DR. YASMIN SULTANA
M.PHARM 1 YEAR (PHARMACEUTICS)
SCHOOL OF PHARMACEUTICAL EDUCATION AND
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
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
Final products not only meets the requirements from the bioavailability but
also from the practical mass production criteria.
Generates information on product development
Predict the direction of improvement
Help formulator to decide optimum conditions for the formulation and
More repetition is required
Not efficient in finding the optimum
Expensive in use.
Why Optimisation is necessary?
Reproducibility Innovation and efficacy
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.
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
Response Surface: A Design of Experiments (DOE) that fully explores the
process window and models the responses.
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
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.
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.
Problem type Variable
Constrained Unconstrained Dependent Independent
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
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
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 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)]:
Figure 2: Graphical location of optimum (maximum and
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.