OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL

FORMULATION AND PROCESSING

ByK.KRANTHI KUMAR M.Pharm.,M.B.A.,(Ph.D)

Asst.profDepartment of pharmaceutics

SKU college of Pharmaceutical SciencesS.K. University

AnantapurAndhra Pradesh

1

• Introduction

• Concept of optimization

• optimization parameters

• classical optimization

• statistical design

• applied optimization methods.2

  OPTIMIZATION

Optimize is defined as "to make perfect”.

OPTIMIZATION is an act, process, or methodology of making design, system or decision as fully perfect, functional or as effective as possible . Optimization of a product or process is the determination of the experimental conditions resulting in its optimal performance. choosing the best element from some set of available alternatives. In Pharmacy word “optimization” is found in the literature referring to any study of formula. In development projects pharmacist generally experiments by a series of logical steps, carefully controlling the variables and changing one at a time until satisfactory results are obtained. This is how the optimization done in pharmaceutical industry . 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.

3

ImportanceIt 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.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.

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.

4

  Optimization parameters 

Variable types

Problem types

Variable types :-Independent variables

Dependent variables

Problem types:- Constrained

Unconstrained

5

variables in optimization: variables in optimization Independent Dependent variables directly under the control responses that are developed of formulator due to the independent variables eg: disintegrant level disintegration time compression force hardness binder level weight uniformity lubricant level thickness mixing time etc.

6

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 in progress material or the resulting drug delivery system.

It is the result of independent variables . 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.

7

Problem types in optimization Unconstrained Constrained no restrictions are restrictions are placed on the system on the system eg: preparation of hardest tablet without any disintegration tablet which has the ability of or dissolution parameters. disintegrate in less than 15min .

8

 variables in optimization Independent Dependent variables directly under the control responses that are developed of formulator due to the independent variables eg: eg: disintegrant level disintegration time compression force hardness binder level weight uniformity lubricant level thickness mixing time etc.

Problem types in optimization Unconstrained Constrained no restrictions are restrictions are placed on the system on the system eg: preparation of hardest eg: preparation of hardest tablet without any disintegration tablet which has the ability of or dissolution parameters. disintegrate in less than 15min

9

 optimization parameters:-response surface curve

Once the relationship between the variable and the response is known, it gives the response surface as represented. Surface is to be evaluated to get the independent variables, X1 and X2, which gave the response, Y. Any number of variables can be considered, it is impossible to represent graphically, but mathematically it can be evaluated.

10

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 variablesFor more than two variables graphical representation is impossibleIt is possible mathematically

GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE

11

 Classic optimization:-Classical optimization is done by using

the calculus to basic problem to find the maximum and the minimum of a function. The curve represents the relationship between the response Y and the single independent variable X and we can obtain the maximum and the minimum. By using the calculus the graphical represented can be avoided. If the relationship, the equation for Y as a function of X, is available : Y = f (X)

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,x1 &X2

Y = f(X1 , X2)

The above function is represented by contour plots on which the axes represents the independent variables x1& x2 12

 When the relationship for the response Y is given as the function of two independent variables, X 1 and X 2 ,

Y = f (X 1, X 2 )

Graphically, there are contour plots on which the axes represents the two independent variables, X 1 and X 2 , and contours represents the response Y . Here the contours are showing the response. (contour represents the connecting point showing the peak level of response)

Contour plot. Contour represents values of the dependent variable Y Classic Optimization

13

The techniques for optimization are broadly divided into two categories:

(A)simultaneous method: Experimentation continues as optimization study proceeds. E.g.: a. Evolutionary Operations Method b. Simplex Method

(B) sequential method: Experimentation is completed before optimization takes place. E.g.: a. Mathematical Method b. Search Method

In case (B), the formulator has to obtain the relationship between the response and one or more independent variables. This includes two approaches: Theoretical Approach & Empirical Approach .

•Optimization Strategy :•Problem definition

• Selection of factors and levels

• Design of experimental protocol

• Formulating and evaluating the dosage form

•Prediction of optimum formula

•Validation of optimization 14

Full factorial designs: Involve study of the effect of all factors(n) at various levels(x) including the interactions among them with total number of experiments as X n . SYMMETRIC ASYMMETRIC Fractional factorial designs: It is a fraction ( 1/ x p ) of a complete or full factorial design, where ‘p’ is the degree of fractionation and the total number of experiments required is given as x n -p . Factorial Designs

15

Applied optimization methods

Evolutionary Operations (EVOP)

