CADD UNIT3 FOR PHARMACEUTICS DEPARTMENTS

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1. COMPUTER AIDED FORMULATION DEVELOPMENT By : BHUVAN SHANKAR D SECOND SEMESTER M.PHARM DEPARTMENT OF PHARMACEUTICS 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 1

2. Contents Concept of Optimization Optimization parameters Factorial design, Optimization technology & Screening design. 2 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT

3. CONCEPT OF OPTIMIZATION Product formulation is often considered as an art, the formulator's experience and creativity of converting raw materials into product . The pharmaceutical scientist has the responsibility to choose and combine ingredients that will result in a formulation, whose result or responses are of expected value. Before the advances in the research technique and availability of computers, the formulation research was based on experience and experimenting by trial and error. In a pharmaceutical formulation and development various formulation trials have to be done to obtain a good process and a suitable formulation. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 3

4. In the trial and error method, a lot of formulations have to be done to get a conclusion. These can be minimized with the help of optimization technique. The word "optimize" is defined as: To make as PERFECT, EFFECTIVE, or FUNCTIONAL as possible. The optimization techniques provide both a depth of understanding and an ability to explore and defend ranges for formulation and processing factors. It is at this point that optimization can become a useful tool to quantitate a formulation which is qualitatively determined. Optimization is used often in pharmacy with respect to formulation and to processing. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 4

5. Optimization is defined as follows: " "Choosing the best element from some set of available alternatives . 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. The objective of designing quality formulation is achieved by various Optimization techniques like DoE (Design of Experiment). 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 5

6. Quality by Design ( QbD ) The pharmaceutical Quality by Design ( QbD ) is a systematic approach to development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management. Quality by Design ( QbD ) is emerging to enhance the assurance of safe, effective drug supply to the consumer, and also offers promise to significantly improve manufacturing quality performance. The Quality of the pharmaceutical product can be evaluated by in vivo or in vitro performance tests " QbD " assures in vitro product performance and in vivo product performance. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 6

7. 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 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 7 FACTOR LEVELS Temperature 30 , 50 Concentration 1%, 2%

8. 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 glidants on hardness of the tablet. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 8

9. DOE(Design of Experiment) It is a mathematical tool for systematically planning and conducting scientific studies that change experimental variables together in order to determine their effect on a given response. It makes controlled changes to input variables in order to gain maximum amounts of information on cause and effect relationships with a minimum sample size for optimizing the formulation. In Optimization Method, various types of Model used from preliminary screening of factors to select their level and for finally study of their effect so it's depend upon the formulator to choose a suitable model for study and help in minimizing the experimenting time. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 9

10. Define the Problem & Select the variables Screening the factor and their level Design the Formulation according to Model Used Analyse the Result Select the Check Point Formulation Validate and Optimize the Model (Basic Flow Chart for using DOE and optimizing the formulation) 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 10

11. Why optimization is necessary? Reduce the cost Save the time Safety and reduce the error Reproducibility Innovation and efficacy 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 11

12. Independent Optimization Parameters 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 12

13. PROBLEM TYPES : Constraint - restriction placed on a system by physical limitations or by simple practicality. Ex., make the hardest tablet possible, but it must disintegrate in less than 15 minutes. Unconstraint – no restriction placed, almost nonexistent. Ex., make the hardest tablet as possible. VARIABLES: Independent or primary Variables (Input variables): Formulation and process variables directly under the control of the formulator. Ex., Level of a given ingredient , Mixing time for a given process step. Dependent or secondary Variables (Output variables): Responses or the characteristics of the in-progress material or the resulting drug delivery system. These are a direct result of any change in the formulation or process. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 13

14. Tablet formulation 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 14 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

15. EXPERIMENTAL DESIGN Experimental design is a statistical design that prescribes or advises a set of combination of variables. The number and layout of these design points within the experimental region, depends on the number of effects that must be estimated. Depending on the number of factors, their levels, possible interactions and order of the model , various experimental designs are chosen. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 15

