Book contents
- Frontmatter
- Contents
- Contributor
- Preface
- Foreword
- SECTION I Basic principles
- 1 Drug passage across the cell membrane
- 2 Absorption, distribution, metabolism and excretion
- 3 Drug action
- 4 Drug interaction
- 5 Isomerism
- 6 Mathematics and pharmacokinetics
- 7 Medicinal chemistry
- SECTION II Core drugs in anaesthetic practice
- SECTION III Cardiovascular drugs
- SECTION IV Other important drugs
- Index
6 - Mathematics and pharmacokinetics
Published online by Cambridge University Press: 01 June 2010
- Frontmatter
- Contents
- Contributor
- Preface
- Foreword
- SECTION I Basic principles
- 1 Drug passage across the cell membrane
- 2 Absorption, distribution, metabolism and excretion
- 3 Drug action
- 4 Drug interaction
- 5 Isomerism
- 6 Mathematics and pharmacokinetics
- 7 Medicinal chemistry
- SECTION II Core drugs in anaesthetic practice
- SECTION III Cardiovascular drugs
- SECTION IV Other important drugs
- Index
Summary
Pharmacokinetics is the study of the way in which the body handles administered drugs. The use of mathematical models allows us to predict how plasma concentration changes with time when the dose and interval between doses are changed, or when infusions of a drug are used. Because there is an association between plasma concentration of a drug and its pharmacodynamic effect, models allow us to predict the extent and duration of clinical effects. Mathematical models may therefore be used to program computers to deliver a variable rate infusion to achieve a predetermined plasma level and hence a desired therapeutic effect.
It should be remembered that these pharmacokinetic models make a number of assumptions. Compartmental models make general assumptions based on virtual volumes without attempting to model ‘real-life’ volumes such as plasma or extracellular fluid volumes. Therefore, although convenient and useful to associate the virtual compartments with various tissue groups such as ‘well perfused’ or ‘poorly perfused’, this remains only an approximation of the physiological state.
Mathematics
Compartmental models are mathematical equations used to predict plasma concentrations of drugs based on experimental observations. Mathematical functions of importance in the understanding of these models are linear, logarithmic and exponential functions. Predicted behaviour and calculation of the parameters that define the model require manipulation of exponential functions, the logarithmic function and calculus. The following sections will cover all these concepts, starting with functions, particularly the exponential function, logarithms and finally calculus.
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- Chapter
- Information
- Pharmacology for Anaesthesia and Intensive Care , pp. 50 - 84Publisher: Cambridge University PressPrint publication year: 2008
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