The document discusses area under the curve (AUC) as it relates to bioavailability and pharmacokinetics. It defines AUC as the definite integral of the plasma drug concentration-time curve, which provides a measure of total drug exposure. Various methods for calculating AUC are described, including trapezoidal rule, which divides the curve into trapezoids and sums their areas. Factors affecting bioavailability and AUC include drug properties, formulation, and patient factors. Clinical applications of AUC include toxicity assessment, bioequivalence studies, and pharmacokinetic dosing.

1. AREA UNDER
THE CURVE

2. “It is only in the mysterious
equations of love that any
logical reasons can be found !!”
- quote from movie A BEAUTIFUL
MIND

3. OVERVIEW
• BIOAVAILABILITY
• BIOEQUIVALENCE
• MEASUREMENT TOOLS OF BIOAVAILABILITY
• AUC CALCULATION METHODS
• FACTORS AFFECTING BIOAVAILABILITY AND
AUC
• IMPLICATIONS OF AUC IN MEDICINE

4. Bioavailability
• Refers to the extent and rate at which the
active moiety (drug or metabolite) enters
systemic circulation, thereby accessing the site
of action.
• Subcategory of absorption
• The fraction of an administered dose of drug
that reaches the systemic circulation in an
unchanged form

5. • Drug administered intravenously-
bioavailability is 100%.
• Administered via other routes (such as
orally), - bioavailability - decreases (due
to incomplete absorption and first-pass
metabolism) or may vary from patient to
patient

6. Bioavailability of a drug - determined by
the properties of the dosage form, which
depend partly on its design and
manufacture.
Differences in bioavailability among
formulations of a given drug can have
clinical significance .

7. Absolute bioavailability
compares the bioavailability of the active drug in
systemic circulation following non-intravenous
administration , with the bioavailability of the same
drug following intravenous administration.
To determine absolute bioavailability –
pharmacokinetic study - obtain a plasma drug
concentration vs time plot for the drug after both
intravenous (iv) and extravascular administration.

8. The absolute bioavailability is the dose-corrected
area under curve (AUC) non-intravenous divided by
AUC intravenous.
For example, the formula for calculating F for a
drug administered by the oral route (po) is given
below.

9. A drug given by the intravenous route -absolute
bioavailability of 100% (f=1), whereas drugs by other
routes usually have absolute bioavailability of less
than one.
If we compare the two different dosage forms having
same active ingredients and compare the two drug
bioavailability is called comparative bioavailability.

10. ISOTOPIC METHOD OF ASSESSMENT
For Absolute Bioavailability we require an intravenous reference
Very low dose of an isotopically labelled drug concomitantly with
a therapeutic non-labelled oral dose
Sufficiently low so as not to perturb the systemic drug
concentrations achieved from the absorbed oral dose
The intravenous and oral pharmacokinetics can be deconvoluted
by virtue of the their different isotopic constitution
Determine the oral and intravenous pharmacokinetics from the
same dose administration.

11. This technique eliminates pharmacokinetic issues on
non-equivalent clearance as well as enabling the
intravenous dose to be administered with a minimum
of toxicology and formulation.
Stable-isotopes - C-13 and mass-spectrometry to
distinguish the isotopes by mass difference.
More recently, C-14 labelled drugs are administered
intravenously and accelerator mass spectrometry
(AMS)

12. Relative bioavailability and bioequivalence
Relative bioavailability measures the bioavailability
(estimated as the AUC) of a formulation (A) of a certain
drug when compared with another formulation (B) of the
same drug, usually an established standard, or through
administration via a different route.
used to assess bioequivalence (BE) between two drug products

13. Chemical equivalence indicates that drug
products contain the same active compound in
the same amount and meet current official
standards( Pharmacopoeia)
Bioequivalence indicates that the drug products,
when given to the same patient in the same
dosage regimen, result in equivalent
concentrations of drug in plasma and tissues.
Therapeutic equivalence indicates that drug
products, when given to the same patient in the
same dosage regimen, have the same
therapeutic and adverse effects. ( trifluperazine
and haloperidol in schizophrenia)

14. Clinical Equivalence The drug products provide
identical in vivo pharmacological response as
measured by control of the disease or symptoms.
Bioequivalent products are expected to be
therapeutically equivalent.
Therapeutic nonequivalence (eg, more adverse
effects, less efficacy) is usually discovered during
long-term treatment when patients who are
stabilized on one formulation are given a
nonequivalent substitute.

