FACTORIAL DESIGN DEPARTMENT OF PHARMACEUTICS AND PHARMACEUTICAL TECHNOLOGY, L.M.COLLEGE OF PHARMACY,...

FACTORIAL DESIGN

DEPARTMENT OF PHARMACEUTICS AND PHARMACEUTICAL TECHNOLOGY,L.M.COLLEGE OF PHARMACY, AHMEDABAD.

Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

Research Process:


Require intelligence planning and approach.

Research scientist Against

the Person who Invest in Stock Market,.,.


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.

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e.g. In process of Extrusion Spheronization,

Three attributes… Binder (%)

Granulation time (Min) Spheronization speed (RPM)


No of trials are more.,.,.

Man Money Material Time

And still for output ???We are not sure !!


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


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)


Basic Terminology:

In scientific language those attributes

are called as variables..


Significant variableMore important..

Go on changing level..

E.g. Polymer Conc,

Granulation time

Insignificant variableNot 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


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.


LEVEL


In General Factor and Level are keep below 3. No of trial depend upon...

No of independent variableNo of level

So choosing the independent variable and no of level that is the crucial step in optimization…

What is level?? Level of factor are the values or designations assigned to the factors.

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


No. X1 X2 Conc. Of Bile salts

Lecithin-Cholate

Molar ratio

Solubility (mg/ml)

1 -1 -1 0.075 0.6:1 6.58

2 +1 -1 0.125 0.6:1 10.18

3 -1 +1 0.075 1.4:1 9.41

4 +1 +1 0.125 1.4:1 14.15


First order or additive linear model:


Complete model:

Y= 10.40 + 2.08 X1 + 1.92 X2

Y= 10.40 + 2.08 X1 + 1.92 X2 + 0.28 X1X2

Full factorial design for 3 factors(2^3)


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


No.

X1 X2 X3 Polysorbate 80(%)

Propylene

glycol(%)

Sucrose(ml)

Turbidity y(ppm)

1 -1 -1 -1 3.7 17 49 3.1

2 +1 -1 -1 4.3 17 49 2.8

3 -1 +1 -1 3.7 23 49 3.9

4 +1 +1 -1 4.3 23 49 3.1

5 -1 -1 +1 3.7 17 61 6.0

6 +1 -1 +1 4.3 17 61 3.4

7 -1 +1 +1 3.7 23 61 3.5

8 +1 +1 +1 4.3 23 61 1.8


Complete synergistic model:


Y= 3.45 -0.675 X1 – 0.375 X2 + 0.225 X3 + 0.05 X1X2 - 0.4 X1X3 – 0.65 X2X3 + 0.175 X1X2X3

32 FULL FACTORIAL DESIGN

GELLAN GUM-ALGINATE BEADS


Why 3 level factorial design???

IndependentFactors

Levels

-1 0 +1

X1: Gellan gum Concentration

1.5 2 2.5

X2: Sodium alginate Concentration

0.5 1 1.5

Percentage entrapment efficiency (Y1), swelling ratio (Y2) and T90 (time taken for 90% drug to be released) (Y3) was selected as dependant factors

Design matrix for 32 full factorial designRun

Coded value

Uncoded value Responses

Batch code

X1 X2Gellan gum

conc.

Sodiumalginate Conc.

Entrapment efficiency

swelling ratio

T90

S1 -1 -1 1.5 0.5 91.84 4.65 5.2

S2 0 -1 2 0.5 93.1 5.92 7.5

S3 1 -1 2.5 0.5 96.44 6.34 9.4

S4 -1 0 1.5 1 94.18 5.39 5.2

S5 0 0 2 1 96.83 6.28 8.2

S6 1 0 2.5 1 98.09 6.85 9.1

S7 -1 1 1.5 1.5 98.4 5.38 7.3

S8 0 1 2 1.5 99.79 6.54 9.5

S9 1 1 2.5 1.5 99.68 7.56 11.1Vipul Patel/ Pharmaceutics and Pharmaceutical Technology

The polynomial equations for three

responses are shown below:Y1= 96.48+1.63X1+2.75X2-0.83X1X2

Y2= 6.15+0.83X1+0.50X2Y3= 7.50+1.98X1+0.96X2+0.83X22


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.


Run Coded value Uncoded value Responses

Batch code X1 X2 X1 X2 Y1 Y2 Y3

S1 -1 -1 1.5 0.5 91.84 4.65 5.2S2 0 -1 2 0.5 93.1 5.92 7.5S3 1 -1 2.5 0.5 96.44 6.34 9.4S4 -1 0 1.5 1 94.18 5.39 5.2S5 0 0 2 1 96.83 6.28 8.2S6 1 0 2.5 1 98.09 6.85 9.1S7 -1 1 1.5 1.5 98.4 5.38 7.3S8 0 1 2 1.5 99.79 6.54 9.5S9 1 1 2.5 1.5 99.68 7.56 11.1


99

98

97

93

9495 96

Y1 Y2

7

6.5

6

5.5

5

10

9

8

7.

6

Y3

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.


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.


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FACTORIAL DESIGN DEPARTMENT OF PHARMACEUTICS AND PHARMACEUTICAL TECHNOLOGY, L.M.COLLEGE OF PHARMACY,...

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