# optimization

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### OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING:

1 OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING PRESENTED BY V.SAI M.Pharm -I(Department of pharmaceutics) K.L.E University,belgaum

### CONTENTS:

2 CONTENTS CONCEPT OF OPTIMIZATION OPTIMIZATION PARAMETERS CLASSICAL OPTIMIZATION STATISTICAL DESIGN DESIGN OF EXPERIMENT OPTIMIZATION METHODS

### INTRODUCTION:

3 INTRODUCTION The term Optimize is defined as “to make perfect”. It is used in pharmacy relative to formulation and processing 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

### Slide 4:

4 Final product not only meets the requirements from the bio-availability but also from the practical mass production criteria Pharmaceutical scientist- to understand theoretical formulation. Target processing parameters – ranges for each excipients & processing factors

### Slide 5:

5 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 It is not a screening technique.

### Optimization parameters:

6 Optimization parameters optimization parameters Problem types variable Constrained unconstrained dependent independent

### Slide 7:

7 VARIABLES Independent Dependent Formulating processing Variables Variables

### Slide 8:

8 Independent variables or primary variables : Formulations and process variables directly under control of the formulator. These includes ingredients Dependent or secondary variables : These are the responses of the inprogress material or the resulting drug delivery system It is the result of independent variables

### Slide 9:

9 Relationship between independent variables and response defines response surface Representing >2 becomes graphically impossible Higher the variables , higher are the complications hence it is to optimize each & everyone.

### Slide 10:

10 Response surface representing the relationship between the independent variables X 1 and X 2 and the dependent variable Y.

### Classic optimization :

11 Classic optimization It involves application of calculus to basic problem for maximum/minimum function. Limited applications i. Problems that are not too complex ii. They do not involve more than two variables For more than two variables graphical representation is impossible It is possible mathematically

### GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE:

12 GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE

### Slide 13:

13 U sing calculus the graph obtained can be solved. Y = f (x) When the relation for the response y is given as the function of two independent variables,x 1 &X 2 Y = f(X 1 , X 2 ) The above function is represented by contour plots on which the axes represents the independent variables x 1 & x 2

### Statistical design:

14 Statistical design Techniques used divided in to two types. Experimentation continues as optimization proceeds It is represented by evolutionary operations(EVOP), simplex methods. Experimentation is completed before optimization takes place. It is represented by classic mathematical & search methods.

### Slide 15:

15 For second type it is necessary that the relation between any dependent variable and one or more independent variable is known. There are two possible approaches for this Theoretical approach- If theoretical equation is known , no experimentation is necessary. Empirical or experimental approach – With single independent variable formulator experiments at several levels.

### Slide 16:

16 The relationship with single independent variable can be obtained by simple regression analysis or by least squares method. The relationship with more than one important variable can be obtained by statistical design of experiment and multi linear regression analysis. Most widely used experimental plan is factorial design

### TERMS USED:

17 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 etc LEVELS : Levels of a factor are the values or designations assigned to the factor FACTOR LEVELS Temperature 30 0 , 50 0 Concentration 1%, 2%

### Slide 18:

18 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

### Slide 19:

19 Optimization by means of an experimental design may be helpful in shortening the experimenting time. The design of experiments is a structured , organised method used to determine the relationship between the factors affecting a process and the output of that process. Statistical DOE refers to the process of planning the experiment in such a way that appropriate data can be collected and analysed statistically.

### TYPES OF EXPERIMENTAL DESIGN:

20 TYPES OF EXPERIMENTAL DESIGN Completely randomised designs Randomised block designs Factorial designs Full Fractional Response surface designs Central composite designs Box-Behnken designs Adding centre points Three level full factorial designs

### Slide 21:

21 Completely randomised Designs These experiment compares the values of a response variable based on different levels of that primary factor. 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. Randomised block designs For this there is one factor or variable that is of primary interest. To control non-significant factors,an important technique called blocking can be used to reduce or eliminate the contribition of these factors to experimental error.

### Slide 22:

22 Factorial design Full Used for small set of factors Fractional It is used to examine multiple factors efficiently with fewer runs than corresponding full factorial design Types of fractional factorial designs Homogenous fractional Mixed level fractional Box-Hunter Plackett-Burman Taguchi Latin square

### Slide 23:

23 Homogenous fractional Useful when large number of factors must be screened Mixed level fractional Useful when variety of factors need to be evaluated for main effects and higher level interactions can be assumed to be negligible. Box-hunter Fractional designs with factors of more than two levels can be specified as homogenous fractional or mixed level fractional

### Plackett-Burman:

24 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 and especially for n*4 experiments.