15. Sometimes therapeutic equivalence is
possible despite differences in
bioavailability. For example- penicillin
In contrast, for drugs with a relatively
narrow therapeutic index, bioavailability
differences may cause substantial
therapeutic nonequivalence.

16. Assessing bioavailability:
1. Peak Plasma concentrations
2. Time to attain the peak plasma convcentration(
tmax)
3. AUC
AUC refers to the extent of bioavailability,
Cmax refers to the rate of bioavailability.
Tmax - it refers to the time it takes for a drug to reach Cmax.

18. Cmax
Refers to the maximum (or peak) serum
concentration that a drug achieves in a
specified compartment or test area of the
body after the drug has been administrated
and prior to the administration of a second
dose.
Tmax - the time at which the Cmax is observed

19. After an intravenous administration, Cmax and Tmax -
concentrations are always decreasing after the dose.
But after oral administration, Cmax and Tmax are dependent
on the extent, and the rate of drug absorption and the
disposition profile of the drug.
Short term drug side effects are most likely to occur at or
near the Cmax
The therapeutic effect of drug with sustained duration of
action usually occurs at concentrations slightly above the
Cmin.

20. The most reliable measure of a drug's
bioavailability is AUC.
Directly proportional to the total amount
of unchanged drug that reaches systemic
circulation.
Drug products may be considered
bioequivalent in extent and rate of
absorption if their plasma concentration
curves are essentially superimposable.

21. What is “area under the curve?”
The definite integral can be used to find
the area between a graph curve and the
‘x’ axis, between two given ‘x’ values. This
area is called the ‘area under the curve’
regardless of whether it is above or below
the ‘x’ axis.

22. Plasma drug concentration increases with extent
of absorption; the maximum (peak) plasma
concentration is reached when drug elimination
rate equals absorption rate.
Bioavailability determinations based on the peak
plasma concentration - misleading because drug
elimination begins as soon as the drug enters the
bloodstream.
Tmax is the most widely used general index of
absorption rate; the slower the absorption, the
later the peak time.

23. Factors influencing bioavailability / AUC
• Drug food interaction
• Drug Drug interaction concomitantly in absorption
• Intestinal motility
• Physical properties of the drug (hydrophobicity, pKa, solubility)
• The drug formulation (immediate release, excipients used,
manufacturing methods, modified release – delayed release,
extended release, sustained release, etc.)
• Whether the formulation is administered in a fed or fasted state
• Gastric emptying rate
• Circadian differences
• First pass metabolism

24. • Transporters: Substrate of efflux transporters (e.g. P-glycoprotein)
• Health of the GI tract
• Enzyme induction/inhibition by other drugs/foods:
• Individual variation in metabolic differences
Pharmacogenetic
Age: In general, drugs are metabolized more slowly in fetal,
neonatal, and geriatric populations
Phenotypic differences, enterohepatic circulation, diet, gender
• Disease state
• hepatic insufficiency, poor renal function

25. CALCULATION OF AUC

26. 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.

