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Another important property of first order kinetics is the half-life of elimination, t_{1/2}.
Equation 5.8.1
Equation 5.8.2
Equation 5.8.3
Equation 5.8.4 |
OR |
Equation 5.8.5 |
Note: Independent of concentration. This a property of first order processes
These equations can be used as an approximate method of calculating kel. If we look at a plot of Cp versus time on semi-log graph paper.
Figure 5.8.1 Semi-log Plot of Cp versus Time Illustrating t_{1/2} Calculation
The steps to take are:
And finally kel = 0.693/t_{1/2} (Equation 5.8.5)
You might also consider determining Cp/4 or Cp/8 after two half-lives or three half-lives, respectively. This should provide a more accurate answer as the differences in Cp and t will be larger.
The line smooths out the bumps. There may be less accurate data points, so by putting in a line you average the data. The half-life is the same whether going from 40 to 20 or from 10 to 5 mg/L. This is a property of the first order process.
Note:
Go from:
Cp - > Cp/2 in 1 half-life i.e. 50.0 % lost 50.0 %
Cp - > Cp/4 in 2 half-lives i.e. 25.0 % lost 75.0 %
Cp - > Cp/8 in 3 half-lives i.e. 12.5 % lost 87.5 %
Cp - > Cp/16 in 4 half-lives i.e. 6.25 % lost 93.75 %
Cp - > Cp/32 in 5 half-lives i.e. 3.125 % lost 96.875 %
Cp - > Cp/64 in 6 half-lives i.e. 1.563 % lost 98.438 %
Cp - > Cp/128 in 7 half-lives i.e. 0.781 % lost 99.219 %
Thus over 95 % is lost or eliminated after 5 half-lives. Typically, with pharmacokinetic processes, this is considered the completion (my definition unless told otherwise) of the process [Although in theory it takes an infinite time]. Others may wish to wait 7 half-lives where over 99% of the process is complete. Others have suggested that three half-lives are sufficient.
Drug | t_{1/2}, hr |
Acetaminophen | 2.5 |
Diazepam | 33 |
Digoxin | 40 |
Gentamicin | 2.1 |
Lidocaine | 1.6 |
Theophylline | 11 |
^{1} Ritschel, W.A. 1980 Handbook of Basic Pharmacokinetics, 2nd ed., Drug Intelligence Publications, p 413-426.
In the pharmacokinetic area of study the half-life of a drug usually refers to the biological or terminal half-life. These terms have different meaning for different people. I tend to view them both as referring to half-life measured for the terminal or slowest slope on the semi-log drug concentration versus time plot. At low concentration more processes tend to follow first order kinetics. However, at later times with lower concentrations assay sensitivity can be a serious problem. Also, if absorption is very slow the slowest slope may refer to the absorption process instead of drug disposition.
Copyright 2001-3 David W. A. Bourne (david@boomer.org)