This document provides an overview of optimization techniques used in pharmaceutical formulation and processing. It discusses key optimization parameters like variables (independent and dependent) and problem types (constrained and unconstrained). Classical optimization methods like response surface methodology are described. The document focuses on experimental design techniques like factorial designs (full and fractional), response surface methodology using central composite design and Box-Behnken design, and adding center points. It provides examples of different types of experimental designs and how they are used to optimize pharmaceutical processes and formulations.

1. Optimization techniques in pharmaceutics, formulation and
processing
By:
CHETAN DHAL,
M.Pharma(Quality Assurance)
Email: dhalchetan@yahoo.co.in

2. OUTLINE OF SLIDES
CONTENT SLIDES
Introduction and approach 3-6
Optimization parameters 7-8
Classical optimization 9-11
DOE 12
Types of experimental design 13-30
Method of optimization 31-46
Application 47-48
Approach to process optimization and
scale-up
49-50
References 51

3. TAGUCHI argued that quality engineering should
start with an understanding of quality costs.
This shows that for a well optimized product
there is a need of understanding the product.

4. INTRODUCTION
• To optimize is to make as perfect as
possible, effective or functionally best.
• In order to make such a product one
has to consider its physical, chemical or
biological parameters, and the final
product which comes out is of
maximum yield, highest bioavailability,
reproducibility characters. etc

5. Best way to optimize is to
know the target.
If the researcher is clear about
the target and various
conditions which he/she will
be facing, makes it very easy to
amend various variables.
OPTIMIZATION IS NOT A SCREENING TECHNIQUE AS IN
CASE OF PREFORMULATION
OPTIMIZATION REQUIREMENT AND PRACTICAL
METHOD:-

6. FLOW CHART TO UNDERSTAND THE
OPTIMIZATION PROCESS

7. 1) OPTIMIZATION PARAMETERS:-
Development of any formulation can be understood
to be based on certain parameters. Mathematically
it is divided as:-
Higher the number
of variables higher
the complications in
the product
development
1) Variables
Dependent
Independent
2) Problem
type
Constrained
Unconstrained

8. Variables: These are the small functions
on which researches are dependent. Its
of 2 types.
INDEPENDENT DEPENDENT
These are the
functions which are
directly under the
control of
formulator.
Are the direct results
to a change in
formulation or
process.
OR
Responses of
alteration in the
independent
variable.
Eg:- Duration of
mixing,
Rate of drying
Eg:- Effect of addition
of Binder on
hardness of a Tablet
when formulating a
floating tablet.
Problem type - In the development
of a formulation in pharmaceutical
system there are some boundations
while optimizing any formulation or
any process.
These may be of 2 types
CONSTRAINED UNCONSTRAINED
Restrictions
placed on the
system by
physical
limitations or by
simple
practicality.
Eg:- economic
conditions
No such
restrictions are
there and its most
non- exsisting.

9. CLASSICAL OPTIMIZATION
Earlier optimization was based on hit and trial method.
But now calculus methodology is applied. It helps in
finding maxima and minima of a function. However this
method is mostly applicable to condition where there is
less variable.
i)2 variables- one dependent(y) and one independent(x)
y=f(x)
ii)3 variables one independent and 2
dependent(x1,x2)
y=f(x1,x2)
for this type of system we have contour plots.
Contd…

10. GRAPH REPRESENTING THE RELATIONSHIP BETWEEN
THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE.
THERE IS DEPENDENCY OF y ON ONLY ONE VARIABLE i.e. x.
Contd…

11. Response surface representing the relationship between the
independent variables X1 and X2 and the dependent variable Y.

12. D.O.E:-
(Design of experiments)
In statistics c/a controlled experimentation.
• It’s the methodology for designing
experiments.
• proposed by RONALD A. FISHER in his book
“The arrangement of field experiments” in
1926.
• DOE is concerned with planning and conduct
of experiments of experiments to analyze the
resulting data so that we obtain valid and
objective conclusion.

