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Optimization Methods
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1- INTRODUCTION
What is Optimization?
Optimization of a formulation or process is finding
the best possible composition or operating conditions.
Determining such a composition or set of conditions is
an enormous task, probably impossible, certainly
unnecessary, and in practice, optimization 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. Thus, the type and components of a formulation
may be selected, according to previous experience,
by expert knowledge (possibly using an expert
system), or by systematic screening as described later.
Then the relative and/or total proportions of the excipients
are varied to obtain the best endpoint, or a process
is chosen, and a study is carried out to determine
the best operating conditions to obtain the desired formulation
properties. Both of these are optimization
studies. This article concentrates on statistical experimental
design-based optimization.
2 -Screening, Factor Studies, and Optimization
Systematic screening and factor influence studies are
closely related to optimization, being often sequential
stages in the development process and involving statistical
experimental design methods. Screening methods
are used to identify important and critical effects, for
example, in the manufacturing process. Factor studies
are quantitative studies of the effects of changing potentially
critical process and formulation parameters. They
involve factorial design and are also quite often referred
to as screening studies; however, the resulting relationships
have just as often been used for optimization.
The type of study carried out will depend on the
stage of the project. In particular, experimental design
may be carried out in stages, and the experiments of a
factor study may be augmented by further experiments
to a design giving the detailed information needed
for true optimization. It cannot be stressed to highly
that the quality of a statistically designed experiment
depends on the choice of experimental run with respect
to an a priori model, and this quality can and must be
assessed before starting the experiments.
3 -Brief Historical Review
Statistical methods for screening, factor studies, and
optimization have been available for a long time: factorial
designs since 1926;[1] screening designs since
1946;[2] and the central composite design for response
surface optimization, was introduced by Box and
Wilson, in 1951.[3] Their use started to be described
in the pharmaceutical literature from the early 1970s,
but it was only from approximately 1988 that there
was a sudden increase in the number of published articles,
and the numbers have continued to rise. A conception
or presupposition of the difficulty or
complexity of experimental design had to be overcome.
The change has been attributed of course to a great
extent to the availability of computing power and of
relatively inexpensive high-performance software that
allows previously difficult or advanced methods to be
applied. In particular, much attention is now being
given to robust processes and formulation, and
there are developments in treating non-linear and
highly correlated responses.[4
4- Methods for Optimization
There are four primary methods. First, there is the statistically
designed experiment, in which experiments are
set up in a (normally regular) matrix to estimate the
coefficients in a mathematical model that predicts
responses within the limits of formulation or operating
conditions being studied. This is generally the most
powerful method, provided the experimentation zone
has been correctly identified, and is the subject of most
of this article.
Second, the direct optimization method, the best
known being the sequential simplex, is a rapid and
powerful method for determining an experimental
domain, best combined with experimental design for
the optimization itself.
Third, there is the one-factor-at-a-time method in
which the experimenter varies first one factor to find the
best value, then another. Its disadvantages are that it cannot
be used for multiple responses and that it will not
work when there are strong interactions between factors.
Finally, the non-systematic approach in which the
knowledge and intuition of the developer allow him
to improve results, changing a number of factors at the
same time is often surprisingly successful in the hands
of a skilled worker. Where he is less skilled or less
lucky, he can waste a remarkable amount of time
and resources.
The use of artificial intelligence and expert systems
is treated elsewhere in this work.
5 -SCREENING
Obtaining a Formulation Suitable
for Optimization
Once the dosage form has been selected, the excipients
must be identified, their choice often limited by practical
considerations of time and resources determined
by patents, company practice, or according to expert
knowledge. However, it may be possible or necessary
to test a number of different excipients for each function,
for example, several diluents, lubricants, binders.
This approach has proved useful in drug–excipient
compatibility testing in which protoformulations are
set up according to a statistical screening design to
assess stability and compatibility.
6 -Here the factor is the excipient’s function. This can
be set at different levels, the level being the excipient
itself. So the factor may be ‘‘binder,’’ and the levels
are, for example, HPMC, povidone, polyvinylacetate,
and no disintegrant present. A mathematical model
relates the response (in this case, degradation) to composition.
It includes variables corresponding to each
factor with (qualitative) levels corresponding to each
excipient. Plackett and Burman[2] described designs
suitable for treating this kind of problem. Designs with
the factors at only two levels are widely used. However,
there are other designs at 3, 4, and 5 levels as well as
asymmetric designs derived from them in which the
various factors take a different number of levels.[5,6]
It is assumed that there are no interactions between
factors; that is to say, the effect of a given excipient on
stability does not depend on what other excipients are
found in the formulation. (The same reasoning applies
to other kinds of factors or responses.) This can only
be an approximation; however, if it should be necessary
to take interactions into account, many more
experiments would be needed, and it would probably
be necessary to limit the number of levels for each
factor to two for the number of experiments to be
manageable.
The choice of excipients may be considered a qualitative
optimization, their quantitative compositions
not having yet been optimized. This and the fact that
the process used will most likely be on a small laboratory
scale may affect the affect the choice of excipients.
However, it is in most circumstances an unavoidable
limitation.
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ترجمة قسم : Optimization Methods