16. 9/8/2024 16 FACTORIAL DESIGN RESPONSE SURFACE METHOD FULL FACTORIAL FRACTIONAL FACTORIAL EXPERIMENTAL DESIGN Homogenous fractional Mixed level fractional Box-Hunter Plackett Burman Taguchi Latin square CENTRAL COMPOSITE DESIGN BOX BEHNKEN DESIGN Axial points ( "star" points) Center points COMPUTER AIDED FORMULATION DEVOLOPMENT

17. 1. Factorial Designs Factorial designs (FDs) are very frequently used response surface designs. 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 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 17

18. Full Factorial Designs : Involves study of the effect of all factors(n) at various levels(x) including the interactions among the total number of experiments as X. If the number of levels is the same for each factor in the optimization study, the FDs are said to be symmetric, whereas in cases of a different number of levels for different factors, FDs are termed asymmetric. Fractional Factorial Design (FFD): Fractional factorial design is generally used for screening of factor. This design has low resolution due to less number of run. It is used to examine multiple factors efficiently with fewer runs than corresponding full factorial design. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 18

19. FULL FACTORIAL DESIGN FFD involve studying the effect of all possible factors at various levels, including the interactions, with the total number of runs. Generally Factorial experiment with two level factors are used. If there are k factors, each at Z levels, a full factorial desi has Zk runs. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 19

20. 3 factors, 2 levels- 2 3 FD = 8 runs 2 factors, 3 levels- 3 2 FD = 9 runs 3 factors, 3 levels- 3 3 FD = 27 runs The simplest form of factorial design is the 2 2 factorial e.g. 2 3 Factorial design of Sustained release Metformin Hcl 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 20

21. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 21 Among all inactive ingredients, microcrystalline cellulose, ethyl cellulose, PVP K30 were taken as the independent factors.

22. The experimental plan for a three-factor, two-level 2ª design is as follows; 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 22

23. The 2³ factorial design show seven effect, i.e. three individual factor effects, three two way interaction (X1X2,X1X3, & X2X3) & one three way interaction (X1,X2X3). 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 23

24. 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. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 24 FRACTIONAL FACTORIAL TYPES

25. Plackett-Burman : It is a popular class of 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. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 25

26. Taguchi: It is similar to PBDs. It is a method of ensuring good performance in the development of products or processes. 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 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 26

27. 2 . Response Surface Designs: These designs are used when we required exact image of response, estimating interaction and even quadratic effects. Response surface designs generally support non linear and quadratic response and capable of detecting curvatures. Two most common designs generally used in this response surface modeling are Central composite designs. Box-Behnken designs. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 27

28. CENTRAL COMPOSITE DESIGN (BOX-WILSON DESIGN) This type contains an embedded factorial or fractional factorial design with c points that is augmented with the group of "star points". The star points represent new extreme value (low & high) for each factor in the design CCD has two groups of design points: Axial points (sometimes called "star" points). Center points. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 28

29. Central composite design (CCD) N = 2 f + 2 f + 1 experiments to examine the f factors The points of the full factorial design are situated at factor levels −1 and +1 , those of the star design at the factor levels 0, − α and + α , and the center point at factor level . Depending on the value of α , two types of designs exist, A face- centered CCD (FCCD) with | α | = 1, and A circumscribed CCD (CCCD) with | α | > 1 In the case of FCCD and CCCD, factors are varied on three or five levels, respectively. 29 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT

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31. CENTRAL COMPOSITE DESIGN OF HEAVY METAL REMOVAL USING POLYMER ADSORBENT 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 31

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37. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 37 Figure : Contour and 3-D response surface plots for removal of Cd2+ . (a) Interaction plots of pH and adsorbent dosage on removal of Cd2+ (Actual factor: Initial concentration = 20 mg.L−1). (b) Interaction plots of adsorbent dosage and initial concentration on removal of Cd2+ (Actual factor: pH = 9). (c) Interaction plots of pH and initial concentration on removal of Cd2+ (Actual factor: Adsorbent dosage = 4 g.L−1).