13. TYPES OF EXPERIMENTAL DESIGN
• 1) Complete randomized design
• 2) Randomized block design
• 3) Statistical design
i) experimentation continue as optimization study proceeds
ii) experimentation completes before optimization study
• 4) Factorial design (it can be 2 factorial or fully 3 factorial)
i) Full factorial
ii) Fractional factorial
• 5) Response surface design
i) Central composite design
ii) Box Behnken design
• 6) Adding center points

14. 1) COMPLETELY RANDOMIZED DESIGN
 These experiment compares the values of a
response variable based on different levels of
that primary factor (independent factors).
 For example, if there are 3 levels of the
primary factor with each level to be run 2 times
then there are 6 possible run sequences.
e.g:- These 3 levels to be run 2 times then,
, , , , , - 6 Different options
TYPES OF EXPERIMENTAL DESIGN
Contd…

15. 2) RANDOMIZED BLOCK DESIGN
 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.
TYPES OF EXPERIMENTAL DESIGN
Contd…

16. 3) FACTORIAL DESIGN
 Factorial design is a proper arrangement of variables in an
expression which tells us about the possible options and
various combinations.
 There are various factors (called as variables) which
determine production output hence the dependency of this
must be checked while optimizing any process or
formulation.
 These factors can be assignable. i.e. which may have a
quantitative or qualitative effect on our final product.
 Factorial design is used for IVIVC study also.
TYPES OF EXPERIMENTAL DESIGN
Contd…

17.  EXAMPLE:- For a system containing 2 variables showing
an inter related effect on the product.
Symbols to denote levels are:
1 - when both the variables are in low concentration.
a - one low variable and second high variable.
b - one high variable and second low variable
ab - both variables are high.
In this case the combined effect could be understood as:-
(b + ab)-(1 - a)
2
TYPES OF EXPERIMENTAL DESIGN
Contd…

18. (A) FRACTIONAL FACTORIAL DESIGN:-
It is used to examine multiple factors
efficiently with fewer runs than corresponding
full factorial design
Types of fractional factorial designs
 1)Homogenous fractional
 2)Mixed level fractional
 3)Box-Hunter
 4)Plackett-Burman
 5)Taguchi
 6)Latin square
(B) FULL FACTORAL DESIGN:-
It is used for small set of factors.
TYPES OF EXPERIMENTAL DESIGN

19. 1) Homogenous fractional factorial design:-
Useful when large number of factors need be
screened.
2) Mixed level fractional factorial design:-
Useful when variety of factors need to be
evaluated for main effects and higher level
interactions can be assumed to be negligible.
3) Box-hunter fractional factorial design:-
Fractional designs with factors of more than
two levels can be specified as homogenous
fractional or mixed level fractional.
TYPES OF FRACTIONAL FACTORIAL
(TYPES OF EXPERIMENTAL DESIGN)
A) FRACTIONAL FACTORIAL DESIGN
Contd…

20. • 4) Plackett-Burman fractional factorial design:-
by R.L. Plackett and J.P. Burman (In 1946)
• Published their now famous paper "The Design of
Optimal Multi-factorial Experiments" in Biometrika
(vol. 33).
• This paper described the construction of very
economical designs with the run number a multiple
of four (rather than a power of 2).
• Its very efficient screening designs when only main
effects are of interest.
• Plackett-Burman in general is heavily confounded
with two-factor interactions. The PB design in 12
runs, for example, may be used for an experiment
containing up to 11 factors TYPES OF FRACTIONAL FACTORIAL
(TYPES OF EXPERIMENTAL DESIGN)Contd…

