OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING

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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