Optimization techniques in pharmaceutical formulation and processing

Optimization Techniques in
pharmaceutical Formulation and
Processing
PRESENTED BY,
PRATIKSHA C CHANDRAGIRIVAR
M PHARMA 1ST SEM
DEPT, OF PHARMACEUTICS
HSK COP BAGALKOT
FACILITATED BY,
AVINASH.S.G.
ASSO.PROFESSOR
DEPT.OF PHARMACEUTICS
HSK COP BAGALKOT
Optimization Techniques in pharmaceutical
Formulation and Processing

CONTENTS:
1. Concept of optimization
2. Parameters of optimization
3. Optimization techniques in pharmaceutical
formulation and processing.

1. CONCEPT OF OPTIMIZATION:
 The term optimize is defined as “ to make perfect”.
 In terms of sentence it is defined as choosing the best element
from some set of available alternatives.
 According to Merriam Webster dictionary, optimization
means, “ An act, process or methodology of making something
(as a design, system or a decision) as a fully perfect, functional
or effective as possible; specially the mathematical procedures.
 Optimization is also defined as “The process of finding the
best values for the variables of a particular problem to
minimize or maximize an objective function.”

 It is used in pharmacy relative formulation and processing.
 It is involved in formulating drug products in various forms.
 Final product not only meets the requirements from the bio-
availability but also from the practical mass production
criteria.
 It helps the pharmaceutical scientist to understand theoretical
formulation and the target processing parameters which ranges
for each excipients & processing factors.
 In development projects, one generally experiments by a series
of logical steps, carefully controlling the variables & changing
one at a time, until a satisfactory system is obtained

 “It is not a screening technique.”
 Optimization is necessary because,
1. It reduces the cost.
2. It provides safety and reduces the error.
3. It provides innovation and efficacy.
4. It saves the time.

2.PARAMETERS OF OPTIMIZATION:
Parameters of optimization is divided into two
main types which is shown schematically:
optimization parameters
problem type variables
constrained unconstrained dependent independent
formulating processing

a. Problem type:
There are two general type are there in the problem type of
optimization technique:
1. Constrained
2. Un constrained
1. Constrained :
These are the restrictions placed on the system by physical
limitations or perhaps by simple practicality.
Example : Economical considerations
2. Un constrained:
Here there are no restrictions.
With the help of flow chart we can predict these two
problem type very easily viz.,

b. Variables:
Mathematically, they can be divided into two groups
a. Independent or primary variables
b. Dependent or secondary variables
a. Independent or primary variables:
Formulations and process variables directly under control of the
formulator.
Example: Ingredients
Mixing time for given process step.

B. Dependent or secondary variables:
These are the responses or the characteristics of
the in-progress material or the resulting drug delivery system.
Example: Direct result of any change in the formulation or
process.

 If greater the variables in a given system, then greater will be
the complicated job of optimization.
 But regardless of the no.of variables, there will be relationship
between a given response and independent variables.
 Once we know this relationship for a given response, then will
able to define a response surface i.e.,

 It involves application of calculus to basic problem for
maximum/minimum function.
 Limited applications
i. Problems those are not too complex.
ii. They do not involve more than two variables.
 For more than two variables, graphical representation is
impossible, but it is possible mathematically.

3.OPTIMIZATION TECHINQUES IN
PHARMACEUTICAL FORMULATION AND
PROCESSING
Deming and king presented a general optimization techniques:

Considering the changes in input and effect on output, the
optimization techniques are categorized into five types:
1. Evolutionary operations
2. Simplex method
3. Lagrangian method
4. Search method
5. Canonical analysis

1.Evolutionary operations:
 It is the one of the most widely used methods of experimental
optimization in fields other than pharmaceutical technology is
the evolutionary operation(EVOP),
 It is well suited to production situation.
 The basic idea is that the production procedure(formulation
and process) is allowed to evolve to the optimum by careful
planning and constant repetition.

