3. INTRODUCTION :
The term Optimize is defined as “to make perfect”. It is used in
pharmacy relative to formulation and processing. It is 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.
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
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5. Primary objective may not be optimize absolutely but to compromise effectively &
thereby produce the best formulation under a given set of restrictions .
Reduces the
cost
Save Time
Safety and
Reduces error
Reproducibility
Innovation and
efficacy
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6. Concept of Optimization
• Optimization is defined as “The process of finding the best values for the variables
of a particular problem to minimize or maximize an objective function.”
Concept of optimization
Black box
Controllable Input Response Out
Uncontrollable Inputs
(Different Machines and different operators) 21-06-2023
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7. It is used in pharmacy relative formulation and processing
It is involved in formulating drug products in various forms.
Final product not only meets the requirements from the bioavailability but also
from the practical mass production criteria.
It helps the pharmaceutical scientist to understand theoretical formulation and
the target processing parameters which ranges for each excipients & processing
factors.
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9. Unconstrained
In unconstrained optimization problems 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 20 minutes.
Problem types
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10. Variable types
Independent Variable
The independent variables are the formulation and process variables,
which are directly under the control of the formulator.
Dependent Variable
The dependent variables are the responses or the characteristics of the in-
process material or the resulting drug delivery system. These are a direct
result or any change in the formulation or process.
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12. • If greater the variables in a given system, then greater will be the
complicated job of optimization.
• But regardless of the number of variables, there will be relationship
between a given response and independent variables.
• Once we know this relationship for a given response, then will able to
define a response surface
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13. 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.
LEVELS: Levels of a factor are the values or designations assigned to
the factor
FACTOR LEVELS
Temperature 30oc
Concentration 1%, 2%
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14. 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.
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15. EXPERIMENTAL DESIGNS:
A blueprint of the procedure that enables the researcher to test his
hypothesis by reaching valid conclusions about relationships between
independent and dependent variables.
It refers to the conceptual framework within which the experiment
is conducted.
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17. Completely randomized Designs:
These designs compares the values of a
response variable based on different levels
of that primary factor.
The levels of the primary factor are
randomly assigned to the experimental
designs.
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. 21-06-2023
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18. Randomized block designs:
For this there is one factor or variable that is of primary interest.
To control non-significant factors(nuisance factor), an important technique
called blocking can be used to reduce or eliminate the contribution of these
factors to experimental error.
General rule- block what is possible & randomize what is not possible.
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19. Factorial Design(FD):
Factorial experiment is an experiment whose design consist of
two or more factor each with different possible values or “levels”.
Factorial design applied in optimization techniques.
Types of FD:
TWO TYPES-
Full Factorial Design.
Fractional Factorial Design.
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20. Factorial Design Testing:
In chromatographic condition responses can be
Efficiency
Retention factor
Asymmetry
Retention time
Resolution
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22. Advantages:
It’s easier to study the combined effect of two or more factors
simultaneously and analyze their interrelationships.
Has a wide range of factor combination are used.
Drawback:
Wasting of time and experimental material.
Increase in factor size leads to increase in block size which increase the
chance of error.
It’s complex when several factors are involved simultaneously.
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23. Full Factorial Design:
A design in which every setting of every factor appears with setting of every
other factor is full FD.
Simplest design to create, but extremely inefficient.
If there is x factor, each at y level, a full FD has yx.
Number of Runs(N) N=y˟
Where, y= number of levels; x= number of factors.
ex: 2³=8
3factors, 2 levels each
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24. It depends on INDEPENDENT VARIABLES for development of new
formulation.
It also depends LEVELS as well as CODING.
can be Quantitative (numerical number) or they are Qualitative.
Factorial design: 2², 2³, 3²,3³
2²FD=2 Factors, 2 levels=4 runs
2³FD=3 Factors, 2 levels=8 runs
3²FD=2 Factors, 3 levels=9 runs
3³FD=3 Factors, 3 levels=27 runs
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25. Two Levels Full FD:
2 factors: X₁ and X₂
2 levels: Low and High
Coding: (-1), (+1)
Three Levels Full FD:
In three level FD,
3 factors: X₁, X₂ and X₃
3 levels are use,
Low(-1)
Intermediate(0)
High(+1) 21-06-2023
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26. Fractional Factorial Design:
In full FD, as a number of factor or level increases , the number
of experiment required exceeds to unmanageable levels.
In such cases, the number of experiment can be reduced
systematically and resulting design is called as fractional
FD(FFD).
Applied if number of factor are more than 5.
Levels combinations are chosen to provide sufficient
information to determine the factor effect. 21-06-2023
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28. Homogenous fractional:
Useful when large number of factors must be screened efficiently & all
variables have the same number of levels.
Mixed level fractional:
Useful when variety of factors needed to be evaluated for main effects and
higher level interactions can be assumed to be negligible.