### Slide 25:

25 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

### Response surface designs:

26 Response surface designs This model has quadratic form Designs for fitting these types of models are known as response surface designs. If defects and yield are the ouputs and the goal is to minimise defects and maximise yield γ = β 0 + β 1 X 1 + β 2 X 2 +…. β 11 X 1 2 + β 22X 2 2

### Slide 27:

27 Two most common designs generally used in this response surface modelling are Central composite designs Box-Behnken designs Box-Wilson central composite Design This type contains an embedded factorial or fractional factorial design with centre points that is augemented with the group of ‘star points’. These always contains twice as many star points as there are factors in the design

### Slide 28:

28 The star points represent new extreme value (low & high) for each factor in the design To picture central composite design,it must imagined that there are several factors that can vary between low and high values. 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 centre 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(CCI) –star points on the faces of the cube.

### Box-Behnken design:

29 Box-Behnken design They do not contain embedded factorial or fractional factorial design. Box-Behnken designs use just three levels of each factor. These designs for three factors with circled point appearing at the origin and possibly repeated for several runs.

### Three-level full factorial designs:

30 Three-level full factorial designs It is written as 3 k factorial design. It means that k factors are considered each at 3 levels. These are usually referred to as low, intermediate & high values. These values are usually expressed as 0, 1 & 2 The third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors

### FACTORIAL DESIGN:

31 FACTORIAL DESIGN These are the designs of choice for simultaneous determination of the effects of several factors & their interactions. Used in experiments where the effects of different factors or conditions on experimental results are to be elucidated. Two types Full factorial- Used for small set of factors Fractional factorial- Used for optimizing more number of factors

### LEVELS OF FACTORS IN THIS FACTORIAL DESIGN:

32 LEVELS OF FACTORS IN THIS FACTORIAL DESIGN FACTOR LOWLEVEL(mg) HIGH LEVEL(mg) A:stearate 0.5 1.5 B:Drug 60.0 120.0 C:starch 30.0 50.0

### EXAMPLE OF FULL FACTORIAL EXPERIMENT:

33 EXAMPLE OF FULL FACTORIAL EXPERIMENT Factor combination stearate drug starch Response Thickness Cm*10 3 (1) _ _ _ 475 a + _ _ 487 b _ + _ 421 ab + + _ 426 c _ _ + 525 ac + _ + 546 bc _ + + 472 abc + + + 522

### :

34 Calculation of main effect of A (stearate) The main effect for factor A is {-(1)+a-b+ab-c+ac-bc+abc] 10 -3 Main effect of A = = = 0.022 cm 4 a + ab + ac + abc 4 _ (1) + b + c + bc 4 [487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 10 -3

### EFFECT OF THE FACTOR STEARATE:

35 EFFECT OF THE FACTOR STEARATE 470 480 490 500 0.5 1.5 Average = 473 * 10 -3 Average = 495 * 10 -3

### STARCH X STEARATE INTERACTION:

36 STARCH X STEARATE INTERACTION 0.5 stearate Thickness High starch(50mg) Low starch(30mg) Starch High stearate(1.5 mg ) Low Stearate(0.5 mg) 450 500 450 500

### General optimization:

37 General optimization By MRA the relationships are generated from experimental data , resulting equations are on the basis of optimization. These equation defines response surface for the system under investigation After collection of all the runs and calculated responses ,calculation of regression coefficient is initiated. Analysis of variance (ANOVA) presents the sum of the squares used to estimate the factor maineffects.

### FLOW CHART FOR OPTIMIZATION:

38 FLOW CHART FOR OPTIMIZATION

### Applied optimization methods :

39 Applied optimization methods Evolutionary operations Simplex method Lagrangian method Search method Canonical analysis

### Evolutionary operations (evop) :

40 Evolutionary operations ( evop ) It is a method of experimental optimization. Technique is well suited to production situations. Small changes in the formulation or process are made (i.e.,repeats the experiment so many times) & statistically analyzed whether it is improved. It continues until no further changes takes place i.e., it has reached optimum-the peak

### Slide 41:

41 Applied mostly to TABLETS. Production procedure is optimized by careful planning and constant repetition It is impractical and expensive to use. It is not a substitute for good laboratory scale investigation

### Simplex method :

42 Simplex method It is an experimental method applied for pharmaceutical systems Technique has wider appeal in analytical method other than formulation and processing Simplex is a geometric figure that has one more point than the no.of factors. It is represented by triangle. It is determined by comparing the magnitude of the responses after each successive calculation

### Graph representing the simplex movements to the optimum conditions :

43 Graph representing the simplex movements to the optimum conditions

### Slide 44:

44 The two independent variables show pump speeds for the two reagents required in the analysis reaction. Initial simplex is represented by lowest triangle. The vertices represents spectrophotometric response. The strategy is to move towards a better response by moving away from worst response. Applied to optimize CAPSULES, DIRECT COMPRESSION TABLET (acetaminophen), liquid systems (physical stability)

