chetan dhal-optimization techniques in pharmaceutics, formulation and processing

Optimization techniques in pharmaceutics, formulation and processing

By:CHETAN DHAL,M.Pharma(Quality Assur-ance)Email: [email protected]

OUTLINE OF SLIDESCONTENT SLIDES

Introduction and approach 3-6

Optimization parameters 7-8

Classical optimization 9-11

DOE 12

Types of experimental design 13-30

Method of optimization 31-46

Application 47-48

Approach to process optimization and scale-up

49-50

References 51

TAGUCHI argued that quality engineering should start with an understanding of quality costs.This shows that for a well optimized product there is a need of understanding the product.

http://en.wikipedia.org/wiki/Quality_engineering

http://en.wikipedia.org/wiki/Quality_costs

INTRODUCTION

• To optimize is to make as perfect as possible, effective or functionally best.

• In order to make such a product one has to consider its physical, chemical or biological parameters, and the final product which comes out is of maximum yield, highest bioavailability, reproducibility characters. etc

Best way to optimize is to know the target. If the researcher is clear about the target and various conditions which he/she will be facing, makes it very easy to amend various variables.

OPTIMIZATION IS NOT A SCREENING TECHNIQUE AS IN CASE OF PREFORMULATION

OPTIMIZATION REQUIREMENT AND PRACTICAL METHOD:-

FLOW CHART TO UNDERSTAND THE OPTIMIZATION PROCESS

1) OPTIMIZATION PARAMETERS:-Development of any formulation can be understood to be based on certain parameters. Mathematically it is divided as:-

Higher the number of variables higherthe complications in the product development

1) Variables

Dependent

Independent

Variables: These are the small functions on which researches are dependent. Its of 2 types.INDEPENDENT DEPENDENTThese are the functions which are directly under the control of formulator.

Are the direct results to a change in formulation or process.ORResponses of alteration in the independent variable.

Eg:- Duration of mixing,Rate of drying

Eg:- Effect of addition of Binder on hardness of a Tablet when formulating a floating tablet.

Problem type - In the development of a formulation in pharmaceutical system there are some boundations while optimizing any formulation or any process. These may be of 2 types

CONSTRAINED UNCONSTRAINEDRestrictions placed on the system by physical limitations or by simple practicality.Eg:- economic conditions

No such restrictions are there and its most non- exsisting.

CLASSICAL OPTIMIZATIONEarlier optimization was based on hit and trial method. But now calculus methodology is applied. It helps in finding maxima and minima of a function. However this method is mostly applicable to condition where there is less variable.i)2 variables- one dependent(y) and one independent(x) y=f(x)ii)3 variables one independent and 2 dependent(x1,x2) y=f(x1,x2) for this type of system we have contour plots.

Contd…

GRAPH REPRESENTING THE RELATIONSHIP BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE.

THERE IS DEPENDENCY OF y ON ONLY ONE VARIABLE i.e. x.

Contd…

Response surface representing the relationship between the independent variables X1 and X2 and the dependent variable Y.

D.O.E:-(Design of experiments)

In statistics c/a controlled experimentation.

• It’s the methodology for designing experiments. • proposed by RONALD A. FISHER in his book

“The arrangement of field experiments” in 1926.

• DOE is concerned with planning and conduct of experiments of experiments to analyze the resulting data so that we obtain valid and objective conclusion.

TYPES OF EXPERIMENTAL DESIGN• 1) Complete randomized design

• 2) Randomized block design

• 3) Statistical design i) experimentation continue as optimization study proceeds ii) experimentation completes before optimization study

• 4) Factorial design (it can be 2 factorial or fully 3 factorial) i) Full factorial ii) Fractional factorial

• 5) Response surface design i) Central composite design ii) Box Behnken design

• 6) Adding center points

1) COMPLETELY RANDOMIZED DESIGN

These experiment compares the values of a response variable based on different levels of that primary factor (independent factors).

