describes the various optimization techniques and parameters and its applications in pharmaceutical industry

1. S.R. College of Pharmacy
Optimization Techniques
in
Pharmaceutical Formulation
and Processing
P. Raja Abhilash, M.pharm
(Ph.D.)
Assistant professor,
S.R. college of pharmacy.

2. Contents
• Introduction
• Optimization Parameters
• Classic Optimization
• Statistical Design
• Applied Optimization Methods
• Use of Computers for Optimization
• Applications
• Conclusion
• References

3. INTRODUCTION
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 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.
3

4. Optimization Parameters
Optimization
parameters
Variable types Problem types
Independent variables Unconstrained
Dependent variables Constrained

5. Problem types in
optimization
Unconstrained Constrained
no restrictions are restrictions are placed
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

6. variables in optimization
Independent Dependent
variables 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

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.
Fig I; response surface curve

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 [Eq. (1)]:
Y = f(X) ---eqn (1)
Figure 2. Graphic location of optimum (maximum or minimum)

9. Classic Optimization
• 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 (Fig. 3.) on which the axes represents the two
independent variables, X1 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)
Figure 3. Contour plot. Contour represents values of the dependent
variable Y
9

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.

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

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 Xn .
 SYMMETRIC
 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 xn-p .

13. Factorial Designs
Pictorial representation , where each point represents the individual experiment

14. Applied optimization methods
A. Evolutionary Operations (EVOP)
B. Simplex Method
C. Lagrangian Method
D. Search Method
A. canonical analysis

15. A. 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.

16. B. 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.
1
• It is of two types:
A. Basic Simplex Method
B. Modified Simplex Method
2 3
• Simplex methods are governed by certain rules.

17. Basic Simplex Method
9 10
Rule 1 :
s8
s7 s9
7 11
The new simplex is formed
s6 8 s10 by keeping the two vertices
s5 from preceding simplex with
5
6
12 best results, and replacing
s4
s3 the rejected vertex (W) with
(N) 1 4 its mirror image across the
s2 (R) line defined by remaining
s1 two vertices.
2 3
(W) (B)

18. Basic Simplex Method
(W) 9 10 (W)
Rule 2 :
s8
s7 s9
7 11
When the new vertex in a
s6 8 s10 simplex is the worst
s5 response, the second lowest
5
6
12 response in the simplex is
s4
s3
(W) eliminated and its mirror
(N) 1 4 image across the line; is
s2 (R) defined as new vertices to
s1 form the new simplex.
2 3
(W) (B)

19. Basic Simplex Method
(W) 9 10 (W) Rule 3 :
s8
When a certain point is
s7 s9 retained in three successive
7 11
s6 8 s10 simplexes, the response at
s5 this point or vertex is re
5
6
12 determined and if same
s4
s3
(W) results are obtained, the
(N) 1 4
point is considered to be the
s2 (R) best optimum that can be
s1 obtained.
2 3
(W) (B)

20. Basic Simplex Method
(W) 9 10 (W) Rule 4 :
s8
If a point falls outside the
s7 s9 boundaries of the chosen
7 11
s6 8 s10 range of factors, an
s5 artificially worse response
5
6
12 should be assigned to it and
s4
s3
(W) one proceeds further with
(N) 1 4
rules 1 to 3. This will force
s2 (R) the simplex back into the
s1 boundaries.
2 3
(W) (B)

21. 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.

22. Modified Simplex Method
E1
• If response at R1 > B,
R1 expansion of simplex to E1.
N
•If response at N<= R1<=B,
C1 no expansion or contraction
is done.
•If response at R1<N,
contraction of the simplex is
B done.
W

23. C. Lagrangian Method
• It represents mathematical method of optimization.
• Steps involved:
1.Determine the objective function.
2. Determine the constraints.
3. Introduce the Lagrange Multiplier (λ) for each constraint.
4. Partially differentiate Lagrange Function (F).
5. Solve the set of simultaneous equations.
6. Substitute the resulting values into objective function.

