OPTIMIZATION TECHNIQUE in pharmaceutical formulation and processing
- 2. CONTENTS Introduction Concepts Parameters Optimization techniques in pharmaceutical formulation & processing.
- 3. What is Optimization? • Optimization is choosing inputs that will result in the best possible outputs or making things the best that they can be.
- 4. INTRODUCTION • The word Optimize is defined by Webster’s New Collegiate Dictionary 1974, as follows: to make as perfect, effective or functional as possible. – Choose the best alternative possible from the available alternatives. Optimization is the process of identifying the best way of utilizing the existing resources; while taking into account of all the factors that will influence the decisions in any experiment.
- 5. In pharmacy, Optimization refers to any study of formula. • It is related to formulation & processing or any study of formulation. • Optimization in pharmaceuticals refer to changing one variable at a time, in order to arrive at a solution for a problematic formulation.
- 6. FORMULATO N VARIABLES composition, porosity, size, shape and density of the pellets type and amount of polymer coating nature, size and amount of tableting excipients.,
- 7. • In pharmaceuticals, product must be safe & effective. • Production process must be reproducible when its quality is determined by specific criteria. • Optimization has to do with this production process of maintaining the products safety & efficacy. • They offer a rational approach for the selection of the several excipients & also for selecting different manufacturing steps for a given product. CONCEPT
- 8. • We use a model to prove that under the given conditions, & judging by the given criteria, “one particular product” is the perfect one. – * this is an ever evolving process. • To understand theoretical formulation & target processing parameters as well as the ranges for each excipients & processing parameters. • Final product must meet bioavailability requirements & practical mass production criteria of process & product reproducibility.
- 10. • It involves systematic design of experiments (DoE) in order to improve formulation abnormalities. – Such as cracking in tablets in case of solid dosage form, Phase separation in emulsions, curdling of suspension.
- 11. Design of experiments: • It is a systematic method to determine the relationship between factors affecting a process and the output of that process. • Used to find cause-and-effect relationships • DoE is a systematic statistical approach that applies mathematical principles and techniques for improving product and process optimization.
- 12. To reduce the cost To save the time Safety and reduce the error Reproducibility Innovation and efficacy Why is Optimization Technique needed??
- 13. • Yield the “Best Solution” within the domain of study • Require fewer experiments to achieve an optimal formulation. • Can trace and rectify problem in a remarkably easier manner. ADVANTAGES
- 14. TYPES OF OPTIMIZATION TECHNIQUE PROBLEM TYPE UNCONSTRAINED CONSTRAINED
- 15. PROBLEM TYPE • There are 2 general types of optimization problem: I. CONSTRAINED Constrains are the restrictions placed on the system by physical limitations or perhaps by simple practicality Ex- economic considerations, tablet with maximum hardness should disintegrate within 15 minutes.
- 16. • If we are homogenising an emulsion using a colloid will, if we increase the time of homogenisation we get a very small globule size which is very good for the product. • But this increases the temperature of the product. – Hence, it act as an restriction on the procedure.
- 17. PROBLEM TYPE • UNCONSTRAINED : – In this technique there are no restrictions. • But in pharmaceutical research its a pseudo phenomenon. Ex- to make a tablet with maximum hardness. Tablet making with a maximum possible hardness is unconstrained, which is merely impossible.
- 18. • The development of a pharmaceutical formulation & the fine tuning of the process for that formulation involve: – the changing of variables(factors) at different levels & – Measuring the dependent variables or responses(effects)
- 19. VARIABLE TYPE • The development procedure of the pharmaceutical formulation involves several variables. Mathematically these variables are divided into two groups. – Independent Variables --Dependent Variables. 1) INDEPENDENT VARIABLES: These variables are under control of the formulator. Ex: Compression force, Compression speed etc.
- 20. • 2) DEPENDENT VARIABLES: These are responses / characters which are developed due to the independent variables. Ex: Hardness - Compression force, Friability - Compression speed.
- 21. dent varia bles • X1 dilue nt ratio • X2 comp ressio nal force • X3 disint egran t level • X4 binde r level • X5 lubric varia bles • Y1 disint egra tion time • Y2 hard ness • Y3 disso lutio n • Y4 friabi lity • Y5 weig ht
- 22. • The more variables one has in a given system, the more complicated the job of optimization becomes. • But regardless of the no of variables, there will be a relationship between a given response & the independent variables. • Once this relationship is known for a given response, it defines a response surface. • This surface when evaluated gives values of independent variables X1 & X2 which gives the most desirable level of response Y.
