Area under the curve- Dr ASHWIN R

AREA UNDER THE CURVE

“It is only in the mysterious equations of love that any logical reasons can be found !!”

- quote from movie A BEAUTIFUL MIND

OVERVIEW

• BIOAVAILABILITY• BIOEQUIVALENCE• MEASUREMENT TOOLS OF

BIOAVAILABILITY• AUC CALCULATION METHODS• FACTORS AFFECTING BIOAVAILABILITY

AND AUC• IMPLICATIONS OF AUC IN MEDICINE

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

• 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

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 .

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.

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.

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.

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.

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)

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

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)

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.

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.

Assessing bioavailability: 

1. Peak Plasma concentrations2. 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.

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

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.

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.

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.

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. 

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

• 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

CALCULATION OF AUC

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

Calculation of AUC

Planimeter :

Cut & Weigh method :

Mathematical :- Trapezoidal rule

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

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 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

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

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 2 4 6 8 10 120

10

20

30

40

50

60

70

80

Time

Conc

.

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

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 . 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 )

2Time 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 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

Unit of AUC

Conc . time

mass . time / volume

mg . hr / litre

So, in our example,

Total AUC = 292.1 mg . hr / L

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.

• TACROLIMUS – In Kidney transplantations

• Clearance and GFR for aminoglycosides like Gentamycin and tobramycin

• Variability of GFR to predict renal outcomes in CKD

CLINICAL IMPLICATIONS

• 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.

• 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.

• 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.

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

THANK YOU