optimization mano.ppt

OPTIMIZATION TECHNIQUES IN
PHARMACEUTICAL FORMULATION AND
PROCESSING
Manoj R
Dept of pharmaceutics
Nandha college of pharmacy
Erode
6/14/2023 1

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CONTENTS
CONCEPT OF OPTIMIZATION
OPTIMIZATION PARAMETERS
CLASSICAL OPTIMIZATION
STATISTICAL DESIGN
DESIGN OF EXPERIMENT
OPTIMIZATION METHODS
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INTRODUCTION
The term Optimize is defined as “to make perfect”.
It is used in pharmacy relative to formulation and
processing
Involved in formulating drug products in various
forms
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
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Final product not only meets the requirements
from the bio-availability but also from the
practical mass production criteria
Pharmaceutical scientist- to understand theoretical
formulation.
Target processing parameters – ranges for each
excipients & processing factors
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INTRODUCTION

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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.
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Optimization parameters
Problem types Variable
Constrained Unconstrained Dependent Independent
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VARIABLES
Independent Dependent
Formulating Processing
Variables Variables
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Independent variables or primary variables :
Formulations and process variables directly under control
of the formulator.
These includes ingredients
Dependent or secondary variables :
These are the responses of the inprogress material or the
resulting drug delivery system.
It is the result of independent variables .
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Relationship between independent variables and
response defines response surface
Representing >2 becomes graphically impossible
Higher the variables , higher are the complications
hence it is to optimize each & everyone.
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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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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
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GRAPH REPRESENTING THE RELATION BETWEEN
THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE
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Using calculus the graph obtained can be solved.
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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Classic optimization

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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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For second type 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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Statistical design

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The relationship with single independent variable can
be obtained by simple regression analysis or by least
squares method.
 The relationship with more than one important
variable can be obtained by statistical design of
experiment and multi linear regression analysis.
 Most widely used experimental plan is factorial
design
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Statistical design

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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
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TERMS USED

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Optimization by means of an experimental design
may be helpful in shortening the experimenting time.
The design of experiments is a structured , organised
method used to determine 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 analysed statistically.
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TERMS USED

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TYPES OF EXPERIMENTAL DESIGN
Completely randomised designs
Randomised block designs
Factorial designs
 Full
 Fractional
Response surface designs
 Central composite designs
 Box-Behnken designs
Adding centre points
Three level full factorial designs
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 Completely randomised Designs
 These experiment 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.
 Randomised 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
contribition of these factors to experimental error.
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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 need to be evaluated
for main effects and higher level interactions can be
assumed to be negligible.
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 and especially for n*4 experiments.
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Taguchi
 It is similar to PBDs.
 It allows estimation of main effects while minimizing
variance.
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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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 ouputs and the goal is to
minimise defects and maximise yield
γ =β0 + β1X1 + β2X2 +….β11X1
2 + β22X2
2
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Two most common designs generally used in this
response surface modelling 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
augemented 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
They do not contain embedded factorial or
fractional factorial design.
Box-Behnken designs use just three levels of
each factor.
These designs for three factors with circled
point appearing at the origin and possibly
repeated for several runs.
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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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FACTORIAL DESIGN
These are the designs of choice for simultaneous
determination of the effects of several factors & their
interactions.
Used in experiments where the effects of different
factors or conditions on experimental results are to
be elucidated.
Two types
 Full factorial- Used for small set of factors
 Fractional factorial- Used for optimizing more
number of factors
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LEVELS 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
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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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Calculation of main effect of A (stearate)
The main effect for factor A is
 {-(1)+a-b+ab-c+ac-bc+abc] X 10-3
Main effect of A =
=
= 0.022 cm
4
a + ab + ac + abc
4
_ (1) + b + c + bc
4
[487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 10-3
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EXAMPLE OF FULL FACTORIAL EXPERIMENT

