Measures of Dispersion and Variability: Range, QD, AD and SD
Similarity factor, higuchi plot, peppas plot
1. Prepared By:-
Garje Mahesh Arjun
Roll No.: 04
M. Pharm Sem-1
(Pharmaceutics)
Guide:-
Prof. A.W. Ambekar
M. Pharm
Dept. of Pharmaceutics
Dr. Vithalrao Vikhe Patil Foundation's
College of Pharmacy
Vilad Ghat, Ahmednagar
2. Introduction
Dissolution:-
The process in which a solid drug substance
solubilises in given solvent i.e. mass transfer from
solid surface to liquid phase.
Rate of dissolution:-
Amount of drug substance that goes in the solution
per unit time under standardised condition of liquid
pH , solvent, temperature.
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4. To study the release of drug in desired amount from
dosage form.
To study the uniformity of drug release from dosage
form of different batches.
To show that drug release is equivalent to those
batches proven to be bioavailable and clinically
effective.
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5. 1. Model independent method:- F1 and f2 comparison
2. Graphical method
3. Statistical method
4. Zero order kinetic model
5. 1st order kinetic model
6. Higuchi model
7. Hixson- Crowell model
8. Korsmeyar Peppas model
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6. Difference factor f1 and similarity factor f2
These equations described by Moore and Flamner
Both equations are endorsed by FDA as acceptable method for
dissolution profile comparison.
f1 value – difference factor
f2 value – similarity factor
They are used to study the comparison of dissolution profiles
of the two dosage form.
It can be calculated using Excel or various readymade
software's (E.g. PhEq_bootstrap)
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7. It calculate % difference between two curves at each time point
& measure relative error between two curves.
f1 equation is sum of absolute values of vertical distance
between reference(Rt) and test(Tt) mean % release values i.e.
(Rt-Tt) at each dissolution point.
Equation:-
Where, Rt:-Reference dissolution value,
N:- No. of dissolution time point
Tt:- Test dissolution value
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8. f2 equation is logarithmic transformation of average squared
vertical distance between reference and test mean dissolution
values at each time point, multiplied by an approximate
weighting i.e. Wt(Rt-Tt)
Equation:-
Where, Rt-Reference dissolution value,
n- No. of dissolution time point
Tt- Test dissolution value
Wt- Optional weighting factor
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9. 1. If both the test and reference product show ≥ 85%
dissolution within 15 minutes,
the profiles are considered to be similar
No calculations are required
2.f1 value(difference Factor):-
if f1=0 to 15
3. f2 value (similarity factor):-
If f2 ≥ 50 , the profiles are regarded similar.
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10. Additional Requirements
At least 12 unit should used .
Same test conditions should maintained.
Dissolution time points for Immediate Release products
like 15,30,45,60 min
For sustained release 1, 2, 3, 5, and 8 hrs until at least
85% of drug is released.
Only one measurement should considered after 85%
dissolution of drug.
SD: ≤ 20% at early time point &
≤ 10% at later time points
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11. Time Rt Tt (Rt-Tt) (Rt-Tt)2
10 45 55 10 100
15 65 75 10 100
20 80 90 10 100
30 90 100 10 100
45 0 0
60 0 0
Sum Of (Rt-Tt)=40
Sum of (Rt-Tt)2=400
Sum of Rt=280
Difference Factor f1= 14
Similarity Factor f2=50
No of time points: 04
Insert No of points where both products ≥85 %
Rt= Cumulative % dissolved of reference product at time t
Tt= Cumulative % dissolved of Test product at time t
Example:
1010
12. In 1961 Higuchi developed mathematical model for
study of release of drug from its matrix.
Initial drug concentration in matrix is much higher.
As drug is released distance for diffusion is
progressively increases.
Drug is leached out polymer matrix by entrance of
surrounding medium.
In release environment perfect sink is maintained.
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13. The Equation Of Higuchi model:
Q= [D(2A-Cs)Cs×t]1/2 or
Q=(2ADCst)1/2
By differentiating above equan we get,
dQ/dt=(ADCs/2t)1/2
The Drug release from granular matrix is given by
Where, dQ/dt – rate of drug release
Cs- Solubility of drug in matrix
A- Total Concentration of drug in matrix
D- Diffusion Coefficient
t- Time, ε -porosity of matrix, τ-Tortuosity
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14. Example
Problem:- 1.What is amount of drug per unit area
released from tablet matrix at time t= 120 ? Total
concentration in homogeneous matrix A is 0.02
g/cm3. Solubility Cs is 1.0×10-3 g/cm3 in polymer.
Diffusion coefficient d at 250c is 360×10-6 cm2/min.
Solution:- we have equation
Q= (2ADCst)1/2
= [ 2 (0.02 g/cm3) (360×10-6 cm2/min)
(1×10-3 g/cm3) (120 min) ]1/2
Q= 1.3 × 10-3 g/cm2
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15. Problem.2: What is instantaneous rate of release of
drug occurring at 120 min?
Solution:-
We have equation,
dQ/dt = (ADCs/2t)1/2
=[ (0.02)(360×10-6)(1.0×10-3)/ 2×120]1/2
= 5.5×10-6 gcm-2min-1
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16. Korsmeyer’s-Peppa’s model
A simple relationship which described drug release from a polymeric
system equation was derived by Korsmeyer-Peppa in 1983
To understand the mechanism of drug release and to compare the
release profile differences among these matrix formulations ,the
percent drug released time versus time were fitted using this equation
Mt / M∞ = k. tn
Mt / M∞ = percent drug released at time t
K= constant incorporating structural and geometrical
characteristics of the sustained release device.
n =exponential which characterizes mechanism of drug release
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17. The n value characterises different releases from
matrix and specify release mechanisms as shown
below
To study release kinetic data obtained plotted as log
cumulative % drug release versus time.
Application: To study modified release dosage form
and release phenomenon of drug.
Release Exponent (n) Drug transport mechanism
0.5 Fickian diffusion
0.5<n=0.89 Non Fickian transport
0.89 Case II transport
Higher than 0.89 Super case II transport
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18. References
Sinko PJ, Singh Y , “Martin’s Physical Pharmacy and
Pharmaceutical Sciences”, Fifth edition, Lippincott Williams
and Wilkins , p. 344 to 346.
Lachman L, Lieberman HA, “Theory And Practice Of
Industrial Pharmacy” Fourth Edition, Reprint 1991, Varghese
Publishing House; p. 205, 206, 207.
Bramhankar DM, Jaiswal SB , “Biopharmaceutics and
Pharmacokinetics-A Treatise”, Third Edition, Reprint 2016,
Vallabh Prakashan; p.334-336, 434-437.
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