OPTIMIZATION TECHNIQUES IN

PHARMACEUTICAL FORMULATION AND

PROCESSING

SUBMITTED TO :-

DR. YASMEEN SULTANA

DEPT. – PHARMACEUTICS

SCHOOL OF PHARMACEUTICAL EDUCATION AND RESEARCH

JAMIA HAMDARD

SUBMITTED BY:-

PRERNA KAPOOR

M.PHARM (PHARMACEUTICS)

1ST SEMESTER

SCHOOL OF PHARMACEUTICAL EDUCATION AND RESEARCH

JAMIA HAMDARD

CONTENTS

• Definition

• Terms

• Advantages

• Optimization parameters

• Problem type

• Variables

• Classic method and experimental designs

• Applied optimisation methods

• Other application

• References

INTRODUCTION

• The term Optimize is defined as to make something as perfect , effective , or

functional as possible , to choose the best element from a set of available

alternatives.

• 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.

• 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 technique.

• Primary objective may not be optimize absolutely but to compromise effectively &

thereby produce the best formulation under a given set of restrictions.

• In development projects pharmacists generally by a series of logical steps

carefully controlling the variables , changing one at a time until

satisfactory results are obtained.

• It is the process of finding the best way of using the existing resources

while taking into account all the factors that influences any decisions.

• Final product not only meets requirements from bioavailability but from

practical mass production criteria.

advantages

• Yield the best solution within the domain of study.

• Require fewer experiments to achieve an optimum formulation

• Can trace and rectify problem in a remarkably easier manner.

FIND OUT THE

OPTIMUM

QUANTIFY

RESPONSE

DETERMINE WRT

THE VARIABLES

VARIABLE

TERMS

1) FACTOR : – It is an assigned variable , such as temperature,

concentration etc.

• Quantitative: Numerical factor assigned to it

Ex; Concentration- 1%, 2%,3% etc..

• Qualitative: Which are not numerical

Ex; Polymer grade, humidity condition etc

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

the factor

FACTOR LEVELS

TEMPERATURE 30℃ , 50℃

CONCENTRATION 1% 2%

3) RESPONSE:- It is an outcome of the experiment.

• It is the effect to evaluate.

• Ex: Disintegration time etc..,

4) EFFECT: It is the change in response caused by varying the levels

• It gives the relationship between various factors & levels .

5) INTERACTION: It gives the overall effect of two or more variables

• Ex: Combined effect of lubricant and glidant on hardness of the tablet

WHY OPTIMIZATION IS NECESSARY ?

REDUCE

THE

COST

SAFETY

SAVE THE AND

REDUCE

TIME

THE

OPTIMIZ ERROR

ATION

INNOVATI

REPROD

ON &

UCIBILIT

EFFICAC

Y

Y

OPTIMIZATION PARAMETERS

PARAMETERS

PROBLEM VARIABLES

CONSTRAINED

DEPENDENT INDEPENDENT

UNCONSTRAINE

D FORMULATING

VARIABLES

PROCESSING

VARIABLES

PROBLEM TYPE

Unconstrained

• In unconstrained optimization problems there are no restrictions.

• For a given pharmaceutical system one might wish to make the hardest

tablet possible.

• The making of the hardest tablet is the unconstrained optimization

problem.

Constrained

• The constrained problem involved in it, is to make the hardest tablet

possible, but it must disintegrate in less than 15 minutes

VARIABLES

Independent variables : The independent variables are under

the control of the formulator. These might include the compression force or

the die cavity filling or the mixing time.

Dependent variables : The dependent variables are the

responses or the characteristics that are developed due to the

independent variables. Ex Particle size of vesicles, hardness of the tablet.

• The more the variables that are present in the system the more the

complications that are involved in the optimization. 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.

Example of independent and dependent

variable

INDEPENDENT DEPENDENT

VARIABLES 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

FORMS OF OPTIMIZATION TECHNIQUE

1. Sequential optimization technique

2. Simultaneous optimization technique

3. Combination of both.

SEQUENTIAL OPTIMIZATION TECHNIQUE:

• Also referred 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

method.

EXAMPLE: Designing a controlled drug delivery system for prolonged

retention in stomach required optimization of variables like :

presence/ absence/ concentration of stomach enzyme

• Ph, volume of fluid & content of gut

• Gastric motility and gastric emptying.

