Pharmacokinetics -Auc - area under curve

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