- 24. CLASSICAL OPTIMIZATION • Carried out using Calculus to find out minimum and maximum of a function. • This technique themselves has limited application, but they are suitable for not too complex problems, & do not involve more than a few variable.
- 25. •The curve represents the relationship between response Y and the single independent variable X. •The relationship equation is = ( ) 𝐘 𝐟 𝐗
- 26. • When the relationship for response Y is given as function of two independent variables X1 and X2, • Then the relationship equation is 𝐘 = ( ) 𝐟 𝑿𝟏 𝑿𝟐 Graphically, there are contour plots on which the axes represents the two independent variables, X1 and X2, and contours represents the response Y . Contour plot. Contour represents values of the dependent variables
- 27. Drawback of classical optimization Classical Optimization is only applicable to the problem that are not too complex. They do not involve more than two variables. For more than two variables graphical representation is impossible
- 28. STATISTICAL DESIGN • The techniques most widely used for optimization may be divided into 2 general categories: – one in which experimentation continues as the optimization study proceeds. These are represented by Evolutionary operations & simplex method.
- 29. –Another one in which the experimentation is completed before the optimization takes place, these are represented by more classical mathematical & search methods. • for this technique it is necessary that the relation between any dependent variable & the one or more independent variables be known. To obtain the necessary relationships, there are 2 possible approaches: the theoretical & the empirical.
- 30. To apply the empirical or experimental approach for a system with a single independent variable, the formulator experiments at several levels, measures the property of interest & obtains a relationship, usually by simple regression analysis or by the least-square method. The concept of interest to the pharmacist planning to utilise optimization techniques is that there are methods available for selecting one’s experimental points so that-...
- 31. • A) The entire area of interest is covered or considered • B) Analysis of the results will allow separation of variables • i.e., statistical analysis can be performed, which allows the experimenter to know which variable caused a specific result.
- 32. APPLIED OPTIMIZATION METHODS • There are many methods that can be, & have been, used for optimization, classic or otherwise. Which are well documented in the literature of several fields. Deming & King presented a general flowchart that can be used to describe general optimization technique.
- 34. • The effect on real system of changing some input (some factor or variable) is observed directly at the output (one measures some property). TYPES OF APPLIED OPTIMISATION METHODS EVOLUTIONARY OPERATIONS SIMPLEX METHODS LAGRANIAN METHODS SEARCH METHOD CANONICAL METHOD
- 35. EVOLUTIONARY OPERATIONS • Most used methods of experimental optimization in fields other than pharmaceutical technology is the evolutionary operation (EVOP). • This technique is widely suited to a production situation. • The basic philosophy is that the procedure(formulation & process) is allowed to evolve to the optimum by careful planning & constant repetition.
- 36. • The process is run away on such a way that it both produces a product that meets all specifications & generates information on product improvement. • 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-peak.
- 37. • Applicable for Tablets. • Applied to an inspection system for Parenteral Products. Formulator can change the concentration of binder which can affect the hardness of tablet. Production procedure is optimized by careful planning and constant repetition. DISADVANTAGES It is impractical and expensive to use. It is not a substitute for good laboratory scale investigation.
- 38. SIMPLEX METHOD • An experimental method, & has been most widely used in pharmaceutical systems. • Has wider application in analytical method other than formulation & processing. • Simplex is a geometric figure- that has no of points or vertices equal to one more than no of factors examined. • Ex: for 2 factors or independent variables, the simplex is represented by triangle.
- 39. • It is determined by comparing the magnitude of the responses after each successive calculation. • Graph representing the simplex movements to the optimum conditions – worst response is at 0.25 – Aim is to move toward a Better response by moving Away from the worst response.
- 40. • The two independent variables show pump speeds for the two reagents required in the analysis reaction. • Applied to optimize capsules, direct compression tablet(acetaminophen), liquid systems (physical stability).