• When given a single oral tablet

(A)

• When same drug given in multiple

doses(B)

• Same drug when given in

optimised controlled release

formulation.(C)

TYPES OF OPTIMIZATION TECHNIQUES

A.CLASSIC METHODS B.APPLIED METHODS

1) FACTORIAL DESIGNS AND

MODIFICATIONS 1) EVOLUTIONARY

a. FULL FACTORIAL DESIGN OPERATION

b. FRACTION FACTORIAL DESIGN 2)SIMPLEX LATTICE

I. HOMOGENOUS FRACTIONAL

II. MIXED LEVEL FRACTIONAL 3)LAGRANGIAN

III. BOX-HUNTER METHOD

IV. PLACKETT BURMANN

V. TAGUCHI 4)SEARCH METHOD

VI. LATIN SQUARE 5)CONANICAL

2) CENTRAL COMPOSITE DESIGN AND

MODIFICATIONS MATHOD

3) MIXTUE DESIGN

4) D-OPTIMAL DESIGN

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 in the fig 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 represention can be

avoided.

• If the relationship, the equation

for Y as a function of X, is

available

[Eq] Y = f(X)

Graphic location of optimum

(maximum or minimum)

• When the relationship for response Y is given as a function of two

independent variables , X1 and X2, Y=f(X1,X2)

• Graphically there are contour plots, on which the axes represents the two

independent variables, X1 and X2 and contours represent the response Y

DRAWBACKS

• Applicable only to the problems that are not too complex.

• They do not involve more than two variables.

• For more than two variables graphical representation is impossible

FLOWCHART FOR OPTIMIZATION

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

• Completely randomized Designs

These experiments compare 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 designs

Homogenous fractional

Mixed level fractional

Box-Hunter

Plackett-Burman

Taguchi

Latin square

Factorial Design

• These are the designs of choice for simultaneous determination of the effects

of several factors & their interactions.

• Symbols to denote levels are:

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

• Homogenous fractional Useful when large number of factors must be

screened.

• Mixed level fractional Useful when variety of factors needs 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.

• Taguchi It is similar to PBDs. It allows estimation of main effects while

minimizing variance. It treats optimization in two ways

a) Static problems: Generally a process to be optimized has several control

factors which directly decide the target or desired value of output.

b) Dynamic problems: if the product to be optimised has a single input &

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.

• 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 effect.

Used to investigate n-1 variables in n experiments proposing

experimental designs for more than seven factors.

• 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

Response surface designs

• This model has a quadratic form

• Designs for fitting these type of models are knows as response surface designs

• If defects and yield are the output , goal is to minimize the defects and maximise the yield.

• 2 most common designs used are: central composite and box –behnken design

• CENTRAL COMPOSITE DESIGN: contains an imbedded factorial or fractional factorial

design with center points that is augmented with a group of ‘star points’ that allow

estimation of curvature.

• The precise value of α depends on certain properties desired for the design and on the

number of factors involved.

• A central composite design always contains twice as many star points as there are factors

in the design.

• The star points represent new extreme values (low and high) for each factor in the design

Central composite design are of 3

types:

• Circumscribed design: cube points

at the corners of the unit cube, star

point along the axis at or outside the

cube and centre point at origin

• Inscribed design: star points take

the value of +1 or -1 and cube

points lie at the interior of the cube.

• Faced design : star point on the

faces of cube.

Box behnken design

• The Box-Behnken design is an

independent quadratic design in that it

does not contain an embedded factorial or

fractional factorial design.

• 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. The designs have limited capability

for orthogonal blocking compared to the

central composite designs.

• The geometry of this design suggests a

sphere within the process space such that

the surface of the sphere protrudes

through each face with the surface of the

sphere tangential to the midpoint of each

edge of the space.

three level full factorial design

• The three-level design is written as a 3k factorial

design.

• It means that k factors are considered, each at 3

levels. These are (usually) referred to as low,

intermediate and high levels.

• These levels are numerically expressed as 0, 1,

and 2. One could have considered the digits -1,

0, and +1, but this may be confusing with

respect to the 2-level designs since 0 is reserved

for center points. Therefore, we will use the 0, 1,

2 scheme.

• The reason that the three-level designs were

proposed is to model possible curvature in the

response function and to handle the case of

nominal factors at 3 levels.

• A third level for a continuous factor facilitates

investigation of a quadratic relationship between

the response and each of the factors.

APPLIED OPTIMIZATION METHODS

• The effect of a real Evolutionary operation

system changing some

input (some factor or

Simplex method

variable) is observed

directly at the output and

that set of real data is Search method

used to develop

mathematical models. Lagrangian method

The responses from the

predictive models are Canonical method

then used for

optimization.

