1. Optimization techniques in
pharmaceutics , formulation
and processing
ABDUL MUHEEM,
M.Pharma(1st sem)
Deptt. of Pharmaceutics,
Faculty of Pharmacy,
Jamia Hamdard
Email: muheem.abdul985@gmail.com
2. 2023-08-19
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Optimization makes the perfect formulation &
reduce the cost
• Primary objective may not be optimize absolutely but to compromise
effectively &thereby produce the best formulation under a given set of
restrictions
3. The term Optimize is defined as to make perfect , effective , or
functional as possible.
It is the process of finding the best way of using the existing resources
while taking in to the account of all the factors that influences decisions in
any experiment
Traditionally, optimization in pharmaceuticals refers to changing one
variable at a time, so to obtain solution of a problematic formulation.
Modern pharmaceutical optimization involves systematic design of
experiments (DoE) to improve formulation irregularities.
In the other word we can say that –quantitate a formulation that has
been qualitatively determined.
It’s not a screening techniques
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TERMS USED
FACTOR: It is an assigned variable such as concentration ,
Temperature etc..,
Quantitative: Numerical factor assigned to it
Ex; Concentration- 1%, 2%,3% etc..
Qualitative: Which are not numerical
Ex; Polymer grade, humidity condition etc
LEVELS: Levels of a factor are the values or designations
assigned to the factor
FACTOR LEVELS
Temperature 300 , 500
Concentration 1%, 2%
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RESPONSE: It is an outcome of the experiment.
It is the effect to evaluate.
Ex: Disintegration time etc..,
EFFECT: It is the change in response caused by varying the
levels
It gives the relationship between various factors & levels
INTERACTION: It gives the overall effect of two or more
variables
Ex: Combined effect of lubricant and glidant on hardness of the
tablet
9. Optimization Parameters
1.Problem types:
Constraints
Example-Making hardest tablet but should disintegrate within 20 mins
( Constraint)
Unconstraint
Example: Making hardest tablet ( Unconstraint)
• 2. Variables:
Independent variable- E.g. - mixing time for a given process step.
granulating time.
10. Dependent variables, which are the responses or the characteristics
of the in process material Eg. Particle size of vesicles, hardness of the
tablet.
Higher the number of variables, more complicated will be the
optimization process.
There should be a relationship between the given response and the
independent variable, and once this relationship is established , a response
surface is generated.
From response surface only, we find the points which will give desirable
value of the response.
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Example of dependent & independent variables
Tablet formulation
Independent variables Dependent variables
X1 Diluent ratio Y1 Disintegration time
X2 compressional force Y2 Hardness
X3 Disintegrant level Y3 Dissolution
X4 Binder level Y4 Friability
X5 Lubricant level Y5 weight uniformity
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Classic optimization
It involves application of calculus to basic problem for
maximum/minimum function.
Limited applications
i. Problems that are not too complex
ii. They do not involve more than two variables
For more than two variables graphical representation is
impossible
It is possible mathematically , but very involved ,making use
of partial derivatives , matrics ,determinants & so on.
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Response surface representing the relationship between the independent variables
X1 and X2 and the dependent variable Y.
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We can take derivative ,set it equal to zero & solve for x to obtain the
maximum or minimum
Using calculus the graph obtained can be
Y = f (x)
When the relation for the response y is given as the function of two
independent variables,x1 &X2
Y = f(X1 , X2)
The above function is represented by contour plots on which the axes
represents the independent variables x1& x2
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Statistical design
Techniques used divided in to two types.
Experimentation continues as optimization proceeds
It is represented by evolutionary operations(EVOP),
simplex methods.
Experimentation is completed before optimization
takes place.
It is represented by classic mathematical & search
methods.
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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
Theoretical approach- If theoretical equation is
known , no experimentation is necessary.
Empirical or experimental approach – With single
independent variable formulator experiments at
several levels.
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Optimization may be helpful in shortening the
experimenting time.
The design of experiments is determined the
relationship between the factors affecting a process
and the output of that process.
Statistical DOE refers to the process of planning the
experiment in such a way that appropriate data can
be collected and analyzed statistically.
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TYPES OF EXPERIMENTAL DESIGN
Completely randomized designs
Randomized block designs
Factorial designs
Full
Fractional
Response surface designs
Central composite designs
Box-Behnken designs
Three level full factorial designs
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Completely randomized Designs
These designs compares the values of a response variable
based on different levels of that primary factor.
For example ,if there are 3 levels of the primary factor with
each level to be run 2 times then there are 6 factorial possible
run sequences.
