Optimization techniques in pharmaceutical formulation and processing

MODERN PHARMACEUTICS

1. Optimization Techniques in pharmaceutical Formulation and Processing PRESENTED BY, PRATIKSHA C CHANDRAGIRIVAR M PHARMA 1 ST SEM DEPT, OF PHARMACEUTICS HSK COP BAGALKOT FACILITATED BY, AVINASH.S.G. ASSO.PROFESSOR DEPT.OF PHARMACEUTICS HSK COP BAGALKOT Optimization Techniques in pharmaceutical Formulation and Processing

2. CONTENTS: Concept of optimization Parameters of optimization Optimization techniques in pharmaceutical formulation and processing. Optimization Techniques in pharmaceutical Formulation and Processing

3. 1. CONCEPT OF OPTIMIZATION : The term optimize is defined as “ to make perfect ”. In terms of sentence it is defined as choosing the best element from some set of available alternatives. According to Merriam Webster dictionary, optimization means, “ An act, process or methodology of making something (as a design, system or a decision) as a fully perfect, functional or effective as possible; specially the mathematical procedures. Optimization is also defined as “The process of finding the best values for the variables of a particular problem to minimize or maximize an objective function.” Optimization Techniques in pharmaceutical Formulation and Processing

4. 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 bio-availability 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. 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 Optimization Techniques in pharmaceutical Formulation and Processing

5. “It is not a screening technique.” Optimization is necessary because, It reduces the cost. It provides safety and reduces the error. It provides innovation and efficacy. It saves the time. Optimization Techniques in pharmaceutical Formulation and Processing

6. 2.PARAMETERS OF OPTIMIZATION: Parameters of optimization is divided into two main types which is shown schematically: optimization parameters problem type variables constrained unconstrained dependent independent formulating processing Optimization Techniques in pharmaceutical Formulation and Processing

7. a. Problem type: There are two general type are there in the problem type of optimization technique: Constrained Un constrained 1. Constrained : These are the restrictions placed on the system by physical limitations or perhaps by simple practicality. Example : Economical considerations 2. Un constrained: Here there are no restrictions. With the help of flow chart we can predict these two problem type very easily viz., Optimization Techniques in pharmaceutical Formulation and Processing

8. Optimization Techniques in pharmaceutical Formulation and Processing

9. b. Variables: Mathematically, they can be divided into two groups Independent or primary variables Dependent or secondary variables a. Independent or primary variables: Formulations and process variables directly under control of the formulator. Example: Ingredients Mixing time for given process step. Optimization Techniques in pharmaceutical Formulation and Processing

10. B. Dependent or secondary variables: These are the responses or the characteristics of the in-progress material or the resulting drug delivery system. Example: Direct result of any change in the formulation or process. Optimization Techniques in pharmaceutical Formulation and Processing

11. If greater the variables in a given system, then greater will be the complicated job of optimization. But regardless of the no.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 i.e., Optimization Techniques in pharmaceutical Formulation and Processing

12. It involves application of calculus to basic problem for maximum/minimum function. Limited applications i . Problems those are not too complex. ii. They do not involve more than two variables. For more than two variables, graphical representation is impossible, but it is possible mathematically.   Optimization Techniques in pharmaceutical Formulation and Processing

13. 3.OPTIMIZATION TECHINQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING Deming and king presented a general optimization techniques: Optimization Techniques in pharmaceutical Formulation and Processing

14. Considering the changes in input and effect on output, the optimization techniques are categorized into five types: Evolutionary operations 2. Simplex method 3. Lagrangian method 4. Search method 5. Canonical analysis Optimization Techniques in pharmaceutical Formulation and Processing

15. 1.Evolutionary operations: It is the one of the most widely used methods of experimental optimization in fields other than pharmaceutical technology is the evolutionary operation(EVOP), It is well suited to production situation. The basic idea is that the production procedure(formulation and process) is allowed to evolve to the optimum by careful planning and constant repetition. Optimization Techniques in pharmaceutical Formulation and Processing

16. Method: This process is run in a such a way that It produces a product that meets all specifications. Simultaneously, it generates information on product improvement. Experimenter makes a very small change in the formulation or process but makes it so many times i.e., repeates the experiment so many times. Then he or she can be able to determine statistically whether the product has improved. And the experimenter makes further any other change in the same direction, many times and notes the results. Optimization Techniques in pharmaceutical Formulation and Processing

17. This continues until further changes do not improve the product or perhaps become detrimental. Applications: It was applied to tablets by Rubinstein. It has also been applied to an inspection system for parenteral products. Drawbacks: It is impractical and expensive to use. It is not a substitute for good laboratory scale investigation. Optimization Techniques in pharmaceutical Formulation and Processing

