The term “optimize” is “to make as perfect”. It is defined as follows: choosing the best element from some set of variable alternatives. An art ,process ,or methodology of making something (a design system or decision ) as perfect ,as functional, as effective as possible .

1. DEPARTMENT OF PHARMACEUTICAL SCIENCES
Dr. HARISINGH GOUR VISHWAVIDYALAYA, SAGAR (M.P.)
Presented By
Jaising Toppo
M.Pharma. 1st sem.
RESPONSE SURFACE METHODOLOGY
&
APPLICATION OF DESIGN OF EXPERIMENT

2. CONTENTS
Objectives
Definition
Introduction
Advantages
Optimization parameters
Types of optimization techniques
Response surface methodology
Statistical software and their application
References
D.R. CHANDRAVANSHI

3. OBJECTIVES
To determine the variation.
To quantify response with respect to variables.
To find out the variables.
D.R. CHANDRAVANSHI

4. DEFINITION
The term “optimize” is “to make as perfect”. It is defined as follows:
choosing the best element from some set of variable alternatives.
An art ,process ,or methodology of making something (a design system
or decision ) as perfect ,as functional, as effective as possible .
D.R. CHANDRAVANSHI

5. INTRODUCTION
In development projects pharmacist generally experiments by a series
of logical steps ,carefully controlling the variables and changing one at a
time until satisfactory results are obtained .This is how the optimization
done in pharmaceutical industry .
It is the process of finding the best way of using the existing resources
while taking in to the account of all the factors that influences the
decision in any experiment.
final products not only meets the requirements from the bioavailability
but also from the practical mass production criteria.
D.R. CHANDRAVANSHI

6. ADVANTAGES
Yield the “best solution” within the domain of study.
Require fewer experiments to achieve an optimum formulation.
Can trace the rectify “problem” in a remarkably easier manner.
D.R. CHANDRAVANSHI

7. OPTIMIZATION PARAMETERS
OPTIMIZATION
PARAMETERS
VARIABLE
TYPES
IDEPENDENT
VARIABLES
DEPENDENT
VARIABLES
PROBLEM
TYPES
UNCONSTRAINED &
CONSTRAINED
D.R. CHANDRAVANSHI

8. PROBLEM TYPES IN OPTIMIZATION
PROBLEM TYPES IN
OPTIMIZATION
Unconstrained :no restrictions are
required
e.g. preparation of hardest
tablet without any
disintegration or dissolution
parameters
Constrained :restrictions
are placed on the system
e .g. preparation of
hardest tablet which has
the ability of disintegrate
in less than 15 min.
D.R. CHANDRAVANSHI

9. VARIABLES IN OPTIMIZATION
Variables in
optimization
Independent variables:
directly under the control of
formulator
e.g. disintegrant level
,compression force ,binder
level uniformity, lubricant
level, mixing time etc.
Dependent variables :
responses that are developed
due to the independent
variables
e.g. disintegration time,
hardness,weight,thickness etc.
D.R. CHANDRAVANSHI

10. PROBLEM TYPE PARAMETERS IN
OPTIMIZATION
Unconstrained:-In unconstrained optimization problem there are no
restrictions .For a given pharmaceutical system one might wish to make
the hardest tablet possible . The making of the hardest tablet is the
unconstrained optimization problem.
Constrained:-The constrained problem involved in it ,is to make the
hardest tablet possible ,but it must disintegrate in less than 15 minutes.
D.R. CHANDRAVANSHI

11. VARIABLES TYPE PARAMETERS IN
OPTIMIZATION
Independent variables:-The independent variable is under the control of
formulator .These might include the compression force or die cavity filing or
the mixing time ,diluents ratio,disintegrant level, binder level, lubricant level
etc.
Dependent variable:- These are the responses or the characteristics that
are develop due to the independent variables e.g. disintegration time
,hardness dissolution friability weight uniformity etc. The more the
variables that are present in the system the more complications that are
involved in the optimization.
Once the relationship between the variables and response is known, it
gives the response surface as represented in the next slide.Surface is to be
evaluated to get the independent variables , X1 & X2 which give the
response Y . Any number of variables can be considered it is impossible to
represent graphically , but mathematically it can be evaluated.
Y = f (X1,X2……) + e
D.R. CHANDRAVANSHI

