1. Area under the curve (AUC) reflects the total amount of active drug that reaches systemic circulation. It is calculated using the dose administered and clearance from the body. 2. AUC is important for assessing drug exposure in toxicology, comparing drug products, and determining pharmacokinetic parameters like clearance and elimination rate. 3. There are several methods to calculate AUC graphically from a plasma concentration-time curve, including planimetry, trapezoidal rule, and counting squares. The trapezoidal rule involves dividing the curve into trapezoidal segments and summing the areas.

1. 1
Area under curve
Area under curve It reflects the total amount of active drug which reaches the systemic
circulation.
[AUC]=F.D0/clearance
It is independent of route of administration and elimination process as long as it does not
changes.
AUC α dose
Area Under Plasma 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 isremoved per unit time. ”
• An overall elimination rate constant
• Describes removal of the drug by all the elimination processesincluding excretion and
metabolism.

2. 2
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
Hr -1
Relation Between Cp & Time
Calculation of AUC
1. Planimeter
2. Cut & Weigh method

3. 3
3. Mathematical :- Trapezoidal rule
4. Counting Squares method
Planimeter
AKA platometer,
measuring instrument - to determine the area of an arbitrary two-dimensional shape
Cut And Weigh Method
 Plot the plasma profile vs time on graph paper
 Cut the curve drawn carefully

4. 4
 Require an analytical balance
 The weight of this cut portion is W1 so we presume
 AUC1 @ W1
 Weight of whole graph paper is W2
 Area of whole paper = AUC2
 Area= length X breath
AUC1/W1 = AUC2/W2
AUC2= 192 ug.hr/ml
W1= 790mg
W2= 2750mh
AUC1= [(192)(790) / 2750 ] = 55.15ug.hr/ml
Units Y axis ug/ml nd X axis is Hours so area
is ug.Hr/ml
Counting Squared Method
 The plasma concentration Vs time graph is plotted on graphpaper
 Total number of squares are counted

5. 5
 Area of each square is measured in cm or the units on x and y axis of graph
 Total full squares counted and total number of small squares in shaded area counted to
get total number number of full squares.
FOR EXAMPLE
Total full squares=96
Total small squares in shaded area= 1485
Full squares in shaded area= 1485/100 = 14.85
Total full squares = 96 + 14.85 = 110.85
Concentration of each square 1cm2 area = 1X 0.5 =0.5ug.hr/ml
AUC= 110.85 X 0.5 = 55.425ug.hr/ml
Trapezoidal Rule
Steps
Dividing whole AUC into trapezoidal segments
⇓
Counting the area of each segments separately
⇓
Summation of all the area
⇓
Total area

6. 6
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
𝟐
x (t3 – t2)

7. 7
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
2
x t1
Calculation of Last Segment
Final segment can be calculated from t last to t infinity

8. 8
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
Calculation of kel
ln(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 )

9. 9
ln Concentration-Time Curve
Slope = kel = - 0.34 / time
Extrapolation of Cp0
- kel . t
Cp0 = Cp / e
Cp = 71
kel = 0.34
Cp0 = 100
Calculation of First Segment
AUC0-1 =
Cp0 + Cp
2
x t1
=
(100 + 71)
2
. 1
= 85.5
Calculation of Last Segment
= 3.1 / 0.34
= 9.11
Total AUC
Time Concentration AUC
0
1 100
2 50 60.5

10. 10
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

11. 11
References
1. Gibaldi, M. and Perrier, D. 1975 Pharmacokinetics, Marcel Dekker, page v.
2. Atkinson et al 2007, Principles of Clinical Pharmacology , Elsevier-2ndedition
3. David Bourne, Ph.D., A First Course in Pharmacokinetics and Biopharmaceutics