Optimization techniques inpharmaceutics , formulation and processing ABDUL MUHEEM, M.Pharma(1st sem) Deptt. of Pharmaceutics, Faculty of Pharmacy, Jamia Hamdard Email: firstname.lastname@example.org
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 2 02/24/13
The term Optimize is defined as to make perfect , effective , orfunctional as possible.It is the process of finding the best way of using the existing resourceswhile taking in to the account of all the factors that influences decisions inany experiment Traditionally, optimization in pharmaceuticals refers to changing onevariable at a time, so to obtain solution of a problematic formulation.Modern pharmaceutical optimization involves systematic design ofexperiments (DoE) to improve formulation irregularities.In the other word we can say that –quantitate a formulation that hasbeen qualitatively determined.It’s not a screening techniques
Why Optimization is necessary? Innovat ion & efficacy4 02/24/13
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 , 5005 Concentration 1%, 2%
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 tablet6
Optimization Parameters1.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.
Dependent variables, which are the responses or the characteristicsof the in process material Eg. Particle size of vesicles, hardness of thetablet.Higher the number of variables, more complicated will be theoptimization process.There should be a relationship between the given response and theindependent variable, and once this relationship is established , a responsesurface is generated.From response surface only, we find the points which will givedesirable value of the response.
Example of dependent & independent variables Independent variables Dependent variables X1 Diluent ratio Y1 Disintegration time X2 compressional force Y2 Hardness Tablet formulation X3 Disintegrant level Y3 Dissolution X4 Binder level Y4 Friability X5 Lubricant level Y5 weight uniformity 11
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. 12
Response surface representing the relationship between the independent variables X1 and X2 and the dependent variable Y. 13
GRAPH REPRESENTING THE RELATION BETWEENTHE RESPONSE VARIABLE AND INDEPENDENTVARIABLE 14
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 x 1& x2 15
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 takesplace. It is represented by classic mathematical & searchmethods. 17
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.18
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.19
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 designs22
Completely randomized Designs These designs compares the values of a response variablebased on different levels of that primary factor. For example ,if there are 3 levels of the primary factor witheach level to be run 2 times then there are 6 factorial possiblerun sequences.Randomized block designsFor this there is one factor or variable that is of primaryinterest.To control non-significant factors, an important techniquecalled blocking can be used to reduce or eliminate thecontribution of these factors to experimental error.23
Factorial DesignThese are the designs of choice for simultaneous determination of theeffects 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.
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.
BCS classification and its expected outcome on IVIVC for Immediaterelease 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
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 27
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 fractional28
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.29
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 30
• Signal-to-Noise ratios (S/N), which are log functions of desired output, 31 02/24/13
We can use the Latin square to allocate treatments. If the rows of the squarerepresent 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 A32 02/24/13
Response surface designs This model has quadratic form γ =β0 + β1X1 + β2X2 +….β11X12 + β22X22 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 33
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 design34
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. 35
Generation of a Central Composite Design for Factors36 02/24/13
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+b7X12 +b8X22+b9X32 38
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 40
V. APPLIED OPTIMIZATION METHODSThere are several methods used for optimization. They are 41
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 theexperiment so many times) & statistically analyzed whether it isimproved.•It continues until no further changes takes place i.e., it has reachedoptimum-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.
Simplex Method(Simplex Lattice)It is an experimental techniques & mostly used in analytical rather thanformulation & processing.Simplex is a geometric figure that has one more point than the number offactors.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 worstresponse.•Applied to optimize CAPSULES, DIRECT COMPRESSION TABLET),liquid systems (physical stability).•It is also called as Downhill Simplex / Nelder-Mead Method.
In simplex lattice, the response may be plotted as 2D(contour plotted) or 3D plots (response surfacemethodology)
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, 0.721Figure 5 The simplex approach to optimization. Response is spectorphotometric readingat a given wavelength 45 02/24/13
Example 2: Two component solvent systemrepresenting simplex lattice.Constraint is the concentration of A and B must add to100%Includes observing responses( solubility) at three point i.e.100% A, 100% B and 50 – 50 mixtures of A and B
Eg: Preparation of tablet with excipients (three components) gives 7 runs.A regular simplex lattice for a three 1 Starchcomponent mixture consist of sevenformulations 4 5 7 2 Lactose 3 Stearic acid 6
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)
• 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 %)
Lagrangian method•It represents mathematical techniques & it is applied to apharmaceutical 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) andminima (lowest possible concentration) depending onthe constraints..•A techniques called “sensitivity analysis“ can provideinformation so that the formulator can further trade off oneproperty for another . Analysis for solves the constrainedoptimization problems.