For example, if there are 3 levels of the primary factor with each level to be run 2 times then there are 6 possible run sequences.e.g:- These 3 levels to be run 2 times then,

, , , , , - 6 Different options

TYPES OF EXPERIMENTAL DESIGN

Contd…

2) RANDOMIZED BLOCK DESIGN

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.


Contd…

3) FACTORIAL DESIGN Factorial design is a proper arrangement of variables in an

expression which tells us about the possible options and various combinations.

There are various factors (called as variables) which determine production output hence the dependency of this must be checked while optimizing any process or formulation.

These factors can be assignable. i.e. which may have a quantitative or qualitative effect on our final product.

Factorial design is used for IVIVC study also.


Contd…

EXAMPLE:- For a system containing 2 variables showing an inter related effect on the product. 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. In this case the combined effect could be understood as:- (b + ab)-(1 - a) 2


Contd…

(A) FRACTIONAL FACTORIAL DESIGN:-

It is used to examine multiple factors efficiently with fewer runs than corresponding full factorial design

Types of fractional factorial designs 1)Homogenous fractional 2)Mixed level fractional 3)Box-Hunter 4)Plackett-Burman 5)Taguchi 6)Latin square

(B) FULL FACTORAL DESIGN:-

It is used for small set of factors.

FACTORIAL DESIGN

Full

Fractional


1) Homogenous fractional factorial design:- Useful when large number of factors need be screened.2) Mixed level fractional factorial design:- Useful when variety of factors need to be evaluated for main effects and higher level interactions can be assumed to be negligible.3) Box-hunter fractional factorial design:- Fractional designs with factors of more than two levels can be specified as homogenous fractional or mixed level fractional.

TYPES OF FRACTIONAL FACTORIAL(TYPES OF EXPERIMENTAL DESIGN)

A) FRACTIONAL FACTORIAL DESIGN

Contd…

• 4) Plackett-Burman fractional factorial design:- by R.L. Plackett and J.P. Burman (In 1946) • Published their now famous paper "The Design of

Optimal Multi-factorial Experiments" in Biometrika (vol. 33).

• This paper described the construction of very economical designs with the run number a multiple of four (rather than a power of 2).

• Its very efficient screening designs when only main effects are of interest.

• Plackett-Burman in general is heavily confounded with two-factor interactions. The PB design in 12 runs, for example, may be used for an experiment containing up to 11 factors TYPES OF FRACTIONAL FACTORIAL

(TYPES OF EXPERIMENTAL DESIGN)Contd…

12 RUN 11 FACTOR(x1 – x11 )DESIGN

TYPES OF FRACTIONAL FACTORIAL

(TYPES OF EXPERIMENTAL

DESIGN)

Contd…

5) Taguchi method of fractional factorial design:- (by Genichi Taguchi 1950)•This method was developed for the improvement of finished product.•Taguchi has developed this design for studying variation.

It treat optimization problem as:- 1)Static Problem:- several control factors are there to control the final optimized product.2)Dynamic Problem:- Problem to be optimized has a single input.


6) Latin square fractional factorial design:- (By Leonhard Euler)a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.Example:-

Type of representations:- a)Orthogonal array representationb)Equivalence classes of latin square.


http://en.wikipedia.org/wiki/Leonhard_Euler

B) LEVEL FULL FACTORIAL(3 level full factorial)

The three-level design is written as a 3k factorial design. It means that k factors are considered, each at 3 levels. These are (usually) referred to as low, intermediate and high levels. These levels are numerically expressed as 0, 1, and 2.

Example:- if we have a condition in which we have 2 variables and all with 3 levels (possibilities) then 32 = 8 options.OR If we have 3 variables and all with 3 levels then 33 = 27 options.


Contd…

5) RESPONSE SURFACE METHODOLOGY (RSM):- (by G. E. P. Box and K. B. Wilson in 1951)It explores the relationships between several independent variables and one or more dependent variables.It utilizes quadratic form of an equation which may be simple quadratic or multifunction quadratic.Types:- Two most common designs generally used in this response surface modeling areCentral composite designs (CCD)Box-Behnken designs


Contd…

a) CCD:- (by Box and Wilson)• It is composed of +2K factorial design or fractional

factorial design.• It help in building a second order (quadratic) model for the

response variable without needing to use a complete three-level factorial experiment.

