This document discusses various optimization techniques used in pharmaceutical formulation and processing. It begins with an introduction to optimization and defines key terms like independent and dependent variables. It then covers classical optimization techniques like factorial designs and response surface methodology. Statistical experimental designs like full and fractional factorial designs are explained. Finally, various applied optimization methods are outlined, including evolutionary operations, simplex method, Lagrangian method, and search method. Optimization is presented as an important process in pharmaceutical development to efficiently develop formulations and processes.

1. OPTIMIZATION TECHNIQUES
IN PHARMACEUTICAL
FORMULATION AND
PROCESSING
By
K.KRANTHI KUMAR M.Pharm.,M.B.A.,(Ph.D)
Asst.prof
Department of pharmaceutics
SKU college of Pharmaceutical Sciences
S.K. University
Anantapur
Andhra Pradesh
1

2. • Introduction
• Concept of optimization
• optimization parameters
• classical optimization
• statistical design
• applied optimization methods.
2

3. OPTIMIZATION
Optimize is defined as "to make perfect”.
OPTIMIZATION is an act, process, or methodology of making design, system
or decision as fully perfect, functional or as effective as possible .
Optimization of a product or process is the determination of the
experimental conditions resulting in its optimal performance. choosing the
best element from some set of available alternatives. In Pharmacy word
“optimization” is found in the literature referring to any study of formula.
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 decisions in any experiment.
3

4. Importance
It is used in pharmacy relative to formulation and processing Involved in
formulating drug products in various forms .
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 decisions in any
experiment.
Final product not only meets the requirements from the bio-availability but
also from the practical mass production criteria Pharmaceutical scientist- to
understand theoretical formulation.
Pharmaceutical scientist- to understand theoretical formulation.
Target processing parameters – ranges for each excipients & processing
factors
In development projects , one generally experiments by a series of logical
steps, carefully controlling the variables & changing one at a time, until a
satisfactory system is obtained
It is not a screening technique.
4

5. Optimization parameters
Variable types
Problem types
Variable types :-Independent variables
Dependent variables
Problem types:- Constrained
Unconstrained
5

6. variables in optimization: variables in optimization
Independent Dependent variables directly under the control responses that are
developed of formulator due to the independent variables eg: disintegrant level
disintegration time compression force hardness binder level weight uniformity
lubricant level thickness mixing time etc.
6

7. Independent variables or primary variables :Formulations and process
variables directly under control of the formulator.
THESE INCLUDES INGREDIENTS
Dependent or secondary variables : These are the responses of the in progress
material or the resulting drug delivery system.
It is the result of independent variables .
Relationship between independent variables and response defines response
surface
Representing >2 becomes graphically impossible
Higher the variables , higher are the complications hence it is to optimize
each & everyone.
7

8. Problem types in optimization Unconstrained Constrained no restrictions are
restrictions are placed on the system on the system eg: preparation of hardest
tablet without any disintegration tablet which has the ability of or dissolution
parameters. disintegrate in less than 15min .
8

9. variables in optimization Independent Dependent variables directly under the
control responses that are developed of formulator due to the independent
variables eg: eg: disintegrant level disintegration time compression force
hardness binder level weight uniformity lubricant level thickness mixing time
etc.
Problem types in optimization Unconstrained Constrained no restrictions are
restrictions are placed on the system on the system eg: preparation of hardest
eg: preparation of hardest tablet without any disintegration tablet which has
the ability of or dissolution parameters. disintegrate in less than 15min
9

10. optimization parameters:-response surface curve
Once the relationship between the variable and the response is known, it gives
the response surface as represented. Surface is to be evaluated to get the
independent variables, X1 and X2, which gave the response, Y. Any number
of variables can be considered, it is impossible to represent graphically, but
mathematically it can be evaluated.
10

11. It involves application of calculus to basic problem for maximum/minimum
function.
Limited applications
i. Problems that are not too complex
ii. They do not involve more than two variables
For more than two variables graphical representation is impossible
It is possible mathematically
GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE
VARIABLE AND INDEPENDENT VARIABLE
11

