This document discusses various optimization techniques used in pharmaceutical formulation and processing. It begins by defining optimization and describing how it is applied in the pharmaceutical industry through experimentation and controlling variables. It then covers specific optimization parameters, classic optimization techniques like response surface methodology, and statistical experimental designs. Finally, it discusses modern applied optimization methods like evolutionary operations, simplex method, and Lagrangian method. It provides examples of how these techniques are used and concludes with the role of computers in optimization and some applications.

1. Optimization Techniques in Pharmaceutical
Formulation and Processing
Tamilselvan.A
M.Pharm 1st semester [pharmaceutics]
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2. Contents
 Introduction
 Optimization Parameters
 Classic Optimization
 Statistical Design
 Applied Optimization Methods
 Use of Computers for Optimization
 Applications
 References
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3. INTRODUCTION OF OPTIMIZATION
It is defined as follows: 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.
OPTIMIZATION is an act, process, or methodology of making design, system
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.
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4. OPTIMIZATION PARAMETERS
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5. 5

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7. Response surface curve
Once the relationship between the variable and the response is known, it gives
the response surface as represented in the Fig. 1. 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.
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8. 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 in the Fig. 2. 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)
Y
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9. Classic Optimization
 When the relationship for the response Y is given as the function of two
independent variables, X, and X₂,
Y = f(x₁,X₂)
 Graphically, there are contour plots (Fig. 3.) on which the axes represents the
two independent variables, X, and X₂, and contours represents the response
Y. Here the contours are showing the response. (contour represents the
connecting point showing the peak level of response)
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10. Optimization Techniques
 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.
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11. 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
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12. Factorial Designs
 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".
a]SYMMETRIC
b]ASYMMETRIC
 Fractional factorial designs: It is a fraction (1/xP) 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-P
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13. FACTORIAL DESIGNS
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14. Applied optimization methods
 Evolutionary Operations (EVOP)
 Simplex Method
 Lagrangian Method
 Search Method
 canonical analysis
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15. Evolutionary operations (EVOP)
 Most widely used method of experimental optimization in fields
other than pharmaceutical technology..
 Experiment 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.
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16. 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
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17. Lagrangian Method
It represents mathematical method of optimization.
Steps involved
 Determine the objective function.
 Determine the constraints.
 Introduce the Lagrange Multiplier (X) for each constraint.
 Partially differentiate Lagrange Function (F).
 Solve the set of simultaneous equations.
 Substitute the resulting values into objective function.
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18. Example for the Lagrangian Method
 The active ingredient, phenyl- propanolamine HCI, was kept at a
constant level, and the level of the levels of disintegrant (corn
starch) and lubricant (stearic acid) were selected as the independent
variables. X and X,. the dependent variables include tablet
hardness, friability, invitro release rate, and urinary excretion rate
in human subject.
 A graphic technique may be obtained from the polynomial
equations.
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19. Lagrangian method [contour plots]
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20. Search methods
Unlike the Lagrangian method, do not require differentiability of the
objective function.
It can be used for more than two independent variables.
The response surface is searched by various methods to find the
combination of independent variables yielding an optimum.
select a system
select variables: independent and dependent
Perform experiments and test product
Set specifications for feasibility program
Select constraints for grid research
Evaluate grid search printout as contour plots
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21. Eg for the search method
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22. Search method
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25. Canonical Analysis
Canonical analysis, or canonical reduction, is a technique used
to reduce a second-order regression equation, to an equation
consisting of a constant and squared terms, as follows:
Y = Y₂+λ, W₁²+λ₂ W₂² 0
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26. Canonical Analysis
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 shown in Fig.14 for
a two dimension system.
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27. Use of Computers for
optimization
 Statistical Analysis Systems (SAS)
 RS/Discover
 eCHIP
 Xstate
 JMP
 Design Expert
 Multi simplex
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28. Applications
 Formulation and Processing
 Clinical Chemistry
 HPLC Analysis
 Medicinal Chemistry
 Studying pharmacokinetic parameters
 Formulation of culture medium in
microbiology studies.
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29. References
 Joseph B. Schwartz. Optimization techniques in product
formulation. Journal of the Society of Cosmetic Chemists. (1981)
Vol 32; p: 287-301.
 Gilbert S. Banker, Christopher T. Rhodes. Modern Pharmaceutics.
4* edition. CRC Press. (2002); p: 900-928.
 Rosilene L. Dutra, Heloisa F. Maltez, Eduardo Carasek,
Development of an on-line preconcentration system for zinc
determination in biological samples, Talanta, (2006) Vol 69(2),
p:488-493.
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30. THANKYOU
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