21. 12 RUN 11 FACTOR(x1 – x11 )DESIGN
TYPES OF
FRACTIONAL
FACTORIAL
(TYPES OF
EXPERIMENTAL
DESIGN)
Contd…

22. 5) Taguchi method of fractional factorial design:-
(by Genichi Taguchi 1950)
•This method was developed for the improvement of
finished product.
•Taguchi has developed this design for studying
variation.
It treat optimization problem as:-
1)Static Problem:- several control factors are there to
control the final optimized product.
2)Dynamic Problem:- Problem to be optimized has a
single input.
TYPES OF FRACTIONAL FACTORIAL
(TYPES OF EXPERIMENTAL DESIGN)

23. 6) Latin square fractional factorial design:-
(By Leonhard Euler)
a Latin square is an n × n array filled with n
different symbols, each occurring exactly once in
each row and exactly once in each column.
Example:-
Type of representations:-
a)Orthogonal array representation
b)Equivalence classes of latin square.
TYPES OF FRACTIONAL FACTORIAL
(TYPES OF EXPERIMENTAL DESIGN)

24. B) LEVEL FULL FACTORIAL
(3 level full factorial)
The three-level design is written as a 3k factorial
design. It means that k factors are considered, each
at 3 levels. These are (usually) referred to as low,
intermediate and high levels. These levels are
numerically expressed as 0, 1, and 2.
Example:- if we have a condition in which we have 2
variables and all with 3 levels (possibilities) then
32 = 8 options.
OR
If we have 3 variables and all with 3 levels then
33 = 27 options.
TYPES OF EXPERIMENTAL DESIGN
Contd…

25. 5) RESPONSE SURFACE METHODOLOGY
(RSM):-
(by G. E. P. Box and K. B. Wilson in 1951)
It explores the relationships between several
independent variables and one or more dependent
variables.
It utilizes quadratic form of an equation which may be
simple quadratic or multifunction quadratic.
Types:- Two most common designs generally used in this
response surface modeling are
Central composite designs (CCD)
Box-Behnken designs
TYPES OF EXPERIMENTAL DESIGN
Contd…

26. a) CCD:-
(by Box and Wilson)
• It is composed of +2K factorial design or fractional
factorial design.
• It help in building a second order (quadratic) model for
the response variable without needing to use a complete
three-level factorial experiment.
# Central composite designs are of three types:-
1) Circumscribed (CCC) designs-Cube points.
(require 5 level of each factor)
2) Inscribed (CCI) designs-Star points.
(require 5 level of each factor)
3) Faced (FCI) –star points on the faces of the cube.
(require 3 level of each factor)
TYPES OF EXPERIMENTAL DESIGN
Contd…

27. TYPES OF EXPERIMENTAL DESIGN
Generation of a Central Composite Design for
Factors. CCC
FCI
CCI
CCC
Contd…

28. b) Box-Behnken design (Alternative to CCD)
(George E. P. Box and Donald Behnken in 1960)
• They do not contain embedded factorial or
fractional factorial design.
• Box-Behnken designs use just 3 levels of each
factor.
• In this design the treatment combination are at
the midpoint of edges of the process space and
the centre.
TYPES OF EXPERIMENTAL DESIGN
Contd…

29. Interpretation of a design by Box-behnken
method
A 3 factor design by box behnken method is a cube
Centre point
Y = b0 + b1x1 +b2x2 + b3x3 +
b4x1x2 + b5x1x3 + b6x2x3
+ b7x2
1 + b8 x2
2 + b9 x2
3.
Where,
b(0-9) represents constants.
x(1-3) represents variables.
DESIGN CONTAINING THREE
VARIABLE TYPES OF EXPERIMENTAL DESIGN
Contd…

30. 6) STATISTICAL DESIGN:-
the statistical design is of 2 types
STATISTICAL DESIGN
Experimentation
study continues as
the study proceeds.
Experimentation is
complete before
optimization.
Represented by
Evolutionary method
and simplex method
Represented by classical
method lagrangian
method and search
method. Requires
relation between
dependent and
independent variable
TYPES OF EXPERIMENTAL DESIGN