# Central composite designs are of three types:-1) Circumscribed (CCC) designs-Cube points.

(require 5 level of each factor)2) Inscribed (CCI) designs-Star points.

(require 5 level of each factor)3) Faced (FCI) –star points on the faces of the cube. (require 3 level of each factor)


Contd…


Generation of a Central Composite Design for Factors. CCC

FCI

CCICCC

Contd…

b) Box-Behnken design (Alternative to CCD) (George E. P. Box and Donald Behnken in 1960)• They do not contain embedded factorial or

fractional factorial design.• Box-Behnken designs use just 3 levels of each

factor.• In this design the treatment combination are at

the midpoint of edges of the process space and the centre.


Contd…

Interpretation of a design by Box-behnken method

A 3 factor design by box behnken method is a cube

Centre point

Y = b0 + b1x1 +b2x2 + b3x3 + b4x1x2 + b5x1x3 + b6x2x3 + b7x2

1 + b8 x22 + b9 x2

3.

Where,b(0-9) represents constants. x(1-3) represents variables.

DESIGN CONTAINING THREE VARIABLE TYPES OF EXPERIMENTAL DESIGN

Contd…

6) STATISTICAL DESIGN:- the statistical design is of 2 types

STATISTICAL DESIGN

Experimentation study continues as the study proceeds.

Experimentation is complete before optimization.

Represented by Evolutionary method and simplex method

Represented by classical method lagrangian method and search method. Requires relation between dependent and independent variable


METHODS OF OPTIMIZATION

• There are many optimization procedures.1)EVOP (evolutionary optimization)2)Simplex method3)Lagrangian method4)Search method5)Canonical analysis

For IN-PROCESS OPTIMIZATION

For OUT-PROCESS OPTIMIZATION

1) EVOP (Evolutionary operation)

• Principle:- The production procedure is allowed to evolve to the optimum by careful planning and constant repetition.

• In this method the researcher makes very small changes in the formulation or process but makes it so many times that he or she can determine statistically whether the product has improved or not.

Contd…

• Alterations requirement upto:- until no improvement in the product quality is required.

• Applications:- very effective work was done on (1) Tablets and later to (2) parenteral by Mitchell H. Rubinstein

• Limitation:- Not a substitute to good laboratory scale work.

Rubinstein MH. Evolutionary operations: To optimize tablet manufacture. D&CI, 44-47,104-109, April, 1975 Contd…

2) SIMPLEX METHODproposed first by spendely et al

applied and known as Downhill Simplex / Nelder-Mead Method

• More widely used method for optimization• The method uses the concept of a simplex,

which is a special polytope of N + 1 vertices in N dimensions. Examples of simplexes include a line segment on a line, a triangle on a plane, a tetrahedron in three-dimensional space and so forth.

Contd…

Method Involved:- Identify the variables and predict the shape and then design the equations using various

constants and concentrations/values. • Example:- shows the three-component system which is represented as an equilateral triangle in two-dimensional space. Three formulations, one each at each vertex, A, B, and C. These formulations represent formulations with the pure components, A, B, and C, respectively.

Three formulations are prepared with 50-50 mixtures of each pair of components,AB, AC, and BC.

A seventh formulation may be prepared with one-third of each component. This lies in the center of the design.

Contd…

• The equation can be formed as, y = Ba(A) + Bb(B) + Bc(C) + ……… + Bab(A)(B) + Bac(A)(C) + Bbc(B)(C) + Babc(A)(B)(C).Where, (A), (B), (C) represents the concentration of component A, B, C. (A)+(B)+(C)+…….+(ABC) = 1.0 Ba, Bb, Bc,……, Babc represents constants.

Response determination:- With the aid of a computer, responses may be calculated over the simplex space, and contour diagrams. The contour plot is a graphic description of the response surface resulting from data derived from experimental designs such as the simplex.