24. Lagrangian Method (polynomial model)
Total Cost = 3x2 + 6y2 – xy ------ objective function determined!
Subject to: x+y = 20 ------------- constraints determined!
We can rewrite the condition as,
0 = 20-x-y ------- This has to be embedded in objective function
LTC = 3x2 + 6y2 – xy + λ ( 20 -x - y) ---------- Lagrange multiplier (λ) introduced
LTC = 3x2 + 6y2 – xy + 20 λ - x λ - y λ --------- Lagrange function (F)
Partial differentiation done! Now
solve the simultaneous equations

25. Lagrangian Method
6x – y - λ = 0
x – 12y + λ = 0
7x - 13y = 0
i.e. 7x = 13y
so Insert in any of the
simultaneous
equations

26. Lagrangian Method
Total Cost = 3x2 + 6y2 – xy ------ objective function
We have determined using Lagrange function, x= 13 and y= 7
Substituting these values in the objective function,
Total Cost = 3x2 + 6y2 – xy
Total Cost = 3(13)2 + 6(7)2 – (13)(7)
Total Cost = 507 + 294 – 91
Hence the total cost to produce 20 units is $ 710

27. Example for the Lagrangian Method
• The active ingredient , phenyl- propanolamine HCl,
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. X1 and X2. 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, as follows:

28. Lagrangian Method (contour plots)
(a) Tablet Hardness
(b) Dissolution
(c) Feasible solution
indicated by
crosshatched area.

29. D. 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
• Submit data for statististical and regressional analysis
• Set specifications for feasibility program
• Select constraints for grid research
• Evaluate grid search printout as contour plots

30. Example for the Search methods
Independent Variables Dependent Variables
X1 = Diluent ratio Y1 = Disintegration time
X2= Compressional force Y2= Hardness
X3= Disintegrant levels Y3 = Dissolution
X4= Binder levels Y4 = Friability
X5 = Lubricant levels Y5 = Porosity

31. Search methods
• The first 16 trials are represented
by +1 and -1.
• The remaining trials are
represented by a -1.547, zero or
1.547
• The type of predictor equation
used in this example is :

32. Search methods
The output includes plots of a given responses as a function of all
five variables.
32

33. Search methods
Contour plots for (a) disintegration time (b) tablet hardness (c)
dissolution response (d) tablet friability.
33

34. E. 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 = Y0+λ1W12+λ2W22+…….

35. 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.
35

36. Use of Computers for optimization
• Statistical Analysis Systems (SAS)
• RS/Discover
• eCHIP
• Xstat
• JMP
• Design Expert
• FICO Xpress Optimization Suite
• Multisimplex

37. Applications
• Formulation and Processing
• Clinical Chemistry
• HPLC Analysis
• Medicinal Chemistry
• Studying pharmacokinetic parameters
• Formulation of culture medium in microbiology studies.

38. Conclusion
• Optimization techniques are a part of development process.
• The levels of variables for getting optimum response is
evaluated.
• Different optimization methods are used for different
optimization problems.
• Optimization helps in getting optimum product with desired
bioavailability criteria as well as mass production.
• More optimum the product = More $$ the company earns
in profits!!!

39. 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. 4th edition. CRC Press.
(2002); p: 900-928.
• Optimization. 2012. In Merriam-Webster Online Dictionary. Retrieved March 07, 2012, from
http://www.merriam-webster.com/dictionary/optimization
• N. Arulsudar, N. Subramanian & R.S.R. Murthy. Comparison of artificial neural network and
multiple linear regressions in the optimization of formulation parameters of leuprolide
acetate loaded liposomes. Journal of Pharmacy & Pharmaceutical Sciences. (2005) Vol. 8(2);
p: 243-258.
• Roma Tauler, Steven D. Brown, Beata Walczak. Comprehensive Chemometrics: Chemical and
Biochemical data analysis. Elsevier. (2009); p: 555-560.
• Khaled S. Al-Sultan, M.A. Rahim. Optimization in Quality Control. Springer. (1997); p: 6-8.
• Donald H.Mc Burney, Theresa L.White. Research Methods. 7th edition. Thomson Wadsworth.
(2007); p: 119.
• 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.