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 51
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..,52
Polynomial models relating the response variables to independents were generated by a backward stepwise regression analysis program. Y= B0+B1X1+B2X2+B3 X12 +B4 X22 +B+5 X1 X2 +B6 X1X2 + B7X12+B8X12X22 Y – Response Bi – Regression coefficient for various terms containing the levels of the independent variables. X – Independent variables 53
EXAMPLE OF FACTORS IN THIS FACTORIALDESIGN FACTOR LOWLEVEL(mg) HIGH LEVEL(mg) A:stearate 0.5 1.5 B:Drug 60.0 120.0 C:starch 30.0 50.0 54 17 August 2012
EXAMPLE OF FULL FACTORIAL EXPERIMENT Factor Stearate Drug Starch Response combination Thickness Cm*103 (1) _ _ _ 475 a + _ _ 487 b _ + _ 421 ab + + _ 426 c _ _ + 525 ac + _ + 546 bc _ + + 472 abc + + + 522 55
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 56
CONTOUR PLOT FOR TABLET HARDNESS & dissolution(T50%) 57
GRAPH OBTAINED BY SUPER IMPOSITION OF TABLETHARDNESS & DISSOLUTION Contour plots for the Lagrangian method: feasible solution space indicated by crosshatched area 58
Optimizing values of stearic acid and strach as a function of restrictions on tablet friability: (A) percent starch; (B) percent stearic acid59
Search methods (RSM) :•It takes five independent variables into account and iscomputer-assisted.•It is defined by appropriate equations.•Response surface methodology is used to determine theconnection between different explanatory variables(independent variables) and one or more of the responsevariables.•Persons unfamiliar with mathematics of optimization & withno previous computer experience could carryout anoptimization study.
THE SEARCH METHODS1. Select a system2. Select variables: a. Independent b. Dependent3. Perform experimens and test product.4. Submit data for statistical and regression analysis5. Set specifications for feasibility program6. Select constraints for grid search7. Evaluate grid search printout 8. Request and evaluate:. a. “Partial derivative” plots, single or composite 61 b. Contour plots
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 +λ1W12 + λ2W22 +..2variables=first order regression equation.3variables/3level design=second order regression equation.62
. In canonical analysis or canonicalreduction, second-order regressionequations are reduced to a simplerform by a rigid rotation and translationof the response surface axes inmultidimensional space, asfor a two dimension system. 63
Forms of Optimization techniques:1. Sequential optimization techniques.2. Simultaneous optimization techniques.3. Combination of both.
Sequential Methods:Also referred as the "Hill climbing method".Initially small number of experiments are done, then research is done using theincrease 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.
Example:- Designing controlled drug deliverysystem for prolonged retention in stomach required optimization of variables like•presence/ absence / concentration of stomachenzymepH, fluid volume and contents of gutsGastric motility and gastric emptying.
When given as single oral tablet(A).Same drug when given inmultiple doses (B)Same drug when given asoptimized controlled releaseformulation (C)
Artificial Neural Network & optimization of pharmaceuticalformulation-ANN has been entered in pharmaceutical studies to forecast therelationship b/w the response variables &casual factors . This isrelationship is nonlinear relationship.ANN is most successfully used in multi objective simultaneousoptimization problem.Radial basis functional network (RBFN) is proposed simultaneousoptimization problems.RBFN is an ANN which activate functions are RBF.RBF is a function whose value depends on the distance from theCentre or origin.69 02/24/13
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• Formulation optimization of nifedipine containing microspheres using factorial design by Solmaz Dehghan In African Journal of Pharmacy and Pharmacology Vol. 4(6), pp.346-354, June 2010 Available online http://www.academicjournals.org/ajpp• https://www.google.co.in/search? tbm=bks&hl=en&q=process+control+of+dosage+forms %2C&btnG=#hl=en&tbm=bks&sclient=psyab&q=Pharmaceutical+statistics+marc el+dekker++optimization+edition&oq=Pharmaceutical+statistics+marcel+dekker+ +optimization+edition&gs_l=serp.3...4379.6969.0.79188.8.131.52.0.0.0.1433.5733.21j5 2j2j2.7.0...0.0...1c.1.1rVBuxjQR64&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp =e427dbbbd305a6fb&bpcl=38625945&biw=1366&bih=677• Mathematical Optimization Techniques in Drug Product Design and Process Analysis by DALE E. FONNER, Jr.*, JAMES R. BUCK, and GILBERT S. BANKER,Vol. 59, No. 11, November 1970 in journal of pharmaceutical sciences74 02/24/13