Small Animal Clinical Pharmacology - CYF MEDICAL DISTRIBUTION

CHAPTER 2 CLINICAL PHARMACOKINETICS
Neal MJ 2005 Medical pharmacology at a glance, 5th edn. Blackwell,
Oxford
Pratt WB (ed.) 1990 Principles of drug action: the basis of
pharmacology, 3rd edn. Churchill Livingstone, New York
Rowland M, Tozer TN 1995 Clinical pharmacokinetics: concepts and
applications, 3rd edn. Williams and Wilkins, Baltimore, MD
Speight TM, Holford NHG (eds) 1997 Avery’s drug treatment: a guide to
properties, choice, therapeutic use and economic value of drugs in
disease management, 4th edn. Adis International, Auckland,
New Zealand
Walsh CT, Schwartz-Bloom RD 2005 Levine’s pharmacology: drug
actions and reactions, 7th edn. Taylor and Francis, London
APPENDIX: PHARMACOKINETIC EQUATIONS FOR CALCULATING PARAMETERS
FROM DOSE ADMINISTRATION EXPERIMENTS
In order to determine the pharmacokinetic parameters
of a drug, experiments are conducted whereby subjects
are given a drug, and blood samples are collected at
various time points after administration. The concentration
of the drug in plasma is then measured. By plotting
concentration versus time, several important parameters
can be derived that help determine, for example, the
dosing regimen for a drug. Some undergraduate veterinary
courses require students to perform these types of
calculations and postgraduate students may also need
to be able to assess such data. Therefore basic methods
for calculating various pharmacokinetic parameters are
given below.
• Plot the natural logarithm of plasma concentrations
against time on linear graph paper or plot plasma
concentrations against time on semilog paper.
• If the plot is linear then the area under the curve
(AUC) can be calculated using equation 3 below. If
the plot is not linear, AUC can only be calculated
using either differential calculus or the trapezoid
method (see Fig. 2.2). An exponential decline in drug
concentration is described by first-order kinetics and
assumes a single compartment model (i.e. the drug
appears to be in one compartment in the body or
immediately distributed to all compartments).
• The rate at which the concentration declines is
described by the constant λ (which is the slope at the
change in concentration when concentration is
plotted as natural logs).
• The concentration at any time is related to the
maximum concentration by the equation:
C t = C max·e −λt
If the plot is not linear (e.g. concave curve initially
then becomes linear) this indicates that the drug has not
been distributed to the tissues instantly, i.e. there are
two (or more compartments), and this can be solved
with a biexponential equation which is beyond the
scope of this chapter. Assuming there is a linear plot
from when the dose is given (time 0 for IV or complete,
rapid IM injections or after rapid absorption or after
infusion turned off):
1. Elimination half-life (t 1/2 )
Calculate t 1/2 from the graph (time it takes for
a concentration anywhere along the graph to
halve).
12
10
C max
T 1 T 2C1
t 1 /2 = T 2 –T 1
= In2/t 1 /2
Drug concentration
8
6
4
T max
1/2 C 1
2
0
0 1 2 3 4 5 6
Time
7 8 9 10 11 12
Fig. 2.2 Estimation of area under the curve: trapezoidal rule. Observed drug concentration is plotted against time
after oral administration of a drug formulation. Key features of this graph include: C max (maximum concentration
observed); T max (time at which maximum concentration observed); elimination half-life (t 1/2 ) (time for concentration to
halve, i.e. fall from C 1 to 1/2C 1 ): elimination rate l (rate of change of concentration).
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