OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING Assoc

OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING Assoc. Prof. S. S. Mani Kiran M. Pharm. , Ph. D Department of Pharmaceutics Chalapathi Institute of Pharmaceutical Sciences, Guntur 2012 CIPS Guntur 1

CONTENTS q. CONCEPT OF OPTIMIZATION q. OPTIMIZATION PARAMETERS q. CLASSICAL OPTIMIZATION q. STATISTICAL DESIGN q. DESIGN OF EXPERIMENT q. OPTIMIZATION METHODS 2012 CIPS Guntur 2

INTRODUCTION q The term Optimize is defined as “to make perfect”. q It is used in pharmacy relative to formulation and processing q Involved in formulating drug products in various forms q 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 2012 CIPS Guntur 3

INTRODUCTION q Final product not only meets the requirements from the bio-availability but also from the practical mass production criteria q Pharmaceutical scientist- to understand theoretical formulation. q Target processing parameters – ranges for each excipients & processing factors 2012 CIPS Guntur 4

INTRODUCTION q 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 q It is not a screening technique. 2012 CIPS Guntur 5

Optimization parameters Problem types Variable Constrained Unconstrained Dependent Independent 2012 CIPS Guntur 6

Optimization parameters VARIABLES Independent Dependent Formulating Processing Variables 2012 CIPS Guntur 7

Optimization parameters q Independent variables or primary variables : Formulations and process variables directly under control of the formulator. These includes ingredients q 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. 2012 CIPS Guntur 8

Optimization parameters q Relationship between independent variables and response defines response surface q Representing >2 becomes graphically impossible q Higher the variables , higher are the complications hence it is to optimize each & everyone. 2012 CIPS Guntur 9

Optimization parameters § Response surface representing the relationship between the independent variables X 1 and X 2 and the dependent variable Y. 2012 CIPS Guntur 10

Classic optimization q It involves application of calculus to basic problem for maximum/minimum function. q Limited applications i. Problems that are not too complex ii. They do not involve more than two variables q For more than two variables graphical representation is impossible q It is possible mathematically 2012 CIPS Guntur 11

GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE 2012 CIPS Guntur 12

Classic optimization q Using calculus the graph obtained can be solved. Y = f (x) q 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 2012 CIPS Guntur 13

Statistical design q 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. 2012 CIPS Guntur 14

Statistical design q For second type it is necessary that the relation between any dependent variable and one or more independent variable is known. q 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. 2012 CIPS Guntur 15

Statistical design q The relationship with single independent variable can be obtained by simple regression analysis or by least squares method. Ø The relationship with more than one important variable can be obtained by statistical design of experiment and multi linear regression analysis. Ø Most widely used experimental plan is factorial design 2012 CIPS Guntur 16

TERMS USED q 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 q LEVELS: Levels of a factor are the values or designations assigned to the factor 2012 FACTOR LEVELS Temperature 300 , 500 Concentration 1%, 2% CIPS Guntur 17

TERMS USED q RESPONSE: It is an outcome of the experiment. § It is the effect to evaluate. § Ex: Disintegration time etc. . , q EFFECT: It is the change in response caused by varying the levels § It gives the relationship between various factors & levels q INTERACTION: It gives the overall effect of two or more variables Ex: Combined effect of lubricant and glidant on hardness of the tablet 2012 CIPS Guntur 18

TERMS USED q Optimization by means of an experimental design may be helpful in shortening the experimenting time. q 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. q Statistical DOE refers to the process of planning the experiment in such a way that appropriate data can be collected analysed statistically. 2012 CIPS Guntur 19

TYPES OF EXPERIMENTAL DESIGN q Completely randomised designs q Randomised block designs q Factorial designs § Full § Fractional q Response surface designs § Central composite designs § Box-Behnken designs q Adding centre points q Three level full factorial designs 2012 CIPS Guntur 20

TYPES OF EXPERIMENTAL DESIGN q 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. q 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. 2012 CIPS Guntur 21

