This document discusses various optimization techniques used in pharmaceutical formulation and processing. It begins by defining optimization and describing how it is applied in preliminary, experimental, analytical, and verification phases. It then covers classical optimization techniques like calculus-based approaches as well as statistical experimental designs. Evolutionary operations, simplex methods, Lagrangian methods, and search methods are also summarized. Finally, applications of these optimization techniques are mentioned for drug delivery systems, pharmacokinetic studies, and culture medium optimization.
1. OPTIMIZATION
TECHNIQUES IN
PHARMACEUTICAL
FORMULATION AND
PROCESSING.
SUSHMA
M.PHARMACY 1ST YEAR
11z51s0315
IntroductIon
Optimization is defined as ‘an act
,process or methodology of making
something(as a design, system or
2. decision)as fully perfect, functional
or effective as possible specifically
the mathematical procedures.
It is an analytical tool for obtaining
optimum formulation.
Trial and error methods can be
improved.
These methods are applied: a.
preliminary stages.
b.
experimental phases.
c.
analytical phases.
d.
verification phases.
Parameters
1.problems
2.variables
3. classIcal
oPtImIzatIon
It results from application of
calculus to the basic problem of
finding the maximum and minimum
of a function.
The relationship is represented as
Y=f(x), where Y is dependent variable
and x is independent variable.
If two independent variables are
used
then Y=f(x1,x2).
statIstIcal desIgn
Divided into two classes:
Experimentation continues as the
optimization study proceeds.
Ex: EVOP and simplex methods.
Experimentation is completed
4. before optimization takes place.
Ex: Lagrangian method and search
methods.
The relationship between dependent
and independent variables can be
estimated by two approaches:
Theoretical approach.
Empirical approach or experimental
approach.
evolutIonary
oPeratIons
The production procedure is allowed
to evolve to the optimum by careful
planning and constant repetition
The process is run in such a way that
it produces a product that meets all
specifications and generates
information on product improvement
The experimenter makes a very
5. small change in formulation or
process but makes it so many times
until there is statistical improvement
in the product.
This continues until further changes
do not improve the product or
perhaps become detrimental. The
experimenter then gets the optimum
which is represented by a peak.
Ex: parenteral preparations.
sImPlex method
It involves a geometrical figure
known as ‘simplex’ that has one
more point than number of
factors.
For two factors or independent
variables , the simplex is
represented by triangle.
Once the shape of simplex has
been determined the method can
employ a simplex of fixed size that
6. are determined by comparing
magnitudes of responses after
each successive calculation.
Ex: pump speeds of two reagents
used in analysis reactions
solubility problem involving
butoconazole nitrate in multi
component system
Physical stability of solutions and
evaluation of acetaminophen
tablets
lagrangIan
method
It is an extension of classic method.
It requires experimentation to be
completed before optimization so
that mathematical models can be
7. generated.
Polynomial models are generated by
backward stepwise regression
analysis which relates the response
variables to independent variables.
y=Bo+B1X1+B2X2+B3X3(POW)2.......
...
The terms are retained or eliminated
accordingly.
Ex: Active ingredient :Phenyl
Propanolamine Hcl
Disintegrant: corn starch
Lubricant: stearic acid.
Independent variables include:
binder level , diluent level , lubricant
levels and compression levels.
Dependent variables:
disintegrationtime,hardness,dissolutio
n.friability,thickness.
8. .
A technique called ‘SENSITIVITY
ANALYSIS’ helps in solving the
constrained optimization problem.
Ex: constraining the tablet friability
to a maximum of 2.73%.When this
constraint is tightened or relaxed
there is substantial improvement in
half life upto 1-2%.
search methods
It does not involve any mathematical
operations like partial differentiation
or continuity of functions.
Only requires computation.
Response surfaces as defined by
appropriate equations are searched
by various methods to find the
combination of independent
variables yielding the optimum.
It takes five independent variables
9. into account and is computer
assisted.
These variables dictates a total of
27 formulations to be prepared and
factorial design known as ‘five
factor, orthogonal, central ,
composite second order design’.
The translation of statistical design
into physical units is done .
.
The data subjected to statistical
analysis followed by multiple
regression analysis.
The global best formulation must be
selected which is done by usage of
second order polynomials.
10. Disadvantage : not all responses will
fit second order regression model.
Advantage : it can be modified to
accept another mathematical
models.
stePs In
oPtImIzatIon
Feasibility search – to locate a set of
response constraints that are just at
limit of possibility .
Grid search- experimental range is
divided into a grid of specific size
and methodically searched.
From an input of desired criteria the
program prints out all formulations
that satisfy the constraints.
Mathematical method for selecting
those variables that best distinguish
between formulations is multivariate
11. statistical technique called
‘PRINCIPLE COMPONENT
ANALYSIS’(PCA).
Besides these programs, graphic
approaches are also available.
The output includes plot of given
response as a function of single
variable or all five variables.
An infinite number of these plots is
possible since each curve
represented, four of five variables
must remain constant.
the slope of any one graph indeed
represents the response for one
independent variables. It will change
depending on the level of the other
four variables.
canonIcal
12. analysIs
Also known as canonical reduction.
Efficient method to explore the
response surface to suggest ideas
for further experimentation.
It reduces higher level regression
equation into an equation consisting
of squared terms and constants.
Y=yo+λW1²+λ₂WW +…………..
It involves the reduction into a
simpler form by rigid rotation and
translation of response surface axis
into multidimensional space.
It makes usage of matrix algebra
containing Eigen values and Eigen
vectors.
Used in combination with grid
search
technique to optimize controlled drug
release
from a pellet system which is made up
13. of
4 components.
aPPlIcatIons
Designed experimentation involving
mostly some type or modification of
factorial design has been used to
study many types of formulations
like tablets, controlled release forms
etc.
To study pharmacokinetic
parameters.
To study process variables in tablet
coating operations.
In high performance liquid
chromatography.
Formulation of culture medium in
virology labs.
Production of riboflavin optimizing
the culture the media growth via
Plackett- Burman factorial design.
Sub micro emulsions with
14. sunscreens using simplex
composite designs.
.
Some of the designs used:
Completely randomised designs.
Randomised block designs.
Factorial designs: 1)Full factorial .
2) Fractional
factorial.
a. Homogeneous
fractional.
b. Mixed level
fractional.
c. Box hunter.
d. Plackett-
Burman.
e. Latin square.
Response surface designs: a.
Central composite
15. designs.
b.Box
Behnken designs.
Adding centre points.
Three level full factorial designs.
reFerences
Websters Marriam dictionary, G
and C Marriam.
L. Cooper and N. Steinberg,
Introduction to methods of
optimization.
O. L. Davis, The design and analysis
of industrial experimentation,
Macmillan.
Gilbert .S. Banker ,Modern
Pharmaceutics.
Google search engine,
www.google.co.in.