12. Continue……..
Factor:- It is Assigned and Independent variables, which affect the
product or output of the process. It is an assigned quantitative and
qualitatively like this.
Quantitative: Numerical factor assigned to it. Ex; Concentration- 1%, 2%,
3% etc.
Qualitative: These are not numerical. Ex; Polymer grade, humidity
condition etc.
Level:- Levels of a factor are the values or designations assigned to the
factor.
Response surface:- Response surface representing the relationship
between the independent variables X1 and X2 and the dependent
variable Y.
Run or trials:- Experiments conducted according to the selected
experimental design
D.R. CHANDRAVANSHI

13. Continue……….
Contour Plot:- Geometric illustration of a response obtained by
plotting one independent variable against another, while holding the
magnitude of response and other variables as constant.
Interaction:- It gives the overall effect of two or more variables means
lack of additively of factor effects Ex: Combined effect of lubricant and
glidant on hardness of the tablets.
D.R. CHANDRAVANSHI

14. TYPES OF OPTIMIZATION TECHNIQUES
1. Plackett-burman designs.
2. Factorial designs.
3. Fractional factorial design (FFD).
4. Response surface methodology.
5. Central composite design (box-wilson design).
6. Box-behnken designs.
D.R. CHANDRAVANSHI

15. GRAPHICALLY REPRESENTATION OF RESPOSE
SURFACE METHOD
Figure : Response surface representating the relationship
between the independent variables X1 & X2 and the
response Y1
D.R. CHANDRAVANSHI

16. CLASSICAL OPTIMIZATION
Classical optimization is done by using the calculus to basic problem to
find the maximum and the minimum of the function.
The curve in the figure represents the relationship between the
response Y and the single independent variable X and we can obtain the
maximum and the minimum.By using the calculus the graphical
representation can be avoided. If the relationship ,the equation for Y as
a function X , is available .
Y = f(X) ……….eq1
When the relationship for the response Y is given as the function of two
independent variables , X1 & X2
Y = f(X1,X2) ……eq2
D.R. CHANDRAVANSHI

17. Graphical representation of single variable and double
variables
D.R. CHANDRAVANSHI

18. DRAWBACK OF CLASSICAL OPTIMIZATION
Applicable only to the problems that are not too complex .
They do not involve more than two variables .
For more than two variables graphical representation is impossible .
D.R. CHANDRAVANSHI

19. APPLIED OPTIMIZATION METHODS
1. Evolutionary operation
2. Sequential Simplex method
3. Lagrangian method
4. Search method
5. Canonical analysis
Evolutionary operations (EOVP):-It is a method of experimental
optimization. Small changes in the formulation or process are made (i.e.
repeat the experiment so many times) & statistically analyzed whether it is
improve .
It continues until no further changes take place i.e. it has reached
optimum the peak. The result of changes are statistically analyzed.
D.R. CHANDRAVANSHI

20. WHERE WE HAVE TO SELECT THIS
TECHNIQUE ?
This techniques especially well suited to a production situation.
The process is run in a way that is both produce a product that meets all specifications and
(at the same time ) generates information on product improvement.
Applied mostly to tablets.
Advantages:-
(1) Generates information product development .
(2) Predict the direction of improvement.
(3) Help formulates to decide optimum condition for the formulation and process.
Limitations :-
(1) More repetition is required .
(2) Time consuming .
(3) Not efficient to finding true optimization .
(4) Expensive to use.
D.R. CHANDRAVANSHI

21. Continue…….
Example:- Tablet
How can we get
hardness
By changing
the conc. Of
binder
Hardness Response
In this example, a formulator can changes the concentration of binder
and get the desired hardness.
D.R. CHANDRAVANSHI

22. SEQUENTIAL SIMPLEX METHOD
It is sequential because the experiments are analyzed one by one ,as each is
carried out .
This procedure may be used to determine the relative proportion of
ingredients that optimizes the formulation with respect to a specified
variables(s) or outcome.
A common problem in pharmaceutics occurs when the components of a
formulation are varied in an attempt to optimize its performance with
respect to such variables as drug solubility, dissolution time and hardness.
An approach is with example ,three components of the formulation will be
varied – stearic acid,satrch and declaim phosphate – with the restriction
that the sum of the total weight must equal 350 mg .The formulation can be
optimized for more than one attribute ,but for the sake of simplicity ,only
one effect dissolution rate,is considered.
D.R. CHANDRAVANSHI

23. Figure:-Special cubic simplex design for a three component mixture.
Each point represents a different formulation.SA=Stearic
acid;ST=Starch;DCP=Dicalcium phosphate.
D.R. CHANDRAVANSHI

24. Seven formulas to be tested –actual and (transformed) values
Transformed % = (actual% -minimum %)/(maximum % -minimum%)
D.R. CHANDRAVANSHI

