Area Under Curve

Dr. Jayesh Vaghela

Pharmacokinetics

• Definition :

“ Study of the time course of –

- the drug & its metabolite levels in different body fluids, tissues &

excreta of body

and,

- the mathematical relationships required to develop models to

interpret such data. ”

• Drug is given by Intravenous bolus

• It follows First order kinetic

• Single compartment open model

Area UnderPlasma Concentration-Time Curve

Linear Plot of Cp versus Time showing AUC and AUC segment

Importance of AUC

• Toxicology :

- Measure of drug exposure

• Biopharmaceutics :

- Comparison of drug products in BABE studies

• Pharmacokinetics :

- Measure of Pharmacokinetic parameters e.g. Clearance, BA.

Elimination Rate Constant, kel

• Definition :

“ The fraction of the total amount of drug in the body which is

removed per unit time. ”

• An overall elimination rate constant

• Describes removal of the drug by all the elimination processes

including excretion and metabolism.

Equation for kel

• Proportionality constant relating,

- The rate of change in drug plasma concentration,

&

- Plasma concentration.

kel = - dCp/dt

Cp

kel as Slope

Calculation of kel

Unit of kel

kel = - dCp/dt

Cp

1 / hourOr

Hr -1

Example

Drug kel (1 / hour)

Acetaminophen 0.28

Diazepam 0.021

Digoxin 0.017

Gentamycin 0.35

Lidocaine 0.43

Theophylline 0.063

Relation Between Cp & Time

Steps

Dividing whole AUC into trapezoidal segments

⇓

Counting the area of each segments separately

⇓

Summation of all the area

⇓

Total area

Trapezoidal Rule

Trapezoid

• 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 x ( 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 x t1

2

Calculation of Last Segment

• Final segment can be calculated from

tlast to tinfinity

Total AUC

Example of calculation of AUC

Time (hr) Concentration (mg / L)

0 ?????

1 71

2 50

3 35

4 25

6 12

8 6.2

10 3.1

AUC

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12

Co

nc.

Time

Calculation of kelln(x) = 2.303 . log(x)

Time Concentration ( 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 Concentration-Time Curve

• Slope = kel = - 0.34 / time

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10 12

ln c

on

c

time

Extrapolation of Cp0

- kel . t

Cp0 = Cp / e

Cp = 71

kel = 0.34

Cp0 = 100

Calculation of First Segment

AUC0-1 = Cp0 + Cp1 x t1

2

= (100 + 71) . 1

2

= 85.5

Calculation of Observed Segments

• AUC2-3 = Cp2 + Cp3 . ( t3 – t2 )

2

Time Concentration 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

??? ??? ???

Calculation of Last Segment

= 3.1 / 0.34

= 9.11

Total AUCTime Concentration 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

So, in our example,

• Total AUC = 292.1 mg . hr / L

References

• Gibaldi, M. and Perrier, D. 1975 Pharmacokinetics, Marcel Dekker, page v.

• Atkinson et al 2007, Principles of Clinical Pharmacology ,Elsevier-2nd

edition

• David Bourne, Ph.D., A First Course in Pharmacokinetics and Biopharmaceutics