TYPES OF EXPERIMENTAL DESIGN q. Factorial design Ø Full • Used for small set of factors Ø Fractional • It is used to examine multiple factors efficiently with fewer runs than corresponding full factorial design ü Types of fractional factorial designs § § § 2012 Homogenous fractional Mixed level fractional Box-Hunter Plackett-Burman Taguchi Latin square CIPS Guntur 22

TYPES OF EXPERIMENTAL DESIGN q Homogenous fractional § Useful when large number of factors must be screened q 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. q Box-hunter § Fractional designs with factors of more than two levels can be specified as homogenous fractional or mixed level fractional 2012 CIPS Guntur 23

TYPES OF EXPERIMENTAL DESIGN Plackett-Burman q It is a popular class of screening design. q These designs are very efficient screening designs when only the main effects are of interest. q These are useful for detecting large main effects economically , assuming all interactions are negligible when compared with important main effects q Used to investigate n-1 variables in n experiments proposing experimental designs for more than seven factors and especially for n*4 experiments. 2012 CIPS Guntur 24

TYPES OF EXPERIMENTAL DESIGN q Taguchi § It is similar to PBDs. § It allows estimation of main effects while minimizing variance. q Latin square § They are special case of fractional factorial design where there is one treatment factor of interest and two or more blocking factors 2012 CIPS Guntur 25

Response surface designs q This model has quadratic form γ =β 0 + β 1 X 1 + β 2 X 2 +…. β 11 X 12 + β 22 X 22 q Designs for fitting these types of models are known as response surface designs. q If defects and yield are the ouputs and the goal is to minimise defects and maximise yield 2012 CIPS Guntur 26

TYPES OF EXPERIMENTAL DESIGN q 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 2012 CIPS Guntur 27

TYPES OF EXPERIMENTAL DESIGN q The star points represent new extreme value (low & high) for each factor in the design q To picture central composite design, it must imagined that there are several factors that can vary between low and high values. q Central composite designs are of three types q 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 q Inscribed (CCI) designs-Star points take the value of +1 & -1 and cube points lie in the interior of the cube q Faced(CCI) –star points on the faces of the cube. 2012 CIPS Guntur 28

Box-Behnken design q. They do not contain embedded factorial or fractional factorial design. q. Box-Behnken designs use just three levels of each factor. q. These designs for three factors with circled point appearing at the origin and possibly repeated for several runs. 2012 CIPS Guntur 29

Three-level full factorial designs q It is written as 3 k factorial design. q It means that k factors are considered each at 3 levels. q These are usually referred to as low, intermediate & high values. q These values are usually expressed as 0, 1 & 2 q The third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors 2012 CIPS Guntur 30

FACTORIAL DESIGN q These are the designs of choice for simultaneous determination of the effects of several factors & their interactions. q Used in experiments where the effects of different factors or conditions on experimental results are to be elucidated. q Two types § Full factorial- Used for small set of factors § Fractional factorial- Used for optimizing more number of factors 2012 CIPS Guntur 31

LEVELS OF FACTORS IN THIS FACTORIAL DESIGN 2012 FACTOR LOWLEVEL(mg) HIGH LEVEL(mg) A: stearate 0. 5 1. 5 B: Drug 60. 0 120. 0 C: starch 30. 0 50. 0 CIPS Guntur 32

EXAMPLE OF FULL FACTORIAL EXPERIMENT 2012 Factor combination Stearate Drug Starch Response Thickness Cm*103 (1) _ _ _ 475 a + _ _ 487 b _ + _ 421 ab + + _ 426 c _ _ + 525 ac + _ + 546 bc _ + + 472 abc + + + 522 CIPS Guntur 33

EXAMPLE OF FULL FACTORIAL EXPERIMENT q. Calculation of main effect of A (stearate) q. The main effect for factor A is q {-(1)+a-b+ab-c+ac-bc+abc] X 10 -3 4 q. Main effect of A = = a + ab + ac + abc _ (1) + b + c + bc 4 [487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 4 10 -3 = 0. 022 cm 2012 CIPS Guntur 34