18. 2.Simplex method: It is most widely applied technique. It was proposed by Spendley et.al. This technique has even wider appeal in areas other than formulation and processing. A good example to explain its principle is the application to the development of an analytical method i.e., a continuous flow anlayzer, it was predicted by Deming and king. Simplex method is a geometric figure that has one or more point than the number of factors. If two factors or any independent variables are there, then simplex is represented triangle. Once the shape of a simplex has been determined, the method can employ a simplex of fixed size or of variable sizes that are determined by comparing the magnitude of the responses after each successive calculation. Optimization Techniques in pharmaceutical Formulation and Processing

19. Graph representing the simplex movements to the optimum conditions Optimization Techniques in pharmaceutical Formulation and Processing

20. Explaination: The two axes in the figure are nothing but two independent variables show the pump speeds for the two reagents required in the analysis reaction. The initial simplex is represented by the lowest triangle. The vertices represent the spectrophotometric response. The strategy is moves towards a better response. The worst response is 0.25, conditions are selected at the vertex, 0.6 and indeed improvement is obtained. Then the experiment path is followed to obtain optimum, 0.721. Optimization Techniques in pharmaceutical Formulation and Processing

21. Applications of method: This method was used by Shek.et.al. to search for an capsule formula. This was applied to study the solubility problem involving butaconazolenitrate in a multicomponent system. Bindschaeder and Gurny published an adaptation of the simplex technique to a TI-59 calculator and applied successfully to a direct compression tablet of acetaminophen. Janeczeck applied the approach to a liquid system i.e., a pharmaceutical solution and was able to optimize physical stability. Optimization Techniques in pharmaceutical Formulation and Processing

22. 3. The Lagragian method: This optimization method represents the mathematical technique, is an extension of the classic method. Fonner.et.al gave ideas of understanding this technique by applying it to a tablet formulation and by considering two independent variables. Optimization Techniques in pharmaceutical Formulation and Processing

23. Explaination : The active ingredient, phenylpropanolamine HCl , was kept at a constant level, and the levels of disintegrant (corn starch) and lubricant (stearic acid) were selected as the independent variables x 1 and x 2 . The dependent variables include tablet hardness, friability, volume, in vitro release rate and urinary excretion rate in human subjects. This techniques requires that the experimentation to be completed before optimization so that mathematical models can be generated. Optimization Techniques in pharmaceutical Formulation and Processing

24. The experimental data for the taken example : Tablet formulation: Optimization Techniques in pharmaceutical Formulation and Processing

25. The analysis is performed on a polynomial form. y = B + B 1 x 1 + B 2 x 2 + B 3 x 1 2 + B 4 x 2 2 + B 5 x 1 x 2 + B 6 x 1 x 2 2 + B 7 x 1 2 x 2 + B 8 x 1 2 x 2 2 And these terms were retained and eliminated according to stand stepwise regression techniques. In above equation , y = Any given response B i = The regression co-efficient for the various terms containing levels of the independent variables, Each response have its own equation. A graphic technique may be obtained from the polynomial equations. Optimization Techniques in pharmaceutical Formulation and Processing

26. Figure a. It shows the contours for tablet hardness as the levels of the independent variables are changed. Optimization Techniques in pharmaceutical Formulation and Processing

27. Figure b, It shows similar contour for the dissolution response t 50 % Optimization Techniques in pharmaceutical Formulation and Processing

28. Figure c. The above graph shows the feasible space with the limits of hardness be 8-10 kg and t 50 % be 20-33 min . This figure is obtained by superimposing a and b. Optimization Techniques in pharmaceutical Formulation and Processing

29. In the mathematical technique slightly different constraints are used. In this example. The constrained optimization problem is to locate levels of stearic acid (x 1 ) and starch (x 2 ) That minimizes the time of invitro release (y 2 ) Such that the average tablet volume (y 4 ) did not exceed 9.422 cm 2 and the average friability (y 3 ) did not exceed 2.72%. Optimization Techniques in pharmaceutical Formulation and Processing

30. To apply the Lagrangian method, this problem must be expressed mathematically as follows: Minimize y 2 = F 2 (x 1 , x 2 ) ……………..(1) such that y 3 = F 3 (x 1 , x 2 ) ≤ 2.72 ……………...(2) y 4 = F 4 (x 1 , x 2 ) ≤ 0.422 ………………(3) And 5 ≤ x 1 ≤ 45 ………….. (4) 1 ≤ x 2 ≤ 41 ………….. (5) Equation (4) and (5) are the solution within the experimental range. Optimization Techniques in pharmaceutical Formulation and Processing

