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Non-Linear Regression Analysis

As mentioned earlier data collected after oral administration alone is not sufficient for the determination of F, separate from V. That is, F/V can be determined but not F or V separately. You should note that in the previous page on the determination of F there is another dosage form or route of administration involved. Thus a relative or absolute bioavailability is determined. If you know the absolute bioavailability of the reference dosage form you can determine the absolute bioavailability (F) of the test dosage form. Usually an IV administered dose has an absolute bioavailability of 100%. Therefore using an IV dosage form as the reference dosage form allows the determination of the absolute bioavailability of the test dosage form. Comparison of AUC or U∞ values can be used as described in the previous page. However, non-linear regression analysis using Boomer or some other such program allows the determination of F and ka together by analyzing IV and oral data simultaneously.

Using Boomer

The first step is to draw the model and assign component numbers to the model.
Simulitaneous Fit to IV and PO Data

Figure 18.6.1 Simultaneous Fit to IV and Oral Data

Components are numbered from 1 to 3. Note also that there are two data sets, 1 and 2, that represent the IV and Oral data. Finally note that the kel - PO is linked to kel - IV and V - PO is linked to V - IV. During the optimization step these parameters will be linked as equal.

Example Data Sets

Table 18.6.1 IV Data - Dose = 100 mg

Time (hr) Concentration (mg/L)
0.25 2.37
1.0 2.1
2.0 1.7
4.0 1.03
6.0 0.785

Table 18.6.2 Oral (PO) Data - Dose = 250 mg

Time (hr) Concentration (mg/L)
0.25 1.91
0.5 2.98
0.75 3.54
1.0 3.8
1.5 3.84
2.0 3.62
3.0 3.04
4.0 2.49
5.0 2.04
6.0 1.67
7.0 1.37

Initial estimates of the parameters kel and V can be determined from the IV data by semi-log regression analysis.

Cp versus time after IV dose

Figure 18.6.2 Semi-log Plot of Drug Concentration versus Time after an IV dose

Thus the intercept value is 2.50 and the apparent volume of distribution is Dose/Cp0 = 100/2.5 = 40 L. From the slope kel can be estimated as 0.201 hr-1. The AUC from the IV data is 12.6 mg.hr.L-1.

Cp versus time after oral dose

Figure 18.6.3 Semi-log Plot of Drug Concentration versus Time after an Oral dose

The time of peak concentration is 1.5 hour, thus the t1/2, absorption might be estimated to be 0.3 hour and the absorption rate constant to be approximately 2.3 hr-1. The AUC from the oral data is 24.91 mg.hr.L-1 and thus the bioavailability might be estimated as (24.9 x 100) / (250 x 12.6) = 0.79.

The next step is to translate this model into parameters according to the Boomer notation. As an example we can analyzed the data from earlier.

Table 18.6.3 Model Parameters and Estimates in Boomer Notation

Name Type Initial Value To Name From
Dose-IV 1 100 1    
kel-IV 2 0.201 0   1
V-IV 18 40.0 1 Cp-IV 1
F 19
Dummy parameter		 0.79      
Dose-PO 19
Dummy parameter		 250      
F • Dose-PO 2 197.5
double dependent		 2    
ka-PO 2 2.3 3   2
kel-PO 2 0.201
single dependent		 0   3
V-PO 18 40.0
single dependent		 2 Cp-PO 3

Note the use of dummy parameters to enter the parameters F and Dose-PO. These are used to calculate (F • Dose-PO) the value that is available for absorption. Also note that kel-PO and V-PO are set by means of single dependence equal to kel-IV and V-IV. The complete Boomer .BAT file can be seen here. The Boomer output obtained after running this analysis is shown here.

Table 18.6.4 Final Parameter Values from Boomer Analysis

Parameter Best-fit Value
kel 0.201 hr-1
V 40.1 L
F 0.804
ka 1.98 hr-1

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

This file was last modified: Wednesday 10 Sep 2003 at 11:58 AM