### Lagrangian method :

45 Lagrangian method It represents mathematical techniques. It is an extension of classic method. It is applied to a pharmaceutical formulation and processing. This technique follows the second type of statistical design Limited to 2 variables - disadvantage

### Steps involved :

46 Steps involved Determine objective formulation Determine constraints. Change inequality constraints to equality constraints. Form the Lagrange function F: Partially differentiate the lagrange function for each variable & set derivatives equal to zero. Solve the set of simultaneous equations. Substitute the resulting values in objective functions

### Example :

47 Example Optimization of a tablet. phenyl propranolol(active ingredient)-kept constant X1 – disintegrate (corn starch) X2 – lubricant (stearic acid) X1 & X2 are independent variables. Dependent variables include tablet hardness, friability ,volume, invitro release rate e.t.c..,

### Slide 48:

48 Polynomial models relating the response variables to independents were generated by a backward stepwise regression analysis program. Y= B 0 +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 + B 7 X 1 2 +B 8 X 1 2 X 2 2 Y – response B i – regression coefficient for various terms containing the levels of the independent variables. X – independent variables

### Tablet formulations :

49 Tablet formulations Formulation no,. Drug Dicalcium phosphate Starch Stearic acid 1 50 326 4(1%) 20(5%) 2 50 246 84(21%) 20 3 50 166 164(41%) 20 4 50 246 4 100(25%) 5 50 166 84 100 6 50 86 164 100 7 50 166 4 180(45%)

### Slide 50:

50 Constrained optimization problem is to locate the levels of stearic acid(x 1 ) and starch(x 2 ). This minimize the time of invitro release(y 2 ),average tablet volume(y 4 ), average friability(y 3 ) To apply the lagrangian method, problem must be expressed mathematically as follows Y 2 = f 2 (X 1 ,X 2 )-invitro release Y 3 = f 3 (X 1 ,X 2 )<2.72-Friability Y 4 = f 4 (x 1 ,x 2 ) <0.422-avg tab.vol

### CONTOUR PLOT FOR TABLET HARDNESS :

51 CONTOUR PLOT FOR TABLET HARDNESS

### CONTOUR PLOT FOR Tablet dissolution(T50%):

52 CONTOUR PLOT FOR Tablet dissolution(T 50% )

### GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET HARDNESS & DISSOLUTION:

53 GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET HARDNESS & DISSOLUTION

54

### Search method :

55 Search method It is defined by appropriate equations. It do 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

### Steps involved in search method :

56 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

### Example :

57 Example Tablet formulation Independent variables Dependent variables X1 Diluent ratio Y1 Disintegration time X2 compressional force Y2 Hardness X3 Disintegrant level Y3 Dissolution X4 Binder level Y4 Friability X5 Lubricant level Y5 weight uniformity

### Slide 58:

58 Five independent variables dictates total of 32 experiments. This design is known as five-factor, orthagonal , 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 factorial.

59 Translation of statistical design in to physical units Experimental conditions Factor -1.54eu -1 eu Base0 +1 eu +1.547eu X 1 = ca.phos/lactose 24.5/55.5 30/50 40/40 50/30 55.5/24.5 X 2 = compression pressure( 0.5 ton) 0.25 0.5 1 1.5 1.75 X 3 = corn starch disintegrant 2.5 3 4 5 5.5 X 4 = Granulating gelatin(0.5mg) 0.2 0.5 1 1.5 1.8 X 5 = mg.stearate (0.5mg) 0.2 0.5 1 1.5 1.8

### Slide 60:

60 Again formulations were prepared and are measured. Then the data is subjected to statistical analysis followed by multiple regression analysis. The equation used in this design is second order polynomial. y = 1 a 0 +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

### Slide 61:

61 A multivariant 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.

### PLOT FOR A SINGLE VARIABLE:

62 PLOT FOR A SINGLE VARIABLE

### Slide 63:

63 PLOT OF FIVE VARIABLES

### Slide 64:

64

65 ADVANTAGES OF SEARCH METHOD It takes five independent variables in to account. Persons unfamiliar with mathematics of optimization & with no previous computer experience could carryout an optimization study.

### Canonical analysis :

66 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.

### Slide 67:

67 It is used to reduce second order regression equation to an equation consisting of a constant and squared terms as follows It was described as an efficient method to explore an empherical response. Y = Y 0 + λ 1 W 1 2 + λ 2 W 2 2 +..

### Important Questions:

68 Important Questions Classic optimization Define optimization and optimization methods Optimization using factorial design Concept of optimization and its parameters Importance of optimization techniques in pharmaceutical processing & formulation Importance of statistical design

### REFERENCE:

69 REFERENCE Modern pharmaceutics- vol 121 Textbook of industrial pharmacy by sobha rani R.Hiremath. Pharmaceutical statistics Pharmaceutical characteristics – Practical and clinical applications www.google.com

### Slide 70:

70 Thank you 