31. METHODS OF OPTIMIZATION
• There are many optimization procedures.
1)EVOP (evolutionary optimization)
2)Simplex method
3)Lagrangian method
4)Search method
5)Canonical analysis
For IN-PROCESS
OPTIMIZATION
For OUT-PROCESS
OPTIMIZATION

32. 1) EVOP (Evolutionary operation)
• Principle:- The production procedure is
allowed to evolve to the optimum by careful
planning and constant repetition.
• In this method the researcher makes very
small changes in the formulation or process
but makes it so many times that he or she can
determine statistically whether the product
has improved or not.
Contd…

33. • Alterations requirement upto:- until no
improvement in the product quality is required.
• Applications:- very effective work was done on
(1) Tablets and later to (2) parenteral by
Mitchell H. Rubinstein
• Limitation:- Not a substitute to good laboratory
scale work.
Rubinstein MH. Evolutionary operations: To optimize tablet manufacture.
D&CI, 44-47,104-109, April, 1975
Contd…

34. 2) SIMPLEX METHOD
proposed first by spendely et al
applied and known as Downhill Simplex / Nelder-
Mead Method
• More widely used method for optimization
• The method uses the concept of a simplex,
which is a special polytope of N + 1 vertices in N
dimensions. Examples of simplexes include a
line segment on a line, a triangle on a plane, a
tetrahedron in three-dimensional space and so
forth.
Contd…

35. Method Involved:- Identify the variables and predict the
shape and then design the equations using various constants
and concentrations/values.
• Example:-
shows the three-component system which is
represented as an equilateral triangle in two-
dimensional space.
Three formulations, one each at each vertex,
A, B, and C. These formulations represent
formulations with the pure components, A, B,
and C, respectively.
Three formulations are prepared with 50-50
mixtures of each pair of components,
AB, AC, and BC.
A seventh formulation may be prepared with
one-third of each component. This lies in the
center of the design.
Contd…

36. • The equation can be formed as,
y = Ba(A) + Bb(B) + Bc(C) + ……… + Bab(A)(B) + Bac(A)(C) + Bbc(B)(C) +
Babc(A)(B)(C).
Where,
(A), (B), (C) represents the concentration of
component A, B, C.
(A)+(B)+(C)+…….+(ABC) = 1.0
Ba, Bb, Bc,……, Babc represents constants.
Response determination:-
With the aid of a computer, responses
may be calculated over the simplex
space, and contour diagrams. The
contour plot is a graphic description of
the response surface resulting from
data derived from experimental
designs such as the simplex.
Contd…

37. Shek et al, 1980
used Simplex method for optimizing a capsule.
• Simplex method also describes about the
expansion, contraction of geometric figures.
• Bindschaedler and gurney applied simplex
method in optimization of direct compressible
tablets of Acetaminophen.
Shek E, Mahmood G, Jones RE. Simplex search in optimization of capsule
formulations. J Pharm Sci, 69(10):1135-1142, 1980 Contd…

38. 3) Lagrangnian Method
Fonner et al 1987
• Mathematical methodology is applied for optimizing a
result.
• Since, mathematical therefore developed after
performing some study and obtaining a limited data for
optimization.
• Disadvantage-Limited to 2 variables .
• Helps in finding the maxima (greatest possible amount)
and minima (lowest possible concentration) depending
on the constraints..
• A techniques called “sensitivity analysis” can provide
information so that the formulator can further trade off
one property for another.
Fonner DE, Buck JR, Banker GS. Mathematical optimization techniques in drug product
design and process analysis. J Pharm Sci, 59(11):1587-1596, 1987 Contd…

39. • Determine constraints.
• Determine objective formulation
• 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
STEPS INVOLVED
Contd…

40. EXAMPLE
•FONNER ET AL. applied methodology in tablet
formulation containing API phenylpropanolamine HcL.
• For the experiment:-
oIndependent variable:- x1 = starch; x2 = stearic acid.
oDependent variables:- Hardness, D.T, friability, drug
release pattern, urinary excretion profile.
•Using the mathematical data a polynomial equation is
formed which gives dependent variable’s relation which
would yield fully optimized product.
Contd…