Randomized block designs
For this there is one factor or variable that is of primary
interest.
To control non-significant factors, an important technique
called blocking can be used to reduce or eliminate the
contribution of these factors to experimental error.
24. Factorial Design
These are the designs of choice for simultaneous determination of the
effects of several factors & their interactions.
Symbols to denote levels are:
(1)- when both the variables are in low concentration.
a- one low variable and second high variable.
b- one high variable and second low variable
ab- both variables are high.
• Factorial designs are optimal to determined the effect of pressure &
lubricant on the hardness of a tablet
• Effect of disintegrant & lubricant conc . on tablet dissolution .
• It is based on theory of probability and test of significance.
25. It identifies the chance variation ( present in the process due to accident) and
the assignable variations ( which are due to specific cause.)
Factorial design are helpful to deduce IVIVC.
IVIVC are helpful to serve a surrogate measure of rate and extent of oral
absorption.
BCS classification is based on solubility and permeability issue of drugs,
which are predictive of IVIVC.
Sound IVIVC omits the need of bioequivalence study.
IVIVC is predicted at three levels:
Level A- point to point relationship of in vitro dissolution and in vivo
performance.
Level B- mean in vitro and mean in vivo dissolution is compared and co
related.
Level C- correlation between amount of drug dissolved at one time and one
pharmacokinetic parameter is deduced.
26. BCS classification and its expected outcome on IVIVC for Immediate
release formulation
BCS Class Solubility Permeability IVIVC
I High High Correlation( if
dissolution is
rate limiting)
II Low High IVIVC is
expected
III High Low Little or no
IVIVC
IV low Low Little or no
IVIVC
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Factorial design
Full
• Used for small set of factors
Fractional
• It is used to examine multiple factors efficiently with fewer runs than
corresponding full factorial design
Types of fractional factorial designs
Homogenous fractional
Mixed level fractional
Box-Hunter
Plackett - Burman
Taguchi
Latin square
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Homogenous fractional
Useful when large number of factors must be screened
Mixed level fractional
Useful when variety of factors needed to be evaluated for
main effects and higher level interactions can be assumed
to be negligible.
Ex-objective is to generate a design for one variable, A, at 2
levels and another, X, at three levels , mixed &evaluated.
Box-hunter
Fractional designs with factors of more than two levels
can be specified as homogenous fractional or mixed level
fractional
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Plackett-Burman
It is a popular class of screening design.
These designs are very efficient screening designs
when only the main effects are of interest.
These are useful for detecting large main effects
economically ,assuming all interactions are negligible
when compared with important main effects
Used to investigate n-1 variables in n experiments
proposing experimental designs for more than seven
factors.
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Taguchi
It is similar to PBDs.
It allows estimation of main effects while minimizing variance.
Taguchi Method treats optimization problems in two categories,
[A] STATIC PROBLEMS :Generally, a process to be optimized has several
control factors which directly decide the target or desired value of the output.
[B] DYNAMIC PROBLEMS :If the product to be optimized has a signal input that
directly decides the output,
Latin square
They are special case of fractional factorial design where there is
one treatment factor of interest and two or more blocking factors
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We can use the Latin square to allocate treatments. If the rows of the square
represent patients and the columns are weeks, then for example the second
patient,in the week of the trial, will be given drug D. Now each patient receives
all five drugs, and in each week all five drugs are tested.
A B C D E
B A D E C
C E A B D
D C E A B
E D B C A
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Response surface designs
This model has quadratic form
Designs for fitting these types of models are known as
response surface designs.
If defects and yield are the outputs and the goal is to
minimize defects and maximize yield
γ =β0 + β1X1 + β2X2 +….β11X1
2 + β22X2
2
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Two most common designs generally used in this
response surface modeling are
Central composite designs
Box-Behnken designs
Box-Wilson central composite Design
This type contains an embedded factorial or fractional
factorial design with centre points that is augmented with
the group of ‘star points’.
These always contains twice as many star points as there
are factors in the design
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The star points represent new extreme value (low & high) for each
factor in the design
To picture central composite design, it must imagined that there are
several factors that can vary between low and high values.
Central composite designs are of three types
Circumscribed(CCC) designs-Cube points at the corners of the unit
cube ,star points along the axes at or outside the cube and centre
point at origin
Inscribed (CCI) designs-Star points take the value of +1 & -1 and
cube points lie in the interior of the cube
Faced(CCI) –star points on the faces of the cube.
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Box-Behnken design
Box-Behnken designs use just three levels of each factor.