12. Classic optimization:-Classical optimization is done by using
the calculus to basic problem to find the maximum and the minimum of a
function. The curve 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 represented can be avoided. If
the relationship, the equation for Y as a function of X, is available : Y = f (X)
Using calculus the graph obtained can be solved.
Y = f (x)
When the relation for the response y is given as the function of two
independent variables,x1 &X2
Y = f(X1 , X2)
The above function is represented by contour plots on which the axes
represents the independent variables x1& x2 12

13. When the relationship for the response Y is given as the function of two
independent variables, X 1 and X 2 ,
Y = f (X 1, X 2 )
Graphically, there are contour plots on which the axes represents the two
independent variables, X 1 and X 2 , and contours represents the response Y .
Here the contours are showing the response. (contour represents the
connecting point showing the peak level of response)
Contour plot. Contour represents values of the dependent variable Y Classic
Optimization
13

14. The techniques for optimization are broadly divided into two categories:
(A)simultaneous method: Experimentation continues as optimization study
proceeds. E.g.: a. Evolutionary Operations Method b. Simplex Method
(B) sequential method: Experimentation is completed before optimization
takes place. E.g.: a. Mathematical Method b. Search Method
In case (B), the formulator has to obtain the relationship between the response
and one or more independent variables. This includes two approaches:
Theoretical Approach & Empirical Approach .
•Optimization Strategy :
•Problem definition
• Selection of factors and levels
• Design of experimental protocol
• Formulating and evaluating the dosage form
•Prediction of optimum formula
•Validation of optimization
14

15. Full factorial designs: Involve study of the effect of all factors(n) at various
levels(x) including the interactions among them with total number of
experiments as X n . SYMMETRIC ASYMMETRIC Fractional factorial
designs: It is a fraction ( 1/ x p ) of a complete or full factorial design, where
‘p’ is the degree of fractionation and the total number of experiments required
is given as x n -p . Factorial Designs
15

16. Applied optimization methods
Evolutionary Operations (EVOP)
Simplex Method
Lagrangian Method
Search Method
canonical analysis
Evolutionary Operations (EVOP):-Most widely used method of experimental
optimization in fields other than pharmaceutical technology.. Experimenter
makes very small changes in formulation repeatedly. The result of changes are
statistically analyzed. If there is improvement, the same step is repeated until
further change doesn’t improve the product. Can be used only in industries
and not on lab scale. Simplex Method It was introduced by Spendley et.al,
which has been applied more widely to pharmaceutical systems. A simplex is
a geometric figure, that has one more point than the no. of factors. so, for two
factors ,the simplex is a triangle. It is of two types: A. Basic Simplex Method
B. Modified Simplex Method Simplex methods are governed by certain rules.
1 3 2
16

17. Simplex Method It was introduced by Spendley et.al, which has been applied
more widely to pharmaceutical systems.
A simplex is a geometric figure, that has one more point than the no. of
factors. so, for two factors ,the simplex is a triangle.
It is of two types:
A. Basic Simplex Method
B. Modified Simplex Method Simplex methods are governed by certain rules.
1 3 2
17

18. Basic Simplex Method
Rule 1 : The new simplex is formed by keeping the two vertices from
preceding simplex with best results, and replacing the rejected vertex (W) with
its mirror image across the line defined by remaining two vertices.
18

19. Rule 2 : When the new vertex in a simplex is the worst response, the
second lowest response in the simplex is eliminated and its mirror image
across the line; is defined as new vertices to form the new simplex.
Rule 3 : When a certain point is retained in three successive simplexes,
the response at this point or vertex is re determined and if same results are
obtained, the point is considered to be the best optimum that can be obtained.
Rule 4 : If a point falls outside the boundaries of the chosen range of
factors, an artificially worse response should be assigned to it and one
proceeds further with rules 1 to 3. This will force the simplex back into the
boundaries.
•Modified Simplex Method It was introduced by Nelder -Mead in 1965. This
method should not be confused with the simplex algorithm of Dantzig for
linear programming. Nelder -Mead method is popular in chemistry, chemical
engg ., pharmacy etc. This method involves the expansion or contraction of
the simplex formed in order to determine the optimum value more effectively.
The two independent variables show pump speeds for the two reagents
required in the analysis reaction. 19

