Pharmacokinetics for the Pharmaceutical Scientist

John G. Wagner

• Publisher: CRC Press
• Year: 2018
• eBook ISBN:
  9781351425117
• Topic: Medicine
• Subtopic: Pharmacology

Major presentation of pharmacokinetics by a leading international expert. Methods for: estimating drug disposition parameters from data obtained after intravascular or extravascular drug administration, estimating rate and extent of drug bioavailability, and comparing rate and extent of drug availability following administration of several different dosage forms of a drug.

CHAPTER 1

Simple Linear Models

Model I. One-Compartment Open Model with Bolus Intravenous Administration

This is the simplest of all pharmacokinetic models and there are few data sets that obey the model. One such set is shown in Figure 1.1 published by Smith et al. [1]. The equation to which these data were fitted is:

$C=C_o{e}^{-Kt}(1)$

The diagram of this model is shown in Scheme 1.1.

SCHEME 1.1

The parameters estimated by nonlinear least squares method with the program MINSQ [2] were C_o = 2.44 (0.121) μg/ml and K = 0.399 (0.0273) hr^-1 where the numbers without parentheses are the estimates and the numbers with parentheses are the standard deviations of the estimates. During the fitting of these data the concentrations were weighted reciprocally, i.e., 1/C_i. The data were obtained by administering 10 ml of a 3.75 mg/ml sterile aqueous solution of the drug (specific activity 1.33 μCi/mg) by bolus intravenous injection to six adult male volunteers.

There are problems with the fit shown in Figure 1.1—specifically, there are systematic deviations. Note that the second to the fourth points lie below the fitted line while the next two points lie above the fitted line. Also, the intercept, C₀ = 2.44, is quite a bit below the first point, C = 2.78. The theoretical model shown in Scheme 1.1 assumes that the dose administered at zero time distributes instantaneously in the volume V and hence the highest concentration is supposed to occur at zero time. For these reasons a biexponential fit was attempted and results are shown in Figure 1.2.

FIGURE 1.1 Mean plasma concentrations of 5-methylpyrazole-3-carboxylic acid-¹⁴C computer-fitted with a monoexponential equation and the parameters C₀ = 2.4 μg/ml and K = 0.399 hr¹.

The equation for the solid line in Figure 1.2 is:

$C=2.28e^{-0.381t}+0.952e^{-11.3t}(2)$

This gave a better fit to the data and solved the problems presented by Figure 1.1. Hence, although this data set appeared monoexponential at first glance, it really is biexponential data.

A better example of the model is shown in Figure 1.3. This figure shows plasma concentrations of tritium after bolus intravenous administration...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Introduction
• Chapter 1 Simple Linear Models
• Chapter 2 More Complicated Linear Models
• Chapter 3 Complicated Linear Models
• Chapter 4 Linear Multicompartment Disposition Parameters from Downslope Extravascular C,t Data
• Chapter 5 Noncompartmental and System Analysis
• Chapter 6 Linear Multiple Dose Equations
• Chapter 7 Simple Nonlinear Models
• Chapter 8 More Complicated Nonlinear Models
• Chapter 9 Urinary Excretion
• Chapter 10 Absorption Analysis and Bioavailability
• Chapter 11 Physiological Pharmacokinetics
• Chapter 12 Relationship between Physiologically Based Flow Models and Usual Compartment Models
• Chapter 13 Protein Binding
• Chapter 14 Pharmacokinetic-Pharmacodynamic Modelling
• Chapter 15 Metabolic Kinetics
• Chapter 16 Laplace Derivation of Linear Pharmacokinetic Equations
• Chapter 17 Measures of Fit
• Appendix
• References
• Index