Ex-objective is to generate a design for one variable A, at 2 levels and
another, X, at three levels , mixed &evaluated.
Box-hunter:
Fractional designs with factors of more than two levels can be specified as
homogenous fractional or mixed level fractional 21-06-2023
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29. 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.
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30. Taguchi:
It is similar to PBDs.
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
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31. Response surface designs
This model has quadratic form
γ =β0 + β1X1 + β2X2 +….β11X1
2 + β22X2
-Designed for fitting these types of models are known as response surface
designs.
the goal is to minimize defects and maximize yield.
Two most common designs generally used in this response surface modeling
are
Central composite designs
Box-Behnken designs
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32. 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 contain 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 be imagined that there are several
factors that can vary between low and high values.
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33. 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 center
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(CCF) designs - Star points on the faces of the cube.
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34. Generation of a Central Composite Design for Factors
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35. Box-Behnken designs:
Box-Behnken designs use just three levels of each factor.
In this design the treatment combinations are at the midpoints of edges of the
process space and at the center. These designs are rotatable (or near rotatable)
and require 3 levels of each factor.
These designs for three factors with circled point appearing at the origin and
possibly repeated for several runs.
It’s alternative to CCD.
The design should be sufficient to fit a quadratic model , that justify equations
based on square term & products of factors.
Y=b0+b1x1+b2x2+b3x3+b4x1x2+b5x1x3+b6X2X3+b7X1
2 +b8X22+b9X3
2
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37. Contour designs:
Definition:
A Contour plot is a graphical representation of the relationships among three
numeric variables in two dimension.
Two variables are for X and Y axes, and a third variable Z is for contour levels.
A contour plot is a graphical technique for representing a 3 dimensional
surface by plotting constant z slice, called contours, on a 2D format. That is,
given a value for z, lines are drawn by connecting the (x, y) co-ordinates where
that z value occurs.
The contour plot is an alternative to a 3-D surface plot.
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38. This contour plot shows that the surface 3-D representation of Contour plot
is symmetric and peaks in the centre.
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39. The contour plots are formed by,
Vertical axis: Independent Variable 2
Horizontal axis: Independent Variable 1
Lines: Iso-response values.
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40. The dex contour plot is a specialized contour plot used in
the design of experiments. In particular, it is useful for full
and fractional designs.
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41. Application in formulation:
Contour plots helps in visualizing the response surface.
Contour plots are useful for establishing desirable response values and
operating conditions.
This plot shows how a response variable relates to two factors based on
a model equation.
Points that have the same response are connected to produce contour lines
of constant responses.
Such type of plots and experimental designs are used for used optimization
techniques in Pharmaceuticals formulation and processing.
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42. Other applications:
Formulation and Processing
Clinical Chemistry
Medicinal Chemistry
High Performance Liquid Chromatographic Analysis
Formulation of Culture Medium in Virological Studies
Study of Pharmacokinetic Parameters
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44. CLASSICAL 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,
Y = f(X)
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45. When the relationship for the response Y is given as the function of two
independent variables, X1 and X2 ,
Y = f(X1, X2)
Graphically, there are contour plots on which the axes represents the two
independent variables, X1 and X2, and contours represents the response Y.
DRAWBACKS:
Limited applications
Problems that are too complex.
They do not involve more than two variables.
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46. Techniques used divided into two types:
Experimentation continues as optimization proceeds.
It is represented by evolutionary operations(EVOP), sequential simplex
methods.
Experimentation is completed before optimization takes place.
It is represented by classic mathematical & search methods.
In later one it is necessary that the relation between any dependent variable
and one or more independent variable is known.
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47. There are two possible approaches for this
Theoretical approach- If theoretical equation is known, no experimentation
is necessary.
Empirical or experimental approach – With single or more independent
variables, formulator experiments at several levels.
Drawback:
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
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48. The effect on a real system of changing some input(some variable) is
observed directly at the output(one measures some property).
Considering the changes in input and effect on output, the optimization
techniques are categorized into five types:
1. Evolutionary operations
2. Simplex method
3. Lagrangian method
4. Search method
5. Canonical analysis
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49. Chodankar RS, Dev A. Optimisaton techniques: a futuristic approach for
formulating and processing of pharmaceuticals. Indian Journal of
Pharmaceutical and Biological Research. 2016 Apr 1;4(2):32.
Ziaee A, Albadarin AB, Padrela L, Femmer T, O'Reilly E, Walker G. Spray
drying of pharmaceuticals and biopharmaceuticals: Critical parameters and
experimental process optimization approaches. European Journal of
Pharmaceutical Sciences. 2019 Jan 15;127:300-18.
Campisi B, Chicco D, Vojnovic D, Phan-Tan-Luu R. Experimental design for
a pharmaceutical formulation: optimisation and robustness. Journal of
pharmaceutical and biomedical analysis. 1998 Oct 1;18(1-2):57-65.
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