20. The two independent variables show pump speeds for the two reagents
required in the analysis reaction.
Initial simplex is represented by lowest triangle.
The vertices represents spectrophotometer response.
The strategy is to move towards a better response by moving away from worst
response. Applied to optimize CAPSULES, DIRECT COMPRESSION
TABLET, liquid systems (physical stability)
LAGRANGIANMETHOD:-
It represents mathematical techniques.
It is an extension of classic method.
It is applied to a pharmaceutical formulation and processing.
This technique follows the second type of statistical design
Limited to 2 variables - disadvantage
Steps involved:-Determine objective formulation. Determine constraints.
Change inequality constraints to equality constraints.
Form the Lagrange function F:Partially differentiate the lagrange function for
each variable & set derivatives equal to zero.
Solve the set of simultaneous equations. Substitute the resulting values in
objective functions.
20

21. Search method:-It is defined by appropriate equations.
It do not require continuity or differentiability of function.
It is applied to pharmaceutical system
For optimization 2 major steps are used
Feasibility search-used to locate set of response constraints that are just at the
limit of possibility.
Grid search – experimental range is divided in to grid of specific size &
methodically searched.
Steps involved in search method
Select a system
Select variables
Perform experiments and test product
Submit data for statistical and regression analysis
Set specifications for feasibility program
Select constraints for grid search
Evaluate grid search printout
21

22. ADVANTAGES OF SEARCH METHOD
It takes five independent variables in to account.
Persons unfamiliar with mathematics of optimization & with no previous
computer experience could carryout an optimization study.
It is a technique used to reduce a second order regression equation.
This allows immediate interpretation of the regression equation by including
the linear and interaction terms in constant term.
Canonical analysis
It is used to reduce second order regression equation to an equation consisting
of a constant and squared terms as follows
It was described as an efficient method to explore an empherical response.
•Applications :-Formulation and Processing
• Clinical Chemistry
•HPLC Analysis
•Medicinal Chemistry Studying
•pharmacokinetic parameters
• Formulation of culture medium in microbiology studies.
Y = Y0 +λ1W1
2
+ λ2W2
2
+..
22

23. Statistical design
Statistical design Techniques used divided in to two types. Experimentation
continues as optimization proceeds It is represented by evolutionary
operations(EVOP), simplex methods. Experimentation is completed before
optimization takes place. It is represented by classic mathematical & search
methods. For second type it is necessary that the relation between any
dependent variable and one or more independent variable is known. There are
two possible approaches for this Theoretical approach- If theoretical equation
is known , no experimentation is necessary. Empirical or experimental
approach – With single independent variable formulator experiments at
several levels. The relationship with single independent variable can be
obtained by simple regression analysis or by least squares method. The
relationship with more than one important variable can be obtained by
statistical design of experiment and multi linear regression analysis. Most
widely used experimental plan is factorial design
23

24. TERMS USED
FACTOR : It is an assigned variable such as concentration , Temperature
etc..,
Quantitative : Numerical factor assigned to it Ex; Concentration- 1%, 2%,3%
etc..
Qualitative : Which are not numerical Ex; Polymer grade, humidity condition
etc LEVELS :
Levels of a factor are the values or designations assigned to the factor
FACTOR LEVELS
Temperature 30 0C
, 50 0
C
Concentration 1%, 2%
24

25. RESPONSE : It is an outcome of the experiment. It is the effect to evaluate.
Ex: Disintegration time etc..,
EFFECT : It is the change in response caused by varying the levels It gives the
relationship between various factors & levels
INTERACTION : It gives the overall effect of two or more variables Ex:
Combined effect of lubricant and glidant on hardness of the tablet
Optimization by means of an experimental design may be helpful in
shortening the experimenting time. The design of experiments is a structured ,
organized method used to determine the relationship between the factors
affecting a process and the output of that process. Statistical DOE refers to the
process of planning the experiment in such a way that appropriate data can be
collected and analyzed statistically.
TYPES OF EXPERIMENTAL DESIGN
1.Completely randomized designs
2.Randomized block designs
3.Factorial designs
4.Full Fractional Response surface designs
5.Central composite designs
6.Box-Behnken designs
7.Adding centre points
8.Three level full factorial designs
25