38. Figure : Contour and 3-D response surface plots removal of Pb2+. (a) Interaction plots of pH and adsorbent dosage on removal of Pb2+ (Actual factor: Initial concentration = 50 mg.L−1). (b) Interaction plots of adsorbent dosage and initial concentration on removal of Pb2+ (Actual factor: pH = 9). (c) Interaction plots of pH and initial concentration on removal of Pb2+ (Actual factor: Adsorbent dosage = 8 g.L−1) 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 38

39. The optimization study on the highest removal heavy metal ions was satisfied through the experimental validation between the predicted and experimental value with a small percentage error of 0.2536% (Cd2+) and 0.4943% (Pb2+). The CCD method proved the suitability and validity of the quadratic polynomial model adopted in optimizing removal of Cd2+ and Pb2+. Hence, the optimum conditions of initial concentration, pH, and adsorbent dosage were successfully estimated using the statistical experimental design of CCD by RSM in optimizing the percentage removal of Cd2+ and Pb2+. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 39

40. BOX BEHNKEN DESIGN A BBD is described for a minimum of three factors Contains N = (2 f ( f − 1)) + c experiments, c is the number of center points. Most common alternative to the CCD . BBDs are second-order designs based on three-level incomplete factorial designs. BBD can be presented in a simplified manner as follows 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 40

41. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 41 When there are 5 or more factors , Box and Behnken recommended using all possible 2 3 designs, holding the other factors constant. Advantages of BBD is that it does not contain combinations for which all factors are simultaneously at their highest or lowest levels.

42. MIXTURE DESIGN Mixture designs are used to study mixture variables such as excipients in a formulation. All mixture components are examined in one design. The characteristic feature of a mixture is that the sum of all its components adds up to 100%, hence cannot be manipulated completely independently of one another. Data analysis is more complicated, since mixture factors are correlated. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 42

43. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 43 OPTIMIZATION TECHNIQUES SIMULTANEOUS METHOD SEQUENTIAL METHOD EVOLUTIONARY OPERATION METHOD SIMPLEX METHOD CANONICAL ANALYSIS CLASSICAL MATHEMATICAL METHOD SEARCH METHOD

44. OPTIMIZATION TECHNIQUES The techniques for optimization are broadly divided into two categories: (A) Simultaneous method: Experimentation continues as optimization study proceeds .E.g. Evolutionary Operations Method ,Simplex Method (B) Sequential method: Experimentation is completed before optimization takes place. E.g. Classic Mathematical Method ,Search Method In case (B), the formulator has to obtain the relationship between any dependent variable and one or more independent variables. This include two approaches: Theoretical Approach and Empirical Approach. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 44

45. EVOLUTIONARY OPERATION One of the most widely used methods of experimental optimization in fields other than pharmaceutical technology is the evolutionary operation , or EVOP . This technique is especially well suited to a production situation. The basic philosophy is that the production procedure (formulation and process) is allowed to evolve to the optimum by careful planning and constant repetition . The process is run in a way such that it both produces a product that meets all specifications and (at the same time) generates information on product improvement. By this method the experimenter makes a very small change in the formulation or process, but makes it so many times (i.e., repeats the experiment so many times) that he or she can determine statistically whether the product has improved . 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 45

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47. If it has, the experimenter makes another change in the same direction, many times, and notes the results. This continues until further changes do not improve the product or perhaps become detrimental . The experimenter then has the optimum-the peak . In an industrial process, this large number of experiments is usually not a problem, since the process will be run over and over again. The pharmaceutical industry is subject to regulatory constraints that make EVOP impossible to employ in validated production processes and, therefore, impractical and expensive to use. Moreover, EVOP is not a substitute for good laboratory-scale investigation, and because of the necessarily small changes utilized, is not particularly suitable to the laboratory. In pharmaceutical development, more efficient methods are desired. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 47

48. SIMPLEX METHOD A simplex is a geometric figure that has one more point than the number of factors. So, for two factors or independent variables, the simplex is represented by a triangle . Once the shape of a simplex has been determined, the method can employ a simplex of fixed size or of variable sizes that are determined by comparing the magnitudes of the responses after each successive calculation. Figure 5 represents the set of simplex movements to the optimum conditions using a variable size technique. The two independent variables (the axes) show the pump speeds for the two reagents required in the analysis reaction. The initial simplex is represented by the lowest triangle; the vertices represent the spectrophotometric response. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 48