Contd…

Shek et al, 1980used Simplex method for optimizing a capsule.

• Simplex method also describes about the expansion, contraction of geometric figures.

• Bindschaedler and gurney applied simplex method in optimization of direct compressible tablets of Acetaminophen.

Shek E, Mahmood G, Jones RE. Simplex search in optimization of capsule formulations. J Pharm Sci, 69(10):1135-1142, 1980 Contd…

3) Lagrangnian MethodFonner et al 1987

• Mathematical methodology is applied for optimizing a result.

• Since, mathematical therefore developed after performing some study and obtaining a limited data for optimization.

• 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.

Fonner DE, Buck JR, Banker GS. Mathematical optimization techniques in drug product design and process analysis. J Pharm Sci, 59(11):1587-1596, 1987 Contd…

• Determine constraints.• Determine objective formulation• 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

STEPS INVOLVED

Contd…

EXAMPLE•FONNER ET AL. applied methodology in tablet formulation containing API phenylpropanolamine HcL.• For the experiment:-oIndependent variable:- x1 = starch; x2 = stearic acid.oDependent variables:- Hardness, D.T, friability, drug

release pattern, urinary excretion profile.

•Using the mathematical data a polynomial equation is formed which gives dependent variable’s relation which would yield fully optimized product.

Contd…

• DECIDING THE FACTORS AND LIMITS

FACTOR LOW lEVEL (mg) HIGH LEVEL (mg)

A:- Stearate 0.5 1.5

B:- Dicalcium

phospate

60.0 120.0

C. Starch 30.0 50.0

Contd…

• DECIDING THE LIMITS AS PER FULL FACTORIAL STRATEGY AND ITS RESULT.

Contd…

Factor Combination

1. Stearate 2.Drug 3.Dicalcium phospate

(1) - - -

a + - -

b - + -

ab + + -

c - - +

ac + - +

bc - + +

abc + + +

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

Contd…

Final optimized

graph depicting the

acceptable product.

Optimizing values of stearic acid and strach as a function of restrictions on

tablet friability: (A) percent starch; (B) percent stearic acid

Contd…

4) SEARCH METHOD

• It is not different than RSM ie Response surface methodology.

• It takes into account 5 variables.• Computer system optimization comes under

this method.

Contd…

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.• 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 + λ2W22 +..

2variables=first order regression equation.3variables/3level design=second order regression equation.

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.

Contd…

APPLICATIONS OF OPTIMIZATION

Formulation and Processing

Clinical Chemistry

Medicinal Chemistry

High Performance Liquid Chromatographic Analysis

Formulation of Culture Medium in Virological Studies.

Study of Pharmacokinetic Parameters.

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

APPLICATIONS OF OPTIMIZATION contd…

Approach to process optimization and scale-up – regulator requirements.

• Quality assured by end product testing:- In this technique the end product testing at a small or large scale would never import the quality in the product. An alternative which comes is to stamp the product prepared to be of best quality.

• Full design of experiments:- QbD approach is utilized that would aditionally include schematic evaluation, understanding and refining of the formulation and manufacturing process.

It includes 1) Identifying the risks 2) Determining the functional relationship 3) managing Quality and risk management.

http://www.pharmtech.com/

pharmtech/article

• FDA expectation is to review all product development data including experiment design so as to understand the firms capabilities to understand its product characteristics for designing operational range of manufacturing and testing.

• ICH Q8 (QbD) compliance is mandatory for regulatory submission.

REFERENCES1) Schwartz J.B, O'Connor R.E, Schnaare R.L chapter 18 - optimization technique in pharmaceutical formulation and processing, Published by Marcel Dekker ©2002.2) Rani S. & Hiremath R. Textbook of industrial pharmacy.3) Stanford B., Bon C. pharmaceutical statistics practical and clinical application Chapter 9 published by Marcel dekker 4) Internet source http:// www.itl.nist.gov Images from google images wikipedia.com KLE university5) Certain review articals

http://www.itl.nist.gov/

chetan dhal-optimization techniques in pharmaceutics, formulation and processing

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