# optimization DRA -4

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### OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING Introduction, Optimization parameters, classical optimization, statistical design, applied optimization methods like EVOP, Simplex, Langrangian techniques. Dr.J.BelsenDavid, MPharm, PhD, Associate Professor:

OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING Introduction, Optimization parameters, classical optimization, statistical design, applied optimization methods like EVOP, Simplex, Langrangian techniques . Dr.J.BelsenDavid, MPharm, PhD, Associate Professor

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The term Optimize is defined as to make perfect , effective , or functional as possible . It is the process of finding the best way of using the existing resources while taking into the account of all the factors that influences decisions in any experiment Final product not only meets the requirements from the bio-availability but also from the practical mass production criteria. Traditionally , optimization in pharmaceuticals refers to changing one variable at a time , so to obtain solution of a problematic formulation.

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Modern pharmaceutical optimization involves systematic design of experiments (DoE) to improve formulation irregularities. Pharmaceutical scientist - to understand theoretical formulation. Target processing parameters – 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. It is not a screening technique. 3

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4 Innovation & efficacy

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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 Interaction It gives the overall effect of two or more variables Ex: Combined effect of lubricant and glidant on hardness of the tablet Response It is an outcome of the experiment. It is the effect to evaluate. Ex: Disintegration time etc.., 5

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Levels Levels of a factor are the values or designations assigned to the factor Effect It is the change in response caused by varying the levels It gives the relationship between various factors & levels 6 FACTOR LEVELS Temperature 30 0 , 50 0 Concentration 1%, 2%

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Optimization by means of an experimental design may be helpful in shortening the experimenting time . The design of experiments is a structured, organized 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 analyzed statistically. 7

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Optimization parameters Problem types Variable Dependent Independent Constrained Unconstrained Formulating Processing Variables Variables 8

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Problem types Constraints Example-Making hardest tablet but should disintegrate within 20 mins ( Constraint) Unconstraint Example: Making hardest tablet ( Unconstraint) Variables Independent variable or primary variables Formulations and process variables directly under control of the formulator. These includes ingredients . E.g. - mixing time for a given process step. granulating time.

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Dependent or secondary variables These are the responses of the in-progress material or the resulting drug delivery system. Eg . hardness of the tablet. It is the result of independent variables . Relationship between independent variables and response defines response surface. Higher the variables, higher are the complications hence it is to optimize each & everyone . Response surface representing the relationship between the independent variables X 1 and X 2 and the dependent variable Y. 10

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11 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

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Classic optimization It involves application of calculus to basic problem for maximum/minimum function. Limited applications Problems that are not too complex They do not involve more than two variables For more than two variables graphical representation is impossible It is possible mathematically 12

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Using 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 13 Graph representing the relation between the response variable and independent variable

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Statistical design Techniques used divided into two types. Experimentation continues as optimization proceeds It is represented by evolutionary operations (EVOP), simplex methods. b) Experimentation is completed before optimization takes place. It is represented by classic mathematical & search methods. For second type it is necessary that the relation between any dependent variable and one or more independent variable is known . 14

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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. 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 15

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TYPES OF EXPERIMENTAL DESIGN Completely randomized designs Randomized block designs Factorial designs Full Fractional Response surface designs Central composite designs Box- Behnken designs Adding centre points Three level full factorial designs 16

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Completely randomized 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. B. Randomized 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 contribution of these factors to experimental error . 17

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C. Factorial design a) Full Used for small set of factors b) 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 18

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Homogenous fractional Useful when large number of factors must be screened ii. 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. iii) Box-hunter Fractional designs with factors of more than two levels can be specified as homogenous fractional or mixed level fractional 19

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iv) 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. v) Taguchi It is similar to PBDs. It allows estimation of main effects while minimizing variance. 20

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vi) Latin square They are special case of fractional factorial design where there is one treatment factor of interest and two or more blocking factors D. 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 outputs and the goal is to minimize defects and maximize yield Two designs used in response surface modeling are Central composite designs Box-Behnken designs 21 γ = β 0 + β 1 X 1 + β 2 X 2 +…. β 11 X 1 2 + β 22X 2 2

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a) 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. 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 i) Circumscribed(CCC) designs -Cube points at the corners of the unit cube ,star points along the axes at or outside the 22

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cube and centre point at origin ii) Inscribed (CCI) designs -Star points take the value of +1 & -1 and cube points lie in the interior of the cube iii) Faced(CCF) –star points on the faces of the cube. b) 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. 23

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E Adding center points design In adding center points design, we add center point runs interspersed among the experimental settings run for two purposes, To provide the measure of process stability and inherent variability. To check for curvature. Center points runs should begin and end the experiment and should be dispersed as possible throughout the design matrix. The center point runs are not randomized. There is no need to randomize them as they guard against process instability. The best way to find instability is to sample process.

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F 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 25

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Applied optimization methods Evolutionary operations Simplex method Lagrangian method Search method Canonical analysis 27

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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 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 28

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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 number of factors. It is represented by triangle . It is determined by comparing the magnitude of the responses after each successive calculation Applied to optimize CAPSULES, DIRECT COMPRESSION TABLET (acetaminophen), liquid systems (physical stability) It is also called as Downhill Simplex / Nelder-Mead Method . 29

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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. 30

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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 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 31

### Search method a:

Search method a 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 32

### Steps involved in search method :

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 33

### ADVANTAGES OF SEARCH METHOD:

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. 34

### Canonical analysis :

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. 35

### Canonical analysis :

Canonical analysis 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. 36 Y = Y 0 + λ 1 W 1 2 + λ 2 W 2 2 +..

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Important Questions Classic optimization Define optimization and optimization methods Concept of optimization and its parameters Importance of optimization techniques in pharmaceutical processing & formulation Importance of statistical design 37

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REFERENCE Modern pharmaceutics- vol 121 Textbook of industrial pharmacy by sobha rani R.Hiremath. Pharmaceutical statistics Pharmaceutical characteristics – Practical and clinical applications 38 