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How to calculate AUC in pharmacology
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AUCDr Nirav , MD Pharmacology , Jamnagar
“It is only in the mysterious equations of love that any logical reasons can be found !!” - quote from movie A BEAUTIFUL MIND
PHARMACOKINETICS
F.H. DOST : founder of pharmacokinetics
ADME
Pharmacokinetics is the study of the time course of drug and metabolite levels in different fluids, tissues, and excreta of the body, and of the mathematical relationships required to develop models to interpret such data." ---from Gibaldi, M. and Perrier, D. 1975 Pharmacokinetics, Marcel Dekker, page v.
Area under the plasma concentration time curve
IMPORTANCE OF AUC
Pharmacokinetics -measurement of bioavaibility
absolute , relative
Biopharmaceutics - comparison of drug products in BABE studies
Calculation of PK parameters
Elimination Rate Constant, kel
overall elimination rate constant describing removal of the drug by all elimination processes including excretion and metabolism
Equation for kel
proportionality constant relating the
rate of change drug concentration and concentration
kel = - dCp/dt
Cp
kel as slope
Calculation of kel
Unit of Kel kel = - dCp/dt Cp
Example
Drug kel, 1 / hour Acetaminophen 0.28
Diazepam 0.021
Digoxin 0.017
Gentamicin 0.35
Lidocaine 0.43
Theophylline 0.063
Relation between Cp and time
Trapezoidal Rule
Calculation of AUC using the Trapezoidal Rule
Trepezoid= Four sided figure with two parallel sides
We can calculate the AUC of each segment if we consider the segments to be trapezoids
CALCULATION OF A SEGMENT
AUC2-3 = Cp2 + Cp3 . ( t3 – t2 )
2
The area from the first to last data point can then be calculated by adding the areas together
Calculation of first segment
• The first segment can be calculated after determining the zero plasma concentration Cp0 by extrapolation
AUC0-1 = Cp0+ Cp1 . t1
2
Calculation of last segment
final segment can be calculated from
tlast to infinity
TOTAL AUC
EXAMPLE OF CALCULATION OF AUC
1
2
3
4
6
8
10
time conc
0 ?????
1 71
2 50
3 35
4 25
6 12
8 6.2
10 3.1
AUC
Calculation of kel
TIME CONC ( ln )
0
1 71 ( 4.26 )
2 50 ( 3.91)
3 35 ( 3.55 )
4 25 ( 3.21 )
6 12 ( 2.48 )
8 6.2 ( 1.82 )
10 3.1 ( 1.13 )
ln(x) = 2.303 . log(x)
ln conc vs time curve
• Slope = kel = - 0.34 1/time
00.5
11.5
22.5
33.5
44.5
5
0 2 4 6 8 10 12
ln co
nc
time
Extrapolation of Cp0
-kel.tCp0 = Cp / e
Cp = 71kel = 0.34
Cp0 = 100
Calculation of first segment
AUC0-1 = Cp0 + Cp1 . t1
2
= (100 + 71)/2 . 1
= 85.5
Calculation of observed segments
time conc AUC
0 100
1 71 85.5
2 50 60.5
3 35 42.5
4 25 30
6 12 37
8 6.2 18.2
10 3.1 = Cplast 9.3
??? ??? ???
AUC2-3 = Cp2 + Cp3 . ( t3 – t2 ) 2
Calculation of last segment
= 3.1 / 0.34
= 9.11
Total AUCAUCtime conc AUC
0 100
1 71 85.5
2 50 60.5
3 35 42.5
4 25 30
6 12 37
8 6.2 18.2
10 3.1 9.3
?? ?? 9.1 = AUClast
total 292.1
Unit of AUC
• Conc . time
• mass . time / volume
• mg . hr / litre
AUC & other PK parameters
AUC = dose = dose
V . kel CL
References
A First Course in Pharmacokinetics and Biopharmaceutics
- David Bourne, Ph.D.
Principles of Clinical Pharmacology ,Elsevier-2nd edition ,Atkinson et al 2007
THANK U
Paul Martini