Method:
This process is run in a such a way that
A. It produces a product that meets all specifications.
B. Simultaneously, it generates information on product
improvement.
 Experimenter makes a very small change in the formulation
or process but makes it so many times i.e., repeates the
experiment so many times.
 Then he or she can be able to determine statistically whether
the product has improved.
 And the experimenter makes further any other change in the
same direction, many times and notes the results.

 This continues until further changes do not improve the
product or perhaps become detrimental.
Applications:
1. It was applied to tablets by Rubinstein.
2. It has also been applied to an inspection system for parenteral
products.
Drawbacks:
1. It is impractical and expensive to use.
2. It is not a substitute for good laboratory scale investigation.

2.Simplex method:
 It is most widely applied technique.
 It was proposed by Spendley et.al.
 This technique has even wider appeal in areas other than
formulation and processing.
 A good example to explain its principle is the application to
the development of an analytical method i.e., a continuous
flow anlayzer, it was predicted by Deming and king.
 Simplex method is a geometric figure that has one or more
point than the number of factors.
 If two factors or any independent variables are there, then
simplex is represented triangle.
 Once the shape of a simplex has been determined, the method
can employ a simplex of fixed size or of variable sizes that are
determined by comparing the magnitude of the responses after
each successive calculation.

Graph representing the simplex movements to the optimum conditionsOptimization Techniques in pharmaceutical

Explaination:
 The two axes in the figure are nothing but two independent
variables show the pump speeds for the two reagents required
in the analysis reaction.
 The initial simplex is represented by the lowest triangle.
 The vertices represent the spectrophotometric response.
 The strategy is moves towards a better response.
 The worst response is 0.25, conditions are selected at the
vertex, 0.6 and indeed improvement is obtained.
 Then the experiment path is followed to obtain optimum,
0.721.

Applications of method:
1. This method was used by Shek.et.al. to search for an capsule
formula.
2. This was applied to study the solubility problem involving
butaconazolenitrate in a multicomponent system.
3. Bindschaeder and Gurny published an adaptation of the
simplex technique to a TI-59 calculator and applied
successfully to a direct compression tablet of acetaminophen.
4. Janeczeck applied the approach to a liquid system i.e., a
pharmaceutical solution and was able to optimize physical
stability.

3. The Lagragian method:
 This optimization method represents the mathematical
technique, is an extension of the classic method.
 Fonner.et.al gave ideas of understanding this technique by
applying it to a tablet formulation and by considering two
independent variables.

Explaination :
 The active ingredient, phenylpropanolamine HCl , was kept at
a constant level, and the levels of disintegrant (corn starch)
and lubricant (stearic acid) were selected as the independent
variables x1 and x2 .
 The dependent variables include tablet hardness, friability,
volume, in vitro release rate and urinary excretion rate in
human subjects.
 This techniques requires that the experimentation to be
completed before optimization so that mathematical models
can be generated.

The experimental data for the taken example :
Tablet formulation:

 The analysis is performed on a polynomial form.
y = B0 + B1x1+ B2x2+ B3x1
2+ B4x2
2 + B5x1 x2 + B6x1x2
2 + B7x1
2
x2+ B8x1
2x2
2
And these terms were retained and eliminated according to stand
stepwise regression techniques.
In above equation ,
y = Any given response
Bi = The regression co-efficient for the various terms containing
levels of the independent variables,
 Each response have its own equation.
 A graphic technique may be obtained from the polynomial
equations.

Figure a.
It shows the contours for tablet hardness as the levels of the
independent variables are changed.

Figure b,
It shows similar contour for the dissolution response t50%

Figure c.
The above graph shows the feasible space with the limits of
hardness be 8-10 kg and t50 % be 20-33 min .
This figure is obtained by superimposing a and b.

In the mathematical technique slightly different constraints are
used.
In this example.
The constrained optimization problem is to locate levels of stearic
acid (x1) and starch (x2)
That minimizes the time of invitro release (y2)
Such that the average tablet volume (y4) did not exceed 9.422
cm2 and the average friability (y3) did not exceed 2.72%.

