Optimization techniques in pharmaceutics , formulation and

processing

ABDUL MUHEEM,M.Pharma(1st sem)Deptt. of Pharmaceutics,Faculty of Pharmacy,Jamia HamdardEmail: muheem.abdul985@gmail.com

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Optimization makes the perfect formulation & reduce the cost

• Primary objective may not be optimize absolutely but to compromise effectively &thereby produce the best formulation under a given set of restrictions

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 in to the account of all the factors that influences decisions in any experiment

Traditionally, optimization in pharmaceuticals refers to changing one variable at a time, so to obtain solution of a problematic formulation.

Modern pharmaceutical optimization involves systematic design of experiments (DoE) to improve formulation irregularities.

In the other word we can say that –quantitate a formulation that has been qualitatively determined.

It’s not a screening techniques

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Why Optimization is necessary?

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

LEVELS: Levels of a factor are the values or designations assigned to the factor

FACTOR LEVELS

Temperature 300 , 500

Concentration 1%, 2%

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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

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Optimization parameters

Optimization parameters

Problem types Variable

Constrained Unconstrained Dependnt Independent

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VARIABLES

Independent Dependent

Formulating Processing

Variables Variables

Optimization parameters

Optimization Parameters1.Problem types:

Constraints

Example-Making hardest tablet but should disintegrate within 20 mins ( Constraint)

Unconstraint

Example: Making hardest tablet ( Unconstraint)

•2. Variables:

Independent variable- E.g. - mixing time for a given process step.

granulating time.

Dependent variables, which are the responses or the characteristics of the in process material Eg. Particle size of vesicles, hardness of the tablet.

Higher the number of variables, more complicated will be the optimization process.

There should be a relationship between the given response and the independent variable, and once this relationship is established , a response surface is generated.

From response surface only, we find the points which will give desirable value of the response.

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Example of dependent & independent variables

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

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 , but very involved ,making use of partial derivatives , matrics ,determinants & so on.

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Response surface representing the relationship between the independent variables X1 and X2 and the dependent variable Y.

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GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE

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We can take derivative ,set it equal to zero & solve for x to obtain the maximum or minimum

Using calculus the graph obtained can be

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

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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.

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In later one 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.

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Optimization may be helpful in shortening the experimenting time.

The design of experiments is determined 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.

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FLOW CHART FOR OPTIMIZATION

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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

Three level full factorial designs

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Completely randomized Designs

These designs 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

These are the designs of choice for simultaneous determination of the effects of several factors & their interactions.

Symbols to denote levels are:

(1)- when both the variables are in low concentration.

a- one low variable and second high variable.

b- one high variable and second low variable

ab- both variables are high.

•Factorial designs are optimal to determined the effect of pressure & lubricant on the hardness of a tablet

•Effect of disintegrant & lubricant conc . on tablet dissolution .

•It is based on theory of probability and test of significance.

It identifies the chance variation ( present in the process due to accident) and the assignable variations ( which are due to specific cause.)

Factorial design are helpful to deduce IVIVC.

IVIVC are helpful to serve a surrogate measure of rate and extent of oral absorption.

BCS classification is based on solubility and permeability issue of drugs, which are predictive of IVIVC.

Sound IVIVC omits the need of bioequivalence study.

IVIVC is predicted at three levels:

Level A- point to point relationship of in vitro dissolution and in vivo performance.

Level B- mean in vitro and mean in vivo dissolution is compared and co related.

Level C- correlation between amount of drug dissolved at one time and one pharmacokinetic parameter is deduced.

BCS classification and its expected outcome on IVIVC for Immediate release formulation

BCS Class Solubility Permeability IVIVC

I High High Correlation( if dissolution is rate limiting)

II Low High IVIVC is expected

III High Low Little or no IVIVC

IV low Low Little or no IVIVC

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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

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Homogenous fractional Useful when large number of factors must be screenedMixed level fractional Useful when variety of factors needed to be evaluated for

main effects and higher level interactions can be assumed to be negligible.

Ex-objective is to generate a design for one variable, A, at 2 levels and another, X, at three levels , mixed &evaluated.

