CONCEPT

AND

PARAMETERS

OF OPTIMISATION

SUBMITTED TO:

DR. YASMIN SULTANA

PRESENTED BY:

AISWARYA CHAUDHURI

ST

M.PHARM 1 YEAR (PHARMACEUTICS)

SCHOOL OF PHARMACEUTICAL EDUCATION AND

RESEARCH

JAMIA HAMDARD

CONCEPT OF OPTIMISATION

DEFINITION OF OPTIMISATION: The word “ optimize” means “ to make as

perfect, effective and functional as possible”. Optimization is often used in

pharmacy for formulation and their processing and practically, it may be considered

as the search for a result that is satisfactory and at the same time the best possible

within a limited field of search.

OBJECTIVE OF OPTIMISATION:

To determine variables

To quantify response with respect to variables

To find out the optimum.

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 optimisation done in

pharmaceutical industry.

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 the decision in any

experiment.

Final products not only meets the requirements from the bioavailability but

also from the practical mass production criteria.

ADVANTAGES

Generates information on product development

Predict the direction of improvement

Help formulator to decide optimum conditions for the formulation and

process.

LIMITATIONS

More repetition is required

Time consuming

Not efficient in finding the optimum

Expensive in use.

Why Optimisation is necessary?

Reduce

The

Cost

Save

Safety

The OPTIMISATION

And reduce

Time

The error

Reproducibility Innovation and efficacy

TERMS USED:

Factor: It is a assigned variables such as concentration, temperature etc.

• Quantitative: Numerical factor is assigned to it.

Example: concentration -1%,2%,3% etc..,

• Qualitative: Numerical factor is not assigned to it.

Example: Polymer grade, humidity condition etc.

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

FACTOR LEVELS

Temperature 30°C, 50 °C

Concentration 1%, 2%

Response: It is an outcome of the experiment.

It is the effect to evaluate

Example: Disintegration time.

Effect: It is the change in response caused by varying the levels.

It gives the relationship between the factor and the levels.

Interaction: It gives the overall effect of two or more variables

Examples: Combined effect of lubricant and glidant on hardness of the tablet.

Coding Factor: Transforming the scale of measurement for a factor so that the

high value becomes +1

Treatment : A treatment is a specific combination of factor levels whose effect

is to be compared with other treatments

Randomization : A schedule for allocating treatment material and for

conducting treatment combinations in a DOE such that the conditions in one

run neither depend on the conditions of the previous run nor predict the

conditions in the subsequent runs

Analysis of Variance (ANOVA): A mathematical process for separating the

variability of a group of observations into assignable causes and setting up

various significance tests

Design : A set of experimental runs which allows you to fit a particular

model and estimate your desired effects

Design Matrix : A matrix description of an experiment that is useful for

constructing and analysing experiments

Error : Unexplained variation in a collection of observations

Random Effect : An effect associated with input variables chosen at random

from a population having a large or infinite number of possible values

Random Error : Error that occurs due to natural variation in the process

Resolution : A term which describes the degree to which estimated main

effects are aliased (or confounded) with estimated 2-level interactions, 3-level

interactions, etc.

Response Surface: A Design of Experiments (DOE) that fully explores the

process window and models the responses.

STATISTICAL DESIGN

Statistical design is divided into two types:

Experimental continues as optimization proceeds.

It is represented by evolutionary operations (EVOP), simplex method.

Experimentation is completed before optimization takes place,

It is represented by classical mathematical and search methods.

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:

1. Theoretical approach

2. Empirical or experimental approach

o Theoretical approach: If theoretical equation is known, no experimentation is

necessary

o Empirical or experimental approach: With single independent variable,

formulator experiments at several levels.

Optimization may be helpful in shortening the experimenting time.

The design of experiments determine the relationship between the factors that

affects the process and the output of the process.

EXPERIMENTAL DESIGN

Comparative objective: If there are one or more factors to be examined and the

main aim is to screen one important factor among other existent factors and its

influence on the responses, then it infers to a comparative problem which can be

solved by employing comparative designs.

Screening objective: The objective of this design is to screen the more

important factors among the lesser ones.

Response surface method objective: When there is a need of investigating the

interaction between the factors, quadratic effects or when the requirement

involves the development of an idea in relation to the shape of response surface,

in such situations, a response surface design is used. These designs are used to

troubleshoot the process problems and to make a product more robust so as to

not be affected by the non controllable influences

Strategies of Experimental Designs

Factorial designs (FD): These designs help in screening the critical

process parameters which can affect the process and product with the

help of interactions between the factors.

Mixture design: This design is applied when the factors are

proportion of blend.

Combined designs : Combined designs are optimal and user defined.

While working with categorical factor in addition to continuous factors

or when there are constraints on experiment optimal design, this is used

to minimize the number of trials.

OPTIMIZATION PARAMETERS

Problem type Variable

Constrained Unconstrained Dependent Independent

Processing

Formulating

PROBLEM TYPE:

1.CONSTRAINTS

2. UNCONSTRAINTS

In unconstraint optimisation problems there are no restrictions. For a given

pharmaceutical system one might wish to make the hardest tablet possible. This

making of the hardest tablet is the unconstrained optimisation problem. The

constrained problem involved in it is to make the hardest tablet possible, but it must

disintegrate in less than 15 minutes.

VARIABLES TYPE: The development procedure of the formulation involves

several variables.

1. INDEPENDENT VARIABLES

2. DEPENDENT VARIABLES

.

The independent variables are under the control of the formulator. These might

includes the compression force or die cavity or the mixing time. The dependent

variables are the responses or the characteristics that are developed due to the

independent variables.

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

that are involved in the optimisation.

Example of dependent and independent variables

INDEPENDENT VARIABLE DEPENDENT VARIABLES

Diluent ratio Disintegration Time

Compression Force Hardness

Disintegration Level Dissolution

Binder Level Friability

Lubricant Level Weight uniformity

Once the relationship between the

variables and the response is

known, it gives the response surface

as represented in the Figure 1.

Surface is to be evaluated to get Figure 1: Response surface representing the relationship

the independent variables, X1 and between the independent variable X1 and X2 and the

dependent variable Y.

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.

CLASSICAL OPTIMISATION:

Classical optimisation is done by using the calculus to basic problem to find

the maximum and the minimum of a function

The curve in the figure 2 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 representation can be avoided.

If the relationship, the equation for Y as a function of X is available.[Eq(1)]:

MAXIMUM

Y= f(X)

MINIMUM

Figure 2: Graphical location of optimum (maximum and

minimum)

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

independent variables X1 and X2

Y= f (X1, X2)

Graphically there are contour plots (Figure 3) on which the axes represents the

two independent variables X1 and X2 and contours represents the response Y.

Figure 3: Contour plot. Contour represents

values of the dependent variables Y.