27. Equation for kel
 Proportionality constant relating,
- The rate of change in drug plasma concentration,
&
- Plasma concentration.
kel = - dCp/dt
Cp

28. kel as Slope

29. Calculation of kel

30. Unit of kel
kel = - dCp/dt
Cp
1 / hour
Or
Hr -1

31. Example
Drug kel (1 / hour)
Acetaminophen 0.28
Diazepam 0.021
Digoxin 0.017
Gentamycin 0.35
Lidocaine 0.43
Theophylline 0.063

32. Relation Between Cp & Time

33. Calculation of AUC
 Planimeter :
 Cut & Weigh method :
 Mathematical :- Trapezoidal rule
Counting Squares method :

34. Planimeter
AKA platometer,
measuring instrument - to determine the area of an arbitrary two-dimensional
shape

36. CUT AND WEIGH METHOD
Plot the plasma profile vs time on graph paper
Cut the curve drawn carefully
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

38. 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

39. COUNTING SQUARED METHOD
The plasma concentration Vs time graph is plotted on graph
paper
Total number of squares are counted
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

41. 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

42. Trapezoidal Rule

43. Steps
Dividing whole AUC into trapezoidal segments
⇓
Counting the area of each segments separately
⇓
Summation of all the area
⇓
Total area

44. Trapezoid
 Four sided figure with two parallel sides

45. We can calculate the AUC of each segment if we
consider the segments to be trapezoids

46. Calculation of a segment
AUC2-3 = Cp2 + Cp3 x ( t3 – t2 )
2

47.  The area from the first to last data point can then be calculated
by adding the areas together

48. 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

49. Calculation of Last Segment
 Final segment can be calculated from tlast to tinfinity

50. Total AUC

51. 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

52. AUC
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12
Conc.
Time

53. 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 )

54. 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
lnconc
time

55. Extrapolation of Cp0
- kel . t
Cp0 = Cp / e
Cp = 71
kel = 0.34
Cp0 = 100

56. Calculation of First Segment
AUC0-1 = Cp0 + Cp1 x t1
2
= (100 + 71) . 1
2
= 85.5

57. 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
??? ??? ???

58. Calculation of Last Segment
= 3.1 / 0.34
= 9.11

59. Total AUC
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 9.3
?? ?? 9.1 = AUClast
Total 292.1

60. Unit of AUC
Conc . time
mass . time / volume
mg . hr / litre

61. So, in our example,
Total AUC = 292.1 mg . hr / L

62. Importance of AUC
 Toxicology :
- Measure of drug exposure
 Biopharmaceutics :
- Comparison of drug products in BA/BE studies
 Pharmacokinetics :
- Measure of Pharmacokinetic parameters e.g. Clearance, BA.

63. • TACROLIMUS – In Kidney transplantations
• Clearance and GFR for aminoglycosides like
Gentamycin and tobramycin
• Variability of GFR to predict renal outcomes in
CKD
CLINICAL IMPLICATIONS

64. • For assessment of Vancomycin safety.
• Glucose AUC as screening for glucose intolerance
in outpatients.
• AUC for antimicrobials with concentration-
dependent pharmacodynamics - daptomycin
• Cyclosporine estimation in pediatric hematopoietic
stem cell transplantation.

65. • Aminoglycoside dosing in patients with obesity
• mycophenolate sodium - mycophenolic acid-
AUC in adult kidney and liver transplant
recipients
• Valganciclovir dosing using AUC in pediatric
solid organ transplant recipients.
• receiver-operating-characteristic AUC - in
mammography and radiology.

66. • 5-fluorouracil AUC - pharmacokinetic dosing
algorithm for colorectal cancer patients
receiving FOLFOX6.
• Methotrexate AUC - prognostic factor - primary
central nervous system lymphoma
• Mycophenolic acid AUC recovery time
• intravenous busulfan dose - AUC-
hematopoietic stem cell transplantation.

67. NEWER ADVANCES IN AUC ESTIMATION
• Use of HPLC with mass spectrometry for plasma
level calculation
• Use of two sample models to estimate AUC-
reduces need for multiple puncturing and samples
• One sample Model is being researched
• Newer computer algorithms for calculating AUC –
Graphical methods obsolete

68. THANK YOU