# Calculation of Bioavailability Parameters

## Calculation of F

So far we have looked at the equation for calculating Cp as a function of time, and then methods of determining ka and kel. That is the method of residuals, the Wagner-Nelson method and the method of inspection. Now to continue, we can look at methods of calculating F, the extent of absorption, i.e. the fraction of the dose which is absorbed.

Returning to the equation for Cp as a function of time Equation 9.5.1 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 oral administration available that is 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 dose then the F value is termed the absolute bioavailability. In the case where the reference dosage form is another oral or other non IV 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 similar rates or use the estimate of the slowest rate to determine the wash-out period.

During the derivation of the Wagner-Nelson equations we calculated Amax, the maximum amount absorbed as:- Equation 9.5.2 Amax, Total Amount Absorbed

or and since  Equation 9.5.3 Bioavailability or Fraction Absorbed

Now by giving two dosage forms A and B, and calculating AUC values for each we can calculate the relative bioavailability of dosage form A with respect to dosage form B, FA/FB. Equation 9.5.4 Bioavailability of Product A Relative to Product B

and if we can assume that kelA = kelB and VA = VB then Equation 9.5.5 Bioavailability, F, from AUC Comparison

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

### Example

AUCA = 12.4 mg.hr/L [Dose = 250 mg] and AUCB = 14.1 mg.hr/L [Dose = 200 mg] then ## Using Urine Data

We can do the same thing using urine data alone.

Since Equation 9.5.6 Fraction Excreted as Unchanged Drug, fe

therefore and for two dosage forms if we assume feA = feB then Equation 9.5.7 Calculation of F from fe Values

### Example

250 mg dose; U∞, A = 175 mg; U∞, B = 183 mg ## Using IV and Oral Plasma Data Equation 9.5.8 Calculation of F from IV and PO AUC values

When both IV and oral data are available it is possible to calculate V from the IV data and V/F from the oral data (for example using the Method of Residuals). The value for F can be calculated from the ratio of V and V/F. Equation 9.5.9. Equation 9.5.9 Calculation of F from V and V/F

For practice try calculating the F from plasma or urine data. Compare your answers with the computer!

The last step after the calculation of absorption rate constant, ka, using the method of residuals involves the calculation of F using Equation 9.5.9.

Student Objectives for this Chapter