Optimization techniques
- 1. Presented by : PRASHIK S SHIMPI M. Pharm 2nd Semester Department of Quality Assurance R.C.Patel Institute of Pharmaceutical Education & Research, Shirpur. 1
- 2. Contents Introduction Optimization parameters Classic optimization Optimization methods Application Reference 2
- 3. Introduction Optimize: To make as perfect, effective or functional as possible. Optimization : It is the process of finding the best way of using the existing resources while taking into account all of the factors that influence decisions in any experiment. The composition of pharmaceutical formulation is often subject to trial & error. Optimization by means of an experimental design may be helpful in shortening the experimenting time. 3
- 4. Optimization Parameters A. Problem type i) Constrained – Restrictions placed on the system due to physical limitations or perhaps due to simple practicality. ii) Unconstrained- No restrictions, but almost nonexistent in pharmaceuticals. B. Variable type i) Independent variable:- ii) Dependent variable:- 4
- 5. Classic Optimization Result from application of calculus to the basic problem of finding the maximum or minimum of a function. Useful for problems that are not too complex and do not involve more than a few variables. Y=f (X) Y=f(X1, X2) 5
- 6. Input Real System Output Response Mathematical Model of System Input Factor Levels Optimization Procedure Applied Optimization Methods These general optimization techniques can be described by following flowchart- 6
- 7. Design of experiment Factorial designs Full Factorial designs Fractional Factorial designs Plackett-Burman design Response surface(second order) designs • Central Composite designs • Box-Behnken designs 7
- 8. Factorial Design A full factorial design for n factors requires runs; with 10 factors that would mean 1024 runs! In fractional factorial designs the number of runs N is a power of 2 (N = 4, 8, 16, 32, and so forth) In Plackett-Burman designs the number of runs N is a multiple of 4 (N = 4, 8, 12, 16, 20, 24, and so forth) Plackett-Burman designs fill in the gaps in the run sizes 8
- 9. Factorial Experiments 3-FACTOR 3 main effects (A, B, C) 3, 2-way Interactions A X B, A X C, B X C 1, 3-way Interaction A X B X C 9 4-FACTOR 4 main effects (A, B, C, D) 6, 2-way Interactions A X B, A X C, A X D, B X C, B X D, C X D 4, 3-way Interactions A X B X C, A X B X D, A X C X D, B X C X D 1, 4-way Interaction A X B X C X D
- 10. - 23 level Factorial Design - Full / Fractional Factorial Design 111 111 111 111 111 111 111 111 321 xxx 2 level Full Factorial Design Fractional Factorial Design Classifications x1 x1 x2 x2 x3 x3 10
- 11. Plackett-Burman Design Plackett and Burman (1946) showed how full factorial designs can be fractionalized in a different manner than traditional 2k fractional factorial designs, in order to screen the max number of (main) effects in the least number of experimental runs. Fractional factorial designs for studying k = N – 1 variables in N runs, where N is a multiple of 4. Only main effects are of interest. 11
- 12. When to use PB designs: Screening Possible to neglect higher order interactions 2-level multi-factor experiments. More than 4 factors, since for 2 to 4 variables a full factorial can be performed. To economically detect large main effects. Particularly useful for N = 12, 20, 24, 28 and 36. 12
- 13. Box-Behnken Design Box-Behnken designs are the equivalent of Plackett-Burman designs for the case of 3-level multi-factor. 13 x1 x2 x3 When to use Box-Behnken designs: • With three-level multi-factor experiments. • When it is required to economically detect large main effects, especially when it is expensive to perform all the necessary runs. • When the experimenter should avoid combined factor extremes. This property prevents a potential loss of data in those cases.
- 14. Number of runs required by Central Composite and Box-Behnken designs Number of factors Box Behnken Central Composite 2 - 13 (5 center points) 3 15 20 (6 center point runs) 4 27 30 (6 center point runs) 5 46 33 (fractional factorial) or 52 (full factorial) 6 54 54 (fractional factorial) or 91 (full factorial) 14
- 15. Example: Improving Yield of a Chemical Process Factor Levels – 0 + Time (min) 70 75 80 Temperature (°C) 127.5 130 132.5 15
- 16. Use a 23 Factorial Design With Central Points Run Factors in original units Factors in coded units Response Time(min.) X1 Temp.(°C) X2 X1 X2 Yield(gms) Y 1 70 127.5 - - 54.3 2 80 127.5 + - 60.3 3 70 132.5 - + 64.6 4 80 132.5 + + 68.0 5 75 130.0 0 0 60.3 6 75 130.0 0 0 64.3 7 75 130.0 0 0 62.3 Results From First Factorial Design 16
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- 18. Results of Second Factorial Design Run Factors in original units Factors in coded units Response Time(min.) X1 Temp.(°C) X2 X1 X2 Yield(gms) Y 11 80 140 - - 78.8 12 100 140 + - 84.5 13 80 150 - + 91.2 14 100 150 + + 77.4 15 90 145 0 0 89.7 16 90 145 0 0 86.8 18
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- 20. Improve process yield Reduce variability Reduce development time Reduce overall costs Evaluate and compare alternatives Evaluate material alternatives 20 Applications of Optimization Techniques
- 21. Applications of Optimization Techniques Optimization techniques are widely used in pharmacy especially used in- Pharmaceutical suspension Controlled release formulations In tablet coating operation In Enteric film coating In HPLC analysis To study formulation of culture medium in virology 21
- 22. Softwares for Optimization Techniques Design Expert 7.1.3 SYSTAT SigmaStat 3.11 SPSS 13 DeltaGraph 5.6 EquivTest PASS 2005 Quickstart manual Prism GraphPad 4.03 CYTEL East 3.1 22
- 23. Reference 1. Banker GS & Rhodes TS. Modern Pharmaceutics. 2nd ed. vol-40, p. 803-828. 2. Hirmath SR. Industrial Pharmacy. Orient Longman Private Ltd. p. 158-168. 3. Lewis GA, Roger DM, Phan-Tan-Luu. Pharmaceutical Experimental Design. vol-92. p.247- 292. 4. Parikh DM. Handbook Of Pharmaceutical Granulation Technology. vol-81. p.253-258. 23
- 24. 5. Alderborn GF & Nystrom CS. Pharmaceutical Powder Compaction Technology. vol-71. p.580-590. 6. Banker GS & Rhodes CT. Modern Pharmaceutics.4th ed. Vol- 121, p. 606-625. 7. Bolton SA. Pharmaceutical Statistics Practical & Clinical Application. 3rd ed. vol-80. p. 590-625. 8. Nielloud F & Marti-Mestres G. Pharmaceutical Emulsion &Suspensions. vol-105, p.51,540,543,549. 24
- 25. Thank You 25