EFFECT OF THE FACTOR STEARATE Average = 495 * 10 -3 500 490 480 470 Average = 473 * 10 -3 0. 5 2012 1. 5 CIPS Guntur 35

STARCH X STEARATE INTERACTION g. 5 m Thickness 0 mg) 5 ( h c r a High st 500 450 30 mg) ( h c r a t s Low 500 450 H ) g. 5 m (0 te a r ea t S w Lo Starch Stearate 2012 te s igh e(1 t a ar ) CIPS Guntur 36

General optimization Ø By MRA the relationships are generated from experimental data , resulting equations are on the basis of optimization. Ø These equation defines response surface for the system under investigation Ø After collection of all the runs and calculated responses , calculation of regression coefficient is initiated. Ø Analysis of variance (ANOVA) presents the sum of the squares used to estimate the factor maineffects. 2012 CIPS Guntur 37

FLOW CHART FOR OPTIMIZATION 2012 CIPS Guntur 38

Applied optimization methods q Evolutionary operations q Simplex method q Lagrangian method q Search method q Canonical analysis 2012 CIPS Guntur 39

Evolutionary operations (evop) q It is a method of experimental optimization. q Technique is well suited to production situations. q Small changes in the formulation or process are made (i. e. , repeats the experiment so many times) & statistically analyzed whether it is improved. q It continues until no further changes takes place i. e. , it has reached optimum-the peak 2012 CIPS Guntur 40

Evolutionary operations (evop) q Applied mostly to TABLETS. q Production procedure is optimized by careful planning and constant repetition q It is impractical and expensive to use. q It is not a substitute for good laboratory scale investigation 2012 CIPS Guntur 41

Simplex method q It is an experimental pharmaceutical systems method applied for q Technique has wider appeal in analytical method other than formulation and processing q Simplex is a geometric figure that has one more point than the number of factors. q It is represented by triangle. q It is determined by comparing the magnitude of the responses after each successive calculation 2012 CIPS Guntur 42

Graph representing the simplex movements to the optimum conditions 2012 CIPS Guntur 43

Simplex method q The two independent variables show pump speeds for the two reagents required in the analysis reaction. q Initial simplex is represented by lowest triangle. q The vertices represents spectrophotometric response. q The strategy is to move towards a better response by moving away from worst response. q Applied to optimize CAPSULES, DIRECT COMPRESSION TABLET (acetaminophen), liquid systems (physical stability) 2012 CIPS Guntur 44

Lagrangian method q It represents mathematical techniques. q It is an extension of classic method. q It is applied to a pharmaceutical formulation and processing. q This technique follows the second type of statistical design q Limited to 2 variables - disadvantage 2012 CIPS Guntur 45

Steps involved q Determine objective formulation q Determine constraints. q Change inequality constraints to equality constraints. q Form the Lagrange function F: q Partially differentiate the lagrange function for each variable & set derivatives equal to zero. q Solve the set of simultaneous equations. q Substitute the resulting values in objective functions 2012 CIPS Guntur 46

Example q Optimization of a tablet. § phenyl propranolol(active ingredient)-kept constant § X 1 – disintegrate (corn starch) § X 2 – lubricant (stearic acid) § X 1 & X 2 are independent variables. § Dependent variables include tablet hardness, friability , volume, invitro release rate e. t. c. . , 2012 CIPS Guntur 47

Example q Polynomial models relating the response variables to independents were generated by a backward stepwise regression analysis program. q Y= B 0+B 1 X 1+B 2 X 2+B 3 X 12 +B 4 X 22 +B+5 X 1 X 2 +B 6 X 1 X 2 + B 7 X 12+B 8 X 12 X 22 Y – Response Bi – Regression coefficient for various terms containing the levels of the independent variables. X – Independent variables 2012 CIPS Guntur 48