25. Respose surface methodology
Response surface method (RSM) is a set of techniques used in the empirical study of
relationships .
RSM is a collection of mathematical and statistical techniques for empirical model
building, in which a response of interest is influenced by several variables and the
objective is to optimize this response .
RSM is useful in three different techniques or methods : (i) statistical experimental
design, in particular two level factorial or fractional factorial design, (ii) regression
modeling techniques, and (iii) optimization methods.
The most common applications of RSM are in Industrial, Biological and Clinical
Science, Social Science, Food Science, and Physical and Engineering Sciences.
D.R. CHANDRAVANSHI

26. Continue…….
The first goal for Response Surface Method is to find the optimum
response.
When there is more than one response then it is important to find the
compromise optimum that does not optimize only one response.
When there are constraints on the design data, then the experimental
design has to meet requirements of the constraints.
The second goal is to understand how the response changes in a given
direction by adjusting the design variables.
D.R. CHANDRAVANSHI

27. Continue….
The probabilistic analysis, an explicit or implicit functional relationship
between input parameters and output response is required, which is
normally difficult to establish except for simple cases and even the
established functional relationship is sometimes too complicated to
perform the conventional probabilistic analysis through integration or
through first or second order derivatives. In such circumstances,
authors propose to use the concept of response surface methodology
to establish an approximate explicit functional relationship between
input variables (x1, x2, x3 …) and output response (y) through
regression analysis for the range of expected variation in the input
parameters.
Y= f (x1, x2, x3…) + e
D.R. CHANDRAVANSHI

28. Continue……….
The essential steps in response-surface methodology are as follows:
1. The objective of the experiment is decided upon.
2. The important factors and their interactions are identified, perhaps
after a screening experiment. The levels of the factors which are to
be used are also established.
3. A possible mathematical model is selected.
4. An experimental design that is appropriate to the model is chosen.
5. The experiments are carried out, and the values of the factors and the
response fitted to the mathematical model.
6. The model is validated.
D.R. CHANDRAVANSHI

29. Continue………
7. If the model does not represent the data in a satisfactory manner,
then another model equation or new experimental design is selected.
Stages 3, 4, 5, and 6 are repeated using models and designs of
increasing complexity until a model is obtained, which is an acceptable
representation of the data.
8. If required, a graphical representation of the surface is generated.
D.R. CHANDRAVANSHI

30. RESPONSE SURFACES GENERATED FROM
FIRST-ORDER MODELS
The principles of response-surface methodology will first be described by a
very simple example that is then developed into a more complex situation.
The objective of the experiment is to investigate the response surface that
illustrates the influence of two factors, namely, compression pressure
(X1) and disintegrant concentration (X2), on the crushing strength of a
tablet formulation (Y1).
It is proposed to use a first-order model equation
Y1=β0+β1X1+β2X2+ε
The initial design is a two-factor, two-level study without replication. There
are thus four experiments in the design.
D.R. CHANDRAVANSHI

31. Continue……
The chosen values of the factors are 100 MPa and
300 MPa for compression pressure and 2.5% and 7.5% for disintegrant
concentration.
The lower value of each factor is designated −1 and the higher value +1.
The experimental design is shown in figure, and possible constraints
must now be considered.
With a linear relationship, there is no maximum or minimum value, and
hence in an unconstrained situation, there is an infinite number of
combinations of the two independent variables which will give a
specified value of the response. However, constraints are applicable to
this experiment.
D.R. CHANDRAVANSHI

32. Continue………
1. The compression pressure X1 cannot be less than 0 MPa. In terms of
experimental units (e.u.), X1 cannot be less than −2.
2. Likewise, the disintegrant concentration X2 cannot be less than 0% or −2
e.u.These two constraints represent the axes of Figure.
3. X1 cannot exceed the maximum pressure that the tablet press can safely
apply. This might be 400 MPa or +2 e.u.
4. The concentration of disintegrating agent (X2) cannot exceed a given
concentration limited by the formulation. This might be 10% or +2 e.u.
5.These constraints are represented by the axes of Figure . and the two
dotted lines drawn at +2 e.u. on each axis. However, it must be
remembered that the experimental data will be generated from a much
smaller domain, represented by the rectangle ABCD in Figure.
D.R. CHANDRAVANSHI

33. Continue……..
Figure:Two-factor, two-level factorial design to investigate the effect of
compression pressure and disintegrant concentration on tablet crushing
strength, showing constraints on the experimental domain.
D.R. CHANDRAVANSHI