31. The foregoining inequality constraints must be converted to equality constraints before the operation begins and this is done by introducing a slack variable ‘q’ for each. The several equations are then combined into a Lagrange function F and this necessitates the introduction of a Lagrange multiplier ⅄ for each constraint. The partial differentiation of Lagrange function and solving the resulting set of six simultaneous equations, value are obtained for x 1 and x 2 to yield an optimum invitro time of 17.9mm (t 50 %). The solution to a constrained optimization program may depend heavily on the constraints applied to the secondary objectives. Optimization Techniques in pharmaceutical Formulation and Processing

32. A technique called “sensitive analysis” can provide information so that the formulator can further trade off one property for another. For sensitivity analysis the formulator solves the constrained optimization problem for systemic changes in the secondary objectives. Example : Optimization Techniques in pharmaceutical Formulation and Processing

33. Optimization Techniques in pharmaceutical Formulation and Processing

34. Explaination: The foregoing problem restricted tablet friability, y 3 to maximum of 2.72 %. The graph illustrates the invitro release profile as constraint is tightened or relaxed and demonstrates that substantial improvement in the t 50 % can be obtained up to 1- 2 %. Optimization Techniques in pharmaceutical Formulation and Processing

35. The several steps in the Lagrangian method can be written as follows: Step-1 : Determine objective function. Step-2 : Determine constraints. Step-3 : Change inequality constraints to equality constraints. Step-4 : Form the Lagrange function, F a. One Lagrange multiplier ⅄ for each constraint. b. One slack variable q for each inequality constraint. Step-5 : Partially differentiate the Lagrange function for each variable and set derivatives equal to zero. Step-6 : Solve the set of simultaneous equations. Step-7 : Substitute the resulting values into the objective functions. Optimization Techniques in pharmaceutical Formulation and Processing

36. This can be phased into four phases, this was given by Buck et.al The phases are: A preliminary planning phase An experimental phase An analytical phase A verification phase Optimization Techniques in pharmaceutical Formulation and Processing

37. 4.Search methods: It is defined by appropriate equations. It does not require continuity or differentiability of function. It is applied to pharmaceutical system For optimization 2 major steps are used Feasibility search-used to locate set of response constraints that are just at the limit of possibility. Grid search – experimental range is divided in to grid of specific size & methodically searched Optimization Techniques in pharmaceutical Formulation and Processing

38. Steps involved in search method Select a system Select variables Perform experiments and test product Submit data for statistical and regression analysis Set specifications for feasibility program Select constraints for grid search Evaluate grid search printout Optimization Techniques in pharmaceutical Formulation and Processing

39. Example: Optimization Techniques in pharmaceutical Formulation and Processing

40. Five independent variables dictates total of 32 experiments. This design is known as five-factor, orthogonal, central, composite, second order design. First 16 formulations represent a half-factorial design for five factors at two levels. The two levels represented by +1 & -1, analogous to high & low values in any two level factorials. Translation of statistical design in to physical units Optimization Techniques in pharmaceutical Formulation and Processing

41. Experimental conditions: Optimization Techniques in pharmaceutical Formulation and Processing

42. Then the data is subjected to statistical analysis followed by multiple regression analysis. The equation used in this design is second order polynomial. y = a +a 1 x 1 +…+a 5 x 5 +a 11 x 1 2 +…+a 55 x 2 5 +a 12 x 1 x 2 +a 13 x 1 x 3 +a 45 x 4 x 5 A multivariate statistical technique called principle component analysis (PCA) is used to select the best formulation. PCA utilizes variance-covariance matrix for the responses involved to determine their interrelationship.   Optimization Techniques in pharmaceutical Formulation and Processing

43. For single variable: Optimization Techniques in pharmaceutical Formulation and Processing

44. Plots for five variables Optimization Techniques in pharmaceutical Formulation and Processing

45. Advantages of search method: It takes five independent variables in to account. Persons unfamiliar with mathematics of optimization & with no previous computer experience could carry out an optimization study. Optimization Techniques in pharmaceutical Formulation and Processing

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. This was firstly adopted by Box and Wilson, It is used to reduce second order regression equation to an equation consisting of a constant and squared terms as follows: Y = Y + λ 1 W 1 2 + λ 2 W 2 2 +… It is described as an efficient method to explore an empherical response. Optimization Techniques in pharmaceutical Formulation and Processing

47. References: Modern Pharmaceutics; By Gillbert and S. Banker – edited in 2002. www.google.com Optimization Techniques in pharmaceutical Formulation and Processing

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