EVOLUTIONARY OPERATION

• It is the method of experimental optimization

• Small changes in the formulation or process are made (i.e. repeats the

experiment many times) & statistically analysed whether it is improved.

• It continues until no further changes takes place i.e., it has reached

optimum-the peak

• The result of changes are statistically analysed.

• This technique is especially well suited to a production situations.

• Applied mostly to TABLETS

EXAMPLE

Advantages

• Generates information on product development.

• Predict the direction of improvement.

• Help formulator to decide optimum conditions for the formulation and process.

Limitation

• More repetition is required

• Time consuming

• Not efficient to finding true optimum

• Expensive to use

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 tablets , liquid systems.

• It is called as DOWNHILL SIMPLEX/ NELDER MEAD METHOD

Types of simplex

Simplex method

Basic simplex method Modified simplex method

Advantages

• This method will find the true

optimum of a response with

fewer trials than the non-

systematic approaches or the

one-variable-at-a-time

method.

Disadvantages

• There are sets of rules for the

selection of the sequential

vertices in the procedure.

• Require mathematical

knowledge

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.

Advantages

• Lagrangian method was able to handle several responses or dependent variables.

Disadvantages

• Although the lagrangian method was able to handle several responses or dependent

variables, it was generally limited to two independent variables.

STEPS INVOLVED

1. Determine the objective function.

2. Determine the constraints.

3. Change inequality constraints to equality

constraints.

4. Form the Lagrange function F.

5. Partially differentiate the Lagrange function for

each variable and set derivatives equal to zero

Solve the set of simultaneous equations.

6. Substitute the resulting values into objective

function

Example

For 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 etc..,

• It is full 3² factorial experimental design.

• Nine formulations were prepared.

• Y₂ =f₂(X₁, X₂) –in vitro release

• Y3 = f3 (X1,X2) <2.72% Friability

• Y4= f4(x1,x2)<0.422cm3 average tablet volume

FORMULATION DRUG DICALCIUM STARCH STEARIC

NO. (PHENYL PHOSPHATE ACID

PROPANOL

AMINE)

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%)

8 50 86 84 180

9 50 6 164 180

a) Contour plots for tablet hardness

b) Contour plots for tablet dissolution

SEARCH METHOD

• It is defined by appropriate equations.

• It do not require continuity or differentiability of function.

• It is applied to pharmaceutical system

• Used for more than two independent variables.

• The response surface is searched by various methods to find the

combination of independent variables yielding an optimum.

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

Steps involved in search method

1. Select a system

2. Select variables :- a. Independent b. Dependent

3. Perform experiments 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

For the optimization itself, two major steps were used:

• The feasibility search

• The grid search

1. The feasibility search : Feasibility us used to locate a set of response

constraints that are at just limit of possibility.

VARIABLE CONSTRAINT EXPERIMENTAL RANGE

DISINTEGRATION TIME 1(1) 1.33-30.87

(MIN) 3(2)

5(3)

HARDNESS (KG) 12(1) 3.82-11.60

8(3)

DISSOLUTION 100(1) 13.30-89.10

(%AT 50 MIN) 90(2)

80(3)

• It is designed so that it stops after first possibility , not full search.

• The formulation obtained may be one of the many possibilities satisfying the constraints.

2. GRID SEARCH or exhaustive method

It is essentially a brute force method in which the experimental range is divided into a

specific size or methodically searched.

From an input of a designed media the program prints all the points that satisfy the

constraints.

CANONICAL ANALYSIS

• Canonical analysis, or canonical

reduction, is a technique used to reduce a

second-order regression equation, to an

equation consisting

• a constant and squared terms, as

follows:

Y = Y0+λ₁W₁²+ λ₂W₂²+……..

• 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, for a two

dimensional system.

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

, matrix ,determinants & so on.

DRAWBACK

• Applicable only to the problems that are not too complex.

• They do not involve more than two variables.

• For more than two variables graphical representation is impossible

application

1. Formulation & processing

2. Medicinal chemistry

3. Clinical chemistry

4. High performance liquid chromatographic analysis

5. Formulation of cultural medium in virological studies

6. Study of pharmacokinetic parameters

7. Provides solution to large scale manufacturing problems

8. Provides string assurances to regulatory agencies , superior drug product quality

9. In microencapsulation process

10.Improvement of physical and biological properties by modification