1. Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
FACTORIAL DESIGN
DEPARTMENT OF PHARMACEUTICS AND PHARMACEUTICAL TECHNOLOGY, L.M.COLLEGE OF PHARMACY, AHMEDABAD.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

2. Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
Research Process:
Require intelligence planning and approach.
Man
Material
Money
Time
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

3. Research scientist Against the Person who Invest in Stock Market,.,.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

4. What happening With Trial And Error Method
Traditional Trend
Randomized fashion of research
Required More number of trials..,
Take more time
Cant predict the extension… i.e. cant say what happen if such change are made within that particular system.

5. e.g. In process of Extrusion Spheronization, Three attributes…
No of trials are more.,.,.
e.g. In process of Extrusion Spheronization,
Three attributes…
Binder (%)
Granulation time (Min)
Spheronization speed (RPM)
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

6. Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
Wastage of …
Man
Money
Material
Time
And still for output ???
We are not sure !!
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

7. Is there Any alternative??
Optimization
Designing experiments to yield the most information from the fewest runs
Reduce the number of trial to minimum but in
logical manner
Carry out research in systematic way
Identify the characteristic you want in your product
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

8. Factorial design Fractional Factorial design Simplex lattice design
Various technique for optimization.,
Factorial design
Fractional Factorial design
Simplex lattice design
Plackett-burman design
Central composite design
Constrained mixture design
Box Behnken design
Face centered cubic design (FCC)
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

9. FACTORIAL DESIGN
Basic Terminology: In scientific language those attributes are called as variables..
Independent variables
Conc. Of Polymer, Agitation Speed
Binder (%), Granulation time
Dependent variables
Friability, hardness
Pharmacological activity
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

10. Independent variable:
Significant variable
More important..
Go on changing level..
E.g. Polymer Conc,
Granulation time
Insignificant variable
Not that much importance
you can keep it at constant level also..
E.g. Effect of lubricant on floating tablet
Independent variable may positive or negative result on
to the dependent variable
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

11. Dependent variable Also Known as Response variable.
Its output of our experiment.
Not limit for dependent variable.
This variable depends on independent variable.
Keep as many as you wish.
e.g. Angle of repose, Disintegration time,
Friability, Hardness.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

12. Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
LEVEL
What is level??
Level of factor are the values or designations
assigned to the factors.
In General Factor and Level are keep below 3.
No of trial depend upon...
No of independent variable
No of level
So choosing the independent variable and no of level that is the crucial step in optimization…
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

13. Full factorial design at 2 levels:
(Solubility of drug in Mixed Micelles)
Factor
Associated variable
Lower level(coded -1)
Upper level(coded +1)
Conc. Of Bile salts X1
0.075
0.125
Lecithin-Cholate Molar ratio X2
0.6:1
1.4:1
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

14. 2^2 Full Factorial design : Solubility of drug in Mixed Micelles)
No. X1 X2
Conc. Of Bile salts
Lecithin-Cholate Molar ratio
Solubility (mg/ml) 1 -1
0.075
0.6:1
6.58 2 +1
0.125
10.18 3
1.4:1
9.41 4
14.15
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

15. First order or additive linear model:
Y= X X2
Complete model:
Y= X X X1X2
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

16. Full factorial design for 3 factors(2^3)
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

17. Formulation of an oral solution:
Factor
Associated variable
Lower level
(coded -1)
Upper level
(coded +1)
Polysorbate 80(%) X1
3.7
4.3
Propylene glycol(%) X2 17 23
Sucrose invert medium(%) X3 49 61
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

18. 2^3 full factorial design:
No. X1 X2 X3
Polysorbate 80(%)
Propylene glycol(%)
Sucrose(ml)
Turbidity y(ppm) 1 -1
3.7 17 49
3.1 2 +1
4.3
2.8 3 23
3.9 4 5 61
6.0 6
3.4 7
3.5 8
1.8
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

19. Complete synergistic model:
Y= X1 – X X X1X X1X3 –
0.65 X2X X1X2X3
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

20. GELLAN GUM-ALGINATE BEADS
32 FULL FACTORIAL DESIGN
Why 3 level factorial design???
Independent
Factors
Levels -1 +1
X1: Gellan gum Concentration
1.5 2
2.5
X2: Sodium alginate Concentration
0.5 1
Percentage entrapment efficiency (Y1), swelling ratio (Y2) and T90 (time taken for 90% drug to be released) (Y3) was selected as dependant factors
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

21. Design matrix for 32 full factorial design
Run
Coded value
Uncoded value
Responses
Batch code X1 X2
Gellan gum conc.
Sodium
alginate
Conc.
Entrapment efficiency
swelling ratio
T90 S1 -1
1.5
0.5
91.84
4.65
5.2 S2 2
93.1
5.92
7.5 S3 1
2.5
96.44
6.34
9.4 S4
94.18
5.39 S5
96.83
6.28
8.2 S6
98.09
6.85
9.1 S7
98.4
5.38
7.3 S8
99.79
6.54
9.5 S9
99.68
7.56
11.1
Design matrix for 32 full factorial design
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

22. The polynomial equations for three responses are shown below:
Y1= X1+2.75X2-0.83X1X2
Y2= X1+0.50X2
Y3= X1+0.96X2+0.83X22
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

23. Contour Plot: It’s a graphical representation of results.
From the Full model equation, eliminate
insignificant terms gives refined equation or
reduced equation.
This refined equation or Full equation is
transferred in form of graphs. That is known as contour plot or response surface methodology plot.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

24. Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
Run
Coded value
Uncoded value
Responses
Batch code X1 X2 Y1 Y2 Y3 S1 -1
1.5
0.5
91.84
4.65
5.2 S2 2
93.1
5.92
7.5 S3 1
2.5
96.44
6.34
9.4 S4
94.18
5.39 S5
96.83
6.28
8.2 S6
98.09
6.85
9.1 S7
98.4
5.38
7.3 S8
99.79
6.54
9.5 S9
99.68
7.56
11.1 99 98 97 93 94 95 96 10 9 8 7. 6 7
6.5 6
5.5 5 Y3 Y2 Y1
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

25. Advantages of Factorial designs:
Maximum efficiency in estimating main effects.
Identification of interaction.
Conclusions apply to a wide range of conditions.
Maximum use of the data.
Saves time and money.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

26. References Gareth A. Lewis, Didier Mathieu, Roger Phan-Tan-Luu.
Pharmaceutical Experimental Design. Marcel Dekker
1999.
Sanford Bolton, Charles Bon. Pharmaceutical statistics,
Practical and Clinical applications. Drugs and Pharmaceutical Sciences Vol-135.
Pritesh C. Mistry. Development Of Gellan Gum Alginate Bead of Aceclofenac, 2006; LMCP THESIS.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

27. Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
Many THANKS for YOUR Attention
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Vipul Patel/ Pharmaceutics and Pharmaceutical Technology