Tablet formulations Formulation no, . 2012 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 CIPS Guntur 180(45%) 49

Tablet formulations q Constrained optimization problem is to locate the levels of stearic acid(x 1) and starch(x 2). q This minimize the time of invitro release(y 2), average tablet volume(y 4), average friability(y 3) q 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 2012 CIPS Guntur 50

CONTOUR PLOT FOR TABLET HARDNESS 2012 CIPS Guntur 51

CONTOUR PLOT FOR Tablet dissolution(T 50%) 2012 CIPS Guntur 52

GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET HARDNESS & DISSOLUTION 2012 CIPS Guntur 53

Tablet formulations 2012 CIPS Guntur 54

Search method q It is defined by appropriate equations. q It do not require continuity or differentiability of function. q It is applied to pharmaceutical system q 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 2012 CIPS Guntur 55

Steps involved in search method q. Select a system q. Select variables q. Perform experiments and test product q. Submit data for statistical and regression analysis q. Set specifications for feasibility program q. Select constraints for grid search q. Evaluate grid search printout 2012 CIPS Guntur 56

Example Tablet formulation Independent variables Dependent variables X 1 Diluent ratio Y 1 Disintegration time X 2 compressional force Y 2 Hardness X 3 Disintegrant level Y 3 Dissolution X 4 Binder level Y 4 Friability X 5 Lubricant level Y 5 weight uniformity 2012 CIPS Guntur 57

Example q Five independent variables dictates total of 32 experiments. q This design is known as five-factor, orthagonal, central, composite, second order design. q First 16 formulations represent a half-factorial design for five factors at two levels. q The two levels represented by +1 & -1, analogous to high & low values in any two level factorial. 2012 CIPS Guntur 58

Translation of statistical design in to physical units Experimental conditions Factor X 1= ca. phos/lactose -1. 54 eu -1 eu Base 0 +1 eu +1. 547 eu 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. 5 mg) 0. 2 0. 5 1 1. 5 1. 8 X 5 = mg. stearate (0. 5 mg) 0. 2 0. 5 1 1. 5 1. 8 2012 CIPS Guntur 59

Translation of statistical design in to physical units q. Again formulations were prepared and are measured. q. Then the data is subjected to statistical analysis followed by multiple regression analysis. q. The equation used in this design is second order polynomial. q y = 1 a 0+a 1 x 1+…+a 5 x 5+a 11 x 12+…+a 55 x 25+a 12 x 1 x 2 +a 13 x 1 x 3+a 45 x 4 x 5 2012 CIPS Guntur 60

Translation of statistical design in to physical units q. A multivariant statistical technique called principle component analysis (PCA) is used to select the best formulation. q. PCA utilizes variance-covariance matrix for the responses involved to determine their interrelationship. 2012 CIPS Guntur 61

PLOT FOR A SINGLE VARIABLE 2012 CIPS Guntur 62

PLOT OF FIVE VARIABLES 2012 CIPS Guntur 63

PLOT OF FIVE VARIABLES 2012 CIPS Guntur 64

ADVANTAGES OF SEARCH METHOD q It takes five independent variables in to account. q Persons unfamiliar with mathematics of optimization & with no previous computer experience could carryout an optimization study. 2012 CIPS Guntur 65

Canonical analysis q It is a technique used to reduce a second order regression equation. q This allows immediate interpretation of the regression equation by including the linear and interaction terms in constant term. 2012 CIPS Guntur 66

Canonical analysis q. It is used to reduce second order regression equation to an equation consisting of a constant and squared terms as follows Y = Y 0 +λ 1 W 12 + λ 2 W 22 +. . q. It was described as an efficient method to explore an empherical response. 2012 CIPS Guntur 67

Important Questions q. Classic optimization q. Define optimization and optimization methods q. Optimization using factorial design q. Concept of optimization and its parameters q. Importance of optimization techniques in pharmaceutical processing & formulation q. Importance of statistical design 2012 CIPS Guntur 68