Box-hunter Fractional designs with factors of more than two levels

can be specified as homogenous fractional or mixed level fractional

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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.

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Taguchi It is similar to PBDs. It allows estimation of main effects while minimizing variance. Taguchi Method treats optimization problems in two categories, 

  [A] STATIC PROBLEMS  :Generally, a process to be optimized has several

control factors which directly decide the target or desired value of the output. [B] DYNAMIC PROBLEMS :If the product to be optimized has a signal input that

directly decides the output,

Latin square They are special case of fractional factorial design where there is

one treatment factor of interest and two or more blocking factors

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•  Signal-to-Noise ratios (S/N), which are log functions of desired output,

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We can use the Latin square to allocate treatments. If the rows of the squarerepresent patients and the columns are weeks, then for example the second patient,in the week of the trial, will be given drug D. Now each patient receives all five drugs, and in each week all five drugs are tested.

A B C D E

B A D E C

C E A B D

D C E A B

E D B C A

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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

γ =β0 + β1X1 + β2X2 +….β11X12 + β22X2

2

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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

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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.

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  Generation of a Central Composite Design for Factors

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o

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Box-Behnken design

Box-Behnken designs use just three levels of each factor.

 In this design the treatment combinations are at the midpoints of edges of the process space and at the center. These designs are rotatable (or near rotatable) and require 3 levels of each factor

These designs for three factors with circled point appearing at the origin and possibly repeated for several runs.

It’s alternative to CCD.

The design should be sufficient to fit a quadratic model , that justify equations based on square term & products of factors.

Y= b0+b1x1+b2x2+b3x3+b4x1x2+b5x1x3+b6X2X3+b7X12 +b8X22+b9X3

2

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A Box-Behnken Design

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Three-level full factorial designs

It is written as 3k 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

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V. APPLIED OPTIMIZATION METHODS

There are several methods used for optimization. They are

Evolutionary operations:

•Widely used method(mostly for tablets)

•Technique is well suited to production situations(formulation & process)

•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.

•EVOP is not a substitute for good laboratory –scale investigation , because of the necessarily small in the EVOP.

•It is not suitable for lab , therefore it’s impractical & expensive.

Simplex Method(Simplex Lattice)

It is an experimental techniques & mostly used in analytical rather than

formulation & processing.

Simplex is a geometric figure that has one more point than the number of

factors.

e.g-If 2 independent variables then simplex is represented as triangle.

•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).

•It is also called as Downhill Simplex / Nelder-Mead Method.

In simplex lattice, the response may be plotted as 2D (contour plotted) or 3D plots (response surface methodology)

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The worst response is 0.25, conditions are selected at the vortex, 0.6, and, indeed, improvement is obtained. One can follow the experimental path to the optimum, 0.721

Figure 5 The simplex approach to optimization. Response is spectorphotometric reading at a given wavelength

Example 2: Two component solvent system representing simplex lattice.

Constraint is the concentration of A and B must add to 100%

Includes observing responses( solubility) at three point i.e.

100% A, 100% B and 50 – 50 mixtures of A and B

Eg: Preparation of tablet with excipients (three components) gives 7 runs.

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Starch

Stearic acid

Lactose 3

1A regular simplex lattice for a three

component mixture consist of seven

formulations

2

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A simplex lattice of four component is shown by 15 formulation

4 formulations of each component A,B,C&D

6 formulation of 50-50 mixture of AB, AC, AD, BC, BD&CD.

4 formulation of 1/3 mixtures of three components ABC, ABD, ACD, & BCD.

1 formulation of 25% of each of four

(ABCD)

• 100% pure component is not taken as un acceptable formulation is obtained, thus vertices does not represent the pure single substance , therefore a transformation is required.

Transformed % = ( Actual %- Minimum %)

(Maximum %-Minimum %)

Lagrangian method

•It represents mathematical techniques & it is applied to a pharmaceutical formulation and processing.

•This technique follows the second type of statistical design

•Disadvantage-Limited to 2 variables .

•Helps in finding the maxima (greatest possible amount) and minima (lowest possible concentration) depending on the constraints..