26. Completely randomized Designs These experiment compares the values of a
response variable based on different levels of that primary factor. For example
,if there are 3 levels of the primary factor with each level to be run 2 times
then there are 6 factorial possible run sequences. Randomized block designs
For this there is one factor or variable that is of primary interest. To control
non-significant factors, an important technique called blocking can be used to
reduce or eliminate the contribution of these factors to experimental error.
Factorial design :-Full Used for small set of factors
Fractional :-It is used to examine multiple factors efficiently with fewer runs
than corresponding full factorial design
TYPES OF FRACTIONAL FACTORIAL DESIGNS
Homogenous fractional
Mixed level fractional
Box-Hunter
Plackett-Burman
Taguchi Latin square
HOMOGENOUS FRACTIONAL Useful when large number of factors must
be screened
26

27. MIXED LEVEL FRACTIONAL:- Useful when variety of factors need to be
evaluated for main effects and higher level interactions can be assumed to be
negligible.
BOX-HUNTER FRACTIONAL DESIGNS:- with factors of more than two
levels can be specified as homogenous fractional or mixed level fractional
PLACKETT-BURMAN:- It is a popular class of screening design. These
designs are very efficient screening designs when only the main effects are of
interest. These are useful for detecting large main effects economically
,assuming all interactions are negligible when compared with important main
effects Used to investigate n-1 variables in n experiments proposing
experimental designs for more than seven factors and especially for n*4
experiments.
TAGUCHI :-It allows estimation of main effects while minimizing variance.
Latin square They are special case of fractional factorial design where there is
one treatment factor of interest and two or more blocking factors
Response surface designs This model has quadratic form
γ = β 0 + β 1 X 1 + β 2 X 2 +…. β 11 X 1 2 + β 22X 2 2
Designs for fitting these types of models are known as response surface
designs. If defects and yield are the out puts and the goal is to minimize
defects and maximize yield
27

28. Two most common designs generally used in this response surface modeling
are Central composite designs Box-Behnken designs Box-Wilson central
composite Design This type contains an embedded factorial or fractional
factorial design with centre points that is augmented with the group of ‘star
points’. These always contains twice as many star points as there are factors in
the design
The star points represent new extreme value (low & high) for each factor in
the design to picture central composite design, it must imagined that there are
several factors that can vary between low and high values.
Central composite designs are of three types Circumscribed(CCC) designs-
Cube points at the corners of the unit cube ,star points along the axes at or
outside the cube and centre point at origin Inscribed (CCI) designs-Star points
take the value of +1 & -1 and cube points lie in the interior of the cube
Faced(CCI) –star points on the faces of the cube.
Box-Behnken design they do not contain embedded factorial or fractional
factorial design. Box-Behnken designs use just three levels of each factor.
These designs for three factors with circled point appearing at the origin and
possibly repeated for several runs.
28

29. Three-level full factorial designs It is written as 3 k factorial design. It means
that k factors are considered each at 3 levels. These are usually referred to as
low, intermediate & high values. These values are usually expressed as 0, 1 &
2 The third level for a continuous factor facilitates investigation of a quadratic
relationship between the response and each of the factors
These are the designs of choice for simultaneous determination of the effects
of several factors & their interactions. Used in experiments where the effects
of different factors or conditions on experimental results are to be elucidated.
Two types Full factorial- Used for small set of factors Fractional factorial-
Used for optimizing more number of factors
LEVELS OF FACTORS IN THIS FACTORIAL DESIGN
FACTOR LOW
LEVEL
(mg)
HIGH
LEVEL (mg)
A:-stearate 0.5 1.5
B:-Drug 60.0 120.0
C:-starch 30.0 50.0 29

30. EXAMPLE OF FULL FACTORIAL EXPERIMENT
Factor
combination
stearate Drug starch Response
Thickness Cm*10 3
(1) - - - 475
a + - - 487
b - + - 421
ab + + - 426
C - - + 525
ac + - + 546
bc - + + 472
abc + + + 522
30

31. Calculation of main effect ofA (stearate)
The main effect for factor A is {-(1)+a-b+ab-c+ac-bc+abc] 10 -3
/4
Main effect of A = {-(1) a - b + ab -c + ac –bc+abcX10 -3
/4
[487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 10 -3
/4= 0.022
31