To apply the Lagrangian method, this problem must be expressed
mathematically as follows:
Minimize y2 = F2 (x1 , x2) ……………..(1)
such that
y3 = F3 (x1 , x2) ≤ 2.72 ……………...(2)
y4 = F4 (x1 , x2) ≤ 0.422 ………………(3)
And 5 ≤ x1 ≤ 45 ………….. (4)
1 ≤ x2 ≤ 41 ………….. (5)
Equation (4) and (5) are the solution within the experimental
range.

 The foregoining inequality constraints must be converted to
equality constraints before the operation begins and this is
done by introducing a slack variable ‘q’ for each.
 The several equations are then combined into a Lagrange
function F and this necessitates the introduction of a Lagrange
multiplier ⅄ for each constraint.
 The partial differentiation of Lagrange function and solving
the resulting set of six simultaneous equations, value are
obtained for x1 and x2 to yield an optimum invitro time of
17.9mm (t50 %).
 The solution to a constrained optimization program may
depend heavily on the constraints applied to the secondary
objectives.

 A technique called “sensitive analysis” can provide
information so that the formulator can further trade off one
property for another.
 For sensitivity analysis the formulator solves the constrained
optimization problem for systemic changes in the secondary
objectives.
Example :

Explaination:
The foregoing problem restricted tablet friability, y3 to maximum
of 2.72 %.
The graph illustrates the invitro release profile as constraint is
tightened or relaxed and demonstrates that substantial
improvement in the t50 % can be obtained up to 1- 2 %.

The several steps in the Lagrangian method can be written as
follows:
Step-1 : Determine objective function.
Step-2 : Determine constraints.
Step-3 : Change inequality constraints to equality constraints.
Step-4 : Form the Lagrange function, F
a. One Lagrange multiplier ⅄ for each constraint.
b. One slack variable q for each inequality constraint.
Step-5 : Partially differentiate the Lagrange function for each
variable and set derivatives equal to zero.
Step-6 : Solve the set of simultaneous equations.
Step-7 : Substitute the resulting values into the objective
functions.

This can be phased into four phases, this was given by Buck et.al
The phases are:
a. A preliminary planning phase
b. An experimental phase
c. An analytical phase
d. A verification phase

4.Search methods:
 It is defined by appropriate equations. It does not require
continuity or differentiability of function. It is applied to
pharmaceutical system
For optimization 2 major steps are used
• Feasibility search-used to locate set of response constraints
that are just at the limit of possibility.
• Grid search – experimental range is divided in to grid of
specific size & methodically searched

Steps involved in search method
 Select a system
 Select variables
 Perform experiments and test product
 Submit data for statistical and regression analysis
 Set specifications for feasibility program
 Select constraints for grid search
 Evaluate grid search printout

Example:

• Five independent variables dictates total of 32 experiments.
This design is known as five-factor, orthogonal, central,
composite, second order design.
• First 16 formulations represent a half-factorial design for five
factors at two levels.
• The two levels represented by +1 & -1, analogous to high &
low values in any two level factorials.
Translation of statistical design in to physical units

Experimental conditions:

 Then the data is subjected to statistical analysis followed by
multiple regression analysis.
 The equation used in this design is second order polynomial.
y = a0+a1x1+…+a5x5+a11x1
2+…+a55x2
5+a12x1x2+a13x1x3+a45x4x5
 A multivariate statistical technique called principle
component analysis (PCA) is used to select the best
formulation.
 PCA utilizes variance-covariance matrix for the responses
involved to determine their interrelationship.

For single variable:

Plots for five variables

Advantages of search method:
 It takes five independent variables in to account.
 Persons unfamiliar with mathematics of optimization & with
no previous computer experience could carry out an
optimization study.

5. Canonical analysis
 It is a technique used to reduce a second order regression
equation. This allows immediate interpretation of the
regression equation by including the linear and interaction
terms in constant term.
 This was firstly adopted by Box and Wilson,
 It is used to reduce second order regression equation to an
equation consisting of a constant and squared terms as follows:
Y = Y0 +λ1W1
2 + λ2W2
2 +…
 It is described as an efficient method to explore an empherical
response.

References:
1. Modern Pharmaceutics; By Gillbert and S.
Banker – edited in 2002.
2. www.google.com

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