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EFFECT OF THE FACTOR STEARATE
470
480
490
500
0.5 1.5
Average = 473 * 10-3
Average = 495 * 10-3
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STARCH X STEARATE INTERACTION
Stearate
Thickness
Starch
450
500 450
500
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General optimization
 By MRA the relationships are generated from
experimental data , resulting equations are on the basis
of optimization.
 These equation defines response surface for the system
under investigation
 After collection of all the runs and calculated responses
,calculation of regression coefficient is initiated.
 Analysis of variance (ANOVA) presents the sum of the
squares used to estimate the factor maineffects.
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FLOW CHART FOR OPTIMIZATION
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Applied optimization methods
Evolutionary operations
Simplex method
Lagrangian method
Search method
Canonical analysis
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Evolutionary operations (evop)
It is a method of experimental optimization.
Technique is well suited to production situations.
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
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Applied mostly to TABLETS.
Production procedure is optimized by careful
planning and constant repetition
 It is impractical and expensive to use.
It is not a substitute for good laboratory scale
investigation
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Evolutionary operations (evop)

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Simplex method
It is an experimental method applied for
pharmaceutical systems
Technique has wider appeal in analytical method
other than formulation and processing
Simplex is a geometric figure that has one more point
than the number of factors.
It is represented by triangle.
It is determined by comparing the magnitude of the
responses after each successive calculation
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Graph representing
the simplex movements to the optimum conditions
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The two independent variables show pump speeds for
the two reagents required in the analysis reaction.
Initial simplex is represented by lowest triangle.
The vertices represents spectrophotometric response.
The strategy is to move towards a better response by
moving away from worst response.
Applied to optimize CAPSULES, DIRECT
COMPRESSION TABLET (acetaminophen), liquid
systems (physical stability)
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Simplex method

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Lagrangian method
It represents mathematical techniques.
It is an extension of classic method.
It is applied to a pharmaceutical formulation and
processing.
This technique follows the second type of statistical
design
Limited to 2 variables - disadvantage
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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, invitro 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

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Tablet formulations
Formulation
no,.
Drug Dicalcium
phosphate
Starch Stearic acid
1 50 326 4(1%) 20(5%)
2 50 246 84(21%) 20
3 50 166 164(41%) 20
4 50 246 4 100(25%)
5 50 166 84 100
6 50 86 164 100
7 50 166 4 180(45%)
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 Constrained optimization problem is to locate the
levels of stearic acid(x1) and starch(x2).
 This minimize the time of invitro 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)-invitro release
Y3 = f3(X1,X2)<2.72-Friability
Y4 = f4(x1,x2) <0.422-avg tab.vol
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Tablet formulations

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CONTOUR PLOT FOR TABLET HARDNESS
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CONTOUR PLOT FOR Tablet dissolution(T50%)
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GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET
HARDNESS & DISSOLUTION
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6/14/2023
Tablet formulations

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Search method
It is defined by appropriate equations.
It do 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
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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
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Example
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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 Five independent variables dictates total of 32
experiments.
This design is known as five-factor, orthagonal,
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 factorial.
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Example

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Translation of statistical design in to physical units
Experimental conditions
Factor -1.54eu -1 eu Base0 +1 eu +1.547eu
X1=
ca.phos/lactose
24.5/55.5 30/50 40/40 50/30 55.5/24.5
X2= compression
pressure( 0.5 ton)
0.25 0.5 1 1.5 1.75
X3 = corn starch
disintegrant
2.5 3 4 5 5.5
X4 = Granulating
gelatin(0.5mg)
0.2 0.5 1 1.5 1.8
X5 = mg.stearate
(0.5mg)
0.2 0.5 1 1.5 1.8
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Again formulations were prepared and are
measured.
Then the data is subjected to statistical
analysis followed by multiple regression
analysis.
The equation used in this design is second
order polynomial.
 y = 1a0+a1x1+…+a5x5+a11x1
2
+…+a55x2
5+a12x1x2
+a13x1x3+a45 x4x5
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A multivariant 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.
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PLOT FOR A SINGLE VARIABLE
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6/14/2023
PLOT OF FIVE VARIABLES

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PLOT OF FIVE VARIABLES
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ADVANTAGES OF SEARCH METHOD
It takes five independent variables in to account.
Persons unfamiliar with mathematics of optimization &
with no previous computer experience could carryout
an optimization study.
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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.
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It is used to reduce second order regression
equation to an equation consisting of a
constant and squared terms as follows
It was described as an efficient method to
explore an empherical response.
Y = Y0 +λ1W1
2 + λ2W2
2 +..
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Canonical analysis

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Important Questions
Classic optimization
Define optimization and optimization
methods
Optimization using factorial design
Concept of optimization and its parameters
Importance of optimization techniques in
pharmaceutical processing & formulation
Importance of statistical design
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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
6/14/2023

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