- 41. TYPES OF SIMPLEX METHOD • A) BASIC SIMPLEX METHOD: • It is easy to understand and apply. • Optimization begins with initial trials • Number of initial trials is equal to number of control variable plus one • These initial trials form the first simplex
- 42. REPRESENTATION OF BASIC SIMPLEX METHOD
- 43. MODIFIED SIMPLEX METHOD • The modified simplex method represents an advance over the basic simplex method which has found some popularity with analytical chemists. • It is a sequential technique which uses information feed back to move around the factor space of interest. • It will expand its size to move rapidly over a more or less even slope and • also reduce its size when an optimal response has been approached
- 44. Advantages of simplex method This method will find the true optimum of a response with fewer trials than the non- systemic approaches or the one-variable-at-a- time method. Disadvantages There are sets of rules for the selection of the sequential vertices in the procedure. Require mathematical knowledge
- 45. LANGRANIAN METHOD • Optimization method which represents mathematical techniques. • Is an extension of Classic method & was the first to our knowledge to be applied to pharmaceutical formulation & processing problems. • It follows the second type of statistical design. • Limited to 2 variables - disadvantage
- 46. Steps involved 1. Determine the objective function. 2. Determine the constrains. 3. Change inequality constrains to equality constrains. 4. Form the lag range function F 5. Partially differentiate the lag range function for each variable and set derivatives equal to zero, solve the set of simultaneous equation 6. Substitute the resulting values into objective function
- 47. • 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
- 48. Advantages Langrangian method was able to handle several responses or dependent variables. Disadvantages Although the lagrangian method was able to handle several responses or dependent variable, it is generally limited to two independent variables.
- 49. Contour plots for the Lagrangian method (a) tablet hardness
- 50. Contour plots for the Lagrangian method (b) dissolution (t50%)
- 51. (c) feasible solution space indicated by crosshatched area
- 52. SEARCH METHOD • It is defined by appropriate equations. • It does not require continuity or differentiability of function. • It is applied to pharmaceutical function • The response surface is searched by various methods to find the combination of independent variables yielding an optimum. • It takes five independent variables into account and is computer assisted.
- 53. Steps involved in search method: 1. Select a system 2. Select variable a. Independent b. Dependent 3. Perform experiments and test products 4. Submit data for statistical and regression analysis. 5. Set specifications for feasibility program. 6. Select constrains for grid search. 7. Evaluate grid search printout 8. Request and evaluate a. “Partial derivative” plots, single or composite. b. Contour plots.
- 54. Example: Different dependent and independent variables or formulation factors selected DEPENDENT VARIABLES. Y1= disintegration time Y2= hardness Y3= dissolution Y4= friability Y5= weight uniformity Y6= thickness Y7= porosity Y8= mean pore diameter
- 55. INDEPENDENT VARIABLES X1= diluents ratio X2= compression force X3= disintegration levels X4= binder levels X5= lubricant levels
- 56. Advantages of search method: It takes five independent variables. Person unfamiliar with mathematics of optimization and with no previous computer experience could carryout an optimization study. It does not require continuity and differentiability of functions. Disadvantages: It is a set up that not all pharmaceutical responses will fit a second-order regression model.
- 57. CANONICAL ANALYSIS Canonical analysis, or canonical reduction, is technique used to reduce a second-order regression equation, i.e., Y1= a0+a1x1+..+a5x5+a11x1 2 +...+a55x5 2 +a12x1x2+ a13x1x3+a45x4x5. Where, Y=level of given response a=the regression coefficient for second-order polynomial x=level of independent variable. to an equation consisting of a constant and squared terms as follows: Y= Y0+λ1w1 2 +λ2w2 2 ...
- 58. CANONICAL ANALYSIS The technique allows immediate interpretation of the regression equation by including the linear and interaction (cross product) terms in the constant term (Y0 or stationary point), thus simplifying the subsequent evaluation of the canonical form of the regression equation
- 59. APPLICATIONS 1. Formulation and processing 2. Clinical chemistry 3. Medicinal chemistry 4. HPLC analysis 5. Formulation of culture medium in virological studies 6. Study of pharmacokinetic properties.
- 60. REFERENCES • Modern Pharmaceutics, 4th Edition by Gilbert S. Banker • Novel drug delivery system, Yie Chein.
Editor's Notes
- #6: An excipient is a substance formulated alongside the active ingredient of a medication, included for the purpose of long-term stabilization, bulking up solid formulations that contain potent active ingredients in small amounts (thus often referred to as "bulking agents", "fillers", or "diluents")