In this design the treatment combinations are at the midpoints of edges of
the process space and at the center. These designs are rotatable (or near
rotatable) and require 3 levels of each factor
These designs for three factors with circled point appearing at the origin and
possibly repeated for several runs.
It’s alternative to CCD.
The design should be sufficient to fit a quadratic model , that justify equations
based on square term & products of factors.
Y= b0+b1x1+b2x2+b3x3+b4x1x2+b5x1x3+b6X2X3+b7X1
2 +b8X22+b9X3
2
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Three-level full factorial designs
It is written as 3k factorial design.
It means that k factors are considered each at 3 levels.
These are usually referred to as low, intermediate & high
values.
These values are usually expressed as 0, 1 & 2
The third level for a continuous factor facilitates
investigation of a quadratic relationship between the
response and each of the factors
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V. APPLIED OPTIMIZATION METHODS
There are several methods used for optimization. They are
Evolutionary
Operations
The Simplex
Method
The
Lagrangian
Method
Search
Method
Canonical
Analysis
42. Evolutionary operations:
• Widely used method(mostly for tablets)
• Technique is well suited to production situations(formulation &
process)
• Small changes in the formulation or process are made (i.e., repeats the
experiment so many times) & statistically analyzed whether it is
improved.
• It continues until no further changes takes place i.e., it has reached
optimum-the peak.
• EVOP is not a substitute for good laboratory –scale investigation ,
because of the necessarily small in the EVOP.
• It is not suitable for lab , therefore it’s impractical & expensive.
43. Simplex Method(Simplex Lattice)
It is an experimental techniques & mostly used in analytical rather than
formulation & processing.
Simplex is a geometric figure that has one more point than the number of
factors.
e.g-If 2 independent variables then simplex is represented as triangle.
• The strategy is to move towards a better response by moving away from
worst response.
• Applied to optimize CAPSULES, DIRECT COMPRESSION TABLET),
liquid systems (physical stability).
• It is also called as Downhill Simplex / Nelder-Mead Method.
44. In simplex lattice, the response may be plotted as 2D
(contour plotted) or 3D plots (response surface
methodology)
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The worst response is
0.25, conditions are
selected at the vortex,
0.6, and, indeed,
improvement is
obtained. One can
follow the experimental
path to the optimum,
0.721
Figure 5 The simplex approach to optimization. Response is spectorphotometric reading at a given
wavelength
46. Example 2: Two component solvent system
representing simplex lattice.
Constraint is the concentration of A and B must add to
100%
Includes observing responses( solubility) at three point i.e.
100% A, 100% B and 50 – 50 mixtures of A and B
47. Eg: Preparation of tablet with excipients (three
components) gives 7 runs.
7
Starch
Stearic acid
Lactose 3
1
A regular simplex lattice for a three
component mixture consist of seven
formulations
2
4
5
6
48. A simplex lattice of four component is shown by 15 formulation
4 formulations of each component A,B,C&D
6 formulation of 50-50 mixture of AB, AC, AD, BC, BD&CD.
4 formulation of 1/3 mixtures of three components ABC, ABD, ACD, & BCD.
1 formulation of 25% of each of four
(ABCD)
49. • 100% pure component is not taken as un acceptable
formulation is obtained, thus vertices does not represent
the pure single substance , therefore a transformation is
required.
Transformed % = ( Actual %- Minimum %)
(Maximum %-Minimum %)
50. Lagrangian method
• It represents mathematical techniques & it is applied to a
pharmaceutical formulation and processing.
• This technique follows the second type of statistical
design
• Disadvantage-Limited to 2 variables .
• Helps in finding the maxima (greatest possible amount)
and minima (lowest possible concentration) depending on
the constraints..
• A techniques called “sensitivity analysis“ can provide
information so that the formulator can further trade off one
property for another . Analysis for solves the constrained
optimization problems.
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Steps involved
.Determine objective formulation
Determine constraints.
Change inequality constraints to equality constraints.
Form the Lagrange function F:
Partially differentiate the lagrange function for each
variable & set derivatives equal to zero.
Solve the set of simultaneous equations.
Substitute the resulting values in objective functions
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Example
Optimization of a tablet.
phenyl propranolol(active ingredient)-kept constant
X1 – disintegrate (corn starch)
X2 – lubricant (stearic acid)
X1 & X2 are independent variables.
Dependent variables include tablet hardness,
friability ,volume, in vitro release rate e.t.c..,
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Polynomial models relating the response variables to
independents were generated by a backward stepwise
regression analysis program.
Y= B0+B1X1+B2X2+B3 X1
2
+B4 X2
2
+B+5 X1 X2 +B6 X1X2
+ B7X1
2
+B8X1
2
X2
2
Y – Response
Bi – Regression coefficient for various terms containing
the levels of the independent variables.