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50. The strategy is to move toward a better response by moving away from the worst response . Since the worst response is 0.25, conditions are selected at the vortex, 0.68 and, indeed, improvement is obtained. One can follow the experimental path to the optimum, 0.721. For pharmaceutical formulations, the simplex method was used by Shek et al. [10] to search for an optimum capsule formula. This report also describes the necessary techniques of reflection, expansion, and contraction for the appropriate geometric figures. The same laboratories applied this method to study a solubility problem involving butoconazole nitrate in a multi- component system [11]. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 50

51. CANONICAL ANALYSIS Canonical analysis, or canonical reduction , is a technique used to reduce a second-order regression equation, The technique allows immediate interpretation of the regression equation by including the linear and interacti on (cross-product) terms in the constant term (Y, or stationary point), thus simplifying the subsequent evaluation of the canonical form of the regression equation. The first report of canonical analysis in the statistical literature was by Box and Wilson for determining optimal conditions in chemical reactions. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 51

52. Canonical analysis, or canonical reduction, was described as an efficient method to explore an empirical response surface to suggest areas for further experimentation. 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 shown in Fig. 14 for a two-dimension system. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 52

53. A reported application of canonical analysis involved a novel combination of the canonical form of the regression equation with a computer-aided grid search technique to optimize con- trolled drug release from a pellet system prepared by extrusion and spheronization [28,29]. Formulation factors were used as independent variables and in vitro dissolution was the main response, or dependent variable. Both a minimum and a maximum drug release rate was predicted and verified by preparation and testing of the predicted formulations. Excellent agreement between the predicted values and the actual values was evident for the four-component pellet system in this study. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 53

54. B. SEQUENTIAL METHOD Classic Mathematical Model: Algebraic expression defining the dependence of a response variable on the independent variables, Two approaches: Theoretical approach- If theoretical equation is known, no experimentation is necessary. Empirical or experimental approach - formulator experiments at several levels. With single independent variable. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 54

55. CLASSIC OPTIMIZATION Classic optimization techniques result from application of calculus to the basic problem of finding the maximum or minimum of a function . The techniques themselves have limited application, but might be useful for problems that are not too complex and do not involve more than a few variables. The curve in Fig. 2 might represent the relation between a response, Y, and a single independent variable X, in a hypothetical system, and since we can see the whole curve, we can pick out the highest point or lowest, the maximum or minimum. If the relationship, that is, the equation for Y as a function of X is available [Eq. (1)]. Y = f(X)we can take the first derivative, set it equal to zero, and solve for X to obtain the maximum or minimum. For many functions of X, there will be more than one solution when the first derivative is set equal to zero. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 55

56. The various solutions may all be maxima or minima, or a mixture of both. There are also techniques to determine whether we are dealing with a maximum or a minimum, that is, by use of the second derivative. And there are techniques to determine whether we simply have a maximum (one of several local peaks) or the maximum. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 56

57. SEARCH METHOD In contrast with the mathematical optimization methods, search methods do not require continuity or differentiability of the function-only that it be computable. In these methods the response surfaces, as defined by the appropriate equations, are searched by various methods to find the combination of independent variables yielding the optimum. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 57

58. STEPS INVOLVED IN SEARCH METHOD Select a system. Select variable (independent , dependent). Perform experiments and test product. Submit data for statistical and regression analysis. Set specification for feasibility program. Select constraints for grid search. Evaluate grid search printout. Request and evaluate. Partial derivative plots, single or composite. Contour plots. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 58

59. REFERENCES Computer Applications in Pharmaceutical Research and Development, Sean Ekins , 2006, John Wiley & Sons. Computer-Aided Applications in Pharmaceutical Technology, 1st edition, Jelena Djuris , Woodhead Publishing Modern Pharmaceutics; By Gillbert and S. Banker. Central composite design of heavy metal removal using polymer adsorbent Nur Amirah Mohd Zahri , Siti Nurul Ain Md Jamil , Luqman Chuah Abdullah , Sim Jia Huey , Mohsen Nourouzi Mobarekeh , Nur Salimah Mohd Rapeia & Thomas Choong Shean Yaw. 9/8/2024 COMPUTER AIDED FORMULATION DEVOLOPMENT 59