Simplex Method

Lagrangian Method

Search Method

canonical analysis

Evolutionary Operations (EVOP):-Most widely used method of experimental optimization in fields other than pharmaceutical technology.. Experimenter makes very small changes in formulation repeatedly. The result of changes are statistically analyzed. If there is improvement, the same step is repeated until further change doesn’t improve the product. Can be used only in industries and not on lab scale. Simplex Method It was introduced by Spendley et.al, which has been applied more widely to pharmaceutical systems. A simplex is a geometric figure, that has one more point than the no. of factors. so, for two factors ,the simplex is a triangle. It is of two types: A. Basic Simplex Method B. Modified Simplex Method Simplex methods are governed by certain rules. 1 3 2

16

Simplex Method It was introduced by Spendley et.al, which has been applied more widely to pharmaceutical systems.

A simplex is a geometric figure, that has one more point than the no. of factors. so, for two factors ,the simplex is a triangle.

It is of two types:

A. Basic Simplex Method

B. Modified Simplex Method Simplex methods are governed by certain rules.

1 3 2

17

Basic Simplex Method Rule 1 : The new simplex is formed by keeping the two vertices from preceding simplex with best results, and replacing the rejected vertex (W) with its mirror image across the line defined by remaining two vertices.

18

Rule 2 : When the new vertex in a simplex is the worst response, the second lowest response in the simplex is eliminated and its mirror image across the line; is defined as new vertices to form the new simplex.

Rule 3 : When a certain point is retained in three successive simplexes, the response at this point or vertex is re determined and if same results are

obtained, the point is considered to be the best optimum that can be obtained. Rule 4 : If a point falls outside the boundaries of the chosen range of factors, an artificially worse response should be assigned to it and one proceeds further with rules 1 to 3. This will force the simplex back into the boundaries.

•Modified Simplex Method It was introduced by Nelder -Mead in 1965. This method should not be confused with the simplex algorithm of Dantzig for linear programming. Nelder -Mead method is popular in chemistry, chemical engg ., pharmacy etc. This method involves the expansion or contraction of the simplex formed in order to determine the optimum value more effectively. The two independent variables show pump speeds for the two reagents required in the analysis reaction. 19

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 spectrophotometer response.

The strategy is to move towards a better response by moving away from worst response. Applied to optimize CAPSULES, DIRECT COMPRESSION TABLET, liquid systems (physical stability)

LAGRANGIANMETHOD:-

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.

20

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 methodSelect 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 printout21

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.

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.

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.

•Applications :-Formulation and Processing

• Clinical Chemistry

•HPLC Analysis

•Medicinal Chemistry Studying

•pharmacokinetic parameters

• Formulation of culture medium in microbiology studies.

Y = Y0 +λ1W12 + λ2W2

2 +..

22

Statistical designStatistical 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. 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. 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

23

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 0C , 50 0 C

Concentration 1%, 2%

24

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 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.TYPES OF EXPERIMENTAL DESIGN 1.Completely randomized designs 2.Randomized block designs 3.Factorial designs 4.Full Fractional Response surface designs5.Central composite designs 6.Box-Behnken designs7.Adding centre points 8.Three level full factorial designs

25

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. 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.

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 DESIGNSHomogenous fractional Mixed level fractional Box-Hunter Plackett-Burman Taguchi Latin square

HOMOGENOUS FRACTIONAL Useful when large number of factors must be screened

 

26

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:- 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. TAGUCHI :-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 factorsResponse surface designs This model has quadratic form γ = β 0 + β 1 X 1 + β 2 X 2 +…. β 11 X 1 2 + β 22X 2 2 Designs for fitting these types of models are known as response surface designs. If defects and yield are the out puts and the goal is to minimize defects and maximize yield

27

Two most common designs generally used in this response surface modeling 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 augmented 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 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 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.

28

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

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

FACTOR LOW LEVEL (mg)

HIGH LEVEL (mg)

A:-stearate 0.5 1.5

B:-Drug 60.0 120.0

C:-starch 30.0 50.0 29

EXAMPLE OF FULL FACTORIAL EXPERIMENT

Factor combination

stearate Drug starch ResponseThickness Cm*10 3

(1) - - - 475

a + - - 487

b - + - 421

ab + + - 426

C - - + 525

ac + - + 546

bc - + + 472

abc + + + 522

30

Calculation of main effect ofA (stearate) The main effect for factor A is {-(1)+a-b+ab-c+ac-bc+abc] 10 -3/4 Main effect of A = {-(1) a - b + ab -c + ac –bc+abcX10 -3/4

[487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 10 -3/4= 0.022

31