34. The Effect of Compression Pressure and Disintegrant
Concentration on Tablet Crushing Strength, Using a
Two-Factor, Two-Level Design
Experiments Compression
pressure( Mpa)
(X1)
Disintegrant
concentration(%)
(X2)
Crushing strength
(kg)(Y1)
(-1,-1) 100 2.5 6.1
(+1,-1) 300 2.5 9.4
(-1,+1) 100 7.5 4.9
(+1,+1) 300 7.5 8.2
Tablets are prepared and the measured values of their crushing strengths
are shown in Table
The relative importance of the factors and the interaction on the tablet
crushing strength are now calculated .Thus, the effect of Factor X1,the
compression pressure on crushing strength (Y1),
Note: 1 e.u. of compression pressure = 100 MPa. 1 e.u. of disintegrant
concentration = 2.5%.
D.R. CHANDRAVANSHI

35. Continue….
Similarly, the effect of Factor X2, the disintegrant concentration, on crushing
strength (Y1)
Thus, both factors have a major influence. As might be expected, an increase
in the compression pressure has a positive effect on crushing strength and an
increase in the concentration of disintegrant has a negative effect. The next
stage is to fit the data from table into a regression equation of the form . This
gives Y1= 7.15 + 1.65X1− 0.6X2
D.R. CHANDRAVANSHI

36. The effect of compression pressure and disintegrant connc. On
tablet crushing strength, using a two factor, two level with
duplicated experiments at the center point.
Y1=β0+β1X1+β2X2+β12X1X2
Experi-
-ment
Compressio
n pressure
(Mpa)(X1)
Disintegra
nt conc.
(%)(X2)
Observed
crushing
strength(kg)Y
1
Crushing
strength
predicted
from(7.4)(kg
)
Residual
observed
value-
practical
value)(kg)
(-1,-1) 100 2.5 6.1 6.12 -0.02
(+1,-1) 300 2.5 9.42 9.42 -0.02
(-1,+1) 100 7.5 4.92 4.92 -0.02
(-1,-1) 300 7.5 8.2 8.22 -0.02
(0,0) 200 5.0 7.3 7.17 +0.13
(0,0) 200 5.0 7.1 7.17 -0.07
Note:-center point(0,0);compression pressure=200MPa;disintegrant
conc=5%,1e.u. of compression pressure=100MPa,1e.u. of disintegrant
conc.=2.5%.
D.R. CHANDRAVANSHI

37. Continue……..
Figuure:-The response surface of tablet crushing strength (kg) as
a function of compression pressure and disintegrant concentration,
using responses derived from previous table
D.R. CHANDRAVANSHI

38. It is now possible to answer a question such as “if tablets of a given
crushing strength (Y1) and containing a given concentration of
disintegrating agent (X2) are required, what compression pressure (X1)
is needed to produce them?” or, in general terms, “what values of the
factors are needed to give a product having specified properties?”
Equation can be rearranged to give
D.R. CHANDRAVANSHI

39. Y1 and X2 are specified, the coefficients are known, and the only
unknown is X1. For example, if the tablets are to contain 5%
disintegrating agent (zero when expressed in experimental units), and
should have a crushing strength of 6 kg, then eq…1 becomes eq….2
The required compression pressure is therefore −0.71 e.u., equivalent to
129 MPa.
X1=6-7.17-0.6×0/1.65
= -1.17/1.65
= 0.71
D.R. CHANDRAVANSHI

40. STATISTICAL SOFTWARE WITH THEIR APPLICATIONS
D.R. CHANDRAVANSHI

41. APPLICATION OF DESIGN OF EXPERIMENTS
Formulation and Processing.
Clinical Chemistry.
Medicinal Chemistry.
High Performance Liquid Chromatographic Analysis.
Study of Pharmacokinetic Parameters.
Allow large number of variables to be investigated in compact trial.
D.R. CHANDRAVANSHI

42. References
1.Roop Khar K,Vyas SP,Farhan Ahmad J,Gaurav jain K,”Industrial
Pharmacy”,CBS Publishers & Distributors New Delhi,Fourth
Edition,2013,356-361.
2.Tattawasart, A. and Armstrong, N. A., The formation of lactose plugs
for hard shell capsule fills, Pharm. Dev. Technol., 2, 335, 1997.
3. Pourkavoos, N. and Peck, G. E., Effect of aqueous film coating
conditions on water removal efficiency and physical properties of
coated tablet cores containing superdisintegrants,Drug Dev. Ind. Pharm.,
20, 1535, 1994.
D.R. CHANDRAVANSHI

43. D.R. CHANDRAVANSHI