# Chapter 9

# Calculation of Bioavailability Parameters

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## Method of Inspection

The method of Residuals and the Wagner-Nelson methods are useful technique for determining good estimates of ka. A computer program providing non-linear regression analysis may be able to provide even more accurate estimates of ka. Therefore, a quick, approximate method might be of interest. The method of inspection could be useful in this role. It is capable of providing a quick, approximate estimate of ka for checking the results obtained from other methods or as an initial estimate for more detailed analysis (Swintosky, J.V. et al., 1969).

## Requirements for the Method of Inspection

- We assume that ka is much larger than kel. That is, that ka is at least five time greater than kel. This is the same requirement as for the Method of Residuals when ka is greater than kel.
- Assume that absorption is complete (i.e. approximately 95 % complete) at the time of the peak concentration. This follows from the first assumption

## The Method

The first step is to estimate the time of the peak drug concentration **by inspection**. If we assume that the time of peak is approximately five time the absorption half-life:

**Equation 9.4.1 Time of Peak Concentration**

or

**Equation 9.4.2 Drug Absorption Half-Life, t**_{1/2 (absorption)}

From this value for t_{1/2 (absorption)} we can estimate the absorption rate constant.

**Equation 9.4.3 Absorption rate constant**

## An Example

Considering the results illustrated in Figure 9.4.1 the time of peak can be estimated to be approximately 1.5 hours.

**Figure 9.4.1 Linear Plot of Drug Concentration ***versus* Time after Oral Administration Illustrating t_{peak}

With a t_{peak} of 1.5 hour the t_{1/2 (absorption)} can be estimated as 1.5/5 = 0.3 hour. And ka can be estimated as ln(2)/0.3 = 0.693/0.3 = 2.3 hr^{-1}. For comparison the ka value used to calculated these data was 2 hr^{-1}.

**References**
- Swintosky, J.V., Dittert, L.W. and Doluisio, J.T. 1969 Estimation of drug absorption rates from blood concentration profiles,
*Amer. J. Hospital Pharmacy*, **26** (Sept), 519-522

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