Product B

and if DOSE^A = DOSE^B and if we can assume that kel^A = kel^B and V^A = V^B then

Equation 18.5.5 Bioavailability, F, from AUC Comparison

Thus a relative bioavailability, F, can be calculated. If dosage form B is an IV administration then F^B = 1 and F = F^A and thus F^A can be called the absolute bioavailability.

Example

Using Urine Data

Since

Equation 18.5.6 Fraction Excreted as Unchanged Drug, fe

therefore

and for two dosage forms

as before if DOSE^A = DOSE^B and fe^A = fe^B then

Example

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Copyright 2001-3 David W. A. Bourne (david@boomer.org)