X – Independent variables
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EXAMPLE OF FACTORS IN THIS FACTORIAL
DESIGN
FACTOR LOWLEVEL(mg) HIGH
LEVEL(mg)
A:stearate 0.5 1.5
B:Drug 60.0 120.0
C:starch 30.0 50.0
17 August 2012
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EXAMPLE OF FULL FACTORIAL EXPERIMENT
Factor
combination
Stearate Drug Starch Response
Thickness
Cm*103
(1) _ _ _ 475
a + _ _ 487
b _ + _ 421
ab + + _ 426
c _ _ + 525
ac + _ + 546
bc _ + + 472
abc + + + 522
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Constrained optimization problem is to locate the levels of
stearic acid(x1) and starch(x2).
This minimize the time of in vitro release(y2),average tablet
volume(y4), average friability(y3)
To apply the lagrangian method, problem must be expressed
mathematically as follows
Y2 = f2(X1,X2)-in vitro release
Y3 = f3(X1,X2)<2.72-Friability
Y4 = f4(x1,x2) <0.422-avg tab.vol
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GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET
HARDNESS & DISSOLUTION
Contour plots for the Lagrangian method: feasible solution space indicated by
crosshatched area
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Optimizing values of stearic acid and strach as a function of restrictions on
tablet friability: (A) percent starch; (B) percent stearic acid
60. Search methods (RSM) :
• It takes five independent variables into account and is
computer-assisted.
• It is defined by appropriate equations.
• Response surface methodology is used to determine the
connection between different explanatory variables
(independent variables) and one or more of the response
variables.
• Persons unfamiliar with mathematics of optimization &
with no previous computer experience could carryout an
optimization study.
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1. Select a system
2. Select variables:
a. Independent
b. Dependent
3. Perform experimens and test product.
4. Submit data for statistical and regression analysis
5. Set specifications for feasibility program
6. Select constraints for grid search
7. Evaluate grid search printout
8. Request and evaluate:.
a. “Partial derivative” plots, single or composite
b. Contour plots
THE SEARCH METHODS
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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.
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 +..
2variables=first order regression equation.
3variables/3level design=second order regression equation.
63. 63
. In canonical analysis or canonical
reduction, second-order regression
equations are reduced to a simpler
form by a rigid rotation and translation
of the response surface axes in
multidimensional space, as
for a two dimension system.
64. Forms of Optimization techniques:
1. Sequential optimization techniques.
2. Simultaneous optimization techniques.
3. Combination of both.
65. Sequential Methods:
Also referred as the "Hill climbing method".
Initially small number of experiments are done, then research is done using the
increase or decrease of response.
Thus, maximum or minimum will be reached i.e. an optimum solution.
Simultaneous Methods:
Involves the use of full range of experiments by an experimental design.
Results are then used to fit in the mathematical model.
Maximum or minimum response will then be found through this fitted model.
66. Example:- Designing controlled drug delivery
system for prolonged retention in stomach required
optimization of variables like
• presence/ absence / concentration of stomach
enzyme
pH, fluid volume and contents of guts
Gastric motility and gastric emptying.
67. When given as single oral tablet
(A).
Same drug when given in
multiple doses (B)
Same drug when given as
optimized controlled release
formulation (C)
69. Artificial Neural Network & optimization of pharmaceutical
formulation-
ANN has been entered in pharmaceutical studies to forecast the
relationship b/w the response variables &casual factors . This is
relationship is nonlinear relationship.
ANN is most successfully used in multi objective simultaneous
optimization problem.
Radial basis functional network (RBFN) is proposed simultaneous
optimization problems.
RBFN is an ANN which activate functions are RBF.
RBF is a function whose value depends on the distance from the
Centre or origin.
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71. 71
Formulation and Processing
Clinical Chemistry
Medicinal Chemistry
High Performance Liquid Chromatographic
Analysis
Formulation of Culture Medium in Virological
Studies.
Study of Pharmacokinetic Parameters.
APPLICATIONS
72. Provide solution to large scale manufacturing
problems
Provides string assurances to regulatory agencies
superior drug product quality
In microencapsulation process
Improvement of physical &biological properties by
modification
73. 73
REFERENCE
Modern pharmaceutics- vol 121
Textbook of industrial pharmacy by sobha rani R.Hiremath.
Pharmaceutical statistics
Pharmaceutical characteristics – Practical and clinical applications
www.google.com
Formulation optimization of nifedipine containing microspheres using factorial
design by Solmaz Dehghan