•A techniques called “sensitivity analysis“ can provide information so that the formulator can further trade off one property for another . Analysis for solves the constrained optimization problems.

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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

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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, in vitro release rate e.t.c..,

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Polynomial models relating the response variables to independents were generated by a backward stepwise regression analysis program.

Y= B0+B1X1+B2X2+B3 X12 +B4 X2

2 +B+5 X1 X2 +B6 X1X2

+ B7X12+B8X1

2X22

Y – Response Bi – Regression coefficient for various terms containing the levels of the independent variables. X – Independent variables

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EXAMPLE 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

17 August 2012

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EXAMPLE OF FULL FACTORIAL EXPERIMENT

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

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Constrained optimization problem is to locate the levels of stearic acid(x1) and starch(x2).

This minimize the time of in vitro release(y2),average tablet volume(y4), average friability(y3)

To apply the lagrangian method, problem must be expressed mathematically as follows

Y2 = f2(X1,X2)-in vitro release

Y3 = f3(X1,X2)<2.72-Friability

Y4 = f4(x1,x2) <0.422-avg tab.vol

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CONTOUR PLOT FOR TABLET HARDNESS & dissolution(T50%)

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GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET HARDNESS & DISSOLUTION

Contour plots for the Lagrangian method: feasible solution space indicated by crosshatched area

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Optimizing values of stearic acid and strach as a function of restrictions on tablet friability: (A) percent starch; (B) percent stearic acid

Search methods (RSM) :

•It takes five independent variables into account and is computer-assisted.

•It is defined by appropriate equations.

•Response surface methodology is used to determine the connection between different explanatory variables (independent variables) and one or more of the response variables.

•Persons unfamiliar with mathematics of optimization & with no previous computer experience could carryout an optimization study.

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1. Select a system

2. Select variables: a. Independent b. Dependent

3. Perform experimens and test product.

4. Submit data for statistical and regression analysis

5. Set specifications for feasibility program

6. Select constraints for grid search

7. Evaluate grid search printout

8. Request and evaluate:. a. “Partial derivative” plots, single or composite b. Contour plots

THE SEARCH METHODS

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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.

It is used to reduce second order regression equation to an equation consisting of a constant and squared terms as follows-

Y = Y0 +λ1W12 + λ2W2

2 +..

2variables=first order regression equation.

3variables/3level design=second order regression equation.

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. In canonical analysis or canonical

reduction, second-order regression

equations are reduced to a simpler

form by a rigid rotation and translation

of the response surface axes in

multidimensional space, as

for a two dimension system.

Forms of Optimization techniques:

1. Sequential optimization techniques.

2. Simultaneous optimization techniques.

3. Combination of both.

Sequential Methods:

Also referred as the "Hill climbing method".

Initially small number of experiments are done, then research is done using the increase or decrease of response.

Thus, maximum or minimum will be reached i.e. an optimum solution.

Simultaneous Methods:

Involves the use of full range of experiments by an experimental design.

Results are then used to fit in the mathematical model.

Maximum or minimum response will then be found through this fitted model.

Example:- Designing controlled drug delivery

system for prolonged retention in stomach required

optimization of variables like

•presence/ absence / concentration of stomach

enzyme

pH, fluid volume and contents of guts

Gastric motility and gastric emptying.

When given as single oral tablet

(A).

Same drug when given in

multiple doses (B)

Same drug when given as

optimized controlled release

formulation (C)

NEW NETWORK FOR OPTIMIZATION

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Artificial Neural Network & optimization of pharmaceutical formulation-

ANN has been entered in pharmaceutical studies to forecast the relationship b/w the response variables &casual factors . This is relationship is nonlinear relationship.

ANN is most successfully used in multi objective simultaneous optimization problem.

Radial basis functional network (RBFN) is proposed simultaneous optimization problems.

RBFN is an ANN which activate functions are RBF.

RBF is a function whose value depends on the distance from the Centre or origin.

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Artificial Neural Networks

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APPLICATIONS

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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

www.google.com Formulation optimization of nifedipine containing microspheres using factorial

design by Solmaz Dehghan

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