41. • DECIDING THE FACTORS AND LIMITS
FACTOR LOW lEVEL (mg) HIGH LEVEL (mg)
A:- Stearate 0.5 1.5
B:- Dicalcium
phospate
60.0 120.0
C. Starch 30.0 50.0
Contd…

42. • DECIDING THE LIMITS AS PER FULL FACTORIAL
STRATEGY AND ITS RESULT.
Contd…
Factor
Combination
1. Stearate 2.Drug 3.Dicalcium
phospate
(1) - - -
a + - -
b - + -
ab + + -
c - - +
ac + - +
bc - + +
abc + + +

43.  Constrained optimization problem is to locate the levels of stearic
acid(x1) and starch(x2).
 This minimize the time of in vitro release(y2),average tablet volume(y4),
average friability(y3)
 To apply the lagrangian method, problem must be expressed
mathematically as follows
Y2 = f2(X1,X2)-in vitro release
Y3 = f3(X1,X2)<2.72-Friability
Y4 = f4(x1,x2) <0.422-avg tab.vol
Contd…

44. Final
optimized
graph
depicting the
acceptable
product.
Optimizing values of stearic acid and
strach as a function of restrictions on
tablet friability: (A) percent starch; (B)
percent stearic acid
Contd…

45. 4) SEARCH METHOD
• It is not different than RSM ie Response
surface methodology.
• It takes into account 5 variables.
• Computer system optimization comes under
this method.
Contd…

46. 5) Canonical analysis
• 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.
• It is used to reduce second order regression equation to an
equation consisting of a constant and squared terms as follows-
Y = Y0 +λ1W1
2 + λ2W2
2 +..
2variables=first order regression equation.
3variables/3level design=second order regression equation.
In canonical analysis or canonical
reduction, second-order regression
equations are reduced to a simpler form
by a rigid rotation and translation of the
response surface axes in multidimensional
space, as for a two dimension system.
Contd…

47. APPLICATIONS OF OPTIMIZATION
Formulation and Processing
Clinical Chemistry
Medicinal Chemistry
High Performance Liquid Chromatographic Analysis
Formulation of Culture Medium in Virological
Studies.
Study of Pharmacokinetic Parameters.

48. Provide solution to large scale
manufacturing problems
Provides string assurances to regulatory
agencies superior drug product quality
In microencapsulation process
Improvement of physical &biological
properties by modification
APPLICATIONS OF OPTIMIZATION contd…

49. Approach to process optimization and
scale-up – regulator requirements.
• Quality assured by end product testing:-
In this technique the end product testing at a small or large scale
would never import the quality in the product. An alternative which
comes is to stamp the product prepared to be of best quality.
• Full design of experiments:-
QbD approach is utilized that would aditionally include schematic
evaluation, understanding and refining of the formulation and
manufacturing process.
It includes
1) Identifying the risks
2) Determining the functional relationship
3) managing Quality and risk management.
http://www.pharmtech.
com/pharmtech/article

50. • FDA expectation is to review all product
development data including experiment
design so as to understand the firms
capabilities to understand its product
characteristics for designing operational range
of manufacturing and testing.
• ICH Q8 (QbD) compliance is mandatory for
regulatory submission.

51. REFERENCES
1) Schwartz J.B, O'Connor R.E, Schnaare R.L chapter 18 -
optimization technique in pharmaceutical formulation and
processing, Published by Marcel Dekker ©2002.
2) Rani S. & Hiremath R. Textbook of industrial pharmacy.
3) Stanford B., Bon C. pharmaceutical statistics practical and clinical
application Chapter 9 published by Marcel dekker
4) Internet source
http:// www.itl.nist.gov
Images from google images
wikipedia.com
KLE university
5) Certain review articals